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author | jan.nijtmans <nijtmans@users.sourceforge.net> | 2019-05-29 22:48:50 (GMT) |
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committer | jan.nijtmans <nijtmans@users.sourceforge.net> | 2019-05-29 22:48:50 (GMT) |
commit | 7a1b66b00db2dcc63f4743c36b4e8e6edcfc4211 (patch) | |
tree | 770e7df5a9383984bb53ff5db2ae72fea43a3f7d /libtommath | |
parent | 4e994192a1fe60802c91b8ffee51720f54093bac (diff) | |
download | tcl-7a1b66b00db2dcc63f4743c36b4e8e6edcfc4211.zip tcl-7a1b66b00db2dcc63f4743c36b4e8e6edcfc4211.tar.gz tcl-7a1b66b00db2dcc63f4743c36b4e8e6edcfc4211.tar.bz2 |
Update some libtommath functions to the latest trunk versions. Small step forward in the upgrade to (upcoming) libtommath 1.2.
Advantage: simplify Tcl code accessing those functions.
Diffstat (limited to 'libtommath')
-rw-r--r-- | libtommath/bn_mp_and.c | 99 | ||||
-rw-r--r-- | libtommath/bn_mp_cmp.c | 51 | ||||
-rw-r--r-- | libtommath/bn_mp_cmp_d.c | 50 | ||||
-rw-r--r-- | libtommath/bn_mp_cmp_mag.c | 66 | ||||
-rw-r--r-- | libtommath/bn_mp_or.c | 92 | ||||
-rw-r--r-- | libtommath/bn_mp_xor.c | 93 | ||||
-rw-r--r-- | libtommath/tommath.h | 353 |
7 files changed, 422 insertions, 382 deletions
diff --git a/libtommath/bn_mp_and.c b/libtommath/bn_mp_and.c index 02bef18..54c0b4e 100644 --- a/libtommath/bn_mp_and.c +++ b/libtommath/bn_mp_and.c @@ -1,53 +1,56 @@ #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) +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement and */ +mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c) { - int res, ix, px; - mp_int t, *x; - - if (a->used > b->used) { - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - px = b->used; - x = b; - } else { - if ((res = mp_init_copy (&t, b)) != MP_OKAY) { - return res; - } - px = a->used; - x = a; - } - - for (ix = 0; ix < px; ix++) { - t.dp[ix] &= x->dp[ix]; - } - - /* zero digits above the last from the smallest mp_int */ - for (; ix < t.used; ix++) { - t.dp[ix] = 0; - } - - mp_clamp (&t); - mp_exch (c, &t); - mp_clear (&t); - return MP_OKAY; + int used = MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = ((a->sign == MP_NEG) && (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x & y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; } #endif diff --git a/libtommath/bn_mp_cmp.c b/libtommath/bn_mp_cmp.c index b965d4b..c042b63 100644 --- a/libtommath/bn_mp_cmp.c +++ b/libtommath/bn_mp_cmp.c @@ -1,39 +1,26 @@ #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 - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* compare two ints (signed)*/ -int -mp_cmp (mp_int * a, mp_int * b) +mp_ord mp_cmp(const mp_int *a, const mp_int *b) { - /* compare based on sign */ - if (a->sign != b->sign) { - if (a->sign == MP_NEG) { - return MP_LT; - } else { - return MP_GT; - } - } - - /* compare digits */ - if (a->sign == MP_NEG) { - /* if negative compare opposite direction */ - return mp_cmp_mag(b, a); - } else { - return mp_cmp_mag(a, b); - } + /* compare based on sign */ + if (a->sign != b->sign) { + if (a->sign == MP_NEG) { + return MP_LT; + } else { + return MP_GT; + } + } + + /* compare digits */ + if (a->sign == MP_NEG) { + /* if negative compare opposite direction */ + return mp_cmp_mag(b, a); + } else { + return mp_cmp_mag(a, b); + } } #endif diff --git a/libtommath/bn_mp_cmp_d.c b/libtommath/bn_mp_cmp_d.c index a446bb4..947c57a 100644 --- a/libtommath/bn_mp_cmp_d.c +++ b/libtommath/bn_mp_cmp_d.c @@ -1,40 +1,28 @@ #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 - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* compare a digit */ -int mp_cmp_d(mp_int * a, mp_digit b) +mp_ord mp_cmp_d(const mp_int *a, mp_digit b) { - /* compare based on sign */ - if (a->sign == MP_NEG) { - return MP_LT; - } + /* compare based on sign */ + if (a->sign == MP_NEG) { + return MP_LT; + } - /* compare based on magnitude */ - if (a->used > 1) { - return MP_GT; - } + /* compare based on magnitude */ + if (a->used > 1) { + return MP_GT; + } - /* compare the only digit of a to b */ - if (a->dp[0] > b) { - return MP_GT; - } else if (a->dp[0] < b) { - return MP_LT; - } else { - return MP_EQ; - } + /* compare the only digit of a to b */ + if (a->dp[0] > b) { + return MP_GT; + } else if (a->dp[0] < b) { + return MP_LT; + } else { + return MP_EQ; + } } #endif diff --git a/libtommath/bn_mp_cmp_mag.c b/libtommath/bn_mp_cmp_mag.c index 3506d2b..850e083 100644 --- a/libtommath/bn_mp_cmp_mag.c +++ b/libtommath/bn_mp_cmp_mag.c @@ -1,51 +1,39 @@ #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 - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* compare maginitude of two ints (unsigned) */ -int mp_cmp_mag (mp_int * a, mp_int * b) +mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b) { - int n; - mp_digit *tmpa, *tmpb; + int n; + const mp_digit *tmpa, *tmpb; - /* compare based on # of non-zero digits */ - if (a->used > b->used) { - return MP_GT; - } - - if (a->used < b->used) { - return MP_LT; - } + /* compare based on # of non-zero digits */ + if (a->used > b->used) { + return MP_GT; + } - /* alias for a */ - tmpa = a->dp + (a->used - 1); + if (a->used < b->used) { + return MP_LT; + } - /* alias for b */ - tmpb = b->dp + (a->used - 1); + /* alias for a */ + tmpa = a->dp + (a->used - 1); - /* compare based on digits */ - for (n = 0; n < a->used; ++n, --tmpa, --tmpb) { - if (*tmpa > *tmpb) { - return MP_GT; - } + /* alias for b */ + tmpb = b->dp + (a->used - 1); - if (*tmpa < *tmpb) { - return MP_LT; - } - } - return MP_EQ; + /* compare based on digits */ + for (n = 0; n < a->used; ++n, --tmpa, --tmpb) { + if (*tmpa > *tmpb) { + return MP_GT; + } + + if (*tmpa < *tmpb) { + return MP_LT; + } + } + return MP_EQ; } #endif diff --git a/libtommath/bn_mp_or.c b/libtommath/bn_mp_or.c index aa5b1bd..afcdd9b 100644 --- a/libtommath/bn_mp_or.c +++ b/libtommath/bn_mp_or.c @@ -1,46 +1,56 @@ #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) +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement or */ +mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c) { - int res, ix, px; - mp_int t, *x; - - if (a->used > b->used) { - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - px = b->used; - x = b; - } else { - if ((res = mp_init_copy (&t, b)) != MP_OKAY) { - return res; - } - px = a->used; - x = a; - } - - for (ix = 0; ix < px; ix++) { - t.dp[ix] |= x->dp[ix]; - } - mp_clamp (&t); - mp_exch (c, &t); - mp_clear (&t); - return MP_OKAY; + int used = MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = ((a->sign == MP_NEG) || (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x | y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; } #endif diff --git a/libtommath/bn_mp_xor.c b/libtommath/bn_mp_xor.c index 432f42e..fba6617 100644 --- a/libtommath/bn_mp_xor.c +++ b/libtommath/bn_mp_xor.c @@ -1,47 +1,56 @@ #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) +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement xor */ +mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c) { - int res, ix, px; - mp_int t, *x; - - if (a->used > b->used) { - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - px = b->used; - x = b; - } else { - if ((res = mp_init_copy (&t, b)) != MP_OKAY) { - return res; - } - px = a->used; - x = a; - } - - for (ix = 0; ix < px; ix++) { - t.dp[ix] ^= x->dp[ix]; - } - mp_clamp (&t); - mp_exch (c, &t); - mp_clear (&t); - return MP_OKAY; + int used = MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = (a->sign != b->sign) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x ^ y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; } #endif diff --git a/libtommath/tommath.h b/libtommath/tommath.h index 49b2c2a..df460f6 100644 --- a/libtommath/tommath.h +++ b/libtommath/tommath.h @@ -1,28 +1,14 @@ -/* 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 - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + #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 @@ -31,6 +17,10 @@ #define MAX(x,y) ((x)>(y)?(x):(y)) #endif +#ifndef MP_NO_FILE +# include <stdio.h> +#endif + #ifdef __cplusplus extern "C" { @@ -131,45 +121,74 @@ extern "C" { #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1)) #define MP_DIGIT_MAX MP_MASK -/* equalities */ -#define MP_LT -1 /* less than */ -#define MP_EQ 0 /* equal to */ -#define MP_GT 1 /* greater than */ +/* Primality generation flags */ +#define LTM_PRIME_BBS 0x0001 /* BBS style prime */ +#define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ +#define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ +#ifdef MP_USE_ENUMS +typedef enum { + MP_ZPOS = 0, + MP_NEG = 1 +} mp_sign; +typedef enum { + MP_LT = -1, + MP_EQ = 0, + MP_GT = 1 +} mp_ord; +typedef enum { + MP_NO = 0, + MP_YES = 1 +} mp_bool; +typedef enum { + MP_OKAY = 0, + MP_ERR = -1, + MP_MEM = -2, + MP_VAL = -3, + MP_ITER = -4 +} mp_err; +#else +typedef int mp_sign; #define MP_ZPOS 0 /* positive integer */ #define MP_NEG 1 /* negative */ - +typedef int mp_ord; +#define MP_LT -1 /* less than */ +#define MP_EQ 0 /* equal to */ +#define MP_GT 1 /* greater than */ +typedef int mp_bool; +#define MP_YES 1 /* yes response */ +#define MP_NO 0 /* no response */ +typedef int mp_err; #define MP_OKAY 0 /* ok result */ +#define MP_ERR -1 /* unknown error */ #define MP_MEM -2 /* out of mem */ #define MP_VAL -3 /* invalid input */ #define MP_RANGE MP_VAL +#define MP_ITER -4 /* Max. iterations reached */ +#endif -#define MP_YES 1 /* yes response */ -#define MP_NO 0 /* no response */ - -/* Primality generation flags */ -#define LTM_PRIME_BBS 0x0001 /* BBS style prime */ -#define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ -#define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ - -typedef int mp_err; +/* tunable cutoffs */ -/* you'll have to tune these... */ -extern int KARATSUBA_MUL_CUTOFF, - KARATSUBA_SQR_CUTOFF, - TOOM_MUL_CUTOFF, - TOOM_SQR_CUTOFF; +#ifndef MP_FIXED_CUTOFFS +extern int +KARATSUBA_MUL_CUTOFF, +KARATSUBA_SQR_CUTOFF, +TOOM_MUL_CUTOFF, +TOOM_SQR_CUTOFF; +#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 +# ifndef MP_LOW_MEM +# define MP_PREC 32 /* default digits of precision */ +# elif defined(MP_8BIT) +# define MP_PREC 16 /* 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) */ @@ -177,8 +196,9 @@ extern int KARATSUBA_MUL_CUTOFF, /* the infamous mp_int structure */ typedef struct { - int used, alloc, sign; - mp_digit *dp; + int used, alloc; + mp_sign sign; + mp_digit *dp; } mp_int; /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */ @@ -190,17 +210,17 @@ typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat); #define SIGN(m) ((m)->sign) /* error code to char* string */ -char *mp_error_to_string(int code); +const char *mp_error_to_string(mp_err code); /* ---> init and deinit bignum functions <--- */ /* init a bignum */ -int mp_init(mp_int *a); +mp_err mp_init(mp_int *a); /* free a bignum */ void mp_clear(mp_int *a); /* init a null terminated series of arguments */ -int mp_init_multi(mp_int *mp, ...); +mp_err mp_init_multi(mp_int *mp, ...); /* clear a null terminated series of arguments */ void mp_clear_multi(mp_int *mp, ...); @@ -209,18 +229,19 @@ void mp_clear_multi(mp_int *mp, ...); void mp_exch(mp_int *a, mp_int *b); /* shrink ram required for a bignum */ -int mp_shrink(mp_int *a); +mp_err mp_shrink(mp_int *a); /* grow an int to a given size */ -int mp_grow(mp_int *a, int size); +mp_err mp_grow(mp_int *a, int size); /* init to a given number of digits */ -int mp_init_size(mp_int *a, int size); +mp_err 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) +#define mp_isneg(a) (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO) /* set to zero */ void mp_zero(mp_int *a); @@ -241,141 +262,153 @@ int mp_init_set (mp_int * a, mp_digit b); int mp_init_set_int (mp_int * a, unsigned long b); /* copy, b = a */ -int mp_copy(mp_int *a, mp_int *b); +mp_err mp_copy(const mp_int *a, mp_int *b); /* inits and copies, a = b */ -int mp_init_copy(mp_int *a, mp_int *b); +mp_err mp_init_copy(mp_int *a, const mp_int *b); /* trim unused digits */ void mp_clamp(mp_int *a); +/* import binary data */ +mp_err mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails, const void *op); + +/* export binary data */ +mp_err mp_export(void *rop, size_t *countp, int order, size_t size, int endian, size_t nails, const 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); +mp_err mp_lshd(mp_int *a, int b); -/* c = a / 2**b */ -int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d); +/* c = a / 2**b, implemented as c = a >> b */ +mp_err 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); +mp_err mp_div_2(const mp_int *a, mp_int *b); -/* c = a * 2**b */ -int mp_mul_2d(mp_int *a, int b, mp_int *c); +/* c = a * 2**b, implemented as c = a << b */ +mp_err 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); +mp_err mp_mul_2(const mp_int *a, mp_int *b); -/* c = a mod 2**d */ -int mp_mod_2d(mp_int *a, int b, mp_int *c); +/* c = a mod 2**b */ +mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c); /* computes a = 2**b */ -int mp_2expt(mp_int *a, int b); +mp_err 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); +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); +mp_err mp_rand(mp_int *a, int digits); /* ---> binary operations <--- */ -/* c = a XOR b */ -int mp_xor(mp_int *a, mp_int *b, mp_int *c); +/* c = a XOR b (two complement) */ +mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c); -/* c = a OR b */ -int mp_or(mp_int *a, mp_int *b, mp_int *c); +/* c = a OR b (two complement) */ +mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c); -/* c = a AND b */ -int mp_and(mp_int *a, mp_int *b, mp_int *c); +/* c = a AND b (two complement) */ +mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c); /* ---> Basic arithmetic <--- */ /* b = -a */ -int mp_neg(mp_int *a, mp_int *b); +mp_err mp_neg(const mp_int *a, mp_int *b); /* b = |a| */ -int mp_abs(mp_int *a, mp_int *b); +mp_err mp_abs(const mp_int *a, mp_int *b); /* compare a to b */ -int mp_cmp(mp_int *a, mp_int *b); +mp_ord mp_cmp(const mp_int *a, const mp_int *b); /* compare |a| to |b| */ -int mp_cmp_mag(mp_int *a, mp_int *b); +mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b); /* c = a + b */ -int mp_add(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c); /* c = a - b */ -int mp_sub(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c); /* c = a * b */ -int mp_mul(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c); /* b = a*a */ -int mp_sqr(mp_int *a, mp_int *b); +mp_err mp_sqr(const mp_int *a, mp_int *b); /* a/b => cb + d == a */ -int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d); /* c = a mod b, 0 <= c < b */ -int mp_mod(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c); /* ---> single digit functions <--- */ /* compare against a single digit */ -int mp_cmp_d(mp_int *a, mp_digit b); +mp_ord mp_cmp_d(const mp_int *a, mp_digit b); /* c = a + b */ -int mp_add_d(mp_int *a, mp_digit b, mp_int *c); +mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c); + +/* Increment "a" by one like "a++". Changes input! */ +mp_err mp_incr(mp_int *a); /* c = a - b */ -int mp_sub_d(mp_int *a, mp_digit b, mp_int *c); +mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c); + +/* Decrement "a" by one like "a--". Changes input! */ +mp_err mp_decr(mp_int *a); /* c = a * b */ -int mp_mul_d(mp_int *a, mp_digit b, mp_int *c); +mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c); /* a/b => cb + d == a */ -int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d); +mp_err mp_div_d(const 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); +mp_err mp_div_3(const 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); +mp_err mp_expt_d(const 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); +mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c); /* ---> number theory <--- */ /* d = a + b (mod c) */ -int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); /* d = a - b (mod c) */ -int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); /* d = a * b (mod c) */ -int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); /* c = a * a (mod b) */ -int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c); /* c = 1/a (mod b) */ -int mp_invmod(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c); /* c = (a, b) */ -int mp_gcd(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c); /* produces value such that U1*a + U2*b = U3 */ -int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3); +mp_err mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3); /* c = [a, b] or (a*b)/(a, b) */ -int mp_lcm(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c); /* finds one of the b'th root of a, such that |c|**b <= |a| * @@ -384,64 +417,64 @@ int mp_lcm(mp_int *a, mp_int *b, mp_int *c); 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); +mp_err mp_sqrt(const mp_int *arg, mp_int *ret); /* is number a square? */ -int mp_is_square(mp_int *arg, int *ret); +mp_err mp_is_square(const mp_int *arg, mp_bool *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 */ -int mp_reduce_setup(mp_int *a, mp_int *b); +mp_err mp_reduce_setup(mp_int *a, const mp_int *b); /* Barrett Reduction, computes a (mod b) with a precomputed value c * - * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely - * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code]. + * Assumes that 0 < x <= m*m, note if 0 > x > -(m*m) then you can merely + * compute the reduction as -1 * mp_reduce(mp_abs(x)) [pseudo code]. */ -int mp_reduce(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu); /* setups the montgomery reduction */ -int mp_montgomery_setup(mp_int *a, mp_digit *mp); +mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho); /* computes a = B**n mod b without division or multiplication useful for * normalizing numbers in a Montgomery system. */ -int mp_montgomery_calc_normalization(mp_int *a, mp_int *b); +mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b); /* computes x/R == x (mod N) via Montgomery Reduction */ -int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); +mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho); /* returns 1 if a is a valid DR modulus */ -int mp_dr_is_modulus(mp_int *a); +mp_bool mp_dr_is_modulus(const mp_int *a); /* sets the value of "d" required for mp_dr_reduce */ -void mp_dr_setup(mp_int *a, mp_digit *d); +void mp_dr_setup(const mp_int *a, mp_digit *d); -/* reduces a modulo b using the Diminished Radix method */ -int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp); +/* reduces a modulo n using the Diminished Radix method */ +mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k); /* returns true if a can be reduced with mp_reduce_2k */ -int mp_reduce_is_2k(mp_int *a); +mp_bool mp_reduce_is_2k(const mp_int *a); /* determines k value for 2k reduction */ -int mp_reduce_2k_setup(mp_int *a, mp_digit *d); +mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d); /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ -int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d); +mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d); /* returns true if a can be reduced with mp_reduce_2k_l */ -int mp_reduce_is_2k_l(mp_int *a); +mp_bool mp_reduce_is_2k_l(const mp_int *a); /* determines k value for 2k reduction */ -int mp_reduce_2k_setup_l(mp_int *a, mp_int *d); +mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d); /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ -int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d); +mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d); -/* d = a**b (mod c) */ -int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +/* Y = G**X (mod P) */ +mp_err mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y); /* ---> Primes <--- */ @@ -456,41 +489,58 @@ int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 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); +mp_err mp_prime_is_divisible(mp_int *a, mp_bool *result); /* performs one Fermat test of "a" using base "b". * Sets result to 0 if composite or 1 if probable prime */ -int mp_prime_fermat(mp_int *a, mp_int *b, int *result); +mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, mp_bool *result); /* 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); +mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, mp_bool *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 + * 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 +/* performs one strong Lucas-Selfridge test of "a". + * Sets result to 0 if composite or 1 if probable prime + */ +mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result); + +/* performs one Frobenius test of "a" as described by Paul Underwood. + * Sets result to 0 if composite or 1 if probable prime + */ +mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result); + +/* performs t random rounds of Miller-Rabin on "a" additional to + * bases 2 and 3. Also performs an initial sieve of trial * division. Determines if "a" is prime with probability * of error no more than (1/4)**t. + * Both a strong Lucas-Selfridge to complete the BPSW test + * and a separate Frobenius test are available at compile time. + * With t<0 a deterministic test is run for primes up to + * 318665857834031151167461. With t<13 (abs(t)-13) additional + * tests with sequential small primes are run starting at 43. + * Is Fips 186.4 compliant if called with t as computed by + * mp_prime_rabin_miller_trials(); * * Sets result to 1 if probably prime, 0 otherwise */ -int mp_prime_is_prime(mp_int *a, int t, int *result); +mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result); /* 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); +mp_err 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 + * 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 @@ -503,38 +553,43 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style); /* 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 + * + * MP_PRIME_BBS - make prime congruent to 3 mod 4 + * MP_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies MP_PRIME_BBS) + * MP_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_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); +mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); -/* ---> radix conversion <--- */ -int mp_count_bits(mp_int *a); - -int mp_unsigned_bin_size(mp_int *a); -int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); -int mp_to_unsigned_bin(mp_int *a, unsigned char *b); -int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); - -int mp_signed_bin_size(mp_int *a); -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); +/* Integer logarithm to integer base */ +mp_err mp_ilogb(const mp_int *a, mp_digit base, mp_int *c); -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); +/* ---> radix conversion <--- */ +int mp_count_bits(const mp_int *a); + +int mp_unsigned_bin_size(const mp_int *a); +mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); +mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b); +mp_err mp_to_unsigned_bin_n(const mp_int * a, unsigned char *b, unsigned long *outlen); + +int mp_signed_bin_size(const mp_int *a); +mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); +mp_err mp_to_signed_bin(const mp_int *a, unsigned char *b); +mp_err mp_to_signed_bin_n(const mp_int * a, unsigned char *b, unsigned long *outlen); + +mp_err mp_read_radix(mp_int *a, const char *str, int radix); +mp_err mp_toradix(const mp_int *a, char *str, int radix); +mp_err mp_toradix_n(const mp_int * a, char *str, int radix, int maxlen); +mp_err mp_radix_size(const mp_int *a, int radix, int *size); + +#ifndef MP_NO_FILE +mp_err mp_fread(mp_int *a, int radix, FILE *stream); +mp_err mp_fwrite(const 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) |