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Overview
Comment:Merge trunk
Downloads: Tarball | ZIP archive | SQL archive
Timelines: family | ancestors | descendants | both | novem
Files: files | file ages | folders
SHA1: a2bc365c8c6fd8187ce907e798d6174dd9ac8687
User & Date: jan.nijtmans 2016-11-18 11:15:27
Context
2016-11-21
10:40
Merge trunk. More internal use of size_t in stead of int (or long) check-in: b68c708bd6 user: jan.nijtmans tags: novem
2016-11-18
18:05
merge novem check-in: 715274166d user: dgp tags: dgp-refactor
12:10
merge novem check-in: 21f9030029 user: jan.nijtmans tags: novem-more-memory-API
11:15
Merge trunk check-in: a2bc365c8c user: jan.nijtmans tags: novem
10:53
Fix mp_cnt_lsb() signature, so it matches the signature used in Tcl check-in: 9ca8b95421 user: jan.nijtmans tags: trunk
2016-11-17
16:27
merge trunk check-in: f365ba1ad9 user: jan.nijtmans tags: novem
Changes
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Changes to .fossil-settings/ignore-glob.

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*/config.status
*/tclConfig.sh
*/tclsh*
*/tcltest*
*/versions.vc
libtommath/bn.ilg
libtommath/bn.ind


libtommath/*.pdf


libtommath/tombc/*
libtommath/pre_gen/*
libtommath/pics/*
libtommath/mtest/*
libtommath/logs/*
libtommath/etc/*
libtommath/demo/*






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*/config.status
*/tclConfig.sh
*/tclsh*
*/tcltest*
*/versions.vc
libtommath/bn.ilg
libtommath/bn.ind
libtommath/pretty.build
libtommath/tommath.src
libtommath/*.pdf
libtommath/*.pl
libtommath/*.sh
libtommath/tombc/*
libtommath/pre_gen/*
libtommath/pics/*
libtommath/mtest/*
libtommath/logs/*
libtommath/etc/*
libtommath/demo/*

Changes to doc/file.n.

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returns
.QW \fB/\0\0foo\0\0./~bar\0\0baz\fR
to ensure that later commands
that use the third component do not attempt to perform tilde
substitution.
.RE
.TP
\fBfile stat  \fIname varName\fR
.
Invokes the \fBstat\fR kernel call on \fIname\fR, and uses the variable
given by \fIvarName\fR to hold information returned from the kernel call.
\fIVarName\fR is treated as an array variable, and the following elements
of that variable are set: \fBatime\fR, \fBctime\fR, \fBdev\fR, \fBgid\fR,
\fBino\fR, \fBmode\fR, \fBmtime\fR, \fBnlink\fR, \fBsize\fR, \fBtype\fR,
\fBuid\fR.  Each element except \fBtype\fR is a decimal string with the






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returns
.QW \fB/\0\0foo\0\0./~bar\0\0baz\fR
to ensure that later commands
that use the third component do not attempt to perform tilde
substitution.
.RE
.TP
\fBfile stat \fIname varName\fR
.
Invokes the \fBstat\fR kernel call on \fIname\fR, and uses the variable
given by \fIvarName\fR to hold information returned from the kernel call.
\fIVarName\fR is treated as an array variable, and the following elements
of that variable are set: \fBatime\fR, \fBctime\fR, \fBdev\fR, \fBgid\fR,
\fBino\fR, \fBmode\fR, \fBmtime\fR, \fBnlink\fR, \fBsize\fR, \fBtype\fR,
\fBuid\fR.  Each element except \fBtype\fR is a decimal string with the

Changes to generic/tclExecute.c.

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	    mp_clear(&big2);
	    Tcl_SetObjResult(interp, Tcl_NewStringObj(
		    "exponent too large", -1));
	    return GENERAL_ARITHMETIC_ERROR;
	}
	Tcl_TakeBignumFromObj(NULL, valuePtr, &big1);
	mp_init(&bigResult);
	mp_expt_d(&big1, big2.dp[0], &bigResult);
	mp_clear(&big1);
	mp_clear(&big2);
	BIG_RESULT(&bigResult);
    }

    case INST_ADD:
    case INST_SUB:






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	    mp_clear(&big2);
	    Tcl_SetObjResult(interp, Tcl_NewStringObj(
		    "exponent too large", -1));
	    return GENERAL_ARITHMETIC_ERROR;
	}
	Tcl_TakeBignumFromObj(NULL, valuePtr, &big1);
	mp_init(&bigResult);
	mp_expt_d_ex(&big1, big2.dp[0], &bigResult, 1);
	mp_clear(&big1);
	mp_clear(&big2);
	BIG_RESULT(&bigResult);
    }

    case INST_ADD:
    case INST_SUB:

Changes to generic/tclStubInit.c.

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    TclBN_s_mp_sub, /* 60 */
    TclBN_mp_init_set_int, /* 61 */
    TclBN_mp_set_int, /* 62 */
    TclBN_mp_cnt_lsb, /* 63 */
    TclBNInitBignumFromLong, /* 64 */
    TclBNInitBignumFromWideInt, /* 65 */
    TclBNInitBignumFromWideUInt, /* 66 */

};

static const TclStubHooks tclStubHooks = {
    &tclPlatStubs,
    &tclIntStubs,
    &tclIntPlatStubs,
    &tclOOStubs,






>







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    TclBN_s_mp_sub, /* 60 */
    TclBN_mp_init_set_int, /* 61 */
    TclBN_mp_set_int, /* 62 */
    TclBN_mp_cnt_lsb, /* 63 */
    TclBNInitBignumFromLong, /* 64 */
    TclBNInitBignumFromWideInt, /* 65 */
    TclBNInitBignumFromWideUInt, /* 66 */
    TclBN_mp_expt_d_ex, /* 67 */
};

static const TclStubHooks tclStubHooks = {
    &tclPlatStubs,
    &tclIntStubs,
    &tclIntPlatStubs,
    &tclOOStubs,

Changes to generic/tclTomMath.decls.

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declare 20 {
    int TclBN_mp_grow(mp_int *a, int size)
}
declare 21 {
    int TclBN_mp_init(mp_int *a)
}
declare 22 {
    int TclBN_mp_init_copy(mp_int *a, mp_int *b)
}
declare 23 {
    int TclBN_mp_init_multi(mp_int *a, ...)
}
declare 24 {
    int TclBN_mp_init_set(mp_int *a, mp_digit b)
}
................................................................................
declare 33 {
    int TclBN_mp_neg(const mp_int *a, mp_int *b)
}
declare 34 {
    int TclBN_mp_or(mp_int *a, mp_int *b, mp_int *c)
}
declare 35 {
    int TclBN_mp_radix_size(mp_int *a, int radix, int *size)
}
declare 36 {
    int TclBN_mp_read_radix(mp_int *a, const char *str, int radix)
}
declare 37 {
    void TclBN_mp_rshd(mp_int *a, int shift)
}
................................................................................
}
declare 65 {
    void TclBNInitBignumFromWideInt(mp_int *bignum, Tcl_WideInt initVal)
}
declare 66 {
    void TclBNInitBignumFromWideUInt(mp_int *bignum, Tcl_WideUInt initVal)
}






# Local Variables:
# mode: tcl
# End:






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declare 20 {
    int TclBN_mp_grow(mp_int *a, int size)
}
declare 21 {
    int TclBN_mp_init(mp_int *a)
}
declare 22 {
    int TclBN_mp_init_copy(mp_int *a, const mp_int *b)
}
declare 23 {
    int TclBN_mp_init_multi(mp_int *a, ...)
}
declare 24 {
    int TclBN_mp_init_set(mp_int *a, mp_digit b)
}
................................................................................
declare 33 {
    int TclBN_mp_neg(const mp_int *a, mp_int *b)
}
declare 34 {
    int TclBN_mp_or(mp_int *a, mp_int *b, mp_int *c)
}
declare 35 {
    int TclBN_mp_radix_size(const mp_int *a, int radix, int *size)
}
declare 36 {
    int TclBN_mp_read_radix(mp_int *a, const char *str, int radix)
}
declare 37 {
    void TclBN_mp_rshd(mp_int *a, int shift)
}
................................................................................
}
declare 65 {
    void TclBNInitBignumFromWideInt(mp_int *bignum, Tcl_WideInt initVal)
}
declare 66 {
    void TclBNInitBignumFromWideUInt(mp_int *bignum, Tcl_WideUInt initVal)
}

# Added in libtommath 1.0
declare 67 {
    int TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c, int fast)
}

# Local Variables:
# mode: tcl
# End:

Changes to generic/tclTomMath.h.

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 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tom[email protected], http://math.libtomcrypt.com
 */
#ifndef BN_H_
#define BN_H_

#include "tclTomMathDecls.h"
#ifndef MODULE_SCOPE
#define MODULE_SCOPE extern
#endif



#ifndef MIN
#   define MIN(x,y) ((x)<(y)?(x):(y))
#endif

#ifndef MAX
#   define MAX(x,y) ((x)>(y)?(x):(y))
#endif

#ifdef __cplusplus
extern "C" {

/* C++ compilers don't like assigning void * to mp_digit * */
#define  OPT_CAST(x)  (x *)

#else

/* C on the other hand doesn't care */
#define  OPT_CAST(x)

#endif


/* detect 64-bit mode if possible */
#if defined(NEVER)  /* 128-bit ints fail in too many places */
#   if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))

#	define MP_64BIT
#   endif
#endif

/* some default configurations.
 *
 * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
 * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
 *
 * At the very least a mp_digit must be able to hold 7 bits
 * [any size beyond that is ok provided it doesn't overflow the data type]
 */
#ifdef MP_8BIT
#ifndef MP_DIGIT_DECLARED
   typedef unsigned char      mp_digit;
#define MP_DIGIT_DECLARED
#endif
   typedef unsigned short     mp_word;




#elif defined(MP_16BIT)
#ifndef MP_DIGIT_DECLARED
   typedef unsigned short     mp_digit;

#define MP_DIGIT_DECLARED
#endif
   typedef unsigned long      mp_word;





#elif defined(MP_64BIT)
   /* for GCC only on supported platforms */
#ifndef CRYPT
   typedef unsigned long long ulong64;
   typedef signed long long   long64;
#endif

#ifndef MP_DIGIT_DECLARED
   typedef unsigned long      mp_digit;
#define MP_DIGIT_DECLARED
#endif



   typedef unsigned long      mp_word __attribute__ ((mode(TI)));






#  define DIGIT_BIT          60
#else
   /* this is the default case, 28-bit digits */
   
   /* this is to make porting into LibTomCrypt easier :-) */
#ifndef CRYPT
#  if defined(_MSC_VER) || defined(__BORLANDC__)
      typedef unsigned __int64   ulong64;
      typedef signed __int64     long64;
#  else
      typedef unsigned long long ulong64;
      typedef signed long long   long64;
#  endif
#endif

#ifndef MP_DIGIT_DECLARED
   typedef unsigned int      mp_digit;
#define MP_DIGIT_DECLARED
#endif
   typedef ulong64            mp_word;

#ifdef MP_31BIT   
   /* this is an extension that uses 31-bit digits */
#  define DIGIT_BIT          31
#else
   /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
#  define DIGIT_BIT          28
#  define MP_28BIT
#endif   
#endif

/* define heap macros */
#if 0 /* these are macros in tclTomMathDecls.h */
#ifndef CRYPT
   /* default to libc stuff */
#  ifndef XMALLOC
#     define XMALLOC  malloc
#     define XFREE    free
#     define XREALLOC realloc
#     define XCALLOC  calloc
#  else
      /* prototypes for our heap functions */
      extern void *XMALLOC(size_t n);
      extern void *XREALLOC(void *p, size_t n);
      extern void *XCALLOC(size_t n, size_t s);
      extern void XFREE(void *p);
#  endif
#endif
#endif


/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
#ifndef DIGIT_BIT
#   define DIGIT_BIT     ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))  /* bits per digit */















#endif

#define MP_DIGIT_BIT     DIGIT_BIT
#define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
#define MP_DIGIT_MAX     MP_MASK

/* equalities */
................................................................................
#endif

/* define this to use lower memory usage routines (exptmods mostly) */
/* #define MP_LOW_MEM */

/* default precision */
#ifndef MP_PREC
#  ifndef MP_LOW_MEM
#     define MP_PREC                 32     /* default digits of precision */
#  else
#     define MP_PREC                 8      /* default digits of precision */
#  endif
#endif

/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
#define MP_WARRAY               (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))

/* the infamous mp_int structure */
#ifndef MP_INT_DECLARED
#define MP_INT_DECLARED
typedef struct mp_int mp_int;
#endif
struct mp_int {
................................................................................


#define USED(m)    ((m)->used)
#define DIGIT(m,k) ((m)->dp[(k)])
#define SIGN(m)    ((m)->sign)

/* error code to char* string */
/*
char *mp_error_to_string(int code);
*/

/* ---> init and deinit bignum functions <--- */
/* init a bignum */
/*
int mp_init(mp_int *a);
*/

................................................................................
/* init to a given number of digits */
/*
int mp_init_size(mp_int *a, int size);
*/

/* ---> Basic Manipulations <--- */
#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
#define mp_iseven(a) (((a)->used == 0 || (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
#define mp_isodd(a)  (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)


/* set to zero */
/*
void mp_zero(mp_int *a);
*/

/* set to a digit */
................................................................................
void mp_set(mp_int *a, mp_digit b);
*/

/* set a 32-bit const */
/*
int mp_set_int(mp_int *a, unsigned long b);
*/











/* get a 32-bit value */
unsigned long mp_get_int(mp_int * a);







/* initialize and set a digit */
/*
int mp_init_set (mp_int * a, mp_digit b);
*/

/* initialize and set 32-bit value */
................................................................................
/* copy, b = a */
/*
int mp_copy(const mp_int *a, mp_int *b);
*/

/* inits and copies, a = b */
/*
int mp_init_copy(mp_int *a, mp_int *b);
*/

/* trim unused digits */
/*
void mp_clamp(mp_int *a);
*/











/* ---> digit manipulation <--- */

/* right shift by "b" digits */
/*
void mp_rshd(mp_int *a, int b);
*/

/* left shift by "b" digits */
/*
int mp_lshd(mp_int *a, int b);
*/

/* c = a / 2**b */
/*
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
*/

/* b = a/2 */
/*
int mp_div_2(mp_int *a, mp_int *b);
*/

/* c = a * 2**b */
/*
int mp_mul_2d(const mp_int *a, int b, mp_int *c);
*/

/* b = a*2 */
/*
int mp_mul_2(mp_int *a, mp_int *b);
*/

/* c = a mod 2**d */
/*
int mp_mod_2d(const mp_int *a, int b, mp_int *c);
*/

/* computes a = 2**b */
/*
int mp_2expt(mp_int *a, int b);
*/

/* Counts the number of lsbs which are zero before the first zero bit */
/*
int mp_cnt_lsb(mp_int *a);
*/

/* I Love Earth! */

/* makes a pseudo-random int of a given size */
/*
int mp_rand(mp_int *a, int digits);
................................................................................
int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
*/

/* c = a**b */
/*
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
*/




/* c = a mod b, 0 <= c < b  */
/*
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
*/

/* ---> number theory <--- */
................................................................................
/* finds one of the b'th root of a, such that |c|**b <= |a|
 *
 * returns error if a < 0 and b is even
 */
/*
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
*/




/* special sqrt algo */
/*
int mp_sqrt(mp_int *arg, mp_int *ret);
*/






/* is number a square? */
/*
int mp_is_square(mp_int *arg, int *ret);
*/

/* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
................................................................................
#  define PRIME_SIZE      31
#else
#  define PRIME_SIZE      256
#endif

/* table of first PRIME_SIZE primes */
#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE const mp_digit ltm_prime_tab[];
#endif

/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
/*
int mp_prime_is_divisible(mp_int *a, int *result);
*/

................................................................................
 * Sets result to 0 if composite or 1 if probable prime
 */
/*
int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
*/

/* This gives [for a given bit size] the number of trials required
 * such that Miller-Rabin gives a prob of failure lower than 2^-96 
 */
/*
int mp_prime_rabin_miller_trials(int size);
*/

/* performs t rounds of Miller-Rabin on "a" using the first
 * t prime bases.  Also performs an initial sieve of trial
................................................................................
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
/*
int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
*/

/* makes a truly random prime of a given size (bytes),
 * call with bbs = 1 if you want it to be congruent to 3 mod 4 
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 * The prime generated will be larger than 2^(8*size).
 */
#define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 * 
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
 *   LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
 *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 */
................................................................................
/*
int mp_toradix(mp_int *a, char *str, int radix);
*/
/*
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
*/
/*
int mp_radix_size(mp_int *a, int radix, int *size);
*/


/*
int mp_fread(mp_int *a, int radix, FILE *stream);
*/
/*
int mp_fwrite(mp_int *a, int radix, FILE *stream);
*/


#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp)           mp_signed_bin_size(mp)
#define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))

#define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
#define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S)     mp_toradix((M), (S), 16)

/* lowlevel functions, do not call! */
/*
int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
*/
#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
/*
int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
*/
/*
int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
*/
/*
int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
*/
/*
int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
*/
/*
int fast_s_mp_sqr(mp_int *a, mp_int *b);
*/
/*
int s_mp_sqr(mp_int *a, mp_int *b);
*/
/*
int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
*/
/*
int mp_toom_sqr(mp_int *a, mp_int *b);
*/
/*
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
*/
/*
int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
*/
/*
int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
*/
/*
int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
*/
/*
void bn_reverse(unsigned char *s, int len);
*/

#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE const char *mp_s_rmap;
#endif

#ifdef __cplusplus
}
#endif

#endif












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 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://math.libtomcrypt.com
 */
#ifndef BN_H_
#define BN_H_

#include "tclTomMathDecls.h"
#ifndef MODULE_SCOPE
#define MODULE_SCOPE extern
#endif











#ifdef __cplusplus
extern "C" {









#endif


/* detect 64-bit mode if possible */
#if defined(NEVER) /* 128-bit ints fail in too many places */

   #if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
      #define MP_64BIT
   #endif
#endif

/* some default configurations.
 *
 * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
 * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
 *
 * At the very least a mp_digit must be able to hold 7 bits
 * [any size beyond that is ok provided it doesn't overflow the data type]
 */
#ifdef MP_8BIT
#ifndef MP_DIGIT_DECLARED
   typedef uint8_t              mp_digit;
#define MP_DIGIT_DECLARED
#endif
   typedef uint16_t             mp_word;
#define MP_SIZEOF_MP_DIGIT      1
#ifdef DIGIT_BIT
#error You must not define DIGIT_BIT when using MP_8BIT
#endif
#elif defined(MP_16BIT)
#ifndef MP_DIGIT_DECLARED

   typedef uint16_t             mp_digit;
#define MP_DIGIT_DECLARED
#endif

   typedef uint32_t             mp_word;
#define MP_SIZEOF_MP_DIGIT      2
#ifdef DIGIT_BIT
#error You must not define DIGIT_BIT when using MP_16BIT
#endif
#elif defined(MP_64BIT)
   /* for GCC only on supported platforms */
#ifndef CRYPT
   typedef unsigned long long   ulong64;
   typedef signed long long     long64;
#endif

#ifndef MP_DIGIT_DECLARED
   typedef ulong64 mp_digit;
#define MP_DIGIT_DECLARED
#endif
#if defined(_WIN32)
   typedef unsigned __int128    mp_word;
#elif defined(__GNUC__)
   typedef unsigned long        mp_word __attribute__ ((mode(TI)));
#else
   /* it seems you have a problem
    * but we assume you can somewhere define your own uint128_t */
   typedef uint128_t            mp_word;
#endif

   #define DIGIT_BIT            60
#else
   /* this is the default case, 28-bit digits */

   /* this is to make porting into LibTomCrypt easier :-) */
#ifndef CRYPT




   typedef unsigned long long   ulong64;
   typedef signed long long     long64;

#endif

#ifndef MP_DIGIT_DECLARED
   typedef uint32_t             mp_digit;
#define MP_DIGIT_DECLARED
#endif
   typedef ulong64              mp_word;

#ifdef MP_31BIT
   /* this is an extension that uses 31-bit digits */
   #define DIGIT_BIT            31
#else
   /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
   #define DIGIT_BIT            28
   #define MP_28BIT
#endif
#endif





















/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
#ifndef DIGIT_BIT
   #define DIGIT_BIT     (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1))  /* bits per digit */
   typedef uint_least32_t mp_min_u32;
#else
   typedef mp_digit mp_min_u32;
#endif

/* platforms that can use a better rand function */
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
    #define MP_USE_ALT_RAND 1
#endif

/* use arc4random on platforms that support it */
#ifdef MP_USE_ALT_RAND
    #define MP_GEN_RANDOM()    arc4random()
#else
    #define MP_GEN_RANDOM()    rand()
#endif

#define MP_DIGIT_BIT     DIGIT_BIT
#define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
#define MP_DIGIT_MAX     MP_MASK

/* equalities */
................................................................................
#endif

/* define this to use lower memory usage routines (exptmods mostly) */
/* #define MP_LOW_MEM */

/* default precision */
#ifndef MP_PREC
   #ifndef MP_LOW_MEM
      #define MP_PREC                 32     /* default digits of precision */
   #else
      #define MP_PREC                 8      /* default digits of precision */
   #endif
#endif

/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
#define MP_WARRAY               (1 << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) + 1))

/* the infamous mp_int structure */
#ifndef MP_INT_DECLARED
#define MP_INT_DECLARED
typedef struct mp_int mp_int;
#endif
struct mp_int {
................................................................................


#define USED(m)    ((m)->used)
#define DIGIT(m,k) ((m)->dp[(k)])
#define SIGN(m)    ((m)->sign)

/* error code to char* string */

const char *mp_error_to_string(int code);


/* ---> init and deinit bignum functions <--- */
/* init a bignum */
/*
int mp_init(mp_int *a);
*/

................................................................................
/* init to a given number of digits */
/*
int mp_init_size(mp_int *a, int size);
*/

/* ---> Basic Manipulations <--- */
#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
#define mp_iseven(a) ((((a)->used == 0) || (((a)->dp[0] & 1u) == 0u)) ? MP_YES : MP_NO)
#define mp_isodd(a)  ((((a)->used > 0) && (((a)->dp[0] & 1u) == 1u)) ? MP_YES : MP_NO)
#define mp_isneg(a)  (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)

/* set to zero */
/*
void mp_zero(mp_int *a);
*/

/* set to a digit */
................................................................................
void mp_set(mp_int *a, mp_digit b);
*/

/* set a 32-bit const */
/*
int mp_set_int(mp_int *a, unsigned long b);
*/

/* set a platform dependent unsigned long value */
/*
int mp_set_long(mp_int *a, unsigned long b);
*/

/* set a platform dependent unsigned long long value */
/*
int mp_set_long_long(mp_int *a, unsigned long long b);
*/

/* get a 32-bit value */
unsigned long mp_get_int(mp_int * a);

/* get a platform dependent unsigned long value */
unsigned long mp_get_long(mp_int * a);

/* get a platform dependent unsigned long long value */
unsigned long long mp_get_long_long(mp_int * a);

/* initialize and set a digit */
/*
int mp_init_set (mp_int * a, mp_digit b);
*/

/* initialize and set 32-bit value */
................................................................................
/* copy, b = a */
/*
int mp_copy(const mp_int *a, mp_int *b);
*/

/* inits and copies, a = b */
/*
int mp_init_copy(mp_int *a, const mp_int *b);
*/

/* trim unused digits */
/*
void mp_clamp(mp_int *a);
*/

/* import binary data */
/*
int mp_import(mp_int* rop, size_t count, int order, size_t size, int endian, size_t nails, const void* op);
*/

/* export binary data */
/*
int mp_export(void* rop, size_t* countp, int order, size_t size, int endian, size_t nails, mp_int* op);
*/

/* ---> digit manipulation <--- */

/* right shift by "b" digits */
/*
void mp_rshd(mp_int *a, int b);
*/

/* left shift by "b" digits */
/*
int mp_lshd(mp_int *a, int b);
*/

/* c = a / 2**b, implemented as c = a >> b */
/*
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
*/

/* b = a/2 */
/*
int mp_div_2(mp_int *a, mp_int *b);
*/

/* c = a * 2**b, implemented as c = a << b */
/*
int mp_mul_2d(const mp_int *a, int b, mp_int *c);
*/

/* b = a*2 */
/*
int mp_mul_2(mp_int *a, mp_int *b);
*/

/* c = a mod 2**b */
/*
int mp_mod_2d(const mp_int *a, int b, mp_int *c);
*/

/* computes a = 2**b */
/*
int mp_2expt(mp_int *a, int b);
*/

/* Counts the number of lsbs which are zero before the first zero bit */
/*
int mp_cnt_lsb(const mp_int *a);
*/

/* I Love Earth! */

/* makes a pseudo-random int of a given size */
/*
int mp_rand(mp_int *a, int digits);
................................................................................
int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
*/

/* c = a**b */
/*
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
*/
/*
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
*/

/* c = a mod b, 0 <= c < b  */
/*
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
*/

/* ---> number theory <--- */
................................................................................
/* finds one of the b'th root of a, such that |c|**b <= |a|
 *
 * returns error if a < 0 and b is even
 */
/*
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
*/
/*
int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
*/

/* special sqrt algo */
/*
int mp_sqrt(mp_int *arg, mp_int *ret);
*/

/* special sqrt (mod prime) */
/*
int mp_sqrtmod_prime(mp_int *arg, mp_int *prime, mp_int *ret);
*/

/* is number a square? */
/*
int mp_is_square(mp_int *arg, int *ret);
*/

/* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
................................................................................
#  define PRIME_SIZE      31
#else
#  define PRIME_SIZE      256
#endif

/* table of first PRIME_SIZE primes */
#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE const mp_digit ltm_prime_tab[PRIME_SIZE];
#endif

/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
/*
int mp_prime_is_divisible(mp_int *a, int *result);
*/

................................................................................
 * Sets result to 0 if composite or 1 if probable prime
 */
/*
int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
*/

/* This gives [for a given bit size] the number of trials required
 * such that Miller-Rabin gives a prob of failure lower than 2^-96
 */
/*
int mp_prime_rabin_miller_trials(int size);
*/

/* performs t rounds of Miller-Rabin on "a" using the first
 * t prime bases.  Also performs an initial sieve of trial
................................................................................
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
/*
int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
*/

/* makes a truly random prime of a given size (bytes),
 * call with bbs = 1 if you want it to be congruent to 3 mod 4
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 * The prime generated will be larger than 2^(8*size).
 */
#define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 *
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)

 *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 */
................................................................................
/*
int mp_toradix(mp_int *a, char *str, int radix);
*/
/*
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
*/
/*
int mp_radix_size(const mp_int *a, int radix, int *size);
*/

#ifndef LTM_NO_FILE
/*
int mp_fread(mp_int *a, int radix, FILE *stream);
*/
/*
int mp_fwrite(mp_int *a, int radix, FILE *stream);
*/
#endif

#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp)           mp_signed_bin_size(mp)
#define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))

#define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
#define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S)     mp_toradix((M), (S), 16)






























































#ifdef __cplusplus
   }
#endif

#endif


/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to generic/tclTomMathDecls.h.

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#define mp_div TclBN_mp_div
#define mp_div_2 TclBN_mp_div_2
#define mp_div_2d TclBN_mp_div_2d
#define mp_div_3 TclBN_mp_div_3
#define mp_div_d TclBN_mp_div_d
#define mp_exch TclBN_mp_exch
#define mp_expt_d TclBN_mp_expt_d

#define mp_grow TclBN_mp_grow
#define mp_init TclBN_mp_init
#define mp_init_copy TclBN_mp_init_copy
#define mp_init_multi TclBN_mp_init_multi
#define mp_init_set TclBN_mp_init_set
#define mp_init_set_int TclBN_mp_init_set_int
#define mp_init_size TclBN_mp_init_size
................................................................................
/* 19 */
TCLAPI int		TclBN_mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
/* 20 */
TCLAPI int		TclBN_mp_grow(mp_int *a, int size);
/* 21 */
TCLAPI int		TclBN_mp_init(mp_int *a);
/* 22 */
TCLAPI int		TclBN_mp_init_copy(mp_int *a, mp_int *b);
/* 23 */
TCLAPI int		TclBN_mp_init_multi(mp_int *a, ...);
/* 24 */
TCLAPI int		TclBN_mp_init_set(mp_int *a, mp_digit b);
/* 25 */
TCLAPI int		TclBN_mp_init_size(mp_int *a, int size);
/* 26 */
................................................................................
/* 32 */
TCLAPI int		TclBN_mp_mul_2d(const mp_int *a, int d, mp_int *p);
/* 33 */
TCLAPI int		TclBN_mp_neg(const mp_int *a, mp_int *b);
/* 34 */
TCLAPI int		TclBN_mp_or(mp_int *a, mp_int *b, mp_int *c);
/* 35 */
TCLAPI int		TclBN_mp_radix_size(mp_int *a, int radix, int *size);

/* 36 */
TCLAPI int		TclBN_mp_read_radix(mp_int *a, const char *str,
				int radix);
/* 37 */
TCLAPI void		TclBN_mp_rshd(mp_int *a, int shift);
/* 38 */
TCLAPI int		TclBN_mp_shrink(mp_int *a);
................................................................................
TCLAPI void		TclBNInitBignumFromLong(mp_int *bignum, long initVal);
/* 65 */
TCLAPI void		TclBNInitBignumFromWideInt(mp_int *bignum,
				Tcl_WideInt initVal);
/* 66 */
TCLAPI void		TclBNInitBignumFromWideUInt(mp_int *bignum,
				Tcl_WideUInt initVal);




typedef struct TclTomMathStubs {
    int magic;
    void *hooks;

    int (*tclBN_epoch) (void); /* 0 */
    int (*tclBN_revision) (void); /* 1 */
................................................................................
    int (*tclBN_mp_div_2) (mp_int *a, mp_int *q); /* 15 */
    int (*tclBN_mp_div_2d) (const mp_int *a, int b, mp_int *q, mp_int *r); /* 16 */
    int (*tclBN_mp_div_3) (mp_int *a, mp_int *q, mp_digit *r); /* 17 */
    void (*tclBN_mp_exch) (mp_int *a, mp_int *b); /* 18 */
    int (*tclBN_mp_expt_d) (mp_int *a, mp_digit b, mp_int *c); /* 19 */
    int (*tclBN_mp_grow) (mp_int *a, int size); /* 20 */
    int (*tclBN_mp_init) (mp_int *a); /* 21 */
    int (*tclBN_mp_init_copy) (mp_int *a, mp_int *b); /* 22 */
    int (*tclBN_mp_init_multi) (mp_int *a, ...); /* 23 */
    int (*tclBN_mp_init_set) (mp_int *a, mp_digit b); /* 24 */
    int (*tclBN_mp_init_size) (mp_int *a, int size); /* 25 */
    int (*tclBN_mp_lshd) (mp_int *a, int shift); /* 26 */
    int (*tclBN_mp_mod) (mp_int *a, mp_int *b, mp_int *r); /* 27 */
    int (*tclBN_mp_mod_2d) (const mp_int *a, int b, mp_int *r); /* 28 */
    int (*tclBN_mp_mul) (mp_int *a, mp_int *b, mp_int *p); /* 29 */
    int (*tclBN_mp_mul_d) (mp_int *a, mp_digit b, mp_int *p); /* 30 */
    int (*tclBN_mp_mul_2) (mp_int *a, mp_int *p); /* 31 */
    int (*tclBN_mp_mul_2d) (const mp_int *a, int d, mp_int *p); /* 32 */
    int (*tclBN_mp_neg) (const mp_int *a, mp_int *b); /* 33 */
    int (*tclBN_mp_or) (mp_int *a, mp_int *b, mp_int *c); /* 34 */
    int (*tclBN_mp_radix_size) (mp_int *a, int radix, int *size); /* 35 */
    int (*tclBN_mp_read_radix) (mp_int *a, const char *str, int radix); /* 36 */
    void (*tclBN_mp_rshd) (mp_int *a, int shift); /* 37 */
    int (*tclBN_mp_shrink) (mp_int *a); /* 38 */
    void (*tclBN_mp_set) (mp_int *a, mp_digit b); /* 39 */
    int (*tclBN_mp_sqr) (mp_int *a, mp_int *b); /* 40 */
    int (*tclBN_mp_sqrt) (mp_int *a, mp_int *b); /* 41 */
    int (*tclBN_mp_sub) (mp_int *a, mp_int *b, mp_int *c); /* 42 */
................................................................................
    int (*tclBN_s_mp_sub) (mp_int *a, mp_int *b, mp_int *c); /* 60 */
    int (*tclBN_mp_init_set_int) (mp_int *a, unsigned long i); /* 61 */
    int (*tclBN_mp_set_int) (mp_int *a, unsigned long i); /* 62 */
    int (*tclBN_mp_cnt_lsb) (const mp_int *a); /* 63 */
    void (*tclBNInitBignumFromLong) (mp_int *bignum, long initVal); /* 64 */
    void (*tclBNInitBignumFromWideInt) (mp_int *bignum, Tcl_WideInt initVal); /* 65 */
    void (*tclBNInitBignumFromWideUInt) (mp_int *bignum, Tcl_WideUInt initVal); /* 66 */

} TclTomMathStubs;

extern const TclTomMathStubs *tclTomMathStubsPtr;

#ifdef __cplusplus
}
#endif
................................................................................
	(tclTomMathStubsPtr->tclBN_mp_cnt_lsb) /* 63 */
#define TclBNInitBignumFromLong \
	(tclTomMathStubsPtr->tclBNInitBignumFromLong) /* 64 */
#define TclBNInitBignumFromWideInt \
	(tclTomMathStubsPtr->tclBNInitBignumFromWideInt) /* 65 */
#define TclBNInitBignumFromWideUInt \
	(tclTomMathStubsPtr->tclBNInitBignumFromWideUInt) /* 66 */



#endif /* defined(USE_TCL_STUBS) */

/* !END!: Do not edit above this line. */

#endif /* _TCLINTDECLS */






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#define mp_div TclBN_mp_div
#define mp_div_2 TclBN_mp_div_2
#define mp_div_2d TclBN_mp_div_2d
#define mp_div_3 TclBN_mp_div_3
#define mp_div_d TclBN_mp_div_d
#define mp_exch TclBN_mp_exch
#define mp_expt_d TclBN_mp_expt_d
#define mp_expt_d_ex TclBN_mp_expt_d_ex
#define mp_grow TclBN_mp_grow
#define mp_init TclBN_mp_init
#define mp_init_copy TclBN_mp_init_copy
#define mp_init_multi TclBN_mp_init_multi
#define mp_init_set TclBN_mp_init_set
#define mp_init_set_int TclBN_mp_init_set_int
#define mp_init_size TclBN_mp_init_size
................................................................................
/* 19 */
TCLAPI int		TclBN_mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
/* 20 */
TCLAPI int		TclBN_mp_grow(mp_int *a, int size);
/* 21 */
TCLAPI int		TclBN_mp_init(mp_int *a);
/* 22 */
TCLAPI int		TclBN_mp_init_copy(mp_int *a, const mp_int *b);
/* 23 */
TCLAPI int		TclBN_mp_init_multi(mp_int *a, ...);
/* 24 */
TCLAPI int		TclBN_mp_init_set(mp_int *a, mp_digit b);
/* 25 */
TCLAPI int		TclBN_mp_init_size(mp_int *a, int size);
/* 26 */
................................................................................
/* 32 */
TCLAPI int		TclBN_mp_mul_2d(const mp_int *a, int d, mp_int *p);
/* 33 */
TCLAPI int		TclBN_mp_neg(const mp_int *a, mp_int *b);
/* 34 */
TCLAPI int		TclBN_mp_or(mp_int *a, mp_int *b, mp_int *c);
/* 35 */
TCLAPI int		TclBN_mp_radix_size(const mp_int *a, int radix,
				int *size);
/* 36 */
TCLAPI int		TclBN_mp_read_radix(mp_int *a, const char *str,
				int radix);
/* 37 */
TCLAPI void		TclBN_mp_rshd(mp_int *a, int shift);
/* 38 */
TCLAPI int		TclBN_mp_shrink(mp_int *a);
................................................................................
TCLAPI void		TclBNInitBignumFromLong(mp_int *bignum, long initVal);
/* 65 */
TCLAPI void		TclBNInitBignumFromWideInt(mp_int *bignum,
				Tcl_WideInt initVal);
/* 66 */
TCLAPI void		TclBNInitBignumFromWideUInt(mp_int *bignum,
				Tcl_WideUInt initVal);
/* 67 */
TCLAPI int		TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c,
				int fast);

typedef struct TclTomMathStubs {
    int magic;
    void *hooks;

    int (*tclBN_epoch) (void); /* 0 */
    int (*tclBN_revision) (void); /* 1 */
................................................................................
    int (*tclBN_mp_div_2) (mp_int *a, mp_int *q); /* 15 */
    int (*tclBN_mp_div_2d) (const mp_int *a, int b, mp_int *q, mp_int *r); /* 16 */
    int (*tclBN_mp_div_3) (mp_int *a, mp_int *q, mp_digit *r); /* 17 */
    void (*tclBN_mp_exch) (mp_int *a, mp_int *b); /* 18 */
    int (*tclBN_mp_expt_d) (mp_int *a, mp_digit b, mp_int *c); /* 19 */
    int (*tclBN_mp_grow) (mp_int *a, int size); /* 20 */
    int (*tclBN_mp_init) (mp_int *a); /* 21 */
    int (*tclBN_mp_init_copy) (mp_int *a, const mp_int *b); /* 22 */
    int (*tclBN_mp_init_multi) (mp_int *a, ...); /* 23 */
    int (*tclBN_mp_init_set) (mp_int *a, mp_digit b); /* 24 */
    int (*tclBN_mp_init_size) (mp_int *a, int size); /* 25 */
    int (*tclBN_mp_lshd) (mp_int *a, int shift); /* 26 */
    int (*tclBN_mp_mod) (mp_int *a, mp_int *b, mp_int *r); /* 27 */
    int (*tclBN_mp_mod_2d) (const mp_int *a, int b, mp_int *r); /* 28 */
    int (*tclBN_mp_mul) (mp_int *a, mp_int *b, mp_int *p); /* 29 */
    int (*tclBN_mp_mul_d) (mp_int *a, mp_digit b, mp_int *p); /* 30 */
    int (*tclBN_mp_mul_2) (mp_int *a, mp_int *p); /* 31 */
    int (*tclBN_mp_mul_2d) (const mp_int *a, int d, mp_int *p); /* 32 */
    int (*tclBN_mp_neg) (const mp_int *a, mp_int *b); /* 33 */
    int (*tclBN_mp_or) (mp_int *a, mp_int *b, mp_int *c); /* 34 */
    int (*tclBN_mp_radix_size) (const mp_int *a, int radix, int *size); /* 35 */
    int (*tclBN_mp_read_radix) (mp_int *a, const char *str, int radix); /* 36 */
    void (*tclBN_mp_rshd) (mp_int *a, int shift); /* 37 */
    int (*tclBN_mp_shrink) (mp_int *a); /* 38 */
    void (*tclBN_mp_set) (mp_int *a, mp_digit b); /* 39 */
    int (*tclBN_mp_sqr) (mp_int *a, mp_int *b); /* 40 */
    int (*tclBN_mp_sqrt) (mp_int *a, mp_int *b); /* 41 */
    int (*tclBN_mp_sub) (mp_int *a, mp_int *b, mp_int *c); /* 42 */
................................................................................
    int (*tclBN_s_mp_sub) (mp_int *a, mp_int *b, mp_int *c); /* 60 */
    int (*tclBN_mp_init_set_int) (mp_int *a, unsigned long i); /* 61 */
    int (*tclBN_mp_set_int) (mp_int *a, unsigned long i); /* 62 */
    int (*tclBN_mp_cnt_lsb) (const mp_int *a); /* 63 */
    void (*tclBNInitBignumFromLong) (mp_int *bignum, long initVal); /* 64 */
    void (*tclBNInitBignumFromWideInt) (mp_int *bignum, Tcl_WideInt initVal); /* 65 */
    void (*tclBNInitBignumFromWideUInt) (mp_int *bignum, Tcl_WideUInt initVal); /* 66 */
    int (*tclBN_mp_expt_d_ex) (mp_int *a, mp_digit b, mp_int *c, int fast); /* 67 */
} TclTomMathStubs;

extern const TclTomMathStubs *tclTomMathStubsPtr;

#ifdef __cplusplus
}
#endif
................................................................................
	(tclTomMathStubsPtr->tclBN_mp_cnt_lsb) /* 63 */
#define TclBNInitBignumFromLong \
	(tclTomMathStubsPtr->tclBNInitBignumFromLong) /* 64 */
#define TclBNInitBignumFromWideInt \
	(tclTomMathStubsPtr->tclBNInitBignumFromWideInt) /* 65 */
#define TclBNInitBignumFromWideUInt \
	(tclTomMathStubsPtr->tclBNInitBignumFromWideUInt) /* 66 */
#define TclBN_mp_expt_d_ex \
	(tclTomMathStubsPtr->tclBN_mp_expt_d_ex) /* 67 */

#endif /* defined(USE_TCL_STUBS) */

/* !END!: Do not edit above this line. */

#endif /* _TCLINTDECLS */

Changes to libtommath/LICENSE.

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LibTomMath is hereby released into the Public Domain.  







-- Tom St Denis




















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LibTomMath is licensed under DUAL licensing terms.

Choose and use the license of your needs.

[LICENSE #1]

LibTomMath is public domain.  As should all quality software be.

Tom St Denis

[/LICENSE #1]

[LICENSE #2]

            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
                    Version 2, December 2004

 Copyright (C) 2004 Sam Hocevar <[email protected]>

 Everyone is permitted to copy and distribute verbatim or modified
 copies of this license document, and changing it is allowed as long
 as the name is changed.

            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

  0. You just DO WHAT THE FUCK YOU WANT TO.

[/LICENSE #2]

Deleted libtommath/bn.tex.

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\documentclass[b5paper]{book}
\usepackage{hyperref}
\usepackage{makeidx}
\usepackage{amssymb}
\usepackage{color}
\usepackage{alltt}
\usepackage{graphicx}
\usepackage{layout}
\def\union{\cup}
\def\intersect{\cap}
\def\getsrandom{\stackrel{\rm R}{\gets}}
\def\cross{\times}
\def\cat{\hspace{0.5em} \| \hspace{0.5em}}
\def\catn{$\|$}
\def\divides{\hspace{0.3em} | \hspace{0.3em}}
\def\nequiv{\not\equiv}
\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
\def\lcm{{\rm lcm}}
\def\gcd{{\rm gcd}}
\def\log{{\rm log}}
\def\ord{{\rm ord}}
\def\abs{{\mathit abs}}
\def\rep{{\mathit rep}}
\def\mod{{\mathit\ mod\ }}
\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
\def\Or{{\rm\ or\ }}
\def\And{{\rm\ and\ }}
\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
\def\implies{\Rightarrow}
\def\undefined{{\rm ``undefined"}}
\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
\let\oldphi\phi
\def\phi{\varphi}
\def\Pr{{\rm Pr}}
\newcommand{\str}[1]{{\mathbf{#1}}}
\def\F{{\mathbb F}}
\def\N{{\mathbb N}}
\def\Z{{\mathbb Z}}
\def\R{{\mathbb R}}
\def\C{{\mathbb C}}
\def\Q{{\mathbb Q}}
\definecolor{DGray}{gray}{0.5}
\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
\def\gap{\vspace{0.5ex}}
\makeindex
\begin{document}
\frontmatter
\pagestyle{empty}
\title{LibTomMath User Manual \\ v0.39}
\author{Tom St Denis \\ [email protected]}
\maketitle
This text, the library and the accompanying textbook are all hereby placed in the public domain.  This book has been 
formatted for B5 [176x250] paper using the \LaTeX{} {\em book} macro package.

\vspace{10cm}

\begin{flushright}Open Source.  Open Academia.  Open Minds.

\mbox{ }

Tom St Denis,

Ontario, Canada
\end{flushright}

\tableofcontents
\listoffigures
\mainmatter
\pagestyle{headings}
\chapter{Introduction}
\section{What is LibTomMath?}
LibTomMath is a library of source code which provides a series of efficient and carefully written functions for manipulating
large integer numbers.  It was written in portable ISO C source code so that it will build on any platform with a conforming
C compiler.  

In a nutshell the library was written from scratch with verbose comments to help instruct computer science students how
to implement ``bignum'' math.  However, the resulting code has proven to be very useful.  It has been used by numerous 
universities, commercial and open source software developers.  It has been used on a variety of platforms ranging from
Linux and Windows based x86 to ARM based Gameboys and PPC based MacOS machines.  

\section{License}
As of the v0.25 the library source code has been placed in the public domain with every new release.  As of the v0.28
release the textbook ``Implementing Multiple Precision Arithmetic'' has been placed in the public domain with every new
release as well.  This textbook is meant to compliment the project by providing a more solid walkthrough of the development
algorithms used in the library.

Since both\footnote{Note that the MPI files under mtest/ are copyrighted by Michael Fromberger.  They are not required to use LibTomMath.} are in the 
public domain everyone is entitled to do with them as they see fit.

\section{Building LibTomMath}

LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well suited for GCC.  However, the library will
also build in MSVC, Borland C out of the box.  For any other ISO C compiler a makefile will have to be made by the end
developer.  

\subsection{Static Libraries}
To build as a static library for GCC issue the following
\begin{alltt}
make
\end{alltt}

command.  This will build the library and archive the object files in ``libtommath.a''.  Now you link against 
that and include ``tommath.h'' within your programs.  Alternatively to build with MSVC issue the following
\begin{alltt}
nmake -f makefile.msvc
\end{alltt}

This will build the library and archive the object files in ``tommath.lib''.  This has been tested with MSVC 
version 6.00 with service pack 5.  

\subsection{Shared Libraries}
To build as a shared library for GCC issue the following
\begin{alltt}
make -f makefile.shared
\end{alltt}
This requires the ``libtool'' package (common on most Linux/BSD systems).  It will build LibTomMath as both shared
and static then install (by default) into /usr/lib as well as install the header files in /usr/include.  The shared 
library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''.  Generally 
you use libtool to link your application against the shared object.  

There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile.  It requires 
Cygwin to work with since it requires the auto-export/import functionality.  The resulting DLL and import library 
``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin.

\subsection{Testing}
To build the library and the test harness type

\begin{alltt}
make test
\end{alltt}

This will build the library, ``test'' and ``mtest/mtest''.  The ``test'' program will accept test vectors and verify the
results.  ``mtest/mtest'' will generate test vectors using the MPI library by Michael Fromberger\footnote{A copy of MPI
is included in the package}.  Simply pipe mtest into test using

\begin{alltt}
mtest/mtest | test
\end{alltt}

If you do not have a ``/dev/urandom'' style RNG source you will have to write your own PRNG and simply pipe that into 
mtest.  For example, if your PRNG program is called ``myprng'' simply invoke

\begin{alltt}
myprng | mtest/mtest | test
\end{alltt}

This will output a row of numbers that are increasing.  Each column is a different test (such as addition, multiplication, etc)
that is being performed.  The numbers represent how many times the test was invoked.  If an error is detected the program
will exit with a dump of the relevent numbers it was working with.

\section{Build Configuration}
LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''.  
Each phase changes how the library is built and they are applied one after another respectively.  

To make the system more powerful you can tweak the build process.  Classes are defined in the file
``tommath\_superclass.h''.  By default, the symbol ``LTM\_ALL'' shall be defined which simply 
instructs the system to build all of the functions.  This is how LibTomMath used to be packaged.  This will give you 
access to every function LibTomMath offers.

However, there are cases where such a build is not optional.  For instance, you want to perform RSA operations.  You 
don't need the vast majority of the library to perform these operations.  Aside from LTM\_ALL there is 
another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt.  Additional 
classes can be defined base on the need of the user.

\subsection{Build Depends}
In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs''
which further define symbols.  All of the symbols (technically they're macros $\ldots$) represent a given C source
file.  For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''.  When a define has been enabled the
function in the respective file will be compiled and linked into the library.  Accordingly when the define
is absent the file will not be compiled and not contribute any size to the library.

You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice).  
This is to help resolve as many dependencies as possible.  In the last pass the symbol LTM\_LAST will be defined.  
This is useful for ``trims''.

\subsection{Build Tweaks}
A tweak is an algorithm ``alternative''.  For example, to provide tradeoffs (usually between size and space).
They can be enabled at any pass of the configuration phase.

\begin{small}
\begin{center}
\begin{tabular}{|l|l|}
\hline \textbf{Define} & \textbf{Purpose} \\
\hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\
                          & functional mp\_div() function \\
\hline
\end{tabular}
\end{center}
\end{small}

\subsection{Build Trims}
A trim is a manner of removing functionality from a function that is not required.  For instance, to perform
RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed.  
Build trims are meant to be defined on the last pass of the configuration which means they are to be defined
only if LTM\_LAST has been defined.

\subsubsection{Moduli Related}
\begin{small}
\begin{center}
\begin{tabular}{|l|l|}
\hline \textbf{Restriction} & \textbf{Undefine} \\
\hline Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\
                                           & BN\_MP\_REDUCE\_C \\
                                           & BN\_MP\_REDUCE\_SETUP\_C \\
                                           & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
                                           & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
\hline Exponentiation with random odd moduli & (The above plus the following) \\
                                           & BN\_MP\_REDUCE\_2K\_C \\
                                           & BN\_MP\_REDUCE\_2K\_SETUP\_C \\
                                           & BN\_MP\_REDUCE\_IS\_2K\_C \\
                                           & BN\_MP\_DR\_IS\_MODULUS\_C \\
                                           & BN\_MP\_DR\_REDUCE\_C \\
                                           & BN\_MP\_DR\_SETUP\_C \\
\hline Modular inverse odd moduli only     & BN\_MP\_INVMOD\_SLOW\_C \\
\hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\
\hline
\end{tabular}
\end{center}
\end{small}

\subsubsection{Operand Size Related}
\begin{small}
\begin{center}
\begin{tabular}{|l|l|}
\hline \textbf{Restriction} & \textbf{Undefine} \\
\hline Moduli $\le 2560$ bits              & BN\_MP\_MONTGOMERY\_REDUCE\_C \\
                                           & BN\_S\_MP\_MUL\_DIGS\_C \\
                                           & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
                                           & BN\_S\_MP\_SQR\_C \\
\hline Polynomial Schmolynomial            & BN\_MP\_KARATSUBA\_MUL\_C \\
                                           & BN\_MP\_KARATSUBA\_SQR\_C \\
                                           & BN\_MP\_TOOM\_MUL\_C \\ 
                                           & BN\_MP\_TOOM\_SQR\_C \\

\hline
\end{tabular}
\end{center}
\end{small}


\section{Purpose of LibTomMath}
Unlike  GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with 
bleeding edge performance in mind.  First and foremost LibTomMath was written to be entirely open.  Not only is the 
source code public domain (unlike various other GPL/etc licensed code), not only is the code freely downloadable but the
source code is also accessible for computer science students attempting to learn ``BigNum'' or multiple precision
arithmetic techniques. 

LibTomMath was written to be an instructive collection of source code.  This is why there are many comments, only one
function per source file and often I use a ``middle-road'' approach where I don't cut corners for an extra 2\% speed
increase.

Source code alone cannot really teach how the algorithms work which is why I also wrote a textbook that accompanies
the library (beat that!).

So you may be thinking ``should I use LibTomMath?'' and the answer is a definite maybe.  Let me tabulate what I think
are the pros and cons of LibTomMath by comparing it to the math routines from GnuPG\footnote{GnuPG v1.2.3 versus LibTomMath v0.28}.

\newpage\begin{figure}[here]
\begin{small}
\begin{center}
\begin{tabular}{|l|c|c|l|}
\hline \textbf{Criteria} & \textbf{Pro} & \textbf{Con} & \textbf{Notes} \\
\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath  $ = 71.97$ \\
\hline Commented function prototypes & X && GnuPG function names are cryptic. \\
\hline Speed && X & LibTomMath is slower.  \\
\hline Totally free & X & & GPL has unfavourable restrictions.\\
\hline Large function base & X & & GnuPG is barebones. \\
\hline Five modular reduction algorithms & X & & Faster modular exponentiation for a variety of moduli. \\
\hline Portable & X & & GnuPG requires configuration to build. \\
\hline
\end{tabular}
\end{center}
\end{small}
\caption{LibTomMath Valuation}
\end{figure}

It may seem odd to compare LibTomMath to GnuPG since the math in GnuPG is only a small portion of the entire application. 
However, LibTomMath was written with cryptography in mind.  It provides essentially all of the functions a cryptosystem
would require when working with large integers.  

So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your
own application but I think there are reasons not to.  While LibTomMath is slower than libraries such as GnuMP it is
not normally significantly slower.  On x86 machines the difference is normally a factor of two when performing modular
exponentiations.  It depends largely on the processor, compiler and the moduli being used.

Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern.  However,
on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library
that is very flexible, complete and performs well in resource contrained environments.  Fast RSA for example can
be performed with as little as 8KB of ram for data (again depending on build options).  

\chapter{Getting Started with LibTomMath}
\section{Building Programs}
In order to use LibTomMath you must include ``tommath.h'' and link against the appropriate library file (typically 
libtommath.a).  There is no library initialization required and the entire library is thread safe.

\section{Return Codes}
There are three possible return codes a function may return.

\index{MP\_OKAY}\index{MP\_YES}\index{MP\_NO}\index{MP\_VAL}\index{MP\_MEM}
\begin{figure}[here!]
\begin{center}
\begin{small}
\begin{tabular}{|l|l|}
\hline \textbf{Code} & \textbf{Meaning} \\
\hline MP\_OKAY & The function succeeded. \\
\hline MP\_VAL  & The function input was invalid. \\
\hline MP\_MEM  & Heap memory exhausted. \\
\hline &\\
\hline MP\_YES  & Response is yes. \\
\hline MP\_NO   & Response is no. \\
\hline
\end{tabular}
\end{small}
\end{center}
\caption{Return Codes}
\end{figure}

The last two codes listed are not actually ``return'ed'' by a function.  They are placed in an integer (the caller must
provide the address of an integer it can store to) which the caller can access.  To convert one of the three return codes
to a string use the following function.

\index{mp\_error\_to\_string}
\begin{alltt}
char *mp_error_to_string(int code);
\end{alltt}

This will return a pointer to a string which describes the given error code.  It will not work for the return codes 
MP\_YES and MP\_NO.  

\section{Data Types}
The basic ``multiple precision integer'' type is known as the ``mp\_int'' within LibTomMath.  This data type is used to
organize all of the data required to manipulate the integer it represents.  Within LibTomMath it has been prototyped
as the following.

\index{mp\_int}
\begin{alltt}
typedef struct  \{
    int used, alloc, sign;
    mp_digit *dp;
\} mp_int;
\end{alltt}

Where ``mp\_digit'' is a data type that represents individual digits of the integer.  By default, an mp\_digit is the
ISO C ``unsigned long'' data type and each digit is $28-$bits long.  The mp\_digit type can be configured to suit other
platforms by defining the appropriate macros.  

All LTM functions that use the mp\_int type will expect a pointer to mp\_int structure.  You must allocate memory to
hold the structure itself by yourself (whether off stack or heap it doesn't matter).  The very first thing that must be
done to use an mp\_int is that it must be initialized.

\section{Function Organization}

The arithmetic functions of the library are all organized to have the same style prototype.  That is source operands
are passed on the left and the destination is on the right.  For instance,

\begin{alltt}
mp_add(&a, &b, &c);       /* c = a + b */
mp_mul(&a, &a, &c);       /* c = a * a */
mp_div(&a, &b, &c, &d);   /* c = [a/b], d = a mod b */
\end{alltt}

Another feature of the way the functions have been implemented is that source operands can be destination operands as well.
For instance,

\begin{alltt}
mp_add(&a, &b, &b);       /* b = a + b */
mp_div(&a, &b, &a, &c);   /* a = [a/b], c = a mod b */
\end{alltt}

This allows operands to be re-used which can make programming simpler.

\section{Initialization}
\subsection{Single Initialization}
A single mp\_int can be initialized with the ``mp\_init'' function. 

\index{mp\_init}
\begin{alltt}
int mp_init (mp_int * a);
\end{alltt}

This function expects a pointer to an mp\_int structure and will initialize the members of the structure so the mp\_int
represents the default integer which is zero.  If the functions returns MP\_OKAY then the mp\_int is ready to be used
by the other LibTomMath functions.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number */

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Single Free}
When you are finished with an mp\_int it is ideal to return the heap it used back to the system.  The following function 
provides this functionality.

\index{mp\_clear}
\begin{alltt}
void mp_clear (mp_int * a);
\end{alltt}

The function expects a pointer to a previously initialized mp\_int structure and frees the heap it uses.  It sets the 
pointer\footnote{The ``dp'' member.} within the mp\_int to \textbf{NULL} which is used to prevent double free situations. 
Is is legal to call mp\_clear() twice on the same mp\_int in a row.  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number */

   /* We're done with it. */
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Multiple Initializations}
Certain algorithms require more than one large integer.  In these instances it is ideal to initialize all of the mp\_int
variables in an ``all or nothing'' fashion.  That is, they are either all initialized successfully or they are all
not initialized.

The  mp\_init\_multi() function provides this functionality.

\index{mp\_init\_multi} \index{mp\_clear\_multi}
\begin{alltt}
int mp_init_multi(mp_int *mp, ...);
\end{alltt}

It accepts a \textbf{NULL} terminated list of pointers to mp\_int structures.  It will attempt to initialize them all
at once.  If the function returns MP\_OKAY then all of the mp\_int variables are ready to use, otherwise none of them
are available for use.  A complementary mp\_clear\_multi() function allows multiple mp\_int variables to be free'd 
from the heap at the same time.  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int num1, num2, num3;
   int result;

   if ((result = mp_init_multi(&num1, 
                               &num2,
                               &num3, NULL)) != MP\_OKAY) \{      
      printf("Error initializing the numbers.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the numbers */

   /* We're done with them. */
   mp_clear_multi(&num1, &num2, &num3, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Other Initializers}
To initialized and make a copy of an mp\_int the mp\_init\_copy() function has been provided.  

\index{mp\_init\_copy}
\begin{alltt}
int mp_init_copy (mp_int * a, mp_int * b);
\end{alltt}

This function will initialize $a$ and make it a copy of $b$ if all goes well.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int num1, num2;
   int result;

   /* initialize and do work on num1 ... */

   /* We want a copy of num1 in num2 now */
   if ((result = mp_init_copy(&num2, &num1)) != MP_OKAY) \{
     printf("Error initializing the copy.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* now num2 is ready and contains a copy of num1 */

   /* We're done with them. */
   mp_clear_multi(&num1, &num2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

Another less common initializer is mp\_init\_size() which allows the user to initialize an mp\_int with a given
default number of digits.  By default, all initializers allocate \textbf{MP\_PREC} digits.  This function lets
you override this behaviour.

\index{mp\_init\_size}
\begin{alltt}
int mp_init_size (mp_int * a, int size);
\end{alltt}

The $size$ parameter must be greater than zero.  If the function succeeds the mp\_int $a$ will be initialized
to have $size$ digits (which are all initially zero).  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   /* we need a 60-digit number */
   if ((result = mp_init_size(&number, 60)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number */

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\section{Maintenance Functions}

\subsection{Reducing Memory Usage}
When an mp\_int is in a state where it won't be changed again\footnote{A Diffie-Hellman modulus for instance.} excess
digits can be removed to return memory to the heap with the mp\_shrink() function.

\index{mp\_shrink}
\begin{alltt}
int mp_shrink (mp_int * a);
\end{alltt}

This will remove excess digits of the mp\_int $a$.  If the operation fails the mp\_int should be intact without the
excess digits being removed.  Note that you can use a shrunk mp\_int in further computations, however, such operations
will require heap operations which can be slow.  It is not ideal to shrink mp\_int variables that you will further
modify in the system (unless you are seriously low on memory).  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number [e.g. pre-computation]  */

   /* We're done with it for now. */
   if ((result = mp_shrink(&number)) != MP_OKAY) \{
      printf("Error shrinking the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* use it .... */


   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Adding additional digits}

Within the mp\_int structure are two parameters which control the limitations of the array of digits that represent
the integer the mp\_int is meant to equal.   The \textit{used} parameter dictates how many digits are significant, that is,
contribute to the value of the mp\_int.  The \textit{alloc} parameter dictates how many digits are currently available in
the array.  If you need to perform an operation that requires more digits you will have to mp\_grow() the mp\_int to
your desired size.  

\index{mp\_grow}
\begin{alltt}
int mp_grow (mp_int * a, int size);
\end{alltt}

This will grow the array of digits of $a$ to $size$.  If the \textit{alloc} parameter is already bigger than
$size$ the function will not do anything.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number */

   /* We need to add 20 digits to the number  */
   if ((result = mp_grow(&number, number.alloc + 20)) != MP_OKAY) \{
      printf("Error growing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}


   /* use the number */

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\chapter{Basic Operations}
\section{Small Constants}
Setting mp\_ints to small constants is a relatively common operation.  To accomodate these instances there are two
small constant assignment functions.  The first function is used to set a single digit constant while the second sets
an ISO C style ``unsigned long'' constant.  The reason for both functions is efficiency.  Setting a single digit is quick but the
domain of a digit can change (it's always at least $0 \ldots 127$).  

\subsection{Single Digit}

Setting a single digit can be accomplished with the following function.

\index{mp\_set}
\begin{alltt}
void mp_set (mp_int * a, mp_digit b);
\end{alltt}

This will zero the contents of $a$ and make it represent an integer equal to the value of $b$.  Note that this
function has a return type of \textbf{void}.  It cannot cause an error so it is safe to assume the function
succeeded.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number to 5 */
   mp_set(&number, 5);

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Long Constants}

To set a constant that is the size of an ISO C ``unsigned long'' and larger than a single digit the following function 
can be used.

\index{mp\_set\_int}
\begin{alltt}
int mp_set_int (mp_int * a, unsigned long b);
\end{alltt}

This will assign the value of the 32-bit variable $b$ to the mp\_int $a$.  Unlike mp\_set() this function will always
accept a 32-bit input regardless of the size of a single digit.  However, since the value may span several digits 
this function can fail if it runs out of heap memory.

To get the ``unsigned long'' copy of an mp\_int the following function can be used.

\index{mp\_get\_int}
\begin{alltt}
unsigned long mp_get_int (mp_int * a);
\end{alltt}

This will return the 32 least significant bits of the mp\_int $a$.  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number to 654321 (note this is bigger than 127) */
   if ((result = mp_set_int(&number, 654321)) != MP_OKAY) \{
      printf("Error setting the value of the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   printf("number == \%lu", mp_get_int(&number));

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

This should output the following if the program succeeds.

\begin{alltt}
number == 654321
\end{alltt}

\subsection{Initialize and Setting Constants}
To both initialize and set small constants the following two functions are available.
\index{mp\_init\_set} \index{mp\_init\_set\_int}
\begin{alltt}
int mp_init_set (mp_int * a, mp_digit b);
int mp_init_set_int (mp_int * a, unsigned long b);
\end{alltt}

Both functions work like the previous counterparts except they first mp\_init $a$ before setting the values.  

\begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int    result;

   /* initialize and set a single digit */
   if ((result = mp_init_set(&number1, 100)) != MP_OKAY) \{
      printf("Error setting number1: \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}             

   /* initialize and set a long */
   if ((result = mp_init_set_int(&number2, 1023)) != MP_OKAY) \{
      printf("Error setting number2: \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* display */
   printf("Number1, Number2 == \%lu, \%lu",
          mp_get_int(&number1), mp_get_int(&number2));

   /* clear */
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt}

If this program succeeds it shall output.
\begin{alltt}
Number1, Number2 == 100, 1023
\end{alltt}

\section{Comparisons}

Comparisons in LibTomMath are always performed in a ``left to right'' fashion.  There are three possible return codes
for any comparison.

\index{MP\_GT} \index{MP\_EQ} \index{MP\_LT}
\begin{figure}[here]
\begin{center}
\begin{tabular}{|c|c|}
\hline \textbf{Result Code} & \textbf{Meaning} \\
\hline MP\_GT & $a > b$ \\
\hline MP\_EQ & $a = b$ \\
\hline MP\_LT & $a < b$ \\
\hline
\end{tabular}
\end{center}
\caption{Comparison Codes for $a, b$}
\label{fig:CMP}
\end{figure}

In figure \ref{fig:CMP} two integers $a$ and $b$ are being compared.  In this case $a$ is said to be ``to the left'' of 
$b$.  

\subsection{Unsigned comparison}

An unsigned comparison considers only the digits themselves and not the associated \textit{sign} flag of the 
mp\_int structures.  This is analogous to an absolute comparison.  The function mp\_cmp\_mag() will compare two
mp\_int variables based on their digits only. 

\index{mp\_cmp\_mag}
\begin{alltt}
int mp_cmp_mag(mp_int * a, mp_int * b);
\end{alltt}
This will compare $a$ to $b$ placing $a$ to the left of $b$.  This function cannot fail and will return one of the
three compare codes listed in figure \ref{fig:CMP}.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int result;

   if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
      printf("Error initializing the numbers.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number1 to 5 */
   mp_set(&number1, 5);
  
   /* set the number2 to -6 */
   mp_set(&number2, 6);
   if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
      printf("Error negating number2.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   switch(mp_cmp_mag(&number1, &number2)) \{
       case MP_GT:  printf("|number1| > |number2|"); break;
       case MP_EQ:  printf("|number1| = |number2|"); break;
       case MP_LT:  printf("|number1| < |number2|"); break;
   \}

   /* we're done with it. */ 
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes 
successfully it should print the following.

\begin{alltt}
|number1| < |number2|
\end{alltt}

This is because $\vert -6 \vert = 6$ and obviously $5 < 6$.

\subsection{Signed comparison}

To compare two mp\_int variables based on their signed value the mp\_cmp() function is provided.

\index{mp\_cmp}
\begin{alltt}
int mp_cmp(mp_int * a, mp_int * b);
\end{alltt}

This will compare $a$ to the left of $b$.  It will first compare the signs of the two mp\_int variables.  If they
differ it will return immediately based on their signs.  If the signs are equal then it will compare the digits
individually.  This function will return one of the compare conditions codes listed in figure \ref{fig:CMP}.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int result;

   if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
      printf("Error initializing the numbers.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number1 to 5 */
   mp_set(&number1, 5);
  
   /* set the number2 to -6 */
   mp_set(&number2, 6);
   if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
      printf("Error negating number2.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   switch(mp_cmp(&number1, &number2)) \{
       case MP_GT:  printf("number1 > number2"); break;
       case MP_EQ:  printf("number1 = number2"); break;
       case MP_LT:  printf("number1 < number2"); break;
   \}

   /* we're done with it. */ 
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes 
successfully it should print the following.

\begin{alltt}
number1 > number2
\end{alltt}

\subsection{Single Digit}

To compare a single digit against an mp\_int the following function has been provided.

\index{mp\_cmp\_d}
\begin{alltt}
int mp_cmp_d(mp_int * a, mp_digit b);
\end{alltt}

This will compare $a$ to the left of $b$ using a signed comparison.  Note that it will always treat $b$ as 
positive.  This function is rather handy when you have to compare against small values such as $1$ (which often
comes up in cryptography).  The function cannot fail and will return one of the tree compare condition codes
listed in figure \ref{fig:CMP}.


\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number to 5 */
   mp_set(&number, 5);

   switch(mp_cmp_d(&number, 7)) \{
       case MP_GT:  printf("number > 7"); break;
       case MP_EQ:  printf("number = 7"); break;
       case MP_LT:  printf("number < 7"); break;
   \}

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program functions properly it will print out the following.

\begin{alltt}
number < 7
\end{alltt}

\section{Logical Operations}

Logical operations are operations that can be performed either with simple shifts or boolean operators such as
AND, XOR and OR directly.  These operations are very quick.

\subsection{Multiplication by two}

Multiplications and divisions by any power of two can be performed with quick logical shifts either left or
right depending on the operation.  

When multiplying or dividing by two a special case routine can be used which are as follows.
\index{mp\_mul\_2} \index{mp\_div\_2}
\begin{alltt}
int mp_mul_2(mp_int * a, mp_int * b);
int mp_div_2(mp_int * a, mp_int * b);
\end{alltt}

The former will assign twice $a$ to $b$ while the latter will assign half $a$ to $b$.  These functions are fast
since the shift counts and maskes are hardcoded into the routines.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number to 5 */
   mp_set(&number, 5);

   /* multiply by two */
   if ((result = mp\_mul\_2(&number, &number)) != MP_OKAY) \{
      printf("Error multiplying the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   switch(mp_cmp_d(&number, 7)) \{
       case MP_GT:  printf("2*number > 7"); break;
       case MP_EQ:  printf("2*number = 7"); break;
       case MP_LT:  printf("2*number < 7"); break;
   \}

   /* now divide by two */
   if ((result = mp\_div\_2(&number, &number)) != MP_OKAY) \{
      printf("Error dividing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   switch(mp_cmp_d(&number, 7)) \{
       case MP_GT:  printf("2*number/2 > 7"); break;
       case MP_EQ:  printf("2*number/2 = 7"); break;
       case MP_LT:  printf("2*number/2 < 7"); break;
   \}

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program is successful it will print out the following text.

\begin{alltt}
2*number > 7
2*number/2 < 7
\end{alltt}

Since $10 > 7$ and $5 < 7$.  To multiply by a power of two the following function can be used.

\index{mp\_mul\_2d}
\begin{alltt}
int mp_mul_2d(mp_int * a, int b, mp_int * c);
\end{alltt}

This will multiply $a$ by $2^b$ and store the result in ``c''.  If the value of $b$ is less than or equal to 
zero the function will copy $a$ to ``c'' without performing any further actions.  

To divide by a power of two use the following.

\index{mp\_div\_2d}
\begin{alltt}
int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
\end{alltt}
Which will divide $a$ by $2^b$, store the quotient in ``c'' and the remainder in ``d'.  If $b \le 0$ then the
function simply copies $a$ over to ``c'' and zeroes $d$.  The variable $d$ may be passed as a \textbf{NULL}
value to signal that the remainder is not desired.

\subsection{Polynomial Basis Operations}

Strictly speaking the organization of the integers within the mp\_int structures is what is known as a 
``polynomial basis''.  This simply means a field element is stored by divisions of a radix.  For example, if
$f(x) = \sum_{i=0}^{k} y_ix^k$ for any vector $\vec y$ then the array of digits in $\vec y$ are said to be 
the polynomial basis representation of $z$ if $f(\beta) = z$ for a given radix $\beta$.  

To multiply by the polynomial $g(x) = x$ all you have todo is shift the digits of the basis left one place.  The
following function provides this operation.

\index{mp\_lshd}
\begin{alltt}
int mp_lshd (mp_int * a, int b);
\end{alltt}

This will multiply $a$ in place by $x^b$ which is equivalent to shifting the digits left $b$ places and inserting zeroes
in the least significant digits.  Similarly to divide by a power of $x$ the following function is provided.

\index{mp\_rshd}
\begin{alltt}
void mp_rshd (mp_int * a, int b)
\end{alltt}
This will divide $a$ in place by $x^b$ and discard the remainder.  This function cannot fail as it performs the operations
in place and no new digits are required to complete it.

\subsection{AND, OR and XOR Operations}

While AND, OR and XOR operations are not typical ``bignum functions'' they can be useful in several instances.  The
three functions are prototyped as follows.

\index{mp\_or} \index{mp\_and} \index{mp\_xor}
\begin{alltt}
int mp_or  (mp_int * a, mp_int * b, mp_int * c);
int mp_and (mp_int * a, mp_int * b, mp_int * c);
int mp_xor (mp_int * a, mp_int * b, mp_int * c);
\end{alltt}

Which compute $c = a \odot b$ where $\odot$ is one of OR, AND or XOR.  

\section{Addition and Subtraction}

To compute an addition or subtraction the following two functions can be used.

\index{mp\_add} \index{mp\_sub}
\begin{alltt}
int mp_add (mp_int * a, mp_int * b, mp_int * c);
int mp_sub (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}

Which perform $c = a \odot b$ where $\odot$ is one of signed addition or subtraction.  The operations are fully sign
aware.

\section{Sign Manipulation}
\subsection{Negation}
\label{sec:NEG}
Simple integer negation can be performed with the following.

\index{mp\_neg}
\begin{alltt}
int mp_neg (mp_int * a, mp_int * b);
\end{alltt}

Which assigns $-a$ to $b$.  

\subsection{Absolute}
Simple integer absolutes can be performed with the following.

\index{mp\_neg}
\begin{alltt}
int mp_abs (mp_int * a, mp_int * b);
\end{alltt}

Which assigns $\vert a \vert$ to $b$.  

\section{Integer Division and Remainder}
To perform a complete and general integer division with remainder use the following function.

\index{mp\_div}
\begin{alltt}
int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
\end{alltt}
                                                        
This divides $a$ by $b$ and stores the quotient in $c$ and $d$.  The signed quotient is computed such that 
$bc + d = a$.  Note that either of $c$ or $d$ can be set to \textbf{NULL} if their value is not required.  If 
$b$ is zero the function returns \textbf{MP\_VAL}.  


\chapter{Multiplication and Squaring}
\section{Multiplication}
A full signed integer multiplication can be performed with the following.
\index{mp\_mul}
\begin{alltt}
int mp_mul (mp_int * a, mp_int * b, mp_int * c);
\end{alltt}
Which assigns the full signed product $ab$ to $c$.  This function actually breaks into one of four cases which are 
specific multiplication routines optimized for given parameters.  First there are the Toom-Cook multiplications which
should only be used with very large inputs.  This is followed by the Karatsuba multiplications which are for moderate
sized inputs.  Then followed by the Comba and baseline multipliers.

Fortunately for the developer you don't really need to know this unless you really want to fine tune the system.  mp\_mul()
will determine on its own\footnote{Some tweaking may be required.} what routine to use automatically when it is called.

\begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int result;

   /* Initialize the numbers */
   if ((result = mp_init_multi(&number1, 
                               &number2, NULL)) != MP_OKAY) \{
      printf("Error initializing the numbers.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* set the terms */
   if ((result = mp_set_int(&number, 257)) != MP_OKAY) \{
      printf("Error setting number1.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   if ((result = mp_set_int(&number2, 1023)) != MP_OKAY) \{
      printf("Error setting number2.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* multiply them */
   if ((result = mp_mul(&number1, &number2,
                        &number1)) != MP_OKAY) \{
      printf("Error multiplying terms.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* display */
   printf("number1 * number2 == \%lu", mp_get_int(&number1));

   /* free terms and return */
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt}   

If this program succeeds it shall output the following.

\begin{alltt}
number1 * number2 == 262911
\end{alltt}

\section{Squaring}
Since squaring can be performed faster than multiplication it is performed it's own function instead of just using
mp\_mul().

\index{mp\_sqr}
\begin{alltt}
int mp_sqr (mp_int * a, mp_int * b);
\end{alltt}

Will square $a$ and store it in $b$.  Like the case of multiplication there are four different squaring
algorithms all which can be called from mp\_sqr().  It is ideal to use mp\_sqr over mp\_mul when squaring terms because
of the speed difference.  

\section{Tuning Polynomial Basis Routines}

Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that
the Comba and baseline algorithms use.  At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require 
considerably less work.  For example, a 10000-digit multiplication would take roughly 724,000 single precision
multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor
of 138).

So why not always use Karatsuba or Toom-Cook?   The simple answer is that they have so much overhead that they're not
actually faster than Comba until you hit distinct  ``cutoff'' points.  For Karatsuba with the default configuration, 
GCC 3.3.1 and an Athlon XP processor the cutoff point is roughly 110 digits (about 70 for the Intel P4).  That is, at 
110 digits Karatsuba and Comba multiplications just about break even and for 110+ digits Karatsuba is faster.

Toom-Cook has incredible overhead and is probably only useful for very large inputs.  So far no known cutoff points 
exist and for the most part I just set the cutoff points very high to make sure they're not called.

A demo program in the ``etc/'' directory of the project called ``tune.c'' can be used to find the cutoff points.  This
can be built with GCC as follows

\begin{alltt}
make XXX
\end{alltt}
Where ``XXX'' is one of the following entries from the table \ref{fig:tuning}.

\begin{figure}[here]
\begin{center}
\begin{small}
\begin{tabular}{|l|l|}
\hline \textbf{Value of XXX} & \textbf{Meaning} \\
\hline tune & Builds portable tuning application \\
\hline tune86 & Builds x86 (pentium and up) program for COFF \\
\hline tune86c & Builds x86 program for Cygwin \\
\hline tune86l & Builds x86 program for Linux (ELF format) \\
\hline
\end{tabular}
\end{small}
\end{center}
\caption{Build Names for Tuning Programs}
\label{fig:tuning}
\end{figure}

When the program is running it will output a series of measurements for different cutoff points.  It will first find
good Karatsuba squaring and multiplication points.  Then it proceeds to find Toom-Cook points.  Note that the Toom-Cook
tuning takes a very long time as the cutoff points are likely to be very high.

\chapter{Modular Reduction}

Modular reduction is process of taking the remainder of one quantity divided by another.  Expressed 
as (\ref{eqn:mod}) the modular reduction is equivalent to the remainder of $b$ divided by $c$.  

\begin{equation}
a \equiv b \mbox{ (mod }c\mbox{)}
\label{eqn:mod}
\end{equation}

Of particular interest to cryptography are reductions where $b$ is limited to the range $0 \le b < c^2$ since particularly 
fast reduction algorithms can be written for the limited range.  

Note that one of the four optimized reduction algorithms are automatically chosen in the modular exponentiation
algorithm mp\_exptmod when an appropriate modulus is detected.  

\section{Straight Division}
In order to effect an arbitrary modular reduction the following algorithm is provided.

\index{mp\_mod}
\begin{alltt}
int mp_mod(mp_int *a, mp_int *b, mp_int *c);
\end{alltt}

This reduces $a$ modulo $b$ and stores the result in $c$.  The sign of $c$ shall agree with the sign 
of $b$.  This algorithm accepts an input $a$ of any range and is not limited by $0 \le a < b^2$.

\section{Barrett Reduction}

Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve
a decent speedup over straight division.  First a $\mu$ value must be precomputed with the following function.

\index{mp\_reduce\_setup}
\begin{alltt}
int mp_reduce_setup(mp_int *a, mp_int *b);
\end{alltt}

Given a modulus in $b$ this produces the required $\mu$ value in $a$.  For any given modulus this only has to
be computed once.  Modular reduction can now be performed with the following.

\index{mp\_reduce}
\begin{alltt}
int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
\end{alltt}

This will reduce $a$ in place modulo $b$ with the precomputed $\mu$ value in $c$.  $a$ must be in the range
$0 \le a < b^2$.

\begin{alltt}
int main(void)
\{
   mp_int   a, b, c, mu;
   int      result;

   /* initialize a,b to desired values, mp_init mu, 
    * c and set c to 1...we want to compute a^3 mod b 
    */

   /* get mu value */
   if ((result = mp_reduce_setup(&mu, b)) != MP_OKAY) \{
      printf("Error getting mu.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* square a to get c = a^2 */
   if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
      printf("Error squaring.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' modulo b */
   if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   
   /* multiply a to get c = a^3 */
   if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' modulo b  */
   if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
  
   /* c now equals a^3 mod b */

   return EXIT_SUCCESS;
\}
\end{alltt} 

This program will calculate $a^3 \mbox{ mod }b$ if all the functions succeed.  

\section{Montgomery Reduction}

Montgomery is a specialized reduction algorithm for any odd moduli.  Like Barrett reduction a pre--computation
step is required.  This is accomplished with the following.

\index{mp\_montgomery\_setup}
\begin{alltt}
int mp_montgomery_setup(mp_int *a, mp_digit *mp);
\end{alltt}

For the given odd moduli $a$ the precomputation value is placed in $mp$.  The reduction is computed with the 
following.

\index{mp\_montgomery\_reduce}
\begin{alltt}
int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
\end{alltt}
This reduces $a$ in place modulo $m$ with the pre--computed value $mp$.   $a$ must be in the range
$0 \le a < b^2$.

Montgomery reduction is faster than Barrett reduction for moduli smaller than the ``comba'' limit.  With the default
setup for instance, the limit is $127$ digits ($3556$--bits).   Note that this function is not limited to
$127$ digits just that it falls back to a baseline algorithm after that point.  

An important observation is that this reduction does not return $a \mbox{ mod }m$ but $aR^{-1} \mbox{ mod }m$ 
where $R = \beta^n$, $n$ is the n number of digits in $m$ and $\beta$ is radix used (default is $2^{28}$).  

To quickly calculate $R$ the following function was provided.

\index{mp\_montgomery\_calc\_normalization}
\begin{alltt}
int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
\end{alltt}
Which calculates $a = R$ for the odd moduli $b$ without using multiplication or division.  

The normal modus operandi for Montgomery reductions is to normalize the integers before entering the system.  For
example, to calculate $a^3 \mbox { mod }b$ using Montgomery reduction the value of $a$ can be normalized by
multiplying it by $R$.  Consider the following code snippet.

\begin{alltt}
int main(void)
\{
   mp_int   a, b, c, R;
   mp_digit mp;
   int      result;

   /* initialize a,b to desired values, 
    * mp_init R, c and set c to 1.... 
    */

   /* get normalization */
   if ((result = mp_montgomery_calc_normalization(&R, b)) != MP_OKAY) \{
      printf("Error getting norm.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* get mp value */
   if ((result = mp_montgomery_setup(&c, &mp)) != MP_OKAY) \{
      printf("Error setting up montgomery.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* normalize `a' so now a is equal to aR */
   if ((result = mp_mulmod(&a, &R, &b, &a)) != MP_OKAY) \{
      printf("Error computing aR.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* square a to get c = a^2R^2 */
   if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
      printf("Error squaring.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' back down to c = a^2R^2 * R^-1 == a^2R */
   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   
   /* multiply a to get c = a^3R^2 */
   if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' back down to c = a^3R^2 * R^-1 == a^3R */
   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   
   /* now reduce (again) `c' back down to c = a^3R * R^-1 == a^3 */
   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* c now equals a^3 mod b */

   return EXIT_SUCCESS;
\}
\end{alltt} 

This particular example does not look too efficient but it demonstrates the point of the algorithm.  By 
normalizing the inputs the reduced results are always of the form $aR$ for some variable $a$.  This allows
a single final reduction to correct for the normalization and the fast reduction used within the algorithm.

For more details consider examining the file \textit{bn\_mp\_exptmod\_fast.c}.

\section{Restricted Dimminished Radix}

``Dimminished Radix'' reduction refers to reduction with respect to moduli that are ameniable to simple
digit shifting and small multiplications.  In this case the ``restricted'' variant refers to moduli of the
form $\beta^k - p$ for some $k \ge 0$ and $0 < p < \beta$ where $\beta$ is the radix (default to $2^{28}$).  

As in the case of Montgomery reduction there is a pre--computation phase required for a given modulus.

\index{mp\_dr\_setup}
\begin{alltt}
void mp_dr_setup(mp_int *a, mp_digit *d);
\end{alltt}

This computes the value required for the modulus $a$ and stores it in $d$.  This function cannot fail
and does not return any error codes.  After the pre--computation a reduction can be performed with the
following.

\index{mp\_dr\_reduce}
\begin{alltt}
int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
\end{alltt}

This reduces $a$ in place modulo $b$ with the pre--computed value $mp$.  $b$ must be of a restricted
dimminished radix form and $a$ must be in the range $0 \le a < b^2$.  Dimminished radix reductions are 
much faster than both Barrett and Montgomery reductions as they have a much lower asymtotic running time.  

Since the moduli are restricted this algorithm is not particularly useful for something like Rabin, RSA or
BBS cryptographic purposes.  This reduction algorithm is useful for Diffie-Hellman and ECC where fixed
primes are acceptable.  

Note that unlike Montgomery reduction there is no normalization process.  The result of this function is
equal to the correct residue.

\section{Unrestricted Dimminshed Radix}

Unrestricted reductions work much like the restricted counterparts except in this case the moduli is of the 
form $2^k - p$ for $0 < p < \beta$.  In this sense the unrestricted reductions are more flexible as they 
can be applied to a wider range of numbers.  

\index{mp\_reduce\_2k\_setup}
\begin{alltt}
int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
\end{alltt}

This will compute the required $d$ value for the given moduli $a$.  

\index{mp\_reduce\_2k}
\begin{alltt}
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
\end{alltt}

This will reduce $a$ in place modulo $n$ with the pre--computed value $d$.  From my experience this routine is 
slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery reduction.  

\chapter{Exponentiation}
\section{Single Digit Exponentiation}
\index{mp\_expt\_d}
\begin{alltt}
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
\end{alltt}
This computes $c = a^b$ using a simple binary left-to-right algorithm.  It is faster than repeated multiplications by 
$a$ for all values of $b$ greater than three.  

\section{Modular Exponentiation}
\index{mp\_exptmod}
\begin{alltt}
int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
\end{alltt}
This computes $Y \equiv G^X \mbox{ (mod }P\mbox{)}$ using a variable width sliding window algorithm.  This function
will automatically detect the fastest modular reduction technique to use during the operation.  For negative values of 
$X$ the operation is performed as $Y \equiv (G^{-1} \mbox{ mod }P)^{\vert X \vert} \mbox{ (mod }P\mbox{)}$ provided that 
$gcd(G, P) = 1$.

This function is actually a shell around the two internal exponentiation functions.  This routine will automatically
detect when Barrett, Montgomery, Restricted and Unrestricted Dimminished Radix based exponentiation can be used.  Generally
moduli of the a ``restricted dimminished radix'' form lead to the fastest modular exponentiations.  Followed by Montgomery
and the other two algorithms.

\section{Root Finding}
\index{mp\_n\_root}
\begin{alltt}
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
\end{alltt}
This computes $c = a^{1/b}$ such that $c^b \le a$ and $(c+1)^b > a$.  The implementation of this function is not 
ideal for values of $b$ greater than three.  It will work but become very slow.  So unless you are working with very small
numbers (less than 1000 bits) I'd avoid $b > 3$ situations.  Will return a positive root only for even roots and return
a root with the sign of the input for odd roots.  For example, performing $4^{1/2}$ will return $2$ whereas $(-8)^{1/3}$ 
will return $-2$.  

This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly.  Since
the algorithm requires raising $a$ to the power of $b$ it is not ideal to attempt to find roots for large
values of $b$.  If particularly large roots are required then a factor method could be used instead.  For example,
$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply 
$\left ( \left ( \left ( a^{1/2} \right )^{1/2} \right )^{1/2} \right )^{1/2}$

\chapter{Prime Numbers}
\section{Trial Division}
\index{mp\_prime\_is\_divisible}
\begin{alltt}
int mp_prime_is_divisible (mp_int * a, int *result)
\end{alltt}
This will attempt to evenly divide $a$ by a list of primes\footnote{Default is the first 256 primes.} and store the 
outcome in ``result''.  That is if $result = 0$ then $a$ is not divisible by the primes, otherwise it is.  Note that 
if the function does not return \textbf{MP\_OKAY} the value in ``result'' should be considered undefined\footnote{Currently
the default is to set it to zero first.}.

\section{Fermat Test}
\index{mp\_prime\_fermat}
\begin{alltt}
int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
\end{alltt}
Performs a Fermat primality test to the base $b$.  That is it computes $b^a \mbox{ mod }a$ and tests whether the value is
equal to $b$ or not.  If the values are equal then $a$ is probably prime and $result$ is set to one.  Otherwise $result$
is set to zero.

\section{Miller-Rabin Test}
\index{mp\_prime\_miller\_rabin}
\begin{alltt}
int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
\end{alltt}
Performs a Miller-Rabin test to the base $b$ of $a$.  This test is much stronger than the Fermat test and is very hard to
fool (besides with Carmichael numbers).  If $a$ passes the test (therefore is probably prime) $result$ is set to one.  
Otherwise $result$ is set to zero.  

Note that is suggested that you use the Miller-Rabin test instead of the Fermat test since all of the failures of 
Miller-Rabin are a subset of the failures of the Fermat test.

\subsection{Required Number of Tests}
Generally to ensure a number is very likely to be prime you have to perform the Miller-Rabin with at least a half-dozen
or so unique bases.  However, it has been proven that the probability of failure goes down as the size of the input goes up.
This is why a simple function has been provided to help out.

\index{mp\_prime\_rabin\_miller\_trials}
\begin{alltt}
int mp_prime_rabin_miller_trials(int size)
\end{alltt}
This returns the number of trials required for a $2^{-96}$ (or lower) probability of failure for a given ``size'' expressed
in bits.  This comes in handy specially since larger numbers are slower to test.  For example, a 512-bit number would
require ten tests whereas a 1024-bit number would only require four tests. 

You should always still perform a trial division before a Miller-Rabin test though.

\section{Primality Testing}
\index{mp\_prime\_is\_prime}
\begin{alltt}
int mp_prime_is_prime (mp_int * a, int t, int *result)
\end{alltt}
This will perform a trial division followed by $t$ rounds of Miller-Rabin tests on $a$ and store the result in $result$.  
If $a$ passes all of the tests $result$ is set to one, otherwise it is set to zero.  Note that $t$ is bounded by 
$1 \le t < PRIME\_SIZE$ where $PRIME\_SIZE$ is the number of primes in the prime number table (by default this is $256$).

\section{Next Prime}
\index{mp\_prime\_next\_prime}
\begin{alltt}
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
\end{alltt}
This finds the next prime after $a$ that passes mp\_prime\_is\_prime() with $t$ tests.  Set $bbs\_style$ to one if you 
want only the next prime congruent to $3 \mbox{ mod } 4$, otherwise set it to zero to find any next prime.  

\section{Random Primes}
\index{mp\_prime\_random}
\begin{alltt}
int mp_prime_random(mp_int *a, int t, int size, int bbs, 
                    ltm_prime_callback cb, void *dat)
\end{alltt}
This will find a prime greater than $256^{size}$ which can be ``bbs\_style'' or not depending on $bbs$ and must pass
$t$ rounds of tests.  The ``ltm\_prime\_callback'' is a typedef for 

\begin{alltt}
typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
\end{alltt}

Which is a function that must read $len$ bytes (and return the amount stored) into $dst$.  The $dat$ variable is simply
copied from the original input.  It can be used to pass RNG context data to the callback.  The function 
mp\_prime\_random() is more suitable for generating primes which must be secret (as in the case of RSA) since there 
is no skew on the least significant bits.

\textit{Note:}  As of v0.30 of the LibTomMath library this function has been deprecated.  It is still available
but users are encouraged to use the new mp\_prime\_random\_ex() function instead.

\subsection{Extended Generation}
\index{mp\_prime\_random\_ex}
\begin{alltt}
int mp_prime_random_ex(mp_int *a,    int t, 
                       int     size, int flags, 
                       ltm_prime_callback cb, void *dat);
\end{alltt}
This will generate a prime in $a$ using $t$ tests of the primality testing algorithms.  The variable $size$
specifies the bit length of the prime desired.  The variable $flags$ specifies one of several options available
(see fig. \ref{fig:primeopts}) which can be OR'ed together.  The callback parameters are used as in 
mp\_prime\_random().

\begin{figure}[here]
\begin{center}
\begin{small}
\begin{tabular}{|r|l|}
\hline \textbf{Flag}         & \textbf{Meaning} \\
\hline LTM\_PRIME\_BBS       & Make the prime congruent to $3$ modulo $4$ \\
\hline LTM\_PRIME\_SAFE      & Make a prime $p$ such that $(p - 1)/2$ is also prime. \\
                             & This option implies LTM\_PRIME\_BBS as well. \\
\hline LTM\_PRIME\_2MSB\_OFF & Makes sure that the bit adjacent to the most significant bit \\
                             & Is forced to zero.  \\
\hline LTM\_PRIME\_2MSB\_ON  & Makes sure that the bit adjacent to the most significant bit \\
                             & Is forced to one. \\
\hline
\end{tabular}
\end{small}
\end{center}
\caption{Primality Generation Options}
\label{fig:primeopts}
\end{figure}

\chapter{Input and Output}
\section{ASCII Conversions}
\subsection{To ASCII}
\index{mp\_toradix}
\begin{alltt}
int mp_toradix (mp_int * a, char *str, int radix);
\end{alltt}
This still store $a$ in ``str'' as a base-``radix'' string of ASCII chars.  This function appends a NUL character
to terminate the string.  Valid values of ``radix'' line in the range $[2, 64]$.  To determine the size (exact) required
by the conversion before storing any data use the following function.

\index{mp\_radix\_size}
\begin{alltt}
int mp_radix_size (mp_int * a, int radix, int *size)
\end{alltt}
This stores in ``size'' the number of characters (including space for the NUL terminator) required.  Upon error this 
function returns an error code and ``size'' will be zero.  

\subsection{From ASCII}
\index{mp\_read\_radix}
\begin{alltt}
int mp_read_radix (mp_int * a, char *str, int radix);
\end{alltt}
This will read the base-``radix'' NUL terminated string from ``str'' into $a$.  It will stop reading when it reads a
character it does not recognize (which happens to include th NUL char... imagine that...).  A single leading $-$ sign
can be used to denote a negative number.

\section{Binary Conversions}

Converting an mp\_int to and from binary is another keen idea.

\index{mp\_unsigned\_bin\_size}
\begin{alltt}
int mp_unsigned_bin_size(mp_int *a);
\end{alltt}

This will return the number of bytes (octets) required to store the unsigned copy of the integer $a$.

\index{mp\_to\_unsigned\_bin}
\begin{alltt}
int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
\end{alltt}
This will store $a$ into the buffer $b$ in big--endian format.  Fortunately this is exactly what DER (or is it ASN?)
requires.  It does not store the sign of the integer.

\index{mp\_read\_unsigned\_bin}
\begin{alltt}
int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
\end{alltt}
This will read in an unsigned big--endian array of bytes (octets) from $b$ of length $c$ into $a$.  The resulting
integer $a$ will always be positive.

For those who acknowledge the existence of negative numbers (heretic!) there are ``signed'' versions of the
previous functions.

\begin{alltt}
int mp_signed_bin_size(mp_int *a);
int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
int mp_to_signed_bin(mp_int *a, unsigned char *b);
\end{alltt}
They operate essentially the same as the unsigned copies except they prefix the data with zero or non--zero
byte depending on the sign.  If the sign is zpos (e.g. not negative) the prefix is zero, otherwise the prefix
is non--zero.  

\chapter{Algebraic Functions}
\section{Extended Euclidean Algorithm}
\index{mp\_exteuclid}
\begin{alltt}
int mp_exteuclid(mp_int *a, mp_int *b, 
                 mp_int *U1, mp_int *U2, mp_int *U3);
\end{alltt}

This finds the triple U1/U2/U3 using the Extended Euclidean algorithm such that the following equation holds.

\begin{equation}
a \cdot U1 + b \cdot U2 = U3
\end{equation}

Any of the U1/U2/U3 paramters can be set to \textbf{NULL} if they are not desired.  

\section{Greatest Common Divisor}
\index{mp\_gcd}
\begin{alltt}
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}
This will compute the greatest common divisor of $a$ and $b$ and store it in $c$.

\section{Least Common Multiple}
\index{mp\_lcm}
\begin{alltt}
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}
This will compute the least common multiple of $a$ and $b$ and store it in $c$.

\section{Jacobi Symbol}
\index{mp\_jacobi}
\begin{alltt}
int mp_jacobi (mp_int * a, mp_int * p, int *c)
\end{alltt}
This will compute the Jacobi symbol for $a$ with respect to $p$.  If $p$ is prime this essentially computes the Legendre
symbol.  The result is stored in $c$ and can take on one of three values $\lbrace -1, 0, 1 \rbrace$.  If $p$ is prime
then the result will be $-1$ when $a$ is not a quadratic residue modulo $p$.  The result will be $0$ if $a$ divides $p$
and the result will be $1$ if $a$ is a quadratic residue modulo $p$.  

\section{Modular Inverse}
\index{mp\_invmod}
\begin{alltt}
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}
Computes the multiplicative inverse of $a$ modulo $b$ and stores the result in $c$ such that $ac \equiv 1 \mbox{ (mod }b\mbox{)}$.

\section{Single Digit Functions}

For those using small numbers (\textit{snicker snicker}) there are several ``helper'' functions

\index{mp\_add\_d} \index{mp\_sub\_d} \index{mp\_mul\_d} \index{mp\_div\_d} \index{mp\_mod\_d}
\begin{alltt}
int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
\end{alltt}

These work like the full mp\_int capable variants except the second parameter $b$ is a mp\_digit.  These
functions fairly handy if you have to work with relatively small numbers since you will not have to allocate
an entire mp\_int to store a number like $1$ or $2$.

\input{bn.ind}

\end{document}
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Changes to libtommath/bn_error.c.

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#include <tommath.h>
#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

static const struct {
     int code;
     char *msg;
} msgs[] = {
     { MP_OKAY, "Successful" },
     { MP_MEM,  "Out of heap" },
     { MP_VAL,  "Value out of range" }
};

/* return a char * string for a given code */
char *mp_error_to_string(int code)
{
   int x;

   /* scan the lookup table for the given message */
   for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
       if (msgs[x].code == code) {
          return msgs[x].msg;
................................................................................
   }

   /* generic reply for invalid code */
   return "Invalid error code";
}

#endif




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#include <tommath_private.h>
#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

static const struct {
     int code;
     const char *msg;
} msgs[] = {
     { MP_OKAY, "Successful" },
     { MP_MEM,  "Out of heap" },
     { MP_VAL,  "Value out of range" }
};

/* return a char * string for a given code */
const char *mp_error_to_string(int code)
{
   int x;

   /* scan the lookup table for the given message */
   for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
       if (msgs[x].code == code) {
          return msgs[x].msg;
................................................................................
   }

   /* generic reply for invalid code */
   return "Invalid error code";
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_fast_mp_invmod.c.

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#include <tommath.h>
#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes the modular inverse via binary extended euclidean algorithm, 
 * that is c = 1/a mod b 
 *
 * Based on slow invmod except this is optimized for the case where b is 
 * odd as per HAC Note 14.64 on pp. 610
................................................................................
 */
int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, B, D;
  int     res, neg;

  /* 2. [modified] b must be odd   */
  if (mp_iseven (b) == 1) {
    return MP_VAL;
  }

  /* init all our temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
     return res;
  }
................................................................................
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
    goto LBL_ERR;
  }
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == 1) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if B is odd then */
    if (mp_isodd (&B) == 1) {
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* B = B/2 */
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == 1) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if D is odd then */
    if (mp_isodd (&D) == 1) {
      /* D = (D-x)/2 */
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* D = D/2 */
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
................................................................................

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == 0) {
    goto top;
  }

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
................................................................................
  c->sign = neg;
  res = MP_OKAY;

LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes the modular inverse via binary extended euclidean algorithm, 
 * that is c = 1/a mod b 
 *
 * Based on slow invmod except this is optimized for the case where b is 
 * odd as per HAC Note 14.64 on pp. 610
................................................................................
 */
int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, B, D;
  int     res, neg;

  /* 2. [modified] b must be odd   */
  if (mp_iseven (b) == MP_YES) {
    return MP_VAL;
  }

  /* init all our temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
     return res;
  }
................................................................................
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
    goto LBL_ERR;
  }
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == MP_YES) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if B is odd then */
    if (mp_isodd (&B) == MP_YES) {
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* B = B/2 */
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == MP_YES) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if D is odd then */
    if (mp_isodd (&D) == MP_YES) {
      /* D = (D-x)/2 */
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* D = D/2 */
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
................................................................................

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == MP_NO) {
    goto top;
  }

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
................................................................................
  c->sign = neg;
  res = MP_OKAY;

LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_fast_mp_montgomery_reduce.c.

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#include <tommath.h>
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction
 *
 * This is an optimized implementation of montgomery_reduce
 * which uses the comba method to quickly calculate the columns of the
 * reduction.
................................................................................
  int     ix, res, olduse;
  mp_word W[MP_WARRAY];

  /* get old used count */
  olduse = x->used;

  /* grow a as required */
  if (x->alloc < n->used + 1) {
    if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* first we have to get the digits of the input into
   * an array of double precision words W[...]
   */
  {
    register mp_word *_W;
    register mp_digit *tmpx;

    /* alias for the W[] array */
    _W   = W;

    /* alias for the digits of  x*/
    tmpx = x->dp;

    /* copy the digits of a into W[0..a->used-1] */
    for (ix = 0; ix < x->used; ix++) {
      *_W++ = *tmpx++;
    }

    /* zero the high words of W[a->used..m->used*2] */
    for (; ix < n->used * 2 + 1; ix++) {
      *_W++ = 0;
    }
  }

  /* now we proceed to zero successive digits
   * from the least significant upwards
   */
................................................................................
  for (ix = 0; ix < n->used; ix++) {
    /* mu = ai * m' mod b
     *
     * We avoid a double precision multiplication (which isn't required)
     * by casting the value down to a mp_digit.  Note this requires
     * that W[ix-1] have  the carry cleared (see after the inner loop)
     */
    register mp_digit mu;
    mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);

    /* a = a + mu * m * b**i
     *
     * This is computed in place and on the fly.  The multiplication
     * by b**i is handled by offseting which columns the results
     * are added to.
................................................................................
     * column since the Montgomery reduction requires digits of the
     * result (so far) [see above] to work.  This is
     * handled by fixing up one carry after the inner loop.  The
     * carry fixups are done in order so after these loops the
     * first m->used words of W[] have the carries fixed
     */
    {
      register int iy;
      register mp_digit *tmpn;
      register mp_word *_W;

      /* alias for the digits of the modulus */
      tmpn = n->dp;

      /* Alias for the columns set by an offset of ix */
      _W = W + ix;

................................................................................
  }

  /* now we have to propagate the carries and
   * shift the words downward [all those least
   * significant digits we zeroed].
   */
  {
    register mp_digit *tmpx;
    register mp_word *_W, *_W1;

    /* nox fix rest of carries */

    /* alias for current word */
    _W1 = W + ix;

    /* alias for next word, where the carry goes */
    _W = W + ++ix;

    for (; ix <= n->used * 2 + 1; ix++) {
      *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
    }

    /* copy out, A = A/b**n
     *
     * The result is A/b**n but instead of converting from an
     * array of mp_word to mp_digit than calling mp_rshd
................................................................................

    /* alias for destination word */
    tmpx = x->dp;

    /* alias for shifted double precision result */
    _W = W + n->used;

    for (ix = 0; ix < n->used + 1; ix++) {
      *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
    }

    /* zero oldused digits, if the input a was larger than
     * m->used+1 we'll have to clear the digits
     */
    for (; ix < olduse; ix++) {
................................................................................
  /* if A >= m then A = A - m */
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction
 *
 * This is an optimized implementation of montgomery_reduce
 * which uses the comba method to quickly calculate the columns of the
 * reduction.
................................................................................
  int     ix, res, olduse;
  mp_word W[MP_WARRAY];

  /* get old used count */
  olduse = x->used;

  /* grow a as required */
  if (x->alloc < (n->used + 1)) {
    if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* first we have to get the digits of the input into
   * an array of double precision words W[...]
   */
  {
    mp_word *_W;
    mp_digit *tmpx;

    /* alias for the W[] array */
    _W   = W;

    /* alias for the digits of  x*/
    tmpx = x->dp;

    /* copy the digits of a into W[0..a->used-1] */
    for (ix = 0; ix < x->used; ix++) {
      *_W++ = *tmpx++;
    }

    /* zero the high words of W[a->used..m->used*2] */
    for (; ix < ((n->used * 2) + 1); ix++) {
      *_W++ = 0;
    }
  }

  /* now we proceed to zero successive digits
   * from the least significant upwards
   */
................................................................................
  for (ix = 0; ix < n->used; ix++) {
    /* mu = ai * m' mod b
     *
     * We avoid a double precision multiplication (which isn't required)
     * by casting the value down to a mp_digit.  Note this requires
     * that W[ix-1] have  the carry cleared (see after the inner loop)
     */
    mp_digit mu;
    mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);

    /* a = a + mu * m * b**i
     *
     * This is computed in place and on the fly.  The multiplication
     * by b**i is handled by offseting which columns the results
     * are added to.
................................................................................
     * column since the Montgomery reduction requires digits of the
     * result (so far) [see above] to work.  This is
     * handled by fixing up one carry after the inner loop.  The
     * carry fixups are done in order so after these loops the
     * first m->used words of W[] have the carries fixed
     */
    {
      int iy;
      mp_digit *tmpn;
      mp_word *_W;

      /* alias for the digits of the modulus */
      tmpn = n->dp;

      /* Alias for the columns set by an offset of ix */
      _W = W + ix;

................................................................................
  }

  /* now we have to propagate the carries and
   * shift the words downward [all those least
   * significant digits we zeroed].
   */
  {
    mp_digit *tmpx;
    mp_word *_W, *_W1;

    /* nox fix rest of carries */

    /* alias for current word */
    _W1 = W + ix;

    /* alias for next word, where the carry goes */
    _W = W + ++ix;

    for (; ix <= ((n->used * 2) + 1); ix++) {
      *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
    }

    /* copy out, A = A/b**n
     *
     * The result is A/b**n but instead of converting from an
     * array of mp_word to mp_digit than calling mp_rshd
................................................................................

    /* alias for destination word */
    tmpx = x->dp;

    /* alias for shifted double precision result */
    _W = W + n->used;

    for (ix = 0; ix < (n->used + 1); ix++) {
      *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
    }

    /* zero oldused digits, if the input a was larger than
     * m->used+1 we'll have to clear the digits
     */
    for (; ix < olduse; ix++) {
................................................................................
  /* if A >= m then A = A - m */
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_fast_s_mp_mul_digs.c.

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#include <tommath.h>
#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Fast (comba) multiplier
 *
 * This is the fast column-array [comba] multiplier.  It is 
 * designed to compute the columns of the product first 
 * then handle the carries afterwards.  This has the effect 
................................................................................
 * Based on Algorithm 14.12 on pp.595 of HAC.
 *
 */
int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
  int     olduse, res, pa, ix, iz;
  mp_digit W[MP_WARRAY];
  register mp_word  _W;

  /* grow the destination as required */
  if (c->alloc < digs) {
    if ((res = mp_grow (c, digs)) != MP_OKAY) {
      return res;
    }
  }
................................................................................
      }

      /* store term */
      W[ix] = ((mp_digit)_W) & MP_MASK;

      /* make next carry */
      _W = _W >> ((mp_word)DIGIT_BIT);
 }

  /* setup dest */
  olduse  = c->used;
  c->used = pa;

  {
    register mp_digit *tmpc;
    tmpc = c->dp;
    for (ix = 0; ix < pa+1; ix++) {
      /* now extract the previous digit [below the carry] */
      *tmpc++ = W[ix];
    }

    /* clear unused digits [that existed in the old copy of c] */
    for (; ix < olduse; ix++) {
      *tmpc++ = 0;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Fast (comba) multiplier
 *
 * This is the fast column-array [comba] multiplier.  It is 
 * designed to compute the columns of the product first 
 * then handle the carries afterwards.  This has the effect 
................................................................................
 * Based on Algorithm 14.12 on pp.595 of HAC.
 *
 */
int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
  int     olduse, res, pa, ix, iz;
  mp_digit W[MP_WARRAY];
  mp_word  _W;

  /* grow the destination as required */
  if (c->alloc < digs) {
    if ((res = mp_grow (c, digs)) != MP_OKAY) {
      return res;
    }
  }
................................................................................
      }

      /* store term */
      W[ix] = ((mp_digit)_W) & MP_MASK;

      /* make next carry */
      _W = _W >> ((mp_word)DIGIT_BIT);
  }

  /* setup dest */
  olduse  = c->used;
  c->used = pa;

  {
    mp_digit *tmpc;
    tmpc = c->dp;
    for (ix = 0; ix < (pa + 1); ix++) {
      /* now extract the previous digit [below the carry] */
      *tmpc++ = W[ix];
    }

    /* clear unused digits [that existed in the old copy of c] */
    for (; ix < olduse; ix++) {
      *tmpc++ = 0;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* this is a modified version of fast_s_mul_digs that only produces
 * output digits *above* digs.  See the comments for fast_s_mul_digs
 * to see how it works.
 *
 * This is used in the Barrett reduction since for one of the multiplications
................................................................................
  }
  
  /* setup dest */
  olduse  = c->used;
  c->used = pa;

  {
    register mp_digit *tmpc;

    tmpc = c->dp + digs;
    for (ix = digs; ix < pa; ix++) {
      /* now extract the previous digit [below the carry] */
      *tmpc++ = W[ix];
    }

................................................................................
      *tmpc++ = 0;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* this is a modified version of fast_s_mul_digs that only produces
 * output digits *above* digs.  See the comments for fast_s_mul_digs
 * to see how it works.
 *
 * This is used in the Barrett reduction since for one of the multiplications
................................................................................
  }
  
  /* setup dest */
  olduse  = c->used;
  c->used = pa;

  {
    mp_digit *tmpc;

    tmpc = c->dp + digs;
    for (ix = digs; ix < pa; ix++) {
      /* now extract the previous digit [below the carry] */
      *tmpc++ = W[ix];
    }

................................................................................
      *tmpc++ = 0;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_fast_s_mp_sqr.c.

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#include <tommath.h>
#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* the jist of squaring...
 * you do like mult except the offset of the tmpx [one that 
 * starts closer to zero] can't equal the offset of tmpy.  
 * So basically you set up iy like before then you min it with
 * (ty-tx) so that it never happens.  You double all those 
................................................................................
       */
      iy = MIN(a->used-tx, ty+1);

      /* now for squaring tx can never equal ty 
       * we halve the distance since they approach at a rate of 2x
       * and we have to round because odd cases need to be executed
       */
      iy = MIN(iy, (ty-tx+1)>>1);

      /* execute loop */
      for (iz = 0; iz < iy; iz++) {
         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
      }

      /* double the inner product and add carry */
................................................................................
      *tmpb++ = 0;
    }
  }
  mp_clamp (b);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* the jist of squaring...
 * you do like mult except the offset of the tmpx [one that 
 * starts closer to zero] can't equal the offset of tmpy.  
 * So basically you set up iy like before then you min it with
 * (ty-tx) so that it never happens.  You double all those 
................................................................................
       */
      iy = MIN(a->used-tx, ty+1);

      /* now for squaring tx can never equal ty 
       * we halve the distance since they approach at a rate of 2x
       * and we have to round because odd cases need to be executed
       */
      iy = MIN(iy, ((ty-tx)+1)>>1);

      /* execute loop */
      for (iz = 0; iz < iy; iz++) {
         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
      }

      /* double the inner product and add carry */
................................................................................
      *tmpb++ = 0;
    }
  }
  mp_clamp (b);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_2expt.c.

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#include <tommath.h>
#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes a = 2**b 
 *
 * Simple algorithm which zeroes the int, grows it then just sets one bit
 * as required.
 */
................................................................................
{
  int     res;

  /* zero a as per default */
  mp_zero (a);

  /* grow a to accomodate the single bit */
  if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
    return res;
  }

  /* set the used count of where the bit will go */
  a->used = b / DIGIT_BIT + 1;

  /* put the single bit in its place */
  a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes a = 2**b 
 *
 * Simple algorithm which zeroes the int, grows it then just sets one bit
 * as required.
 */
................................................................................
{
  int     res;

  /* zero a as per default */
  mp_zero (a);

  /* grow a to accomodate the single bit */
  if ((res = mp_grow (a, (b / DIGIT_BIT) + 1)) != MP_OKAY) {
    return res;
  }

  /* set the used count of where the bit will go */
  a->used = (b / DIGIT_BIT) + 1;

  /* put the single bit in its place */
  a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_abs.c.

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#include <tommath.h>
#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* b = |a| 
 *
 * Simple function copies the input and fixes the sign to positive
 */
int
................................................................................

  /* force the sign of b to positive */
  b->sign = MP_ZPOS;

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* b = |a| 
 *
 * Simple function copies the input and fixes the sign to positive
 */
int
................................................................................

  /* force the sign of b to positive */
  b->sign = MP_ZPOS;

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_add.c.

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#include <tommath.h>
#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
{
  int     sa, sb, res;

................................................................................
      res = s_mp_sub (a, b, c);
    }
  }
  return res;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
{
  int     sa, sb, res;

................................................................................
      res = s_mp_sub (a, b, c);
    }
  }
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_add_d.c.

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#include <tommath.h>
#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tom[email protected], http://libtom.org
 */

/* single digit addition */
int
mp_add_d (mp_int * a, mp_digit b, mp_int * c)
{
  int     res, ix, oldused;
  mp_digit *tmpa, *tmpc, mu;

  /* grow c as required */
  if (c->alloc < a->used + 1) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }

  /* if a is negative and |a| >= b, call c = |a| - b */
  if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
     /* temporarily fix sign of a */
     a->sign = MP_ZPOS;

     /* c = |a| - b */
     res = mp_sub_d(a, b, c);

     /* fix sign  */
................................................................................

  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision: 0.41 $ */
/* $Date: 2007-04-18 09:58:18 +0000 $ */
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#include <tommath_private.h>
#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* single digit addition */
int
mp_add_d (mp_int * a, mp_digit b, mp_int * c)
{
  int     res, ix, oldused;
  mp_digit *tmpa, *tmpc, mu;

  /* grow c as required */
  if (c->alloc < (a->used + 1)) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }

  /* if a is negative and |a| >= b, call c = |a| - b */
  if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) {
     /* temporarily fix sign of a */
     a->sign = MP_ZPOS;

     /* c = |a| - b */
     res = mp_sub_d(a, b, c);

     /* fix sign  */
................................................................................

  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_addmod.c.

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#include <tommath.h>
#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* d = a + b (mod c) */
int
mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* d = a + b (mod c) */
int
mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* AND two ints together */
int
mp_and (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
................................................................................

  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* AND two ints together */
int
mp_and (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
................................................................................

  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* trim unused digits 
 *
 * This is used to ensure that leading zero digits are
 * trimed and the leading "used" digit will be non-zero
 * Typically very fast.  Also fixes the sign if there
................................................................................
 */
void
mp_clamp (mp_int * a)
{
  /* decrease used while the most significant digit is
   * zero.
   */
  while (a->used > 0 && a->dp[a->used - 1] == 0) {
    --(a->used);
  }

  /* reset the sign flag if used == 0 */
  if (a->used == 0) {
    a->sign = MP_ZPOS;
  }
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* trim unused digits 
 *
 * This is used to ensure that leading zero digits are
 * trimed and the leading "used" digit will be non-zero
 * Typically very fast.  Also fixes the sign if there
................................................................................
 */
void
mp_clamp (mp_int * a)
{
  /* decrease used while the most significant digit is
   * zero.
   */
  while ((a->used > 0) && (a->dp[a->used - 1] == 0)) {
    --(a->used);
  }

  /* reset the sign flag if used == 0 */
  if (a->used == 0) {
    a->sign = MP_ZPOS;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* clear one (frees)  */
void
mp_clear (mp_int * a)
{
  int i;
................................................................................
    /* reset members to make debugging easier */
    a->dp    = NULL;
    a->alloc = a->used = 0;
    a->sign  = MP_ZPOS;
  }
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* clear one (frees)  */
void
mp_clear (mp_int * a)
{
  int i;
................................................................................
    /* reset members to make debugging easier */
    a->dp    = NULL;
    a->alloc = a->used = 0;
    a->sign  = MP_ZPOS;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */
#include <stdarg.h>

void mp_clear_multi(mp_int *mp, ...) 
{
    mp_int* next_mp = mp;
    va_list args;
................................................................................
    while (next_mp != NULL) {
        mp_clear(next_mp);
        next_mp = va_arg(args, mp_int*);
    }
    va_end(args);
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */
#include <stdarg.h>

void mp_clear_multi(mp_int *mp, ...) 
{
    mp_int* next_mp = mp;
    va_list args;
................................................................................
    while (next_mp != NULL) {
        mp_clear(next_mp);
        next_mp = va_arg(args, mp_int*);
    }
    va_end(args);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* compare two ints (signed)*/
int
mp_cmp (const mp_int * a, const mp_int * b)
{
  /* compare based on sign */
................................................................................
     /* if negative compare opposite direction */
     return mp_cmp_mag(b, a);
  } else {
     return mp_cmp_mag(a, b);
  }
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* compare two ints (signed)*/
int
mp_cmp (const mp_int * a, const mp_int * b)
{
  /* compare based on sign */
................................................................................
     /* if negative compare opposite direction */
     return mp_cmp_mag(b, a);
  } else {
     return mp_cmp_mag(a, b);
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* compare a digit */
int mp_cmp_d(const mp_int * a, mp_digit b)
{
  /* compare based on sign */
  if (a->sign == MP_NEG) {
................................................................................
  } else if (a->dp[0] < b) {
    return MP_LT;
  } else {
    return MP_EQ;
  }
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* compare a digit */
int mp_cmp_d(const mp_int * a, mp_digit b)
{
  /* compare based on sign */
  if (a->sign == MP_NEG) {
................................................................................
  } else if (a->dp[0] < b) {
    return MP_LT;
  } else {
    return MP_EQ;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (const mp_int * a, const mp_int * b)
{
  int     n;
  mp_digit *tmpa, *tmpb;
................................................................................
    if (*tmpa < *tmpb) {
      return MP_LT;
    }
  }
  return MP_EQ;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (const mp_int * a, const mp_int * b)
{
  int     n;
  mp_digit *tmpa, *tmpb;
................................................................................
    if (*tmpa < *tmpb) {
      return MP_LT;
    }
  }
  return MP_EQ;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

static const int lnz[16] = { 
   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};

/* Counts the number of lsbs which are zero before the first zero bit */
int mp_cnt_lsb(const mp_int *a)
{
   int x;
   mp_digit q, qq;

   /* easy out */
   if (mp_iszero(a) == 1) {
      return 0;
   }

   /* scan lower digits until non-zero */
   for (x = 0; x < a->used && a->dp[x] == 0; x++);
   q = a->dp[x];
   x *= DIGIT_BIT;

   /* now scan this digit until a 1 is found */
   if ((q & 1) == 0) {
      do {
         qq  = q & 15;
................................................................................
         q >>= 4;
      } while (qq == 0);
   }
   return x;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

static const int lnz[16] = { 
   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};

/* Counts the number of lsbs which are zero before the first zero bit */
int mp_cnt_lsb(const mp_int *a)
{
   int x;
   mp_digit q, qq;

   /* easy out */
   if (mp_iszero(a) == MP_YES) {
      return 0;
   }

   /* scan lower digits until non-zero */
   for (x = 0; (x < a->used) && (a->dp[x] == 0); x++) {}
   q = a->dp[x];
   x *= DIGIT_BIT;

   /* now scan this digit until a 1 is found */
   if ((q & 1) == 0) {
      do {
         qq  = q & 15;
................................................................................
         q >>= 4;
      } while (qq == 0);
   }
   return x;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_copy.c.

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#include <tommath.h>
#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* copy, b = a */
int
mp_copy (const mp_int * a, mp_int * b)
{
  int     res, n;
................................................................................
     if ((res = mp_grow (b, a->used)) != MP_OKAY) {
        return res;
     }
  }

  /* zero b and copy the parameters over */
  {
    register mp_digit *tmpa, *tmpb;

    /* pointer aliases */

    /* source */
    tmpa = a->dp;

    /* destination */
................................................................................

  /* copy used count and sign */
  b->used = a->used;
  b->sign = a->sign;
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* copy, b = a */
int
mp_copy (const mp_int * a, mp_int * b)
{
  int     res, n;
................................................................................
     if ((res = mp_grow (b, a->used)) != MP_OKAY) {
        return res;
     }
  }

  /* zero b and copy the parameters over */
  {
    mp_digit *tmpa, *tmpb;

    /* pointer aliases */

    /* source */
    tmpa = a->dp;

    /* destination */
................................................................................

  /* copy used count and sign */
  b->used = a->used;
  b->sign = a->sign;
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_count_bits.c.

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#include <tommath.h>
#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* returns the number of bits in an int */
int
mp_count_bits (const mp_int * a)
{
  int     r;
................................................................................
  while (q > ((mp_digit) 0)) {
    ++r;
    q >>= ((mp_digit) 1);
  }
  return r;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* returns the number of bits in an int */
int
mp_count_bits (const mp_int * a)
{
  int     r;
................................................................................
  while (q > ((mp_digit) 0)) {
    ++r;
    q >>= ((mp_digit) 1);
  }
  return r;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

#ifdef BN_MP_DIV_SMALL

/* slower bit-bang division... also smaller */
int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
   mp_int ta, tb, tq, q;
   int    res, n, n2;

  /* is divisor zero ? */
  if (mp_iszero (b) == 1) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
................................................................................
      res = MP_OKAY;
    }
    if (c != NULL) {
      mp_zero (c);
    }
    return res;
  }
	
  /* init our temps */
  if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
     return res;
  }


  mp_set(&tq, 1);
  n = mp_count_bits(a) - mp_count_bits(b);
  if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
      ((res = mp_abs(b, &tb)) != MP_OKAY) || 
      ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
      ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
      goto LBL_ERR;
  }

  while (n-- >= 0) {
     if (mp_cmp(&tb, &ta) != MP_GT) {
................................................................................
         ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
           goto LBL_ERR;
     }
  }

  /* now q == quotient and ta == remainder */
  n  = a->sign;
  n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
  if (c != NULL) {
     mp_exch(c, &q);
     c->sign  = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
  }
  if (d != NULL) {
     mp_exch(d, &ta);
     d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
................................................................................
LBL_ERR:
   mp_clear_multi(&ta, &tb, &tq, &q, NULL);
   return res;
}

#else

/* integer signed division. 
 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
 * HAC pp.598 Algorithm 14.20
 *
 * Note that the description in HAC is horribly 
 * incomplete.  For example, it doesn't consider 
 * the case where digits are removed from 'x' in 
 * the inner loop.  It also doesn't consider the 
 * case that y has fewer than three digits, etc..
 *
 * The overall algorithm is as described as 
 * 14.20 from HAC but fixed to treat these cases.
*/
int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  mp_int  q, x, y, t1, t2;
  int     res, n, t, i, norm, neg;

  /* is divisor zero ? */
  if (mp_iszero (b) == 1) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
................................................................................

  /* step 3. for i from n down to (t + 1) */
  for (i = n; i >= (t + 1); i--) {
    if (i > x.used) {
      continue;
    }

    /* step 3.1 if xi == yt then set q{i-t-1} to b-1, 
     * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
    if (x.dp[i] == y.dp[t]) {
      q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
    } else {
      mp_word tmp;
      tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
      tmp |= ((mp_word) x.dp[i - 1]);
      tmp /= ((mp_word) y.dp[t]);
      if (tmp > (mp_word) MP_MASK)
        tmp = MP_MASK;

      q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
    }

    /* while (q{i-t-1} * (yt * b + y{t-1})) > 
             xi * b**2 + xi-1 * b + xi-2 
     
       do q{i-t-1} -= 1; 
    */
    q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;

    do {
      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;


      /* find left hand */
      mp_zero (&t1);
      t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
      t1.dp[1] = y.dp[t];
      t1.used = 2;
      if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
        goto LBL_Y;
      }

      /* find right hand */
      t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
      t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
      t2.dp[2] = x.dp[i];
      t2.used = 3;
    } while (mp_cmp_mag(&t1, &t2) == MP_GT);

    /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
    if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
      goto LBL_Y;
    }

    if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
      goto LBL_Y;
    }

    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
      goto LBL_Y;
    }

    /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
    if (x.sign == MP_NEG) {
      if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
        goto LBL_Y;
      }
      if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
        goto LBL_Y;
      }
      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
        goto LBL_Y;
      }

      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
    }
  }

  /* now q is the quotient and x is the remainder 
   * [which we have to normalize] 
   */
  
  /* get sign before writing to c */
  x.sign = x.used == 0 ? MP_ZPOS : a->sign;

  if (c != NULL) {
    mp_clamp (&q);
    mp_exch (&q, c);
    c->sign = neg;
  }

  if (d != NULL) {
    mp_div_2d (&x, norm, &x, NULL);


    mp_exch (&x, d);
  }

  res = MP_OKAY;

LBL_Y:mp_clear (&y);
LBL_X:mp_clear (&x);
................................................................................
LBL_Q:mp_clear (&q);
  return res;
}

#endif

#endif




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#include <tommath_private.h>
#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

#ifdef BN_MP_DIV_SMALL

/* slower bit-bang division... also smaller */
int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
   mp_int ta, tb, tq, q;
   int    res, n, n2;

  /* is divisor zero ? */
  if (mp_iszero (b) == MP_YES) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
................................................................................
      res = MP_OKAY;
    }
    if (c != NULL) {
      mp_zero (c);
    }
    return res;
  }

  /* init our temps */
  if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) {
     return res;
  }


  mp_set(&tq, 1);
  n = mp_count_bits(a) - mp_count_bits(b);
  if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
      ((res = mp_abs(b, &tb)) != MP_OKAY) ||
      ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
      ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
      goto LBL_ERR;
  }

  while (n-- >= 0) {
     if (mp_cmp(&tb, &ta) != MP_GT) {
................................................................................
         ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
           goto LBL_ERR;
     }
  }

  /* now q == quotient and ta == remainder */
  n  = a->sign;
  n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
  if (c != NULL) {
     mp_exch(c, &q);
     c->sign  = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
  }
  if (d != NULL) {
     mp_exch(d, &ta);
     d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
................................................................................
LBL_ERR:
   mp_clear_multi(&ta, &tb, &tq, &q, NULL);
   return res;
}

#else

/* integer signed division.
 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
 * HAC pp.598 Algorithm 14.20
 *
 * Note that the description in HAC is horribly
 * incomplete.  For example, it doesn't consider
 * the case where digits are removed from 'x' in
 * the inner loop.  It also doesn't consider the
 * case that y has fewer than three digits, etc..
 *
 * The overall algorithm is as described as
 * 14.20 from HAC but fixed to treat these cases.
*/
int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  mp_int  q, x, y, t1, t2;
  int     res, n, t, i, norm, neg;

  /* is divisor zero ? */
  if (mp_iszero (b) == MP_YES) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
................................................................................

  /* step 3. for i from n down to (t + 1) */
  for (i = n; i >= (t + 1); i--) {
    if (i > x.used) {
      continue;
    }

    /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
     * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
    if (x.dp[i] == y.dp[t]) {
      q.dp[(i - t) - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
    } else {
      mp_word tmp;
      tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
      tmp |= ((mp_word) x.dp[i - 1]);
      tmp /= ((mp_word) y.dp[t]);
      if (tmp > (mp_word) MP_MASK) {
        tmp = MP_MASK;
      }
      q.dp[(i - t) - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
    }

    /* while (q{i-t-1} * (yt * b + y{t-1})) >
             xi * b**2 + xi-1 * b + xi-2

       do q{i-t-1} -= 1;
    */

    q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1) & MP_MASK;
    do {

      q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1) & MP_MASK;

      /* find left hand */
      mp_zero (&t1);
      t1.dp[0] = ((t - 1) < 0) ? 0 : y.dp[t - 1];
      t1.dp[1] = y.dp[t];
      t1.used = 2;
      if ((res = mp_mul_d (&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) {
        goto LBL_Y;
      }

      /* find right hand */
      t2.dp[0] = ((i - 2) < 0) ? 0 : x.dp[i - 2];
      t2.dp[1] = ((i - 1) < 0) ? 0 : x.dp[i - 1];
      t2.dp[2] = x.dp[i];
      t2.used = 3;
    } while (mp_cmp_mag(&t1, &t2) == MP_GT);

    /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
    if ((res = mp_mul_d (&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) {
      goto LBL_Y;
    }

    if ((res = mp_lshd (&t1, (i - t) - 1)) != MP_OKAY) {
      goto LBL_Y;
    }

    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
      goto LBL_Y;
    }

    /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
    if (x.sign == MP_NEG) {
      if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
        goto LBL_Y;
      }
      if ((res = mp_lshd (&t1, (i - t) - 1)) != MP_OKAY) {
        goto LBL_Y;
      }
      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
        goto LBL_Y;
      }

      q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1UL) & MP_MASK;
    }
  }

  /* now q is the quotient and x is the remainder
   * [which we have to normalize]
   */

  /* get sign before writing to c */
  x.sign = (x.used == 0) ? MP_ZPOS : a->sign;

  if (c != NULL) {
    mp_clamp (&q);
    mp_exch (&q, c);
    c->sign = neg;
  }

  if (d != NULL) {
    if ((res = mp_div_2d (&x, norm, &x, NULL)) != MP_OKAY) {
      goto LBL_Y;
    }
    mp_exch (&x, d);
  }

  res = MP_OKAY;

LBL_Y:mp_clear (&y);
LBL_X:mp_clear (&x);
................................................................................
LBL_Q:mp_clear (&q);
  return res;
}

#endif

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_div_2.c.

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#include <tommath.h>
#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
{
  int     x, res, oldused;

................................................................................
      return res;
    }
  }

  oldused = b->used;
  b->used = a->used;
  {
    register mp_digit r, rr, *tmpa, *tmpb;

    /* source alias */
    tmpa = a->dp + b->used - 1;

    /* dest alias */
    tmpb = b->dp + b->used - 1;

................................................................................
    }
  }
  b->sign = a->sign;
  mp_clamp (b);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
{
  int     x, res, oldused;

................................................................................
      return res;
    }
  }

  oldused = b->used;
  b->used = a->used;
  {
    mp_digit r, rr, *tmpa, *tmpb;

    /* source alias */
    tmpa = a->dp + b->used - 1;

    /* dest alias */
    tmpb = b->dp + b->used - 1;

................................................................................
    }
  }
  b->sign = a->sign;
  mp_clamp (b);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_div_2d.c.

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#include <tommath.h>
#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (const mp_int * a, int b, mp_int * c, mp_int * d)
{
  mp_digit D, r, rr;
  int     x, res;
................................................................................
  if (b >= (int)DIGIT_BIT) {
    mp_rshd (c, b / DIGIT_BIT);
  }

  /* shift any bit count < DIGIT_BIT */
  D = (mp_digit) (b % DIGIT_BIT);
  if (D != 0) {
    register mp_digit *tmpc, mask, shift;

    /* mask */
    mask = (((mp_digit)1) << D) - 1;

    /* shift for lsb */
    shift = DIGIT_BIT - D;

................................................................................
  if (d != NULL) {
    mp_exch (&t, d);
  }
  mp_clear (&t);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (const mp_int * a, int b, mp_int * c, mp_int * d)
{
  mp_digit D, r, rr;
  int     x, res;
................................................................................
  if (b >= (int)DIGIT_BIT) {
    mp_rshd (c, b / DIGIT_BIT);
  }

  /* shift any bit count < DIGIT_BIT */
  D = (mp_digit) (b % DIGIT_BIT);
  if (D != 0) {
    mp_digit *tmpc, mask, shift;

    /* mask */
    mask = (((mp_digit)1) << D) - 1;

    /* shift for lsb */
    shift = DIGIT_BIT - D;

................................................................................
  if (d != NULL) {
    mp_exch (&t, d);
  }
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_div_3.c.

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#include <tommath.h>
#ifdef BN_MP_DIV_3_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* divide by three (based on routine from MPI and the GMP manual) */
int
mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
{
  mp_int   q;
................................................................................
  }
  mp_clear(&q);
  
  return res;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_DIV_3_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* divide by three (based on routine from MPI and the GMP manual) */
int
mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
{
  mp_int   q;
................................................................................
  }
  mp_clear(&q);
  
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_div_d.c.

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#include <tommath.h>
#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

static int s_is_power_of_two(mp_digit b, int *p)
{
   int x;

   /* quick out - if (b & (b-1)) isn't zero, b isn't a power of two */
   if ((b==0) || (b & (b-1))) {
       return 0;
   }
   for (x = 1; x < DIGIT_BIT; x++) {
      if (b == (((mp_digit)1)<<x)) {
         *p = x;
         return 1;
      }
................................................................................

  /* cannot divide by zero */
  if (b == 0) {
     return MP_VAL;
  }

  /* quick outs */
  if (b == 1 || mp_iszero(a) == 1) {
     if (d != NULL) {
        *d = 0;
     }
     if (c != NULL) {
        return mp_copy(a, c);
     }
     return MP_OKAY;
................................................................................
  }
  mp_clear(&q);
  
  return res;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

static int s_is_power_of_two(mp_digit b, int *p)
{
   int x;

   /* quick out - if (b & (b-1)) isn't zero, b isn't a power of two */
   if ((b == 0) || ((b & (b-1)) != 0)) {
       return 0;
   }
   for (x = 1; x < DIGIT_BIT; x++) {
      if (b == (((mp_digit)1)<<x)) {
         *p = x;
         return 1;
      }
................................................................................

  /* cannot divide by zero */
  if (b == 0) {
     return MP_VAL;
  }

  /* quick outs */
  if ((b == 1) || (mp_iszero(a) == MP_YES)) {
     if (d != NULL) {
        *d = 0;
     }
     if (c != NULL) {
        return mp_copy(a, c);
     }
     return MP_OKAY;
................................................................................
  }
  mp_clear(&q);
  
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_dr_is_modulus.c.

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#include <tommath.h>
#ifdef BN_MP_DR_IS_MODULUS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
{
   int ix;

................................................................................
          return 0;
       }
   }
   return 1;
}

#endif




|













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#include <tommath_private.h>
#ifdef BN_MP_DR_IS_MODULUS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
{
   int ix;

................................................................................
          return 0;
       }
   }
   return 1;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_dr_reduce.c.

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#include <tommath.h>
#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
 *
 * Based on algorithm from the paper
 *
 * "Generating Efficient Primes for Discrete Log Cryptosystems"
................................................................................
  mp_word  r;
  mp_digit mu, *tmpx1, *tmpx2;

  /* m = digits in modulus */
  m = n->used;

  /* ensure that "x" has at least 2m digits */
  if (x->alloc < m + m) {
    if ((err = mp_grow (x, m + m)) != MP_OKAY) {
      return err;
    }
  }

/* top of loop, this is where the code resumes if
 * another reduction pass is required.
................................................................................
  tmpx2 = x->dp + m;

  /* set carry to zero */
  mu = 0;

  /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
  for (i = 0; i < m; i++) {
      r         = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
      *tmpx1++  = (mp_digit)(r & MP_MASK);
      mu        = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
  }

  /* set final carry */
  *tmpx1++ = mu;

................................................................................
  /* clamp, sub and return */
  mp_clamp (x);

  /* if x >= n then subtract and reduce again
   * Each successive "recursion" makes the input smaller and smaller.
   */
  if (mp_cmp_mag (x, n) != MP_LT) {
    s_mp_sub(x, n, x);


    goto top;
  }
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
 *
 * Based on algorithm from the paper
 *
 * "Generating Efficient Primes for Discrete Log Cryptosystems"
................................................................................
  mp_word  r;
  mp_digit mu, *tmpx1, *tmpx2;

  /* m = digits in modulus */
  m = n->used;

  /* ensure that "x" has at least 2m digits */
  if (x->alloc < (m + m)) {
    if ((err = mp_grow (x, m + m)) != MP_OKAY) {
      return err;
    }
  }

/* top of loop, this is where the code resumes if
 * another reduction pass is required.
................................................................................
  tmpx2 = x->dp + m;

  /* set carry to zero */
  mu = 0;

  /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
  for (i = 0; i < m; i++) {
      r         = (((mp_word)*tmpx2++) * (mp_word)k) + *tmpx1 + mu;
      *tmpx1++  = (mp_digit)(r & MP_MASK);
      mu        = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
  }

  /* set final carry */
  *tmpx1++ = mu;

................................................................................
  /* clamp, sub and return */
  mp_clamp (x);

  /* if x >= n then subtract and reduce again
   * Each successive "recursion" makes the input smaller and smaller.
   */
  if (mp_cmp_mag (x, n) != MP_LT) {
    if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
      return err;
    }
    goto top;
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_dr_setup.c.

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#include <tommath.h>
#ifdef BN_MP_DR_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
{
   /* the casts are required if DIGIT_BIT is one less than
    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
    */
   *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - 
        ((mp_word)a->dp[0]));
}

#endif




|













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#include <tommath_private.h>
#ifdef BN_MP_DR_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
{
   /* the casts are required if DIGIT_BIT is one less than
    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
    */
   *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - 
        ((mp_word)a->dp[0]));
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_exch.c.

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#include <tommath.h>
#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* swap the elements of two integers, for cases where you can't simply swap the 
 * mp_int pointers around
 */
void
mp_exch (mp_int * a, mp_int * b)
................................................................................
  mp_int  t;

  t  = *a;
  *a = *b;
  *b = t;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* swap the elements of two integers, for cases where you can't simply swap the 
 * mp_int pointers around
 */
void
mp_exch (mp_int * a, mp_int * b)
................................................................................
  mp_int  t;

  t  = *a;
  *a = *b;
  *b = t;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Added libtommath/bn_mp_export.c.
















































































































































































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#include <tommath_private.h>
#ifdef BN_MP_EXPORT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* based on gmp's mpz_export.
 * see http://gmplib.org/manual/Integer-Import-and-Export.html
 */
int mp_export(void* rop, size_t* countp, int order, size_t size, 
                                int endian, size_t nails, mp_int* op) {
	int result;
	size_t odd_nails, nail_bytes, i, j, bits, count;
	unsigned char odd_nail_mask;

	mp_int t;

	if ((result = mp_init_copy(&t, op)) != MP_OKAY) {
		return result;
	}

	if (endian == 0) {
		union {
			unsigned int i;
			char c[4];
		} lint;
		lint.i = 0x01020304;

		endian = (lint.c[0] == 4) ? -1 : 1;
	}

	odd_nails = (nails % 8);
	odd_nail_mask = 0xff;
	for (i = 0; i < odd_nails; ++i) {
		odd_nail_mask ^= (1 << (7 - i));
	}
	nail_bytes = nails / 8;

	bits = mp_count_bits(&t);
	count = (bits / ((size * 8) - nails)) + (((bits % ((size * 8) - nails)) != 0) ? 1 : 0);

	for (i = 0; i < count; ++i) {
		for (j = 0; j < size; ++j) {
			unsigned char* byte = (
				(unsigned char*)rop + 
				(((order == -1) ? i : ((count - 1) - i)) * size) +
				((endian == -1) ? j : ((size - 1) - j))
			);

			if (j >= (size - nail_bytes)) {
				*byte = 0;
				continue;
			}

			*byte = (unsigned char)((j == ((size - nail_bytes) - 1)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFF));

			if ((result = mp_div_2d(&t, ((j == ((size - nail_bytes) - 1)) ? (8 - odd_nails) : 8), &t, NULL)) != MP_OKAY) {
				mp_clear(&t);
				return result;
			}
		}
	}

	mp_clear(&t);

	if (countp != NULL) {
		*countp = count;
	}

	return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* calculate c = a**b  using a square-multiply algorithm */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
{
  int     res, x;
  mp_int  g;

  if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
    return res;
  }




  /* set initial result */
  mp_set (c, 1);

  for (x = 0; x < (int) DIGIT_BIT; x++) {
    /* square */
    if ((res = mp_sqr (c, c)) != MP_OKAY) {
      mp_clear (&g);
      return res;
    }

    /* if the bit is set multiply */
    if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
      if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
         mp_clear (&g);
         return res;
      }
    }

    /* shift to next bit */
    b <<= 1;
  }

  mp_clear (&g);
  return MP_OKAY;
}
#endif
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#include <tommath_private.h>
#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* wrapper function for mp_expt_d_ex() */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
{
  return mp_expt_d_ex(a, b, c, 0);

}



#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

























Added libtommath/bn_mp_expt_d_ex.c.






































































































































































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#include <tommath_private.h>
#ifdef BN_MP_EXPT_D_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* calculate c = a**b  using a square-multiply algorithm */
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
{
  int     res;
  unsigned int x;

  mp_int  g;

  if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
    return res;
  }

  /* set initial result */
  mp_set (c, 1);

  if (fast != 0) {
    while (b > 0) {
      /* if the bit is set multiply */
      if ((b & 1) != 0) {
        if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
          mp_clear (&g);
          return res;
        }
      }

      /* square */
      if (b > 1) {
        if ((res = mp_sqr (&g, &g)) != MP_OKAY) {
          mp_clear (&g);
          return res;
        }
      }

      /* shift to next bit */
      b >>= 1;
    }
  }
  else {
    for (x = 0; x < DIGIT_BIT; x++) {
      /* square */
      if ((res = mp_sqr (c, c)) != MP_OKAY) {
        mp_clear (&g);
        return res;
      }

      /* if the bit is set multiply */
      if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
        if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
           mp_clear (&g);
           return res;
        }
      }

      /* shift to next bit */
      b <<= 1;
    }
  } /* if ... else */

  mp_clear (&g);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_exptmod.c.

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#include <tommath.h>
#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */


/* this is a shell function that calls either the normal or Montgomery
 * exptmod functions.  Originally the call to the montgomery code was
 * embedded in the normal function but that wasted alot of stack space
 * for nothing (since 99% of the time the Montgomery code would be called)
................................................................................
  if (dr == 0) {
     dr = mp_reduce_is_2k(P) << 1;
  }
#endif
    
  /* if the modulus is odd or dr != 0 use the montgomery method */
#ifdef BN_MP_EXPTMOD_FAST_C
  if (mp_isodd (P) == 1 || dr !=  0) {
    return mp_exptmod_fast (G, X, P, Y, dr);
  } else {
#endif
#ifdef BN_S_MP_EXPTMOD_C
    /* otherwise use the generic Barrett reduction technique */
    return s_mp_exptmod (G, X, P, Y, 0);
#else
................................................................................
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
  }
#endif
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */


/* this is a shell function that calls either the normal or Montgomery
 * exptmod functions.  Originally the call to the montgomery code was
 * embedded in the normal function but that wasted alot of stack space
 * for nothing (since 99% of the time the Montgomery code would be called)
................................................................................
  if (dr == 0) {
     dr = mp_reduce_is_2k(P) << 1;
  }
#endif
    
  /* if the modulus is odd or dr != 0 use the montgomery method */
#ifdef BN_MP_EXPTMOD_FAST_C
  if ((mp_isodd (P) == MP_YES) || (dr !=  0)) {
    return mp_exptmod_fast (G, X, P, Y, dr);
  } else {
#endif
#ifdef BN_S_MP_EXPTMOD_C
    /* otherwise use the generic Barrett reduction technique */
    return s_mp_exptmod (G, X, P, Y, 0);
#else
................................................................................
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
  }
#endif
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_exptmod_fast.c.

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#include <tommath.h>
#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
 *
 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
 * The value of k changes based on the size of the exponent.
 *
................................................................................
#else
     err = MP_VAL;
     goto LBL_M;
#endif

     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
     if (((P->used * 2 + 1) < MP_WARRAY) &&
          P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
        redux = fast_mp_montgomery_reduce;
     } else 
#endif
     {
#ifdef BN_MP_MONTGOMERY_REDUCE_C
        /* use slower baseline Montgomery method */
        redux = mp_montgomery_reduce;
................................................................................
    buf <<= (mp_digit)1;

    /* if the bit is zero and mode == 0 then we ignore it
     * These represent the leading zero bits before the first 1 bit
     * in the exponent.  Technically this opt is not required but it
     * does lower the # of trivial squaring/reductions used
     */
    if (mode == 0 && y == 0) {
      continue;
    }

    /* if the bit is zero and mode == 1 then we square */
    if (mode == 1 && y == 0) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto LBL_RES;
      }
      continue;
................................................................................
      bitcpy = 0;
      bitbuf = 0;
      mode   = 1;
    }
  }

  /* if bits remain then square/multiply */
  if (mode == 2 && bitcpy > 0) {
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto LBL_RES;
................................................................................
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}
#endif





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|







 







>
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#include <tommath_private.h>
#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
 *
 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
 * The value of k changes based on the size of the exponent.
 *
................................................................................
#else
     err = MP_VAL;
     goto LBL_M;
#endif

     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
     if ((((P->used * 2) + 1) < MP_WARRAY) &&
          (P->used < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
        redux = fast_mp_montgomery_reduce;
     } else 
#endif
     {
#ifdef BN_MP_MONTGOMERY_REDUCE_C
        /* use slower baseline Montgomery method */
        redux = mp_montgomery_reduce;
................................................................................
    buf <<= (mp_digit)1;

    /* if the bit is zero and mode == 0 then we ignore it
     * These represent the leading zero bits before the first 1 bit
     * in the exponent.  Technically this opt is not required but it
     * does lower the # of trivial squaring/reductions used
     */
    if ((mode == 0) && (y == 0)) {
      continue;
    }

    /* if the bit is zero and mode == 1 then we square */
    if ((mode == 1) && (y == 0)) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto LBL_RES;
      }
      continue;
................................................................................
      bitcpy = 0;
      bitbuf = 0;
      mode   = 1;
    }
  }

  /* if bits remain then square/multiply */
  if ((mode == 2) && (bitcpy > 0)) {
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto LBL_RES;
................................................................................
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}
#endif


/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_exteuclid.c.

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#include <tommath.h>
#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Extended euclidean algorithm of (a, b) produces 
   a*u1 + b*u2 = u3
 */
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{
   mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
   int err;

................................................................................
       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto _ERR; }
   }

   /* make sure U3 >= 0 */
   if (u3.sign == MP_NEG) {
      mp_neg(&u1, &u1);
      mp_neg(&u2, &u2);
      mp_neg(&u3, &u3);
   }

   /* copy result out */
   if (U1 != NULL) { mp_exch(U1, &u1); }
   if (U2 != NULL) { mp_exch(U2, &u2); }
   if (U3 != NULL) { mp_exch(U3, &u3); }

   err = MP_OKAY;
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
   return err;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Extended euclidean algorithm of (a, b) produces
   a*u1 + b*u2 = u3
 */
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{
   mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
   int err;

................................................................................
       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto _ERR; }
   }

   /* make sure U3 >= 0 */
   if (u3.sign == MP_NEG) {
       if ((err = mp_neg(&u1, &u1)) != MP_OKAY)                                   { goto _ERR; }
       if ((err = mp_neg(&u2, &u2)) != MP_OKAY)                                   { goto _ERR; }
       if ((err = mp_neg(&u3, &u3)) != MP_OKAY)                                   { goto _ERR; }
   }

   /* copy result out */
   if (U1 != NULL) { mp_exch(U1, &u1); }
   if (U2 != NULL) { mp_exch(U2, &u2); }
   if (U3 != NULL) { mp_exch(U3, &u3); }

   err = MP_OKAY;
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
   return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_fread.c.

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#include <tommath.h>
#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
{
   int err, ch, neg, y;
   
................................................................................
      a->sign = neg;
   }
   
   return MP_OKAY;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
{
   int err, ch, neg, y;
   
................................................................................
      a->sign = neg;
   }
   
   return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
   char *buf;
   int err, len, x;
   
................................................................................
   }
   
   XFREE (buf);
   return MP_OKAY;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
   char *buf;
   int err, len, x;
   
................................................................................
   }
   
   XFREE (buf);
   return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  u, v;
  int     k, u_lsb, v_lsb, res;
................................................................................

  if (v_lsb != k) {
     if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
        goto LBL_V;
     }
  }

  while (mp_iszero(&v) == 0) {
     /* make sure v is the largest */
     if (mp_cmp_mag(&u, &v) == MP_GT) {
        /* swap u and v to make sure v is >= u */
        mp_exch(&u, &v);
     }
     
     /* subtract smallest from largest */
................................................................................
  c->sign = MP_ZPOS;
  res = MP_OKAY;
LBL_V:mp_clear (&u);
LBL_U:mp_clear (&v);
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  u, v;
  int     k, u_lsb, v_lsb, res;
................................................................................

  if (v_lsb != k) {
     if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
        goto LBL_V;
     }
  }

  while (mp_iszero(&v) == MP_NO) {
     /* make sure v is the largest */
     if (mp_cmp_mag(&u, &v) == MP_GT) {
        /* swap u and v to make sure v is >= u */
        mp_exch(&u, &v);
     }
     
     /* subtract smallest from largest */
................................................................................
  c->sign = MP_ZPOS;
  res = MP_OKAY;
LBL_V:mp_clear (&u);
LBL_U:mp_clear (&v);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a) 
{
  int i;
  unsigned long res;

  if (a->used == 0) {
     return 0;
  }

  /* get number of digits of the lsb we have to read */
  i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;

  /* get most significant digit of result */
  res = DIGIT(a,i);
   
  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }

  /* force result to 32-bits always so it is consistent on non 32-bit platforms */
  return res & 0xFFFFFFFFUL;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a)
{
  int i;
  mp_min_u32 res;

  if (a->used == 0) {
     return 0;
  }

  /* get number of digits of the lsb we have to read */
  i = MIN(a->used,(int)(((sizeof(unsigned long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;

  /* get most significant digit of result */
  res = DIGIT(a,i);

  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }

  /* force result to 32-bits always so it is consistent on non 32-bit platforms */
  return res & 0xFFFFFFFFUL;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Added libtommath/bn_mp_get_long.c.


















































































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#include <tommath_private.h>
#ifdef BN_MP_GET_LONG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* get the lower unsigned long of an mp_int, platform dependent */
unsigned long mp_get_long(mp_int * a)
{
  int i;
  unsigned long res;

  if (a->used == 0) {
     return 0;
  }

  /* get number of digits of the lsb we have to read */
  i = MIN(a->used,(int)(((sizeof(unsigned long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;

  /* get most significant digit of result */
  res = DIGIT(a,i);

#if (ULONG_MAX != 0xffffffffuL) || (DIGIT_BIT < 32)
  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }
#endif
  return res;
}
#endif

Added libtommath/bn_mp_get_long_long.c.


















































































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#include <tommath_private.h>
#ifdef BN_MP_GET_LONG_LONG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* get the lower unsigned long long of an mp_int, platform dependent */
unsigned long long mp_get_long_long (mp_int * a)
{
  int i;
  unsigned long long res;

  if (a->used == 0) {
     return 0;
  }

  /* get number of digits of the lsb we have to read */
  i = MIN(a->used,(int)(((sizeof(unsigned long long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;

  /* get most significant digit of result */
  res = DIGIT(a,i);

#if DIGIT_BIT < 64
  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }
#endif
  return res;
}
#endif

Changes to libtommath/bn_mp_grow.c.

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#include <tommath.h>
#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* grow as required */
int mp_grow (mp_int * a, int size)
{
  int     i;
  mp_digit *tmp;
................................................................................
    for (; i < a->alloc; i++) {
      a->dp[i] = 0;
    }
  }
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* grow as required */
int mp_grow (mp_int * a, int size)
{
  int     i;
  mp_digit *tmp;
................................................................................
    for (; i < a->alloc; i++) {
      a->dp[i] = 0;
    }
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Added libtommath/bn_mp_import.c.


















































































































































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#include <tommath_private.h>
#ifdef BN_MP_IMPORT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* based on gmp's mpz_import.
 * see http://gmplib.org/manual/Integer-Import-and-Export.html
 */
int mp_import(mp_int* rop, size_t count, int order, size_t size, 
                            int endian, size_t nails, const void* op) {
	int result;
	size_t odd_nails, nail_bytes, i, j;
	unsigned char odd_nail_mask;

	mp_zero(rop);

	if (endian == 0) {
		union {
			unsigned int i;
			char c[4];
		} lint;
		lint.i = 0x01020304;

		endian = (lint.c[0] == 4) ? -1 : 1;
	}

	odd_nails = (nails % 8);
	odd_nail_mask = 0xff;
	for (i = 0; i < odd_nails; ++i) {
		odd_nail_mask ^= (1 << (7 - i));
	}
	nail_bytes = nails / 8;

	for (i = 0; i < count; ++i) {
		for (j = 0; j < (size - nail_bytes); ++j) {
			unsigned char byte = *(
					(unsigned char*)op + 
					(((order == 1) ? i : ((count - 1) - i)) * size) +
					((endian == 1) ? (j + nail_bytes) : (((size - 1) - j) - nail_bytes))
				);

			if (
				(result = mp_mul_2d(rop, ((j == 0) ? (8 - odd_nails) : 8), rop)) != MP_OKAY) {
				return result;
			}

			rop->dp[0] |= (j == 0) ? (byte & odd_nail_mask) : byte;
			rop->used  += 1;
		}
	}

	mp_clamp(rop);

	return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_init.c.

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#include <tommath.h>
#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* init a new mp_int */
int mp_init (mp_int * a)
{
  int i;

................................................................................
  a->used  = 0;
  a->alloc = MP_PREC;
  a->sign  = MP_ZPOS;

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* init a new mp_int */
int mp_init (mp_int * a)
{
  int i;

................................................................................
  a->used  = 0;
  a->alloc = MP_PREC;
  a->sign  = MP_ZPOS;

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_init_copy.c.

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#include <tommath.h>
#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
{
  int     res;

  if ((res = mp_init (a)) != MP_OKAY) {
    return res;
  }
  return mp_copy (b, a);
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, const mp_int * b)
{
  int     res;

  if ((res = mp_init_size (a, b->used)) != MP_OKAY) {
    return res;
  }
  return mp_copy (b, a);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_init_multi.c.

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#include <tommath.h>
#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */
#include <stdarg.h>

int mp_init_multi(mp_int *mp, ...) 
{
    mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
    int n = 0;                 /* Number of ok inits */
................................................................................
            
            /* end the current list */
            va_end(args);
            
            /* now start cleaning up */            
            cur_arg = mp;
            va_start(clean_args, mp);
            while (n--) {
                mp_clear(cur_arg);
                cur_arg = va_arg(clean_args, mp_int*);
            }
            va_end(clean_args);
            res = MP_MEM;
            break;
        }
................................................................................
        cur_arg = va_arg(args, mp_int*);
    }
    va_end(args);
    return res;                /* Assumed ok, if error flagged above. */
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */
#include <stdarg.h>

int mp_init_multi(mp_int *mp, ...) 
{
    mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
    int n = 0;                 /* Number of ok inits */
................................................................................
            
            /* end the current list */
            va_end(args);
            
            /* now start cleaning up */            
            cur_arg = mp;
            va_start(clean_args, mp);
            while (n-- != 0) {
                mp_clear(cur_arg);
                cur_arg = va_arg(clean_args, mp_int*);
            }
            va_end(clean_args);
            res = MP_MEM;
            break;
        }
................................................................................
        cur_arg = va_arg(args, mp_int*);
    }
    va_end(args);
    return res;                /* Assumed ok, if error flagged above. */
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_init_set.c.

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#include <tommath.h>
#ifdef BN_MP_INIT_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  mp_set(a, b);
  return err;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_INIT_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  mp_set(a, b);
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_init_set_int.c.

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#include <tommath.h>
#ifdef BN_MP_INIT_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  return mp_set_int(a, b);
}
#endif




|













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>
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#include <tommath_private.h>
#ifdef BN_MP_INIT_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  return mp_set_int(a, b);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_init_size.c.

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#include <tommath.h>
#ifdef BN_MP_INIT_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
  int x;

................................................................................
  for (x = 0; x < size; x++) {
      a->dp[x] = 0;
  }

  return MP_OKAY;
}
#endif




|













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>
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#include <tommath_private.h>
#ifdef BN_MP_INIT_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
  int x;

................................................................................
  for (x = 0; x < size; x++) {
      a->dp[x] = 0;
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_invmod.c.

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38
39




#include <tommath.h>
#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  /* b cannot be negative */
  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
    return MP_VAL;
  }

#ifdef BN_FAST_MP_INVMOD_C
  /* if the modulus is odd we can use a faster routine instead */
  if (mp_isodd (b) == 1) {
    return fast_mp_invmod (a, b, c);
  }
#endif

#ifdef BN_MP_INVMOD_SLOW_C
  return mp_invmod_slow(a, b, c);
#endif

  return MP_VAL;

}
#endif




|













|






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|






|
<

>


>
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>
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36
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#include <tommath_private.h>
#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  /* b cannot be negative */
  if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
    return MP_VAL;
  }

#ifdef BN_FAST_MP_INVMOD_C
  /* if the modulus is odd we can use a faster routine instead */
  if (mp_isodd (b) == MP_YES) {
    return fast_mp_invmod (a, b, c);
  }
#endif

#ifdef BN_MP_INVMOD_SLOW_C
  return mp_invmod_slow(a, b, c);
#else

  return MP_VAL;
#endif
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_invmod_slow.c.

1
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#include <tommath.h>
#ifdef BN_MP_INVMOD_SLOW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* hac 14.61, pp608 */
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, A, B, C, D;
  int     res;

  /* b cannot be negative */
  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
    return MP_VAL;
  }

  /* init temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, 
                           &A, &B, &C, &D, NULL)) != MP_OKAY) {
     return res;
................................................................................
      goto LBL_ERR;
  }
  if ((res = mp_copy (b, &y)) != MP_OKAY) {
    goto LBL_ERR;
  }

  /* 2. [modified] if x,y are both even then return an error! */
  if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
    res = MP_VAL;
    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
    goto LBL_ERR;
................................................................................
    goto LBL_ERR;
  }
  mp_set (&A, 1);
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == 1) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if A or B is odd then */
    if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
      /* A = (A+y)/2, B = (B-x)/2 */
      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
         goto LBL_ERR;
      }
................................................................................
    }
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == 1) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if C or D is odd then */
    if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
      /* C = (C+y)/2, D = (D-x)/2 */
      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
         goto LBL_ERR;
      }
................................................................................

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == 0)
    goto top;

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
................................................................................
  /* C is now the inverse */
  mp_exch (&C, c);
  res = MP_OKAY;
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_INVMOD_SLOW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* hac 14.61, pp608 */
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, A, B, C, D;
  int     res;

  /* b cannot be negative */
  if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
    return MP_VAL;
  }

  /* init temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, 
                           &A, &B, &C, &D, NULL)) != MP_OKAY) {
     return res;
................................................................................
      goto LBL_ERR;
  }
  if ((res = mp_copy (b, &y)) != MP_OKAY) {
    goto LBL_ERR;
  }

  /* 2. [modified] if x,y are both even then return an error! */
  if ((mp_iseven (&x) == MP_YES) && (mp_iseven (&y) == MP_YES)) {
    res = MP_VAL;
    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
    goto LBL_ERR;
................................................................................
    goto LBL_ERR;
  }
  mp_set (&A, 1);
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == MP_YES) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if A or B is odd then */
    if ((mp_isodd (&A) == MP_YES) || (mp_isodd (&B) == MP_YES)) {
      /* A = (A+y)/2, B = (B-x)/2 */
      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
         goto LBL_ERR;
      }
................................................................................
    }
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == MP_YES) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if C or D is odd then */
    if ((mp_isodd (&C) == MP_YES) || (mp_isodd (&D) == MP_YES)) {
      /* C = (C+y)/2, D = (D-x)/2 */
      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
         goto LBL_ERR;
      }
................................................................................

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == MP_NO)
    goto top;

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
................................................................................
  /* C is now the inverse */
  mp_exch (&C, c);
  res = MP_OKAY;
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_is_square.c.

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5
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99
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105




#include <tommath.h>
#ifdef BN_MP_IS_SQUARE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
................................................................................
     goto ERR;
  }
  r = mp_get_int(&t);
  /* Check for other prime modules, note it's not an ERROR but we must
   * free "t" so the easiest way is to goto ERR.  We know that res
   * is already equal to MP_OKAY from the mp_mod call 
   */ 
  if ( (1L<<(r%11)) & 0x5C4L )             goto ERR;
  if ( (1L<<(r%13)) & 0x9E4L )             goto ERR;
  if ( (1L<<(r%17)) & 0x5CE8L )            goto ERR;
  if ( (1L<<(r%19)) & 0x4F50CL )           goto ERR;
  if ( (1L<<(r%23)) & 0x7ACCA0L )          goto ERR;
  if ( (1L<<(r%29)) & 0xC2EDD0CL )         goto ERR;
  if ( (1L<<(r%31)) & 0x6DE2B848L )        goto ERR;

  /* Final check - is sqr(sqrt(arg)) == arg ? */
  if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
     goto ERR;
  }
  if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
     goto ERR;
................................................................................
  }

  *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
ERR:mp_clear(&t);
  return res;
}
#endif




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>
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109
#include <tommath_private.h>
#ifdef BN_MP_IS_SQUARE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
................................................................................
     goto ERR;
  }
  r = mp_get_int(&t);
  /* Check for other prime modules, note it's not an ERROR but we must
   * free "t" so the easiest way is to goto ERR.  We know that res
   * is already equal to MP_OKAY from the mp_mod call 
   */ 
  if (((1L<<(r%11)) & 0x5C4L) != 0L)       goto ERR;
  if (((1L<<(r%13)) & 0x9E4L) != 0L)       goto ERR;
  if (((1L<<(r%17)) & 0x5CE8L) != 0L)      goto ERR;
  if (((1L<<(r%19)) & 0x4F50CL) != 0L)     goto ERR;
  if (((1L<<(r%23)) & 0x7ACCA0L) != 0L)    goto ERR;
  if (((1L<<(r%29)) & 0xC2EDD0CL) != 0L)   goto ERR;
  if (((1L<<(r%31)) & 0x6DE2B848L) != 0L)  goto ERR;

  /* Final check - is sqr(sqrt(arg)) == arg ? */
  if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
     goto ERR;
  }
  if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
     goto ERR;
................................................................................
  }

  *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
ERR:mp_clear(&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_jacobi.c.

1
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#include <tommath.h>
#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * HAC pp. 73 Algorithm 2.149


 */
int mp_jacobi (mp_int * a, mp_int * p, int *c)
{
  mp_int  a1, p1;
  int     k, s, r, res;
  mp_digit residue;






  /* if p <= 0 return MP_VAL */
  if (mp_cmp_d(p, 0) != MP_GT) {
     return MP_VAL;
  }

  /* step 1.  if a == 0, return 0 */
  if (mp_iszero (a) == 1) {




    *c = 0;

    return MP_OKAY;
  }

  /* step 2.  if a == 1, return 1 */
  if (mp_cmp_d (a, 1) == MP_EQ) {
    *c = 1;
    return MP_OKAY;
  }
................................................................................
  }

  /* step 4.  if e is even set s=1 */
  if ((k & 1) == 0) {
    s = 1;
  } else {
    /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
    residue = p->dp[0] & 7;

    if (residue == 1 || residue == 7) {
      s = 1;
    } else if (residue == 3 || residue == 5) {
      s = -1;
    }
  }

  /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
  if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
    s = -s;
  }

  /* if a1 == 1 we're done */
  if (mp_cmp_d (&a1, 1) == MP_EQ) {
    *c = s;
  } else {
    /* n1 = n mod a1 */
    if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
      goto LBL_P1;
    }
    if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
      goto LBL_P1;
    }
    *c = s * r;
  }
................................................................................
  /* done */
  res = MP_OKAY;
LBL_P1:mp_clear (&p1);
LBL_A1:mp_clear (&a1);
  return res;
}
#endif




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>
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105
...
107
108
109
110
111
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114
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116
117
#include <tommath_private.h>
#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * HAC pp. 73 Algorithm 2.149
 * HAC is wrong here, as the special case of (0 | 1) is not
 * handled correctly.
 */
int mp_jacobi (mp_int * a, mp_int * n, int *c)
{
  mp_int  a1, p1;
  int     k, s, r, res;
  mp_digit residue;

  /* if a < 0 return MP_VAL */
  if (mp_isneg(a) == MP_YES) {
     return MP_VAL;
  }

  /* if n <= 0 return MP_VAL */
  if (mp_cmp_d(n, 0) != MP_GT) {
     return MP_VAL;
  }

  /* step 1. handle case of a == 0 */
  if (mp_iszero (a) == MP_YES) {
     /* special case of a == 0 and n == 1 */
     if (mp_cmp_d (n, 1) == MP_EQ) {
       *c = 1;
     } else {
       *c = 0;
     }
     return MP_OKAY;
  }

  /* step 2.  if a == 1, return 1 */
  if (mp_cmp_d (a, 1) == MP_EQ) {
    *c = 1;
    return MP_OKAY;
  }
................................................................................
  }

  /* step 4.  if e is even set s=1 */
  if ((k & 1) == 0) {
    s = 1;
  } else {
    /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
    residue = n->dp[0] & 7;

    if ((residue == 1) || (residue == 7)) {
      s = 1;
    } else if ((residue == 3) || (residue == 5)) {
      s = -1;
    }
  }

  /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
  if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
    s = -s;
  }

  /* if a1 == 1 we're done */
  if (mp_cmp_d (&a1, 1) == MP_EQ) {
    *c = s;
  } else {
    /* n1 = n mod a1 */
    if ((res = mp_mod (n, &a1, &p1)) != MP_OKAY) {
      goto LBL_P1;
    }
    if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
      goto LBL_P1;
    }
    *c = s * r;
  }
................................................................................
  /* done */
  res = MP_OKAY;
LBL_P1:mp_clear (&p1);
LBL_A1:mp_clear (&a1);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_karatsuba_mul.c.

1
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3
4
5
6
7
8
9
10
11
12
13
14
15
16
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20
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78
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88
89
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91
92
93
...
157
158
159
160
161
162
163




#include <tommath.h>
#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* c = |a| * |b| using Karatsuba Multiplication using 
 * three half size multiplications
 *
 * Let B represent the radix [e.g. 2**DIGIT_BIT] and 
 * let n represent half of the number of digits in 
................................................................................

  /* now shift the digits */
  x0.used = y0.used = B;
  x1.used = a->used - B;
  y1.used = b->used - B;

  {
    register int x;
    register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;

    /* we copy the digits directly instead of using higher level functions
     * since we also need to shift the digits
     */
    tmpa = a->dp;
    tmpb = b->dp;

................................................................................
Y0:mp_clear (&y0);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif




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>
>
>
>
1
2
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5
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8
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78
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157
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163
164
165
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167
#include <tommath_private.h>
#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* c = |a| * |b| using Karatsuba Multiplication using 
 * three half size multiplications
 *
 * Let B represent the radix [e.g. 2**DIGIT_BIT] and 
 * let n represent half of the number of digits in 
................................................................................

  /* now shift the digits */
  x0.used = y0.used = B;
  x1.used = a->used - B;
  y1.used = b->used - B;

  {
    int x;
    mp_digit *tmpa, *tmpb, *tmpx, *tmpy;

    /* we copy the digits directly instead of using higher level functions
     * since we also need to shift the digits
     */
    tmpa = a->dp;
    tmpb = b->dp;

................................................................................
Y0:mp_clear (&y0);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_karatsuba_sqr.c.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
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..
48
49
50
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56
57
58
59
60
61
62
63
...
111
112
113
114
115
116
117




#include <tommath.h>
#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Karatsuba squaring, computes b = a*a using three 
 * half size squarings
 *
 * See comments of karatsuba_mul for details.  It 
 * is essentially the same algorithm but merely 
................................................................................
    goto T1;
  if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
    goto T2;
  if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
    goto X0X0;

  {
    register int x;
    register mp_digit *dst, *src;

    src = a->dp;

    /* now shift the digits */
    dst = x0.dp;
    for (x = 0; x < B; x++) {
      *dst++ = *src++;
................................................................................
T1:mp_clear (&t1);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif




|













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>
>
>
>
1
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48
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...
111
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118
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121
#include <tommath_private.h>
#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Karatsuba squaring, computes b = a*a using three 
 * half size squarings
 *
 * See comments of karatsuba_mul for details.  It 
 * is essentially the same algorithm but merely 
................................................................................
    goto T1;
  if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
    goto T2;
  if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
    goto X0X0;

  {
    int x;
    mp_digit *dst, *src;

    src = a->dp;

    /* now shift the digits */
    dst = x0.dp;
    for (x = 0; x < B; x++) {
      *dst++ = *src++;
................................................................................
T1:mp_clear (&t1);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_lcm.c.

1
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5
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#include <tommath.h>
#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
{
  int     res;
  mp_int  t1, t2;
................................................................................
  c->sign = MP_ZPOS;

LBL_T:
  mp_clear_multi (&t1, &t2, NULL);
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
{
  int     res;
  mp_int  t1, t2;
................................................................................
  c->sign = MP_ZPOS;

LBL_T:
  mp_clear_multi (&t1, &t2, NULL);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
{
  int     x, res;

  /* if its less than zero return */
  if (b <= 0) {
    return MP_OKAY;
  }

  /* grow to fit the new digits */
  if (a->alloc < a->used + b) {
     if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
       return res;
     }
  }

  {
    register mp_digit *top, *bottom;

    /* increment the used by the shift amount then copy upwards */
    a->used += b;

    /* top */
    top = a->dp + a->used - 1;

    /* base */
    bottom = a->dp + a->used - 1 - b;

    /* much like mp_rshd this is implemented using a sliding window
     * except the window goes the otherway around.  Copying from
     * the bottom to the top.  see bn_mp_rshd.c for more info.
     */
    for (x = a->used - 1; x >= b; x--) {
      *top-- = *bottom--;
................................................................................
    for (x = 0; x < b; x++) {
      *top++ = 0;
    }
  }
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
{
  int     x, res;

  /* if its less than zero return */
  if (b <= 0) {
    return MP_OKAY;
  }

  /* grow to fit the new digits */
  if (a->alloc < (a->used + b)) {
     if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
       return res;
     }
  }

  {
    mp_digit *top, *bottom;

    /* increment the used by the shift amount then copy upwards */
    a->used += b;

    /* top */
    top = a->dp + a->used - 1;

    /* base */
    bottom = (a->dp + a->used - 1) - b;

    /* much like mp_rshd this is implemented using a sliding window
     * except the window goes the otherway around.  Copying from
     * the bottom to the top.  see bn_mp_rshd.c for more info.
     */
    for (x = a->used - 1; x >= b; x--) {
      *top-- = *bottom--;
................................................................................
    for (x = 0; x < b; x++) {
      *top++ = 0;
    }
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_mod.c.

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#include <tommath.h>
#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* c = a mod b, 0 <= c < b */
int
mp_mod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  t;
  int     res;

  if ((res = mp_init (&t)) != MP_OKAY) {
................................................................................
  }

  if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
    mp_clear (&t);
    return res;
  }

  if (t.sign != b->sign) {
    res = mp_add (b, &t, c);
  } else {
    res = MP_OKAY;
    mp_exch (&t, c);


  }

  mp_clear (&t);
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
int
mp_mod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  t;
  int     res;

  if ((res = mp_init (&t)) != MP_OKAY) {
................................................................................
  }

  if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
    mp_clear (&t);
    return res;
  }

  if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {


    res = MP_OKAY;
    mp_exch (&t, c);
  } else {
    res = mp_add (b, &t, c);
  }

  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_mod_2d.c.

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#include <tommath.h>
#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* calc a value mod 2**b */
int
mp_mod_2d (const mp_int * a, int b, mp_int * c)
{
  int     x, res;
................................................................................

  /* copy */
  if ((res = mp_copy (a, c)) != MP_OKAY) {
    return res;
  }

  /* zero digits above the last digit of the modulus */
  for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
    c->dp[x] = 0;
  }
  /* clear the digit that is not completely outside/inside the modulus */
  c->dp[b / DIGIT_BIT] &=
    (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
  mp_clamp (c);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* calc a value mod 2**b */
int
mp_mod_2d (const mp_int * a, int b, mp_int * c)
{
  int     x, res;
................................................................................

  /* copy */
  if ((res = mp_copy (a, c)) != MP_OKAY) {
    return res;
  }

  /* zero digits above the last digit of the modulus */
  for (x = (b / DIGIT_BIT) + (((b % DIGIT_BIT) == 0) ? 0 : 1); x < c->used; x++) {
    c->dp[x] = 0;
  }
  /* clear the digit that is not completely outside/inside the modulus */
  c->dp[b / DIGIT_BIT] &=
    (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_mod_d.c.

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#include <tommath.h>
#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
  return mp_div_d(a, b, NULL, c);
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
  return mp_div_d(a, b, NULL, c);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/*
 * shifts with subtractions when the result is greater than b.
 *
 * The method is slightly modified to shift B unconditionally upto just under
 * the leading bit of b.  This saves alot of multiple precision shifting.
................................................................................
{
  int     x, bits, res;

  /* how many bits of last digit does b use */
  bits = mp_count_bits (b) % DIGIT_BIT;

  if (b->used > 1) {
     if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
        return res;
     }
  } else {
     mp_set(a, 1);
     bits = 1;
  }

................................................................................
      }
    }
  }

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/*
 * shifts with subtractions when the result is greater than b.
 *
 * The method is slightly modified to shift B unconditionally upto just under
 * the leading bit of b.  This saves alot of multiple precision shifting.
................................................................................
{
  int     x, bits, res;

  /* how many bits of last digit does b use */
  bits = mp_count_bits (b) % DIGIT_BIT;

  if (b->used > 1) {
     if ((res = mp_2expt (a, ((b->used - 1) * DIGIT_BIT) + bits - 1)) != MP_OKAY) {
        return res;
     }
  } else {
     mp_set(a, 1);
     bits = 1;
  }

................................................................................
      }
    }
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_montgomery_reduce.c.

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#include <tommath.h>
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
  int     ix, res, digs;
................................................................................

  /* can the fast reduction [comba] method be used?
   *
   * Note that unlike in mul you're safely allowed *less*
   * than the available columns [255 per default] since carries
   * are fixed up in the inner loop.
   */
  digs = n->used * 2 + 1;
  if ((digs < MP_WARRAY) &&
      n->used <
      (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
    return fast_mp_montgomery_reduce (x, n, rho);
  }

  /* grow the input as required */
  if (x->alloc < digs) {
    if ((res = mp_grow (x, digs)) != MP_OKAY) {
      return res;
................................................................................
     *
     * The value of rho must be precalculated via
     * montgomery_setup() such that
     * it equals -1/n0 mod b this allows the
     * following inner loop to reduce the
     * input one digit at a time
     */
    mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);

    /* a = a + mu * m * b**i */
    {
      register int iy;
      register mp_digit *tmpn, *tmpx, u;
      register mp_word r;

      /* alias for digits of the modulus */
      tmpn = n->dp;

      /* alias for the digits of x [the input] */
      tmpx = x->dp + ix;

      /* set the carry to zero */
      u = 0;

      /* Multiply and add in place */
      for (iy = 0; iy < n->used; iy++) {
        /* compute product and sum */
        r       = ((mp_word)mu) * ((mp_word)*tmpn++) +
                  ((mp_word) u) + ((mp_word) * tmpx);

        /* get carry */
        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

        /* fix digit */
        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
      }
      /* At this point the ix'th digit of x should be zero */


      /* propagate carries upwards as required*/
      while (u) {
        *tmpx   += u;
        u        = *tmpx >> DIGIT_BIT;
        *tmpx++ &= MP_MASK;
      }
    }
  }

................................................................................
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
  int     ix, res, digs;
................................................................................

  /* can the fast reduction [comba] method be used?
   *
   * Note that unlike in mul you're safely allowed *less*
   * than the available columns [255 per default] since carries
   * are fixed up in the inner loop.
   */
  digs = (n->used * 2) + 1;
  if ((digs < MP_WARRAY) &&
      (n->used <
      (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
    return fast_mp_montgomery_reduce (x, n, rho);
  }

  /* grow the input as required */
  if (x->alloc < digs) {
    if ((res = mp_grow (x, digs)) != MP_OKAY) {
      return res;
................................................................................
     *
     * The value of rho must be precalculated via
     * montgomery_setup() such that
     * it equals -1/n0 mod b this allows the
     * following inner loop to reduce the
     * input one digit at a time
     */
    mu = (mp_digit) (((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);

    /* a = a + mu * m * b**i */
    {
      int iy;
      mp_digit *tmpn, *tmpx, u;
      mp_word r;

      /* alias for digits of the modulus */
      tmpn = n->dp;

      /* alias for the digits of x [the input] */
      tmpx = x->dp + ix;

      /* set the carry to zero */
      u = 0;

      /* Multiply and add in place */
      for (iy = 0; iy < n->used; iy++) {
        /* compute product and sum */
        r       = ((mp_word)mu * (mp_word)*tmpn++) +
                   (mp_word) u + (mp_word) *tmpx;

        /* get carry */
        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

        /* fix digit */
        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
      }
      /* At this point the ix'th digit of x should be zero */


      /* propagate carries upwards as required*/
      while (u != 0) {
        *tmpx   += u;
        u        = *tmpx >> DIGIT_BIT;
        *tmpx++ &= MP_MASK;
      }
    }
  }

................................................................................
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* setups the montgomery reduction stuff */
int
mp_montgomery_setup (mp_int * n, mp_digit * rho)
{
  mp_digit x, b;
................................................................................
  b = n->dp[0];

  if ((b & 1) == 0) {
    return MP_VAL;
  }

  x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
  x *= 2 - b * x;               /* here x*a==1 mod 2**8 */
#if !defined(MP_8BIT)
  x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
#endif
#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
  x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
#endif
#ifdef MP_64BIT
  x *= 2 - b * x;               /* here x*a==1 mod 2**64 */
#endif

  /* rho = -1/m mod b */
  *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* setups the montgomery reduction stuff */
int
mp_montgomery_setup (mp_int * n, mp_digit * rho)
{
  mp_digit x, b;
................................................................................
  b = n->dp[0];

  if ((b & 1) == 0) {
    return MP_VAL;
  }

  x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
  x *= 2 - (b * x);             /* here x*a==1 mod 2**8 */
#if !defined(MP_8BIT)
  x *= 2 - (b * x);             /* here x*a==1 mod 2**16 */
#endif
#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
  x *= 2 - (b * x);             /* here x*a==1 mod 2**32 */
#endif
#ifdef MP_64BIT
  x *= 2 - (b * x);             /* here x*a==1 mod 2**64 */
#endif

  /* rho = -1/m mod b */
  *rho = (mp_digit)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, neg;
  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
................................................................................
     * have less than MP_WARRAY digits and the number of 
     * digits won't affect carry propagation
     */
    int     digs = a->used + b->used + 1;

#ifdef BN_FAST_S_MP_MUL_DIGS_C
    if ((digs < MP_WARRAY) &&
        MIN(a->used, b->used) <= 
        (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
      res = fast_s_mp_mul_digs (a, b, c, digs);
    } else 
#endif

#ifdef BN_S_MP_MUL_DIGS_C
      res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
#else
      res = MP_VAL;
#endif

  }
  c->sign = (c->used > 0) ? neg : MP_ZPOS;
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, neg;
  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
................................................................................
     * have less than MP_WARRAY digits and the number of 
     * digits won't affect carry propagation
     */
    int     digs = a->used + b->used + 1;

#ifdef BN_FAST_S_MP_MUL_DIGS_C
    if ((digs < MP_WARRAY) &&
        (MIN(a->used, b->used) <= 
         (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
      res = fast_s_mp_mul_digs (a, b, c, digs);
    } else 
#endif
    {
#ifdef BN_S_MP_MUL_DIGS_C
      res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
#else
      res = MP_VAL;
#endif
    }
  }
  c->sign = (c->used > 0) ? neg : MP_ZPOS;
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
{
  int     x, res, oldused;

  /* grow to accomodate result */
  if (b->alloc < a->used + 1) {
    if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  oldused = b->used;
  b->used = a->used;

  {
    register mp_digit r, rr, *tmpa, *tmpb;

    /* alias for source */
    tmpa = a->dp;
    
    /* alias for dest */
    tmpb = b->dp;

................................................................................
      *tmpb++ = 0;
    }
  }
  b->sign = a->sign;
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
{
  int     x, res, oldused;

  /* grow to accomodate result */
  if (b->alloc < (a->used + 1)) {
    if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  oldused = b->used;
  b->used = a->used;

  {
    mp_digit r, rr, *tmpa, *tmpb;

    /* alias for source */
    tmpa = a->dp;
    
    /* alias for dest */
    tmpb = b->dp;

................................................................................
      *tmpb++ = 0;
    }
  }
  b->sign = a->sign;
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shift left by a certain bit count */
int mp_mul_2d (const mp_int * a, int b, mp_int * c)
{
  mp_digit d;
  int      res;
................................................................................
  /* copy */
  if (a != c) {
     if ((res = mp_copy (a, c)) != MP_OKAY) {
       return res;
     }
  }

  if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
     if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
       return res;
     }
  }

  /* shift by as many digits in the bit count */
  if (b >= (int)DIGIT_BIT) {
    if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
................................................................................
      return res;
    }
  }

  /* shift any bit count < DIGIT_BIT */
  d = (mp_digit) (b % DIGIT_BIT);
  if (d != 0) {
    register mp_digit *tmpc, shift, mask, r, rr;
    register int x;

    /* bitmask for carries */
    mask = (((mp_digit)1) << d) - 1;

    /* shift for msbs */
    shift = DIGIT_BIT - d;

................................................................................
       c->dp[(c->used)++] = r;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shift left by a certain bit count */
int mp_mul_2d (const mp_int * a, int b, mp_int * c)
{
  mp_digit d;
  int      res;
................................................................................
  /* copy */
  if (a != c) {
     if ((res = mp_copy (a, c)) != MP_OKAY) {
       return res;
     }
  }

  if (c->alloc < (int)(c->used + (b / DIGIT_BIT) + 1)) {
     if ((res = mp_grow (c, c->used + (b / DIGIT_BIT) + 1)) != MP_OKAY) {
       return res;
     }
  }

  /* shift by as many digits in the bit count */
  if (b >= (int)DIGIT_BIT) {
    if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
................................................................................
      return res;
    }
  }

  /* shift any bit count < DIGIT_BIT */
  d = (mp_digit) (b % DIGIT_BIT);
  if (d != 0) {
    mp_digit *tmpc, shift, mask, r, rr;
    int x;

    /* bitmask for carries */
    mask = (((mp_digit)1) << d) - 1;

    /* shift for msbs */
    shift = DIGIT_BIT - d;

................................................................................
       c->dp[(c->used)++] = r;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* multiply by a digit */
int
mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
{
  mp_digit u, *tmpa, *tmpc;
  mp_word  r;
  int      ix, res, olduse;

  /* make sure c is big enough to hold a*b */
  if (c->alloc < a->used + 1) {
    if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* get the original destinations used count */
  olduse = c->used;
................................................................................

  /* zero carry */
  u = 0;

  /* compute columns */
  for (ix = 0; ix < a->used; ix++) {
    /* compute product and carry sum for this term */
    r       = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);

    /* mask off higher bits to get a single digit */
    *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));

    /* send carry into next iteration */
    u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
  }
................................................................................
  /* set used count */
  c->used = a->used + 1;
  mp_clamp(c);

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* multiply by a digit */
int
mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
{
  mp_digit u, *tmpa, *tmpc;
  mp_word  r;
  int      ix, res, olduse;

  /* make sure c is big enough to hold a*b */
  if (c->alloc < (a->used + 1)) {
    if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* get the original destinations used count */
  olduse = c->used;
................................................................................

  /* zero carry */
  u = 0;

  /* compute columns */
  for (ix = 0; ix < a->used; ix++) {
    /* compute product and carry sum for this term */
    r       = (mp_word)u + ((mp_word)*tmpa++ * (mp_word)b);

    /* mask off higher bits to get a single digit */
    *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));

    /* send carry into next iteration */
    u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
  }
................................................................................
  /* set used count */
  c->used = a->used + 1;
  mp_clamp(c);

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* d = a * b (mod c) */
int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
  mp_int  t;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif




|













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#include <tommath_private.h>
#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* d = a * b (mod c) */
int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
  mp_int  t;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_n_root.c.

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#include <tommath.h>
#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* find the n'th root of an integer 
 *
 * Result found such that (c)**b <= a and (c+1)**b > a 
 *
 * This algorithm uses Newton's approximation 
 * x[i+1] = x[i] - f(x[i])/f'(x[i]) 
 * which will find the root in log(N) time where 
 * each step involves a fair bit.  This is not meant to 
 * find huge roots [square and cube, etc].
 */
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
{
  mp_int  t1, t2, t3;
  int     res, neg;

  /* input must be positive if b is even */
  if ((b & 1) == 0 && a->sign == MP_NEG) {
    return MP_VAL;
  }

  if ((res = mp_init (&t1)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_init (&t2)) != MP_OKAY) {
    goto LBL_T1;
  }

  if ((res = mp_init (&t3)) != MP_OKAY) {
    goto LBL_T2;
  }

  /* if a is negative fudge the sign but keep track */
  neg     = a->sign;
  a->sign = MP_ZPOS;

  /* t2 = 2 */
  mp_set (&t2, 2);

  do {
    /* t1 = t2 */
    if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
      goto LBL_T3;
    }

    /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
    
    /* t3 = t1**(b-1) */
    if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {   
      goto LBL_T3;
    }

    /* numerator */
    /* t2 = t1**b */
    if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {    
      goto LBL_T3;
    }

    /* t2 = t1**b - a */
    if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {  
      goto LBL_T3;
    }

    /* denominator */
    /* t3 = t1**(b-1) * b  */
    if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {    
      goto LBL_T3;
    }

    /* t3 = (t1**b - a)/(b * t1**(b-1)) */
    if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {  
      goto LBL_T3;
    }

    if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
      goto LBL_T3;
    }
  }  while (mp_cmp (&t1, &t2) != MP_EQ);

  /* result can be off by a few so check */
  for (;;) {
    if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
      goto LBL_T3;
    }

    if (mp_cmp (&t2, a) == MP_GT) {
      if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
         goto LBL_T3;
      }
    } else {
      break;
    }
  }

  /* reset the sign of a first */
  a->sign = neg;

  /* set the result */
  mp_exch (&t1, c);

  /* set the sign of the result */
  c->sign = neg;

  res = MP_OKAY;

LBL_T3:mp_clear (&t3);
LBL_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* wrapper function for mp_n_root_ex()

 * computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a






 */
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
{
  return mp_n_root_ex(a, b, c, 0);

}































































































#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Added libtommath/bn_mp_n_root_ex.c.








































































































































































































































































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#include <tommath_private.h>
#ifdef BN_MP_N_ROOT_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* find the n'th root of an integer
 *
 * Result found such that (c)**b <= a and (c+1)**b > a
 *
 * This algorithm uses Newton's approximation
 * x[i+1] = x[i] - f(x[i])/f'(x[i])
 * which will find the root in log(N) time where
 * each step involves a fair bit.  This is not meant to
 * find huge roots [square and cube, etc].
 */
int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
{
  mp_int  t1, t2, t3;
  int     res, neg;

  /* input must be positive if b is even */
  if (((b & 1) == 0) && (a->sign == MP_NEG)) {
    return MP_VAL;
  }

  if ((res = mp_init (&t1)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_init (&t2)) != MP_OKAY) {
    goto LBL_T1;
  }

  if ((res = mp_init (&t3)) != MP_OKAY) {
    goto LBL_T2;
  }

  /* if a is negative fudge the sign but keep track */
  neg     = a->sign;
  a->sign = MP_ZPOS;

  /* t2 = 2 */
  mp_set (&t2, 2);

  do {
    /* t1 = t2 */
    if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
      goto LBL_T3;
    }

    /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */

    /* t3 = t1**(b-1) */
    if ((res = mp_expt_d_ex (&t1, b - 1, &t3, fast)) != MP_OKAY) {
      goto LBL_T3;
    }

    /* numerator */
    /* t2 = t1**b */
    if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
      goto LBL_T3;
    }

    /* t2 = t1**b - a */
    if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
      goto LBL_T3;
    }

    /* denominator */
    /* t3 = t1**(b-1) * b  */
    if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
      goto LBL_T3;
    }

    /* t3 = (t1**b - a)/(b * t1**(b-1)) */
    if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
      goto LBL_T3;
    }

    if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
      goto LBL_T3;
    }
  }  while (mp_cmp (&t1, &t2) != MP_EQ);

  /* result can be off by a few so check */
  for (;;) {
    if ((res = mp_expt_d_ex (&t1, b, &t2, fast)) != MP_OKAY) {
      goto LBL_T3;
    }

    if (mp_cmp (&t2, a) == MP_GT) {
      if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
         goto LBL_T3;
      }
    } else {
      break;
    }
  }

  /* reset the sign of a first */
  a->sign = neg;

  /* set the result */
  mp_exch (&t1, c);

  /* set the sign of the result */
  c->sign = neg;

  res = MP_OKAY;

LBL_T3:mp_clear (&t3);
LBL_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_neg.c.

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#include <tommath.h>
#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* b = -a */
int mp_neg (const mp_int * a, mp_int * b)
{
  int     res;
  if (a != b) {
................................................................................
  } else {
     b->sign = MP_ZPOS;
  }

  return MP_OKAY;
}
#endif




|













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#include <tommath_private.h>
#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* b = -a */
int mp_neg (const mp_int * a, mp_int * b)
{
  int     res;
  if (a != b) {
................................................................................
  } else {
     b->sign = MP_ZPOS;
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_or.c.

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#include <tommath.h>
#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
  mp_int  t, *x;
................................................................................
  }
  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif




|













|







 







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#include <tommath_private.h>
#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
  mp_int  t, *x;
................................................................................
  }
  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_prime_fermat.c.

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#include <tommath.h>
#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* performs one Fermat test.
 * 
 * If "a" were prime then b**a == b (mod a) since the order of
 * the multiplicative sub-group would be phi(a) = a-1.  That means
 * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
................................................................................
  }

  err = MP_OKAY;
LBL_T:mp_clear (&t);
  return err;
}
#endif




|













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#include <tommath_private.h>
#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* performs one Fermat test.
 * 
 * If "a" were prime then b**a == b (mod a) since the order of
 * the multiplicative sub-group would be phi(a) = a-1.  That means
 * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
................................................................................
  }

  err = MP_OKAY;
LBL_T:mp_clear (&t);
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_prime_is_divisible.c.

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#include <tommath.h>
#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines if an integers is divisible by one 
 * of the first PRIME_SIZE primes or not
 *
 * sets result to 0 if not, 1 if yes
 */
................................................................................
      return MP_OKAY;
    }
  }

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines if an integers is divisible by one 
 * of the first PRIME_SIZE primes or not
 *
 * sets result to 0 if not, 1 if yes
 */
................................................................................
      return MP_OKAY;
    }
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_prime_is_prime.c.

1
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#include <tommath.h>
#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* performs a variable number of rounds of Miller-Rabin
 *
 * Probability of error after t rounds is no more than

 *
................................................................................
  mp_int  b;
  int     ix, err, res;

  /* default to no */
  *result = MP_NO;

  /* valid value of t? */
  if (t <= 0 || t > PRIME_SIZE) {
    return MP_VAL;
  }

  /* is the input equal to one of the primes in the table? */
  for (ix = 0; ix < PRIME_SIZE; ix++) {
      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
         *result = 1;
................................................................................

  /* passed the test */
  *result = MP_YES;
LBL_B:mp_clear (&b);
  return err;
}
#endif




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>
>
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#include <tommath_private.h>
#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* performs a variable number of rounds of Miller-Rabin
 *
 * Probability of error after t rounds is no more than

 *
................................................................................
  mp_int  b;
  int     ix, err, res;

  /* default to no */
  *result = MP_NO;

  /* valid value of t? */
  if ((t <= 0) || (t > PRIME_SIZE)) {
    return MP_VAL;
  }

  /* is the input equal to one of the primes in the table? */
  for (ix = 0; ix < PRIME_SIZE; ix++) {
      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
         *result = 1;
................................................................................

  /* passed the test */
  *result = MP_YES;
LBL_B:mp_clear (&b);
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_prime_miller_rabin.c.

1
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3
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5
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#include <tommath.h>
#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Miller-Rabin test of "a" to the base of "b" as described in 
 * HAC pp. 139 Algorithm 4.24
 *
 * Sets result to 0 if definitely composite or 1 if probably prime.
 * Randomly the chance of error is no more than 1/4 and often 
................................................................................
    goto LBL_R;
  }
  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
    goto LBL_Y;
  }

  /* if y != 1 and y != n1 do */
  if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
    j = 1;
    /* while j <= s-1 and y != n1 */
    while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
      if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
         goto LBL_Y;
      }

      /* if y == 1 then composite */
      if (mp_cmp_d (&y, 1) == MP_EQ) {
         goto LBL_Y;
................................................................................
  *result = MP_YES;
LBL_Y:mp_clear (&y);
LBL_R:mp_clear (&r);
LBL_N1:mp_clear (&n1);
  return err;
}
#endif




|













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|







 







>
>
>
>
1
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63
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#include <tommath_private.h>
#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Miller-Rabin test of "a" to the base of "b" as described in 
 * HAC pp. 139 Algorithm 4.24
 *
 * Sets result to 0 if definitely composite or 1 if probably prime.
 * Randomly the chance of error is no more than 1/4 and often 
................................................................................
    goto LBL_R;
  }
  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
    goto LBL_Y;
  }

  /* if y != 1 and y != n1 do */
  if ((mp_cmp_d (&y, 1) != MP_EQ) && (mp_cmp (&y, &n1) != MP_EQ)) {
    j = 1;
    /* while j <= s-1 and y != n1 */
    while ((j <= (s - 1)) && (mp_cmp (&y, &n1) != MP_EQ)) {
      if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
         goto LBL_Y;
      }

      /* if y == 1 then composite */
      if (mp_cmp_d (&y, 1) == MP_EQ) {
         goto LBL_Y;
................................................................................
  *result = MP_YES;
LBL_Y:mp_clear (&y);
LBL_R:mp_clear (&r);
LBL_N1:mp_clear (&n1);
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_prime_next_prime.c.

1
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160
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#include <tommath.h>
#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* finds the next prime after the number "a" using "t" trials
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
   int      err, res, x, y;
   mp_digit res_tab[PRIME_SIZE], step, kstep;
   mp_int   b;

   /* ensure t is valid */
   if (t <= 0 || t > PRIME_SIZE) {
      return MP_VAL;
   }

   /* force positive */
   a->sign = MP_ZPOS;

   /* simple algo if a is less than the largest prime in the table */
................................................................................

   if (bbs_style == 1) {
      /* if a mod 4 != 3 subtract the correct value to make it so */
      if ((a->dp[0] & 3) != 3) {
         if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
      }
   } else {
      if (mp_iseven(a) == 1) {
         /* force odd */
         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
            return err;
         }
      }
   }

................................................................................
             }

             /* set flag if zero */
             if (res_tab[x] == 0) {
                y = 1;
             }
         }
      } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));

      /* add the step */
      if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
         goto LBL_ERR;
      }

      /* if didn't pass sieve and step == MAX then skip test */
      if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
         continue;
      }

      /* is this prime? */
      for (x = 0; x < t; x++) {
          mp_set(&b, ltm_prime_tab[x]);
          if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
................................................................................
   err = MP_OKAY;
LBL_ERR:
   mp_clear(&b);
   return err;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* finds the next prime after the number "a" using "t" trials
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
   int      err, res = MP_NO, x, y;
   mp_digit res_tab[PRIME_SIZE], step, kstep;
   mp_int   b;

   /* ensure t is valid */
   if ((t <= 0) || (t > PRIME_SIZE)) {
      return MP_VAL;
   }

   /* force positive */
   a->sign = MP_ZPOS;

   /* simple algo if a is less than the largest prime in the table */
................................................................................

   if (bbs_style == 1) {
      /* if a mod 4 != 3 subtract the correct value to make it so */
      if ((a->dp[0] & 3) != 3) {
         if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
      }
   } else {
      if (mp_iseven(a) == MP_YES) {
         /* force odd */
         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
            return err;
         }
      }
   }

................................................................................
             }

             /* set flag if zero */
             if (res_tab[x] == 0) {
                y = 1;
             }
         }
      } while ((y == 1) && (step < ((((mp_digit)1) << DIGIT_BIT) - kstep)));

      /* add the step */
      if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
         goto LBL_ERR;
      }

      /* if didn't pass sieve and step == MAX then skip test */
      if ((y == 1) && (step >= ((((mp_digit)1) << DIGIT_BIT) - kstep))) {
         continue;
      }

      /* is this prime? */
      for (x = 0; x < t; x++) {
          mp_set(&b, ltm_prime_tab[x]);
          if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
................................................................................
   err = MP_OKAY;
LBL_ERR:
   mp_clear(&b);
   return err;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_prime_rabin_miller_trials.c.

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#include <tommath.h>
#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */


static const struct {
   int k, t;
} sizes[] = {
{   128,    28 },
................................................................................
       }
   }
   return sizes[x-1].t + 1;
}


#endif




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#include <tommath_private.h>
#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */


static const struct {
   int k, t;
} sizes[] = {
{   128,    28 },
................................................................................
       }
   }
   return sizes[x-1].t + 1;
}


#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_prime_random_ex.c.

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#include <tommath.h>
#ifdef BN_MP_PRIME_RANDOM_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 * 
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
 *   LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
 *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 */
................................................................................
/* This is possibly the mother of all prime generation functions, muahahahahaha! */
int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
{
   unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
   int res, err, bsize, maskOR_msb_offset;

   /* sanity check the input */
   if (size <= 1 || t <= 0) {
      return MP_VAL;
   }

   /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
   if (flags & LTM_PRIME_SAFE) {
      flags |= LTM_PRIME_BBS;
   }

   /* calc the byte size */
   bsize = (size>>3) + ((size&7)?1:0);

   /* we need a buffer of bsize bytes */
................................................................................

   /* calc the maskAND value for the MSbyte*/
   maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));

   /* calc the maskOR_msb */
   maskOR_msb        = 0;
   maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
   if (flags & LTM_PRIME_2MSB_ON) {
      maskOR_msb       |= 0x80 >> ((9 - size) & 7);
   }  

   /* get the maskOR_lsb */
   maskOR_lsb         = 1;
   if (flags & LTM_PRIME_BBS) {
      maskOR_lsb     |= 3;
   }

   do {
      /* read the bytes */
      if (cb(tmp, bsize, dat) != bsize) {
         err = MP_VAL;
................................................................................

      /* is it prime? */
      if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)           { goto error; }
      if (res == MP_NO) {  
         continue;
      }

      if (flags & LTM_PRIME_SAFE) {
         /* see if (a-1)/2 is prime */
         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY)                    { goto error; }
         if ((err = mp_div_2(a, a)) != MP_OKAY)                       { goto error; }
 
         /* is it prime? */
         if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)        { goto error; }
      }
   } while (res == MP_NO);

   if (flags & LTM_PRIME_SAFE) {
      /* restore a to the original value */
      if ((err = mp_mul_2(a, a)) != MP_OKAY)                          { goto error; }
      if ((err = mp_add_d(a, 1, a)) != MP_OKAY)                       { goto error; }
   }

   err = MP_OKAY;
error:
   XFREE(tmp);
   return err;
}


#endif




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#include <tommath_private.h>
#ifdef BN_MP_PRIME_RANDOM_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 * 
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)

 *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 */
................................................................................
/* This is possibly the mother of all prime generation functions, muahahahahaha! */
int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
{
   unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
   int res, err, bsize, maskOR_msb_offset;

   /* sanity check the input */
   if ((size <= 1) || (t <= 0)) {
      return MP_VAL;
   }

   /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
   if ((flags & LTM_PRIME_SAFE) != 0) {
      flags |= LTM_PRIME_BBS;
   }

   /* calc the byte size */
   bsize = (size>>3) + ((size&7)?1:0);

   /* we need a buffer of bsize bytes */
................................................................................

   /* calc the maskAND value for the MSbyte*/
   maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));

   /* calc the maskOR_msb */
   maskOR_msb        = 0;
   maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
   if ((flags & LTM_PRIME_2MSB_ON) != 0) {
      maskOR_msb       |= 0x80 >> ((9 - size) & 7);
   }  

   /* get the maskOR_lsb */
   maskOR_lsb         = 1;
   if ((flags & LTM_PRIME_BBS) != 0) {
      maskOR_lsb     |= 3;
   }

   do {
      /* read the bytes */
      if (cb(tmp, bsize, dat) != bsize) {
         err = MP_VAL;
................................................................................

      /* is it prime? */
      if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)           { goto error; }
      if (res == MP_NO) {  
         continue;
      }

      if ((flags & LTM_PRIME_SAFE) != 0) {
         /* see if (a-1)/2 is prime */
         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY)                    { goto error; }
         if ((err = mp_div_2(a, a)) != MP_OKAY)                       { goto error; }
 
         /* is it prime? */
         if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)        { goto error; }
      }
   } while (res == MP_NO);

   if ((flags & LTM_PRIME_SAFE) != 0) {
      /* restore a to the original value */
      if ((err = mp_mul_2(a, a)) != MP_OKAY)                          { goto error; }
      if ((err = mp_add_d(a, 1, a)) != MP_OKAY)                       { goto error; }
   }

   err = MP_OKAY;
error:
   XFREE(tmp);
   return err;
}


#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_RADIX_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tom[email protected], http://libtom.org
 */

/* returns size of ASCII reprensentation */
int mp_radix_size (mp_int * a, int radix, int *size)
{
  int     res, digs;
  mp_int  t;
  mp_digit d;

  *size = 0;

  /* special case for binary */
  if (radix == 2) {
    *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
    return MP_OKAY;
  }

  /* make sure the radix is in range */
  if (radix < 2 || radix > 64) {

    return MP_VAL;
  }

  if (mp_iszero(a) == MP_YES) {
    *size = 2;
    return MP_OKAY;
  }







  /* digs is the digit count */
  digs = 0;

  /* if it's negative add one for the sign */
  if (a->sign == MP_NEG) {
    ++digs;
................................................................................
  *size = digs + 1;
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision: 0.41 $ */
/* $Date: 2007-04-18 09:58:18 +0000 $ */
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#include <tommath_private.h>
#ifdef BN_MP_RADIX_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* returns size of ASCII reprensentation */
int mp_radix_size (const mp_int * a, int radix, int *size)
{
  int     res, digs;
  mp_int  t;
  mp_digit d;

  *size = 0;







  /* make sure the radix is in range */

  if ((radix < 2) || (radix > 64)) {
    return MP_VAL;
  }

  if (mp_iszero(a) == MP_YES) {
    *size = 2;
    return MP_OKAY;
  }

  /* special case for binary */
  if (radix == 2) {
    *size = mp_count_bits (a) + ((a->sign == MP_NEG) ? 1 : 0) + 1;
    return MP_OKAY;
  }

  /* digs is the digit count */
  digs = 0;

  /* if it's negative add one for the sign */
  if (a->sign == MP_NEG) {
    ++digs;
................................................................................
  *size = digs + 1;
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_RADIX_SMAP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
#endif




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#include <tommath_private.h>
#ifdef BN_MP_RADIX_SMAP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* makes a pseudo-random int of a given size */
int
mp_rand (mp_int * a, int digits)
{
  int     res;
................................................................................
  mp_zero (a);
  if (digits <= 0) {
    return MP_OKAY;
  }

  /* first place a random non-zero digit */
  do {
    d = ((mp_digit) abs (rand ())) & MP_MASK;
  } while (d == 0);

  if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
    return res;
  }

  while (--digits > 0) {
    if ((res = mp_lshd (a, 1)) != MP_OKAY) {
      return res;
    }

    if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) {
      return res;
    }
  }

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* makes a pseudo-random int of a given size */
int
mp_rand (mp_int * a, int digits)
{
  int     res;
................................................................................
  mp_zero (a);
  if (digits <= 0) {
    return MP_OKAY;
  }

  /* first place a random non-zero digit */
  do {
    d = ((mp_digit) abs (MP_GEN_RANDOM())) & MP_MASK;
  } while (d == 0);

  if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
    return res;
  }

  while (--digits > 0) {
    if ((res = mp_lshd (a, 1)) != MP_OKAY) {
      return res;
    }

    if ((res = mp_add_d (a, ((mp_digit) abs (MP_GEN_RANDOM())), a)) != MP_OKAY) {
      return res;
    }
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_read_radix.c.

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#include <tommath.h>
#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, const char *str, int radix)
{
  int     y, res, neg;
  char    ch;

  /* zero the digit bignum */
  mp_zero(a);

  /* make sure the radix is ok */
  if (radix < 2 || radix > 64) {
    return MP_VAL;
  }

  /* if the leading digit is a 
   * minus set the sign to negative. 
   */
  if (*str == '-') {
................................................................................
    neg = MP_ZPOS;
  }

  /* set the integer to the default of zero */
  mp_zero (a);
  
  /* process each digit of the string */
  while (*str) {
    /* if the radix < 36 the conversion is case insensitive
     * this allows numbers like 1AB and 1ab to represent the same  value
     * [e.g. in hex]
     */
    ch = (char) ((radix < 36) ? toupper ((unsigned char) *str) : *str);
    for (y = 0; y < 64; y++) {
      if (ch == mp_s_rmap[y]) {
         break;
      }
    }

    /* if the char was found in the map 
................................................................................

  if ( *str != '\0' ) {
      mp_zero( a );
      return MP_VAL;
  }

  /* set the sign only if a != 0 */
  if (mp_iszero(a) != 1) {
     a->sign = neg;
  }
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, const char *str, int radix)
{
  int     y, res, neg;
  char    ch;

  /* zero the digit bignum */
  mp_zero(a);

  /* make sure the radix is ok */
  if ((radix < 2) || (radix > 64)) {
    return MP_VAL;
  }

  /* if the leading digit is a 
   * minus set the sign to negative. 
   */
  if (*str == '-') {
................................................................................
    neg = MP_ZPOS;
  }

  /* set the integer to the default of zero */
  mp_zero (a);
  
  /* process each digit of the string */
  while (*str != '\0') {
    /* if the radix <= 36 the conversion is case insensitive
     * this allows numbers like 1AB and 1ab to represent the same  value
     * [e.g. in hex]
     */
    ch = (radix <= 36) ? (char)toupper((unsigned char)*str) : *str;
    for (y = 0; y < 64; y++) {
      if (ch == mp_s_rmap[y]) {
         break;
      }
    }

    /* if the char was found in the map 
................................................................................

  if ( *str != '\0' ) {
      mp_zero( a );
      return MP_VAL;
  }

  /* set the sign only if a != 0 */
  if (mp_iszero(a) != MP_YES) {
     a->sign = neg;
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_read_signed_bin.c.

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#include <tommath.h>
#ifdef BN_MP_READ_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
{
  int     res;

................................................................................
  } else {
     a->sign = MP_NEG;
  }

  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_READ_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
{
  int     res;

................................................................................
  } else {
     a->sign = MP_NEG;
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_read_unsigned_bin.c.

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#include <tommath.h>
#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
{
  int     res;

................................................................................
  /* read the bytes in */
  while (c-- > 0) {
    if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
      return res;
    }

#ifndef MP_8BIT
      a->dp[0] |= *b++;
      a->used += 1;
#else
      a->dp[0] = (*b & MP_MASK);
      a->dp[1] |= ((*b++ >> 7U) & 1);
      a->used += 2;
#endif
  }
  mp_clamp (a);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
{
  int     res;

................................................................................
  /* read the bytes in */
  while (c-- > 0) {
    if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
      return res;
    }

#ifndef MP_8BIT
    a->dp[0] |= *b++;
    a->used += 1;
#else
    a->dp[0] = (*b & MP_MASK);
    a->dp[1] |= ((*b++ >> 7U) & 1);
    a->used += 2;
#endif
  }
  mp_clamp (a);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_reduce.c.

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#include <tommath.h>
#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reduces x mod m, assumes 0 < x < m**2, mu is 
 * precomputed via mp_reduce_setup.
 * From HAC pp.604 Algorithm 14.42
 */
int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
{
  mp_int  q;
  int     res, um = m->used;
................................................................................

  /* q = x */
  if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
    return res;
  }

  /* q1 = x / b**(k-1)  */
  mp_rshd (&q, um - 1);         

  /* according to HAC this optimization is ok */
  if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
    if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
      goto CLEANUP;
    }
  } else {
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
    if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
    if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
#else 
    { 
      res = MP_VAL;
      goto CLEANUP;
    }
#endif
  }

  /* q3 = q2 / b**(k+1) */
  mp_rshd (&q, um + 1);         

  /* x = x mod b**(k+1), quick (no division) */
  if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
    goto CLEANUP;
  }

  /* q = q * m mod b**(k+1), quick (no division) */
................................................................................

  /* Back off if it's too big */
  while (mp_cmp (x, m) != MP_LT) {
    if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
      goto CLEANUP;
    }
  }
  
CLEANUP:
  mp_clear (&q);

  return res;
}
#endif




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>
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#include <tommath_private.h>
#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reduces x mod m, assumes 0 < x < m**2, mu is
 * precomputed via mp_reduce_setup.
 * From HAC pp.604 Algorithm 14.42
 */
int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
{
  mp_int  q;
  int     res, um = m->used;
................................................................................

  /* q = x */
  if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
    return res;
  }

  /* q1 = x / b**(k-1)  */
  mp_rshd (&q, um - 1);

  /* according to HAC this optimization is ok */
  if (((mp_digit) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
    if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
      goto CLEANUP;
    }
  } else {
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
    if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
    if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
#else
    {
      res = MP_VAL;
      goto CLEANUP;
    }
#endif
  }

  /* q3 = q2 / b**(k+1) */
  mp_rshd (&q, um + 1);

  /* x = x mod b**(k+1), quick (no division) */
  if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
    goto CLEANUP;
  }

  /* q = q * m mod b**(k+1), quick (no division) */
................................................................................

  /* Back off if it's too big */
  while (mp_cmp (x, m) != MP_LT) {
    if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
      goto CLEANUP;
    }
  }

CLEANUP:
  mp_clear (&q);

  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_reduce_2k.c.

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49
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#include <tommath.h>
#ifdef BN_MP_REDUCE_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reduces a modulo n where n is of the form 2**p - d */
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
{
   mp_int q;
   int    p, res;
   
   if ((res = mp_init(&q)) != MP_OKAY) {
      return res;
   }
   
   p = mp_count_bits(n);    
top:
   /* q = a/2**p, a = a mod 2**p */
   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
      goto ERR;
   }
   
   if (d != 1) {
      /* q = q * d */
      if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) { 
         goto ERR;
      }
   }
   
   /* a = a + q */
   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
      goto ERR;
   }
   
   if (mp_cmp_mag(a, n) != MP_LT) {
      s_mp_sub(a, n, a);


      goto top;
   }
   
ERR:
   mp_clear(&q);
   return res;
}

#endif




|













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>
>


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>
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#include <tommath_private.h>
#ifdef BN_MP_REDUCE_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reduces a modulo n where n is of the form 2**p - d */
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
{
   mp_int q;
   int    p, res;

   if ((res = mp_init(&q)) != MP_OKAY) {
      return res;
   }

   p = mp_count_bits(n);
top:
   /* q = a/2**p, a = a mod 2**p */
   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
      goto ERR;
   }

   if (d != 1) {
      /* q = q * d */
      if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
         goto ERR;
      }
   }

   /* a = a + q */
   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
      goto ERR;
   }

   if (mp_cmp_mag(a, n) != MP_LT) {
      if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
         goto ERR;
      }
      goto top;
   }

ERR:
   mp_clear(&q);
   return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_reduce_2k_l.c.

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#include <tommath.h>
#ifdef BN_MP_REDUCE_2K_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reduces a modulo n where n is of the form 2**p - d 
   This differs from reduce_2k since "d" can be larger
   than a single digit.
*/
int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
{
   mp_int q;
   int    p, res;
   
   if ((res = mp_init(&q)) != MP_OKAY) {
      return res;
   }
   
   p = mp_count_bits(n);    
top:
   /* q = a/2**p, a = a mod 2**p */
   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
      goto ERR;
   }
   
   /* q = q * d */
   if ((res = mp_mul(&q, d, &q)) != MP_OKAY) { 
      goto ERR;
   }
   
   /* a = a + q */
   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
      goto ERR;
   }
   
   if (mp_cmp_mag(a, n) != MP_LT) {
      s_mp_sub(a, n, a);


      goto top;
   }
   
ERR:
   mp_clear(&q);
   return res;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_REDUCE_2K_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reduces a modulo n where n is of the form 2**p - d
   This differs from reduce_2k since "d" can be larger
   than a single digit.
*/
int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
{
   mp_int q;
   int    p, res;

   if ((res = mp_init(&q)) != MP_OKAY) {
      return res;
   }

   p = mp_count_bits(n);
top:
   /* q = a/2**p, a = a mod 2**p */
   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
      goto ERR;
   }

   /* q = q * d */
   if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
      goto ERR;
   }

   /* a = a + q */
   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
      goto ERR;
   }

   if (mp_cmp_mag(a, n) != MP_LT) {
      if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
         goto ERR;
      }
      goto top;
   }

ERR:
   mp_clear(&q);
   return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_reduce_2k_setup.c.

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#include <tommath.h>
#ifdef BN_MP_REDUCE_2K_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines the setup value */
int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
{
   int res, p;
   mp_int tmp;
................................................................................
   }
   
   *d = tmp.dp[0];
   mp_clear(&tmp);
   return MP_OKAY;
}
#endif




|













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#include <tommath_private.h>
#ifdef BN_MP_REDUCE_2K_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines the setup value */
int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
{
   int res, p;
   mp_int tmp;
................................................................................
   }
   
   *d = tmp.dp[0];
   mp_clear(&tmp);
   return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_reduce_2k_setup_l.c.

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#include <tommath.h>
#ifdef BN_MP_REDUCE_2K_SETUP_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines the setup value */
int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
{
   int    res;
   mp_int tmp;
................................................................................
   }
   
ERR:
   mp_clear(&tmp);
   return res;
}
#endif




|













|







 







>
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#include <tommath_private.h>
#ifdef BN_MP_REDUCE_2K_SETUP_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines the setup value */
int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
{
   int    res;
   mp_int tmp;
................................................................................
   }
   
ERR:
   mp_clear(&tmp);
   return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_reduce_is_2k.c.

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#include <tommath.h>
#ifdef BN_MP_REDUCE_IS_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(mp_int *a)
{
   int ix, iy, iw;
   mp_digit iz;
................................................................................
          }
      }
   }
   return MP_YES;
}

#endif




|













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#include <tommath_private.h>
#ifdef BN_MP_REDUCE_IS_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(mp_int *a)
{
   int ix, iy, iw;
   mp_digit iz;
................................................................................
          }
      }
   }
   return MP_YES;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_reduce_is_2k_l.c.

1
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#include <tommath.h>
#ifdef BN_MP_REDUCE_IS_2K_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines if reduce_2k_l can be used */
int mp_reduce_is_2k_l(mp_int *a)
{
   int ix, iy;
   
................................................................................
      return (iy >= (a->used/2)) ? MP_YES : MP_NO;
      
   }
   return MP_NO;
}

#endif




|













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>
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#include <tommath_private.h>
#ifdef BN_MP_REDUCE_IS_2K_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines if reduce_2k_l can be used */
int mp_reduce_is_2k_l(mp_int *a)
{
   int ix, iy;
   
................................................................................
      return (iy >= (a->used/2)) ? MP_YES : MP_NO;
      
   }
   return MP_NO;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_reduce_setup.c.

1
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#include <tommath.h>
#ifdef BN_MP_REDUCE_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* pre-calculate the value required for Barrett reduction
 * For a given modulus "b" it calulates the value required in "a"
 */
int mp_reduce_setup (mp_int * a, mp_int * b)
{
................................................................................
  
  if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
    return res;
  }
  return mp_div (a, b, a, NULL);
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_REDUCE_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* pre-calculate the value required for Barrett reduction
 * For a given modulus "b" it calulates the value required in "a"
 */
int mp_reduce_setup (mp_int * a, mp_int * b)
{
................................................................................
  
  if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
    return res;
  }
  return mp_div (a, b, a, NULL);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shift right a certain amount of digits */
void mp_rshd (mp_int * a, int b)
{
  int     x;

................................................................................
  /* if b > used then simply zero it and return */
  if (a->used <= b) {
    mp_zero (a);
    return;
  }

  {
    register mp_digit *bottom, *top;

    /* shift the digits down */

    /* bottom */
    bottom = a->dp;

    /* top [offset into digits] */
................................................................................
    }
  }
  
  /* remove excess digits */
  a->used -= b;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shift right a certain amount of digits */
void mp_rshd (mp_int * a, int b)
{
  int     x;

................................................................................
  /* if b > used then simply zero it and return */
  if (a->used <= b) {
    mp_zero (a);
    return;
  }

  {
    mp_digit *bottom, *top;

    /* shift the digits down */

    /* bottom */
    bottom = a->dp;

    /* top [offset into digits] */
................................................................................
    }
  }
  
  /* remove excess digits */
  a->used -= b;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* set to a digit */
void mp_set (mp_int * a, mp_digit b)
{
  mp_zero (a);
  a->dp[0] = b & MP_MASK;
  a->used  = (a->dp[0] != 0) ? 1 : 0;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* set to a digit */
void mp_set (mp_int * a, mp_digit b)
{
  mp_zero (a);
  a->dp[0] = b & MP_MASK;
  a->used  = (a->dp[0] != 0) ? 1 : 0;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* set a 32-bit const */
int mp_set_int (mp_int * a, unsigned long b)
{
  int     x, res;

................................................................................
    /* ensure that digits are not clamped off */
    a->used += 1;
  }
  mp_clamp (a);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* set a 32-bit const */
int mp_set_int (mp_int * a, unsigned long b)
{
  int     x, res;

................................................................................
    /* ensure that digits are not clamped off */
    a->used += 1;
  }
  mp_clamp (a);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Added libtommath/bn_mp_set_long.c.
















































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#include <tommath_private.h>
#ifdef BN_MP_SET_LONG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* set a platform dependent unsigned long int */
MP_SET_XLONG(mp_set_long, unsigned long)
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Added libtommath/bn_mp_set_long_long.c.
















































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#include <tommath_private.h>
#ifdef BN_MP_SET_LONG_LONG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* set a platform dependent unsigned long long int */
MP_SET_XLONG(mp_set_long_long, unsigned long long)
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shrink a bignum */
int mp_shrink (mp_int * a)
{
  mp_digit *tmp;
  int used = 1;
  
  if(a->used > 0)
    used = a->used;

  
  if (a->alloc != used) {
    if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * used)) == NULL) {
      return MP_MEM;
    }
    a->dp    = tmp;
    a->alloc = used;
  }
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shrink a bignum */
int mp_shrink (mp_int * a)
{
  mp_digit *tmp;
  int used = 1;
  
  if(a->used > 0) {
    used = a->used;
  }
  
  if (a->alloc != used) {
    if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * used)) == NULL) {
      return MP_MEM;
    }
    a->dp    = tmp;
    a->alloc = used;
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_SIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* get the size for an signed equivalent */
int mp_signed_bin_size (mp_int * a)
{
  return 1 + mp_unsigned_bin_size (a);
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_SIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* get the size for an signed equivalent */
int mp_signed_bin_size (mp_int * a)
{
  return 1 + mp_unsigned_bin_size (a);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes b = a*a */
int
mp_sqr (mp_int * a, mp_int * b)
{
  int     res;
................................................................................
  /* use Toom-Cook? */
  if (a->used >= TOOM_SQR_CUTOFF) {
    res = mp_toom_sqr(a, b);
  /* Karatsuba? */
  } else 
#endif
#ifdef BN_MP_KARATSUBA_SQR_C
if (a->used >= KARATSUBA_SQR_CUTOFF) {
    res = mp_karatsuba_sqr (a, b);
  } else 
#endif
  {
#ifdef BN_FAST_S_MP_SQR_C
    /* can we use the fast comba multiplier? */
    if ((a->used * 2 + 1) < MP_WARRAY && 
         a->used < 
         (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
      res = fast_s_mp_sqr (a, b);
    } else
#endif

#ifdef BN_S_MP_SQR_C
      res = s_mp_sqr (a, b);
#else
      res = MP_VAL;
#endif

  }
  b->sign = MP_ZPOS;
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes b = a*a */
int
mp_sqr (mp_int * a, mp_int * b)
{
  int     res;
................................................................................
  /* use Toom-Cook? */
  if (a->used >= TOOM_SQR_CUTOFF) {
    res = mp_toom_sqr(a, b);
  /* Karatsuba? */
  } else 
#endif
#ifdef BN_MP_KARATSUBA_SQR_C
  if (a->used >= KARATSUBA_SQR_CUTOFF) {
    res = mp_karatsuba_sqr (a, b);
  } else 
#endif
  {
#ifdef BN_FAST_S_MP_SQR_C
    /* can we use the fast comba multiplier? */
    if ((((a->used * 2) + 1) < MP_WARRAY) &&
         (a->used <
         (1 << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) - 1)))) {
      res = fast_s_mp_sqr (a, b);
    } else
#endif
    {
#ifdef BN_S_MP_SQR_C
      res = s_mp_sqr (a, b);
#else
      res = MP_VAL;
#endif
    }
  }
  b->sign = MP_ZPOS;
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_sqrmod.c.

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#include <tommath.h>
#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* c = a * a (mod b) */
int
mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, b, c);
  mp_clear (&t);
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* c = a * a (mod b) */
int
mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, b, c);
  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_sqrt.c.

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#include <tommath.h>

#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

#ifndef NO_FLOATING_POINT
#include <math.h>
#endif

/* this function is less generic than mp_n_root, simpler and faster */
................................................................................

E1: mp_clear(&t2);
E2: mp_clear(&t1);
  return res;
}

#endif




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#include <tommath_private.h>

#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

#ifndef NO_FLOATING_POINT
#include <math.h>
#endif

/* this function is less generic than mp_n_root, simpler and faster */
................................................................................

E1: mp_clear(&t2);
E2: mp_clear(&t1);
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Added libtommath/bn_mp_sqrtmod_prime.c.
























































































































































































































































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#include <tommath_private.h>
#ifdef BN_MP_SQRTMOD_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* Tonelli-Shanks algorithm
 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
 *
 */

int mp_sqrtmod_prime(mp_int *n, mp_int *prime, mp_int *ret)
{
  int res, legendre;
  mp_int t1, C, Q, S, Z, M, T, R, two;
  mp_digit i;

  /* first handle the simple cases */
  if (mp_cmp_d(n, 0) == MP_EQ) {
    mp_zero(ret);
    return MP_OKAY;
  }
  if (mp_cmp_d(prime, 2) == MP_EQ)                              return MP_VAL; /* prime must be odd */
  if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY)        return res;
  if (legendre == -1)                                           return MP_VAL; /* quadratic non-residue mod prime */

  if ((res = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
	return res;
  }

  /* SPECIAL CASE: if prime mod 4 == 3
   * compute directly: res = n^(prime+1)/4 mod prime
   * Handbook of Applied Cryptography algorithm 3.36
   */
  if ((res = mp_mod_d(prime, 4, &i)) != MP_OKAY)                goto cleanup;
  if (i == 3) {
    if ((res = mp_add_d(prime, 1, &t1)) != MP_OKAY)             goto cleanup;
    if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                  goto cleanup;
    if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                  goto cleanup;
    if ((res = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY)      goto cleanup;
    res = MP_OKAY;
    goto cleanup;
  }

  /* NOW: Tonelli-Shanks algorithm */

  /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */
  if ((res = mp_copy(prime, &Q)) != MP_OKAY)                    goto cleanup;
  if ((res = mp_sub_d(&Q, 1, &Q)) != MP_OKAY)                   goto cleanup;
  /* Q = prime - 1 */
  mp_zero(&S);
  /* S = 0 */
  while (mp_iseven(&Q) != MP_NO) {
    if ((res = mp_div_2(&Q, &Q)) != MP_OKAY)                    goto cleanup;
    /* Q = Q / 2 */
    if ((res = mp_add_d(&S, 1, &S)) != MP_OKAY)                 goto cleanup;
    /* S = S + 1 */
  }

  /* find a Z such that the Legendre symbol (Z|prime) == -1 */
  if ((res = mp_set_int(&Z, 2)) != MP_OKAY)                     goto cleanup;
  /* Z = 2 */
  while(1) {
    if ((res = mp_jacobi(&Z, prime, &legendre)) != MP_OKAY)     goto cleanup;
    if (legendre == -1) break;
    if ((res = mp_add_d(&Z, 1, &Z)) != MP_OKAY)                 goto cleanup;
    /* Z = Z + 1 */
  }

  if ((res = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY)         goto cleanup;
  /* C = Z ^ Q mod prime */
  if ((res = mp_add_d(&Q, 1, &t1)) != MP_OKAY)                  goto cleanup;
  if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                    goto cleanup;
  /* t1 = (Q + 1) / 2 */
  if ((res = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY)         goto cleanup;
  /* R = n ^ ((Q + 1) / 2) mod prime */
  if ((res = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY)          goto cleanup;
  /* T = n ^ Q mod prime */
  if ((res = mp_copy(&S, &M)) != MP_OKAY)                       goto cleanup;
  /* M = S */
  if ((res = mp_set_int(&two, 2)) != MP_OKAY)                   goto cleanup;

  res = MP_VAL;
  while (1) {
    if ((res = mp_copy(&T, &t1)) != MP_OKAY)                    goto cleanup;
    i = 0;
    while (1) {
      if (mp_cmp_d(&t1, 1) == MP_EQ) break;
      if ((res = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
      i++;
    }
    if (i == 0) {
      if ((res = mp_copy(&R, ret)) != MP_OKAY)                  goto cleanup;
      res = MP_OKAY;
      goto cleanup;
    }
    if ((res = mp_sub_d(&M, i, &t1)) != MP_OKAY)                goto cleanup;
    if ((res = mp_sub_d(&t1, 1, &t1)) != MP_OKAY)               goto cleanup;
    if ((res = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY)   goto cleanup;
    /* t1 = 2 ^ (M - i - 1) */
    if ((res = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY)     goto cleanup;
    /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
    if ((res = mp_sqrmod(&t1, prime, &C)) != MP_OKAY)           goto cleanup;
    /* C = (t1 * t1) mod prime */
    if ((res = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY)       goto cleanup;
    /* R = (R * t1) mod prime */
    if ((res = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY)        goto cleanup;
    /* T = (T * C) mod prime */
    mp_set(&M, i);
    /* M = i */
  }

cleanup:
  mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
  return res;
}

#endif

Changes to libtommath/bn_mp_sub.c.

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#include <tommath.h>
#ifdef BN_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* high level subtraction (handles signs) */
int
mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
  int     sa, sb, res;
................................................................................
      res = s_mp_sub (b, a, c);
    }
  }
  return res;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* high level subtraction (handles signs) */
int
mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
  int     sa, sb, res;
................................................................................
      res = s_mp_sub (b, a, c);
    }
  }
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_SUB_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* single digit subtraction */
int
mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
{
  mp_digit *tmpa, *tmpc, mu;
  int       res, ix, oldused;

  /* grow c as required */
  if (c->alloc < a->used + 1) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }

  /* if a is negative just do an unsigned
   * addition [with fudged signs]
................................................................................

  /* setup regs */
  oldused = c->used;
  tmpa    = a->dp;
  tmpc    = c->dp;

  /* if a <= b simply fix the single digit */
  if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
     if (a->used == 1) {
        *tmpc++ = b - *tmpa;
     } else {
        *tmpc++ = b;
     }
     ix      = 1;

................................................................................
  } else {
     /* positive/size */
     c->sign = MP_ZPOS;
     c->used = a->used;

     /* subtract first digit */
     *tmpc    = *tmpa++ - b;
     mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
     *tmpc++ &= MP_MASK;

     /* handle rest of the digits */
     for (ix = 1; ix < a->used; ix++) {
        *tmpc    = *tmpa++ - mu;
        mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
        *tmpc++ &= MP_MASK;
     }
  }

  /* zero excess digits */
  while (ix++ < oldused) {
     *tmpc++ = 0;
  }
  mp_clamp(c);
  return MP_OKAY;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_SUB_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* single digit subtraction */
int
mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
{
  mp_digit *tmpa, *tmpc, mu;
  int       res, ix, oldused;

  /* grow c as required */
  if (c->alloc < (a->used + 1)) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }

  /* if a is negative just do an unsigned
   * addition [with fudged signs]
................................................................................

  /* setup regs */
  oldused = c->used;
  tmpa    = a->dp;
  tmpc    = c->dp;

  /* if a <= b simply fix the single digit */
  if (((a->used == 1) && (a->dp[0] <= b)) || (a->used == 0)) {
     if (a->used == 1) {
        *tmpc++ = b - *tmpa;
     } else {
        *tmpc++ = b;
     }
     ix      = 1;

................................................................................
  } else {
     /* positive/size */
     c->sign = MP_ZPOS;
     c->used = a->used;

     /* subtract first digit */
     *tmpc    = *tmpa++ - b;
     mu       = *tmpc >> ((sizeof(mp_digit) * CHAR_BIT) - 1);
     *tmpc++ &= MP_MASK;

     /* handle rest of the digits */
     for (ix = 1; ix < a->used; ix++) {
        *tmpc    = *tmpa++ - mu;
        mu       = *tmpc >> ((sizeof(mp_digit) * CHAR_BIT) - 1);
        *tmpc++ &= MP_MASK;
     }
  }

  /* zero excess digits */
  while (ix++ < oldused) {
     *tmpc++ = 0;
  }
  mp_clamp(c);
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* d = a - b (mod c) */
int
mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* d = a - b (mod c) */
int
mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_to_signed_bin.c.

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#include <tommath.h>
#ifdef BN_MP_TO_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* store in signed [big endian] format */
int mp_to_signed_bin (mp_int * a, unsigned char *b)
{
  int     res;

  if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
    return res;
  }
  b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_TO_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* store in signed [big endian] format */
int mp_to_signed_bin (mp_int * a, unsigned char *b)
{
  int     res;

  if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
    return res;
  }
  b[0] = (a->sign == MP_ZPOS) ? (unsigned char)0 : (unsigned char)1;
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_to_signed_bin_n.c.

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#include <tommath.h>
#ifdef BN_MP_TO_SIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* store in signed [big endian] format */
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
      return MP_VAL;
   }
   *outlen = mp_signed_bin_size(a);
   return mp_to_signed_bin(a, b);
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_TO_SIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* store in signed [big endian] format */
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
      return MP_VAL;
   }
   *outlen = mp_signed_bin_size(a);
   return mp_to_signed_bin(a, b);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_TO_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
{
  int     x, res;
  mp_int  t;

  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
    return res;
  }

  x = 0;
  while (mp_iszero (&t) == 0) {
#ifndef MP_8BIT
      b[x++] = (unsigned char) (t.dp[0] & 255);
#else
      b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
#endif
    if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
      mp_clear (&t);
................................................................................
    }
  }
  bn_reverse (b, x);
  mp_clear (&t);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_TO_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
{
  int     x, res;
  mp_int  t;

  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
    return res;
  }

  x = 0;
  while (mp_iszero (&t) == MP_NO) {
#ifndef MP_8BIT
      b[x++] = (unsigned char) (t.dp[0] & 255);
#else
      b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
#endif
    if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
      mp_clear (&t);
................................................................................
    }
  }
  bn_reverse (b, x);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_to_unsigned_bin_n.c.

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#include <tommath.h>
#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
      return MP_VAL;
   }
   *outlen = mp_unsigned_bin_size(a);
   return mp_to_unsigned_bin(a, b);
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
      return MP_VAL;
   }
   *outlen = mp_unsigned_bin_size(a);
   return mp_to_unsigned_bin(a, b);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* multiplication using the Toom-Cook 3-way algorithm 
 *
 * Much more complicated than Karatsuba but has a lower 
 * asymptotic running time of O(N**1.464).  This algorithm is 
 * only particularly useful on VERY large inputs 
 * (we're talking 1000s of digits here...).
*/
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
    mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
    int res, B;
        
    /* init temps */
    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, 
                             &a0, &a1, &a2, &b0, &b1, 
                             &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
       return res;
    }
    
    /* B */
    B = MIN(a->used, b->used) / 3;
    
    /* a = a2 * B**2 + a1 * B + a0 */
    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a1, B);
    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);



    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a2, B*2);
    
    /* b = b2 * B**2 + b1 * B + b0 */
    if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(b, &b1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&b1, B);
    mp_mod_2d(&b1, DIGIT_BIT * B, &b1);

    if ((res = mp_copy(b, &b2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&b2, B*2);
    
    /* w0 = a0*b0 */
    if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
       goto ERR;
    }
    
    /* w4 = a2 * b2 */
    if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
       goto ERR;
    }
    
    /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    
    if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    
    if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    
    /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    
    if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    
    if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    

    /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
       goto ERR;
................................................................................
    }
    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
       goto ERR;
    }
    
    /* now solve the matrix 
    
       0  0  0  0  1
       1  2  4  8  16
       1  1  1  1  1
       16 8  4  2  1
       1  0  0  0  0
       
       using 12 subtractions, 4 shifts, 
              2 small divisions and 1 small multiplication 
     */
     
     /* r1 - r4 */
     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r0 */
     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1/2 */
     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3/2 */
     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r2 - r0 - r4 */
     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - r2 */
     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r2 */
     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - 8r0 */
     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - 8r4 */
     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* 3r2 - r1 - r3 */
     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - r2 */
     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r2 */
     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1/3 */
     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
        goto ERR;
     }
     /* r3/3 */
     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
        goto ERR;
     }
     
     /* at this point shift W[n] by B*n */
     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
        goto ERR;
     }     
     
     if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
        goto ERR;
     }     
     
ERR:
     mp_clear_multi(&w0, &w1, &w2, &w3, &w4, 
                    &a0, &a1, &a2, &b0, &b1, 
                    &b2, &tmp1, &tmp2, NULL);
     return res;
}     
     
#endif




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#include <tommath_private.h>
#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* multiplication using the Toom-Cook 3-way algorithm
 *
 * Much more complicated than Karatsuba but has a lower
 * asymptotic running time of O(N**1.464).  This algorithm is
 * only particularly useful on VERY large inputs
 * (we're talking 1000s of digits here...).
*/
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
    mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
    int res, B;

    /* init temps */
    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
                             &a0, &a1, &a2, &b0, &b1,
                             &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
       return res;
    }

    /* B */
    B = MIN(a->used, b->used) / 3;

    /* a = a2 * B**2 + a1 * B + a0 */
    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a1, B);
    if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a2, B*2);

    /* b = b2 * B**2 + b1 * B + b0 */
    if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(b, &b1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&b1, B);
    (void)mp_mod_2d(&b1, DIGIT_BIT * B, &b1);

    if ((res = mp_copy(b, &b2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&b2, B*2);

    /* w0 = a0*b0 */
    if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
       goto ERR;
    }

    /* w4 = a2 * b2 */
    if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
       goto ERR;
    }

    /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
       goto ERR;
    }

    /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
       goto ERR;
    }


    /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
       goto ERR;
................................................................................
    }
    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
       goto ERR;
    }

    /* now solve the matrix

       0  0  0  0  1
       1  2  4  8  16
       1  1  1  1  1
       16 8  4  2  1
       1  0  0  0  0

       using 12 subtractions, 4 shifts,
              2 small divisions and 1 small multiplication
     */

    /* r1 - r4 */
    if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r0 */
    if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1/2 */
    if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3/2 */
    if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r2 - r0 - r4 */
    if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - r2 */
    if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r2 */
    if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - 8r0 */
    if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - 8r4 */
    if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* 3r2 - r1 - r3 */
    if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - r2 */
    if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r2 */
    if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1/3 */
    if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
       goto ERR;
    }
    /* r3/3 */
    if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
       goto ERR;
    }

    /* at this point shift W[n] by B*n */
    if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
       goto ERR;
    }

ERR:
    mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
                   &a0, &a1, &a2, &b0, &b1,
                   &b2, &tmp1, &tmp2, NULL);
    return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_toom_sqr.c.

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#include <tommath.h>
#ifdef BN_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* squaring using Toom-Cook 3-way algorithm */
int
mp_toom_sqr(mp_int *a, mp_int *b)
{
    mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
................................................................................
       goto ERR;
    }

    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a1, B);
    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);



    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a2, B*2);

    /* w0 = a0*a0 */
................................................................................
       1  1  1  1  1
       16 8  4  2  1
       1  0  0  0  0

       using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
     */

     /* r1 - r4 */
     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r0 */
     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1/2 */
     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3/2 */
     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r2 - r0 - r4 */
     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - r2 */
     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r2 */
     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - 8r0 */
     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - 8r4 */
     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* 3r2 - r1 - r3 */
     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - r2 */
     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r2 */
     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1/3 */
     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
        goto ERR;
     }
     /* r3/3 */
     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
        goto ERR;
     }

     /* at this point shift W[n] by B*n */
     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
        goto ERR;
     }

     if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
        goto ERR;
     }

ERR:
     mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
     return res;
}

#endif




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>
>
>
>
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2
3
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7
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9
10
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12
13
14
15
16
17
18
19
20
21
22
..
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
...
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
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#include <tommath_private.h>
#ifdef BN_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* squaring using Toom-Cook 3-way algorithm */
int
mp_toom_sqr(mp_int *a, mp_int *b)
{
    mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
................................................................................
       goto ERR;
    }

    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a1, B);
    if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a2, B*2);

    /* w0 = a0*a0 */
................................................................................
       1  1  1  1  1
       16 8  4  2  1
       1  0  0  0  0

       using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
     */

    /* r1 - r4 */
    if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r0 */
    if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1/2 */
    if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3/2 */
    if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r2 - r0 - r4 */
    if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - r2 */
    if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r2 */
    if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - 8r0 */
    if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - 8r4 */
    if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* 3r2 - r1 - r3 */
    if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - r2 */
    if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r2 */
    if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1/3 */
    if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
       goto ERR;
    }
    /* r3/3 */
    if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
       goto ERR;
    }

    /* at this point shift W[n] by B*n */
    if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
       goto ERR;
    }

ERR:
    mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
    return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_mp_toradix.c.

1
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#include <tommath.h>
#ifdef BN_MP_TORADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix (mp_int * a, char *str, int radix)
{
  int     res, digs;
  mp_int  t;
  mp_digit d;
  char   *_s = str;

  /* check range of the radix */
  if (radix < 2 || radix > 64) {
    return MP_VAL;
  }

  /* quick out if its zero */
  if (mp_iszero(a) == 1) {
     *str++ = '0';
     *str = '\0';
     return MP_OKAY;
  }

  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
    return res;
................................................................................
  if (t.sign == MP_NEG) {
    ++_s;
    *str++ = '-';
    t.sign = MP_ZPOS;
  }

  digs = 0;
  while (mp_iszero (&t) == 0) {
    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
      mp_clear (&t);
      return res;
    }
    *str++ = mp_s_rmap[d];
    ++digs;
  }
................................................................................
  *str = '\0';

  mp_clear (&t);
  return MP_OKAY;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_TORADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix (mp_int * a, char *str, int radix)
{
  int     res, digs;
  mp_int  t;
  mp_digit d;
  char   *_s = str;

  /* check range of the radix */
  if ((radix < 2) || (radix > 64)) {
    return MP_VAL;
  }

  /* quick out if its zero */
  if (mp_iszero(a) == MP_YES) {
     *str++ = '0';
     *str = '\0';
     return MP_OKAY;
  }

  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
    return res;
................................................................................
  if (t.sign == MP_NEG) {
    ++_s;
    *str++ = '-';
    t.sign = MP_ZPOS;
  }

  digs = 0;
  while (mp_iszero (&t) == MP_NO) {
    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
      mp_clear (&t);
      return res;
    }
    *str++ = mp_s_rmap[d];
    ++digs;
  }
................................................................................
  *str = '\0';

  mp_clear (&t);
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_TORADIX_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* stores a bignum as a ASCII string in a given radix (2..64) 
 *
 * Stores upto maxlen-1 chars and always a NULL byte 
 */
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
................................................................................
{
  int     res, digs;
  mp_int  t;
  mp_digit d;
  char   *_s = str;

  /* check range of the maxlen, radix */
  if (maxlen < 2 || radix < 2 || radix > 64) {
    return MP_VAL;
  }

  /* quick out if its zero */
  if (mp_iszero(a) == MP_YES) {
     *str++ = '0';
     *str = '\0';
................................................................................
    t.sign = MP_ZPOS;
 
    /* subtract a char */
    --maxlen;
  }

  digs = 0;
  while (mp_iszero (&t) == 0) {
    if (--maxlen < 1) {
       /* no more room */
       break;
    }
    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
      mp_clear (&t);
      return res;
................................................................................
  *str = '\0';

  mp_clear (&t);
  return MP_OKAY;
}

#endif




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#include <tommath_private.h>
#ifdef BN_MP_TORADIX_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* stores a bignum as a ASCII string in a given radix (2..64) 
 *
 * Stores upto maxlen-1 chars and always a NULL byte 
 */
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
................................................................................
{
  int     res, digs;
  mp_int  t;
  mp_digit d;
  char   *_s = str;

  /* check range of the maxlen, radix */
  if ((maxlen < 2) || (radix < 2) || (radix > 64)) {
    return MP_VAL;
  }

  /* quick out if its zero */
  if (mp_iszero(a) == MP_YES) {
     *str++ = '0';
     *str = '\0';
................................................................................
    t.sign = MP_ZPOS;
 
    /* subtract a char */
    --maxlen;
  }

  digs = 0;
  while (mp_iszero (&t) == MP_NO) {
    if (--maxlen < 1) {
       /* no more room */
       break;
    }
    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
      mp_clear (&t);
      return res;
................................................................................
  *str = '\0';

  mp_clear (&t);
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* get the size for an unsigned equivalent */
int mp_unsigned_bin_size (mp_int * a)
{
  int     size = mp_count_bits (a);
  return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* get the size for an unsigned equivalent */
int mp_unsigned_bin_size (mp_int * a)
{
  int     size = mp_count_bits (a);
  return (size / 8) + (((size & 7) != 0) ? 1 : 0);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_XOR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* XOR two ints together */
int
mp_xor (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
................................................................................
  }
  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_XOR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* XOR two ints together */
int
mp_xor (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
................................................................................
  }
  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_MP_ZERO_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* set to zero */
void mp_zero (mp_int * a)
{
  int       n;
  mp_digit *tmp;
................................................................................

  tmp = a->dp;
  for (n = 0; n < a->alloc; n++) {
     *tmp++ = 0;
  }
}
#endif




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#include <tommath_private.h>
#ifdef BN_MP_ZERO_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* set to zero */
void mp_zero (mp_int * a)
{
  int       n;
  mp_digit *tmp;
................................................................................

  tmp = a->dp;
  for (n = 0; n < a->alloc; n++) {
     *tmp++ = 0;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

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#include <tommath.h>
#ifdef BN_PRIME_TAB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */
const mp_digit ltm_prime_tab[] = {
  0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
  0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
  0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
  0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
#ifndef MP_8BIT
................................................................................
  0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
  0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
  0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
  0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
#endif
};
#endif




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#include <tommath_private.h>
#ifdef BN_PRIME_TAB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */
const mp_digit ltm_prime_tab[] = {
  0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
  0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
  0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
  0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
#ifndef MP_8BIT
................................................................................
  0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
  0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
  0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
  0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
#endif
};
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_reverse.c.

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#include <tommath.h>
#ifdef BN_REVERSE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reverse an array, used for radix code */
void
bn_reverse (unsigned char *s, int len)
{
  int     ix, iy;
................................................................................
    s[ix] = s[iy];
    s[iy] = t;
    ++ix;
    --iy;
  }
}
#endif




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#include <tommath_private.h>
#ifdef BN_REVERSE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reverse an array, used for radix code */
void
bn_reverse (unsigned char *s, int len)
{
  int     ix, iy;
................................................................................
    s[ix] = s[iy];
    s[iy] = t;
    ++ix;
    --iy;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_s_mp_add.c.

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#include <tommath.h>
#ifdef BN_S_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
s_mp_add (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int *x;
................................................................................
  } else {
    min = a->used;
    max = b->used;
    x = b;
  }

  /* init result */
  if (c->alloc < max + 1) {
    if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* get old used digit count and set new one */
  olduse = c->used;
  c->used = max + 1;

  {
    register mp_digit u, *tmpa, *tmpb, *tmpc;
    register int i;

    /* alias for digit pointers */

    /* first input */
    tmpa = a->dp;

    /* second input */
................................................................................
    }
  }

  mp_clamp (c);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_S_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
s_mp_add (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int *x;
................................................................................
  } else {
    min = a->used;
    max = b->used;
    x = b;
  }

  /* init result */
  if (c->alloc < (max + 1)) {
    if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* get old used digit count and set new one */
  olduse = c->used;
  c->used = max + 1;

  {
    mp_digit u, *tmpa, *tmpb, *tmpc;
    int i;

    /* alias for digit pointers */

    /* first input */
    tmpa = a->dp;

    /* second input */
................................................................................
    }
  }

  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_s_mp_exptmod.c.

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#include <tommath.h>
#ifdef BN_S_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */
#ifdef MP_LOW_MEM
   #define TAB_SIZE 32
#else
   #define TAB_SIZE 256
#endif

................................................................................
    buf <<= (mp_digit)1;

    /* if the bit is zero and mode == 0 then we ignore it
     * These represent the leading zero bits before the first 1 bit
     * in the exponent.  Technically this opt is not required but it
     * does lower the # of trivial squaring/reductions used
     */
    if (mode == 0 && y == 0) {
      continue;
    }

    /* if the bit is zero and mode == 1 then we square */
    if (mode == 1 && y == 0) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
        goto LBL_RES;
      }
      continue;
................................................................................
      bitcpy = 0;
      bitbuf = 0;
      mode   = 1;
    }
  }

  /* if bits remain then square/multiply */
  if (mode == 2 && bitcpy > 0) {
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
        goto LBL_RES;
................................................................................
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}
#endif




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#include <tommath_private.h>
#ifdef BN_S_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */
#ifdef MP_LOW_MEM
   #define TAB_SIZE 32
#else
   #define TAB_SIZE 256
#endif

................................................................................
    buf <<= (mp_digit)1;

    /* if the bit is zero and mode == 0 then we ignore it
     * These represent the leading zero bits before the first 1 bit
     * in the exponent.  Technically this opt is not required but it
     * does lower the # of trivial squaring/reductions used
     */
    if ((mode == 0) && (y == 0)) {
      continue;
    }

    /* if the bit is zero and mode == 1 then we square */
    if ((mode == 1) && (y == 0)) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
        goto LBL_RES;
      }
      continue;
................................................................................
      bitcpy = 0;
      bitbuf = 0;
      mode   = 1;
    }
  }

  /* if bits remain then square/multiply */
  if ((mode == 2) && (bitcpy > 0)) {
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
        goto LBL_RES;
................................................................................
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_s_mp_mul_digs.c.

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#include <tommath.h>
#ifdef BN_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* multiplies |a| * |b| and only computes upto digs digits of result
 * HAC pp. 595, Algorithm 14.12  Modified so you can control how 
 * many digits of output are created.
 */
int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
................................................................................
  int     res, pa, pb, ix, iy;
  mp_digit u;
  mp_word r;
  mp_digit tmpx, *tmpt, *tmpy;

  /* can we use the fast multiplier? */
  if (((digs) < MP_WARRAY) &&
      MIN (a->used, b->used) < 
          (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
    return fast_s_mp_mul_digs (a, b, c, digs);
  }

  if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
    return res;
  }
  t.used = digs;
................................................................................
    
    /* an alias for the digits of b */
    tmpy = b->dp;

    /* compute the columns of the output and propagate the carry */
    for (iy = 0; iy < pb; iy++) {
      /* compute the column as a mp_word */
      r       = ((mp_word)*tmpt) +
                ((mp_word)tmpx) * ((mp_word)*tmpy++) +
                ((mp_word) u);

      /* the new column is the lower part of the result */
      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

      /* get the carry word from the result */
      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
    }
    /* set carry if it is placed below digs */
    if (ix + iy < digs) {
      *tmpt = u;
    }
  }

  mp_clamp (&t);
  mp_exch (&t, c);

  mp_clear (&t);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* multiplies |a| * |b| and only computes upto digs digits of result
 * HAC pp. 595, Algorithm 14.12  Modified so you can control how 
 * many digits of output are created.
 */
int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
................................................................................
  int     res, pa, pb, ix, iy;
  mp_digit u;
  mp_word r;
  mp_digit tmpx, *tmpt, *tmpy;

  /* can we use the fast multiplier? */
  if (((digs) < MP_WARRAY) &&
      (MIN (a->used, b->used) < 
          (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
    return fast_s_mp_mul_digs (a, b, c, digs);
  }

  if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
    return res;
  }
  t.used = digs;
................................................................................
    
    /* an alias for the digits of b */
    tmpy = b->dp;

    /* compute the columns of the output and propagate the carry */
    for (iy = 0; iy < pb; iy++) {
      /* compute the column as a mp_word */
      r       = (mp_word)*tmpt +
                ((mp_word)tmpx * (mp_word)*tmpy++) +
                (mp_word)u;

      /* the new column is the lower part of the result */
      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

      /* get the carry word from the result */
      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
    }
    /* set carry if it is placed below digs */
    if ((ix + iy) < digs) {
      *tmpt = u;
    }
  }

  mp_clamp (&t);
  mp_exch (&t, c);

  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_s_mp_mul_high_digs.c.

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#include <tommath.h>
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* multiplies |a| * |b| and does not compute the lower digs digits
 * [meant to get the higher part of the product]
 */
int
s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
................................................................................
  mp_digit u;
  mp_word r;
  mp_digit tmpx, *tmpt, *tmpy;

  /* can we use the fast multiplier? */
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
  if (((a->used + b->used + 1) < MP_WARRAY)
      && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
    return fast_s_mp_mul_high_digs (a, b, c, digs);
  }
#endif

  if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
    return res;
  }
................................................................................
    tmpt = &(t.dp[digs]);

    /* alias for where to read the right hand side from */
    tmpy = b->dp + (digs - ix);

    for (iy = digs - ix; iy < pb; iy++) {
      /* calculate the double precision result */
      r       = ((mp_word)*tmpt) +
                ((mp_word)tmpx) * ((mp_word)*tmpy++) +
                ((mp_word) u);

      /* get the lower part */
      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

      /* carry the carry */
      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
    }
................................................................................
  }
  mp_clamp (&t);
  mp_exch (&t, c);
  mp_clear (&t);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* multiplies |a| * |b| and does not compute the lower digs digits
 * [meant to get the higher part of the product]
 */
int
s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
................................................................................
  mp_digit u;
  mp_word r;
  mp_digit tmpx, *tmpt, *tmpy;

  /* can we use the fast multiplier? */
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
  if (((a->used + b->used + 1) < MP_WARRAY)
      && (MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
    return fast_s_mp_mul_high_digs (a, b, c, digs);
  }
#endif

  if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
    return res;
  }
................................................................................
    tmpt = &(t.dp[digs]);

    /* alias for where to read the right hand side from */
    tmpy = b->dp + (digs - ix);

    for (iy = digs - ix; iy < pb; iy++) {
      /* calculate the double precision result */
      r       = (mp_word)*tmpt +
                ((mp_word)tmpx * (mp_word)*tmpy++) +
                (mp_word)u;

      /* get the lower part */
      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

      /* carry the carry */
      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
    }
................................................................................
  }
  mp_clamp (&t);
  mp_exch (&t, c);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_s_mp_sqr.c.

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#include <tommath.h>
#ifdef BN_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int s_mp_sqr (mp_int * a, mp_int * b)
{
  mp_int  t;
  int     res, ix, iy, pa;
  mp_word r;
  mp_digit u, tmpx, *tmpt;

  pa = a->used;
  if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
    return res;
  }

  /* default used is maximum possible size */
  t.used = 2*pa + 1;

  for (ix = 0; ix < pa; ix++) {
    /* first calculate the digit at 2*ix */
    /* calculate double precision result */
    r = ((mp_word) t.dp[2*ix]) +
        ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);

    /* store lower part in result */
    t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));

    /* get the carry */
    u           = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

    /* left hand side of A[ix] * A[iy] */
    tmpx        = a->dp[ix];

    /* alias for where to store the results */
    tmpt        = t.dp + (2*ix + 1);
    
    for (iy = ix + 1; iy < pa; iy++) {
      /* first calculate the product */
      r       = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);

      /* now calculate the double precision result, note we use
       * addition instead of *2 since it's easier to optimize
................................................................................

  mp_clamp (&t);
  mp_exch (&t, b);
  mp_clear (&t);
  return MP_OKAY;
}
#endif




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#include <tommath_private.h>
#ifdef BN_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int s_mp_sqr (mp_int * a, mp_int * b)
{
  mp_int  t;
  int     res, ix, iy, pa;
  mp_word r;
  mp_digit u, tmpx, *tmpt;

  pa = a->used;
  if ((res = mp_init_size (&t, (2 * pa) + 1)) != MP_OKAY) {
    return res;
  }

  /* default used is maximum possible size */
  t.used = (2 * pa) + 1;

  for (ix = 0; ix < pa; ix++) {
    /* first calculate the digit at 2*ix */
    /* calculate double precision result */
    r = (mp_word)t.dp[2*ix] +
        ((mp_word)a->dp[ix] * (mp_word)a->dp[ix]);

    /* store lower part in result */
    t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));

    /* get the carry */
    u           = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

    /* left hand side of A[ix] * A[iy] */
    tmpx        = a->dp[ix];

    /* alias for where to store the results */
    tmpt        = t.dp + ((2 * ix) + 1);
    
    for (iy = ix + 1; iy < pa; iy++) {
      /* first calculate the product */
      r       = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);

      /* now calculate the double precision result, note we use
       * addition instead of *2 since it's easier to optimize
................................................................................

  mp_clamp (&t);
  mp_exch (&t, b);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bn_s_mp_sub.c.

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#include <tommath.h>
#ifdef BN_S_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int
s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
  int     olduse, res, min, max;
................................................................................
      return res;
    }
  }
  olduse = c->used;
  c->used = max;

  {
    register mp_digit u, *tmpa, *tmpb, *tmpc;
    register int i;

    /* alias for digit pointers */
    tmpa = a->dp;
    tmpb = b->dp;
    tmpc = c->dp;

    /* set carry to zero */
    u = 0;
    for (i = 0; i < min; i++) {
      /* T[i] = A[i] - B[i] - U */
      *tmpc = *tmpa++ - *tmpb++ - u;

      /* U = carry bit of T[i]
       * Note this saves performing an AND operation since
       * if a carry does occur it will propagate all the way to the
       * MSB.  As a result a single shift is enough to get the carry
       */
      u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));

      /* Clear carry from T[i] */
      *tmpc++ &= MP_MASK;
    }

    /* now copy higher words if any, e.g. if A has more digits than B  */
    for (; i < max; i++) {
      /* T[i] = A[i] - U */
      *tmpc = *tmpa++ - u;

      /* U = carry bit of T[i] */
      u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));

      /* Clear carry from T[i] */
      *tmpc++ &= MP_MASK;
    }

    /* clear digits above used (since we may not have grown result above) */
    for (i = c->used; i < olduse; i++) {
................................................................................
  }

  mp_clamp (c);
  return MP_OKAY;
}

#endif




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#include <tommath_private.h>
#ifdef BN_S_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int
s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
  int     olduse, res, min, max;
................................................................................
      return res;
    }
  }
  olduse = c->used;
  c->used = max;

  {
    mp_digit u, *tmpa, *tmpb, *tmpc;
    int i;

    /* alias for digit pointers */
    tmpa = a->dp;
    tmpb = b->dp;
    tmpc = c->dp;

    /* set carry to zero */
    u = 0;
    for (i = 0; i < min; i++) {
      /* T[i] = A[i] - B[i] - U */
      *tmpc = (*tmpa++ - *tmpb++) - u;

      /* U = carry bit of T[i]
       * Note this saves performing an AND operation since
       * if a carry does occur it will propagate all the way to the
       * MSB.  As a result a single shift is enough to get the carry
       */
      u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));

      /* Clear carry from T[i] */
      *tmpc++ &= MP_MASK;
    }

    /* now copy higher words if any, e.g. if A has more digits than B  */
    for (; i < max; i++) {
      /* T[i] = A[i] - U */
      *tmpc = *tmpa++ - u;

      /* U = carry bit of T[i] */
      u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));

      /* Clear carry from T[i] */
      *tmpc++ &= MP_MASK;
    }

    /* clear digits above used (since we may not have grown result above) */
    for (i = c->used; i < olduse; i++) {
................................................................................
  }

  mp_clamp (c);
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Changes to libtommath/bncore.c.

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#include <tommath.h>
#ifdef BNCORE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Known optimal configurations

 CPU                    /Compiler     /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
 Intel P4 Northwood     /GCC v3.4.1   /        88/       128/LTM 0.32 ;-)
................................................................................

int     KARATSUBA_MUL_CUTOFF = 80,      /* Min. number of digits before Karatsuba multiplication is used. */
        KARATSUBA_SQR_CUTOFF = 120,     /* Min. number of digits before Karatsuba squaring is used. */
        
        TOOM_MUL_CUTOFF      = 350,      /* no optimal values of these are known yet so set em high */
        TOOM_SQR_CUTOFF      = 400; 
#endif




|













|







 







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#include <tommath_private.h>
#ifdef BNCORE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Known optimal configurations

 CPU                    /Compiler     /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
 Intel P4 Northwood     /GCC v3.4.1   /        88/       128/LTM 0.32 ;-)
................................................................................

int     KARATSUBA_MUL_CUTOFF = 80,      /* Min. number of digits before Karatsuba multiplication is used. */
        KARATSUBA_SQR_CUTOFF = 120,     /* Min. number of digits before Karatsuba squaring is used. */
        
        TOOM_MUL_CUTOFF      = 350,      /* no optimal values of these are known yet so set em high */
        TOOM_SQR_CUTOFF      = 400; 
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

Deleted libtommath/booker.pl.

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#!/bin/perl
#
#Used to prepare the book "tommath.src" for LaTeX by pre-processing it into a .tex file
#
#Essentially you write the "tommath.src" as normal LaTex except where you want code snippets you put
#
#EXAM,file
#
#This preprocessor will then open "file" and insert it as a verbatim copy.
#
#Tom St Denis

#get graphics type
if (shift =~ /PDF/) {
   $graph = "";
} else {
   $graph = ".ps";
}   

open(IN,"<tommath.src") or die "Can't open source file";
open(OUT,">tommath.tex") or die "Can't open destination file";

print "Scanning for sections\n";
$chapter = $section = $subsection = 0;
$x = 0;
while (<IN>) {
   print ".";
   if (!(++$x % 80)) { print "\n"; }
   #update the headings 
   if (~($_ =~ /\*/)) {
      if ($_ =~ /\\chapter{.+}/) {
          ++$chapter;
          $section = $subsection = 0;
      } elsif ($_ =~ /\\section{.+}/) {
          ++$section;
          $subsection = 0;
      } elsif ($_ =~ /\\subsection{.+}/) {
          ++$subsection;
      }
   }      

   if ($_ =~ m/MARK/) {
      @m = split(",",$_);
      chomp(@m[1]);
      $index1{@m[1]} = $chapter;
      $index2{@m[1]} = $section;
      $index3{@m[1]} = $subsection;
   }
}
close(IN);

open(IN,"<tommath.src") or die "Can't open source file";
$readline = $wroteline = 0;
$srcline = 0;

while (<IN>) {
   ++$readline;
   ++$srcline;
   
   if ($_ =~ m/MARK/) {
   } elsif ($_ =~ m/EXAM/ || $_ =~ m/LIST/) {
      if ($_ =~ m/EXAM/) {
         $skipheader = 1;
      } else {
         $skipheader = 0;
      }
      
      # EXAM,file
      chomp($_);
      @m = split(",",$_);
      open(SRC,"<$m[1]") or die "Error:$srcline:Can't open source file $m[1]";
      
      print "$srcline:Inserting $m[1]:";
      
      $line = 0;
      $tmp = $m[1];
      $tmp =~ s/_/"\\_"/ge;
      print OUT "\\vspace{+3mm}\\begin{small}\n\\hspace{-5.1mm}{\\bf File}: $tmp\n\\vspace{-3mm}\n\\begin{alltt}\n";
      $wroteline += 5;
      
      if ($skipheader == 1) {
         # scan till next end of comment, e.g. skip license 
         while (<SRC>) {
            $text[$line++] = $_;
            last if ($_ =~ /math\.libtomcrypt\.org/);
         }
         <SRC>;   
      }
      
      $inline = 0;
      while (<SRC>) {
      next if ($_ =~ /\$Source/);
      next if ($_ =~ /\$Revision/);
      next if ($_ =~ /\$Date/);
         $text[$line++] = $_;
         ++$inline;
         chomp($_);
         $_ =~ s/\t/"    "/ge;
         $_ =~ s/{/"^{"/ge;
         $_ =~ s/}/"^}"/ge;
         $_ =~ s/\\/'\symbol{92}'/ge;
         $_ =~ s/\^/"\\"/ge;
           
         printf OUT ("%03d   ", $line);
         for ($x = 0; $x < length($_); $x++) {
             print OUT chr(vec($_, $x, 8));
             if ($x == 75) { 
                 print OUT "\n      ";
                 ++$wroteline;
             }
         }
         print OUT "\n";
         ++$wroteline;
      }
      $totlines = $line;
      print OUT "\\end{alltt}\n\\end{small}\n";
      close(SRC);
      print "$inline lines\n";
      $wroteline += 2;
   } elsif ($_ =~ m/@\d+,[email protected]/) {
     # line contains [number,text]
     # e.g. @14,for (ix = 0)@
     $txt = $_;
     while ($txt =~ m/@\d+,[email protected]/) {
        @m = split("@",$txt);      # splits into text, one, two
        @parms = split(",",$m[1]);  # splits one,two into two elements 
                
        # now search from $parms[0] down for $parms[1] 
        $found1 = 0;
        $found2 = 0;
        for ($i = $parms[0]; $i < $totlines && $found1 == 0; $i++) {
           if ($text[$i] =~ m/\Q$parms[1]\E/) {
              $foundline1 = $i + 1;
              $found1 = 1;
           }
        }
        
        # now search backwards
        for ($i = $parms[0] - 1; $i >= 0 && $found2 == 0; $i--) {
           if ($text[$i] =~ m/\Q$parms[1]\E/) {
              $foundline2 = $i + 1;
              $found2 = 1;
           }
        }
        
        # now use the closest match or the first if tied
        if ($found1 == 1 && $found2 == 0) {
           $found = 1;
           $foundline = $foundline1;
        } elsif ($found1 == 0 && $found2 == 1) {
           $found = 1;
           $foundline = $foundline2;
        } elsif ($found1 == 1 && $found2 == 1) {
           $found = 1;
           if (($foundline1 - $parms[0]) <= ($parms[0] - $foundline2)) {
              $foundline = $foundline1;
           } else {
              $foundline = $foundline2;
           }
        } else {
           $found = 0;
        }
                      
        # if found replace 
        if ($found == 1) {
           $delta = $parms[0] - $foundline;
           print "Found replacement tag for \"$parms[1]\" on line $srcline which refers to line $foundline (delta $delta)\n";
           $_ =~ s/@\Q$m[1]\[email protected]/$foundline/;
        } else {
           print "ERROR:  The tag \"$parms[1]\" on line $srcline was not found in the most recently parsed source!\n";
        }
        
        # remake the rest of the line 
        $cnt = @m;
        $txt = "";
        for ($i = 2; $i < $cnt; $i++) {
            $txt = $txt . $m[$i] . "@";
        }
     }
     print OUT $_;
     ++$wroteline;
   } elsif ($_ =~ /~.+~/) {
      # line contains a ~text~ pair used to refer to indexing :-)
      $txt = $_;
      while ($txt =~ /~.+~/) {
         @m = split("~", $txt);
         
         # word is the second position
         $word = @m[1];
         $a = $index1{$word};
         $b = $index2{$word};
         $c = $index3{$word};
         
         # if chapter (a) is zero it wasn't found
         if ($a == 0) {
            print "ERROR: the tag \"$word\" on line $srcline was not found previously marked.\n";
         } else {
            # format the tag as x, x.y or x.y.z depending on the values
            $str = $a;
            $str = $str . ".$b" if ($b != 0);
            $str = $str . ".$c" if ($c != 0);
            
            if ($b == 0 && $c == 0) {
               # its a chapter
               if ($a <= 10) {
                  if ($a == 1) {
                     $str = "chapter one";
                  } elsif ($a == 2) {
                     $str = "chapter two";
                  } elsif ($a == 3) {
                     $str = "chapter three";
                  } elsif ($a == 4) {
                     $str = "chapter four";
                  } elsif ($a == 5) {
                     $str = "chapter five";
                  } elsif ($a == 6) {
                     $str = "chapter six";
                  } elsif ($a == 7) {
                     $str = "chapter seven";
                  } elsif ($a == 8) {
                     $str = "chapter eight";
                  } elsif ($a == 9) {
                     $str = "chapter nine";
                  } elsif ($a == 10) {
                     $str = "chapter ten";
                  }
               } else {
                  $str = "chapter " . $str;
               }
            } else {
               $str = "section " . $str     if ($b != 0 && $c == 0);            
               $str = "sub-section " . $str if ($b != 0 && $c != 0);
            }
            
            #substitute
            $_ =~ s/~\Q$word\E~/$str/;
            
            print "Found replacement tag for marker \"$word\" on line $srcline which refers to $str\n";
         }
         
         # remake rest of the line
         $cnt = @m;
         $txt = "";
         for ($i = 2; $i < $cnt; $i++) {
             $txt = $txt . $m[$i] . "~";
         }
      }
      print OUT $_;
      ++$wroteline;
   } elsif ($_ =~ m/FIGU/) {
      # FIGU,file,caption
      chomp($_);
      @m = split(",", $_);
      print OUT "\\begin{center}\n\\begin{figure}[here]\n\\includegraphics{pics/$m[1]$graph}\n";
      print OUT "\\caption{$m[2]}\n\\label{pic:$m[1]}\n\\end{figure}\n\\end{center}\n";
      $wroteline += 4;
   } else {
      print OUT $_;
      ++$wroteline;
   }
}
print "Read $readline lines, wrote $wroteline lines\n";

close (OUT);
close (IN);
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Changes to libtommath/callgraph.txt.

more than 10,000 changes

Changes to libtommath/changes.txt.






















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July 23rd, 2010
v0.42.0
       -- Fix for mp_prime_next_prime() bug when checking generated prime
       -- allow mp_shrink to shrink initialized, but empty MPI's
       -- Added project and solution files for Visual Studio 2005 and Visual Studio 2008. 

March 10th, 2007
v0.41  -- Wolfgang Ehrhardt suggested a quick fix to mp_div_d() which makes the detection of powers of two quicker. 
       -- [CRI] Added libtommath.dsp for Visual C++ users.

December 24th, 2006
v0.40  -- Updated makefile to properly support LIBNAME
       -- Fixed bug in fast_s_mp_mul_high_digs() which overflowed (line 83), thanks Valgrind!

April 4th, 2006
................................................................................
       -- "mm" from sci.crypt pointed out that my mp_gcd was sub-optimal (I also updated and corrected the book)
       -- updated some of the @@ tags in tommath.src to reflect source changes.
       -- updated email and url info in all source files

Jan 26th, 2006
v0.38  -- broken makefile.shared fixed
       -- removed some carry stores that were not required [updated text]
       
November 18th, 2005
v0.37  -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs.  Fixed.
       -- [[email protected]] reported the makefile.bcc was messed up.  Fixed.
       -- [Kevin Kenny] reported some issues with mp_toradix_n().  Now it doesn't require a min of 3 chars of output.  
       -- Made the make command renamable.  Wee

August 1st, 2005
v0.36  -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed.
       -- [Peter LaDow] found a typo in the XREALLOC macro
       -- [Peter LaDow] pointed out that mp_read_(un)signed_bin should have "const" on the input
       -- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags]
       -- Kevin Kenny pointed out a stray //
       -- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code]
       -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use 
          unsigned operations in the routine.  
       -- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix)
       -- Updated makefiles to be way more flexible

March 12th, 2005
v0.35  -- Stupid XOR function missing line again... oops.
       -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt]
       -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ]
       -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns.  ;-)
       -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops
       -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly
       -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs" 
       -- Fixed bug in mp_toradix_size for "0" [Kevin Kenny]
       -- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code!

February 12th, 2005
v0.34  -- Fixed two more small errors in mp_prime_random_ex()
       -- Fixed overflow in mp_mul_d() [Kevin Kenny]
       -- Added mp_to_(un)signed_bin_n() functions which do bounds checking for ya [and report the size]
       -- Added "large" diminished radix support.  Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so
          Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4)
       -- Updated the manual a bit
       -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the 
          end of Feb/05.  Once I get back I'll have tons of free time and I plan to go to town on the book.
          As of this release the API will freeze.  At least until the book catches up with all the changes.  I welcome
          bug reports but new algorithms will have to wait.

December 23rd, 2004
v0.33  -- Fixed "small" variant for mp_div() which would munge with negative dividends...
       -- Fixed bug in mp_prime_random_ex() which would set the most significant byte to zero when
................................................................................
       -- Made the makefiles easier to configure the group/user that ltm will install as
       -- Fixed "final carry" bug in comba multipliers. (Volkan Ceylan)
       -- Matt Johnston pointed out a missing semi-colon in mp_exptmod

October 29th, 2004
v0.32  -- Added "makefile.shared" for shared object support
       -- Added more to the build options/configs in the manual
       -- Started the Depends framework, wrote dep.pl to scan deps and 
          produce "callgraph.txt" ;-)
       -- Wrote SC_RSA_1 which will enable close to the minimum required to perform
          RSA on 32-bit [or 64-bit] platforms with LibTomCrypt
       -- Merged in the small/slower mp_div replacement.  You can now toggle which
          you want to use as your mp_div() at build time.  Saves roughly 8KB or so.
       -- Renamed a few files and changed some comments to make depends system work better.
          (No changes to function names)
       -- Merged in new Combas that perform 2 reads per inner loop instead of the older 
          3reads/2writes per inner loop of the old code.  Really though if you want speed
          learn to use TomsFastMath ;-)

August 9th, 2004
v0.31  -- "profiled" builds now :-) new timings for Intel Northwoods
       -- Added "pretty" build target
       -- Update mp_init() to actually assign 0's instead of relying on calloc()
................................................................................
          is only accurate to byte lengths).  See the new LTM_PRIME_* flags ;-)
       -- Alex Polushin contributed an optimized mp_sqrt() as well as mp_get_int() and mp_is_square().
          I've cleaned them all up to be a little more consistent [along with one bug fix] for this release.
       -- Added mp_init_set and mp_init_set_int to initialize and set small constants with one function
          call.
       -- Removed /etclib directory [um LibTomPoly deprecates this].
       -- Fixed mp_mod() so the sign of the result agrees with the sign of the modulus.
       ++ N.B.  My semester is almost up so expect updates to the textbook to be posted to the libtomcrypt.org 
          website.  

Jan 25th, 2004
v0.29  ++ Note: "Henrik" from the v0.28 changelog refers to Henrik Goldman ;-)
       -- Added fix to mp_shrink to prevent a realloc when used == 0 [e.g. realloc zero bytes???]
       -- Made the mp_prime_rabin_miller_trials() function internal table smaller and also
          set the minimum number of tests to two (sounds a bit safer).
       -- Added a mp_exteuclid() which computes the extended euclidean algorithm.
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Feb 5th, 2016
v1.0.0
       -- Bump to 1.0.0
       -- Dirkjan Bussink provided a faster version of mp_expt_d()
       -- Moritz Lenz contributed a fix to mp_mod()
          and provided mp_get_long() and mp_set_long()
       -- Fixed bugs in mp_read_radix(), mp_radix_size
          Thanks to shameister, Gerhard R,
       -- Christopher Brown provided mp_export() and mp_import()
       -- Improvements in the code of mp_init_copy()
          Thanks to ramkumarkoppu,
       -- lomereiter provided mp_balance_mul()
       -- Alexander Boström from the heimdal project contributed patches to
          mp_prime_next_prime() and mp_invmod() and added a mp_isneg() macro
       -- Fix build issues for Linux x32 ABI
       -- Added mp_get_long_long() and mp_set_long_long()
       -- Carlin provided a patch to use arc4random() instead of rand()
          on platforms where it is supported
       -- Karel Miko provided mp_sqrtmod_prime()


July 23rd, 2010
v0.42.0
       -- Fix for mp_prime_next_prime() bug when checking generated prime
       -- allow mp_shrink to shrink initialized, but empty MPI's
       -- Added project and solution files for Visual Studio 2005 and Visual Studio 2008.

March 10th, 2007
v0.41  -- Wolfgang Ehrhardt suggested a quick fix to mp_div_d() which makes the detection of powers of two quicker.
       -- [CRI] Added libtommath.dsp for Visual C++ users.

December 24th, 2006
v0.40  -- Updated makefile to properly support LIBNAME
       -- Fixed bug in fast_s_mp_mul_high_digs() which overflowed (line 83), thanks Valgrind!

April 4th, 2006
................................................................................
       -- "mm" from sci.crypt pointed out that my mp_gcd was sub-optimal (I also updated and corrected the book)
       -- updated some of the @@ tags in tommath.src to reflect source changes.
       -- updated email and url info in all source files

Jan 26th, 2006
v0.38  -- broken makefile.shared fixed
       -- removed some carry stores that were not required [updated text]

November 18th, 2005
v0.37  -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs.  Fixed.
       -- [[email protected]] reported the makefile.bcc was messed up.  Fixed.
       -- [Kevin Kenny] reported some issues with mp_toradix_n().  Now it doesn't require a min of 3 chars of output.
       -- Made the make command renamable.  Wee

August 1st, 2005
v0.36  -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed.
       -- [Peter LaDow] found a typo in the XREALLOC macro
       -- [Peter LaDow] pointed out that mp_read_(un)signed_bin should have "const" on the input
       -- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags]
       -- Kevin Kenny pointed out a stray //
       -- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code]
       -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use
          unsigned operations in the routine.
       -- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix)
       -- Updated makefiles to be way more flexible

March 12th, 2005
v0.35  -- Stupid XOR function missing line again... oops.
       -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt]
       -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ]
       -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns.  ;-)
       -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops
       -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly
       -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs"
       -- Fixed bug in mp_toradix_size for "0" [Kevin Kenny]
       -- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code!

February 12th, 2005
v0.34  -- Fixed two more small errors in mp_prime_random_ex()
       -- Fixed overflow in mp_mul_d() [Kevin Kenny]
       -- Added mp_to_(un)signed_bin_n() functions which do bounds checking for ya [and report the size]
       -- Added "large" diminished radix support.  Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so
          Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4)
       -- Updated the manual a bit
       -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the
          end of Feb/05.  Once I get back I'll have tons of free time and I plan to go to town on the book.
          As of this release the API will freeze.  At least until the book catches up with all the changes.  I welcome
          bug reports but new algorithms will have to wait.

December 23rd, 2004
v0.33  -- Fixed "small" variant for mp_div() which would munge with negative dividends...
       -- Fixed bug in mp_prime_random_ex() which would set the most significant byte to zero when
................................................................................
       -- Made the makefiles easier to configure the group/user that ltm will install as
       -- Fixed "final carry" bug in comba multipliers. (Volkan Ceylan)
       -- Matt Johnston pointed out a missing semi-colon in mp_exptmod

October 29th, 2004
v0.32  -- Added "makefile.shared" for shared object support
       -- Added more to the build options/configs in the manual
       -- Started the Depends framework, wrote dep.pl to scan deps and
          produce "callgraph.txt" ;-)
       -- Wrote SC_RSA_1 which will enable close to the minimum required to perform
          RSA on 32-bit [or 64-bit] platforms with LibTomCrypt
       -- Merged in the small/slower mp_div replacement.  You can now toggle which
          you want to use as your mp_div() at build time.  Saves roughly 8KB or so.
       -- Renamed a few files and changed some comments to make depends system work better.
          (No changes to function names)
       -- Merged in new Combas that perform 2 reads per inner loop instead of the older
          3reads/2writes per inner loop of the old code.  Really though if you want speed
          learn to use TomsFastMath ;-)

August 9th, 2004
v0.31  -- "profiled" builds now :-) new timings for Intel Northwoods
       -- Added "pretty" build target
       -- Update mp_init() to actually assign 0's instead of relying on calloc()
................................................................................
          is only accurate to byte lengths).  See the new LTM_PRIME_* flags ;-)
       -- Alex Polushin contributed an optimized mp_sqrt() as well as mp_get_int() and mp_is_square().
          I've cleaned them all up to be a little more consistent [along with one bug fix] for this release.
       -- Added mp_init_set and mp_init_set_int to initialize and set small constants with one function
          call.
       -- Removed /etclib directory [um LibTomPoly deprecates this].
       -- Fixed mp_mod() so the sign of the result agrees with the sign of the modulus.
       ++ N.B.  My semester is almost up so expect updates to the textbook to be posted to the libtomcrypt.org
          website.

Jan 25th, 2004
v0.29  ++ Note: "Henrik" from the v0.28 changelog refers to Henrik Goldman ;-)
       -- Added fix to mp_shrink to prevent a realloc when used == 0 [e.g. realloc zero bytes???]
       -- Made the mp_prime_rabin_miller_trials() function internal table smaller and also
          set the minimum number of tests to two (sounds a bit safer).
       -- Added a mp_exteuclid() which computes the extended euclidean algorithm.

Deleted libtommath/dep.pl.

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#!/usr/bin/perl 
#
# Walk through source, add labels and make classes
#
#use strict;

my %deplist;

#open class file and write preamble 
open(CLASS, ">tommath_class.h") or die "Couldn't open tommath_class.h for writing\n";
print CLASS "#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))\n#if defined(LTM2)\n#define LTM3\n#endif\n#if defined(LTM1)\n#define LTM2\n#endif\n#define LTM1\n\n#if defined(LTM_ALL)\n";

foreach my $filename (glob "bn*.c") {
   my $define = $filename;

print "Processing $filename\n";

   # convert filename to upper case so we can use it as a define 
   $define =~ tr/[a-z]/[A-Z]/;
   $define =~ tr/\./_/;
   print CLASS "#define $define\n";

   # now copy text and apply #ifdef as required 
   my $apply = 0;
   open(SRC, "<$filename");
   open(OUT, ">tmp");

   # first line will be the #ifdef
   my $line = <SRC>;
   if ($line =~ /include/) {
      print OUT $line;
   } else {
      print OUT "#include <tommath.h>\n#ifdef $define\n$line";
      $apply = 1;
   }
   while (<SRC>) {
      if (!($_ =~ /tommath\.h/)) {
         print OUT $_;
      }
   }
   if ($apply == 1) {
      print OUT "#endif\n";
   }
   close SRC;
   close OUT;

   unlink($filename);
   rename("tmp", $filename);
}
print CLASS "#endif\n\n";

# now do classes 

foreach my $filename (glob "bn*.c") {
   open(SRC, "<$filename") or die "Can't open source file!\n"; 

   # convert filename to upper case so we can use it as a define 
   $filename =~ tr/[a-z]/[A-Z]/;
   $filename =~ tr/\./_/;

   print CLASS "#if defined($filename)\n";
   my $list = $filename;

   # scan for mp_* and make classes
   while (<SRC>) {
      my $line = $_;
      while ($line =~ m/(fast_)*(s_)*mp\_[a-z_0-9]*/) {
          $line = $';
          # now $& is the match, we want to skip over LTM keywords like
          # mp_int, mp_word, mp_digit
          if (!($& eq "mp_digit") && !($& eq "mp_word") && !($& eq "mp_int")) {
             my $a = $&;
             $a =~ tr/[a-z]/[A-Z]/;
             $a = "BN_" . $a . "_C";
             if (!($list =~ /$a/)) {
                print CLASS "   #define $a\n";
             }
             $list = $list . "," . $a;
          }
      }
   }
   @deplist{$filename} = $list;

   print CLASS "#endif\n\n";
   close SRC;
}

print CLASS "#ifdef LTM3\n#define LTM_LAST\n#endif\n#include <tommath_superclass.h>\n#include <tommath_class.h>\n#else\n#define LTM_LAST\n#endif\n";
close CLASS;

#now let's make a cool call graph... 

open(OUT,">callgraph.txt");
$indent = 0;
foreach (keys %deplist) {
   $list = "";
   draw_func(@deplist{$_});
   print OUT "\n\n";
}
close(OUT);

sub draw_func()
{
   my @funcs = split(",", $_[0]);
   if ($list =~ /@funcs[0]/) {
      return;
   } else {
      $list = $list . @funcs[0];
   }
   if ($indent == 0) { }
   elsif ($indent >= 1) { print OUT "|   " x ($indent - 1) . "+--->"; }
   print OUT @funcs[0] . "\n";   
   shift @funcs;
      my $temp = $list;
   foreach my $i (@funcs) {
      ++$indent;
      draw_func(@deplist{$i});
      --$indent;
   }
      $list = $temp;
}


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#!/usr/bin/perl -w
#
# Generates a "single file" you can use to quickly
# add the whole source without any makefile troubles
#
use strict;

open( OUT, ">mpi.c" ) or die "Couldn't open mpi.c for writing: $!";
foreach my $filename (glob "bn*.c") {
   open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!";
   print OUT "/* Start: $filename */\n";
   print OUT while <SRC>;
   print OUT "\n/* End: $filename */\n\n";
   close SRC or die "Error closing $filename after reading: $!";
}
print OUT "\n/* EOF */\n";
close OUT or die "Error closing mpi.c after writing: $!";
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Changes to libtommath/makefile.

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#Makefile for GCC
#
#Tom St Denis

#version of library 
VERSION=0.42.0

CFLAGS  +=  -I./ -Wall -W -Wshadow -Wsign-compare

ifndef MAKE
   MAKE=make
endif

ifndef IGNORE_SPEED

#for speed 
CFLAGS += -O3 -funroll-loops

#for size 
#CFLAGS += -Os

#x86 optimizations [should be valid for any GCC install though]
CFLAGS  += -fomit-frame-pointer

#debug
#CFLAGS += -g3

endif

#install as this user
ifndef INSTALL_GROUP
   GROUP=wheel

else
   GROUP=$(INSTALL_GROUP)

endif

ifndef INSTALL_USER
   USER=root
else
   USER=$(INSTALL_USER)



endif


#default files to install
ifndef LIBNAME
   LIBNAME=libtommath.a
endif

default: ${LIBNAME}


HEADERS=tommath.h tommath_class.h tommath_superclass.h


#LIBPATH-The directory for libtommath to be installed to.
#INCPATH-The directory to install the header files for libtommath.
#DATAPATH-The directory to install the pdf docs.
DESTDIR=
LIBPATH=/usr/lib
INCPATH=/usr/include
DATAPATH=/usr/share/doc/libtommath/pdf


OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
bn_mp_clamp.o bn_mp_zero.o  bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \


bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o  \
bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \


bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \

bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \







bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \






bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o





$(LIBNAME):  $(OBJECTS)
	$(AR) $(ARFLAGS) [email protected] $(OBJECTS)
	ranlib [email protected]


#make a profiled library (takes a while!!!)
#
# This will build the library with profile generation
# then run the test demo and rebuild the library.
# 
# So far I've seen improvements in the MP math
profiled:
	make CFLAGS="$(CFLAGS) -fprofile-arcs -DTESTING" timing
	./ltmtest
	rm -f *.a *.o ltmtest
	make CFLAGS="$(CFLAGS) -fbranch-probabilities"

#make a single object profiled library 
profiled_single:
	perl gen.pl
	$(CC) $(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o
	$(CC) $(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -o ltmtest
	./ltmtest
	rm -f *.o ltmtest
	$(CC) $(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o
	$(AR) $(ARFLAGS) $(LIBNAME) mpi.o
	ranlib $(LIBNAME)	

install: $(LIBNAME)
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
	install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)

test: $(LIBNAME) demo/demo.o
	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) -o test
	




mtest: test	
	cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest
        
timing: $(LIBNAME)
	$(CC) $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME) -o ltmtest




# makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think]
docdvi: tommath.src
	cd pics ; MAKE=${MAKE} ${MAKE} 
	echo "hello" > tommath.ind
	perl booker.pl
	latex tommath > /dev/null
	latex tommath > /dev/null
	makeindex tommath
	latex tommath > /dev/null

# poster, makes the single page PDF poster
poster: poster.tex









	pdflatex poster


	rm -f poster.aux poster.log 

# makes the LTM book PDF file, requires tetex, cleans up the LaTeX temp files
docs:   docdvi
	dvipdf tommath
	rm -f tommath.log tommath.aux tommath.dvi tommath.idx tommath.toc tommath.lof tommath.ind tommath.ilg
	cd pics ; MAKE=${MAKE} ${MAKE} clean
	
#LTM user manual
mandvi: bn.tex









	echo "hello" > bn.ind
	latex bn > /dev/null
	latex bn > /dev/null
	makeindex bn
	latex bn > /dev/null

#LTM user manual [pdf]
manual:	mandvi
	pdflatex bn >/dev/null


	rm -f bn.aux bn.dvi bn.log bn.idx bn.lof bn.out bn.toc

pretty: 
	perl pretty.build

clean:
	rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
        *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find . -type f | grep [~] | xargs` *.lo *.la
	rm -rf .libs
	cd etc ; MAKE=${MAKE} ${MAKE} clean
	cd pics ; MAKE=${MAKE} ${MAKE} clean

#zipup the project (take that!)
no_oops: clean
	cd .. ; cvs commit 
	echo Scanning for scratch/dirty files
	find . -type f | grep -v CVS | xargs -n 1 bash mess.sh

zipup: clean manual poster docs


	perl gen.pl ; mv mpi.c pre_gen/ ; \




	cd .. ; rm -rf ltm* libtommath-$(VERSION) ; mkdir libtommath-$(VERSION) ; \


	cp -R ./libtommath/* ./libtommath-$(VERSION)/ ; \

	tar -c libtommath-$(VERSION)/* | bzip2 -9vvc > ltm-$(VERSION).tar.bz2 ; \
	zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/* ; \
	mv -f ltm* ~ ; rm -rf libtommath-$(VERSION)








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#Makefile for GCC
#
#Tom St Denis

ifeq ($V,1)



























silent=
else

[email protected]
endif





%.o: %.c
ifneq ($V,1)
	@echo "   * ${CC} [email protected]"
endif
	${silent} ${CC} -c ${CFLAGS} $^ -o [email protected]

#default files to install
ifndef LIBNAME
   LIBNAME=libtommath.a
endif


coverage: LIBNAME:=-Wl,--whole-archive $(LIBNAME)  -Wl,--no-whole-archive


include makefile.include








LCOV_ARGS=--directory .






#START_INS
OBJECTS=bncore.o bn_error.o bn_fast_mp_invmod.o bn_fast_mp_montgomery_reduce.o bn_fast_s_mp_mul_digs.o \
bn_fast_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o \











bn_mp_addmod.o bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_cmp_mag.o bn_mp_cnt_lsb.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_div_2.o bn_mp_div_2d.o bn_mp_div_3.o \
bn_mp_div.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o bn_mp_exch.o \




bn_mp_export.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_exptmod.o bn_mp_exptmod_fast.o bn_mp_exteuclid.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_int.o bn_mp_get_long.o bn_mp_get_long_long.o \


bn_mp_grow.o bn_mp_import.o bn_mp_init.o bn_mp_init_copy.o bn_mp_init_multi.o bn_mp_init_set.o \
bn_mp_init_set_int.o bn_mp_init_size.o bn_mp_invmod.o bn_mp_invmod_slow.o bn_mp_is_square.o \
bn_mp_jacobi.o bn_mp_karatsuba_mul.o bn_mp_karatsuba_sqr.o bn_mp_lcm.o bn_mp_lshd.o bn_mp_mod_2d.o \
bn_mp_mod.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \
bn_mp_montgomery_setup.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \
bn_mp_n_root.o bn_mp_n_root_ex.o bn_mp_or.o bn_mp_prime_fermat.o bn_mp_prime_is_divisible.o \
bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \
bn_mp_prime_rabin_miller_trials.o bn_mp_prime_random_ex.o bn_mp_radix_size.o bn_mp_radix_smap.o \
bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.o bn_mp_reduce_2k.o \
bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce.o \
bn_mp_reduce_is_2k.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
bn_mp_set_long.o bn_mp_set_long_long.o bn_mp_shrink.o bn_mp_signed_bin_size.o bn_mp_sqr.o bn_mp_sqrmod.o \
bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o bn_mp_toom_mul.o \
bn_mp_toom_sqr.o bn_mp_toradix.o bn_mp_toradix_n.o bn_mp_to_signed_bin.o bn_mp_to_signed_bin_n.o \
bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o bn_mp_unsigned_bin_size.o bn_mp_xor.o bn_mp_zero.o \
bn_prime_tab.o bn_reverse.o bn_s_mp_add.o bn_s_mp_exptmod.o bn_s_mp_mul_digs.o bn_s_mp_mul_high_digs.o \
bn_s_mp_sqr.o bn_s_mp_sub.o

#END_INS

$(LIBNAME):  $(OBJECTS)
	$(AR) $(ARFLAGS) [email protected] $(OBJECTS)

	$(RANLIB) [email protected]

#make a profiled library (takes a while!!!)
#
# This will build the library with profile generation
# then run the test demo and rebuild the library.
#
# So far I've seen improvements in the MP math
profiled:
	make CFLAGS="$(CFLAGS) -fprofile-arcs -DTESTING" timing
	./ltmtest
	rm -f *.a *.o ltmtest
	make CFLAGS="$(CFLAGS) -fbranch-probabilities"

#make a single object profiled library
profiled_single:
	perl gen.pl
	$(CC) $(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o
	$(CC) $(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -lgcov -o ltmtest
	./ltmtest
	rm -f *.o ltmtest
	$(CC) $(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o
	$(AR) $(ARFLAGS) $(LIBNAME) mpi.o
	ranlib $(LIBNAME)

install: $(LIBNAME)
	install -d $(DESTDIR)$(LIBPATH)
	install -d $(DESTDIR)$(INCPATH)
	install -m 644 $(LIBNAME) $(DESTDIR)$(LIBPATH)
	install -m 644 $(HEADERS_PUB) $(DESTDIR)$(INCPATH)

test: $(LIBNAME) demo/demo.o
	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) $(LFLAGS) -o test

test_standalone: $(LIBNAME) demo/demo.o
	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) $(LFLAGS) -o test

.PHONY: mtest
mtest:
	cd mtest ; $(CC) $(CFLAGS) -O0 mtest.c $(LFLAGS) -o mtest

timing: $(LIBNAME)
	$(CC) $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME) $(LFLAGS) -o ltmtest

coveralls: coverage
	cpp-coveralls

# makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think]
docdvi: tommath.src
	cd pics ; MAKE=${MAKE} ${MAKE}
	echo "hello" > tommath.ind
	perl booker.pl
	latex tommath > /dev/null
	latex tommath > /dev/null
	makeindex tommath
	latex tommath > /dev/null

# poster, makes the single page PDF poster
poster: poster.tex
	cp poster.tex poster.bak
	touch --reference=poster.tex poster.bak
	(printf "%s" "\def\fixedpdfdate{"; date +'D:%Y%m%d%H%M%S%:z' -d @$$(stat --format=%Y poster.tex) | sed "s/:\([0-9][0-9]\)$$/'\1'}/g") > poster-deterministic.tex
	printf "%s\n" "\pdfinfo{" >> poster-deterministic.tex
	printf "%s\n" "  /CreationDate (\fixedpdfdate)" >> poster-deterministic.tex
	printf "%s\n}\n" "  /ModDate (\fixedpdfdate)" >> poster-deterministic.tex
	cat poster.tex >> poster-deterministic.tex
	mv poster-deterministic.tex poster.tex
	touch --reference=poster.bak poster.tex
	pdflatex poster
	sed -b -i 's,^/ID \[.*\]$$,/ID [<0> <0>],g' poster.pdf
	mv poster.bak poster.tex
	rm -f poster.aux poster.log poster.out

# makes the LTM book PDF file, requires tetex, cleans up the LaTeX temp files
docs:   docdvi
	dvipdf tommath
	rm -f tommath.log tommath.aux tommath.dvi tommath.idx tommath.toc tommath.lof tommath.ind tommath.ilg
	cd pics ; MAKE=${MAKE} ${MAKE} clean

#LTM user manual
mandvi: bn.tex
	cp bn.tex bn.bak
	touch --reference=bn.tex bn.bak
	(printf "%s" "\def\fixedpdfdate{"; date +'D:%Y%m%d%H%M%S%:z' -d @$$(stat --format=%Y bn.tex) | sed "s/:\([0-9][0-9]\)$$/'\1'}/g") > bn-deterministic.tex
	printf "%s\n" "\pdfinfo{" >> bn-deterministic.tex
	printf "%s\n" "  /CreationDate (\fixedpdfdate)" >> bn-deterministic.tex
	printf "%s\n}\n" "  /ModDate (\fixedpdfdate)" >> bn-deterministic.tex
	cat bn.tex >> bn-deterministic.tex
	mv bn-deterministic.tex bn.tex
	touch --reference=bn.bak bn.tex
	echo "hello" > bn.ind
	latex bn > /dev/null
	latex bn > /dev/null
	makeindex bn
	latex bn > /dev/null

#LTM user manual [pdf]
manual:	mandvi
	pdflatex bn >/dev/null
	sed -b -i 's,^/ID \[.*\]$$,/ID [<0> <0>],g' bn.pdf
	mv bn.bak bn.tex
	rm -f bn.aux bn.dvi bn.log bn.idx bn.lof bn.out bn.toc

pretty:
	perl pretty.build








#\zipup the project (take that!)
no_oops: clean
	cd .. ; cvs commit
	echo Scanning for scratch/dirty files
	find . -type f | grep -v CVS | xargs -n 1 bash mess.sh


.PHONY: pre_gen
pre_gen:
	perl gen.pl
	sed -e 's/[[:blank:]]*$$//' mpi.c > pre_gen/mpi.c
	rm mpi.c

zipup:
	rm -rf ../libtommath-$(VERSION) \
		&& rm -f ../ltm-$(VERSION).zip ../ltm-$(VERSION).zip.asc ../ltm-$(VERSION).tar.xz ../ltm-$(VERSION).tar.xz.asc
	git archive HEAD --prefix=libtommath-$(VERSION)/ > ../libtommath-$(VERSION).tar
	cd .. ; tar xf libtommath-$(VERSION).tar
	MAKE=${MAKE} ${MAKE} -C ../libtommath-$(VERSION) clean manual poster docs
	tar -c ../libtommath-$(VERSION)/* | xz -9 > ../ltm-$(VERSION).tar.xz
	find ../libtommath-$(VERSION)/ -type f -exec unix2dos -q {} \;
	cd .. ; zip -9r ltm-$(VERSION).zip libtommath-$(VERSION)
	gpg -b -a ../ltm-$(VERSION).tar.xz && gpg -b -a ../ltm-$(VERSION).zip

new_file:
	bash updatemakes.sh
	perl dep.pl

Changes to libtommath/makefile.bcc.

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#


LIB = tlib
CC = bcc32
CFLAGS = -c -O2 -I.

OBJECTS=bncore.obj bn_mp_init.obj bn_mp_clear.obj bn_mp_exch.obj bn_mp_grow.obj bn_mp_shrink.obj \
bn_mp_clamp.obj bn_mp_zero.obj  bn_mp_set.obj bn_mp_set_int.obj bn_mp_init_size.obj bn_mp_copy.obj \
bn_mp_init_copy.obj bn_mp_abs.obj bn_mp_neg.obj bn_mp_cmp_mag.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
bn_mp_rshd.obj bn_mp_lshd.obj bn_mp_mod_2d.obj bn_mp_div_2d.obj bn_mp_mul_2d.obj bn_mp_div_2.obj \
bn_mp_mul_2.obj bn_s_mp_add.obj bn_s_mp_sub.obj bn_fast_s_mp_mul_digs.obj bn_s_mp_mul_digs.obj \
bn_fast_s_mp_mul_high_digs.obj bn_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_s_mp_sqr.obj \
bn_mp_add.obj bn_mp_sub.obj bn_mp_karatsuba_mul.obj bn_mp_mul.obj bn_mp_karatsuba_sqr.obj \
bn_mp_sqr.obj bn_mp_div.obj bn_mp_mod.obj bn_mp_add_d.obj bn_mp_sub_d.obj bn_mp_mul_d.obj \
bn_mp_div_d.obj bn_mp_mod_d.obj bn_mp_expt_d.obj bn_mp_addmod.obj bn_mp_submod.obj \
bn_mp_mulmod.obj bn_mp_sqrmod.obj bn_mp_gcd.obj bn_mp_lcm.obj bn_fast_mp_invmod.obj bn_mp_invmod.obj \
bn_mp_reduce.obj bn_mp_montgomery_setup.obj bn_fast_mp_montgomery_reduce.obj bn_mp_montgomery_reduce.obj \
bn_mp_exptmod_fast.obj bn_mp_exptmod.obj bn_mp_2expt.obj bn_mp_n_root.obj bn_mp_jacobi.obj bn_reverse.obj \
bn_mp_count_bits.obj bn_mp_read_unsigned_bin.obj bn_mp_read_signed_bin.obj bn_mp_to_unsigned_bin.obj \
bn_mp_to_signed_bin.obj bn_mp_unsigned_bin_size.obj bn_mp_signed_bin_size.obj  \
bn_mp_xor.obj bn_mp_and.obj bn_mp_or.obj bn_mp_rand.obj bn_mp_montgomery_calc_normalization.obj \
bn_mp_prime_is_divisible.obj bn_prime_tab.obj bn_mp_prime_fermat.obj bn_mp_prime_miller_rabin.obj \

bn_mp_prime_is_prime.obj bn_mp_prime_next_prime.obj bn_mp_dr_reduce.obj \
bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \
bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \


bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \
bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj







TARGET = libtommath.lib

$(TARGET): $(OBJECTS)

.c.obj:
	$(CC) $(CFLAGS) $<
	$(LIB) $(TARGET) [email protected]






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#


LIB = tlib
CC = bcc32
CFLAGS = -c -O2 -I.

#START_INS
OBJECTS=bncore.obj bn_error.obj bn_fast_mp_invmod.obj bn_fast_mp_montgomery_reduce.obj bn_fast_s_mp_mul_digs.obj \
bn_fast_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_mp_2expt.obj bn_mp_abs.obj bn_mp_add.obj bn_mp_add_d.obj \
bn_mp_addmod.obj bn_mp_and.obj bn_mp_clamp.obj bn_mp_clear.obj bn_mp_clear_multi.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
bn_mp_cmp_mag.obj bn_mp_cnt_lsb.obj bn_mp_copy.obj bn_mp_count_bits.obj bn_mp_div_2.obj bn_mp_div_2d.obj bn_mp_div_3.obj \
bn_mp_div.obj bn_mp_div_d.obj bn_mp_dr_is_modulus.obj bn_mp_dr_reduce.obj bn_mp_dr_setup.obj bn_mp_exch.obj \
bn_mp_export.obj bn_mp_expt_d.obj bn_mp_expt_d_ex.obj bn_mp_exptmod.obj bn_mp_exptmod_fast.obj bn_mp_exteuclid.obj \
bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_gcd.obj bn_mp_get_int.obj bn_mp_get_long.obj bn_mp_get_long_long.obj \
bn_mp_grow.obj bn_mp_import.obj bn_mp_init.obj bn_mp_init_copy.obj bn_mp_init_multi.obj bn_mp_init_set.obj \
bn_mp_init_set_int.obj bn_mp_init_size.obj bn_mp_invmod.obj bn_mp_invmod_slow.obj bn_mp_is_square.obj \
bn_mp_jacobi.obj bn_mp_karatsuba_mul.obj bn_mp_karatsuba_sqr.obj bn_mp_lcm.obj bn_mp_lshd.obj bn_mp_mod_2d.obj \
bn_mp_mod.obj bn_mp_mod_d.obj bn_mp_montgomery_calc_normalization.obj bn_mp_montgomery_reduce.obj \
bn_mp_montgomery_setup.obj bn_mp_mul_2.obj bn_mp_mul_2d.obj bn_mp_mul.obj bn_mp_mul_d.obj bn_mp_mulmod.obj bn_mp_neg.obj \
bn_mp_n_root.obj bn_mp_n_root_ex.obj bn_mp_or.obj bn_mp_prime_fermat.obj bn_mp_prime_is_divisible.obj \

bn_mp_prime_is_prime.obj bn_mp_prime_miller_rabin.obj bn_mp_prime_next_prime.obj \
bn_mp_prime_rabin_miller_trials.obj bn_mp_prime_random_ex.obj bn_mp_radix_size.obj bn_mp_radix_smap.obj \
bn_mp_rand.obj bn_mp_read_radix.obj bn_mp_read_signed_bin.obj bn_mp_read_unsigned_bin.obj bn_mp_reduce_2k.obj \


bn_mp_reduce_2k_l.obj bn_mp_reduce_2k_setup.obj bn_mp_reduce_2k_setup_l.obj bn_mp_reduce.obj \
bn_mp_reduce_is_2k.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_setup.obj bn_mp_rshd.obj bn_mp_set.obj bn_mp_set_int.obj \
bn_mp_set_long.obj bn_mp_set_long_long.obj bn_mp_shrink.obj bn_mp_signed_bin_size.obj bn_mp_sqr.obj bn_mp_sqrmod.obj \
bn_mp_sqrt.obj bn_mp_sqrtmod_prime.obj bn_mp_sub.obj bn_mp_sub_d.obj bn_mp_submod.obj bn_mp_toom_mul.obj \
bn_mp_toom_sqr.obj bn_mp_toradix.obj bn_mp_toradix_n.obj bn_mp_to_signed_bin.obj bn_mp_to_signed_bin_n.obj \




bn_mp_to_unsigned_bin.obj bn_mp_to_unsigned_bin_n.obj bn_mp_unsigned_bin_size.obj bn_mp_xor.obj bn_mp_zero.obj \
bn_prime_tab.obj bn_reverse.obj bn_s_mp_add.obj bn_s_mp_exptmod.obj bn_s_mp_mul_digs.obj bn_s_mp_mul_high_digs.obj \
bn_s_mp_sqr.obj bn_s_mp_sub.obj

#END_INS

HEADERS=tommath.h tommath_class.h tommath_superclass.h

TARGET = libtommath.lib

$(TARGET): $(OBJECTS)

.c.obj:
	$(CC) $(CFLAGS) $<
	$(LIB) $(TARGET) [email protected]

Changes to libtommath/makefile.cygwin_dll.

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#libtommath.dll.  The import library is in libtommath.dll.a.  Remember to add
#"-Wl,--enable-auto-import" to your client build to avoid the auto-import warnings
#
#Tom St Denis
CFLAGS  +=  -I./ -Wall -W -Wshadow -O3 -funroll-loops -mno-cygwin

#x86 optimizations [should be valid for any GCC install though]
CFLAGS  += -fomit-frame-pointer 

default: windll

OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
bn_mp_clamp.o bn_mp_zero.o  bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o  \
bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \


bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \

bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o







# make a Windows DLL via Cygwin
windll:  $(OBJECTS)
	gcc -mno-cygwin -mdll -o libtommath.dll -Wl,--out-implib=libtommath.dll.a -Wl,--export-all-symbols *.o
	ranlib libtommath.dll.a

# build the test program using the windows DLL
test: $(OBJECTS) windll
	gcc $(CFLAGS) demo/demo.c libtommath.dll.a -Wl,--enable-auto-import -o test -s
	cd mtest ; $(CC) -O3 -fomit-frame-pointer -funroll-loops mtest.c -o mtest -s






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#libtommath.dll.  The import library is in libtommath.dll.a.  Remember to add
#"-Wl,--enable-auto-import" to your client build to avoid the auto-import warnings
#
#Tom St Denis
CFLAGS  +=  -I./ -Wall -W -Wshadow -O3 -funroll-loops -mno-cygwin

#x86 optimizations [should be valid for any GCC install though]
CFLAGS  += -fomit-frame-pointer

default: windll

#START_INS
OBJECTS=bncore.o bn_error.o bn_fast_mp_invmod.o bn_fast_mp_montgomery_reduce.o bn_fast_s_mp_mul_digs.o \
bn_fast_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o \
bn_mp_addmod.o bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_cmp_mag.o bn_mp_cnt_lsb.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_div_2.o bn_mp_div_2d.o bn_mp_div_3.o \
bn_mp_div.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o bn_mp_exch.o \
bn_mp_export.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_exptmod.o bn_mp_exptmod_fast.o bn_mp_exteuclid.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_int.o bn_mp_get_long.o bn_mp_get_long_long.o \
bn_mp_grow.o bn_mp_import.o bn_mp_init.o bn_mp_init_copy.o bn_mp_init_multi.o bn_mp_init_set.o \
bn_mp_init_set_int.o bn_mp_init_size.o bn_mp_invmod.o bn_mp_invmod_slow.o bn_mp_is_square.o \
bn_mp_jacobi.o bn_mp_karatsuba_mul.o bn_mp_karatsuba_sqr.o bn_mp_lcm.o bn_mp_lshd.o bn_mp_mod_2d.o \
bn_mp_mod.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \
bn_mp_montgomery_setup.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \
bn_mp_n_root.o bn_mp_n_root_ex.o bn_mp_or.o bn_mp_prime_fermat.o bn_mp_prime_is_divisible.o \


bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \
bn_mp_prime_rabin_miller_trials.o bn_mp_prime_random_ex.o bn_mp_radix_size.o bn_mp_radix_smap.o \
bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.o bn_mp_reduce_2k.o \
bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce.o \

bn_mp_reduce_is_2k.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
bn_mp_set_long.o bn_mp_set_long_long.o bn_mp_shrink.o bn_mp_signed_bin_size.o bn_mp_sqr.o bn_mp_sqrmod.o \
bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o bn_mp_toom_mul.o \
bn_mp_toom_sqr.o bn_mp_toradix.o bn_mp_toradix_n.o bn_mp_to_signed_bin.o bn_mp_to_signed_bin_n.o \




bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o bn_mp_unsigned_bin_size.o bn_mp_xor.o bn_mp_zero.o \
bn_prime_tab.o bn_reverse.o bn_s_mp_add.o bn_s_mp_exptmod.o bn_s_mp_mul_digs.o bn_s_mp_mul_high_digs.o \
bn_s_mp_sqr.o bn_s_mp_sub.o

#END_INS

HEADERS=tommath.h tommath_class.h tommath_superclass.h

# make a Windows DLL via Cygwin
windll:  $(OBJECTS)
	gcc -mno-cygwin -mdll -o libtommath.dll -Wl,--out-implib=libtommath.dll.a -Wl,--export-all-symbols *.o
	ranlib libtommath.dll.a

# build the test program using the windows DLL
test: $(OBJECTS) windll
	gcc $(CFLAGS) demo/demo.c libtommath.dll.a -Wl,--enable-auto-import -o test -s
	cd mtest ; $(CC) -O3 -fomit-frame-pointer -funroll-loops mtest.c -o mtest -s

Changes to libtommath/makefile.icc.

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# optimize for SPEED
#
# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4
# -ax?   specifies make code specifically for ? but compatible with IA-32
# -x?    specifies compile solely for ? [not specifically IA-32 compatible]
#
# where ? is 
#   K - PIII
#   W - first P4 [Williamette]
#   N - P4 Northwood
#   P - P4 Prescott
#   B - Blend of P4 and PM [mobile]
#
# Default to just generic max opts
................................................................................
USER=root
GROUP=root

default: libtommath.a

#default files to install
LIBNAME=libtommath.a
HEADERS=tommath.h

#LIBPATH-The directory for libtomcrypt to be installed to.
#INCPATH-The directory to install the header files for libtommath.
#DATAPATH-The directory to install the pdf docs.
DESTDIR=
LIBPATH=/usr/lib
INCPATH=/usr/include
DATAPATH=/usr/share/doc/libtommath/pdf

OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
bn_mp_clamp.o bn_mp_zero.o  bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o  \
bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \


bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \

bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o







libtommath.a:  $(OBJECTS)
	$(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
	ranlib libtommath.a

#make a profiled library (takes a while!!!)
#
# This will build the library with profile generation
# then run the test demo and rebuild the library.
# 
# So far I've seen improvements in the MP math
profiled:
	make -f makefile.icc CFLAGS="$(CFLAGS) -prof_gen -DTESTING" timing
	./ltmtest
	rm -f *.a *.o ltmtest
	make -f makefile.icc CFLAGS="$(CFLAGS) -prof_use"

#make a single object profiled library 
profiled_single:
	perl gen.pl
	$(CC) $(CFLAGS) -prof_gen -DTESTING -c mpi.c -o mpi.o
	$(CC) $(CFLAGS) -DTESTING -DTIMER demo/demo.c mpi.o -o ltmtest
	./ltmtest
	rm -f *.o ltmtest
	$(CC) $(CFLAGS) -prof_use -ip -DTESTING -c mpi.c -o mpi.o
	$(AR) $(ARFLAGS) libtommath.a mpi.o
	ranlib libtommath.a	

install: libtommath.a
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
	install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)

test: libtommath.a demo/demo.o
	$(CC) demo/demo.o libtommath.a -o test
	
mtest: test	
	cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest
        
timing: libtommath.a
	$(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest

clean:
	rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
        *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.il etc/*.il *.dyn
	cd etc ; make clean
	cd pics ; make clean






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# optimize for SPEED
#
# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4
# -ax?   specifies make code specifically for ? but compatible with IA-32
# -x?    specifies compile solely for ? [not specifically IA-32 compatible]
#
# where ? is
#   K - PIII
#   W - first P4 [Williamette]
#   N - P4 Northwood
#   P - P4 Prescott
#   B - Blend of P4 and PM [mobile]
#
# Default to just generic max opts
................................................................................
USER=root
GROUP=root

default: libtommath.a

#default files to install
LIBNAME=libtommath.a


#LIBPATH-The directory for libtomcrypt to be installed to.
#INCPATH-The directory to install the header files for libtommath.
#DATAPATH-The directory to install the pdf docs.
DESTDIR=
LIBPATH=/usr/lib
INCPATH=/usr/include
DATAPATH=/usr/share/doc/libtommath/pdf

#START_INS
OBJECTS=bncore.o bn_error.o bn_fast_mp_invmod.o bn_fast_mp_montgomery_reduce.o bn_fast_s_mp_mul_digs.o \
bn_fast_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o \
bn_mp_addmod.o bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_cmp_mag.o bn_mp_cnt_lsb.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_div_2.o bn_mp_div_2d.o bn_mp_div_3.o \
bn_mp_div.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o bn_mp_exch.o \
bn_mp_export.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_exptmod.o bn_mp_exptmod_fast.o bn_mp_exteuclid.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_int.o bn_mp_get_long.o bn_mp_get_long_long.o \
bn_mp_grow.o bn_mp_import.o bn_mp_init.o bn_mp_init_copy.o bn_mp_init_multi.o bn_mp_init_set.o \
bn_mp_init_set_int.o bn_mp_init_size.o bn_mp_invmod.o bn_mp_invmod_slow.o bn_mp_is_square.o \
bn_mp_jacobi.o bn_mp_karatsuba_mul.o bn_mp_karatsuba_sqr.o bn_mp_lcm.o bn_mp_lshd.o bn_mp_mod_2d.o \
bn_mp_mod.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \
bn_mp_montgomery_setup.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \
bn_mp_n_root.o bn_mp_n_root_ex.o bn_mp_or.o bn_mp_prime_fermat.o bn_mp_prime_is_divisible.o \


bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \
bn_mp_prime_rabin_miller_trials.o bn_mp_prime_random_ex.o bn_mp_radix_size.o bn_mp_radix_smap.o \
bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.o bn_mp_reduce_2k.o \
bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce.o \

bn_mp_reduce_is_2k.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
bn_mp_set_long.o bn_mp_set_long_long.o bn_mp_shrink.o bn_mp_signed_bin_size.o bn_mp_sqr.o bn_mp_sqrmod.o \
bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o bn_mp_toom_mul.o \
bn_mp_toom_sqr.o bn_mp_toradix.o bn_mp_toradix_n.o bn_mp_to_signed_bin.o bn_mp_to_signed_bin_n.o \




bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o bn_mp_unsigned_bin_size.o bn_mp_xor.o bn_mp_zero.o \
bn_prime_tab.o bn_reverse.o bn_s_mp_add.o bn_s_mp_exptmod.o bn_s_mp_mul_digs.o bn_s_mp_mul_high_digs.o \
bn_s_mp_sqr.o bn_s_mp_sub.o

#END_INS

HEADERS=tommath.h tommath_class.h tommath_superclass.h

libtommath.a:  $(OBJECTS)
	$(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
	ranlib libtommath.a

#make a profiled library (takes a while!!!)
#
# This will build the library with profile generation
# then run the test demo and rebuild the library.
#
# So far I've seen improvements in the MP math
profiled:
	make -f makefile.icc CFLAGS="$(CFLAGS) -prof_gen -DTESTING" timing
	./ltmtest
	rm -f *.a *.o ltmtest
	make -f makefile.icc CFLAGS="$(CFLAGS) -prof_use"

#make a single object profiled library
profiled_single:
	perl gen.pl
	$(CC) $(CFLAGS) -prof_gen -DTESTING -c mpi.c -o mpi.o
	$(CC) $(CFLAGS) -DTESTING -DTIMER demo/demo.c mpi.o -o ltmtest
	./ltmtest
	rm -f *.o ltmtest
	$(CC) $(CFLAGS) -prof_use -ip -DTESTING -c mpi.c -o mpi.o
	$(AR) $(ARFLAGS) libtommath.a mpi.o
	ranlib libtommath.a

install: libtommath.a
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
	install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)

test: libtommath.a demo/demo.o
	$(CC) demo/demo.o libtommath.a -o test

mtest: test
	cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest

timing: libtommath.a
	$(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest

clean:
	rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
        *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.il etc/*.il *.dyn
	cd etc ; make clean
	cd pics ; make clean

Added libtommath/makefile.include.


















































































































































































































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#
# Include makefile for libtommath
#

#version of library
VERSION=1.0
VERSION_SO=1:0

# default make target
default: ${LIBNAME}

# Compiler and Linker Names
ifndef PREFIX
  PREFIX=
endif

ifeq ($(CC),cc)
  CC = $(PREFIX)gcc
endif
LD=$(PREFIX)ld
AR=$(PREFIX)ar
RANLIB=$(PREFIX)ranlib

ifndef MAKE
   MAKE=make
endif

CFLAGS += -I./ -Wall -Wsign-compare -Wextra -Wshadow

ifndef NO_ADDTL_WARNINGS
# additional warnings
CFLAGS += -Wsystem-headers -Wdeclaration-after-statement -Wbad-function-cast -Wcast-align
CFLAGS += -Wstrict-prototypes -Wpointer-arith
endif

ifdef COMPILE_DEBUG
#debug
CFLAGS += -g3
else

ifdef COMPILE_SIZE
#for size
CFLAGS += -Os
else

ifndef IGNORE_SPEED
#for speed
CFLAGS += -O3 -funroll-loops

#x86 optimizations [should be valid for any GCC install though]
CFLAGS  += -fomit-frame-pointer
endif

endif # COMPILE_SIZE
endif # COMPILE_DEBUG

# adjust coverage set
ifneq ($(filter $(shell arch), i386 i686 x86_64 amd64 ia64),)
   COVERAGE = test_standalone timing
   COVERAGE_APP = ./test && ./ltmtest
else
   COVERAGE = test_standalone
   COVERAGE_APP = ./test
endif

HEADERS_PUB=tommath.h tommath_class.h tommath_superclass.h
HEADERS=tommath_private.h $(HEADERS_PUB)

test_standalone: CFLAGS+=-DLTM_DEMO_TEST_VS_MTEST=0

#LIBPATH-The directory for libtommath to be installed to.
#INCPATH-The directory to install the header files for libtommath.
#DATAPATH-The directory to install the pdf docs.
LIBPATH?=/usr/lib
INCPATH?=/usr/include
DATAPATH?=/usr/share/doc/libtommath/pdf

#make the code coverage of the library
#
coverage: CFLAGS += -fprofile-arcs -ftest-coverage -DTIMING_NO_LOGS
coverage: LFLAGS += -lgcov
coverage: LDFLAGS += -lgcov

coverage: $(COVERAGE)
	$(COVERAGE_APP)

lcov: coverage
	rm -f coverage.info
	lcov --capture --no-external --no-recursion $(LCOV_ARGS) --output-file coverage.info -q
	genhtml coverage.info --output-directory coverage -q

# target that removes all coverage output
cleancov-clean:
	rm -f `find . -type f -name "*.info" | xargs`
	rm -rf coverage/

# cleans everything - coverage output and standard 'clean'
cleancov: cleancov-clean clean

clean:
	rm -f *.gcda *.gcno *.bat *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
        *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find . -type f | grep [~] | xargs` *.lo *.la
	rm -rf .libs/
	cd etc ; MAKE=${MAKE} ${MAKE} clean
	cd pics ; MAKE=${MAKE} ${MAKE} clean

Changes to libtommath/makefile.msvc.

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#
#Tom St Denis

CFLAGS = /I. /Ox /DWIN32 /W3 /[email protected]

default: library

OBJECTS=bncore.obj bn_mp_init.obj bn_mp_clear.obj bn_mp_exch.obj bn_mp_grow.obj bn_mp_shrink.obj \
bn_mp_clamp.obj bn_mp_zero.obj  bn_mp_set.obj bn_mp_set_int.obj bn_mp_init_size.obj bn_mp_copy.obj \
bn_mp_init_copy.obj bn_mp_abs.obj bn_mp_neg.obj bn_mp_cmp_mag.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
bn_mp_rshd.obj bn_mp_lshd.obj bn_mp_mod_2d.obj bn_mp_div_2d.obj bn_mp_mul_2d.obj bn_mp_div_2.obj \
bn_mp_mul_2.obj bn_s_mp_add.obj bn_s_mp_sub.obj bn_fast_s_mp_mul_digs.obj bn_s_mp_mul_digs.obj \
bn_fast_s_mp_mul_high_digs.obj bn_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_s_mp_sqr.obj \
bn_mp_add.obj bn_mp_sub.obj bn_mp_karatsuba_mul.obj bn_mp_mul.obj bn_mp_karatsuba_sqr.obj \
bn_mp_sqr.obj bn_mp_div.obj bn_mp_mod.obj bn_mp_add_d.obj bn_mp_sub_d.obj bn_mp_mul_d.obj \
bn_mp_div_d.obj bn_mp_mod_d.obj bn_mp_expt_d.obj bn_mp_addmod.obj bn_mp_submod.obj \
bn_mp_mulmod.obj bn_mp_sqrmod.obj bn_mp_gcd.obj bn_mp_lcm.obj bn_fast_mp_invmod.obj bn_mp_invmod.obj \
bn_mp_reduce.obj bn_mp_montgomery_setup.obj bn_fast_mp_montgomery_reduce.obj bn_mp_montgomery_reduce.obj \
bn_mp_exptmod_fast.obj bn_mp_exptmod.obj bn_mp_2expt.obj bn_mp_n_root.obj bn_mp_jacobi.obj bn_reverse.obj \
bn_mp_count_bits.obj bn_mp_read_unsigned_bin.obj bn_mp_read_signed_bin.obj bn_mp_to_unsigned_bin.obj \
bn_mp_to_signed_bin.obj bn_mp_unsigned_bin_size.obj bn_mp_signed_bin_size.obj  \
bn_mp_xor.obj bn_mp_and.obj bn_mp_or.obj bn_mp_rand.obj bn_mp_montgomery_calc_normalization.obj \
bn_mp_prime_is_divisible.obj bn_prime_tab.obj bn_mp_prime_fermat.obj bn_mp_prime_miller_rabin.obj \

bn_mp_prime_is_prime.obj bn_mp_prime_next_prime.obj bn_mp_dr_reduce.obj \
bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \
bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \


bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \
bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj





HEADERS=tommath.h tommath_class.h tommath_superclass.h

library: $(OBJECTS)
	lib /out:tommath.lib $(OBJECTS)






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#
#Tom St Denis

CFLAGS = /I. /Ox /DWIN32 /W3 /[email protected]

default: library

#START_INS
OBJECTS=bncore.obj bn_error.obj bn_fast_mp_invmod.obj bn_fast_mp_montgomery_reduce.obj bn_fast_s_mp_mul_digs.obj \
bn_fast_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_mp_2expt.obj bn_mp_abs.obj bn_mp_add.obj bn_mp_add_d.obj \
bn_mp_addmod.obj bn_mp_and.obj bn_mp_clamp.obj bn_mp_clear.obj bn_mp_clear_multi.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
bn_mp_cmp_mag.obj bn_mp_cnt_lsb.obj bn_mp_copy.obj bn_mp_count_bits.obj bn_mp_div_2.obj bn_mp_div_2d.obj bn_mp_div_3.obj \
bn_mp_div.obj bn_mp_div_d.obj bn_mp_dr_is_modulus.obj bn_mp_dr_reduce.obj bn_mp_dr_setup.obj bn_mp_exch.obj \
bn_mp_export.obj bn_mp_expt_d.obj bn_mp_expt_d_ex.obj bn_mp_exptmod.obj bn_mp_exptmod_fast.obj bn_mp_exteuclid.obj \
bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_gcd.obj bn_mp_get_int.obj bn_mp_get_long.obj bn_mp_get_long_long.obj \
bn_mp_grow.obj bn_mp_import.obj bn_mp_init.obj bn_mp_init_copy.obj bn_mp_init_multi.obj bn_mp_init_set.obj \
bn_mp_init_set_int.obj bn_mp_init_size.obj bn_mp_invmod.obj bn_mp_invmod_slow.obj bn_mp_is_square.obj \
bn_mp_jacobi.obj bn_mp_karatsuba_mul.obj bn_mp_karatsuba_sqr.obj bn_mp_lcm.obj bn_mp_lshd.obj bn_mp_mod_2d.obj \
bn_mp_mod.obj bn_mp_mod_d.obj bn_mp_montgomery_calc_normalization.obj bn_mp_montgomery_reduce.obj \
bn_mp_montgomery_setup.obj bn_mp_mul_2.obj bn_mp_mul_2d.obj bn_mp_mul.obj bn_mp_mul_d.obj bn_mp_mulmod.obj bn_mp_neg.obj \
bn_mp_n_root.obj bn_mp_n_root_ex.obj bn_mp_or.obj bn_mp_prime_fermat.obj bn_mp_prime_is_divisible.obj \

bn_mp_prime_is_prime.obj bn_mp_prime_miller_rabin.obj bn_mp_prime_next_prime.obj \
bn_mp_prime_rabin_miller_trials.obj bn_mp_prime_random_ex.obj bn_mp_radix_size.obj bn_mp_radix_smap.obj \
bn_mp_rand.obj bn_mp_read_radix.obj bn_mp_read_signed_bin.obj bn_mp_read_unsigned_bin.obj bn_mp_reduce_2k.obj \


bn_mp_reduce_2k_l.obj bn_mp_reduce_2k_setup.obj bn_mp_reduce_2k_setup_l.obj bn_mp_reduce.obj \
bn_mp_reduce_is_2k.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_setup.obj bn_mp_rshd.obj bn_mp_set.obj bn_mp_set_int.obj \
bn_mp_set_long.obj bn_mp_set_long_long.obj bn_mp_shrink.obj bn_mp_signed_bin_size.obj bn_mp_sqr.obj bn_mp_sqrmod.obj \
bn_mp_sqrt.obj bn_mp_sqrtmod_prime.obj bn_mp_sub.obj bn_mp_sub_d.obj bn_mp_submod.obj bn_mp_toom_mul.obj \
bn_mp_toom_sqr.obj bn_mp_toradix.obj bn_mp_toradix_n.obj bn_mp_to_signed_bin.obj bn_mp_to_signed_bin_n.obj \




bn_mp_to_unsigned_bin.obj bn_mp_to_unsigned_bin_n.obj bn_mp_unsigned_bin_size.obj bn_mp_xor.obj bn_mp_zero.obj \
bn_prime_tab.obj bn_reverse.obj bn_s_mp_add.obj bn_s_mp_exptmod.obj bn_s_mp_mul_digs.obj bn_s_mp_mul_high_digs.obj \
bn_s_mp_sqr.obj bn_s_mp_sub.obj

#END_INS

HEADERS=tommath.h tommath_class.h tommath_superclass.h

library: $(OBJECTS)
	lib /out:tommath.lib $(OBJECTS)

Changes to libtommath/makefile.shared.

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#Makefile for GCC
#
#Tom St Denis
VERSION=0:41

CC = libtool --mode=compile --tag=CC gcc

CFLAGS  +=  -I./ -Wall -W -Wshadow -Wsign-compare

ifndef IGNORE_SPEED

#for speed 
CFLAGS += -O3 -funroll-loops

#for size 
#CFLAGS += -Os

#x86 optimizations [should be valid for any GCC install though]
CFLAGS  += -fomit-frame-pointer

endif

#install as this user
ifndef INSTALL_GROUP
   GROUP=wheel
else
   GROUP=$(INSTALL_GROUP)
endif

ifndef INSTALL_USER
   USER=root
else
   USER=$(INSTALL_USER)
endif

default: libtommath.la

#default files to install
ifndef LIBNAME
   LIBNAME=libtommath.la
endif
ifndef LIBNAME_S
   LIBNAME_S=libtommath.a
endif
HEADERS=tommath.h tommath_class.h tommath_superclass.h

#LIBPATH-The directory for libtommath to be installed to.
#INCPATH-The directory to install the header files for libtommath.
#DATAPATH-The directory to install the pdf docs.
DESTDIR=
LIBPATH=/usr/lib
INCPATH=/usr/include
DATAPATH=/usr/share/doc/libtommath/pdf

OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
bn_mp_clamp.o bn_mp_zero.o  bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o  \
bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o

objs: $(OBJECTS)

$(LIBNAME):  $(OBJECTS)
	libtool --mode=link gcc *.lo -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION)

install: $(LIBNAME)
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
	libtool --mode=install install -c $(LIBNAME) $(DESTDIR)$(LIBPATH)/$(LIBNAME)
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)

test: $(LIBNAME) demo/demo.o
	gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o
	libtool --mode=link gcc -o test demo/demo.o $(LIBNAME_S)
	
mtest: test	
	cd mtest ; gcc $(CFLAGS) mtest.c -o mtest
        
timing: $(LIBNAME)
	gcc $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME_S) -o ltmtest


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#Makefile for GCC
#
#Tom St Denis

#default files to install
ifndef LIBNAME
   LIBNAME=libtommath.la
endif

include makefile.include

LT	?= libtool
LTCOMPILE = $(LT) --mode=compile --tag=CC $(CC)

LCOV_ARGS=--directory .libs --directory .

#START_INS
OBJECTS=bncore.o bn_error.o bn_fast_mp_invmod.o bn_fast_mp_montgomery_reduce.o bn_fast_s_mp_mul_digs.o \
bn_fast_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o \
bn_mp_addmod.o bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_cmp_mag.o bn_mp_cnt_lsb.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_div_2.o bn_mp_div_2d.o bn_mp_div_3.o \
bn_mp_div.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o bn_mp_exch.o \
bn_mp_export.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_exptmod.o bn_mp_exptmod_fast.o bn_mp_exteuclid.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_int.o bn_mp_get_long.o bn_mp_get_long_long.o \
bn_mp_grow.o bn_mp_import.o bn_mp_init.o bn_mp_init_copy.o bn_mp_init_multi.o bn_mp_init_set.o \
bn_mp_init_set_int.o bn_mp_init_size.o bn_mp_invmod.o bn_mp_invmod_slow.o bn_mp_is_square.o \
bn_mp_jacobi.o bn_mp_karatsuba_mul.o bn_mp_karatsuba_sqr.o bn_mp_lcm.o bn_mp_lshd.o bn_mp_mod_2d.o \
bn_mp_mod.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \
bn_mp_montgomery_setup.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \
bn_mp_n_root.o bn_mp_n_root_ex.o bn_mp_or.o bn_mp_prime_fermat.o bn_mp_prime_is_divisible.o \
bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \
bn_mp_prime_rabin_miller_trials.o bn_mp_prime_random_ex.o bn_mp_radix_size.o bn_mp_radix_smap.o \
bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.o bn_mp_reduce_2k.o \
bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce.o \
bn_mp_reduce_is_2k.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
bn_mp_set_long.o bn_mp_set_long_long.o bn_mp_shrink.o bn_mp_signed_bin_size.o bn_mp_sqr.o bn_mp_sqrmod.o \
bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o bn_mp_toom_mul.o \
bn_mp_toom_sqr.o bn_mp_toradix.o bn_mp_toradix_n.o bn_mp_to_signed_bin.o bn_mp_to_signed_bin_n.o \
bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o bn_mp_unsigned_bin_size.o bn_mp_xor.o bn_mp_zero.o \
bn_prime_tab.o bn_reverse.o bn_s_mp_add.o bn_s_mp_exptmod.o bn_s_mp_mul_digs.o bn_s_mp_mul_high_digs.o \
bn_s_mp_sqr.o bn_s_mp_sub.o

#END_INS

objs: $(OBJECTS)

.c.o:
	$(LTCOMPILE) $(CFLAGS) $(LDFLAGS) -o [email protected] -c $<

$(LIBNAME):  $(OBJECTS)
	$(LT) --mode=link --tag=CC $(CC) $(LDFLAGS) *.lo -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION_SO)

install: $(LIBNAME)
	install -d $(DESTDIR)$(LIBPATH)
	install -d $(DESTDIR)$(INCPATH)
	$(LT) --mode=install install -c $(LIBNAME) $(DESTDIR)$(LIBPATH)/$(LIBNAME)
	install -m 644 $(HEADERS_PUB) $(DESTDIR)$(INCPATH)

test: $(LIBNAME) demo/demo.o
	$(CC) $(CFLAGS) -c demo/demo.c -o demo/demo.o
	$(LT) --mode=link $(CC) $(LDFLAGS) -o test demo/demo.o $(LIBNAME)

test_standalone: $(LIBNAME) demo/demo.o
	$(CC) $(CFLAGS) -c demo/demo.c -o demo/demo.o
	$(LT) --mode=link $(CC) $(LDFLAGS) -o test demo/demo.o $(LIBNAME)

mtest:
	cd mtest ; $(CC) $(CFLAGS) $(LDFLAGS) mtest.c -o mtest

timing: $(LIBNAME)
	$(LT) --mode=link $(CC) $(CFLAGS) $(LDFLAGS) -DTIMER demo/timing.c $(LIBNAME) -o ltmtest































Deleted libtommath/mess.sh.

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#!/bin/bash
if cvs log $1 >/dev/null 2>/dev/null; then exit 0; else echo "$1 shouldn't be here" ; exit 1; fi


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Deleted libtommath/poster.tex.

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\documentclass[landscape,11pt]{article}
\usepackage{amsmath, amssymb}
\usepackage{hyperref}
\begin{document}
\hspace*{-3in}
\begin{tabular}{llllll}
$c = a + b$  & {\tt mp\_add(\&a, \&b, \&c)} & $b = 2a$  & {\tt mp\_mul\_2(\&a, \&b)} & \\
$c = a - b$  & {\tt mp\_sub(\&a, \&b, \&c)} & $b = a/2$ & {\tt mp\_div\_2(\&a, \&b)} & \\
$c = ab $   & {\tt mp\_mul(\&a, \&b, \&c)}  & $c = 2^ba$  & {\tt mp\_mul\_2d(\&a, b, \&c)}  \\
$b = a^2 $  & {\tt mp\_sqr(\&a, \&b)}       & $c = a/2^b, d = a \mod 2^b$ & {\tt mp\_div\_2d(\&a, b, \&c, \&d)} \\
$c = \lfloor a/b \rfloor, d = a \mod b$ & {\tt mp\_div(\&a, \&b, \&c, \&d)} & $c = a \mod 2^b $  & {\tt mp\_mod\_2d(\&a, b, \&c)}  \\
 && \\
$a = b $  & {\tt mp\_set\_int(\&a, b)}  & $c = a \vee b$  & {\tt mp\_or(\&a, \&b, \&c)}  \\
$b = a $  & {\tt mp\_copy(\&a, \&b)} & $c = a \wedge b$  & {\tt mp\_and(\&a, \&b, \&c)}  \\
 && $c = a \oplus b$  & {\tt mp\_xor(\&a, \&b, \&c)}  \\
 & \\
$b = -a $  & {\tt mp\_neg(\&a, \&b)}  & $d = a + b \mod c$  & {\tt mp\_addmod(\&a, \&b, \&c, \&d)}  \\
$b = |a| $  & {\tt mp\_abs(\&a, \&b)} & $d = a - b \mod c$  & {\tt mp\_submod(\&a, \&b, \&c, \&d)}  \\
 && $d = ab \mod c$  & {\tt mp\_mulmod(\&a, \&b, \&c, \&d)}  \\
Compare $a$ and $b$ & {\tt mp\_cmp(\&a, \&b)} & $c = a^2 \mod b$  & {\tt mp\_sqrmod(\&a, \&b, \&c)}  \\
Is Zero? & {\tt mp\_iszero(\&a)} & $c = a^{-1} \mod b$  & {\tt mp\_invmod(\&a, \&b, \&c)} \\
Is Even? & {\tt mp\_iseven(\&a)} & $d = a^b \mod c$ & {\tt mp\_exptmod(\&a, \&b, \&c, \&d)} \\
Is Odd ? & {\tt mp\_isodd(\&a)} \\
&\\
$\vert \vert a \vert \vert$ & {\tt mp\_unsigned\_bin\_size(\&a)} & $res$ = 1 if $a$ prime to $t$ rounds? & {\tt mp\_prime\_is\_prime(\&a, t, \&res)} \\
$buf \leftarrow a$          & {\tt mp\_to\_unsigned\_bin(\&a, buf)} & Next prime after $a$ to $t$ rounds. & {\tt mp\_prime\_next\_prime(\&a, t, bbs\_style)} \\
$a \leftarrow buf[0..len-1]$          & {\tt mp\_read\_unsigned\_bin(\&a, buf, len)} \\
&\\
$b = \sqrt{a}$ & {\tt mp\_sqrt(\&a, \&b)}  & $c = \mbox{gcd}(a, b)$ & {\tt mp\_gcd(\&a, \&b, \&c)} \\
$c = a^{1/b}$ & {\tt mp\_n\_root(\&a, b, \&c)} & $c = \mbox{lcm}(a, b)$ & {\tt mp\_lcm(\&a, \&b, \&c)} \\
&\\
Greater Than & MP\_GT & Equal To & MP\_EQ \\
Less Than & MP\_LT & Bits per digit & DIGIT\_BIT \\
\end{tabular}
\end{document}
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Deleted libtommath/pretty.build.

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#!/bin/perl -w
#
# Cute little builder for perl 
# Total waste of development time...
#
# This will build all the object files and then the archive .a file
# requires GCC, GNU make and a sense of humour.
#
# Tom St Denis
use strict;

my $count = 0;
my $starttime = time;
my $rate  = 0;
print "Scanning for source files...\n";
foreach my $filename (glob "*.c") {
       ++$count;
}
print "Source files to build: $count\nBuilding...\n";
my $i = 0;
my $lines = 0;
my $filesbuilt = 0;
foreach my $filename (glob "*.c") {
       printf("Building %3.2f%%, ", (++$i/$count)*100.0);
       if ($i % 4 == 0) { print "/, "; }
       if ($i % 4 == 1) { print "-, "; }
       if ($i % 4 == 2) { print "\\, "; }
       if ($i % 4 == 3) { print "|, "; }
       if ($rate > 0) {
           my $tleft = ($count - $i) / $rate;
           my $tsec  = $tleft%60;
           my $tmin  = ($tleft/60)%60;
           my $thour = ($tleft/3600)%60;
           printf("%2d:%02d:%02d left, ", $thour, $tmin, $tsec);
       }
       my $cnt = ($i/$count)*30.0;
       my $x   = 0;
       print "[";
       for (; $x < $cnt; $x++) { print "#"; }
       for (; $x < 30; $x++)   { print " "; }
       print "]\r";
       my $tmp = $filename;
       $tmp =~ s/\.c/".o"/ge;
       if (open(SRC, "<$tmp")) {
          close SRC;
       } else {
          !system("make $tmp > /dev/null 2>/dev/null") or die "\nERROR: Failed to make $tmp!!!\n";
          open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!";
          ++$lines while (<SRC>);
          close SRC or die "Error closing $filename after reading: $!";
          ++$filesbuilt;
       }      

       # update timer 
       if (time != $starttime) {
          my $delay = time - $starttime;
          $rate = $i/$delay;
       }
}

# finish building the library 
printf("\nFinished building source (%d seconds, %3.2f files per second).\n", time - $starttime, $rate);
print "Compiled approximately $filesbuilt files and $lines lines of code.\n";
print "Doing final make (building archive...)\n";
!system("make > /dev/null 2>/dev/null") or die "\nERROR: Failed to perform last make command!!!\n";
print "done.\n";
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 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tom[email protected], http://math.libtomcrypt.com
 */
#ifndef BN_H_
#define BN_H_

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <ctype.h>
#include <limits.h>

#include <tommath_class.h>

#ifndef MIN
#   define MIN(x,y) ((x)<(y)?(x):(y))
#endif

#ifndef MAX
#   define MAX(x,y) ((x)>(y)?(x):(y))
#endif

#ifdef __cplusplus
extern "C" {

/* C++ compilers don't like assigning void * to mp_digit * */
#define  OPT_CAST(x)  (x *)

#else

/* C on the other hand doesn't care */
#define  OPT_CAST(x)

#endif


/* detect 64-bit mode if possible */
#if defined(__x86_64__) 
#   if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))

#	define MP_64BIT
#   endif
#endif

/* some default configurations.
 *
 * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
 * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
 *
 * At the very least a mp_digit must be able to hold 7 bits
 * [any size beyond that is ok provided it doesn't overflow the data type]
 */
#ifdef MP_8BIT
   typedef unsigned char      mp_digit;
   typedef unsigned short     mp_word;




#elif defined(MP_16BIT)
   typedef unsigned short     mp_digit;
   typedef unsigned long      mp_word;






#elif defined(MP_64BIT)
   /* for GCC only on supported platforms */
#ifndef CRYPT
   typedef unsigned long long ulong64;
   typedef signed long long   long64;
#endif



   typedef unsigned long      mp_digit;

   typedef unsigned long      mp_word __attribute__ ((mode(TI)));






#  define DIGIT_BIT          60
#else
   /* this is the default case, 28-bit digits */
   
   /* this is to make porting into LibTomCrypt easier :-) */
#ifndef CRYPT
#  if defined(_MSC_VER) || defined(__BORLANDC__)
      typedef unsigned __int64   ulong64;
      typedef signed __int64     long64;
#  else
      typedef unsigned long long ulong64;
      typedef signed long long   long64;
#  endif
#endif

   typedef unsigned long      mp_digit;

   typedef ulong64            mp_word;

#ifdef MP_31BIT   
   /* this is an extension that uses 31-bit digits */
#  define DIGIT_BIT          31
#else
   /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
#  define DIGIT_BIT          28
#  define MP_28BIT
#endif   
#endif

/* define heap macros */
#ifndef CRYPT
   /* default to libc stuff */
#  ifndef XMALLOC
#     define XMALLOC  malloc
#     define XFREE    free
#     define XREALLOC realloc
#     define XCALLOC  calloc
#  else
      /* prototypes for our heap functions */
      extern void *XMALLOC(size_t n);
      extern void *XREALLOC(void *p, size_t n);
      extern void *XCALLOC(size_t n, size_t s);
      extern void XFREE(void *p);
#  endif
#endif


/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
#ifndef DIGIT_BIT
#   define DIGIT_BIT     ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))  /* bits per digit */















#endif

#define MP_DIGIT_BIT     DIGIT_BIT
#define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
#define MP_DIGIT_MAX     MP_MASK

/* equalities */
................................................................................
           TOOM_SQR_CUTOFF;

/* define this to use lower memory usage routines (exptmods mostly) */
/* #define MP_LOW_MEM */

/* default precision */
#ifndef MP_PREC
#  ifndef MP_LOW_MEM
#     define MP_PREC                 32     /* default digits of precision */
#  else
#     define MP_PREC                 8      /* default digits of precision */
#  endif
#endif

/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
#define MP_WARRAY               (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))

/* the infamous mp_int structure */
typedef struct  {
    int used, alloc, sign;
    mp_digit *dp;
} mp_int;

................................................................................


#define USED(m)    ((m)->used)
#define DIGIT(m,k) ((m)->dp[(k)])
#define SIGN(m)    ((m)->sign)

/* error code to char* string */
char *mp_error_to_string(int code);

/* ---> init and deinit bignum functions <--- */
/* init a bignum */
int mp_init(mp_int *a);

/* free a bignum */
void mp_clear(mp_int *a);
................................................................................
int mp_grow(mp_int *a, int size);

/* init to a given number of digits */
int mp_init_size(mp_int *a, int size);

/* ---> Basic Manipulations <--- */
#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
#define mp_iseven(a) (((a)->used == 0 || (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
#define mp_isodd(a)  (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)


/* set to zero */
void mp_zero(mp_int *a);

/* set to a digit */
void mp_set(mp_int *a, mp_digit b);

/* set a 32-bit const */
int mp_set_int(mp_int *a, unsigned long b);







/* get a 32-bit value */
unsigned long mp_get_int(mp_int * a);







/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b);

/* initialize and set 32-bit value */
int mp_init_set_int (mp_int * a, unsigned long b);

/* copy, b = a */
int mp_copy(const mp_int *a, mp_int *b);

/* inits and copies, a = b */
int mp_init_copy(mp_int *a, mp_int *b);

/* trim unused digits */
void mp_clamp(mp_int *a);







/* ---> digit manipulation <--- */

/* right shift by "b" digits */
void mp_rshd(mp_int *a, int b);

/* left shift by "b" digits */
int mp_lshd(mp_int *a, int b);

/* c = a / 2**b */
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);

/* b = a/2 */
int mp_div_2(mp_int *a, mp_int *b);

/* c = a * 2**b */
int mp_mul_2d(const mp_int *a, int b, mp_int *c);

/* b = a*2 */
int mp_mul_2(mp_int *a, mp_int *b);

/* c = a mod 2**d */
int mp_mod_2d(const mp_int *a, int b, mp_int *c);

/* computes a = 2**b */
int mp_2expt(mp_int *a, int b);

/* Counts the number of lsbs which are zero before the first zero bit */
int mp_cnt_lsb(mp_int *a);

/* I Love Earth! */

/* makes a pseudo-random int of a given size */
int mp_rand(mp_int *a, int digits);

/* ---> binary operations <--- */
................................................................................
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);

/* a/3 => 3c + d == a */
int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);

/* c = a**b */
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);


/* c = a mod b, 0 <= c < b  */
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);

/* ---> number theory <--- */

/* d = a + b (mod c) */
................................................................................
int mp_lcm(mp_int *a, mp_int *b, mp_int *c);

/* finds one of the b'th root of a, such that |c|**b <= |a|
 *
 * returns error if a < 0 and b is even
 */
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);


/* special sqrt algo */
int mp_sqrt(mp_int *arg, mp_int *ret);




/* is number a square? */
int mp_is_square(mp_int *arg, int *ret);

/* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
int mp_jacobi(mp_int *a, mp_int *n, int *c);

/* used to setup the Barrett reduction for a given modulus b */
................................................................................
#ifdef MP_8BIT
#  define PRIME_SIZE      31
#else
#  define PRIME_SIZE      256
#endif

/* table of first PRIME_SIZE primes */
extern const mp_digit ltm_prime_tab[];

/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
int mp_prime_is_divisible(mp_int *a, int *result);

/* performs one Fermat test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
................................................................................

/* performs one Miller-Rabin test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);

/* This gives [for a given bit size] the number of trials required
 * such that Miller-Rabin gives a prob of failure lower than 2^-96 
 */
int mp_prime_rabin_miller_trials(int size);

/* performs t rounds of Miller-Rabin on "a" using the first
 * t prime bases.  Also performs an initial sieve of trial
 * division.  Determines if "a" is prime with probability
 * of error no more than (1/4)**t.
................................................................................
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
int mp_prime_next_prime(mp_int *a, int t, int bbs_style);

/* makes a truly random prime of a given size (bytes),
 * call with bbs = 1 if you want it to be congruent to 3 mod 4 
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 * The prime generated will be larger than 2^(8*size).
 */
#define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 * 
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
 *   LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
 *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 */
................................................................................
int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
int mp_to_signed_bin(mp_int *a,  unsigned char *b);
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);

int mp_read_radix(mp_int *a, const char *str, int radix);
int mp_toradix(mp_int *a, char *str, int radix);
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
int mp_radix_size(mp_int *a, int radix, int *size);


int mp_fread(mp_int *a, int radix, FILE *stream);
int mp_fwrite(mp_int *a, int radix, FILE *stream);


#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp)           mp_signed_bin_size(mp)
#define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))

#define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
#define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S)     mp_toradix((M), (S), 16)

/* lowlevel functions, do not call! */
int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int fast_s_mp_sqr(mp_int *a, mp_int *b);
int s_mp_sqr(mp_int *a, mp_int *b);
int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
int mp_toom_sqr(mp_int *a, mp_int *b);
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
void bn_reverse(unsigned char *s, int len);

extern const char *mp_s_rmap;

#ifdef __cplusplus
}
#endif

#endif











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 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://math.libtomcrypt.com
 */
#ifndef BN_H_
#define BN_H_

#include <stdio.h>

#include <stdlib.h>
#include <stdint.h>
#include <limits.h>

#include <tommath_class.h>









#ifdef __cplusplus
extern "C" {









#endif


/* detect 64-bit mode if possible */
#if defined(__x86_64__)

   #if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
      #define MP_64BIT
   #endif
#endif

/* some default configurations.
 *
 * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
 * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
 *
 * At the very least a mp_digit must be able to hold 7 bits
 * [any size beyond that is ok provided it doesn't overflow the data type]
 */
#ifdef MP_8BIT
   typedef uint8_t              mp_digit;
   typedef uint16_t             mp_word;
#define MP_SIZEOF_MP_DIGIT      1
#ifdef DIGIT_BIT
#error You must not define DIGIT_BIT when using MP_8BIT
#endif
#elif defined(MP_16BIT)


   typedef uint16_t             mp_digit;
   typedef uint32_t             mp_word;
#define MP_SIZEOF_MP_DIGIT      2
#ifdef DIGIT_BIT
#error You must not define DIGIT_BIT when using MP_16BIT
#endif
#elif defined(MP_64BIT)
   /* for GCC only on supported platforms */
#ifndef CRYPT
   typedef unsigned long long   ulong64;
   typedef signed long long     long64;
#endif

   typedef ulong64 mp_digit;
#if defined(_WIN32)
   typedef unsigned __int128    mp_word;
#elif defined(__GNUC__)
   typedef unsigned long        mp_word __attribute__ ((mode(TI)));
#else
   /* it seems you have a problem
    * but we assume you can somewhere define your own uint128_t */
   typedef uint128_t            mp_word;
#endif

   #define DIGIT_BIT            60
#else
   /* this is the default case, 28-bit digits */

   /* this is to make porting into LibTomCrypt easier :-) */
#ifndef CRYPT




   typedef unsigned long long   ulong64;
   typedef signed long long     long64;

#endif


   typedef uint32_t             mp_digit;
   typedef ulong64              mp_word;

#ifdef MP_31BIT
   /* this is an extension that uses 31-bit digits */
   #define DIGIT_BIT            31
#else
   /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
   #define DIGIT_BIT            28
   #define MP_28BIT
#endif
#endif



















/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
#ifndef DIGIT_BIT
   #define DIGIT_BIT     (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1))  /* bits per digit */
   typedef uint_least32_t mp_min_u32;
#else
   typedef mp_digit mp_min_u32;
#endif

/* platforms that can use a better rand function */
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
    #define MP_USE_ALT_RAND 1
#endif

/* use arc4random on platforms that support it */
#ifdef MP_USE_ALT_RAND
    #define MP_GEN_RANDOM()    arc4random()
#else
    #define MP_GEN_RANDOM()    rand()
#endif

#define MP_DIGIT_BIT     DIGIT_BIT
#define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
#define MP_DIGIT_MAX     MP_MASK

/* equalities */
................................................................................
           TOOM_SQR_CUTOFF;

/* define this to use lower memory usage routines (exptmods mostly) */
/* #define MP_LOW_MEM */

/* default precision */
#ifndef MP_PREC
   #ifndef MP_LOW_MEM
      #define MP_PREC                 32     /* default digits of precision */
   #else
      #define MP_PREC                 8      /* default digits of precision */
   #endif
#endif

/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
#define MP_WARRAY               (1 << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) + 1))

/* the infamous mp_int structure */
typedef struct  {
    int used, alloc, sign;
    mp_digit *dp;
} mp_int;

................................................................................


#define USED(m)    ((m)->used)
#define DIGIT(m,k) ((m)->dp[(k)])
#define SIGN(m)    ((m)->sign)

/* error code to char* string */
const char *mp_error_to_string(int code);

/* ---> init and deinit bignum functions <--- */
/* init a bignum */
int mp_init(mp_int *a);

/* free a bignum */
void mp_clear(mp_int *a);
................................................................................
int mp_grow(mp_int *a, int size);

/* init to a given number of digits */
int mp_init_size(mp_int *a, int size);

/* ---> Basic Manipulations <--- */
#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
#define mp_iseven(a) ((((a)->used == 0) || (((a)->dp[0] & 1u) == 0u)) ? MP_YES : MP_NO)
#define mp_isodd(a)  ((((a)->used > 0) && (((a)->dp[0] & 1u) == 1u)) ? MP_YES : MP_NO)
#define mp_isneg(a)  (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)

/* set to zero */
void mp_zero(mp_int *a);

/* set to a digit */
void mp_set(mp_int *a, mp_digit b);

/* set a 32-bit const */
int mp_set_int(mp_int *a, unsigned long b);

/* set a platform dependent unsigned long value */
int mp_set_long(mp_int *a, unsigned long b);

/* set a platform dependent unsigned long long value */
int mp_set_long_long(mp_int *a, unsigned long long b);

/* get a 32-bit value */
unsigned long mp_get_int(mp_int * a);

/* get a platform dependent unsigned long value */
unsigned long mp_get_long(mp_int * a);

/* get a platform dependent unsigned long long value */
unsigned long long mp_get_long_long(mp_int * a);

/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b);

/* initialize and set 32-bit value */
int mp_init_set_int (mp_int * a, unsigned long b);

/* copy, b = a */
int mp_copy(const mp_int *a, mp_int *b);

/* inits and copies, a = b */
int mp_init_copy(mp_int *a, const mp_int *b);

/* trim unused digits */
void mp_clamp(mp_int *a);

/* import binary data */
int mp_import(mp_int* rop, size_t count, int order, size_t size, int endian, size_t nails, const void* op);

/* export binary data */
int mp_export(void* rop, size_t* countp, int order, size_t size, int endian, size_t nails, mp_int* op);

/* ---> digit manipulation <--- */

/* right shift by "b" digits */
void mp_rshd(mp_int *a, int b);

/* left shift by "b" digits */
int mp_lshd(mp_int *a, int b);

/* c = a / 2**b, implemented as c = a >> b */
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);

/* b = a/2 */
int mp_div_2(mp_int *a, mp_int *b);

/* c = a * 2**b, implemented as c = a << b */
int mp_mul_2d(const mp_int *a, int b, mp_int *c);

/* b = a*2 */
int mp_mul_2(mp_int *a, mp_int *b);

/* c = a mod 2**b */
int mp_mod_2d(const mp_int *a, int b, mp_int *c);

/* computes a = 2**b */
int mp_2expt(mp_int *a, int b);

/* Counts the number of lsbs which are zero before the first zero bit */
int mp_cnt_lsb(const mp_int *a);

/* I Love Earth! */

/* makes a pseudo-random int of a given size */
int mp_rand(mp_int *a, int digits);

/* ---> binary operations <--- */
................................................................................
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);

/* a/3 => 3c + d == a */
int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);

/* c = a**b */
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast);

/* c = a mod b, 0 <= c < b  */
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);

/* ---> number theory <--- */

/* d = a + b (mod c) */
................................................................................
int mp_lcm(mp_int *a, mp_int *b, mp_int *c);

/* finds one of the b'th root of a, such that |c|**b <= |a|
 *
 * returns error if a < 0 and b is even
 */
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast);

/* special sqrt algo */
int mp_sqrt(mp_int *arg, mp_int *ret);

/* special sqrt (mod prime) */
int mp_sqrtmod_prime(mp_int *arg, mp_int *prime, mp_int *ret);

/* is number a square? */
int mp_is_square(mp_int *arg, int *ret);

/* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
int mp_jacobi(mp_int *a, mp_int *n, int *c);

/* used to setup the Barrett reduction for a given modulus b */
................................................................................
#ifdef MP_8BIT
#  define PRIME_SIZE      31
#else
#  define PRIME_SIZE      256
#endif

/* table of first PRIME_SIZE primes */
extern const mp_digit ltm_prime_tab[PRIME_SIZE];

/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
int mp_prime_is_divisible(mp_int *a, int *result);

/* performs one Fermat test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
................................................................................

/* performs one Miller-Rabin test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);

/* This gives [for a given bit size] the number of trials required
 * such that Miller-Rabin gives a prob of failure lower than 2^-96
 */
int mp_prime_rabin_miller_trials(int size);

/* performs t rounds of Miller-Rabin on "a" using the first
 * t prime bases.  Also performs an initial sieve of trial
 * division.  Determines if "a" is prime with probability
 * of error no more than (1/4)**t.
................................................................................
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
int mp_prime_next_prime(mp_int *a, int t, int bbs_style);

/* makes a truly random prime of a given size (bytes),
 * call with bbs = 1 if you want it to be congruent to 3 mod 4
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 * The prime generated will be larger than 2^(8*size).
 */
#define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 *
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)

 *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 */
................................................................................
int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
int mp_to_signed_bin(mp_int *a,  unsigned char *b);
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);

int mp_read_radix(mp_int *a, const char *str, int radix);
int mp_toradix(mp_int *a, char *str, int radix);
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
int mp_radix_size(const mp_int *a, int radix, int *size);

#ifndef LTM_NO_FILE
int mp_fread(mp_int *a, int radix, FILE *stream);
int mp_fwrite(mp_int *a, int radix, FILE *stream);
#endif

#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp)           mp_signed_bin_size(mp)
#define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))

#define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
#define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S)     mp_toradix((M), (S), 16)
























#ifdef __cplusplus
   }
#endif

#endif


/* $Source$ */
/* $Revision$ */
/* $Date$ */

Deleted libtommath/tommath.src.

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\documentclass[b5paper]{book}
\usepackage{hyperref}
\usepackage{makeidx}
\usepackage{amssymb}
\usepackage{color}
\usepackage{alltt}
\usepackage{graphicx}
\usepackage{layout}
\def\union{\cup}
\def\intersect{\cap}
\def\getsrandom{\stackrel{\rm R}{\gets}}
\def\cross{\times}
\def\cat{\hspace{0.5em} \| \hspace{0.5em}}
\def\catn{$\|$}
\def\divides{\hspace{0.3em} | \hspace{0.3em}}
\def\nequiv{\not\equiv}
\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
\def\lcm{{\rm lcm}}
\def\gcd{{\rm gcd}}
\def\log{{\rm log}}
\def\ord{{\rm ord}}
\def\abs{{\mathit abs}}
\def\rep{{\mathit rep}}
\def\mod{{\mathit\ mod\ }}
\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
\def\Or{{\rm\ or\ }}
\def\And{{\rm\ and\ }}
\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
\def\implies{\Rightarrow}
\def\undefined{{\rm ``undefined"}}
\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
\let\oldphi\phi
\def\phi{\varphi}
\def\Pr{{\rm Pr}}
\newcommand{\str}[1]{{\mathbf{#1}}}
\def\F{{\mathbb F}}
\def\N{{\mathbb N}}
\def\Z{{\mathbb Z}}
\def\R{{\mathbb R}}
\def\C{{\mathbb C}}
\def\Q{{\mathbb Q}}
\definecolor{DGray}{gray}{0.5}
\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
\def\gap{\vspace{0.5ex}}
\makeindex
\begin{document}
\frontmatter
\pagestyle{empty}
\title{Multi--Precision Math}
\author{\mbox{
%\begin{small}
\begin{tabular}{c}
Tom St Denis \\
Algonquin College \\
\\
Mads Rasmussen \\
Open Communications Security \\
\\
Greg Rose \\
QUALCOMM Australia \\
\end{tabular}
%\end{small}
}
}
\maketitle
This text has been placed in the public domain.  This text corresponds to the v0.39 release of the 
LibTomMath project.

\begin{alltt}
Tom St Denis
111 Banning Rd
Ottawa, Ontario
K2L 1C3
Canada

Phone: 1-613-836-3160
Email: [email protected]
\end{alltt}

This text is formatted to the international B5 paper size of 176mm wide by 250mm tall using the \LaTeX{} 
{\em book} macro package and the Perl {\em booker} package.

\tableofcontents
\listoffigures
\chapter*{Prefaces}
When I tell people about my LibTom projects and that I release them as public domain they are often puzzled.  
They ask why I did it and especially why I continue to work on them for free.  The best I can explain it is ``Because I can.''  
Which seems odd and perhaps too terse for adult conversation. I often qualify it with ``I am able, I am willing.'' which 
perhaps explains it better.  I am the first to admit there is not anything that special with what I have done.  Perhaps
others can see that too and then we would have a society to be proud of.  My LibTom projects are what I am doing to give 
back to society in the form of tools and knowledge that can help others in their endeavours.

I started writing this book because it was the most logical task to further my goal of open academia.  The LibTomMath source
code itself was written to be easy to follow and learn from.  There are times, however, where pure C source code does not
explain the algorithms properly.  Hence this book.  The book literally starts with the foundation of the library and works
itself outwards to the more complicated algorithms.  The use of both pseudo--code and verbatim source code provides a duality
of ``theory'' and ``practice'' that the computer science students of the world shall appreciate.  I never deviate too far
from relatively straightforward algebra and I hope that this book can be a valuable learning asset.

This book and indeed much of the LibTom projects would not exist in their current form if it was not for a plethora
of kind people donating their time, resources and kind words to help support my work.  Writing a text of significant
length (along with the source code) is a tiresome and lengthy process.  Currently the LibTom project is four years old,
comprises of literally thousands of users and over 100,000 lines of source code, TeX and other material.  People like Mads and Greg 
were there at the beginning to encourage me to work well.  It is amazing how timely validation from others can boost morale to 
continue the project. Definitely my parents were there for me by providing room and board during the many months of work in 2003.  

To my many friends whom I have met through the years I thank you for the good times and the words of encouragement.  I hope I
honour your kind gestures with this project.

Open Source.  Open Academia.  Open Minds.

\begin{flushright} Tom St Denis \end{flushright}

\newpage
I found the opportunity to work with Tom appealing for several reasons, not only could I broaden my own horizons, but also 
contribute to educate others facing the problem of having to handle big number mathematical calculations.

This book is Tom's child and he has been caring and fostering the project ever since the beginning with a clear mind of 
how he wanted the project to turn out. I have helped by proofreading the text and we have had several discussions about 
the layout and language used.

I hold a masters degree in cryptography from the University of Southern Denmark and have always been interested in the 
practical aspects of cryptography. 

Having worked in the security consultancy business for several years in S\~{a}o Paulo, Brazil, I have been in touch with a 
great deal of work in which multiple precision mathematics was needed. Understanding the possibilities for speeding up 
multiple precision calculations is often very important since we deal with outdated machine architecture where modular 
reductions, for example, become painfully slow.

This text is for people who stop and wonder when first examining algorithms such as RSA for the first time and asks 
themselves, ``You tell me this is only secure for large numbers, fine; but how do you implement these numbers?''

\begin{flushright}
Mads Rasmussen

S\~{a}o Paulo - SP

Brazil
\end{flushright}

\newpage
It's all because I broke my leg. That just happened to be at about the same time that Tom asked for someone to review the section of the book about 
Karatsuba multiplication. I was laid up, alone and immobile, and thought ``Why not?'' I vaguely knew what Karatsuba multiplication was, but not 
really, so I thought I could help, learn, and stop myself from watching daytime cable TV, all at once.

At the time of writing this, I've still not met Tom or Mads in meatspace. I've been following Tom's progress since his first splash on the 
sci.crypt Usenet news group. I watched him go from a clueless newbie, to the cryptographic equivalent of a reformed smoker, to a real
contributor to the field, over a period of about two years. I've been impressed with his obvious intelligence, and astounded by his productivity. 
Of course, he's young enough to be my own child, so he doesn't have my problems with staying awake.

When I reviewed that single section of the book, in its very earliest form, I was very pleasantly surprised. So I decided to collaborate more fully, 
and at least review all of it, and perhaps write some bits too. There's still a long way to go with it, and I have watched a number of close 
friends go through the mill of publication, so I think that the way to go is longer than Tom thinks it is. Nevertheless, it's a good effort, 
and I'm pleased to be involved with it.

\begin{flushright}
Greg Rose, Sydney, Australia, June 2003. 
\end{flushright}

\mainmatter
\pagestyle{headings}
\chapter{Introduction}
\section{Multiple Precision Arithmetic}

\subsection{What is Multiple Precision Arithmetic?}
When we think of long-hand arithmetic such as addition or multiplication we rarely consider the fact that we instinctively
raise or lower the precision of the numbers we are dealing with.  For example, in decimal we almost immediate can 
reason that $7$ times $6$ is $42$.  However, $42$ has two digits of precision as opposed to one digit we started with.  
Further multiplications of say $3$ result in a larger precision result $126$.  In these few examples we have multiple 
precisions for the numbers we are working with.  Despite the various levels of precision a single subset\footnote{With the occasional optimization.}
 of algorithms can be designed to accomodate them.  

By way of comparison a fixed or single precision operation would lose precision on various operations.  For example, in
the decimal system with fixed precision $6 \cdot 7 = 2$.

Essentially at the heart of computer based multiple precision arithmetic are the same long-hand algorithms taught in
schools to manually add, subtract, multiply and divide.  

\subsection{The Need for Multiple Precision Arithmetic}
The most prevalent need for multiple precision arithmetic, often referred to as ``bignum'' math, is within the implementation
of public-key cryptography algorithms.   Algorithms such as RSA \cite{RSAREF} and Diffie-Hellman \cite{DHREF} require 
integers of significant magnitude to resist known cryptanalytic attacks.  For example, at the time of this writing a 
typical RSA modulus would be at least greater than $10^{309}$.  However, modern programming languages such as ISO C \cite{ISOC} and 
Java \cite{JAVA} only provide instrinsic support for integers which are relatively small and single precision.

\begin{figure}[!here]
\begin{center}
\begin{tabular}{|r|c|}
\hline \textbf{Data Type} & \textbf{Range} \\
\hline char  & $-128 \ldots 127$ \\
\hline short & $-32768 \ldots 32767$ \\
\hline long  & $-2147483648 \ldots 2147483647$ \\
\hline long long & $-9223372036854775808 \ldots 9223372036854775807$ \\
\hline
\end{tabular}
\end{center}
\caption{Typical Data Types for the C Programming Language}
\label{fig:ISOC}
\end{figure}

The largest data type guaranteed to be provided by the ISO C programming 
language\footnote{As per the ISO C standard.  However, each compiler vendor is allowed to augment the precision as they 
see fit.}  can only represent values up to $10^{19}$ as shown in figure \ref{fig:ISOC}. On its own the C language is 
insufficient to accomodate the magnitude required for the problem at hand.  An RSA modulus of magnitude $10^{19}$ could be 
trivially factored\footnote{A Pollard-Rho factoring would take only $2^{16}$ time.} on the average desktop computer, 
rendering any protocol based on the algorithm insecure.  Multiple precision algorithms solve this very problem by 
extending the range of representable integers while using single precision data types.

Most advancements in fast multiple precision arithmetic stem from the need for faster and more efficient cryptographic 
primitives.  Faster modular reduction and exponentiation algorithms such as Barrett's algorithm, which have appeared in 
various cryptographic journals, can render algorithms such as RSA and Diffie-Hellman more efficient.  In fact, several 
major companies such as RSA Security, Certicom and Entrust have built entire product lines on the implementation and 
deployment of efficient algorithms.

However, cryptography is not the only field of study that can benefit from fast multiple precision integer routines.  
Another auxiliary use of multiple precision integers is high precision floating point data types.  
The basic IEEE \cite{IEEE} standard floating point type is made up of an integer mantissa $q$, an exponent $e$ and a sign bit $s$.  
Numbers are given in the form $n = q \cdot b^e \cdot -1^s$ where $b = 2$ is the most common base for IEEE.  Since IEEE 
floating point is meant to be implemented in hardware the precision of the mantissa is often fairly small 
(\textit{23, 48 and 64 bits}).  The mantissa is merely an integer and a multiple precision integer could be used to create
a mantissa of much larger precision than hardware alone can efficiently support.  This approach could be useful where 
scientific applications must minimize the total output error over long calculations.

Yet another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$).
In fact the library discussed within this text has already been used to form a polynomial basis library\footnote{See \url{http://poly.libtomcrypt.org} for more details.}.

\subsection{Benefits of Multiple Precision Arithmetic}
\index{precision}
The benefit of multiple precision representations over single or fixed precision representations is that 
no precision is lost while representing the result of an operation which requires excess precision.  For example, 
the product of two $n$-bit integers requires at least $2n$ bits of precision to be represented faithfully.  A multiple 
precision algorithm would augment the precision of the destination to accomodate the result while a single precision system 
would truncate excess bits to maintain a fixed level of precision.

It is possible to implement algorithms which require large integers with fixed precision algorithms.  For example, elliptic
curve cryptography (\textit{ECC}) is often implemented on smartcards by fixing the precision of the integers to the maximum 
size the system will ever need.  Such an approach can lead to vastly simpler algorithms which can accomodate the 
integers required even if the host platform cannot natively accomodate them\footnote{For example, the average smartcard 
processor has an 8 bit accumulator.}.  However, as efficient as such an approach may be, the resulting source code is not
normally very flexible.  It cannot, at runtime, accomodate inputs of higher magnitude than the designer anticipated.

Multiple precision algorithms have the most overhead of any style of arithmetic.  For the the most part the 
overhead can be kept to a minimum with careful planning, but overall, it is not well suited for most memory starved
platforms.  However, multiple precision algorithms do offer the most flexibility in terms of the magnitude of the 
inputs.  That is, the same algorithms based on multiple precision integers can accomodate any reasonable size input 
without the designer's explicit forethought.  This leads to lower cost of ownership for the code as it only has to 
be written and tested once.

\section{Purpose of This Text}
The purpose of this text is to instruct the reader regarding how to implement efficient multiple precision algorithms.  
That is to not only explain a limited subset of the core theory behind the algorithms but also the various ``house keeping'' 
elements that are neglected by authors of other texts on the subject.  Several well reknowned texts \cite{TAOCPV2,HAC} 
give considerably detailed explanations of the theoretical aspects of algorithms and often very little information 
regarding the practical implementation aspects.  

In most cases how an algorithm is explained and how it is actually implemented are two very different concepts.  For 
example, the Handbook of Applied Cryptography (\textit{HAC}), algorithm 14.7 on page 594, gives a relatively simple 
algorithm for performing multiple precision integer addition.  However, the description lacks any discussion concerning 
the fact that the two integer inputs may be of differing magnitudes.  As a result the implementation is not as simple
as the text would lead people to believe.  Similarly the division routine (\textit{algorithm 14.20, pp. 598}) does not 
discuss how to handle sign or handle the dividend's decreasing magnitude in the main loop (\textit{step \#3}).

Both texts also do not discuss several key optimal algorithms required such as ``Comba'' and Karatsuba multipliers 
and fast modular inversion, which we consider practical oversights.  These optimal algorithms are vital to achieve 
any form of useful performance in non-trivial applications.  

To solve this problem the focus of this text is on the practical aspects of implementing a multiple precision integer
package.  As a case study the ``LibTomMath''\footnote{Available at \url{http://math.libtomcrypt.com}} package is used 
to demonstrate algorithms with real implementations\footnote{In the ISO C programming language.} that have been field 
tested and work very well.  The LibTomMath library is freely available on the Internet for all uses and this text 
discusses a very large portion of the inner workings of the library.

The algorithms that are presented will always include at least one ``pseudo-code'' description followed 
by the actual C source code that implements the algorithm.  The pseudo-code can be used to implement the same 
algorithm in other programming languages as the reader sees fit.  

This text shall also serve as a walkthrough of the creation of multiple precision algorithms from scratch.  Showing
the reader how the algorithms fit together as well as where to start on various taskings.  

\section{Discussion and Notation}
\subsection{Notation}
A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1}, \ldots, x_1, x_0)_{ \beta }$ and represent
the integer $x \equiv \sum_{i=0}^{n-1} x_i\beta^i$.  The elements of the array $x$ are said to be the radix $\beta$ digits 
of the integer.  For example, $x = (1,2,3)_{10}$ would represent the integer 
$1\cdot 10^2 + 2\cdot10^1 + 3\cdot10^0 = 123$.  

\index{mp\_int}
The term ``mp\_int'' shall refer to a composite structure which contains the digits of the integer it represents, as well 
as auxilary data required to manipulate the data.  These additional members are discussed further in section 
\ref{sec:MPINT}.  For the purposes of this text a ``multiple precision integer'' and an ``mp\_int'' are assumed to be 
synonymous.  When an algorithm is specified to accept an mp\_int variable it is assumed the various auxliary data members 
are present as well.  An expression of the type \textit{variablename.item} implies that it should evaluate to the 
member named ``item'' of the variable.  For example, a string of characters may have a member ``length'' which would 
evaluate to the number of characters in the string.  If the string $a$ equals ``hello'' then it follows that 
$a.length = 5$.  

For certain discussions more generic algorithms are presented to help the reader understand the final algorithm used
to solve a given problem.  When an algorithm is described as accepting an integer input it is assumed the input is 
a plain integer with no additional multiple-precision members.  That is, algorithms that use integers as opposed to 
mp\_ints as inputs do not concern themselves with the housekeeping operations required such as memory management.  These 
algorithms will be used to establish the relevant theory which will subsequently be used to describe a multiple
precision algorithm to solve the same problem.  

\subsection{Precision Notation}
The variable $\beta$ represents the radix of a single digit of a multiple precision integer and 
must be of the form $q^p$ for $q, p \in \Z^+$.  A single precision variable must be able to represent integers in 
the range $0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range 
$0 \le x < q \beta^2$.  The extra radix-$q$ factor allows additions and subtractions to proceed without truncation of the 
carry.  Since all modern computers are binary, it is assumed that $q$ is two.

\index{mp\_digit} \index{mp\_word}
Within the source code that will be presented for each algorithm, the data type \textbf{mp\_digit} will represent 
a single precision integer type, while, the data type \textbf{mp\_word} will represent a double precision integer type.  In 
several algorithms (notably the Comba routines) temporary results will be stored in arrays of double precision mp\_words.  
For the purposes of this text $x_j$ will refer to the $j$'th digit of a single precision array and $\hat x_j$ will refer to 
the $j$'th digit of a double precision array.  Whenever an expression is to be assigned to a double precision
variable it is assumed that all single precision variables are promoted to double precision during the evaluation.  
Expressions that are assigned to a single precision variable are truncated to fit within the precision of a single
precision data type.

For example, if $\beta = 10^2$ a single precision data type may represent a value in the 
range $0 \le x < 10^3$, while a double precision data type may represent a value in the range $0 \le x < 10^5$.  Let
$a = 23$ and $b = 49$ represent two single precision variables.  The single precision product shall be written
as $c \leftarrow a \cdot b$ while the double precision product shall be written as $\hat c \leftarrow a \cdot b$.
In this particular case, $\hat c = 1127$ and $c = 127$.  The most significant digit of the product would not fit 
in a single precision data type and as a result $c \ne \hat c$.  

\subsection{Algorithm Inputs and Outputs}
Within the algorithm descriptions all variables are assumed to be scalars of either single or double precision
as indicated.  The only exception to this rule is when variables have been indicated to be of type mp\_int.  This 
distinction is important as scalars are often used as array indicies and various other counters.  

\subsection{Mathematical Expressions}
The $\lfloor \mbox{ } \rfloor$ brackets imply an expression truncated to an integer not greater than the expression 
itself.  For example, $\lfloor 5.7 \rfloor = 5$.  Similarly the $\lceil \mbox{ } \rceil$ brackets imply an expression
rounded to an integer not less than the expression itself.  For example, $\lceil 5.1 \rceil = 6$.  Typically when 
the $/$ division symbol is used the intention is to perform an integer division with truncation.  For example, 
$5/2 = 2$ which will often be written as $\lfloor 5/2 \rfloor = 2$ for clarity.  When an expression is written as a 
fraction a real value division is implied, for example ${5 \over 2} = 2.5$.  

The norm of a multiple precision integer, for example $\vert \vert x \vert \vert$, will be used to represent the number of digits in the representation
of the integer.  For example, $\vert \vert 123 \vert \vert = 3$ and $\vert \vert 79452 \vert \vert = 5$.  

\subsection{Work Effort}
\index{big-Oh}
To measure the efficiency of the specified algorithms, a modified big-Oh notation is used.  In this system all 
single precision operations are considered to have the same cost\footnote{Except where explicitly noted.}.  
That is a single precision addition, multiplication and division are assumed to take the same time to 
complete.  While this is generally not true in practice, it will simplify the discussions considerably.

Some algorithms have slight advantages over others which is why some constants will not be removed in 
the notation.  For example, a normal baseline multiplication (section \ref{sec:basemult}) requires $O(n^2)$ work while a 
baseline squaring (section \ref{sec:basesquare}) requires $O({{n^2 + n}\over 2})$ work.  In standard big-Oh notation these 
would both be said to be equivalent to $O(n^2)$.  However, 
in the context of the this text this is not the case as the magnitude of the inputs will typically be rather small.  As a 
result small constant factors in the work effort will make an observable difference in algorithm efficiency.

All of the algorithms presented in this text have a polynomial time work level.  That is, of the form 
$O(n^k)$ for $n, k \in \Z^{+}$.  This will help make useful comparisons in terms of the speed of the algorithms and how 
various optimizations will help pay off in the long run.

\section{Exercises}
Within the more advanced chapters a section will be set aside to give the reader some challenging exercises related to
the discussion at hand.  These exercises are not designed to be prize winning problems, but instead to be thought 
provoking.  Wherever possible the problems are forward minded, stating problems that will be answered in subsequent 
chapters.  The reader is encouraged to finish the exercises as they appear to get a better understanding of the 
subject material.  

That being said, the problems are designed to affirm knowledge of a particular subject matter.  Students in particular
are encouraged to verify they can answer the problems correctly before moving on.

Similar to the exercises of \cite[pp. ix]{TAOCPV2} these exercises are given a scoring system based on the difficulty of
the problem.  However, unlike \cite{TAOCPV2} the problems do not get nearly as hard.  The scoring of these 
exercises ranges from one (the easiest) to five (the hardest).  The following table sumarizes the 
scoring system used.

\begin{figure}[here]
\begin{center}
\begin{small}
\begin{tabular}{|c|l|}
\hline $\left [ 1 \right ]$ & An easy problem that should only take the reader a manner of \\
                            & minutes to solve.  Usually does not involve much computer time \\
                            & to solve. \\
\hline $\left [ 2 \right ]$ & An easy problem that involves a marginal amount of computer \\
                     & time usage.  Usually requires a program to be written to \\
                     & solve the problem. \\
\hline $\left [ 3 \right ]$ & A moderately hard problem that requires a non-trivial amount \\
                     & of work.  Usually involves trivial research and development of \\
                     & new theory from the perspective of a student. \\
\hline $\left [ 4 \right ]$ & A moderately hard problem that involves a non-trivial amount \\
                     & of work and research, the solution to which will demonstrate \\
                     & a higher mastery of the subject matter. \\
\hline $\left [ 5 \right ]$ & A hard problem that involves concepts that are difficult for a \\
                     & novice to solve.  Solutions to these problems will demonstrate a \\
                     & complete mastery of the given subject. \\
\hline
\end{tabular}
\end{small}
\end{center}
\caption{Exercise Scoring System}
\end{figure}

Problems at the first level are meant to be simple questions that the reader can answer quickly without programming a solution or
devising new theory.  These problems are quick tests to see if the material is understood.  Problems at the second level 
are also designed to be easy but will require a program or algorithm to be implemented to arrive at the answer.  These
two levels are essentially entry level questions.  

Problems at the third level are meant to be a bit more difficult than the first two levels.  The answer is often 
fairly obvious but arriving at an exacting solution requires some thought and skill.  These problems will almost always 
involve devising a new algorithm or implementing a variation of another algorithm previously presented.  Readers who can
answer these questions will feel comfortable with the concepts behind the topic at hand.

Problems at the fourth level are meant to be similar to those of the level three questions except they will require 
additional research to be completed.  The reader will most likely not know the answer right away, nor will the text provide 
the exact details of the answer until a subsequent chapter.  

Problems at the fifth level are meant to be the hardest 
problems relative to all the other problems in the chapter.  People who can correctly answer fifth level problems have a 
mastery of the subject matter at hand.

Often problems will be tied together.  The purpose of this is to start a chain of thought that will be discussed in future chapters.  The reader
is encouraged to answer the follow-up problems and try to draw the relevance of problems.

\section{Introduction to LibTomMath}

\subsection{What is LibTomMath?}
LibTomMath is a free and open source multiple precision integer library written entirely in portable ISO C.  By portable it 
is meant that the library does not contain any code that is computer platform dependent or otherwise problematic to use on 
any given platform.  

The library has been successfully tested under numerous operating systems including Unix\footnote{All of these
trademarks belong to their respective rightful owners.}, MacOS, Windows, Linux, PalmOS and on standalone hardware such 
as the Gameboy Advance.  The library is designed to contain enough functionality to be able to develop applications such 
as public key cryptosystems and still maintain a relatively small footprint.

\subsection{Goals of LibTomMath}

Libraries which obtain the most efficiency are rarely written in a high level programming language such as C.  However, 
even though this library is written entirely in ISO C, considerable care has been taken to optimize the algorithm implementations within the 
library.  Specifically the code has been written to work well with the GNU C Compiler (\textit{GCC}) on both x86 and ARM 
processors.  Wherever possible, highly efficient algorithms, such as Karatsuba multiplication, sliding window 
exponentiation and Montgomery reduction have been provided to make the library more efficient.  

Even with the nearly optimal and specialized algorithms that have been included the Application Programing Interface 
(\textit{API}) has been kept as simple as possible.  Often generic place holder routines will make use of specialized 
algorithms automatically without the developer's specific attention.  One such example is the generic multiplication 
algorithm \textbf{mp\_mul()} which will automatically use Toom--Cook, Karatsuba, Comba or baseline multiplication 
based on the magnitude of the inputs and the configuration of the library.  

Making LibTomMath as efficient as possible is not the only goal of the LibTomMath project.  Ideally the library should 
be source compatible with another popular library which makes it more attractive for developers to use.  In this case the
MPI library was used as a API template for all the basic functions.  MPI was chosen because it is another library that fits 
in the same niche as LibTomMath.  Even though LibTomMath uses MPI as the template for the function names and argument 
passing conventions, it has been written from scratch by Tom St Denis.

The project is also meant to act as a learning tool for students, the logic being that no easy-to-follow ``bignum'' 
library exists which can be used to teach computer science students how to perform fast and reliable multiple precision 
integer arithmetic.  To this end the source code has been given quite a few comments and algorithm discussion points.  

\section{Choice of LibTomMath}
LibTomMath was chosen as the case study of this text not only because the author of both projects is one and the same but
for more worthy reasons.  Other libraries such as GMP \cite{GMP}, MPI \cite{MPI}, LIP \cite{LIP} and OpenSSL 
\cite{OPENSSL} have multiple precision integer arithmetic routines but would not be ideal for this text for 
reasons that will be explained in the following sub-sections.

\subsection{Code Base}
The LibTomMath code base is all portable ISO C source code.  This means that there are no platform dependent conditional
segments of code littered throughout the source.  This clean and uncluttered approach to the library means that a
developer can more readily discern the true intent of a given section of source code without trying to keep track of
what conditional code will be used.

The code base of LibTomMath is well organized.  Each function is in its own separate source code file 
which allows the reader to find a given function very quickly.  On average there are $76$ lines of code per source
file which makes the source very easily to follow.  By comparison MPI and LIP are single file projects making code tracing
very hard.  GMP has many conditional code segments which also hinder tracing.  

When compiled with GCC for the x86 processor and optimized for speed the entire library is approximately $100$KiB\footnote{The notation ``KiB'' means $2^{10}$ octets, similarly ``MiB'' means $2^{20}$ octets.}
 which is fairly small compared to GMP (over $250$KiB).  LibTomMath is slightly larger than MPI (which compiles to about 
$50$KiB) but LibTomMath is also much faster and more complete than MPI.

\subsection{API Simplicity}
LibTomMath is designed after the MPI library and shares the API design.  Quite often programs that use MPI will build 
with LibTomMath without change. The function names correlate directly to the action they perform.  Almost all of the 
functions share the same parameter passing convention.  The learning curve is fairly shallow with the API provided 
which is an extremely valuable benefit for the student and developer alike.  

The LIP library is an example of a library with an API that is awkward to work with.  LIP uses function names that are often ``compressed'' to 
illegible short hand.  LibTomMath does not share this characteristic.  

The GMP library also does not return error codes.  Instead it uses a POSIX.1 \cite{POSIX1} signal system where errors
are signaled to the host application.  This happens to be the fastest approach but definitely not the most versatile.  In
effect a math error (i.e. invalid input, heap error, etc) can cause a program to stop functioning which is definitely 
undersireable in many situations.

\subsection{Optimizations}
While LibTomMath is certainly not the fastest library (GMP often beats LibTomMath by a factor of two) it does
feature a set of optimal algorithms for tasks such as modular reduction, exponentiation, multiplication and squaring.  GMP 
and LIP also feature such optimizations while MPI only uses baseline algorithms with no optimizations.  GMP lacks a few
of the additional modular reduction optimizations that LibTomMath features\footnote{At the time of this writing GMP
only had Barrett and Montgomery modular reduction algorithms.}.  

LibTomMath is almost always an order of magnitude faster than the MPI library at computationally expensive tasks such as modular
exponentiation.  In the grand scheme of ``bignum'' libraries LibTomMath is faster than the average library and usually  
slower than the best libraries such as GMP and OpenSSL by only a small factor.

\subsection{Portability and Stability}
LibTomMath will build ``out of the box'' on any platform equipped with a modern version of the GNU C Compiler 
(\textit{GCC}).  This means that without changes the library will build without configuration or setting up any 
variables.  LIP and MPI will build ``out of the box'' as well but have numerous known bugs.  Most notably the author of 
MPI has recently stopped working on his library and LIP has long since been discontinued.  

GMP requires a configuration script to run and will not build out of the box.   GMP and LibTomMath are still in active
development and are very stable across a variety of platforms.

\subsection{Choice}
LibTomMath is a relatively compact, well documented, highly optimized and portable library which seems only natural for
the case study of this text.  Various source files from the LibTomMath project will be included within the text.  However, 
the reader is encouraged to download their own copy of the library to actually be able to work with the library.  

\chapter{Getting Started}
\section{Library Basics}
The trick to writing any useful library of source code is to build a solid foundation and work outwards from it.  First, 
a problem along with allowable solution parameters should be identified and analyzed.  In this particular case the 
inability to accomodate multiple precision integers is the problem.  Futhermore, the solution must be written
as portable source code that is reasonably efficient across several different computer platforms.

After a foundation is formed the remainder of the library can be designed and implemented in a hierarchical fashion.  
That is, to implement the lowest level dependencies first and work towards the most abstract functions last.  For example, 
before implementing a modular exponentiation algorithm one would implement a modular reduction algorithm.
By building outwards from a base foundation instead of using a parallel design methodology the resulting project is 
highly modular.  Being highly modular is a desirable property of any project as it often means the resulting product
has a small footprint and updates are easy to perform.  

Usually when I start a project I will begin with the header files.  I define the data types I think I will need and 
prototype the initial functions that are not dependent on other functions (within the library).  After I 
implement these base functions I prototype more dependent functions and implement them.   The process repeats until
I implement all of the functions I require.  For example, in the case of LibTomMath I implemented functions such as 
mp\_init() well before I implemented mp\_mul() and even further before I implemented mp\_exptmod().  As an example as to 
why this design works note that the Karatsuba and Toom-Cook multipliers were written \textit{after} the 
dependent function mp\_exptmod() was written.  Adding the new multiplication algorithms did not require changes to the 
mp\_exptmod() function itself and lowered the total cost of ownership (\textit{so to speak}) and of development 
for new algorithms.  This methodology allows new algorithms to be tested in a complete framework with relative ease.

FIGU,design_process,Design Flow of the First Few Original LibTomMath Functions.

Only after the majority of the functions were in place did I pursue a less hierarchical approach to auditing and optimizing
the source code.  For example, one day I may audit the multipliers and the next day the polynomial basis functions.  

It only makes sense to begin the text with the preliminary data types and support algorithms required as well.  
This chapter discusses the core algorithms of the library which are the dependents for every other algorithm.

\section{What is a Multiple Precision Integer?}
Recall that most programming languages, in particular ISO C \cite{ISOC}, only have fixed precision data types that on their own cannot 
be used to represent values larger than their precision will allow. The purpose of multiple precision algorithms is 
to use fixed precision data types to create and manipulate multiple precision integers which may represent values 
that are very large.  

As a well known analogy, school children are taught how to form numbers larger than nine by prepending more radix ten digits.  In the decimal system
the largest single digit value is $9$.  However, by concatenating digits together larger numbers may be represented.  Newly prepended digits 
(\textit{to the left}) are said to be in a different power of ten column.  That is, the number $123$ can be described as having a $1$ in the hundreds 
column, $2$ in the tens column and $3$ in the ones column.  Or more formally $123 = 1 \cdot 10^2 + 2 \cdot 10^1 + 3 \cdot 10^0$.  Computer based 
multiple precision arithmetic is essentially the same concept.  Larger integers are represented by adjoining fixed 
precision computer words with the exception that a different radix is used.

What most people probably do not think about explicitly are the various other attributes that describe a multiple precision 
integer.  For example, the integer $154_{10}$ has two immediately obvious properties.  First, the integer is positive, 
that is the sign of this particular integer is positive as opposed to negative.  Second, the integer has three digits in 
its representation.  There is an additional property that the integer posesses that does not concern pencil-and-paper 
arithmetic.  The third property is how many digits placeholders are available to hold the integer.  

The human analogy of this third property is ensuring there is enough space on the paper to write the integer.  For example,
if one starts writing a large number too far to the right on a piece of paper they will have to erase it and move left.  
Similarly, computer algorithms must maintain strict control over memory usage to ensure that the digits of an integer
will not exceed the allowed boundaries.  These three properties make up what is known as a multiple precision 
integer or mp\_int for short.  

\subsection{The mp\_int Structure}
\label{sec:MPINT}
The mp\_int structure is the ISO C based manifestation of what represents a multiple precision integer.  The ISO C standard does not provide for 
any such data type but it does provide for making composite data types known as structures.  The following is the structure definition 
used within LibTomMath.

\index{mp\_int}
\begin{figure}[here]
\begin{center}
\begin{small}
%\begin{verbatim}
\begin{tabular}{|l|}
\hline
typedef struct \{ \\
\hspace{3mm}int used, alloc, sign;\\
\hspace{3mm}mp\_digit *dp;\\
\} \textbf{mp\_int}; \\
\hline
\end{tabular}
%\end{verbatim}
\end{small}
\caption{The mp\_int Structure}
\label{fig:mpint}
\end{center}
\end{figure}

The mp\_int structure (fig. \ref{fig:mpint}) can be broken down as follows.

\begin{enumerate}
\item The \textbf{used} parameter denotes how many digits of the array \textbf{dp} contain the digits used to represent
a given integer.  The \textbf{used} count must be positive (or zero) and may not exceed the \textbf{alloc} count.  

\item The \textbf{alloc} parameter denotes how 
many digits are available in the array to use by functions before it has to increase in size.  When the \textbf{used} count 
of a result would exceed the \textbf{alloc} count all of the algorithms will automatically increase the size of the 
array to accommodate the precision of the result.  

\item The pointer \textbf{dp} points to a dynamically allocated array of digits that represent the given multiple 
precision integer.  It is padded with $(\textbf{alloc} - \textbf{used})$ zero digits.  The array is maintained in a least 
significant digit order.  As a pencil and paper analogy the array is organized such that the right most digits are stored
first starting at the location indexed by zero\footnote{In C all arrays begin at zero.} in the array.  For example, 
if \textbf{dp} contains $\lbrace a, b, c, \ldots \rbrace$ where \textbf{dp}$_0 = a$, \textbf{dp}$_1 = b$, \textbf{dp}$_2 = c$, $\ldots$ then 
it would represent the integer $a + b\beta + c\beta^2 + \ldots$  

\index{MP\_ZPOS} \index{MP\_NEG}
\item The \textbf{sign} parameter denotes the sign as either zero/positive (\textbf{MP\_ZPOS}) or negative (\textbf{MP\_NEG}).  
\end{enumerate}

\subsubsection{Valid mp\_int Structures}
Several rules are placed on the state of an mp\_int structure and are assumed to be followed for reasons of efficiency.  
The only exceptions are when the structure is passed to initialization functions such as mp\_init() and mp\_init\_copy().

\begin{enumerate}
\item The value of \textbf{alloc} may not be less than one.  That is \textbf{dp} always points to a previously allocated
array of digits.
\item The value of \textbf{used} may not exceed \textbf{alloc} and must be greater than or equal to zero.
\item The value of \textbf{used} implies the digit at index $(used - 1)$ of the \textbf{dp} array is non-zero.  That is, 
leading zero digits in the most significant positions must be trimmed.
   \begin{enumerate}
   \item Digits in the \textbf{dp} array at and above the \textbf{used} location must be zero.
   \end{enumerate}
\item The value of \textbf{sign} must be \textbf{MP\_ZPOS} if \textbf{used} is zero; 
this represents the mp\_int value of zero.
\end{enumerate}

\section{Argument Passing}
A convention of argument passing must be adopted early on in the development of any library.  Making the function 
prototypes consistent will help eliminate many headaches in the future as the library grows to significant complexity.  
In LibTomMath the multiple precision integer functions accept parameters from left to right as pointers to mp\_int 
structures.  That means that the source (input) operands are placed on the left and the destination (output) on the right.   
Consider the following examples.

\begin{verbatim}
   mp_mul(&a, &b, &c);   /* c = a * b */
   mp_add(&a, &b, &a);   /* a = a + b */
   mp_sqr(&a, &b);       /* b = a * a */
\end{verbatim}

The left to right order is a fairly natural way to implement the functions since it lets the developer read aloud the
functions and make sense of them.  For example, the first function would read ``multiply a and b and store in c''.

Certain libraries (\textit{LIP by Lenstra for instance}) accept parameters the other way around, to mimic the order
of assignment expressions.  That is, the destination (output) is on the left and arguments (inputs) are on the right.  In 
truth, it is entirely a matter of preference.  In the case of LibTomMath the convention from the MPI library has been 
adopted.  

Another very useful design consideration, provided for in LibTomMath, is whether to allow argument sources to also be a 
destination.  For example, the second example (\textit{mp\_add}) adds $a$ to $b$ and stores in $a$.  This is an important 
feature to implement since it allows the calling functions to cut down on the number of variables it must maintain.  
However, to implement this feature specific care has to be given to ensure the destination is not modified before the 
source is fully read.

\section{Return Values}
A well implemented application, no matter what its purpose, should trap as many runtime errors as possible and return them 
to the caller.  By catching runtime errors a library can be guaranteed to prevent undefined behaviour.  However, the end 
developer can still manage to cause a library to crash.  For example, by passing an invalid pointer an application may
fault by dereferencing memory not owned by the application.

In the case of LibTomMath the only errors that are checked for are related to inappropriate inputs (division by zero for 
instance) and memory allocation errors.  It will not check that the mp\_int passed to any function is valid nor 
will it check pointers for validity.  Any function that can cause a runtime error will return an error code as an 
\textbf{int} data type with one of the following values (fig \ref{fig:errcodes}).

\index{MP\_OKAY} \index{MP\_VAL} \index{MP\_MEM}
\begin{figure}[here]
\begin{center}
\begin{tabular}{|l|l|}
\hline \textbf{Value} & \textbf{Meaning} \\
\hline \textbf{MP\_OKAY} & The function was successful \\
\hline \textbf{MP\_VAL}  & One of the input value(s) was invalid \\
\hline \textbf{MP\_MEM}  & The function ran out of heap memory \\
\hline
\end{tabular}
\end{center}
\caption{LibTomMath Error Codes}
\label{fig:errcodes}
\end{figure}

When an error is detected within a function it should free any memory it allocated, often during the initialization of
temporary mp\_ints, and return as soon as possible.  The goal is to leave the system in the same state it was when the 
function was called.  Error checking with this style of API is fairly simple.

\begin{verbatim}
   int err;
   if ((err = mp_add(&a, &b, &c)) != MP_OKAY) {
      printf("Error: %s\n", mp_error_to_string(err));
      exit(EXIT_FAILURE);
   }
\end{verbatim}

The GMP \cite{GMP} library uses C style \textit{signals} to flag errors which is of questionable use.  Not all errors are fatal 
and it was not deemed ideal by the author of LibTomMath to force developers to have signal handlers for such cases.

\section{Initialization and Clearing}
The logical starting point when actually writing multiple precision integer functions is the initialization and 
clearing of the mp\_int structures.  These two algorithms will be used by the majority of the higher level algorithms.

Given the basic mp\_int structure an initialization routine must first allocate memory to hold the digits of
the integer.  Often it is optimal to allocate a sufficiently large pre-set number of digits even though
the initial integer will represent zero.  If only a single digit were allocated quite a few subsequent re-allocations
would occur when operations are performed on the integers.  There is a tradeoff between how many default digits to allocate
and how many re-allocations are tolerable.  Obviously allocating an excessive amount of digits initially will waste 
memory and become unmanageable.  

If the memory for the digits has been successfully allocated then the rest of the members of the structure must
be initialized.  Since the initial state of an mp\_int is to represent the zero integer, the allocated digits must be set
to zero.  The \textbf{used} count set to zero and \textbf{sign} set to \textbf{MP\_ZPOS}.

\subsection{Initializing an mp\_int}
An mp\_int is said to be initialized if it is set to a valid, preferably default, state such that all of the members of the
structure are set to valid values.  The mp\_init algorithm will perform such an action.

\index{mp\_init}
\begin{figure}[here]
\begin{center}
\begin{tabular}{l}
\hline Algorithm \textbf{mp\_init}. \\
\textbf{Input}.   An mp\_int $a$ \\
\textbf{Output}.  Allocate memory and initialize $a$ to a known valid mp\_int state.  \\
\hline \\
1.  Allocate memory for \textbf{MP\_PREC} digits. \\
2.  If the allocation failed return(\textit{MP\_MEM}) \\
3.  for $n$ from $0$ to $MP\_PREC - 1$ do  \\
\hspace{3mm}3.1  $a_n \leftarrow 0$\\
4.  $a.sign \leftarrow MP\_ZPOS$\\
5.  $a.used \leftarrow 0$\\
6.  $a.alloc \leftarrow MP\_PREC$\\
7.  Return(\textit{MP\_OKAY})\\
\hline
\end{tabular}
\end{center}
\caption{Algorithm mp\_init}
\end{figure}

\textbf{Algorithm mp\_init.}
The purpose of this function is to initialize an mp\_int structure so that the rest of the library can properly
manipulte it.  It is assumed that the input may not have had any of its members previously initialized which is certainly
a valid assumption if the input resides on the stack.  

Before any of the members such as \textbf{sign}, \textbf{used} or \textbf{alloc} are initialized the memory for
the digits is allocated.  If this fails the function returns before setting any of the other members.  The \textbf{MP\_PREC} 
name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.} 
used to dictate the minimum precision of newly initialized mp\_int integers.  Ideally, it is at least equal to the smallest
precision number you'll be working with.

Allocating a block of digits at first instead of a single digit has the benefit of lowering the number of usually slow
heap operations later functions will have to perform in the future.  If \textbf{MP\_PREC} is set correctly the slack 
memory and the number of heap operations will be trivial.

Once the allocation has been made the digits have to be set to zero as well as the \textbf{used}, \textbf{sign} and
\textbf{alloc} members initialized.  This ensures that the mp\_int will always represent the default state of zero regardless
of the original condition of the input.

\textbf{Remark.}
This function introduces the idiosyncrasy that all iterative loops, commonly initiated with the ``for'' keyword, iterate incrementally
when the ``to'' keyword is placed between two expressions.  For example, ``for $a$ from $b$ to $c$ do'' means that
a subsequent expression (or body of expressions) are to be evaluated upto $c - b$ times so long as $b \le c$.  In each
iteration the variable $a$ is substituted for a new integer that lies inclusively between $b$ and $c$.  If $b > c$ occured
the loop would not iterate.  By contrast if the ``downto'' keyword were used in place of ``to'' the loop would iterate 
decrementally.

EXAM,bn_mp_init.c

One immediate observation of this initializtion function is that it does not return a pointer to a mp\_int structure.  It 
is assumed that the caller has already allocated memory for the mp\_int structure, typically on the application stack.  The 
call to mp\_init() is used only to initialize the members of the structure to a known default state.  

Here we see (line @23,[email protected]) the memory allocation is performed first.  This allows us to exit cleanly and quickly
if there is an error.  If the allocation fails the routine will return \textbf{MP\_MEM} to the caller to indicate there
was a memory error.  The function XMALLOC is what actually allocates the memory.  Technically XMALLOC is not a function
but a macro defined in ``tommath.h``.  By default, XMALLOC will evaluate to malloc() which is the C library's built--in
memory allocation routine.

In order to assure the mp\_int is in a known state the digits must be set to zero.  On most platforms this could have been
accomplished by using calloc() instead of malloc().  However,  to correctly initialize a integer type to a given value in a 
portable fashion you have to actually assign the value.  The for loop (line @28,[email protected]) performs this required
operation.

After the memory has been successfully initialized the remainder of the members are initialized 
(lines @29,[email protected] through @31,[email protected]) to their respective default states.  At this point the algorithm has succeeded and
a success code is returned to the calling function.  If this function returns \textbf{MP\_OKAY} it is safe to assume the 
mp\_int