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Merge branch 'feature/mp_sqrtmod_prime' into develop 

Signed-off-by: Tom St Denis <tstdenis82@gmail.com>
This commit is contained in:
Tom St Denis 2015-10-30 18:05:12 -04:00
parent 079b0f65a9 c31102bc0e
commit 5b3178d83e
10 changed files with 9439 additions and 7989 deletions
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122
bn_mp_sqrtmod_prime.c Normal file
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@ -0,0 +1,122 @@
#include <tommath.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 */
mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
/* 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)) {
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 */
mp_set_int(&Z, 2);
/* 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) {
mp_copy(&R, ret);
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

17228
callgraph.txt
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9
makefile
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@ -67,10 +67,11 @@ bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.
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_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
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

9
makefile.bcc
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@ -27,10 +27,11 @@ bn_mp_rand.obj bn_mp_read_radix.obj bn_mp_read_signed_bin.obj bn_mp_read_unsigne
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_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
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

9
makefile.cygwin_dll
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@ -32,10 +32,11 @@ bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.
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_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
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

9
makefile.icc
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@ -58,10 +58,11 @@ bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.
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_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
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

9
makefile.msvc
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@ -26,10 +26,11 @@ bn_mp_rand.obj bn_mp_read_radix.obj bn_mp_read_signed_bin.obj bn_mp_read_unsigne
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_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
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

9
makefile.shared
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@ -59,10 +59,11 @@ bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.
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_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
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

3
tommath.h
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@ -430,6 +430,9 @@ 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);

21
tommath_class.h
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@ -112,6 +112,7 @@
#define BN_MP_SQR_C
#define BN_MP_SQRMOD_C
#define BN_MP_SQRT_C
#define BN_MP_SQRTMOD_PRIME_C
#define BN_MP_SUB_C
#define BN_MP_SUB_D_C
#define BN_MP_SUBMOD_C
@ -423,7 +424,6 @@
#endif
#if defined(BN_MP_GET_LONG_LONG_C)
#define BN_MP_GET_LONG_C
#endif
#if defined(BN_MP_GROW_C)
@ -866,6 +866,25 @@
#define BN_MP_CLEAR_C
#endif
#if defined(BN_MP_SQRTMOD_PRIME_C)
#define BN_MP_CMP_D_C
#define BN_MP_ZERO_C
#define BN_MP_JACOBI_C
#define BN_MP_INIT_MULTI_C
#define BN_MP_MOD_D_C
#define BN_MP_ADD_D_C
#define BN_MP_DIV_2_C
#define BN_MP_EXPTMOD_C
#define BN_MP_COPY_C
#define BN_MP_SUB_D_C
#define BN_MP_ISEVEN_C
#define BN_MP_SET_INT_C
#define BN_MP_SQRMOD_C
#define BN_MP_MULMOD_C
#define BN_MP_SET_C
#define BN_MP_CLEAR_MULTI_C
#endif
#if defined(BN_MP_SUB_C)
#define BN_S_MP_ADD_C
#define BN_MP_CMP_MAG_C