9542 lines
244 KiB
C
9542 lines
244 KiB
C
/* Start: bn_cutoffs.c */
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#include "tommath_private.h"
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#ifdef BN_CUTOFFS_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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#ifndef MP_FIXED_CUTOFFS
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#include "tommath_cutoffs.h"
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int KARATSUBA_MUL_CUTOFF = MP_DEFAULT_KARATSUBA_MUL_CUTOFF,
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KARATSUBA_SQR_CUTOFF = MP_DEFAULT_KARATSUBA_SQR_CUTOFF,
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TOOM_MUL_CUTOFF = MP_DEFAULT_TOOM_MUL_CUTOFF,
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TOOM_SQR_CUTOFF = MP_DEFAULT_TOOM_SQR_CUTOFF;
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#endif
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#endif
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/* End: bn_cutoffs.c */
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/* Start: bn_deprecated.c */
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#include "tommath_private.h"
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#ifdef BN_DEPRECATED_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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#ifdef BN_MP_GET_BIT_C
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int mp_get_bit(const mp_int *a, int b)
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{
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if (b < 0) {
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return MP_VAL;
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}
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return (s_mp_get_bit(a, (unsigned int)b) == MP_YES) ? MP_YES : MP_NO;
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}
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#endif
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#ifdef BN_MP_JACOBI_C
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mp_err mp_jacobi(const mp_int *a, const mp_int *n, int *c)
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{
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if (a->sign == MP_NEG) {
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return MP_VAL;
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}
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if (mp_cmp_d(n, 0uL) != MP_GT) {
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return MP_VAL;
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}
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return mp_kronecker(a, n, c);
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}
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#endif
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#ifdef BN_MP_PRIME_RANDOM_EX_C
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mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat)
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{
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return s_mp_prime_random_ex(a, t, size, flags, cb, dat);
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}
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#endif
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#ifdef BN_MP_RAND_DIGIT_C
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mp_err mp_rand_digit(mp_digit *r)
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{
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mp_err err = s_mp_rand_source(r, sizeof(mp_digit));
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*r &= MP_MASK;
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return err;
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}
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#endif
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#ifdef BN_FAST_MP_INVMOD_C
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mp_err fast_mp_invmod(const mp_int *a, const mp_int *b, mp_int *c)
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{
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return s_mp_invmod_fast(a, b, c);
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}
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#endif
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#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
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mp_err fast_mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
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{
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return s_mp_montgomery_reduce_fast(x, n, rho);
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}
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#endif
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#ifdef BN_FAST_S_MP_MUL_DIGS_C
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mp_err fast_s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
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{
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return s_mp_mul_digs_fast(a, b, c, digs);
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}
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#endif
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#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
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mp_err fast_s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
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{
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return s_mp_mul_high_digs_fast(a, b, c, digs);
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}
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#endif
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#ifdef BN_FAST_S_MP_SQR_C
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mp_err fast_s_mp_sqr(const mp_int *a, mp_int *b)
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{
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return s_mp_sqr_fast(a, b);
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}
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#endif
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#ifdef BN_MP_BALANCE_MUL_C
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mp_err mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c)
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{
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return s_mp_balance_mul(a, b, c);
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}
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#endif
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#ifdef BN_MP_EXPTMOD_FAST_C
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mp_err mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode)
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{
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return s_mp_exptmod_fast(G, X, P, Y, redmode);
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}
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#endif
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#ifdef BN_MP_INVMOD_SLOW_C
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mp_err mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c)
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{
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return s_mp_invmod_slow(a, b, c);
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}
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#endif
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#ifdef BN_MP_KARATSUBA_MUL_C
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mp_err mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
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{
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return s_mp_karatsuba_mul(a, b, c);
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}
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#endif
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#ifdef BN_MP_KARATSUBA_SQR_C
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mp_err mp_karatsuba_sqr(const mp_int *a, mp_int *b)
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{
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return s_mp_karatsuba_sqr(a, b);
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}
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#endif
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#ifdef BN_MP_TOOM_MUL_C
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mp_err mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c)
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{
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return s_mp_toom_mul(a, b, c);
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}
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#endif
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#ifdef BN_MP_TOOM_SQR_C
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mp_err mp_toom_sqr(const mp_int *a, mp_int *b)
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{
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return s_mp_toom_sqr(a, b);
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}
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#endif
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#ifdef S_MP_REVERSE_C
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void bn_reverse(unsigned char *s, int len)
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{
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if (len > 0) {
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s_mp_reverse(s, (size_t)len);
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}
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}
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#endif
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#ifdef BN_MP_TC_AND_C
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mp_err mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c)
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{
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return mp_and(a, b, c);
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}
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#endif
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#ifdef BN_MP_TC_OR_C
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mp_err mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c)
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{
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return mp_or(a, b, c);
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}
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#endif
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#ifdef BN_MP_TC_XOR_C
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mp_err mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c)
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{
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return mp_xor(a, b, c);
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}
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#endif
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#ifdef BN_MP_TC_DIV_2D_C
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mp_err mp_tc_div_2d(const mp_int *a, int b, mp_int *c)
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{
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return mp_signed_rsh(a, b, c);
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}
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#endif
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#ifdef BN_MP_INIT_SET_INT_C
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mp_err mp_init_set_int(mp_int *a, unsigned long b)
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{
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return mp_init_u32(a, (uint32_t)b);
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}
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#endif
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#ifdef BN_MP_SET_INT_C
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mp_err mp_set_int(mp_int *a, unsigned long b)
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{
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mp_set_u32(a, (uint32_t)b);
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return MP_OKAY;
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}
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#endif
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#ifdef BN_MP_SET_LONG_C
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mp_err mp_set_long(mp_int *a, unsigned long b)
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{
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mp_set_u64(a, b);
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return MP_OKAY;
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}
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#endif
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#ifdef BN_MP_SET_LONG_LONG_C
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mp_err mp_set_long_long(mp_int *a, unsigned long long b)
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{
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mp_set_u64(a, b);
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return MP_OKAY;
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}
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#endif
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#ifdef BN_MP_GET_INT_C
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unsigned long mp_get_int(const mp_int *a)
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{
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return (unsigned long)mp_get_mag_u32(a);
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}
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#endif
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#ifdef BN_MP_GET_LONG_C
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unsigned long mp_get_long(const mp_int *a)
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{
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return (unsigned long)mp_get_mag_ul(a);
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}
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#endif
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#ifdef BN_MP_GET_LONG_LONG_C
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unsigned long long mp_get_long_long(const mp_int *a)
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{
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return mp_get_mag_ull(a);
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}
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#endif
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#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
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mp_err mp_prime_is_divisible(const mp_int *a, mp_bool *result)
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{
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return s_mp_prime_is_divisible(a, result);
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}
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#endif
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#ifdef BN_MP_EXPT_D_EX_C
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mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
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{
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(void)fast;
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if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) {
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return MP_VAL;
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}
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return mp_expt_u32(a, (uint32_t)b, c);
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}
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#endif
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#ifdef BN_MP_EXPT_D_C
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mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c)
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{
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if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) {
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return MP_VAL;
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}
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return mp_expt_u32(a, (uint32_t)b, c);
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}
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#endif
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#ifdef BN_MP_N_ROOT_EX_C
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mp_err mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
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{
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(void)fast;
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if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) {
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return MP_VAL;
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}
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return mp_root_u32(a, (uint32_t)b, c);
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}
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#endif
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#ifdef BN_MP_N_ROOT_C
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mp_err mp_n_root(const mp_int *a, mp_digit b, mp_int *c)
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{
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if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) {
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return MP_VAL;
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}
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return mp_root_u32(a, (uint32_t)b, c);
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}
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#endif
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#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
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int mp_unsigned_bin_size(const mp_int *a)
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{
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return (int)mp_ubin_size(a);
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}
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#endif
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#ifdef BN_MP_READ_UNSIGNED_BIN_C
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mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c)
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{
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return mp_from_ubin(a, b, (size_t) c);
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}
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#endif
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#ifdef BN_MP_TO_UNSIGNED_BIN_C
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mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b)
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{
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return mp_to_ubin(a, b, SIZE_MAX, NULL);
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}
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#endif
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#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
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mp_err mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen)
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{
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size_t n = mp_ubin_size(a);
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if (*outlen < (unsigned long)n) {
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return MP_VAL;
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}
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*outlen = (unsigned long)n;
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return mp_to_ubin(a, b, n, NULL);
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}
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#endif
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#ifdef BN_MP_SIGNED_BIN_SIZE_C
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int mp_signed_bin_size(const mp_int *a)
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{
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return (int)mp_sbin_size(a);
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}
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#endif
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#ifdef BN_MP_READ_SIGNED_BIN_C
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mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c)
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{
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return mp_from_sbin(a, b, (size_t) c);
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}
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#endif
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#ifdef BN_MP_TO_SIGNED_BIN_C
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mp_err mp_to_signed_bin(const mp_int *a, unsigned char *b)
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{
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return mp_to_sbin(a, b, SIZE_MAX, NULL);
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}
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#endif
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#ifdef BN_MP_TO_SIGNED_BIN_N_C
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mp_err mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen)
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{
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size_t n = mp_sbin_size(a);
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if (*outlen < (unsigned long)n) {
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return MP_VAL;
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}
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*outlen = (unsigned long)n;
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return mp_to_sbin(a, b, n, NULL);
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}
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#endif
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#ifdef BN_MP_TORADIX_N_C
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mp_err mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen)
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{
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if (maxlen < 0) {
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return MP_VAL;
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}
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return mp_to_radix(a, str, (size_t)maxlen, NULL, radix);
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}
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#endif
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#ifdef BN_MP_TORADIX_C
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mp_err mp_toradix(const mp_int *a, char *str, int radix)
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{
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return mp_to_radix(a, str, SIZE_MAX, NULL, radix);
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}
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#endif
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#ifdef BN_MP_IMPORT_C
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mp_err mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails,
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const void *op)
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{
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return mp_unpack(rop, count, order, size, endian, nails, op);
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}
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#endif
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#ifdef BN_MP_EXPORT_C
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mp_err mp_export(void *rop, size_t *countp, int order, size_t size,
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int endian, size_t nails, const mp_int *op)
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{
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return mp_pack(rop, SIZE_MAX, countp, order, size, endian, nails, op);
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}
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#endif
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#endif
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/* End: bn_deprecated.c */
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/* Start: bn_mp_2expt.c */
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#include "tommath_private.h"
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#ifdef BN_MP_2EXPT_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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/* computes a = 2**b
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*
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* Simple algorithm which zeroes the int, grows it then just sets one bit
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* as required.
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*/
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mp_err mp_2expt(mp_int *a, int b)
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{
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mp_err err;
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/* zero a as per default */
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mp_zero(a);
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/* grow a to accomodate the single bit */
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if ((err = mp_grow(a, (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) {
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return err;
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}
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/* set the used count of where the bit will go */
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a->used = (b / MP_DIGIT_BIT) + 1;
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/* put the single bit in its place */
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a->dp[b / MP_DIGIT_BIT] = (mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT);
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return MP_OKAY;
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}
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#endif
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/* End: bn_mp_2expt.c */
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/* Start: bn_mp_abs.c */
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#include "tommath_private.h"
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#ifdef BN_MP_ABS_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
|
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|
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/* b = |a|
|
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*
|
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* Simple function copies the input and fixes the sign to positive
|
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*/
|
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mp_err mp_abs(const mp_int *a, mp_int *b)
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{
|
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mp_err err;
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/* copy a to b */
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if (a != b) {
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if ((err = mp_copy(a, b)) != MP_OKAY) {
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return err;
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}
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}
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/* force the sign of b to positive */
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b->sign = MP_ZPOS;
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|
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return MP_OKAY;
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}
|
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#endif
|
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|
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/* End: bn_mp_abs.c */
|
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|
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/* Start: bn_mp_add.c */
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#include "tommath_private.h"
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#ifdef BN_MP_ADD_C
|
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
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/* high level addition (handles signs) */
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mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c)
|
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{
|
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mp_sign sa, sb;
|
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mp_err err;
|
|
|
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/* get sign of both inputs */
|
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sa = a->sign;
|
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sb = b->sign;
|
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|
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/* handle two cases, not four */
|
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if (sa == sb) {
|
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/* both positive or both negative */
|
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/* add their magnitudes, copy the sign */
|
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c->sign = sa;
|
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err = s_mp_add(a, b, c);
|
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} else {
|
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/* one positive, the other negative */
|
|
/* subtract the one with the greater magnitude from */
|
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/* the one of the lesser magnitude. The result gets */
|
|
/* the sign of the one with the greater magnitude. */
|
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if (mp_cmp_mag(a, b) == MP_LT) {
|
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c->sign = sb;
|
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err = s_mp_sub(b, a, c);
|
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} else {
|
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c->sign = sa;
|
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err = s_mp_sub(a, b, c);
|
|
}
|
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}
|
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return err;
|
|
}
|
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|
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#endif
|
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|
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/* End: bn_mp_add.c */
|
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|
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/* Start: bn_mp_add_d.c */
|
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#include "tommath_private.h"
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#ifdef BN_MP_ADD_D_C
|
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* single digit addition */
|
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mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c)
|
|
{
|
|
mp_err err;
|
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int ix, oldused;
|
|
mp_digit *tmpa, *tmpc;
|
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|
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/* grow c as required */
|
|
if (c->alloc < (a->used + 1)) {
|
|
if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* if a is negative and |a| >= b, call c = |a| - b */
|
|
if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) {
|
|
mp_int a_ = *a;
|
|
/* temporarily fix sign of a */
|
|
a_.sign = MP_ZPOS;
|
|
|
|
/* c = |a| - b */
|
|
err = mp_sub_d(&a_, b, c);
|
|
|
|
/* fix sign */
|
|
c->sign = MP_NEG;
|
|
|
|
/* clamp */
|
|
mp_clamp(c);
|
|
|
|
return err;
|
|
}
|
|
|
|
/* old number of used digits in c */
|
|
oldused = c->used;
|
|
|
|
/* source alias */
|
|
tmpa = a->dp;
|
|
|
|
/* destination alias */
|
|
tmpc = c->dp;
|
|
|
|
/* if a is positive */
|
|
if (a->sign == MP_ZPOS) {
|
|
/* add digits, mu is carry */
|
|
mp_digit mu = b;
|
|
for (ix = 0; ix < a->used; ix++) {
|
|
*tmpc = *tmpa++ + mu;
|
|
mu = *tmpc >> MP_DIGIT_BIT;
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
/* set final carry */
|
|
ix++;
|
|
*tmpc++ = mu;
|
|
|
|
/* setup size */
|
|
c->used = a->used + 1;
|
|
} else {
|
|
/* a was negative and |a| < b */
|
|
c->used = 1;
|
|
|
|
/* the result is a single digit */
|
|
if (a->used == 1) {
|
|
*tmpc++ = b - a->dp[0];
|
|
} else {
|
|
*tmpc++ = b;
|
|
}
|
|
|
|
/* setup count so the clearing of oldused
|
|
* can fall through correctly
|
|
*/
|
|
ix = 1;
|
|
}
|
|
|
|
/* sign always positive */
|
|
c->sign = MP_ZPOS;
|
|
|
|
/* now zero to oldused */
|
|
MP_ZERO_DIGITS(tmpc, oldused - ix);
|
|
mp_clamp(c);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_add_d.c */
|
|
|
|
/* Start: bn_mp_addmod.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_ADDMOD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* d = a + b (mod c) */
|
|
mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
|
|
{
|
|
mp_err err;
|
|
mp_int t;
|
|
|
|
if ((err = mp_init(&t)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_add(a, b, &t)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
err = mp_mod(&t, c, d);
|
|
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_addmod.c */
|
|
|
|
/* Start: bn_mp_and.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_AND_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 used = MP_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
|
|
|
|
/* End: bn_mp_and.c */
|
|
|
|
/* Start: bn_mp_clamp.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_CLAMP_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
* are no more leading digits
|
|
*/
|
|
void mp_clamp(mp_int *a)
|
|
{
|
|
/* decrease used while the most significant digit is
|
|
* zero.
|
|
*/
|
|
while ((a->used > 0) && (a->dp[a->used - 1] == 0u)) {
|
|
--(a->used);
|
|
}
|
|
|
|
/* reset the sign flag if used == 0 */
|
|
if (a->used == 0) {
|
|
a->sign = MP_ZPOS;
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_clamp.c */
|
|
|
|
/* Start: bn_mp_clear.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_CLEAR_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* clear one (frees) */
|
|
void mp_clear(mp_int *a)
|
|
{
|
|
/* only do anything if a hasn't been freed previously */
|
|
if (a->dp != NULL) {
|
|
/* free ram */
|
|
MP_FREE_DIGITS(a->dp, a->alloc);
|
|
|
|
/* reset members to make debugging easier */
|
|
a->dp = NULL;
|
|
a->alloc = a->used = 0;
|
|
a->sign = MP_ZPOS;
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_clear.c */
|
|
|
|
/* Start: bn_mp_clear_multi.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_CLEAR_MULTI_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
#include <stdarg.h>
|
|
|
|
void mp_clear_multi(mp_int *mp, ...)
|
|
{
|
|
mp_int *next_mp = mp;
|
|
va_list args;
|
|
va_start(args, mp);
|
|
while (next_mp != NULL) {
|
|
mp_clear(next_mp);
|
|
next_mp = va_arg(args, mp_int *);
|
|
}
|
|
va_end(args);
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_clear_multi.c */
|
|
|
|
/* Start: bn_mp_cmp.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_CMP_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* compare two ints (signed)*/
|
|
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);
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_cmp.c */
|
|
|
|
/* Start: bn_mp_cmp_d.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_CMP_D_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* compare a digit */
|
|
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 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;
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_cmp_d.c */
|
|
|
|
/* Start: bn_mp_cmp_mag.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_CMP_MAG_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* compare maginitude of two ints (unsigned) */
|
|
mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b)
|
|
{
|
|
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;
|
|
}
|
|
|
|
/* alias for a */
|
|
tmpa = a->dp + (a->used - 1);
|
|
|
|
/* alias for b */
|
|
tmpb = b->dp + (a->used - 1);
|
|
|
|
/* 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
|
|
|
|
/* End: bn_mp_cmp_mag.c */
|
|
|
|
/* Start: bn_mp_cnt_lsb.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_CNT_LSB_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
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_IS_ZERO(a)) {
|
|
return 0;
|
|
}
|
|
|
|
/* scan lower digits until non-zero */
|
|
for (x = 0; (x < a->used) && (a->dp[x] == 0u); x++) {}
|
|
q = a->dp[x];
|
|
x *= MP_DIGIT_BIT;
|
|
|
|
/* now scan this digit until a 1 is found */
|
|
if ((q & 1u) == 0u) {
|
|
do {
|
|
qq = q & 15u;
|
|
x += lnz[qq];
|
|
q >>= 4;
|
|
} while (qq == 0u);
|
|
}
|
|
return x;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_cnt_lsb.c */
|
|
|
|
/* Start: bn_mp_complement.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_COMPLEMENT_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* b = ~a */
|
|
mp_err mp_complement(const mp_int *a, mp_int *b)
|
|
{
|
|
mp_err err = mp_neg(a, b);
|
|
return (err == MP_OKAY) ? mp_sub_d(b, 1uL, b) : err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_complement.c */
|
|
|
|
/* Start: bn_mp_copy.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_COPY_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* copy, b = a */
|
|
mp_err mp_copy(const mp_int *a, mp_int *b)
|
|
{
|
|
int n;
|
|
mp_digit *tmpa, *tmpb;
|
|
mp_err err;
|
|
|
|
/* if dst == src do nothing */
|
|
if (a == b) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* grow dest */
|
|
if (b->alloc < a->used) {
|
|
if ((err = mp_grow(b, a->used)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* zero b and copy the parameters over */
|
|
/* pointer aliases */
|
|
|
|
/* source */
|
|
tmpa = a->dp;
|
|
|
|
/* destination */
|
|
tmpb = b->dp;
|
|
|
|
/* copy all the digits */
|
|
for (n = 0; n < a->used; n++) {
|
|
*tmpb++ = *tmpa++;
|
|
}
|
|
|
|
/* clear high digits */
|
|
MP_ZERO_DIGITS(tmpb, b->used - n);
|
|
|
|
/* copy used count and sign */
|
|
b->used = a->used;
|
|
b->sign = a->sign;
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_copy.c */
|
|
|
|
/* Start: bn_mp_count_bits.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_COUNT_BITS_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* returns the number of bits in an int */
|
|
int mp_count_bits(const mp_int *a)
|
|
{
|
|
int r;
|
|
mp_digit q;
|
|
|
|
/* shortcut */
|
|
if (MP_IS_ZERO(a)) {
|
|
return 0;
|
|
}
|
|
|
|
/* get number of digits and add that */
|
|
r = (a->used - 1) * MP_DIGIT_BIT;
|
|
|
|
/* take the last digit and count the bits in it */
|
|
q = a->dp[a->used - 1];
|
|
while (q > 0u) {
|
|
++r;
|
|
q >>= 1u;
|
|
}
|
|
return r;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_count_bits.c */
|
|
|
|
/* Start: bn_mp_decr.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_DECR_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* Decrement "a" by one like "a--". Changes input! */
|
|
mp_err mp_decr(mp_int *a)
|
|
{
|
|
if (MP_IS_ZERO(a)) {
|
|
mp_set(a,1uL);
|
|
a->sign = MP_NEG;
|
|
return MP_OKAY;
|
|
} else if (a->sign == MP_NEG) {
|
|
mp_err err;
|
|
a->sign = MP_ZPOS;
|
|
if ((err = mp_incr(a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
/* There is no -0 in LTM */
|
|
if (!MP_IS_ZERO(a)) {
|
|
a->sign = MP_NEG;
|
|
}
|
|
return MP_OKAY;
|
|
} else if (a->dp[0] > 1uL) {
|
|
a->dp[0]--;
|
|
if (a->dp[0] == 0u) {
|
|
mp_zero(a);
|
|
}
|
|
return MP_OKAY;
|
|
} else {
|
|
return mp_sub_d(a, 1uL,a);
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_decr.c */
|
|
|
|
/* Start: bn_mp_div.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_DIV_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
#ifdef BN_MP_DIV_SMALL
|
|
|
|
/* slower bit-bang division... also smaller */
|
|
mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
|
|
{
|
|
mp_int ta, tb, tq, q;
|
|
int n, n2;
|
|
mp_err err;
|
|
|
|
/* is divisor zero ? */
|
|
if (MP_IS_ZERO(b)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if a < b then q=0, r = a */
|
|
if (mp_cmp_mag(a, b) == MP_LT) {
|
|
if (d != NULL) {
|
|
err = mp_copy(a, d);
|
|
} else {
|
|
err = MP_OKAY;
|
|
}
|
|
if (c != NULL) {
|
|
mp_zero(c);
|
|
}
|
|
return err;
|
|
}
|
|
|
|
/* init our temps */
|
|
if ((err = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
|
|
mp_set(&tq, 1uL);
|
|
n = mp_count_bits(a) - mp_count_bits(b);
|
|
if ((err = mp_abs(a, &ta)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_abs(b, &tb)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_mul_2d(&tq, n, &tq)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
while (n-- >= 0) {
|
|
if (mp_cmp(&tb, &ta) != MP_GT) {
|
|
if ((err = mp_sub(&ta, &tb, &ta)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_add(&q, &tq, &q)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
if ((err = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = 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_IS_ZERO(c) ? MP_ZPOS : n2;
|
|
}
|
|
if (d != NULL) {
|
|
mp_exch(d, &ta);
|
|
d->sign = MP_IS_ZERO(d) ? MP_ZPOS : n;
|
|
}
|
|
LBL_ERR:
|
|
mp_clear_multi(&ta, &tb, &tq, &q, NULL);
|
|
return err;
|
|
}
|
|
|
|
#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.
|
|
*/
|
|
mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
|
|
{
|
|
mp_int q, x, y, t1, t2;
|
|
int n, t, i, norm;
|
|
mp_sign neg;
|
|
mp_err err;
|
|
|
|
/* is divisor zero ? */
|
|
if (MP_IS_ZERO(b)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if a < b then q=0, r = a */
|
|
if (mp_cmp_mag(a, b) == MP_LT) {
|
|
if (d != NULL) {
|
|
err = mp_copy(a, d);
|
|
} else {
|
|
err = MP_OKAY;
|
|
}
|
|
if (c != NULL) {
|
|
mp_zero(c);
|
|
}
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_init_size(&q, a->used + 2)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
q.used = a->used + 2;
|
|
|
|
if ((err = mp_init(&t1)) != MP_OKAY) goto LBL_Q;
|
|
|
|
if ((err = mp_init(&t2)) != MP_OKAY) goto LBL_T1;
|
|
|
|
if ((err = mp_init_copy(&x, a)) != MP_OKAY) goto LBL_T2;
|
|
|
|
if ((err = mp_init_copy(&y, b)) != MP_OKAY) goto LBL_X;
|
|
|
|
/* fix the sign */
|
|
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
|
|
x.sign = y.sign = MP_ZPOS;
|
|
|
|
/* normalize both x and y, ensure that y >= b/2, [b == 2**MP_DIGIT_BIT] */
|
|
norm = mp_count_bits(&y) % MP_DIGIT_BIT;
|
|
if (norm < (MP_DIGIT_BIT - 1)) {
|
|
norm = (MP_DIGIT_BIT - 1) - norm;
|
|
if ((err = mp_mul_2d(&x, norm, &x)) != MP_OKAY) goto LBL_Y;
|
|
if ((err = mp_mul_2d(&y, norm, &y)) != MP_OKAY) goto LBL_Y;
|
|
} else {
|
|
norm = 0;
|
|
}
|
|
|
|
/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
|
|
n = x.used - 1;
|
|
t = y.used - 1;
|
|
|
|
/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
|
|
/* y = y*b**{n-t} */
|
|
if ((err = mp_lshd(&y, n - t)) != MP_OKAY) goto LBL_Y;
|
|
|
|
while (mp_cmp(&x, &y) != MP_LT) {
|
|
++(q.dp[n - t]);
|
|
if ((err = mp_sub(&x, &y, &x)) != MP_OKAY) goto LBL_Y;
|
|
}
|
|
|
|
/* reset y by shifting it back down */
|
|
mp_rshd(&y, n - t);
|
|
|
|
/* 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 << (mp_digit)MP_DIGIT_BIT) - (mp_digit)1;
|
|
} else {
|
|
mp_word tmp;
|
|
tmp = (mp_word)x.dp[i] << (mp_word)MP_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] + 1uL) & (mp_digit)MP_MASK;
|
|
do {
|
|
q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & (mp_digit)MP_MASK;
|
|
|
|
/* find left hand */
|
|
mp_zero(&t1);
|
|
t1.dp[0] = ((t - 1) < 0) ? 0u : y.dp[t - 1];
|
|
t1.dp[1] = y.dp[t];
|
|
t1.used = 2;
|
|
if ((err = mp_mul_d(&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y;
|
|
|
|
/* find right hand */
|
|
t2.dp[0] = ((i - 2) < 0) ? 0u : x.dp[i - 2];
|
|
t2.dp[1] = x.dp[i - 1]; /* i >= 1 always holds */
|
|
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 ((err = mp_mul_d(&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y;
|
|
|
|
if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y;
|
|
|
|
if ((err = 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 ((err = mp_copy(&y, &t1)) != MP_OKAY) goto LBL_Y;
|
|
if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y;
|
|
if ((err = 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 ((err = mp_div_2d(&x, norm, &x, NULL)) != MP_OKAY) goto LBL_Y;
|
|
mp_exch(&x, d);
|
|
}
|
|
|
|
err = MP_OKAY;
|
|
|
|
LBL_Y:
|
|
mp_clear(&y);
|
|
LBL_X:
|
|
mp_clear(&x);
|
|
LBL_T2:
|
|
mp_clear(&t2);
|
|
LBL_T1:
|
|
mp_clear(&t1);
|
|
LBL_Q:
|
|
mp_clear(&q);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_div.c */
|
|
|
|
/* Start: bn_mp_div_2.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_DIV_2_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* b = a/2 */
|
|
mp_err mp_div_2(const mp_int *a, mp_int *b)
|
|
{
|
|
int x, oldused;
|
|
mp_digit r, rr, *tmpa, *tmpb;
|
|
mp_err err;
|
|
|
|
/* copy */
|
|
if (b->alloc < a->used) {
|
|
if ((err = mp_grow(b, a->used)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
oldused = b->used;
|
|
b->used = a->used;
|
|
|
|
/* source alias */
|
|
tmpa = a->dp + b->used - 1;
|
|
|
|
/* dest alias */
|
|
tmpb = b->dp + b->used - 1;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = b->used - 1; x >= 0; x--) {
|
|
/* get the carry for the next iteration */
|
|
rr = *tmpa & 1u;
|
|
|
|
/* shift the current digit, add in carry and store */
|
|
*tmpb-- = (*tmpa-- >> 1) | (r << (MP_DIGIT_BIT - 1));
|
|
|
|
/* forward carry to next iteration */
|
|
r = rr;
|
|
}
|
|
|
|
/* zero excess digits */
|
|
MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used);
|
|
|
|
b->sign = a->sign;
|
|
mp_clamp(b);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_div_2.c */
|
|
|
|
/* Start: bn_mp_div_2d.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_DIV_2D_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
|
|
mp_err mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d)
|
|
{
|
|
mp_digit D, r, rr;
|
|
int x;
|
|
mp_err err;
|
|
|
|
/* if the shift count is <= 0 then we do no work */
|
|
if (b <= 0) {
|
|
err = mp_copy(a, c);
|
|
if (d != NULL) {
|
|
mp_zero(d);
|
|
}
|
|
return err;
|
|
}
|
|
|
|
/* copy */
|
|
if ((err = mp_copy(a, c)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
/* 'a' should not be used after here - it might be the same as d */
|
|
|
|
/* get the remainder */
|
|
if (d != NULL) {
|
|
if ((err = mp_mod_2d(a, b, d)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* shift by as many digits in the bit count */
|
|
if (b >= MP_DIGIT_BIT) {
|
|
mp_rshd(c, b / MP_DIGIT_BIT);
|
|
}
|
|
|
|
/* shift any bit count < MP_DIGIT_BIT */
|
|
D = (mp_digit)(b % MP_DIGIT_BIT);
|
|
if (D != 0u) {
|
|
mp_digit *tmpc, mask, shift;
|
|
|
|
/* mask */
|
|
mask = ((mp_digit)1 << D) - 1uL;
|
|
|
|
/* shift for lsb */
|
|
shift = (mp_digit)MP_DIGIT_BIT - D;
|
|
|
|
/* alias */
|
|
tmpc = c->dp + (c->used - 1);
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = c->used - 1; x >= 0; x--) {
|
|
/* get the lower bits of this word in a temp */
|
|
rr = *tmpc & mask;
|
|
|
|
/* shift the current word and mix in the carry bits from the previous word */
|
|
*tmpc = (*tmpc >> D) | (r << shift);
|
|
--tmpc;
|
|
|
|
/* set the carry to the carry bits of the current word found above */
|
|
r = rr;
|
|
}
|
|
}
|
|
mp_clamp(c);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_div_2d.c */
|
|
|
|
/* Start: bn_mp_div_3.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_DIV_3_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* divide by three (based on routine from MPI and the GMP manual) */
|
|
mp_err mp_div_3(const mp_int *a, mp_int *c, mp_digit *d)
|
|
{
|
|
mp_int q;
|
|
mp_word w, t;
|
|
mp_digit b;
|
|
mp_err err;
|
|
int ix;
|
|
|
|
/* b = 2**MP_DIGIT_BIT / 3 */
|
|
b = ((mp_word)1 << (mp_word)MP_DIGIT_BIT) / (mp_word)3;
|
|
|
|
if ((err = mp_init_size(&q, a->used)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
q.used = a->used;
|
|
q.sign = a->sign;
|
|
w = 0;
|
|
for (ix = a->used - 1; ix >= 0; ix--) {
|
|
w = (w << (mp_word)MP_DIGIT_BIT) | (mp_word)a->dp[ix];
|
|
|
|
if (w >= 3u) {
|
|
/* multiply w by [1/3] */
|
|
t = (w * (mp_word)b) >> (mp_word)MP_DIGIT_BIT;
|
|
|
|
/* now subtract 3 * [w/3] from w, to get the remainder */
|
|
w -= t+t+t;
|
|
|
|
/* fixup the remainder as required since
|
|
* the optimization is not exact.
|
|
*/
|
|
while (w >= 3u) {
|
|
t += 1u;
|
|
w -= 3u;
|
|
}
|
|
} else {
|
|
t = 0;
|
|
}
|
|
q.dp[ix] = (mp_digit)t;
|
|
}
|
|
|
|
/* [optional] store the remainder */
|
|
if (d != NULL) {
|
|
*d = (mp_digit)w;
|
|
}
|
|
|
|
/* [optional] store the quotient */
|
|
if (c != NULL) {
|
|
mp_clamp(&q);
|
|
mp_exch(&q, c);
|
|
}
|
|
mp_clear(&q);
|
|
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_div_3.c */
|
|
|
|
/* Start: bn_mp_div_d.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_DIV_D_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* single digit division (based on routine from MPI) */
|
|
mp_err mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d)
|
|
{
|
|
mp_int q;
|
|
mp_word w;
|
|
mp_digit t;
|
|
mp_err err;
|
|
int ix;
|
|
|
|
/* cannot divide by zero */
|
|
if (b == 0u) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* quick outs */
|
|
if ((b == 1u) || MP_IS_ZERO(a)) {
|
|
if (d != NULL) {
|
|
*d = 0;
|
|
}
|
|
if (c != NULL) {
|
|
return mp_copy(a, c);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* power of two ? */
|
|
if ((b & (b - 1u)) == 0u) {
|
|
ix = 1;
|
|
while ((ix < MP_DIGIT_BIT) && (b != (((mp_digit)1)<<ix))) {
|
|
ix++;
|
|
}
|
|
if (d != NULL) {
|
|
*d = a->dp[0] & (((mp_digit)1<<(mp_digit)ix) - 1uL);
|
|
}
|
|
if (c != NULL) {
|
|
return mp_div_2d(a, ix, c, NULL);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* three? */
|
|
if (MP_HAS(MP_DIV_3) && (b == 3u)) {
|
|
return mp_div_3(a, c, d);
|
|
}
|
|
|
|
/* no easy answer [c'est la vie]. Just division */
|
|
if ((err = mp_init_size(&q, a->used)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
q.used = a->used;
|
|
q.sign = a->sign;
|
|
w = 0;
|
|
for (ix = a->used - 1; ix >= 0; ix--) {
|
|
w = (w << (mp_word)MP_DIGIT_BIT) | (mp_word)a->dp[ix];
|
|
|
|
if (w >= b) {
|
|
t = (mp_digit)(w / b);
|
|
w -= (mp_word)t * (mp_word)b;
|
|
} else {
|
|
t = 0;
|
|
}
|
|
q.dp[ix] = t;
|
|
}
|
|
|
|
if (d != NULL) {
|
|
*d = (mp_digit)w;
|
|
}
|
|
|
|
if (c != NULL) {
|
|
mp_clamp(&q);
|
|
mp_exch(&q, c);
|
|
}
|
|
mp_clear(&q);
|
|
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_div_d.c */
|
|
|
|
/* Start: bn_mp_dr_is_modulus.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_DR_IS_MODULUS_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* determines if a number is a valid DR modulus */
|
|
mp_bool mp_dr_is_modulus(const mp_int *a)
|
|
{
|
|
int ix;
|
|
|
|
/* must be at least two digits */
|
|
if (a->used < 2) {
|
|
return MP_NO;
|
|
}
|
|
|
|
/* must be of the form b**k - a [a <= b] so all
|
|
* but the first digit must be equal to -1 (mod b).
|
|
*/
|
|
for (ix = 1; ix < a->used; ix++) {
|
|
if (a->dp[ix] != MP_MASK) {
|
|
return MP_NO;
|
|
}
|
|
}
|
|
return MP_YES;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_dr_is_modulus.c */
|
|
|
|
/* Start: bn_mp_dr_reduce.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_DR_REDUCE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
|
|
*
|
|
* Based on algorithm from the paper
|
|
*
|
|
* "Generating Efficient Primes for Discrete Log Cryptosystems"
|
|
* Chae Hoon Lim, Pil Joong Lee,
|
|
* POSTECH Information Research Laboratories
|
|
*
|
|
* The modulus must be of a special format [see manual]
|
|
*
|
|
* Has been modified to use algorithm 7.10 from the LTM book instead
|
|
*
|
|
* Input x must be in the range 0 <= x <= (n-1)**2
|
|
*/
|
|
mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k)
|
|
{
|
|
mp_err err;
|
|
int i, m;
|
|
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.
|
|
*/
|
|
top:
|
|
/* aliases for digits */
|
|
/* alias for lower half of x */
|
|
tmpx1 = x->dp;
|
|
|
|
/* alias for upper half of x, or x/B**m */
|
|
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)MP_DIGIT_BIT));
|
|
}
|
|
|
|
/* set final carry */
|
|
*tmpx1++ = mu;
|
|
|
|
/* zero words above m */
|
|
MP_ZERO_DIGITS(tmpx1, (x->used - m) - 1);
|
|
|
|
/* 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
|
|
|
|
/* End: bn_mp_dr_reduce.c */
|
|
|
|
/* Start: bn_mp_dr_setup.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_DR_SETUP_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* determines the setup value */
|
|
void mp_dr_setup(const mp_int *a, mp_digit *d)
|
|
{
|
|
/* the casts are required if MP_DIGIT_BIT is one less than
|
|
* the number of bits in a mp_digit [e.g. MP_DIGIT_BIT==31]
|
|
*/
|
|
*d = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - (mp_word)a->dp[0]);
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_dr_setup.c */
|
|
|
|
/* Start: bn_mp_error_to_string.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_ERROR_TO_STRING_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* return a char * string for a given code */
|
|
const char *mp_error_to_string(mp_err code)
|
|
{
|
|
switch (code) {
|
|
case MP_OKAY:
|
|
return "Successful";
|
|
case MP_ERR:
|
|
return "Unknown error";
|
|
case MP_MEM:
|
|
return "Out of heap";
|
|
case MP_VAL:
|
|
return "Value out of range";
|
|
case MP_ITER:
|
|
return "Max. iterations reached";
|
|
case MP_BUF:
|
|
return "Buffer overflow";
|
|
default:
|
|
return "Invalid error code";
|
|
}
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_error_to_string.c */
|
|
|
|
/* Start: bn_mp_exch.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_EXCH_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
|
|
/* End: bn_mp_exch.c */
|
|
|
|
/* Start: bn_mp_expt_u32.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_EXPT_U32_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* calculate c = a**b using a square-multiply algorithm */
|
|
mp_err mp_expt_u32(const mp_int *a, uint32_t b, mp_int *c)
|
|
{
|
|
mp_err err;
|
|
|
|
mp_int g;
|
|
|
|
if ((err = mp_init_copy(&g, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* set initial result */
|
|
mp_set(c, 1uL);
|
|
|
|
while (b > 0u) {
|
|
/* if the bit is set multiply */
|
|
if ((b & 1u) != 0u) {
|
|
if ((err = mp_mul(c, &g, c)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* square */
|
|
if (b > 1u) {
|
|
if ((err = mp_sqr(&g, &g)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* shift to next bit */
|
|
b >>= 1;
|
|
}
|
|
|
|
err = MP_OKAY;
|
|
|
|
LBL_ERR:
|
|
mp_clear(&g);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_expt_u32.c */
|
|
|
|
/* Start: bn_mp_exptmod.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_EXPTMOD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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)
|
|
*/
|
|
mp_err mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y)
|
|
{
|
|
int dr;
|
|
|
|
/* modulus P must be positive */
|
|
if (P->sign == MP_NEG) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if exponent X is negative we have to recurse */
|
|
if (X->sign == MP_NEG) {
|
|
mp_int tmpG, tmpX;
|
|
mp_err err;
|
|
|
|
if (!MP_HAS(MP_INVMOD)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
if ((err = mp_init_multi(&tmpG, &tmpX, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* first compute 1/G mod P */
|
|
if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* now get |X| */
|
|
if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* and now compute (1/G)**|X| instead of G**X [X < 0] */
|
|
err = mp_exptmod(&tmpG, &tmpX, P, Y);
|
|
LBL_ERR:
|
|
mp_clear_multi(&tmpG, &tmpX, NULL);
|
|
return err;
|
|
}
|
|
|
|
/* modified diminished radix reduction */
|
|
if (MP_HAS(MP_REDUCE_IS_2K_L) && MP_HAS(MP_REDUCE_2K_L) && MP_HAS(S_MP_EXPTMOD) &&
|
|
(mp_reduce_is_2k_l(P) == MP_YES)) {
|
|
return s_mp_exptmod(G, X, P, Y, 1);
|
|
}
|
|
|
|
/* is it a DR modulus? default to no */
|
|
dr = (MP_HAS(MP_DR_IS_MODULUS) && (mp_dr_is_modulus(P) == MP_YES)) ? 1 : 0;
|
|
|
|
/* if not, is it a unrestricted DR modulus? */
|
|
if (MP_HAS(MP_REDUCE_IS_2K) && (dr == 0)) {
|
|
dr = (mp_reduce_is_2k(P) == MP_YES) ? 2 : 0;
|
|
}
|
|
|
|
/* if the modulus is odd or dr != 0 use the montgomery method */
|
|
if (MP_HAS(S_MP_EXPTMOD_FAST) && (MP_IS_ODD(P) || (dr != 0))) {
|
|
return s_mp_exptmod_fast(G, X, P, Y, dr);
|
|
} else if (MP_HAS(S_MP_EXPTMOD)) {
|
|
/* otherwise use the generic Barrett reduction technique */
|
|
return s_mp_exptmod(G, X, P, Y, 0);
|
|
} else {
|
|
/* no exptmod for evens */
|
|
return MP_VAL;
|
|
}
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_exptmod.c */
|
|
|
|
/* Start: bn_mp_exteuclid.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_EXTEUCLID_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* Extended euclidean algorithm of (a, b) produces
|
|
a*u1 + b*u2 = u3
|
|
*/
|
|
mp_err mp_exteuclid(const mp_int *a, const 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;
|
|
mp_err err;
|
|
|
|
if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* initialize, (u1,u2,u3) = (1,0,a) */
|
|
mp_set(&u1, 1uL);
|
|
if ((err = mp_copy(a, &u3)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* initialize, (v1,v2,v3) = (0,1,b) */
|
|
mp_set(&v2, 1uL);
|
|
if ((err = mp_copy(b, &v3)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* loop while v3 != 0 */
|
|
while (!MP_IS_ZERO(&v3)) {
|
|
/* q = u3/v3 */
|
|
if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
|
|
if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* (u1,u2,u3) = (v1,v2,v3) */
|
|
if ((err = mp_copy(&v1, &u1)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_copy(&v2, &u2)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_copy(&v3, &u3)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* (v1,v2,v3) = (t1,t2,t3) */
|
|
if ((err = mp_copy(&t1, &v1)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_copy(&t2, &v2)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_copy(&t3, &v3)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* make sure U3 >= 0 */
|
|
if (u3.sign == MP_NEG) {
|
|
if ((err = mp_neg(&u1, &u1)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_neg(&u2, &u2)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_neg(&u3, &u3)) != MP_OKAY) goto LBL_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;
|
|
LBL_ERR:
|
|
mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_exteuclid.c */
|
|
|
|
/* Start: bn_mp_fread.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_FREAD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
#ifndef MP_NO_FILE
|
|
/* read a bigint from a file stream in ASCII */
|
|
mp_err mp_fread(mp_int *a, int radix, FILE *stream)
|
|
{
|
|
mp_err err;
|
|
mp_sign neg;
|
|
|
|
/* if first digit is - then set negative */
|
|
int ch = fgetc(stream);
|
|
if (ch == (int)'-') {
|
|
neg = MP_NEG;
|
|
ch = fgetc(stream);
|
|
} else {
|
|
neg = MP_ZPOS;
|
|
}
|
|
|
|
/* no digits, return error */
|
|
if (ch == EOF) {
|
|
return MP_ERR;
|
|
}
|
|
|
|
/* clear a */
|
|
mp_zero(a);
|
|
|
|
do {
|
|
int y;
|
|
unsigned pos = (unsigned)(ch - (int)'(');
|
|
if (mp_s_rmap_reverse_sz < pos) {
|
|
break;
|
|
}
|
|
|
|
y = (int)mp_s_rmap_reverse[pos];
|
|
|
|
if ((y == 0xff) || (y >= radix)) {
|
|
break;
|
|
}
|
|
|
|
/* shift up and add */
|
|
if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
} while ((ch = fgetc(stream)) != EOF);
|
|
|
|
if (a->used != 0) {
|
|
a->sign = neg;
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_fread.c */
|
|
|
|
/* Start: bn_mp_from_sbin.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_FROM_SBIN_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* read signed bin, big endian, first byte is 0==positive or 1==negative */
|
|
mp_err mp_from_sbin(mp_int *a, const unsigned char *buf, size_t size)
|
|
{
|
|
mp_err err;
|
|
|
|
/* read magnitude */
|
|
if ((err = mp_from_ubin(a, buf + 1, size - 1u)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* first byte is 0 for positive, non-zero for negative */
|
|
if (buf[0] == (unsigned char)0) {
|
|
a->sign = MP_ZPOS;
|
|
} else {
|
|
a->sign = MP_NEG;
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_from_sbin.c */
|
|
|
|
/* Start: bn_mp_from_ubin.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_FROM_UBIN_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
|
|
mp_err mp_from_ubin(mp_int *a, const unsigned char *buf, size_t size)
|
|
{
|
|
mp_err err;
|
|
|
|
/* make sure there are at least two digits */
|
|
if (a->alloc < 2) {
|
|
if ((err = mp_grow(a, 2)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* zero the int */
|
|
mp_zero(a);
|
|
|
|
/* read the bytes in */
|
|
while (size-- > 0u) {
|
|
if ((err = mp_mul_2d(a, 8, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
#ifndef MP_8BIT
|
|
a->dp[0] |= *buf++;
|
|
a->used += 1;
|
|
#else
|
|
a->dp[0] = (*buf & MP_MASK);
|
|
a->dp[1] |= ((*buf++ >> 7) & 1u);
|
|
a->used += 2;
|
|
#endif
|
|
}
|
|
mp_clamp(a);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_from_ubin.c */
|
|
|
|
/* Start: bn_mp_fwrite.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_FWRITE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
#ifndef MP_NO_FILE
|
|
mp_err mp_fwrite(const mp_int *a, int radix, FILE *stream)
|
|
{
|
|
char *buf;
|
|
mp_err err;
|
|
int len;
|
|
size_t written;
|
|
|
|
/* TODO: this function is not in this PR */
|
|
if (MP_HAS(MP_RADIX_SIZE_OVERESTIMATE)) {
|
|
/* if ((err = mp_radix_size_overestimate(&t, base, &len)) != MP_OKAY) goto LBL_ERR; */
|
|
} else {
|
|
if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
buf = (char *) MP_MALLOC((size_t)len);
|
|
if (buf == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
|
|
if ((err = mp_to_radix(a, buf, (size_t)len, &written, radix)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if (fwrite(buf, written, 1uL, stream) != 1uL) {
|
|
err = MP_ERR;
|
|
goto LBL_ERR;
|
|
}
|
|
err = MP_OKAY;
|
|
|
|
|
|
LBL_ERR:
|
|
MP_FREE_BUFFER(buf, (size_t)len);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_fwrite.c */
|
|
|
|
/* Start: bn_mp_gcd.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GCD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* Greatest Common Divisor using the binary method */
|
|
mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_int u, v;
|
|
int k, u_lsb, v_lsb;
|
|
mp_err err;
|
|
|
|
/* either zero than gcd is the largest */
|
|
if (MP_IS_ZERO(a)) {
|
|
return mp_abs(b, c);
|
|
}
|
|
if (MP_IS_ZERO(b)) {
|
|
return mp_abs(a, c);
|
|
}
|
|
|
|
/* get copies of a and b we can modify */
|
|
if ((err = mp_init_copy(&u, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_init_copy(&v, b)) != MP_OKAY) {
|
|
goto LBL_U;
|
|
}
|
|
|
|
/* must be positive for the remainder of the algorithm */
|
|
u.sign = v.sign = MP_ZPOS;
|
|
|
|
/* B1. Find the common power of two for u and v */
|
|
u_lsb = mp_cnt_lsb(&u);
|
|
v_lsb = mp_cnt_lsb(&v);
|
|
k = MP_MIN(u_lsb, v_lsb);
|
|
|
|
if (k > 0) {
|
|
/* divide the power of two out */
|
|
if ((err = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
|
|
if ((err = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
}
|
|
|
|
/* divide any remaining factors of two out */
|
|
if (u_lsb != k) {
|
|
if ((err = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
}
|
|
|
|
if (v_lsb != k) {
|
|
if ((err = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
}
|
|
|
|
while (!MP_IS_ZERO(&v)) {
|
|
/* 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 */
|
|
if ((err = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
|
|
/* Divide out all factors of two */
|
|
if ((err = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
}
|
|
|
|
/* multiply by 2**k which we divided out at the beginning */
|
|
if ((err = mp_mul_2d(&u, k, c)) != MP_OKAY) {
|
|
goto LBL_V;
|
|
}
|
|
c->sign = MP_ZPOS;
|
|
err = MP_OKAY;
|
|
LBL_V:
|
|
mp_clear(&u);
|
|
LBL_U:
|
|
mp_clear(&v);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_gcd.c */
|
|
|
|
/* Start: bn_mp_get_double.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GET_DOUBLE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
double mp_get_double(const mp_int *a)
|
|
{
|
|
int i;
|
|
double d = 0.0, fac = 1.0;
|
|
for (i = 0; i < MP_DIGIT_BIT; ++i) {
|
|
fac *= 2.0;
|
|
}
|
|
for (i = a->used; i --> 0;) {
|
|
d = (d * fac) + (double)a->dp[i];
|
|
}
|
|
return (a->sign == MP_NEG) ? -d : d;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_get_double.c */
|
|
|
|
/* Start: bn_mp_get_i32.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GET_I32_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_GET_SIGNED(mp_get_i32, mp_get_mag_u32, int32_t, uint32_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_get_i32.c */
|
|
|
|
/* Start: bn_mp_get_i64.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GET_I64_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_GET_SIGNED(mp_get_i64, mp_get_mag_u64, int64_t, uint64_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_get_i64.c */
|
|
|
|
/* Start: bn_mp_get_l.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GET_L_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_GET_SIGNED(mp_get_l, mp_get_mag_ul, long, unsigned long)
|
|
#endif
|
|
|
|
/* End: bn_mp_get_l.c */
|
|
|
|
/* Start: bn_mp_get_ll.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GET_LL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_GET_SIGNED(mp_get_ll, mp_get_mag_ull, long long, unsigned long long)
|
|
#endif
|
|
|
|
/* End: bn_mp_get_ll.c */
|
|
|
|
/* Start: bn_mp_get_mag_u32.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GET_MAG_U32_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_GET_MAG(mp_get_mag_u32, uint32_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_get_mag_u32.c */
|
|
|
|
/* Start: bn_mp_get_mag_u64.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GET_MAG_U64_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_GET_MAG(mp_get_mag_u64, uint64_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_get_mag_u64.c */
|
|
|
|
/* Start: bn_mp_get_mag_ul.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GET_MAG_UL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_GET_MAG(mp_get_mag_ul, unsigned long)
|
|
#endif
|
|
|
|
/* End: bn_mp_get_mag_ul.c */
|
|
|
|
/* Start: bn_mp_get_mag_ull.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GET_MAG_ULL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_GET_MAG(mp_get_mag_ull, unsigned long long)
|
|
#endif
|
|
|
|
/* End: bn_mp_get_mag_ull.c */
|
|
|
|
/* Start: bn_mp_grow.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_GROW_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* grow as required */
|
|
mp_err mp_grow(mp_int *a, int size)
|
|
{
|
|
int i;
|
|
mp_digit *tmp;
|
|
|
|
/* if the alloc size is smaller alloc more ram */
|
|
if (a->alloc < size) {
|
|
/* reallocate the array a->dp
|
|
*
|
|
* We store the return in a temporary variable
|
|
* in case the operation failed we don't want
|
|
* to overwrite the dp member of a.
|
|
*/
|
|
tmp = (mp_digit *) MP_REALLOC(a->dp,
|
|
(size_t)a->alloc * sizeof(mp_digit),
|
|
(size_t)size * sizeof(mp_digit));
|
|
if (tmp == NULL) {
|
|
/* reallocation failed but "a" is still valid [can be freed] */
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* reallocation succeeded so set a->dp */
|
|
a->dp = tmp;
|
|
|
|
/* zero excess digits */
|
|
i = a->alloc;
|
|
a->alloc = size;
|
|
MP_ZERO_DIGITS(a->dp + i, a->alloc - i);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_grow.c */
|
|
|
|
/* Start: bn_mp_incr.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INCR_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* Increment "a" by one like "a++". Changes input! */
|
|
mp_err mp_incr(mp_int *a)
|
|
{
|
|
if (MP_IS_ZERO(a)) {
|
|
mp_set(a,1uL);
|
|
return MP_OKAY;
|
|
} else if (a->sign == MP_NEG) {
|
|
mp_err err;
|
|
a->sign = MP_ZPOS;
|
|
if ((err = mp_decr(a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
/* There is no -0 in LTM */
|
|
if (!MP_IS_ZERO(a)) {
|
|
a->sign = MP_NEG;
|
|
}
|
|
return MP_OKAY;
|
|
} else if (a->dp[0] < MP_DIGIT_MAX) {
|
|
a->dp[0]++;
|
|
return MP_OKAY;
|
|
} else {
|
|
return mp_add_d(a, 1uL,a);
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_incr.c */
|
|
|
|
/* Start: bn_mp_init.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* init a new mp_int */
|
|
mp_err mp_init(mp_int *a)
|
|
{
|
|
/* allocate memory required and clear it */
|
|
a->dp = (mp_digit *) MP_CALLOC((size_t)MP_PREC, sizeof(mp_digit));
|
|
if (a->dp == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* set the used to zero, allocated digits to the default precision
|
|
* and sign to positive */
|
|
a->used = 0;
|
|
a->alloc = MP_PREC;
|
|
a->sign = MP_ZPOS;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_init.c */
|
|
|
|
/* Start: bn_mp_init_copy.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_COPY_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* creates "a" then copies b into it */
|
|
mp_err mp_init_copy(mp_int *a, const mp_int *b)
|
|
{
|
|
mp_err err;
|
|
|
|
if ((err = mp_init_size(a, b->used)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_copy(b, a)) != MP_OKAY) {
|
|
mp_clear(a);
|
|
}
|
|
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_init_copy.c */
|
|
|
|
/* Start: bn_mp_init_i32.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_I32_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_INIT_INT(mp_init_i32, mp_set_i32, int32_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_init_i32.c */
|
|
|
|
/* Start: bn_mp_init_i64.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_I64_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_INIT_INT(mp_init_i64, mp_set_i64, int64_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_init_i64.c */
|
|
|
|
/* Start: bn_mp_init_l.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_L_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_INIT_INT(mp_init_l, mp_set_l, long)
|
|
#endif
|
|
|
|
/* End: bn_mp_init_l.c */
|
|
|
|
/* Start: bn_mp_init_ll.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_LL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_INIT_INT(mp_init_ll, mp_set_ll, long long)
|
|
#endif
|
|
|
|
/* End: bn_mp_init_ll.c */
|
|
|
|
/* Start: bn_mp_init_multi.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_MULTI_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
#include <stdarg.h>
|
|
|
|
mp_err mp_init_multi(mp_int *mp, ...)
|
|
{
|
|
mp_err err = MP_OKAY; /* Assume ok until proven otherwise */
|
|
int n = 0; /* Number of ok inits */
|
|
mp_int *cur_arg = mp;
|
|
va_list args;
|
|
|
|
va_start(args, mp); /* init args to next argument from caller */
|
|
while (cur_arg != NULL) {
|
|
if (mp_init(cur_arg) != MP_OKAY) {
|
|
/* Oops - error! Back-track and mp_clear what we already
|
|
succeeded in init-ing, then return error.
|
|
*/
|
|
va_list clean_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);
|
|
err = MP_MEM;
|
|
break;
|
|
}
|
|
n++;
|
|
cur_arg = va_arg(args, mp_int *);
|
|
}
|
|
va_end(args);
|
|
return err; /* Assumed ok, if error flagged above. */
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_init_multi.c */
|
|
|
|
/* Start: bn_mp_init_set.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_SET_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* initialize and set a digit */
|
|
mp_err mp_init_set(mp_int *a, mp_digit b)
|
|
{
|
|
mp_err err;
|
|
if ((err = mp_init(a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
mp_set(a, b);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_init_set.c */
|
|
|
|
/* Start: bn_mp_init_size.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_SIZE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* init an mp_init for a given size */
|
|
mp_err mp_init_size(mp_int *a, int size)
|
|
{
|
|
size = MP_MAX(MP_MIN_PREC, size);
|
|
|
|
/* alloc mem */
|
|
a->dp = (mp_digit *) MP_CALLOC((size_t)size, sizeof(mp_digit));
|
|
if (a->dp == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* set the members */
|
|
a->used = 0;
|
|
a->alloc = size;
|
|
a->sign = MP_ZPOS;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_init_size.c */
|
|
|
|
/* Start: bn_mp_init_u32.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_U32_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_INIT_INT(mp_init_u32, mp_set_u32, uint32_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_init_u32.c */
|
|
|
|
/* Start: bn_mp_init_u64.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_U64_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_INIT_INT(mp_init_u64, mp_set_u64, uint64_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_init_u64.c */
|
|
|
|
/* Start: bn_mp_init_ul.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_UL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_INIT_INT(mp_init_ul, mp_set_ul, unsigned long)
|
|
#endif
|
|
|
|
/* End: bn_mp_init_ul.c */
|
|
|
|
/* Start: bn_mp_init_ull.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INIT_ULL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_INIT_INT(mp_init_ull, mp_set_ull, unsigned long long)
|
|
#endif
|
|
|
|
/* End: bn_mp_init_ull.c */
|
|
|
|
/* Start: bn_mp_invmod.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_INVMOD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* hac 14.61, pp608 */
|
|
mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
/* b cannot be negative and has to be >1 */
|
|
if ((b->sign == MP_NEG) || (mp_cmp_d(b, 1uL) != MP_GT)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if the modulus is odd we can use a faster routine instead */
|
|
if (MP_HAS(S_MP_INVMOD_FAST) && MP_IS_ODD(b)) {
|
|
return s_mp_invmod_fast(a, b, c);
|
|
}
|
|
|
|
return MP_HAS(S_MP_INVMOD_SLOW)
|
|
? s_mp_invmod_slow(a, b, c)
|
|
: MP_VAL;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_invmod.c */
|
|
|
|
/* Start: bn_mp_is_square.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_IS_SQUARE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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,
|
|
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
|
|
0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
|
|
1, 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,
|
|
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
|
|
};
|
|
|
|
static const char rem_105[105] = {
|
|
0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
|
|
0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
|
|
0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
|
|
1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
|
|
0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
|
|
1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
|
|
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
|
|
};
|
|
|
|
/* Store non-zero to ret if arg is square, and zero if not */
|
|
mp_err mp_is_square(const mp_int *arg, mp_bool *ret)
|
|
{
|
|
mp_err err;
|
|
mp_digit c;
|
|
mp_int t;
|
|
unsigned long r;
|
|
|
|
/* Default to Non-square :) */
|
|
*ret = MP_NO;
|
|
|
|
if (arg->sign == MP_NEG) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
if (MP_IS_ZERO(arg)) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* First check mod 128 (suppose that MP_DIGIT_BIT is at least 7) */
|
|
if (rem_128[127u & arg->dp[0]] == (char)1) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Next check mod 105 (3*5*7) */
|
|
if ((err = mp_mod_d(arg, 105uL, &c)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if (rem_105[c] == (char)1) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
if ((err = mp_init_u32(&t, 11u*13u*17u*19u*23u*29u*31u)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_mod(arg, &t, &t)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
r = mp_get_u32(&t);
|
|
/* Check for other prime modules, note it's not an ERROR but we must
|
|
* free "t" so the easiest way is to goto LBL_ERR. We know that err
|
|
* is already equal to MP_OKAY from the mp_mod call
|
|
*/
|
|
if (((1uL<<(r%11uL)) & 0x5C4uL) != 0uL) goto LBL_ERR;
|
|
if (((1uL<<(r%13uL)) & 0x9E4uL) != 0uL) goto LBL_ERR;
|
|
if (((1uL<<(r%17uL)) & 0x5CE8uL) != 0uL) goto LBL_ERR;
|
|
if (((1uL<<(r%19uL)) & 0x4F50CuL) != 0uL) goto LBL_ERR;
|
|
if (((1uL<<(r%23uL)) & 0x7ACCA0uL) != 0uL) goto LBL_ERR;
|
|
if (((1uL<<(r%29uL)) & 0xC2EDD0CuL) != 0uL) goto LBL_ERR;
|
|
if (((1uL<<(r%31uL)) & 0x6DE2B848uL) != 0uL) goto LBL_ERR;
|
|
|
|
/* Final check - is sqr(sqrt(arg)) == arg ? */
|
|
if ((err = mp_sqrt(arg, &t)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((err = mp_sqr(&t, &t)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
*ret = (mp_cmp_mag(&t, arg) == MP_EQ) ? MP_YES : MP_NO;
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_is_square.c */
|
|
|
|
/* Start: bn_mp_iseven.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_ISEVEN_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
mp_bool mp_iseven(const mp_int *a)
|
|
{
|
|
return MP_IS_EVEN(a) ? MP_YES : MP_NO;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_iseven.c */
|
|
|
|
/* Start: bn_mp_isodd.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_ISODD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
mp_bool mp_isodd(const mp_int *a)
|
|
{
|
|
return MP_IS_ODD(a) ? MP_YES : MP_NO;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_isodd.c */
|
|
|
|
/* Start: bn_mp_kronecker.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_KRONECKER_C
|
|
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/*
|
|
Kronecker symbol (a|p)
|
|
Straightforward implementation of algorithm 1.4.10 in
|
|
Henri Cohen: "A Course in Computational Algebraic Number Theory"
|
|
|
|
@book{cohen2013course,
|
|
title={A course in computational algebraic number theory},
|
|
author={Cohen, Henri},
|
|
volume={138},
|
|
year={2013},
|
|
publisher={Springer Science \& Business Media}
|
|
}
|
|
*/
|
|
mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c)
|
|
{
|
|
mp_int a1, p1, r;
|
|
mp_err err;
|
|
int v, k;
|
|
|
|
static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1};
|
|
|
|
if (MP_IS_ZERO(p)) {
|
|
if ((a->used == 1) && (a->dp[0] == 1u)) {
|
|
*c = 1;
|
|
} else {
|
|
*c = 0;
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
if (MP_IS_EVEN(a) && MP_IS_EVEN(p)) {
|
|
*c = 0;
|
|
return MP_OKAY;
|
|
}
|
|
|
|
if ((err = mp_init_copy(&a1, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_init_copy(&p1, p)) != MP_OKAY) {
|
|
goto LBL_KRON_0;
|
|
}
|
|
|
|
v = mp_cnt_lsb(&p1);
|
|
if ((err = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) {
|
|
goto LBL_KRON_1;
|
|
}
|
|
|
|
if ((v & 1) == 0) {
|
|
k = 1;
|
|
} else {
|
|
k = table[a->dp[0] & 7u];
|
|
}
|
|
|
|
if (p1.sign == MP_NEG) {
|
|
p1.sign = MP_ZPOS;
|
|
if (a1.sign == MP_NEG) {
|
|
k = -k;
|
|
}
|
|
}
|
|
|
|
if ((err = mp_init(&r)) != MP_OKAY) {
|
|
goto LBL_KRON_1;
|
|
}
|
|
|
|
for (;;) {
|
|
if (MP_IS_ZERO(&a1)) {
|
|
if (mp_cmp_d(&p1, 1uL) == MP_EQ) {
|
|
*c = k;
|
|
goto LBL_KRON;
|
|
} else {
|
|
*c = 0;
|
|
goto LBL_KRON;
|
|
}
|
|
}
|
|
|
|
v = mp_cnt_lsb(&a1);
|
|
if ((err = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) {
|
|
goto LBL_KRON;
|
|
}
|
|
|
|
if ((v & 1) == 1) {
|
|
k = k * table[p1.dp[0] & 7u];
|
|
}
|
|
|
|
if (a1.sign == MP_NEG) {
|
|
/*
|
|
* Compute k = (-1)^((a1)*(p1-1)/4) * k
|
|
* a1.dp[0] + 1 cannot overflow because the MSB
|
|
* of the type mp_digit is not set by definition
|
|
*/
|
|
if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) {
|
|
k = -k;
|
|
}
|
|
} else {
|
|
/* compute k = (-1)^((a1-1)*(p1-1)/4) * k */
|
|
if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) {
|
|
k = -k;
|
|
}
|
|
}
|
|
|
|
if ((err = mp_copy(&a1, &r)) != MP_OKAY) {
|
|
goto LBL_KRON;
|
|
}
|
|
r.sign = MP_ZPOS;
|
|
if ((err = mp_mod(&p1, &r, &a1)) != MP_OKAY) {
|
|
goto LBL_KRON;
|
|
}
|
|
if ((err = mp_copy(&r, &p1)) != MP_OKAY) {
|
|
goto LBL_KRON;
|
|
}
|
|
}
|
|
|
|
LBL_KRON:
|
|
mp_clear(&r);
|
|
LBL_KRON_1:
|
|
mp_clear(&p1);
|
|
LBL_KRON_0:
|
|
mp_clear(&a1);
|
|
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_kronecker.c */
|
|
|
|
/* Start: bn_mp_lcm.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_LCM_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* computes least common multiple as |a*b|/(a, b) */
|
|
mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_err err;
|
|
mp_int t1, t2;
|
|
|
|
|
|
if ((err = mp_init_multi(&t1, &t2, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* t1 = get the GCD of the two inputs */
|
|
if ((err = mp_gcd(a, b, &t1)) != MP_OKAY) {
|
|
goto LBL_T;
|
|
}
|
|
|
|
/* divide the smallest by the GCD */
|
|
if (mp_cmp_mag(a, b) == MP_LT) {
|
|
/* store quotient in t2 such that t2 * b is the LCM */
|
|
if ((err = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
|
|
goto LBL_T;
|
|
}
|
|
err = mp_mul(b, &t2, c);
|
|
} else {
|
|
/* store quotient in t2 such that t2 * a is the LCM */
|
|
if ((err = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
|
|
goto LBL_T;
|
|
}
|
|
err = mp_mul(a, &t2, c);
|
|
}
|
|
|
|
/* fix the sign to positive */
|
|
c->sign = MP_ZPOS;
|
|
|
|
LBL_T:
|
|
mp_clear_multi(&t1, &t2, NULL);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_lcm.c */
|
|
|
|
/* Start: bn_mp_log_u32.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_LOG_U32_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* Compute log_{base}(a) */
|
|
static mp_word s_pow(mp_word base, mp_word exponent)
|
|
{
|
|
mp_word result = 1uLL;
|
|
while (exponent != 0u) {
|
|
if ((exponent & 1u) == 1u) {
|
|
result *= base;
|
|
}
|
|
exponent >>= 1;
|
|
base *= base;
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
static mp_digit s_digit_ilogb(mp_digit base, mp_digit n)
|
|
{
|
|
mp_word bracket_low = 1uLL, bracket_mid, bracket_high, N;
|
|
mp_digit ret, high = 1uL, low = 0uL, mid;
|
|
|
|
if (n < base) {
|
|
return 0uL;
|
|
}
|
|
if (n == base) {
|
|
return 1uL;
|
|
}
|
|
|
|
bracket_high = (mp_word) base ;
|
|
N = (mp_word) n;
|
|
|
|
while (bracket_high < N) {
|
|
low = high;
|
|
bracket_low = bracket_high;
|
|
high <<= 1;
|
|
bracket_high *= bracket_high;
|
|
}
|
|
|
|
while (((mp_digit)(high - low)) > 1uL) {
|
|
mid = (low + high) >> 1;
|
|
bracket_mid = bracket_low * s_pow(base, (mp_word)(mid - low));
|
|
|
|
if (N < bracket_mid) {
|
|
high = mid ;
|
|
bracket_high = bracket_mid ;
|
|
}
|
|
if (N > bracket_mid) {
|
|
low = mid ;
|
|
bracket_low = bracket_mid ;
|
|
}
|
|
if (N == bracket_mid) {
|
|
return (mp_digit) mid;
|
|
}
|
|
}
|
|
|
|
if (bracket_high == N) {
|
|
ret = high;
|
|
} else {
|
|
ret = low;
|
|
}
|
|
|
|
return ret;
|
|
}
|
|
|
|
/* TODO: output could be "int" because the output of mp_radix_size is int, too,
|
|
as is the output of mp_bitcount.
|
|
With the same problem: max size is INT_MAX * MP_DIGIT not INT_MAX only!
|
|
*/
|
|
mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c)
|
|
{
|
|
mp_err err;
|
|
mp_ord cmp;
|
|
uint32_t high, low, mid;
|
|
mp_int bracket_low, bracket_high, bracket_mid, t, bi_base;
|
|
|
|
err = MP_OKAY;
|
|
|
|
if (a->sign == MP_NEG) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
if (MP_IS_ZERO(a)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
if (base < 2u) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* A small shortcut for bases that are powers of two. */
|
|
if ((base & (base - 1u)) == 0u) {
|
|
int y, bit_count;
|
|
for (y=0; (y < 7) && ((base & 1u) == 0u); y++) {
|
|
base >>= 1;
|
|
}
|
|
bit_count = mp_count_bits(a) - 1;
|
|
*c = (uint32_t)(bit_count/y);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
if (a->used == 1) {
|
|
*c = (uint32_t)s_digit_ilogb(base, a->dp[0]);
|
|
return err;
|
|
}
|
|
|
|
cmp = mp_cmp_d(a, base);
|
|
if ((cmp == MP_LT) || (cmp == MP_EQ)) {
|
|
*c = cmp == MP_EQ;
|
|
return err;
|
|
}
|
|
|
|
if ((err =
|
|
mp_init_multi(&bracket_low, &bracket_high,
|
|
&bracket_mid, &t, &bi_base, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
low = 0u;
|
|
mp_set(&bracket_low, 1uL);
|
|
high = 1u;
|
|
|
|
mp_set(&bracket_high, base);
|
|
|
|
/*
|
|
A kind of Giant-step/baby-step algorithm.
|
|
Idea shamelessly stolen from https://programmingpraxis.com/2010/05/07/integer-logarithms/2/
|
|
The effect is asymptotic, hence needs benchmarks to test if the Giant-step should be skipped
|
|
for small n.
|
|
*/
|
|
while (mp_cmp(&bracket_high, a) == MP_LT) {
|
|
low = high;
|
|
if ((err = mp_copy(&bracket_high, &bracket_low)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
high <<= 1;
|
|
if ((err = mp_sqr(&bracket_high, &bracket_high)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
mp_set(&bi_base, base);
|
|
|
|
while ((high - low) > 1u) {
|
|
mid = (high + low) >> 1;
|
|
|
|
if ((err = mp_expt_u32(&bi_base, (uint32_t)(mid - low), &t)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((err = mp_mul(&bracket_low, &t, &bracket_mid)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
cmp = mp_cmp(a, &bracket_mid);
|
|
if (cmp == MP_LT) {
|
|
high = mid;
|
|
mp_exch(&bracket_mid, &bracket_high);
|
|
}
|
|
if (cmp == MP_GT) {
|
|
low = mid;
|
|
mp_exch(&bracket_mid, &bracket_low);
|
|
}
|
|
if (cmp == MP_EQ) {
|
|
*c = mid;
|
|
goto LBL_END;
|
|
}
|
|
}
|
|
|
|
*c = (mp_cmp(&bracket_high, a) == MP_EQ) ? high : low;
|
|
|
|
LBL_END:
|
|
LBL_ERR:
|
|
mp_clear_multi(&bracket_low, &bracket_high, &bracket_mid,
|
|
&t, &bi_base, NULL);
|
|
return err;
|
|
}
|
|
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_log_u32.c */
|
|
|
|
/* Start: bn_mp_lshd.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_LSHD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* shift left a certain amount of digits */
|
|
mp_err mp_lshd(mp_int *a, int b)
|
|
{
|
|
int x;
|
|
mp_err err;
|
|
mp_digit *top, *bottom;
|
|
|
|
/* if its less than zero return */
|
|
if (b <= 0) {
|
|
return MP_OKAY;
|
|
}
|
|
/* no need to shift 0 around */
|
|
if (MP_IS_ZERO(a)) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* grow to fit the new digits */
|
|
if (a->alloc < (a->used + b)) {
|
|
if ((err = mp_grow(a, a->used + b)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* 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--;
|
|
}
|
|
|
|
/* zero the lower digits */
|
|
MP_ZERO_DIGITS(a->dp, b);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_lshd.c */
|
|
|
|
/* Start: bn_mp_mod.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MOD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
|
|
mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_int t;
|
|
mp_err err;
|
|
|
|
if ((err = mp_init_size(&t, b->used)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_div(a, b, NULL, &t)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if (MP_IS_ZERO(&t) || (t.sign == b->sign)) {
|
|
err = MP_OKAY;
|
|
mp_exch(&t, c);
|
|
} else {
|
|
err = mp_add(b, &t, c);
|
|
}
|
|
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_mod.c */
|
|
|
|
/* Start: bn_mp_mod_2d.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MOD_2D_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* calc a value mod 2**b */
|
|
mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c)
|
|
{
|
|
int x;
|
|
mp_err err;
|
|
|
|
/* if b is <= 0 then zero the int */
|
|
if (b <= 0) {
|
|
mp_zero(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* if the modulus is larger than the value than return */
|
|
if (b >= (a->used * MP_DIGIT_BIT)) {
|
|
return mp_copy(a, c);
|
|
}
|
|
|
|
/* copy */
|
|
if ((err = mp_copy(a, c)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* zero digits above the last digit of the modulus */
|
|
x = (b / MP_DIGIT_BIT) + (((b % MP_DIGIT_BIT) == 0) ? 0 : 1);
|
|
MP_ZERO_DIGITS(c->dp + x, c->used - x);
|
|
|
|
/* clear the digit that is not completely outside/inside the modulus */
|
|
c->dp[b / MP_DIGIT_BIT] &=
|
|
((mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT)) - (mp_digit)1;
|
|
mp_clamp(c);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_mod_2d.c */
|
|
|
|
/* Start: bn_mp_mod_d.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MOD_D_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c)
|
|
{
|
|
return mp_div_d(a, b, NULL, c);
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_mod_d.c */
|
|
|
|
/* Start: bn_mp_montgomery_calc_normalization.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/*
|
|
* 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.
|
|
*/
|
|
mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b)
|
|
{
|
|
int x, bits;
|
|
mp_err err;
|
|
|
|
/* how many bits of last digit does b use */
|
|
bits = mp_count_bits(b) % MP_DIGIT_BIT;
|
|
|
|
if (b->used > 1) {
|
|
if ((err = mp_2expt(a, ((b->used - 1) * MP_DIGIT_BIT) + bits - 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
} else {
|
|
mp_set(a, 1uL);
|
|
bits = 1;
|
|
}
|
|
|
|
|
|
/* now compute C = A * B mod b */
|
|
for (x = bits - 1; x < (int)MP_DIGIT_BIT; x++) {
|
|
if ((err = mp_mul_2(a, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if (mp_cmp_mag(a, b) != MP_LT) {
|
|
if ((err = s_mp_sub(a, b, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_montgomery_calc_normalization.c */
|
|
|
|
/* Start: bn_mp_montgomery_reduce.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MONTGOMERY_REDUCE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
|
|
mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
|
|
{
|
|
int ix, digs;
|
|
mp_err err;
|
|
mp_digit mu;
|
|
|
|
/* 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) &&
|
|
(x->used <= MP_WARRAY) &&
|
|
(n->used < MP_MAXFAST)) {
|
|
return s_mp_montgomery_reduce_fast(x, n, rho);
|
|
}
|
|
|
|
/* grow the input as required */
|
|
if (x->alloc < digs) {
|
|
if ((err = mp_grow(x, digs)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
x->used = digs;
|
|
|
|
for (ix = 0; ix < n->used; ix++) {
|
|
/* mu = ai * rho mod b
|
|
*
|
|
* 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)MP_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 != 0u) {
|
|
*tmpx += u;
|
|
u = *tmpx >> MP_DIGIT_BIT;
|
|
*tmpx++ &= MP_MASK;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* at this point the n.used'th least
|
|
* significant digits of x are all zero
|
|
* which means we can shift x to the
|
|
* right by n.used digits and the
|
|
* residue is unchanged.
|
|
*/
|
|
|
|
/* x = x/b**n.used */
|
|
mp_clamp(x);
|
|
mp_rshd(x, n->used);
|
|
|
|
/* if x >= n then x = x - n */
|
|
if (mp_cmp_mag(x, n) != MP_LT) {
|
|
return s_mp_sub(x, n, x);
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_montgomery_reduce.c */
|
|
|
|
/* Start: bn_mp_montgomery_setup.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MONTGOMERY_SETUP_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* setups the montgomery reduction stuff */
|
|
mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho)
|
|
{
|
|
mp_digit x, b;
|
|
|
|
/* fast inversion mod 2**k
|
|
*
|
|
* Based on the fact that
|
|
*
|
|
* XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
|
|
* => 2*X*A - X*X*A*A = 1
|
|
* => 2*(1) - (1) = 1
|
|
*/
|
|
b = n->dp[0];
|
|
|
|
if ((b & 1u) == 0u) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
x = (((b + 2u) & 4u) << 1) + b; /* here x*a==1 mod 2**4 */
|
|
x *= 2u - (b * x); /* here x*a==1 mod 2**8 */
|
|
#if !defined(MP_8BIT)
|
|
x *= 2u - (b * x); /* here x*a==1 mod 2**16 */
|
|
#endif
|
|
#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
|
|
x *= 2u - (b * x); /* here x*a==1 mod 2**32 */
|
|
#endif
|
|
#ifdef MP_64BIT
|
|
x *= 2u - (b * x); /* here x*a==1 mod 2**64 */
|
|
#endif
|
|
|
|
/* rho = -1/m mod b */
|
|
*rho = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - x) & MP_MASK;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_montgomery_setup.c */
|
|
|
|
/* Start: bn_mp_mul.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MUL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* high level multiplication (handles sign) */
|
|
mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_err err;
|
|
int min_len = MP_MIN(a->used, b->used),
|
|
max_len = MP_MAX(a->used, b->used),
|
|
digs = a->used + b->used + 1;
|
|
mp_sign neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
|
|
|
|
if (MP_HAS(S_MP_BALANCE_MUL) &&
|
|
/* Check sizes. The smaller one needs to be larger than the Karatsuba cut-off.
|
|
* The bigger one needs to be at least about one MP_KARATSUBA_MUL_CUTOFF bigger
|
|
* to make some sense, but it depends on architecture, OS, position of the
|
|
* stars... so YMMV.
|
|
* Using it to cut the input into slices small enough for fast_s_mp_mul_digs
|
|
* was actually slower on the author's machine, but YMMV.
|
|
*/
|
|
(min_len >= MP_KARATSUBA_MUL_CUTOFF) &&
|
|
((max_len / 2) >= MP_KARATSUBA_MUL_CUTOFF) &&
|
|
/* Not much effect was observed below a ratio of 1:2, but again: YMMV. */
|
|
(max_len >= (2 * min_len))) {
|
|
err = s_mp_balance_mul(a,b,c);
|
|
} else if (MP_HAS(S_MP_TOOM_MUL) &&
|
|
(min_len >= MP_TOOM_MUL_CUTOFF)) {
|
|
err = s_mp_toom_mul(a, b, c);
|
|
} else if (MP_HAS(S_MP_KARATSUBA_MUL) &&
|
|
(min_len >= MP_KARATSUBA_MUL_CUTOFF)) {
|
|
err = s_mp_karatsuba_mul(a, b, c);
|
|
} else if (MP_HAS(S_MP_MUL_DIGS_FAST) &&
|
|
/* can we use the fast multiplier?
|
|
*
|
|
* The fast multiplier can be used if the output will
|
|
* have less than MP_WARRAY digits and the number of
|
|
* digits won't affect carry propagation
|
|
*/
|
|
(digs < MP_WARRAY) &&
|
|
(min_len <= MP_MAXFAST)) {
|
|
err = s_mp_mul_digs_fast(a, b, c, digs);
|
|
} else if (MP_HAS(S_MP_MUL_DIGS)) {
|
|
err = s_mp_mul_digs(a, b, c, digs);
|
|
} else {
|
|
err = MP_VAL;
|
|
}
|
|
c->sign = (c->used > 0) ? neg : MP_ZPOS;
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_mul.c */
|
|
|
|
/* Start: bn_mp_mul_2.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MUL_2_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* b = a*2 */
|
|
mp_err mp_mul_2(const mp_int *a, mp_int *b)
|
|
{
|
|
int x, oldused;
|
|
mp_err err;
|
|
|
|
/* grow to accomodate result */
|
|
if (b->alloc < (a->used + 1)) {
|
|
if ((err = mp_grow(b, a->used + 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
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;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = 0; x < a->used; x++) {
|
|
|
|
/* get what will be the *next* carry bit from the
|
|
* MSB of the current digit
|
|
*/
|
|
rr = *tmpa >> (mp_digit)(MP_DIGIT_BIT - 1);
|
|
|
|
/* now shift up this digit, add in the carry [from the previous] */
|
|
*tmpb++ = ((*tmpa++ << 1uL) | r) & MP_MASK;
|
|
|
|
/* copy the carry that would be from the source
|
|
* digit into the next iteration
|
|
*/
|
|
r = rr;
|
|
}
|
|
|
|
/* new leading digit? */
|
|
if (r != 0u) {
|
|
/* add a MSB which is always 1 at this point */
|
|
*tmpb = 1;
|
|
++(b->used);
|
|
}
|
|
|
|
/* now zero any excess digits on the destination
|
|
* that we didn't write to
|
|
*/
|
|
MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used);
|
|
}
|
|
b->sign = a->sign;
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_mul_2.c */
|
|
|
|
/* Start: bn_mp_mul_2d.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MUL_2D_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* shift left by a certain bit count */
|
|
mp_err mp_mul_2d(const mp_int *a, int b, mp_int *c)
|
|
{
|
|
mp_digit d;
|
|
mp_err err;
|
|
|
|
/* copy */
|
|
if (a != c) {
|
|
if ((err = mp_copy(a, c)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
if (c->alloc < (c->used + (b / MP_DIGIT_BIT) + 1)) {
|
|
if ((err = mp_grow(c, c->used + (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* shift by as many digits in the bit count */
|
|
if (b >= MP_DIGIT_BIT) {
|
|
if ((err = mp_lshd(c, b / MP_DIGIT_BIT)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* shift any bit count < MP_DIGIT_BIT */
|
|
d = (mp_digit)(b % MP_DIGIT_BIT);
|
|
if (d != 0u) {
|
|
mp_digit *tmpc, shift, mask, r, rr;
|
|
int x;
|
|
|
|
/* bitmask for carries */
|
|
mask = ((mp_digit)1 << d) - (mp_digit)1;
|
|
|
|
/* shift for msbs */
|
|
shift = (mp_digit)MP_DIGIT_BIT - d;
|
|
|
|
/* alias */
|
|
tmpc = c->dp;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = 0; x < c->used; x++) {
|
|
/* get the higher bits of the current word */
|
|
rr = (*tmpc >> shift) & mask;
|
|
|
|
/* shift the current word and OR in the carry */
|
|
*tmpc = ((*tmpc << d) | r) & MP_MASK;
|
|
++tmpc;
|
|
|
|
/* set the carry to the carry bits of the current word */
|
|
r = rr;
|
|
}
|
|
|
|
/* set final carry */
|
|
if (r != 0u) {
|
|
c->dp[(c->used)++] = r;
|
|
}
|
|
}
|
|
mp_clamp(c);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_mul_2d.c */
|
|
|
|
/* Start: bn_mp_mul_d.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MUL_D_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* multiply by a digit */
|
|
mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c)
|
|
{
|
|
mp_digit u, *tmpa, *tmpc;
|
|
mp_word r;
|
|
mp_err err;
|
|
int ix, olduse;
|
|
|
|
/* make sure c is big enough to hold a*b */
|
|
if (c->alloc < (a->used + 1)) {
|
|
if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* get the original destinations used count */
|
|
olduse = c->used;
|
|
|
|
/* set the sign */
|
|
c->sign = a->sign;
|
|
|
|
/* alias for a->dp [source] */
|
|
tmpa = a->dp;
|
|
|
|
/* alias for c->dp [dest] */
|
|
tmpc = c->dp;
|
|
|
|
/* 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)MP_DIGIT_BIT);
|
|
}
|
|
|
|
/* store final carry [if any] and increment ix offset */
|
|
*tmpc++ = u;
|
|
++ix;
|
|
|
|
/* now zero digits above the top */
|
|
MP_ZERO_DIGITS(tmpc, olduse - ix);
|
|
|
|
/* set used count */
|
|
c->used = a->used + 1;
|
|
mp_clamp(c);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_mul_d.c */
|
|
|
|
/* Start: bn_mp_mulmod.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_MULMOD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* d = a * b (mod c) */
|
|
mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
|
|
{
|
|
mp_err err;
|
|
mp_int t;
|
|
|
|
if ((err = mp_init_size(&t, c->used)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_mul(a, b, &t)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
err = mp_mod(&t, c, d);
|
|
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_mulmod.c */
|
|
|
|
/* Start: bn_mp_neg.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_NEG_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* b = -a */
|
|
mp_err mp_neg(const mp_int *a, mp_int *b)
|
|
{
|
|
mp_err err;
|
|
if (a != b) {
|
|
if ((err = mp_copy(a, b)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
if (!MP_IS_ZERO(b)) {
|
|
b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
|
|
} else {
|
|
b->sign = MP_ZPOS;
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_neg.c */
|
|
|
|
/* Start: bn_mp_or.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_OR_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 used = MP_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
|
|
|
|
/* End: bn_mp_or.c */
|
|
|
|
/* Start: bn_mp_pack.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PACK_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* based on gmp's mpz_export.
|
|
* see http://gmplib.org/manual/Integer-Import-and-Export.html
|
|
*/
|
|
mp_err mp_pack(void *rop, size_t maxcount, size_t *written, mp_order order, size_t size,
|
|
mp_endian endian, size_t nails, const mp_int *op)
|
|
{
|
|
mp_err err;
|
|
size_t odd_nails, nail_bytes, i, j, count;
|
|
unsigned char odd_nail_mask;
|
|
|
|
mp_int t;
|
|
|
|
count = mp_pack_count(op, nails, size);
|
|
|
|
if (count > maxcount) {
|
|
return MP_BUF;
|
|
}
|
|
|
|
if ((err = mp_init_copy(&t, op)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if (endian == MP_NATIVE_ENDIAN) {
|
|
MP_GET_ENDIANNESS(endian);
|
|
}
|
|
|
|
odd_nails = (nails % 8u);
|
|
odd_nail_mask = 0xff;
|
|
for (i = 0u; i < odd_nails; ++i) {
|
|
odd_nail_mask ^= (unsigned char)(1u << (7u - i));
|
|
}
|
|
nail_bytes = nails / 8u;
|
|
|
|
for (i = 0u; i < count; ++i) {
|
|
for (j = 0u; j < size; ++j) {
|
|
unsigned char *byte = (unsigned char *)rop +
|
|
(((order == MP_LSB_FIRST) ? i : ((count - 1u) - i)) * size) +
|
|
((endian == MP_LITTLE_ENDIAN) ? j : ((size - 1u) - j));
|
|
|
|
if (j >= (size - nail_bytes)) {
|
|
*byte = 0;
|
|
continue;
|
|
}
|
|
|
|
*byte = (unsigned char)((j == ((size - nail_bytes) - 1u)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFFuL));
|
|
|
|
if ((err = mp_div_2d(&t, (j == ((size - nail_bytes) - 1u)) ? (int)(8u - odd_nails) : 8, &t, NULL)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
if (written != NULL) {
|
|
*written = count;
|
|
}
|
|
err = MP_OKAY;
|
|
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_pack.c */
|
|
|
|
/* Start: bn_mp_pack_count.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PACK_COUNT_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
size_t mp_pack_count(const mp_int *a, size_t nails, size_t size)
|
|
{
|
|
size_t bits = (size_t)mp_count_bits(a);
|
|
return ((bits / ((size * 8u) - nails)) + (((bits % ((size * 8u) - nails)) != 0u) ? 1u : 0u));
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_pack_count.c */
|
|
|
|
/* Start: bn_mp_prime_fermat.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PRIME_FERMAT_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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).
|
|
*
|
|
* Sets result to 1 if the congruence holds, or zero otherwise.
|
|
*/
|
|
mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, mp_bool *result)
|
|
{
|
|
mp_int t;
|
|
mp_err err;
|
|
|
|
/* default to composite */
|
|
*result = MP_NO;
|
|
|
|
/* ensure b > 1 */
|
|
if (mp_cmp_d(b, 1uL) != MP_GT) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* init t */
|
|
if ((err = mp_init(&t)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* compute t = b**a mod a */
|
|
if ((err = mp_exptmod(b, a, a, &t)) != MP_OKAY) {
|
|
goto LBL_T;
|
|
}
|
|
|
|
/* is it equal to b? */
|
|
if (mp_cmp(&t, b) == MP_EQ) {
|
|
*result = MP_YES;
|
|
}
|
|
|
|
err = MP_OKAY;
|
|
LBL_T:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_prime_fermat.c */
|
|
|
|
/* Start: bn_mp_prime_frobenius_underwood.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PRIME_FROBENIUS_UNDERWOOD_C
|
|
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/*
|
|
* See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
|
|
*/
|
|
#ifndef LTM_USE_ONLY_MR
|
|
|
|
#ifdef MP_8BIT
|
|
/*
|
|
* floor of positive solution of
|
|
* (2^16)-1 = (a+4)*(2*a+5)
|
|
* TODO: Both values are smaller than N^(1/4), would have to use a bigint
|
|
* for a instead but any a biger than about 120 are already so rare that
|
|
* it is possible to ignore them and still get enough pseudoprimes.
|
|
* But it is still a restriction of the set of available pseudoprimes
|
|
* which makes this implementation less secure if used stand-alone.
|
|
*/
|
|
#define LTM_FROBENIUS_UNDERWOOD_A 177
|
|
#else
|
|
#define LTM_FROBENIUS_UNDERWOOD_A 32764
|
|
#endif
|
|
mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result)
|
|
{
|
|
mp_int T1z, T2z, Np1z, sz, tz;
|
|
|
|
int a, ap2, length, i, j;
|
|
mp_err err;
|
|
|
|
*result = MP_NO;
|
|
|
|
if ((err = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) {
|
|
/* TODO: That's ugly! No, really, it is! */
|
|
if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) ||
|
|
(a==14) || (a==18) || (a==23) || (a==26) || (a==28)) {
|
|
continue;
|
|
}
|
|
/* (32764^2 - 4) < 2^31, no bigint for >MP_8BIT needed) */
|
|
mp_set_u32(&T1z, (uint32_t)a);
|
|
|
|
if ((err = mp_sqr(&T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
|
|
if ((err = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
|
|
if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_FU_ERR;
|
|
|
|
if (j == -1) {
|
|
break;
|
|
}
|
|
|
|
if (j == 0) {
|
|
/* composite */
|
|
goto LBL_FU_ERR;
|
|
}
|
|
}
|
|
/* Tell it a composite and set return value accordingly */
|
|
if (a >= LTM_FROBENIUS_UNDERWOOD_A) {
|
|
err = MP_ITER;
|
|
goto LBL_FU_ERR;
|
|
}
|
|
/* Composite if N and (a+4)*(2*a+5) are not coprime */
|
|
mp_set_u32(&T1z, (uint32_t)((a+4)*((2*a)+5)));
|
|
|
|
if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
|
|
if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) goto LBL_FU_ERR;
|
|
|
|
ap2 = a + 2;
|
|
if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
|
|
mp_set(&sz, 1uL);
|
|
mp_set(&tz, 2uL);
|
|
length = mp_count_bits(&Np1z);
|
|
|
|
for (i = length - 2; i >= 0; i--) {
|
|
/*
|
|
* temp = (sz*(a*sz+2*tz))%N;
|
|
* tz = ((tz-sz)*(tz+sz))%N;
|
|
* sz = temp;
|
|
*/
|
|
if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
|
|
/* a = 0 at about 50% of the cases (non-square and odd input) */
|
|
if (a != 0) {
|
|
if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
}
|
|
|
|
if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if (s_mp_get_bit(&Np1z, (unsigned int)i) == MP_YES) {
|
|
/*
|
|
* temp = (a+2) * sz + tz
|
|
* tz = 2 * tz - sz
|
|
* sz = temp
|
|
*/
|
|
if (a == 0) {
|
|
if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
} else {
|
|
if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
}
|
|
if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_FU_ERR;
|
|
mp_exch(&sz, &T1z);
|
|
}
|
|
}
|
|
|
|
mp_set_u32(&T1z, (uint32_t)((2 * a) + 5));
|
|
if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
|
|
if (MP_IS_ZERO(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ)) {
|
|
*result = MP_YES;
|
|
}
|
|
|
|
LBL_FU_ERR:
|
|
mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
#endif
|
|
|
|
/* End: bn_mp_prime_frobenius_underwood.c */
|
|
|
|
/* Start: bn_mp_prime_is_prime.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PRIME_IS_PRIME_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* portable integer log of two with small footprint */
|
|
static unsigned int s_floor_ilog2(int value)
|
|
{
|
|
unsigned int r = 0;
|
|
while ((value >>= 1) != 0) {
|
|
r++;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
|
|
mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result)
|
|
{
|
|
mp_int b;
|
|
int ix, p_max = 0, size_a, len;
|
|
mp_bool res;
|
|
mp_err err;
|
|
unsigned int fips_rand, mask;
|
|
|
|
/* default to no */
|
|
*result = MP_NO;
|
|
|
|
/* Some shortcuts */
|
|
/* N > 3 */
|
|
if (a->used == 1) {
|
|
if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) {
|
|
*result = MP_NO;
|
|
return MP_OKAY;
|
|
}
|
|
if (a->dp[0] == 2u) {
|
|
*result = MP_YES;
|
|
return MP_OKAY;
|
|
}
|
|
}
|
|
|
|
/* N must be odd */
|
|
if (MP_IS_EVEN(a)) {
|
|
return MP_OKAY;
|
|
}
|
|
/* N is not a perfect square: floor(sqrt(N))^2 != N */
|
|
if ((err = mp_is_square(a, &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if (res != MP_NO) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* is the input equal to one of the primes in the table? */
|
|
for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) {
|
|
if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) {
|
|
*result = MP_YES;
|
|
return MP_OKAY;
|
|
}
|
|
}
|
|
#ifdef MP_8BIT
|
|
/* The search in the loop above was exhaustive in this case */
|
|
if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) {
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* first perform trial division */
|
|
if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* return if it was trivially divisible */
|
|
if (res == MP_YES) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/*
|
|
Run the Miller-Rabin test with base 2 for the BPSW test.
|
|
*/
|
|
if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
if (res == MP_NO) {
|
|
goto LBL_B;
|
|
}
|
|
/*
|
|
Rumours have it that Mathematica does a second M-R test with base 3.
|
|
Other rumours have it that their strong L-S test is slightly different.
|
|
It does not hurt, though, beside a bit of extra runtime.
|
|
*/
|
|
b.dp[0]++;
|
|
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
if (res == MP_NO) {
|
|
goto LBL_B;
|
|
}
|
|
|
|
/*
|
|
* Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
|
|
* slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with
|
|
* bases 2, 3 and t random bases.
|
|
*/
|
|
#ifndef LTM_USE_ONLY_MR
|
|
if (t >= 0) {
|
|
/*
|
|
* Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for
|
|
* MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit
|
|
* integers but the necesssary analysis is on the todo-list).
|
|
*/
|
|
#if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST)
|
|
err = mp_prime_frobenius_underwood(a, &res);
|
|
if ((err != MP_OKAY) && (err != MP_ITER)) {
|
|
goto LBL_B;
|
|
}
|
|
if (res == MP_NO) {
|
|
goto LBL_B;
|
|
}
|
|
#else
|
|
if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
if (res == MP_NO) {
|
|
goto LBL_B;
|
|
}
|
|
#endif
|
|
}
|
|
#endif
|
|
|
|
/* run at least one Miller-Rabin test with a random base */
|
|
if (t == 0) {
|
|
t = 1;
|
|
}
|
|
|
|
/*
|
|
Only recommended if the input range is known to be < 3317044064679887385961981
|
|
|
|
It uses the bases necessary for a deterministic M-R test if the input is
|
|
smaller than 3317044064679887385961981
|
|
The caller has to check the size.
|
|
TODO: can be made a bit finer grained but comparing is not free.
|
|
*/
|
|
if (t < 0) {
|
|
/*
|
|
Sorenson, Jonathan; Webster, Jonathan (2015).
|
|
"Strong Pseudoprimes to Twelve Prime Bases".
|
|
*/
|
|
/* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */
|
|
if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
|
|
if (mp_cmp(a, &b) == MP_LT) {
|
|
p_max = 12;
|
|
} else {
|
|
/* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */
|
|
if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
|
|
if (mp_cmp(a, &b) == MP_LT) {
|
|
p_max = 13;
|
|
} else {
|
|
err = MP_VAL;
|
|
goto LBL_B;
|
|
}
|
|
}
|
|
|
|
/* we did bases 2 and 3 already, skip them */
|
|
for (ix = 2; ix < p_max; ix++) {
|
|
mp_set(&b, s_mp_prime_tab[ix]);
|
|
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
if (res == MP_NO) {
|
|
goto LBL_B;
|
|
}
|
|
}
|
|
}
|
|
/*
|
|
Do "t" M-R tests with random bases between 3 and "a".
|
|
See Fips 186.4 p. 126ff
|
|
*/
|
|
else if (t > 0) {
|
|
/*
|
|
* The mp_digit's have a defined bit-size but the size of the
|
|
* array a.dp is a simple 'int' and this library can not assume full
|
|
* compliance to the current C-standard (ISO/IEC 9899:2011) because
|
|
* it gets used for small embeded processors, too. Some of those MCUs
|
|
* have compilers that one cannot call standard compliant by any means.
|
|
* Hence the ugly type-fiddling in the following code.
|
|
*/
|
|
size_a = mp_count_bits(a);
|
|
mask = (1u << s_floor_ilog2(size_a)) - 1u;
|
|
/*
|
|
Assuming the General Rieman hypothesis (never thought to write that in a
|
|
comment) the upper bound can be lowered to 2*(log a)^2.
|
|
E. Bach, "Explicit bounds for primality testing and related problems,"
|
|
Math. Comp. 55 (1990), 355-380.
|
|
|
|
size_a = (size_a/10) * 7;
|
|
len = 2 * (size_a * size_a);
|
|
|
|
E.g.: a number of size 2^2048 would be reduced to the upper limit
|
|
|
|
floor(2048/10)*7 = 1428
|
|
2 * 1428^2 = 4078368
|
|
|
|
(would have been ~4030331.9962 with floats and natural log instead)
|
|
That number is smaller than 2^28, the default bit-size of mp_digit.
|
|
*/
|
|
|
|
/*
|
|
How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame
|
|
does exactly 1. In words: one. Look at the end of _GMP_is_prime() in
|
|
Math-Prime-Util-GMP-0.50/primality.c if you do not believe it.
|
|
|
|
The function mp_rand() goes to some length to use a cryptographically
|
|
good PRNG. That also means that the chance to always get the same base
|
|
in the loop is non-zero, although very low.
|
|
If the BPSW test and/or the addtional Frobenious test have been
|
|
performed instead of just the Miller-Rabin test with the bases 2 and 3,
|
|
a single extra test should suffice, so such a very unlikely event
|
|
will not do much harm.
|
|
|
|
To preemptivly answer the dangling question: no, a witness does not
|
|
need to be prime.
|
|
*/
|
|
for (ix = 0; ix < t; ix++) {
|
|
/* mp_rand() guarantees the first digit to be non-zero */
|
|
if ((err = mp_rand(&b, 1)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
/*
|
|
* Reduce digit before casting because mp_digit might be bigger than
|
|
* an unsigned int and "mask" on the other side is most probably not.
|
|
*/
|
|
fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask);
|
|
#ifdef MP_8BIT
|
|
/*
|
|
* One 8-bit digit is too small, so concatenate two if the size of
|
|
* unsigned int allows for it.
|
|
*/
|
|
if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) {
|
|
if ((err = mp_rand(&b, 1)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
fips_rand <<= MP_SIZEOF_BITS(mp_digit);
|
|
fips_rand |= (unsigned int) b.dp[0];
|
|
fips_rand &= mask;
|
|
}
|
|
#endif
|
|
if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) {
|
|
len = INT_MAX / MP_DIGIT_BIT;
|
|
} else {
|
|
len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT);
|
|
}
|
|
/* Unlikely. */
|
|
if (len < 0) {
|
|
ix--;
|
|
continue;
|
|
}
|
|
/*
|
|
* As mentioned above, one 8-bit digit is too small and
|
|
* although it can only happen in the unlikely case that
|
|
* an "unsigned int" is smaller than 16 bit a simple test
|
|
* is cheap and the correction even cheaper.
|
|
*/
|
|
#ifdef MP_8BIT
|
|
/* All "a" < 2^8 have been caught before */
|
|
if (len == 1) {
|
|
len++;
|
|
}
|
|
#endif
|
|
if ((err = mp_rand(&b, len)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
/*
|
|
* That number might got too big and the witness has to be
|
|
* smaller than "a"
|
|
*/
|
|
len = mp_count_bits(&b);
|
|
if (len >= size_a) {
|
|
len = (len - size_a) + 1;
|
|
if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
}
|
|
/* Although the chance for b <= 3 is miniscule, try again. */
|
|
if (mp_cmp_d(&b, 3uL) != MP_GT) {
|
|
ix--;
|
|
continue;
|
|
}
|
|
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
|
|
goto LBL_B;
|
|
}
|
|
if (res == MP_NO) {
|
|
goto LBL_B;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* passed the test */
|
|
*result = MP_YES;
|
|
LBL_B:
|
|
mp_clear(&b);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_prime_is_prime.c */
|
|
|
|
/* Start: bn_mp_prime_miller_rabin.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PRIME_MILLER_RABIN_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
* very much lower.
|
|
*/
|
|
mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, mp_bool *result)
|
|
{
|
|
mp_int n1, y, r;
|
|
mp_err err;
|
|
int s, j;
|
|
|
|
/* default */
|
|
*result = MP_NO;
|
|
|
|
/* ensure b > 1 */
|
|
if (mp_cmp_d(b, 1uL) != MP_GT) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* get n1 = a - 1 */
|
|
if ((err = mp_init_copy(&n1, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_sub_d(&n1, 1uL, &n1)) != MP_OKAY) {
|
|
goto LBL_N1;
|
|
}
|
|
|
|
/* set 2**s * r = n1 */
|
|
if ((err = mp_init_copy(&r, &n1)) != MP_OKAY) {
|
|
goto LBL_N1;
|
|
}
|
|
|
|
/* count the number of least significant bits
|
|
* which are zero
|
|
*/
|
|
s = mp_cnt_lsb(&r);
|
|
|
|
/* now divide n - 1 by 2**s */
|
|
if ((err = mp_div_2d(&r, s, &r, NULL)) != MP_OKAY) {
|
|
goto LBL_R;
|
|
}
|
|
|
|
/* compute y = b**r mod a */
|
|
if ((err = mp_init(&y)) != MP_OKAY) {
|
|
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, 1uL) != 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, 1uL) == MP_EQ) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
++j;
|
|
}
|
|
|
|
/* if y != n1 then composite */
|
|
if (mp_cmp(&y, &n1) != MP_EQ) {
|
|
goto LBL_Y;
|
|
}
|
|
}
|
|
|
|
/* probably prime now */
|
|
*result = MP_YES;
|
|
LBL_Y:
|
|
mp_clear(&y);
|
|
LBL_R:
|
|
mp_clear(&r);
|
|
LBL_N1:
|
|
mp_clear(&n1);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_prime_miller_rabin.c */
|
|
|
|
/* Start: bn_mp_prime_next_prime.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PRIME_NEXT_PRIME_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
*/
|
|
mp_err mp_prime_next_prime(mp_int *a, int t, int bbs_style)
|
|
{
|
|
int x, y;
|
|
mp_ord cmp;
|
|
mp_err err;
|
|
mp_bool res = MP_NO;
|
|
mp_digit res_tab[PRIVATE_MP_PRIME_TAB_SIZE], step, kstep;
|
|
mp_int b;
|
|
|
|
/* force positive */
|
|
a->sign = MP_ZPOS;
|
|
|
|
/* simple algo if a is less than the largest prime in the table */
|
|
if (mp_cmp_d(a, s_mp_prime_tab[PRIVATE_MP_PRIME_TAB_SIZE-1]) == MP_LT) {
|
|
/* find which prime it is bigger than "a" */
|
|
for (x = 0; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) {
|
|
cmp = mp_cmp_d(a, s_mp_prime_tab[x]);
|
|
if (cmp == MP_EQ) {
|
|
continue;
|
|
}
|
|
if (cmp != MP_GT) {
|
|
if ((bbs_style == 1) && ((s_mp_prime_tab[x] & 3u) != 3u)) {
|
|
/* try again until we get a prime congruent to 3 mod 4 */
|
|
continue;
|
|
} else {
|
|
mp_set(a, s_mp_prime_tab[x]);
|
|
return MP_OKAY;
|
|
}
|
|
}
|
|
}
|
|
/* fall through to the sieve */
|
|
}
|
|
|
|
/* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
|
|
if (bbs_style == 1) {
|
|
kstep = 4;
|
|
} else {
|
|
kstep = 2;
|
|
}
|
|
|
|
/* at this point we will use a combination of a sieve and Miller-Rabin */
|
|
|
|
if (bbs_style == 1) {
|
|
/* if a mod 4 != 3 subtract the correct value to make it so */
|
|
if ((a->dp[0] & 3u) != 3u) {
|
|
if ((err = mp_sub_d(a, (a->dp[0] & 3u) + 1u, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
} else {
|
|
if (MP_IS_EVEN(a)) {
|
|
/* force odd */
|
|
if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* generate the restable */
|
|
for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) {
|
|
if ((err = mp_mod_d(a, s_mp_prime_tab[x], res_tab + x)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* init temp used for Miller-Rabin Testing */
|
|
if ((err = mp_init(&b)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
for (;;) {
|
|
/* skip to the next non-trivially divisible candidate */
|
|
step = 0;
|
|
do {
|
|
/* y == 1 if any residue was zero [e.g. cannot be prime] */
|
|
y = 0;
|
|
|
|
/* increase step to next candidate */
|
|
step += kstep;
|
|
|
|
/* compute the new residue without using division */
|
|
for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) {
|
|
/* add the step to each residue */
|
|
res_tab[x] += kstep;
|
|
|
|
/* subtract the modulus [instead of using division] */
|
|
if (res_tab[x] >= s_mp_prime_tab[x]) {
|
|
res_tab[x] -= s_mp_prime_tab[x];
|
|
}
|
|
|
|
/* set flag if zero */
|
|
if (res_tab[x] == 0u) {
|
|
y = 1;
|
|
}
|
|
}
|
|
} while ((y == 1) && (step < (((mp_digit)1 << MP_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 == MP_MAX then skip test */
|
|
if ((y == 1) && (step >= (((mp_digit)1 << MP_DIGIT_BIT) - kstep))) {
|
|
continue;
|
|
}
|
|
|
|
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if (res == MP_YES) {
|
|
break;
|
|
}
|
|
}
|
|
|
|
err = MP_OKAY;
|
|
LBL_ERR:
|
|
mp_clear(&b);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_prime_next_prime.c */
|
|
|
|
/* Start: bn_mp_prime_rabin_miller_trials.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
static const struct {
|
|
int k, t;
|
|
} sizes[] = {
|
|
{ 80, -1 }, /* Use deterministic algorithm for size <= 80 bits */
|
|
{ 81, 37 }, /* max. error = 2^(-96)*/
|
|
{ 96, 32 }, /* max. error = 2^(-96)*/
|
|
{ 128, 40 }, /* max. error = 2^(-112)*/
|
|
{ 160, 35 }, /* max. error = 2^(-112)*/
|
|
{ 256, 27 }, /* max. error = 2^(-128)*/
|
|
{ 384, 16 }, /* max. error = 2^(-128)*/
|
|
{ 512, 18 }, /* max. error = 2^(-160)*/
|
|
{ 768, 11 }, /* max. error = 2^(-160)*/
|
|
{ 896, 10 }, /* max. error = 2^(-160)*/
|
|
{ 1024, 12 }, /* max. error = 2^(-192)*/
|
|
{ 1536, 8 }, /* max. error = 2^(-192)*/
|
|
{ 2048, 6 }, /* max. error = 2^(-192)*/
|
|
{ 3072, 4 }, /* max. error = 2^(-192)*/
|
|
{ 4096, 5 }, /* max. error = 2^(-256)*/
|
|
{ 5120, 4 }, /* max. error = 2^(-256)*/
|
|
{ 6144, 4 }, /* max. error = 2^(-256)*/
|
|
{ 8192, 3 }, /* max. error = 2^(-256)*/
|
|
{ 9216, 3 }, /* max. error = 2^(-256)*/
|
|
{ 10240, 2 } /* For bigger keysizes use always at least 2 Rounds */
|
|
};
|
|
|
|
/* returns # of RM trials required for a given bit size */
|
|
int mp_prime_rabin_miller_trials(int size)
|
|
{
|
|
int x;
|
|
|
|
for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
|
|
if (sizes[x].k == size) {
|
|
return sizes[x].t;
|
|
} else if (sizes[x].k > size) {
|
|
return (x == 0) ? sizes[0].t : sizes[x - 1].t;
|
|
}
|
|
}
|
|
return sizes[x-1].t;
|
|
}
|
|
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_prime_rabin_miller_trials.c */
|
|
|
|
/* Start: bn_mp_prime_rand.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PRIME_RAND_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* makes a truly random prime of a given size (bits),
|
|
*
|
|
* Flags are as follows:
|
|
*
|
|
* 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
|
|
*
|
|
*/
|
|
|
|
/* This is possibly the mother of all prime generation functions, muahahahahaha! */
|
|
mp_err s_mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat)
|
|
{
|
|
unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
|
|
int bsize, maskOR_msb_offset;
|
|
mp_bool res;
|
|
mp_err err;
|
|
|
|
/* sanity check the input */
|
|
if ((size <= 1) || (t <= 0)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* MP_PRIME_SAFE implies MP_PRIME_BBS */
|
|
if ((flags & MP_PRIME_SAFE) != 0) {
|
|
flags |= MP_PRIME_BBS;
|
|
}
|
|
|
|
/* calc the byte size */
|
|
bsize = (size>>3) + ((size&7)?1:0);
|
|
|
|
/* we need a buffer of bsize bytes */
|
|
tmp = (unsigned char *) MP_MALLOC((size_t)bsize);
|
|
if (tmp == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* calc the maskAND value for the MSbyte*/
|
|
maskAND = ((size&7) == 0) ? 0xFFu : (unsigned char)(0xFFu >> (8 - (size & 7)));
|
|
|
|
/* calc the maskOR_msb */
|
|
maskOR_msb = 0;
|
|
maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
|
|
if ((flags & MP_PRIME_2MSB_ON) != 0) {
|
|
maskOR_msb |= (unsigned char)(0x80 >> ((9 - size) & 7));
|
|
}
|
|
|
|
/* get the maskOR_lsb */
|
|
maskOR_lsb = 1u;
|
|
if ((flags & MP_PRIME_BBS) != 0) {
|
|
maskOR_lsb |= 3u;
|
|
}
|
|
|
|
do {
|
|
/* read the bytes */
|
|
if (cb(tmp, bsize, dat) != bsize) {
|
|
err = MP_VAL;
|
|
goto error;
|
|
}
|
|
|
|
/* work over the MSbyte */
|
|
tmp[0] &= maskAND;
|
|
tmp[0] |= (unsigned char)(1 << ((size - 1) & 7));
|
|
|
|
/* mix in the maskORs */
|
|
tmp[maskOR_msb_offset] |= maskOR_msb;
|
|
tmp[bsize-1] |= maskOR_lsb;
|
|
|
|
/* read it in */
|
|
/* TODO: casting only for now until all lengths have been changed to the type "size_t"*/
|
|
if ((err = mp_from_ubin(a, tmp, (size_t)bsize)) != MP_OKAY) {
|
|
goto error;
|
|
}
|
|
|
|
/* is it prime? */
|
|
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
|
|
goto error;
|
|
}
|
|
if (res == MP_NO) {
|
|
continue;
|
|
}
|
|
|
|
if ((flags & MP_PRIME_SAFE) != 0) {
|
|
/* see if (a-1)/2 is prime */
|
|
if ((err = mp_sub_d(a, 1uL, 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 & MP_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, 1uL, a)) != MP_OKAY) {
|
|
goto error;
|
|
}
|
|
}
|
|
|
|
err = MP_OKAY;
|
|
error:
|
|
MP_FREE_BUFFER(tmp, (size_t)bsize);
|
|
return err;
|
|
}
|
|
|
|
static int s_mp_rand_cb(unsigned char *dst, int len, void *dat)
|
|
{
|
|
(void)dat;
|
|
if (len <= 0) {
|
|
return len;
|
|
}
|
|
if (s_mp_rand_source(dst, (size_t)len) != MP_OKAY) {
|
|
return 0;
|
|
}
|
|
return len;
|
|
}
|
|
|
|
mp_err mp_prime_rand(mp_int *a, int t, int size, int flags)
|
|
{
|
|
return s_mp_prime_random_ex(a, t, size, flags, s_mp_rand_cb, NULL);
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_prime_rand.c */
|
|
|
|
/* Start: bn_mp_prime_strong_lucas_selfridge.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C
|
|
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/*
|
|
* See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
|
|
*/
|
|
#ifndef LTM_USE_ONLY_MR
|
|
|
|
/*
|
|
* 8-bit is just too small. You can try the Frobenius test
|
|
* but that frobenius test can fail, too, for the same reason.
|
|
*/
|
|
#ifndef MP_8BIT
|
|
|
|
/*
|
|
* multiply bigint a with int d and put the result in c
|
|
* Like mp_mul_d() but with a signed long as the small input
|
|
*/
|
|
static mp_err s_mp_mul_si(const mp_int *a, int32_t d, mp_int *c)
|
|
{
|
|
mp_int t;
|
|
mp_err err;
|
|
|
|
if ((err = mp_init(&t)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/*
|
|
* mp_digit might be smaller than a long, which excludes
|
|
* the use of mp_mul_d() here.
|
|
*/
|
|
mp_set_i32(&t, d);
|
|
err = mp_mul(a, &t, c);
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
/*
|
|
Strong Lucas-Selfridge test.
|
|
returns MP_YES if it is a strong L-S prime, MP_NO if it is composite
|
|
|
|
Code ported from Thomas Ray Nicely's implementation of the BPSW test
|
|
at http://www.trnicely.net/misc/bpsw.html
|
|
|
|
Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>.
|
|
Released into the public domain by the author, who disclaims any legal
|
|
liability arising from its use
|
|
|
|
The multi-line comments are made by Thomas R. Nicely and are copied verbatim.
|
|
Additional comments marked "CZ" (without the quotes) are by the code-portist.
|
|
|
|
(If that name sounds familiar, he is the guy who found the fdiv bug in the
|
|
Pentium (P5x, I think) Intel processor)
|
|
*/
|
|
mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result)
|
|
{
|
|
/* CZ TODO: choose better variable names! */
|
|
mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz;
|
|
/* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */
|
|
int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits;
|
|
mp_err err;
|
|
mp_bool oddness;
|
|
|
|
*result = MP_NO;
|
|
/*
|
|
Find the first element D in the sequence {5, -7, 9, -11, 13, ...}
|
|
such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory
|
|
indicates that, if N is not a perfect square, D will "nearly
|
|
always" be "small." Just in case, an overflow trap for D is
|
|
included.
|
|
*/
|
|
|
|
if ((err = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz,
|
|
NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
D = 5;
|
|
sign = 1;
|
|
|
|
for (;;) {
|
|
Ds = sign * D;
|
|
sign = -sign;
|
|
mp_set_u32(&Dz, (uint32_t)D);
|
|
if ((err = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) goto LBL_LS_ERR;
|
|
|
|
/* if 1 < GCD < N then N is composite with factor "D", and
|
|
Jacobi(D,N) is technically undefined (but often returned
|
|
as zero). */
|
|
if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) {
|
|
goto LBL_LS_ERR;
|
|
}
|
|
if (Ds < 0) {
|
|
Dz.sign = MP_NEG;
|
|
}
|
|
if ((err = mp_kronecker(&Dz, a, &J)) != MP_OKAY) goto LBL_LS_ERR;
|
|
|
|
if (J == -1) {
|
|
break;
|
|
}
|
|
D += 2;
|
|
|
|
if (D > (INT_MAX - 2)) {
|
|
err = MP_VAL;
|
|
goto LBL_LS_ERR;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
P = 1; /* Selfridge's choice */
|
|
Q = (1 - Ds) / 4; /* Required so D = P*P - 4*Q */
|
|
|
|
/* NOTE: The conditions (a) N does not divide Q, and
|
|
(b) D is square-free or not a perfect square, are included by
|
|
some authors; e.g., "Prime numbers and computer methods for
|
|
factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston),
|
|
p. 130. For this particular application of Lucas sequences,
|
|
these conditions were found to be immaterial. */
|
|
|
|
/* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the
|
|
odd positive integer d and positive integer s for which
|
|
N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test).
|
|
The strong Lucas-Selfridge test then returns N as a strong
|
|
Lucas probable prime (slprp) if any of the following
|
|
conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0,
|
|
V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0
|
|
(all equalities mod N). Thus d is the highest index of U that
|
|
must be computed (since V_2m is independent of U), compared
|
|
to U_{N+1} for the standard Lucas-Selfridge test; and no
|
|
index of V beyond (N+1)/2 is required, just as in the
|
|
standard Lucas-Selfridge test. However, the quantity Q^d must
|
|
be computed for use (if necessary) in the latter stages of
|
|
the test. The result is that the strong Lucas-Selfridge test
|
|
has a running time only slightly greater (order of 10 %) than
|
|
that of the standard Lucas-Selfridge test, while producing
|
|
only (roughly) 30 % as many pseudoprimes (and every strong
|
|
Lucas pseudoprime is also a standard Lucas pseudoprime). Thus
|
|
the evidence indicates that the strong Lucas-Selfridge test is
|
|
more effective than the standard Lucas-Selfridge test, and a
|
|
Baillie-PSW test based on the strong Lucas-Selfridge test
|
|
should be more reliable. */
|
|
|
|
if ((err = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) goto LBL_LS_ERR;
|
|
s = mp_cnt_lsb(&Np1);
|
|
|
|
/* CZ
|
|
* This should round towards zero because
|
|
* Thomas R. Nicely used GMP's mpz_tdiv_q_2exp()
|
|
* and mp_div_2d() is equivalent. Additionally:
|
|
* dividing an even number by two does not produce
|
|
* any leftovers.
|
|
*/
|
|
if ((err = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) goto LBL_LS_ERR;
|
|
/* We must now compute U_d and V_d. Since d is odd, the accumulated
|
|
values U and V are initialized to U_1 and V_1 (if the target
|
|
index were even, U and V would be initialized instead to U_0=0
|
|
and V_0=2). The values of U_2m and V_2m are also initialized to
|
|
U_1 and V_1; the FOR loop calculates in succession U_2 and V_2,
|
|
U_4 and V_4, U_8 and V_8, etc. If the corresponding bits
|
|
(1, 2, 3, ...) of t are on (the zero bit having been accounted
|
|
for in the initialization of U and V), these values are then
|
|
combined with the previous totals for U and V, using the
|
|
composition formulas for addition of indices. */
|
|
|
|
mp_set(&Uz, 1uL); /* U=U_1 */
|
|
mp_set(&Vz, (mp_digit)P); /* V=V_1 */
|
|
mp_set(&U2mz, 1uL); /* U_1 */
|
|
mp_set(&V2mz, (mp_digit)P); /* V_1 */
|
|
|
|
mp_set_i32(&Qmz, Q);
|
|
if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
/* Initializes calculation of Q^d */
|
|
mp_set_i32(&Qkdz, Q);
|
|
|
|
Nbits = mp_count_bits(&Dz);
|
|
|
|
for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */
|
|
/* Formulas for doubling of indices (carried out mod N). Note that
|
|
* the indices denoted as "2m" are actually powers of 2, specifically
|
|
* 2^(ul-1) beginning each loop and 2^ul ending each loop.
|
|
*
|
|
* U_2m = U_m*V_m
|
|
* V_2m = V_m*V_m - 2*Q^m
|
|
*/
|
|
|
|
if ((err = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
|
|
/* Must calculate powers of Q for use in V_2m, also for Q^d later */
|
|
if ((err = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
|
|
/* prevents overflow */ /* CZ still necessary without a fixed prealloc'd mem.? */
|
|
if ((err = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
|
|
if (s_mp_get_bit(&Dz, (unsigned int)u) == MP_YES) {
|
|
/* Formulas for addition of indices (carried out mod N);
|
|
*
|
|
* U_(m+n) = (U_m*V_n + U_n*V_m)/2
|
|
* V_(m+n) = (V_m*V_n + D*U_m*U_n)/2
|
|
*
|
|
* Be careful with division by 2 (mod N)!
|
|
*/
|
|
if ((err = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = s_mp_mul_si(&T4z, Ds, &T4z)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if (MP_IS_ODD(&Uz)) {
|
|
if ((err = mp_add(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
}
|
|
/* CZ
|
|
* This should round towards negative infinity because
|
|
* Thomas R. Nicely used GMP's mpz_fdiv_q_2exp().
|
|
* But mp_div_2() does not do so, it is truncating instead.
|
|
*/
|
|
oddness = MP_IS_ODD(&Uz) ? MP_YES : MP_NO;
|
|
if ((err = mp_div_2(&Uz, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) {
|
|
if ((err = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
}
|
|
if ((err = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if (MP_IS_ODD(&Vz)) {
|
|
if ((err = mp_add(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
}
|
|
oddness = MP_IS_ODD(&Vz) ? MP_YES : MP_NO;
|
|
if ((err = mp_div_2(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) {
|
|
if ((err = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
}
|
|
if ((err = mp_mod(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
|
|
/* Calculating Q^d for later use */
|
|
if ((err = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
}
|
|
}
|
|
|
|
/* If U_d or V_d is congruent to 0 mod N, then N is a prime or a
|
|
strong Lucas pseudoprime. */
|
|
if (MP_IS_ZERO(&Uz) || MP_IS_ZERO(&Vz)) {
|
|
*result = MP_YES;
|
|
goto LBL_LS_ERR;
|
|
}
|
|
|
|
/* NOTE: Ribenboim ("The new book of prime number records," 3rd ed.,
|
|
1995/6) omits the condition V0 on p.142, but includes it on
|
|
p. 130. The condition is NECESSARY; otherwise the test will
|
|
return false negatives---e.g., the primes 29 and 2000029 will be
|
|
returned as composite. */
|
|
|
|
/* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d}
|
|
by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of
|
|
these are congruent to 0 mod N, then N is a prime or a strong
|
|
Lucas pseudoprime. */
|
|
|
|
/* Initialize 2*Q^(d*2^r) for V_2m */
|
|
if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
|
|
for (r = 1; r < s; r++) {
|
|
if ((err = mp_sqr(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if (MP_IS_ZERO(&Vz)) {
|
|
*result = MP_YES;
|
|
goto LBL_LS_ERR;
|
|
}
|
|
/* Calculate Q^{d*2^r} for next r (final iteration irrelevant). */
|
|
if (r < (s - 1)) {
|
|
if ((err = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR;
|
|
}
|
|
}
|
|
LBL_LS_ERR:
|
|
mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL);
|
|
return err;
|
|
}
|
|
#endif
|
|
#endif
|
|
#endif
|
|
|
|
/* End: bn_mp_prime_strong_lucas_selfridge.c */
|
|
|
|
/* Start: bn_mp_radix_size.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_RADIX_SIZE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* returns size of ASCII representation */
|
|
mp_err mp_radix_size(const mp_int *a, int radix, int *size)
|
|
{
|
|
mp_err err;
|
|
int 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_IS_ZERO(a)) {
|
|
*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;
|
|
}
|
|
|
|
/* init a copy of the input */
|
|
if ((err = mp_init_copy(&t, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* force temp to positive */
|
|
t.sign = MP_ZPOS;
|
|
|
|
/* fetch out all of the digits */
|
|
while (!MP_IS_ZERO(&t)) {
|
|
if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
++digs;
|
|
}
|
|
|
|
/* return digs + 1, the 1 is for the NULL byte that would be required. */
|
|
*size = digs + 1;
|
|
err = MP_OKAY;
|
|
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_radix_size.c */
|
|
|
|
/* Start: bn_mp_radix_smap.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_RADIX_SMAP_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* chars used in radix conversions */
|
|
const char *const mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
|
|
const uint8_t mp_s_rmap_reverse[] = {
|
|
0xff, 0xff, 0xff, 0x3e, 0xff, 0xff, 0xff, 0x3f, /* ()*+,-./ */
|
|
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, /* 01234567 */
|
|
0x08, 0x09, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* 89:;<=>? */
|
|
0xff, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, /* @ABCDEFG */
|
|
0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, /* HIJKLMNO */
|
|
0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, /* PQRSTUVW */
|
|
0x21, 0x22, 0x23, 0xff, 0xff, 0xff, 0xff, 0xff, /* XYZ[\]^_ */
|
|
0xff, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, /* `abcdefg */
|
|
0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, /* hijklmno */
|
|
0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, /* pqrstuvw */
|
|
0x3b, 0x3c, 0x3d, 0xff, 0xff, 0xff, 0xff, 0xff, /* xyz{|}~. */
|
|
};
|
|
const size_t mp_s_rmap_reverse_sz = sizeof(mp_s_rmap_reverse);
|
|
#endif
|
|
|
|
/* End: bn_mp_radix_smap.c */
|
|
|
|
/* Start: bn_mp_rand.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_RAND_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
mp_err(*s_mp_rand_source)(void *out, size_t size) = s_mp_rand_platform;
|
|
|
|
void mp_rand_source(mp_err(*source)(void *out, size_t size))
|
|
{
|
|
s_mp_rand_source = (source == NULL) ? s_mp_rand_platform : source;
|
|
}
|
|
|
|
mp_err mp_rand(mp_int *a, int digits)
|
|
{
|
|
int i;
|
|
mp_err err;
|
|
|
|
mp_zero(a);
|
|
|
|
if (digits <= 0) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
if ((err = mp_grow(a, digits)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = s_mp_rand_source(a->dp, (size_t)digits * sizeof(mp_digit))) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* TODO: We ensure that the highest digit is nonzero. Should this be removed? */
|
|
while ((a->dp[digits - 1] & MP_MASK) == 0u) {
|
|
if ((err = s_mp_rand_source(a->dp + digits - 1, sizeof(mp_digit))) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
a->used = digits;
|
|
for (i = 0; i < digits; ++i) {
|
|
a->dp[i] &= MP_MASK;
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_rand.c */
|
|
|
|
/* Start: bn_mp_read_radix.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_READ_RADIX_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
#define MP_TOUPPER(c) ((((c) >= 'a') && ((c) <= 'z')) ? (((c) + 'A') - 'a') : (c))
|
|
|
|
/* read a string [ASCII] in a given radix */
|
|
mp_err mp_read_radix(mp_int *a, const char *str, int radix)
|
|
{
|
|
mp_err err;
|
|
int y;
|
|
mp_sign neg;
|
|
unsigned pos;
|
|
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 == '-') {
|
|
++str;
|
|
neg = MP_NEG;
|
|
} else {
|
|
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)MP_TOUPPER((int)*str) : *str;
|
|
pos = (unsigned)(ch - '(');
|
|
if (mp_s_rmap_reverse_sz < pos) {
|
|
break;
|
|
}
|
|
y = (int)mp_s_rmap_reverse[pos];
|
|
|
|
/* if the char was found in the map
|
|
* and is less than the given radix add it
|
|
* to the number, otherwise exit the loop.
|
|
*/
|
|
if ((y == 0xff) || (y >= radix)) {
|
|
break;
|
|
}
|
|
if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
++str;
|
|
}
|
|
|
|
/* if an illegal character was found, fail. */
|
|
if (!((*str == '\0') || (*str == '\r') || (*str == '\n'))) {
|
|
mp_zero(a);
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* set the sign only if a != 0 */
|
|
if (!MP_IS_ZERO(a)) {
|
|
a->sign = neg;
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_read_radix.c */
|
|
|
|
/* Start: bn_mp_reduce.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_REDUCE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* reduces x mod m, assumes 0 < x < m**2, mu is
|
|
* precomputed via mp_reduce_setup.
|
|
* From HAC pp.604 Algorithm 14.42
|
|
*/
|
|
mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu)
|
|
{
|
|
mp_int q;
|
|
mp_err err;
|
|
int um = m->used;
|
|
|
|
/* q = x */
|
|
if ((err = mp_init_copy(&q, x)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* q1 = x / b**(k-1) */
|
|
mp_rshd(&q, um - 1);
|
|
|
|
/* according to HAC this optimization is ok */
|
|
if ((mp_digit)um > ((mp_digit)1 << (MP_DIGIT_BIT - 1))) {
|
|
if ((err = mp_mul(&q, mu, &q)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
} else if (MP_HAS(S_MP_MUL_HIGH_DIGS)) {
|
|
if ((err = s_mp_mul_high_digs(&q, mu, &q, um)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
} else if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST)) {
|
|
if ((err = s_mp_mul_high_digs_fast(&q, mu, &q, um)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
} else {
|
|
err = MP_VAL;
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* q3 = q2 / b**(k+1) */
|
|
mp_rshd(&q, um + 1);
|
|
|
|
/* x = x mod b**(k+1), quick (no division) */
|
|
if ((err = mp_mod_2d(x, MP_DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* q = q * m mod b**(k+1), quick (no division) */
|
|
if ((err = s_mp_mul_digs(&q, m, &q, um + 1)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* x = x - q */
|
|
if ((err = mp_sub(x, &q, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* If x < 0, add b**(k+1) to it */
|
|
if (mp_cmp_d(x, 0uL) == MP_LT) {
|
|
mp_set(&q, 1uL);
|
|
if ((err = mp_lshd(&q, um + 1)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
if ((err = mp_add(x, &q, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
}
|
|
|
|
/* Back off if it's too big */
|
|
while (mp_cmp(x, m) != MP_LT) {
|
|
if ((err = s_mp_sub(x, m, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
}
|
|
|
|
CLEANUP:
|
|
mp_clear(&q);
|
|
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_reduce.c */
|
|
|
|
/* Start: bn_mp_reduce_2k.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_REDUCE_2K_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* reduces a modulo n where n is of the form 2**p - d */
|
|
mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d)
|
|
{
|
|
mp_int q;
|
|
mp_err err;
|
|
int p;
|
|
|
|
if ((err = mp_init(&q)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
p = mp_count_bits(n);
|
|
top:
|
|
/* q = a/2**p, a = a mod 2**p */
|
|
if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if (d != 1u) {
|
|
/* q = q * d */
|
|
if ((err = mp_mul_d(&q, d, &q)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* a = a + q */
|
|
if ((err = s_mp_add(a, &q, a)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if (mp_cmp_mag(a, n) != MP_LT) {
|
|
if ((err = s_mp_sub(a, n, a)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
goto top;
|
|
}
|
|
|
|
LBL_ERR:
|
|
mp_clear(&q);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_reduce_2k.c */
|
|
|
|
/* Start: bn_mp_reduce_2k_l.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_REDUCE_2K_L_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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.
|
|
*/
|
|
mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d)
|
|
{
|
|
mp_int q;
|
|
mp_err err;
|
|
int p;
|
|
|
|
if ((err = mp_init(&q)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
p = mp_count_bits(n);
|
|
top:
|
|
/* q = a/2**p, a = a mod 2**p */
|
|
if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* q = q * d */
|
|
if ((err = mp_mul(&q, d, &q)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* a = a + q */
|
|
if ((err = s_mp_add(a, &q, a)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if (mp_cmp_mag(a, n) != MP_LT) {
|
|
if ((err = s_mp_sub(a, n, a)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
goto top;
|
|
}
|
|
|
|
LBL_ERR:
|
|
mp_clear(&q);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_reduce_2k_l.c */
|
|
|
|
/* Start: bn_mp_reduce_2k_setup.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_REDUCE_2K_SETUP_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* determines the setup value */
|
|
mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d)
|
|
{
|
|
mp_err err;
|
|
mp_int tmp;
|
|
int p;
|
|
|
|
if ((err = mp_init(&tmp)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
p = mp_count_bits(a);
|
|
if ((err = mp_2expt(&tmp, p)) != MP_OKAY) {
|
|
mp_clear(&tmp);
|
|
return err;
|
|
}
|
|
|
|
if ((err = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
|
|
mp_clear(&tmp);
|
|
return err;
|
|
}
|
|
|
|
*d = tmp.dp[0];
|
|
mp_clear(&tmp);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_reduce_2k_setup.c */
|
|
|
|
/* Start: bn_mp_reduce_2k_setup_l.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_REDUCE_2K_SETUP_L_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* determines the setup value */
|
|
mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d)
|
|
{
|
|
mp_err err;
|
|
mp_int tmp;
|
|
|
|
if ((err = mp_init(&tmp)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((err = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
LBL_ERR:
|
|
mp_clear(&tmp);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_reduce_2k_setup_l.c */
|
|
|
|
/* Start: bn_mp_reduce_is_2k.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_REDUCE_IS_2K_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* determines if mp_reduce_2k can be used */
|
|
mp_bool mp_reduce_is_2k(const mp_int *a)
|
|
{
|
|
int ix, iy, iw;
|
|
mp_digit iz;
|
|
|
|
if (a->used == 0) {
|
|
return MP_NO;
|
|
} else if (a->used == 1) {
|
|
return MP_YES;
|
|
} else if (a->used > 1) {
|
|
iy = mp_count_bits(a);
|
|
iz = 1;
|
|
iw = 1;
|
|
|
|
/* Test every bit from the second digit up, must be 1 */
|
|
for (ix = MP_DIGIT_BIT; ix < iy; ix++) {
|
|
if ((a->dp[iw] & iz) == 0u) {
|
|
return MP_NO;
|
|
}
|
|
iz <<= 1;
|
|
if (iz > MP_DIGIT_MAX) {
|
|
++iw;
|
|
iz = 1;
|
|
}
|
|
}
|
|
return MP_YES;
|
|
} else {
|
|
return MP_YES;
|
|
}
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_reduce_is_2k.c */
|
|
|
|
/* Start: bn_mp_reduce_is_2k_l.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_REDUCE_IS_2K_L_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* determines if reduce_2k_l can be used */
|
|
mp_bool mp_reduce_is_2k_l(const mp_int *a)
|
|
{
|
|
int ix, iy;
|
|
|
|
if (a->used == 0) {
|
|
return MP_NO;
|
|
} else if (a->used == 1) {
|
|
return MP_YES;
|
|
} else if (a->used > 1) {
|
|
/* if more than half of the digits are -1 we're sold */
|
|
for (iy = ix = 0; ix < a->used; ix++) {
|
|
if (a->dp[ix] == MP_DIGIT_MAX) {
|
|
++iy;
|
|
}
|
|
}
|
|
return (iy >= (a->used/2)) ? MP_YES : MP_NO;
|
|
} else {
|
|
return MP_NO;
|
|
}
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_reduce_is_2k_l.c */
|
|
|
|
/* Start: bn_mp_reduce_setup.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_REDUCE_SETUP_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* pre-calculate the value required for Barrett reduction
|
|
* For a given modulus "b" it calulates the value required in "a"
|
|
*/
|
|
mp_err mp_reduce_setup(mp_int *a, const mp_int *b)
|
|
{
|
|
mp_err err;
|
|
if ((err = mp_2expt(a, b->used * 2 * MP_DIGIT_BIT)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
return mp_div(a, b, a, NULL);
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_reduce_setup.c */
|
|
|
|
/* Start: bn_mp_root_u32.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_ROOT_U32_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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.
|
|
*/
|
|
mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c)
|
|
{
|
|
mp_int t1, t2, t3, a_;
|
|
mp_ord cmp;
|
|
int ilog2;
|
|
mp_err err;
|
|
|
|
/* input must be positive if b is even */
|
|
if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* if a is negative fudge the sign but keep track */
|
|
a_ = *a;
|
|
a_.sign = MP_ZPOS;
|
|
|
|
/* Compute seed: 2^(log_2(n)/b + 2)*/
|
|
ilog2 = mp_count_bits(a);
|
|
|
|
/*
|
|
If "b" is larger than INT_MAX it is also larger than
|
|
log_2(n) because the bit-length of the "n" is measured
|
|
with an int and hence the root is always < 2 (two).
|
|
*/
|
|
if (b > (uint32_t)(INT_MAX/2)) {
|
|
mp_set(c, 1uL);
|
|
c->sign = a->sign;
|
|
err = MP_OKAY;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* "b" is smaller than INT_MAX, we can cast safely */
|
|
if (ilog2 < (int)b) {
|
|
mp_set(c, 1uL);
|
|
c->sign = a->sign;
|
|
err = MP_OKAY;
|
|
goto LBL_ERR;
|
|
}
|
|
ilog2 = ilog2 / ((int)b);
|
|
if (ilog2 == 0) {
|
|
mp_set(c, 1uL);
|
|
c->sign = a->sign;
|
|
err = MP_OKAY;
|
|
goto LBL_ERR;
|
|
}
|
|
/* Start value must be larger than root */
|
|
ilog2 += 2;
|
|
if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY) goto LBL_ERR;
|
|
do {
|
|
/* t1 = t2 */
|
|
if ((err = mp_copy(&t2, &t1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
|
|
|
|
/* t3 = t1**(b-1) */
|
|
if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* numerator */
|
|
/* t2 = t1**b */
|
|
if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* t2 = t1**b - a */
|
|
if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* denominator */
|
|
/* t3 = t1**(b-1) * b */
|
|
if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* t3 = (t1**b - a)/(b * t1**(b-1)) */
|
|
if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/*
|
|
Number of rounds is at most log_2(root). If it is more it
|
|
got stuck, so break out of the loop and do the rest manually.
|
|
*/
|
|
if (ilog2-- == 0) {
|
|
break;
|
|
}
|
|
} while (mp_cmp(&t1, &t2) != MP_EQ);
|
|
|
|
/* result can be off by a few so check */
|
|
/* Loop beneath can overshoot by one if found root is smaller than actual root */
|
|
for (;;) {
|
|
if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR;
|
|
cmp = mp_cmp(&t2, &a_);
|
|
if (cmp == MP_EQ) {
|
|
err = MP_OKAY;
|
|
goto LBL_ERR;
|
|
}
|
|
if (cmp == MP_LT) {
|
|
if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR;
|
|
} else {
|
|
break;
|
|
}
|
|
}
|
|
/* correct overshoot from above or from recurrence */
|
|
for (;;) {
|
|
if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR;
|
|
if (mp_cmp(&t2, &a_) == MP_GT) {
|
|
if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR;
|
|
} else {
|
|
break;
|
|
}
|
|
}
|
|
|
|
/* set the result */
|
|
mp_exch(&t1, c);
|
|
|
|
/* set the sign of the result */
|
|
c->sign = a->sign;
|
|
|
|
err = MP_OKAY;
|
|
|
|
LBL_ERR:
|
|
mp_clear_multi(&t1, &t2, &t3, NULL);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_root_u32.c */
|
|
|
|
/* Start: bn_mp_rshd.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_RSHD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* shift right a certain amount of digits */
|
|
void mp_rshd(mp_int *a, int b)
|
|
{
|
|
int x;
|
|
mp_digit *bottom, *top;
|
|
|
|
/* if b <= 0 then ignore it */
|
|
if (b <= 0) {
|
|
return;
|
|
}
|
|
|
|
/* if b > used then simply zero it and return */
|
|
if (a->used <= b) {
|
|
mp_zero(a);
|
|
return;
|
|
}
|
|
|
|
/* shift the digits down */
|
|
|
|
/* bottom */
|
|
bottom = a->dp;
|
|
|
|
/* top [offset into digits] */
|
|
top = a->dp + b;
|
|
|
|
/* this is implemented as a sliding window where
|
|
* the window is b-digits long and digits from
|
|
* the top of the window are copied to the bottom
|
|
*
|
|
* e.g.
|
|
|
|
b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
|
|
/\ | ---->
|
|
\-------------------/ ---->
|
|
*/
|
|
for (x = 0; x < (a->used - b); x++) {
|
|
*bottom++ = *top++;
|
|
}
|
|
|
|
/* zero the top digits */
|
|
MP_ZERO_DIGITS(bottom, a->used - x);
|
|
|
|
/* remove excess digits */
|
|
a->used -= b;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_rshd.c */
|
|
|
|
/* Start: bn_mp_sbin_size.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SBIN_SIZE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* get the size for an signed equivalent */
|
|
size_t mp_sbin_size(const mp_int *a)
|
|
{
|
|
return 1u + mp_ubin_size(a);
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_sbin_size.c */
|
|
|
|
/* Start: bn_mp_set.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* set to a digit */
|
|
void mp_set(mp_int *a, mp_digit b)
|
|
{
|
|
a->dp[0] = b & MP_MASK;
|
|
a->sign = MP_ZPOS;
|
|
a->used = (a->dp[0] != 0u) ? 1 : 0;
|
|
MP_ZERO_DIGITS(a->dp + a->used, a->alloc - a->used);
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_set.c */
|
|
|
|
/* Start: bn_mp_set_double.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_DOUBLE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
#if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559)
|
|
mp_err mp_set_double(mp_int *a, double b)
|
|
{
|
|
uint64_t frac;
|
|
int exp;
|
|
mp_err err;
|
|
union {
|
|
double dbl;
|
|
uint64_t bits;
|
|
} cast;
|
|
cast.dbl = b;
|
|
|
|
exp = (int)((unsigned)(cast.bits >> 52) & 0x7FFu);
|
|
frac = (cast.bits & ((1uLL << 52) - 1uLL)) | (1uLL << 52);
|
|
|
|
if (exp == 0x7FF) { /* +-inf, NaN */
|
|
return MP_VAL;
|
|
}
|
|
exp -= 1023 + 52;
|
|
|
|
mp_set_u64(a, frac);
|
|
|
|
err = (exp < 0) ? mp_div_2d(a, -exp, a, NULL) : mp_mul_2d(a, exp, a);
|
|
if (err != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if (((cast.bits >> 63) != 0uLL) && !MP_IS_ZERO(a)) {
|
|
a->sign = MP_NEG;
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#else
|
|
/* pragma message() not supported by several compilers (in mostly older but still used versions) */
|
|
# ifdef _MSC_VER
|
|
# pragma message("mp_set_double implementation is only available on platforms with IEEE754 floating point format")
|
|
# else
|
|
# warning "mp_set_double implementation is only available on platforms with IEEE754 floating point format"
|
|
# endif
|
|
#endif
|
|
#endif
|
|
|
|
/* End: bn_mp_set_double.c */
|
|
|
|
/* Start: bn_mp_set_i32.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_I32_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_SET_SIGNED(mp_set_i32, mp_set_u32, int32_t, uint32_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_set_i32.c */
|
|
|
|
/* Start: bn_mp_set_i64.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_I64_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_SET_SIGNED(mp_set_i64, mp_set_u64, int64_t, uint64_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_set_i64.c */
|
|
|
|
/* Start: bn_mp_set_l.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_L_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_SET_SIGNED(mp_set_l, mp_set_ul, long, unsigned long)
|
|
#endif
|
|
|
|
/* End: bn_mp_set_l.c */
|
|
|
|
/* Start: bn_mp_set_ll.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_LL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_SET_SIGNED(mp_set_ll, mp_set_ull, long long, unsigned long long)
|
|
#endif
|
|
|
|
/* End: bn_mp_set_ll.c */
|
|
|
|
/* Start: bn_mp_set_u32.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_U32_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_SET_UNSIGNED(mp_set_u32, uint32_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_set_u32.c */
|
|
|
|
/* Start: bn_mp_set_u64.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_U64_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_SET_UNSIGNED(mp_set_u64, uint64_t)
|
|
#endif
|
|
|
|
/* End: bn_mp_set_u64.c */
|
|
|
|
/* Start: bn_mp_set_ul.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_UL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_SET_UNSIGNED(mp_set_ul, unsigned long)
|
|
#endif
|
|
|
|
/* End: bn_mp_set_ul.c */
|
|
|
|
/* Start: bn_mp_set_ull.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SET_ULL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
MP_SET_UNSIGNED(mp_set_ull, unsigned long long)
|
|
#endif
|
|
|
|
/* End: bn_mp_set_ull.c */
|
|
|
|
/* Start: bn_mp_shrink.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SHRINK_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* shrink a bignum */
|
|
mp_err mp_shrink(mp_int *a)
|
|
{
|
|
mp_digit *tmp;
|
|
int alloc = MP_MAX(MP_MIN_PREC, a->used);
|
|
if (a->alloc != alloc) {
|
|
if ((tmp = (mp_digit *) MP_REALLOC(a->dp,
|
|
(size_t)a->alloc * sizeof(mp_digit),
|
|
(size_t)alloc * sizeof(mp_digit))) == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
a->dp = tmp;
|
|
a->alloc = alloc;
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_shrink.c */
|
|
|
|
/* Start: bn_mp_signed_rsh.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SIGNED_RSH_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* shift right by a certain bit count with sign extension */
|
|
mp_err mp_signed_rsh(const mp_int *a, int b, mp_int *c)
|
|
{
|
|
mp_err res;
|
|
if (a->sign == MP_ZPOS) {
|
|
return mp_div_2d(a, b, c, NULL);
|
|
}
|
|
|
|
res = mp_add_d(a, 1uL, c);
|
|
if (res != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
res = mp_div_2d(c, b, c, NULL);
|
|
return (res == MP_OKAY) ? mp_sub_d(c, 1uL, c) : res;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_signed_rsh.c */
|
|
|
|
/* Start: bn_mp_sqr.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SQR_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* computes b = a*a */
|
|
mp_err mp_sqr(const mp_int *a, mp_int *b)
|
|
{
|
|
mp_err err;
|
|
if (MP_HAS(S_MP_TOOM_SQR) && /* use Toom-Cook? */
|
|
(a->used >= MP_TOOM_SQR_CUTOFF)) {
|
|
err = s_mp_toom_sqr(a, b);
|
|
} else if (MP_HAS(S_MP_KARATSUBA_SQR) && /* Karatsuba? */
|
|
(a->used >= MP_KARATSUBA_SQR_CUTOFF)) {
|
|
err = s_mp_karatsuba_sqr(a, b);
|
|
} else if (MP_HAS(S_MP_SQR_FAST) && /* can we use the fast comba multiplier? */
|
|
(((a->used * 2) + 1) < MP_WARRAY) &&
|
|
(a->used < (MP_MAXFAST / 2))) {
|
|
err = s_mp_sqr_fast(a, b);
|
|
} else if (MP_HAS(S_MP_SQR)) {
|
|
err = s_mp_sqr(a, b);
|
|
} else {
|
|
err = MP_VAL;
|
|
}
|
|
b->sign = MP_ZPOS;
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_sqr.c */
|
|
|
|
/* Start: bn_mp_sqrmod.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SQRMOD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* c = a * a (mod b) */
|
|
mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_err err;
|
|
mp_int t;
|
|
|
|
if ((err = mp_init(&t)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_sqr(a, &t)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
err = mp_mod(&t, b, c);
|
|
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_sqrmod.c */
|
|
|
|
/* Start: bn_mp_sqrt.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SQRT_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* this function is less generic than mp_n_root, simpler and faster */
|
|
mp_err mp_sqrt(const mp_int *arg, mp_int *ret)
|
|
{
|
|
mp_err err;
|
|
mp_int t1, t2;
|
|
|
|
/* must be positive */
|
|
if (arg->sign == MP_NEG) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* easy out */
|
|
if (MP_IS_ZERO(arg)) {
|
|
mp_zero(ret);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
if ((err = mp_init_copy(&t1, arg)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_init(&t2)) != MP_OKAY) {
|
|
goto E2;
|
|
}
|
|
|
|
/* First approx. (not very bad for large arg) */
|
|
mp_rshd(&t1, t1.used/2);
|
|
|
|
/* t1 > 0 */
|
|
if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
|
|
goto E1;
|
|
}
|
|
if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
|
|
goto E1;
|
|
}
|
|
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) {
|
|
goto E1;
|
|
}
|
|
/* And now t1 > sqrt(arg) */
|
|
do {
|
|
if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
|
|
goto E1;
|
|
}
|
|
if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
|
|
goto E1;
|
|
}
|
|
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) {
|
|
goto E1;
|
|
}
|
|
/* t1 >= sqrt(arg) >= t2 at this point */
|
|
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
|
|
|
|
mp_exch(&t1, ret);
|
|
|
|
E1:
|
|
mp_clear(&t2);
|
|
E2:
|
|
mp_clear(&t1);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_sqrt.c */
|
|
|
|
/* Start: bn_mp_sqrtmod_prime.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SQRTMOD_PRIME_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* Tonelli-Shanks algorithm
|
|
* https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
|
|
* https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
|
|
*
|
|
*/
|
|
|
|
mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret)
|
|
{
|
|
mp_err err;
|
|
int 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, 0uL) == MP_EQ) {
|
|
mp_zero(ret);
|
|
return MP_OKAY;
|
|
}
|
|
if (mp_cmp_d(prime, 2uL) == MP_EQ) return MP_VAL; /* prime must be odd */
|
|
if ((err = mp_kronecker(n, prime, &legendre)) != MP_OKAY) return err;
|
|
if (legendre == -1) return MP_VAL; /* quadratic non-residue mod prime */
|
|
|
|
if ((err = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* SPECIAL CASE: if prime mod 4 == 3
|
|
* compute directly: err = n^(prime+1)/4 mod prime
|
|
* Handbook of Applied Cryptography algorithm 3.36
|
|
*/
|
|
if ((err = mp_mod_d(prime, 4uL, &i)) != MP_OKAY) goto cleanup;
|
|
if (i == 3u) {
|
|
if ((err = mp_add_d(prime, 1uL, &t1)) != MP_OKAY) goto cleanup;
|
|
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
|
|
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
|
|
if ((err = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup;
|
|
err = 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 ((err = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup;
|
|
if ((err = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY) goto cleanup;
|
|
/* Q = prime - 1 */
|
|
mp_zero(&S);
|
|
/* S = 0 */
|
|
while (MP_IS_EVEN(&Q)) {
|
|
if ((err = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup;
|
|
/* Q = Q / 2 */
|
|
if ((err = mp_add_d(&S, 1uL, &S)) != MP_OKAY) goto cleanup;
|
|
/* S = S + 1 */
|
|
}
|
|
|
|
/* find a Z such that the Legendre symbol (Z|prime) == -1 */
|
|
mp_set_u32(&Z, 2u);
|
|
/* Z = 2 */
|
|
for (;;) {
|
|
if ((err = mp_kronecker(&Z, prime, &legendre)) != MP_OKAY) goto cleanup;
|
|
if (legendre == -1) break;
|
|
if ((err = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup;
|
|
/* Z = Z + 1 */
|
|
}
|
|
|
|
if ((err = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup;
|
|
/* C = Z ^ Q mod prime */
|
|
if ((err = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) goto cleanup;
|
|
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
|
|
/* t1 = (Q + 1) / 2 */
|
|
if ((err = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup;
|
|
/* R = n ^ ((Q + 1) / 2) mod prime */
|
|
if ((err = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup;
|
|
/* T = n ^ Q mod prime */
|
|
if ((err = mp_copy(&S, &M)) != MP_OKAY) goto cleanup;
|
|
/* M = S */
|
|
mp_set_u32(&two, 2u);
|
|
|
|
for (;;) {
|
|
if ((err = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup;
|
|
i = 0;
|
|
for (;;) {
|
|
if (mp_cmp_d(&t1, 1uL) == MP_EQ) break;
|
|
if ((err = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
|
|
i++;
|
|
}
|
|
if (i == 0u) {
|
|
if ((err = mp_copy(&R, ret)) != MP_OKAY) goto cleanup;
|
|
err = MP_OKAY;
|
|
goto cleanup;
|
|
}
|
|
if ((err = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup;
|
|
if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup;
|
|
if ((err = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
|
|
/* t1 = 2 ^ (M - i - 1) */
|
|
if ((err = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
|
|
/* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
|
|
if ((err = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup;
|
|
/* C = (t1 * t1) mod prime */
|
|
if ((err = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup;
|
|
/* R = (R * t1) mod prime */
|
|
if ((err = 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 err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_sqrtmod_prime.c */
|
|
|
|
/* Start: bn_mp_sub.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SUB_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* high level subtraction (handles signs) */
|
|
mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_sign sa = a->sign, sb = b->sign;
|
|
mp_err err;
|
|
|
|
if (sa != sb) {
|
|
/* subtract a negative from a positive, OR */
|
|
/* subtract a positive from a negative. */
|
|
/* In either case, ADD their magnitudes, */
|
|
/* and use the sign of the first number. */
|
|
c->sign = sa;
|
|
err = s_mp_add(a, b, c);
|
|
} else {
|
|
/* subtract a positive from a positive, OR */
|
|
/* subtract a negative from a negative. */
|
|
/* First, take the difference between their */
|
|
/* magnitudes, then... */
|
|
if (mp_cmp_mag(a, b) != MP_LT) {
|
|
/* Copy the sign from the first */
|
|
c->sign = sa;
|
|
/* The first has a larger or equal magnitude */
|
|
err = s_mp_sub(a, b, c);
|
|
} else {
|
|
/* The result has the *opposite* sign from */
|
|
/* the first number. */
|
|
c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
|
|
/* The second has a larger magnitude */
|
|
err = s_mp_sub(b, a, c);
|
|
}
|
|
}
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_sub.c */
|
|
|
|
/* Start: bn_mp_sub_d.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SUB_D_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* single digit subtraction */
|
|
mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c)
|
|
{
|
|
mp_digit *tmpa, *tmpc;
|
|
mp_err err;
|
|
int ix, oldused;
|
|
|
|
/* grow c as required */
|
|
if (c->alloc < (a->used + 1)) {
|
|
if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* if a is negative just do an unsigned
|
|
* addition [with fudged signs]
|
|
*/
|
|
if (a->sign == MP_NEG) {
|
|
mp_int a_ = *a;
|
|
a_.sign = MP_ZPOS;
|
|
err = mp_add_d(&a_, b, c);
|
|
c->sign = MP_NEG;
|
|
|
|
/* clamp */
|
|
mp_clamp(c);
|
|
|
|
return err;
|
|
}
|
|
|
|
/* 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;
|
|
|
|
/* negative/1digit */
|
|
c->sign = MP_NEG;
|
|
c->used = 1;
|
|
} else {
|
|
mp_digit mu = b;
|
|
|
|
/* positive/size */
|
|
c->sign = MP_ZPOS;
|
|
c->used = a->used;
|
|
|
|
/* subtract digits, mu is carry */
|
|
for (ix = 0; ix < a->used; ix++) {
|
|
*tmpc = *tmpa++ - mu;
|
|
mu = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u);
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
}
|
|
|
|
/* zero excess digits */
|
|
MP_ZERO_DIGITS(tmpc, oldused - ix);
|
|
|
|
mp_clamp(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_sub_d.c */
|
|
|
|
/* Start: bn_mp_submod.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_SUBMOD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* d = a - b (mod c) */
|
|
mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
|
|
{
|
|
mp_err err;
|
|
mp_int t;
|
|
|
|
if ((err = mp_init(&t)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
if ((err = mp_sub(a, b, &t)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
err = mp_mod(&t, c, d);
|
|
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_submod.c */
|
|
|
|
/* Start: bn_mp_to_radix.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_TO_RADIX_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* stores a bignum as a ASCII string in a given radix (2..64)
|
|
*
|
|
* Stores upto "size - 1" chars and always a NULL byte, puts the number of characters
|
|
* written, including the '\0', in "written".
|
|
*/
|
|
mp_err mp_to_radix(const mp_int *a, char *str, size_t maxlen, size_t *written, int radix)
|
|
{
|
|
size_t digs;
|
|
mp_err err;
|
|
mp_int t;
|
|
mp_digit d;
|
|
char *_s = str;
|
|
|
|
/* check range of radix and size*/
|
|
if (maxlen < 2u) {
|
|
return MP_BUF;
|
|
}
|
|
if ((radix < 2) || (radix > 64)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* quick out if its zero */
|
|
if (MP_IS_ZERO(a)) {
|
|
*str++ = '0';
|
|
*str = '\0';
|
|
if (written != NULL) {
|
|
*written = 2u;
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
if ((err = mp_init_copy(&t, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* if it is negative output a - */
|
|
if (t.sign == MP_NEG) {
|
|
/* we have to reverse our digits later... but not the - sign!! */
|
|
++_s;
|
|
|
|
/* store the flag and mark the number as positive */
|
|
*str++ = '-';
|
|
t.sign = MP_ZPOS;
|
|
|
|
/* subtract a char */
|
|
--maxlen;
|
|
}
|
|
digs = 0u;
|
|
while (!MP_IS_ZERO(&t)) {
|
|
if (--maxlen < 1u) {
|
|
/* no more room */
|
|
err = MP_BUF;
|
|
goto LBL_ERR;
|
|
}
|
|
if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
*str++ = mp_s_rmap[d];
|
|
++digs;
|
|
}
|
|
/* reverse the digits of the string. In this case _s points
|
|
* to the first digit [exluding the sign] of the number
|
|
*/
|
|
s_mp_reverse((unsigned char *)_s, digs);
|
|
|
|
/* append a NULL so the string is properly terminated */
|
|
*str = '\0';
|
|
digs++;
|
|
|
|
if (written != NULL) {
|
|
*written = (a->sign == MP_NEG) ? (digs + 1u): digs;
|
|
}
|
|
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_to_radix.c */
|
|
|
|
/* Start: bn_mp_to_sbin.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_TO_SBIN_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* store in signed [big endian] format */
|
|
mp_err mp_to_sbin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written)
|
|
{
|
|
mp_err err;
|
|
if (maxlen == 0u) {
|
|
return MP_BUF;
|
|
}
|
|
if ((err = mp_to_ubin(a, buf + 1, maxlen - 1u, written)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if (written != NULL) {
|
|
(*written)++;
|
|
}
|
|
buf[0] = (a->sign == MP_ZPOS) ? (unsigned char)0 : (unsigned char)1;
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_to_sbin.c */
|
|
|
|
/* Start: bn_mp_to_ubin.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_TO_UBIN_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* store in unsigned [big endian] format */
|
|
mp_err mp_to_ubin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written)
|
|
{
|
|
size_t x, count;
|
|
mp_err err;
|
|
mp_int t;
|
|
|
|
count = mp_ubin_size(a);
|
|
if (count > maxlen) {
|
|
return MP_BUF;
|
|
}
|
|
|
|
if ((err = mp_init_copy(&t, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
for (x = count; x --> 0u;) {
|
|
#ifndef MP_8BIT
|
|
buf[x] = (unsigned char)(t.dp[0] & 255u);
|
|
#else
|
|
buf[x] = (unsigned char)(t.dp[0] | ((t.dp[1] & 1u) << 7));
|
|
#endif
|
|
if ((err = mp_div_2d(&t, 8, &t, NULL)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
if (written != NULL) {
|
|
*written = count;
|
|
}
|
|
|
|
LBL_ERR:
|
|
mp_clear(&t);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_to_ubin.c */
|
|
|
|
/* Start: bn_mp_ubin_size.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_UBIN_SIZE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* get the size for an unsigned equivalent */
|
|
size_t mp_ubin_size(const mp_int *a)
|
|
{
|
|
size_t size = (size_t)mp_count_bits(a);
|
|
return (size / 8u) + (((size & 7u) != 0u) ? 1u : 0u);
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_ubin_size.c */
|
|
|
|
/* Start: bn_mp_unpack.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_UNPACK_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* based on gmp's mpz_import.
|
|
* see http://gmplib.org/manual/Integer-Import-and-Export.html
|
|
*/
|
|
mp_err mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size,
|
|
mp_endian endian, size_t nails, const void *op)
|
|
{
|
|
mp_err err;
|
|
size_t odd_nails, nail_bytes, i, j;
|
|
unsigned char odd_nail_mask;
|
|
|
|
mp_zero(rop);
|
|
|
|
if (endian == MP_NATIVE_ENDIAN) {
|
|
MP_GET_ENDIANNESS(endian);
|
|
}
|
|
|
|
odd_nails = (nails % 8u);
|
|
odd_nail_mask = 0xff;
|
|
for (i = 0; i < odd_nails; ++i) {
|
|
odd_nail_mask ^= (unsigned char)(1u << (7u - i));
|
|
}
|
|
nail_bytes = nails / 8u;
|
|
|
|
for (i = 0; i < count; ++i) {
|
|
for (j = 0; j < (size - nail_bytes); ++j) {
|
|
unsigned char byte = *((const unsigned char *)op +
|
|
(((order == MP_MSB_FIRST) ? i : ((count - 1u) - i)) * size) +
|
|
((endian == MP_BIG_ENDIAN) ? (j + nail_bytes) : (((size - 1u) - j) - nail_bytes)));
|
|
|
|
if ((err = mp_mul_2d(rop, (j == 0u) ? (int)(8u - odd_nails) : 8, rop)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
rop->dp[0] |= (j == 0u) ? (mp_digit)(byte & odd_nail_mask) : (mp_digit)byte;
|
|
rop->used += 1;
|
|
}
|
|
}
|
|
|
|
mp_clamp(rop);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_mp_unpack.c */
|
|
|
|
/* Start: bn_mp_xor.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_XOR_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 used = MP_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
|
|
|
|
/* End: bn_mp_xor.c */
|
|
|
|
/* Start: bn_mp_zero.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_MP_ZERO_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* set to zero */
|
|
void mp_zero(mp_int *a)
|
|
{
|
|
a->sign = MP_ZPOS;
|
|
a->used = 0;
|
|
MP_ZERO_DIGITS(a->dp, a->alloc);
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_mp_zero.c */
|
|
|
|
/* Start: bn_prime_tab.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_PRIME_TAB_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
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
|
|
0x0083,
|
|
0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
|
|
0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
|
|
0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
|
|
0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
|
|
|
|
0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
|
|
0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
|
|
0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
|
|
0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
|
|
0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
|
|
0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
|
|
0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
|
|
0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
|
|
|
|
0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
|
|
0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
|
|
0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
|
|
0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
|
|
0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
|
|
0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
|
|
0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
|
|
0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
|
|
|
|
0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
|
|
0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
|
|
0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
|
|
0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
|
|
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
|
|
};
|
|
|
|
#if defined(__GNUC__) && __GNUC__ >= 4
|
|
#pragma GCC diagnostic push
|
|
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
|
|
const mp_digit *s_mp_prime_tab = ltm_prime_tab;
|
|
#pragma GCC diagnostic pop
|
|
#elif defined(_MSC_VER) && _MSC_VER >= 1500
|
|
#pragma warning(push)
|
|
#pragma warning(disable: 4996)
|
|
const mp_digit *s_mp_prime_tab = ltm_prime_tab;
|
|
#pragma warning(pop)
|
|
#else
|
|
const mp_digit *s_mp_prime_tab = ltm_prime_tab;
|
|
#endif
|
|
|
|
#endif
|
|
|
|
/* End: bn_prime_tab.c */
|
|
|
|
/* Start: bn_s_mp_add.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_ADD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* low level addition, based on HAC pp.594, Algorithm 14.7 */
|
|
mp_err s_mp_add(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
const mp_int *x;
|
|
mp_err err;
|
|
int olduse, min, max;
|
|
|
|
/* find sizes, we let |a| <= |b| which means we have to sort
|
|
* them. "x" will point to the input with the most digits
|
|
*/
|
|
if (a->used > b->used) {
|
|
min = b->used;
|
|
max = a->used;
|
|
x = a;
|
|
} else {
|
|
min = a->used;
|
|
max = b->used;
|
|
x = b;
|
|
}
|
|
|
|
/* init result */
|
|
if (c->alloc < (max + 1)) {
|
|
if ((err = mp_grow(c, max + 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* 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 */
|
|
tmpb = b->dp;
|
|
|
|
/* destination */
|
|
tmpc = c->dp;
|
|
|
|
/* zero the carry */
|
|
u = 0;
|
|
for (i = 0; i < min; i++) {
|
|
/* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
|
|
*tmpc = *tmpa++ + *tmpb++ + u;
|
|
|
|
/* U = carry bit of T[i] */
|
|
u = *tmpc >> (mp_digit)MP_DIGIT_BIT;
|
|
|
|
/* take away carry bit from T[i] */
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
|
|
/* now copy higher words if any, that is in A+B
|
|
* if A or B has more digits add those in
|
|
*/
|
|
if (min != max) {
|
|
for (; i < max; i++) {
|
|
/* T[i] = X[i] + U */
|
|
*tmpc = x->dp[i] + u;
|
|
|
|
/* U = carry bit of T[i] */
|
|
u = *tmpc >> (mp_digit)MP_DIGIT_BIT;
|
|
|
|
/* take away carry bit from T[i] */
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
}
|
|
|
|
/* add carry */
|
|
*tmpc++ = u;
|
|
|
|
/* clear digits above oldused */
|
|
MP_ZERO_DIGITS(tmpc, olduse - c->used);
|
|
}
|
|
|
|
mp_clamp(c);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_add.c */
|
|
|
|
/* Start: bn_s_mp_balance_mul.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_BALANCE_MUL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* single-digit multiplication with the smaller number as the single-digit */
|
|
mp_err s_mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
int count, len_a, len_b, nblocks, i, j, bsize;
|
|
mp_int a0, tmp, A, B, r;
|
|
mp_err err;
|
|
|
|
len_a = a->used;
|
|
len_b = b->used;
|
|
|
|
nblocks = MP_MAX(a->used, b->used) / MP_MIN(a->used, b->used);
|
|
bsize = MP_MIN(a->used, b->used) ;
|
|
|
|
if ((err = mp_init_size(&a0, bsize + 2)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_init_multi(&tmp, &r, NULL)) != MP_OKAY) {
|
|
mp_clear(&a0);
|
|
return err;
|
|
}
|
|
|
|
/* Make sure that A is the larger one*/
|
|
if (len_a < len_b) {
|
|
B = *a;
|
|
A = *b;
|
|
} else {
|
|
A = *a;
|
|
B = *b;
|
|
}
|
|
|
|
for (i = 0, j=0; i < nblocks; i++) {
|
|
/* Cut a slice off of a */
|
|
a0.used = 0;
|
|
for (count = 0; count < bsize; count++) {
|
|
a0.dp[count] = A.dp[ j++ ];
|
|
a0.used++;
|
|
}
|
|
mp_clamp(&a0);
|
|
/* Multiply with b */
|
|
if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
/* Shift tmp to the correct position */
|
|
if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
/* Add to output. No carry needed */
|
|
if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
/* The left-overs; there are always left-overs */
|
|
if (j < A.used) {
|
|
a0.used = 0;
|
|
for (count = 0; j < A.used; count++) {
|
|
a0.dp[count] = A.dp[ j++ ];
|
|
a0.used++;
|
|
}
|
|
mp_clamp(&a0);
|
|
if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
mp_exch(&r,c);
|
|
LBL_ERR:
|
|
mp_clear_multi(&a0, &tmp, &r,NULL);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_balance_mul.c */
|
|
|
|
/* Start: bn_s_mp_exptmod.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_EXPTMOD_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
#ifdef MP_LOW_MEM
|
|
# define TAB_SIZE 32
|
|
# define MAX_WINSIZE 5
|
|
#else
|
|
# define TAB_SIZE 256
|
|
# define MAX_WINSIZE 0
|
|
#endif
|
|
|
|
mp_err s_mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode)
|
|
{
|
|
mp_int M[TAB_SIZE], res, mu;
|
|
mp_digit buf;
|
|
mp_err err;
|
|
int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
mp_err(*redux)(mp_int *x, const mp_int *m, const mp_int *mu);
|
|
|
|
/* find window size */
|
|
x = mp_count_bits(X);
|
|
if (x <= 7) {
|
|
winsize = 2;
|
|
} else if (x <= 36) {
|
|
winsize = 3;
|
|
} else if (x <= 140) {
|
|
winsize = 4;
|
|
} else if (x <= 450) {
|
|
winsize = 5;
|
|
} else if (x <= 1303) {
|
|
winsize = 6;
|
|
} else if (x <= 3529) {
|
|
winsize = 7;
|
|
} else {
|
|
winsize = 8;
|
|
}
|
|
|
|
winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize;
|
|
|
|
/* init M array */
|
|
/* init first cell */
|
|
if ((err = mp_init(&M[1])) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* now init the second half of the array */
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
if ((err = mp_init(&M[x])) != MP_OKAY) {
|
|
for (y = 1<<(winsize-1); y < x; y++) {
|
|
mp_clear(&M[y]);
|
|
}
|
|
mp_clear(&M[1]);
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* create mu, used for Barrett reduction */
|
|
if ((err = mp_init(&mu)) != MP_OKAY) goto LBL_M;
|
|
|
|
if (redmode == 0) {
|
|
if ((err = mp_reduce_setup(&mu, P)) != MP_OKAY) goto LBL_MU;
|
|
redux = mp_reduce;
|
|
} else {
|
|
if ((err = mp_reduce_2k_setup_l(P, &mu)) != MP_OKAY) goto LBL_MU;
|
|
redux = mp_reduce_2k_l;
|
|
}
|
|
|
|
/* create M table
|
|
*
|
|
* The M table contains powers of the base,
|
|
* e.g. M[x] = G**x mod P
|
|
*
|
|
* The first half of the table is not
|
|
* computed though accept for M[0] and M[1]
|
|
*/
|
|
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) goto LBL_MU;
|
|
|
|
/* compute the value at M[1<<(winsize-1)] by squaring
|
|
* M[1] (winsize-1) times
|
|
*/
|
|
if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU;
|
|
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
/* square it */
|
|
if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)],
|
|
&M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU;
|
|
|
|
/* reduce modulo P */
|
|
if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, &mu)) != MP_OKAY) goto LBL_MU;
|
|
}
|
|
|
|
/* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
|
|
* for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
|
|
*/
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) goto LBL_MU;
|
|
if ((err = redux(&M[x], P, &mu)) != MP_OKAY) goto LBL_MU;
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init(&res)) != MP_OKAY) goto LBL_MU;
|
|
mp_set(&res, 1uL);
|
|
|
|
/* set initial mode and bit cnt */
|
|
mode = 0;
|
|
bitcnt = 1;
|
|
buf = 0;
|
|
digidx = X->used - 1;
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
|
|
for (;;) {
|
|
/* grab next digit as required */
|
|
if (--bitcnt == 0) {
|
|
/* if digidx == -1 we are out of digits */
|
|
if (digidx == -1) {
|
|
break;
|
|
}
|
|
/* read next digit and reset the bitcnt */
|
|
buf = X->dp[digidx--];
|
|
bitcnt = (int)MP_DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (buf >> (mp_digit)(MP_DIGIT_BIT - 1)) & 1uL;
|
|
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;
|
|
}
|
|
|
|
/* else we add it to the window */
|
|
bitbuf |= (y << (winsize - ++bitcpy));
|
|
mode = 2;
|
|
|
|
if (bitcpy == winsize) {
|
|
/* ok window is filled so square as required and multiply */
|
|
/* square first */
|
|
for (x = 0; x < winsize; x++) {
|
|
if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES;
|
|
if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES;
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) goto LBL_RES;
|
|
if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES;
|
|
|
|
/* empty window and reset */
|
|
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;
|
|
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) goto LBL_RES;
|
|
if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES;
|
|
}
|
|
}
|
|
}
|
|
|
|
mp_exch(&res, Y);
|
|
err = MP_OKAY;
|
|
LBL_RES:
|
|
mp_clear(&res);
|
|
LBL_MU:
|
|
mp_clear(&mu);
|
|
LBL_M:
|
|
mp_clear(&M[1]);
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
mp_clear(&M[x]);
|
|
}
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_exptmod.c */
|
|
|
|
/* Start: bn_s_mp_exptmod_fast.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_EXPTMOD_FAST_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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.
|
|
*
|
|
* Uses Montgomery or Diminished Radix reduction [whichever appropriate]
|
|
*/
|
|
|
|
#ifdef MP_LOW_MEM
|
|
# define TAB_SIZE 32
|
|
# define MAX_WINSIZE 5
|
|
#else
|
|
# define TAB_SIZE 256
|
|
# define MAX_WINSIZE 0
|
|
#endif
|
|
|
|
mp_err s_mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode)
|
|
{
|
|
mp_int M[TAB_SIZE], res;
|
|
mp_digit buf, mp;
|
|
int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
mp_err err;
|
|
|
|
/* use a pointer to the reduction algorithm. This allows us to use
|
|
* one of many reduction algorithms without modding the guts of
|
|
* the code with if statements everywhere.
|
|
*/
|
|
mp_err(*redux)(mp_int *x, const mp_int *n, mp_digit rho);
|
|
|
|
/* find window size */
|
|
x = mp_count_bits(X);
|
|
if (x <= 7) {
|
|
winsize = 2;
|
|
} else if (x <= 36) {
|
|
winsize = 3;
|
|
} else if (x <= 140) {
|
|
winsize = 4;
|
|
} else if (x <= 450) {
|
|
winsize = 5;
|
|
} else if (x <= 1303) {
|
|
winsize = 6;
|
|
} else if (x <= 3529) {
|
|
winsize = 7;
|
|
} else {
|
|
winsize = 8;
|
|
}
|
|
|
|
winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize;
|
|
|
|
/* init M array */
|
|
/* init first cell */
|
|
if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* now init the second half of the array */
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) {
|
|
for (y = 1<<(winsize-1); y < x; y++) {
|
|
mp_clear(&M[y]);
|
|
}
|
|
mp_clear(&M[1]);
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* determine and setup reduction code */
|
|
if (redmode == 0) {
|
|
if (MP_HAS(MP_MONTGOMERY_SETUP)) {
|
|
/* now setup montgomery */
|
|
if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) goto LBL_M;
|
|
} else {
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
}
|
|
|
|
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
|
|
if (MP_HAS(S_MP_MONTGOMERY_REDUCE_FAST) &&
|
|
(((P->used * 2) + 1) < MP_WARRAY) &&
|
|
(P->used < MP_MAXFAST)) {
|
|
redux = s_mp_montgomery_reduce_fast;
|
|
} else if (MP_HAS(MP_MONTGOMERY_REDUCE)) {
|
|
/* use slower baseline Montgomery method */
|
|
redux = mp_montgomery_reduce;
|
|
} else {
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
}
|
|
} else if (redmode == 1) {
|
|
if (MP_HAS(MP_DR_SETUP) && MP_HAS(MP_DR_REDUCE)) {
|
|
/* setup DR reduction for moduli of the form B**k - b */
|
|
mp_dr_setup(P, &mp);
|
|
redux = mp_dr_reduce;
|
|
} else {
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
}
|
|
} else if (MP_HAS(MP_REDUCE_2K_SETUP) && MP_HAS(MP_REDUCE_2K)) {
|
|
/* setup DR reduction for moduli of the form 2**k - b */
|
|
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) goto LBL_M;
|
|
redux = mp_reduce_2k;
|
|
} else {
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init_size(&res, P->alloc)) != MP_OKAY) goto LBL_M;
|
|
|
|
/* create M table
|
|
*
|
|
|
|
*
|
|
* The first half of the table is not computed though accept for M[0] and M[1]
|
|
*/
|
|
|
|
if (redmode == 0) {
|
|
if (MP_HAS(MP_MONTGOMERY_CALC_NORMALIZATION)) {
|
|
/* now we need R mod m */
|
|
if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) goto LBL_RES;
|
|
|
|
/* now set M[1] to G * R mod m */
|
|
if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) goto LBL_RES;
|
|
} else {
|
|
err = MP_VAL;
|
|
goto LBL_RES;
|
|
}
|
|
} else {
|
|
mp_set(&res, 1uL);
|
|
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) goto LBL_RES;
|
|
}
|
|
|
|
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
|
|
if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES;
|
|
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES;
|
|
if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, mp)) != MP_OKAY) goto LBL_RES;
|
|
}
|
|
|
|
/* create upper table */
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) goto LBL_RES;
|
|
if ((err = redux(&M[x], P, mp)) != MP_OKAY) goto LBL_RES;
|
|
}
|
|
|
|
/* set initial mode and bit cnt */
|
|
mode = 0;
|
|
bitcnt = 1;
|
|
buf = 0;
|
|
digidx = X->used - 1;
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
|
|
for (;;) {
|
|
/* grab next digit as required */
|
|
if (--bitcnt == 0) {
|
|
/* if digidx == -1 we are out of digits so break */
|
|
if (digidx == -1) {
|
|
break;
|
|
}
|
|
/* read next digit and reset bitcnt */
|
|
buf = X->dp[digidx--];
|
|
bitcnt = (int)MP_DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (mp_digit)(buf >> (MP_DIGIT_BIT - 1)) & 1uL;
|
|
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;
|
|
}
|
|
|
|
/* else we add it to the window */
|
|
bitbuf |= (y << (winsize - ++bitcpy));
|
|
mode = 2;
|
|
|
|
if (bitcpy == winsize) {
|
|
/* ok window is filled so square as required and multiply */
|
|
/* square first */
|
|
for (x = 0; x < winsize; x++) {
|
|
if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES;
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) goto LBL_RES;
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
|
|
|
|
/* empty window and reset */
|
|
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;
|
|
|
|
/* get next bit of the window */
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) goto LBL_RES;
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (redmode == 0) {
|
|
/* fixup result if Montgomery reduction is used
|
|
* recall that any value in a Montgomery system is
|
|
* actually multiplied by R mod n. So we have
|
|
* to reduce one more time to cancel out the factor
|
|
* of R.
|
|
*/
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
|
|
}
|
|
|
|
/* swap res with Y */
|
|
mp_exch(&res, Y);
|
|
err = MP_OKAY;
|
|
LBL_RES:
|
|
mp_clear(&res);
|
|
LBL_M:
|
|
mp_clear(&M[1]);
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
mp_clear(&M[x]);
|
|
}
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_exptmod_fast.c */
|
|
|
|
/* Start: bn_s_mp_get_bit.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_GET_BIT_C
|
|
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* Get bit at position b and return MP_YES if the bit is 1, MP_NO if it is 0 */
|
|
mp_bool s_mp_get_bit(const mp_int *a, unsigned int b)
|
|
{
|
|
mp_digit bit;
|
|
int limb = (int)(b / MP_DIGIT_BIT);
|
|
|
|
if (limb >= a->used) {
|
|
return MP_NO;
|
|
}
|
|
|
|
bit = (mp_digit)1 << (b % MP_DIGIT_BIT);
|
|
return ((a->dp[limb] & bit) != 0u) ? MP_YES : MP_NO;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_s_mp_get_bit.c */
|
|
|
|
/* Start: bn_s_mp_invmod_fast.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_INVMOD_FAST_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
*/
|
|
mp_err s_mp_invmod_fast(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_int x, y, u, v, B, D;
|
|
mp_sign neg;
|
|
mp_err err;
|
|
|
|
/* 2. [modified] b must be odd */
|
|
if (MP_IS_EVEN(b)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* init all our temps */
|
|
if ((err = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* x == modulus, y == value to invert */
|
|
if ((err = mp_copy(b, &x)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* we need y = |a| */
|
|
if ((err = mp_mod(a, b, &y)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* if one of x,y is zero return an error! */
|
|
if (MP_IS_ZERO(&x) || MP_IS_ZERO(&y)) {
|
|
err = MP_VAL;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR;
|
|
mp_set(&D, 1uL);
|
|
|
|
top:
|
|
/* 4. while u is even do */
|
|
while (MP_IS_EVEN(&u)) {
|
|
/* 4.1 u = u/2 */
|
|
if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* 4.2 if B is odd then */
|
|
if (MP_IS_ODD(&B)) {
|
|
if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
/* B = B/2 */
|
|
if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* 5. while v is even do */
|
|
while (MP_IS_EVEN(&v)) {
|
|
/* 5.1 v = v/2 */
|
|
if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* 5.2 if D is odd then */
|
|
if (MP_IS_ODD(&D)) {
|
|
/* D = (D-x)/2 */
|
|
if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
/* D = D/2 */
|
|
if ((err = mp_div_2(&D, &D)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* 6. if u >= v then */
|
|
if (mp_cmp(&u, &v) != MP_LT) {
|
|
/* u = u - v, B = B - D */
|
|
if ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR;
|
|
} else {
|
|
/* v - v - u, D = D - B */
|
|
if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* if not zero goto step 4 */
|
|
if (!MP_IS_ZERO(&u)) {
|
|
goto top;
|
|
}
|
|
|
|
/* now a = C, b = D, gcd == g*v */
|
|
|
|
/* if v != 1 then there is no inverse */
|
|
if (mp_cmp_d(&v, 1uL) != MP_EQ) {
|
|
err = MP_VAL;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* b is now the inverse */
|
|
neg = a->sign;
|
|
while (D.sign == MP_NEG) {
|
|
if ((err = mp_add(&D, b, &D)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* too big */
|
|
while (mp_cmp_mag(&D, b) != MP_LT) {
|
|
if ((err = mp_sub(&D, b, &D)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
mp_exch(&D, c);
|
|
c->sign = neg;
|
|
err = MP_OKAY;
|
|
|
|
LBL_ERR:
|
|
mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_invmod_fast.c */
|
|
|
|
/* Start: bn_s_mp_invmod_slow.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_INVMOD_SLOW_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* hac 14.61, pp608 */
|
|
mp_err s_mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_int x, y, u, v, A, B, C, D;
|
|
mp_err err;
|
|
|
|
/* b cannot be negative */
|
|
if ((b->sign == MP_NEG) || MP_IS_ZERO(b)) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* init temps */
|
|
if ((err = mp_init_multi(&x, &y, &u, &v,
|
|
&A, &B, &C, &D, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* x = a, y = b */
|
|
if ((err = mp_mod(a, b, &x)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_copy(b, &y)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* 2. [modified] if x,y are both even then return an error! */
|
|
if (MP_IS_EVEN(&x) && MP_IS_EVEN(&y)) {
|
|
err = MP_VAL;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR;
|
|
mp_set(&A, 1uL);
|
|
mp_set(&D, 1uL);
|
|
|
|
top:
|
|
/* 4. while u is even do */
|
|
while (MP_IS_EVEN(&u)) {
|
|
/* 4.1 u = u/2 */
|
|
if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* 4.2 if A or B is odd then */
|
|
if (MP_IS_ODD(&A) || MP_IS_ODD(&B)) {
|
|
/* A = (A+y)/2, B = (B-x)/2 */
|
|
if ((err = mp_add(&A, &y, &A)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
/* A = A/2, B = B/2 */
|
|
if ((err = mp_div_2(&A, &A)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* 5. while v is even do */
|
|
while (MP_IS_EVEN(&v)) {
|
|
/* 5.1 v = v/2 */
|
|
if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/* 5.2 if C or D is odd then */
|
|
if (MP_IS_ODD(&C) || MP_IS_ODD(&D)) {
|
|
/* C = (C+y)/2, D = (D-x)/2 */
|
|
if ((err = mp_add(&C, &y, &C)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
/* C = C/2, D = D/2 */
|
|
if ((err = mp_div_2(&C, &C)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_div_2(&D, &D)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* 6. if u >= v then */
|
|
if (mp_cmp(&u, &v) != MP_LT) {
|
|
/* u = u - v, A = A - C, B = B - D */
|
|
if ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
if ((err = mp_sub(&A, &C, &A)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR;
|
|
} else {
|
|
/* v - v - u, C = C - A, D = D - B */
|
|
if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
if ((err = mp_sub(&C, &A, &C)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* if not zero goto step 4 */
|
|
if (!MP_IS_ZERO(&u)) {
|
|
goto top;
|
|
}
|
|
|
|
/* now a = C, b = D, gcd == g*v */
|
|
|
|
/* if v != 1 then there is no inverse */
|
|
if (mp_cmp_d(&v, 1uL) != MP_EQ) {
|
|
err = MP_VAL;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* if its too low */
|
|
while (mp_cmp_d(&C, 0uL) == MP_LT) {
|
|
if ((err = mp_add(&C, b, &C)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* too big */
|
|
while (mp_cmp_mag(&C, b) != MP_LT) {
|
|
if ((err = mp_sub(&C, b, &C)) != MP_OKAY) goto LBL_ERR;
|
|
}
|
|
|
|
/* C is now the inverse */
|
|
mp_exch(&C, c);
|
|
err = MP_OKAY;
|
|
LBL_ERR:
|
|
mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL);
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_invmod_slow.c */
|
|
|
|
/* Start: bn_s_mp_karatsuba_mul.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_KARATSUBA_MUL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* c = |a| * |b| using Karatsuba Multiplication using
|
|
* three half size multiplications
|
|
*
|
|
* Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and
|
|
* let n represent half of the number of digits in
|
|
* the min(a,b)
|
|
*
|
|
* a = a1 * B**n + a0
|
|
* b = b1 * B**n + b0
|
|
*
|
|
* Then, a * b =>
|
|
a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
|
|
*
|
|
* Note that a1b1 and a0b0 are used twice and only need to be
|
|
* computed once. So in total three half size (half # of
|
|
* digit) multiplications are performed, a0b0, a1b1 and
|
|
* (a1+b1)(a0+b0)
|
|
*
|
|
* Note that a multiplication of half the digits requires
|
|
* 1/4th the number of single precision multiplications so in
|
|
* total after one call 25% of the single precision multiplications
|
|
* are saved. Note also that the call to mp_mul can end up back
|
|
* in this function if the a0, a1, b0, or b1 are above the threshold.
|
|
* This is known as divide-and-conquer and leads to the famous
|
|
* O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
|
|
* the standard O(N**2) that the baseline/comba methods use.
|
|
* Generally though the overhead of this method doesn't pay off
|
|
* until a certain size (N ~ 80) is reached.
|
|
*/
|
|
mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
|
|
int B;
|
|
mp_err err = MP_MEM; /* default the return code to an error */
|
|
|
|
/* min # of digits */
|
|
B = MP_MIN(a->used, b->used);
|
|
|
|
/* now divide in two */
|
|
B = B >> 1;
|
|
|
|
/* init copy all the temps */
|
|
if (mp_init_size(&x0, B) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if (mp_init_size(&x1, a->used - B) != MP_OKAY) {
|
|
goto X0;
|
|
}
|
|
if (mp_init_size(&y0, B) != MP_OKAY) {
|
|
goto X1;
|
|
}
|
|
if (mp_init_size(&y1, b->used - B) != MP_OKAY) {
|
|
goto Y0;
|
|
}
|
|
|
|
/* init temps */
|
|
if (mp_init_size(&t1, B * 2) != MP_OKAY) {
|
|
goto Y1;
|
|
}
|
|
if (mp_init_size(&x0y0, B * 2) != MP_OKAY) {
|
|
goto T1;
|
|
}
|
|
if (mp_init_size(&x1y1, B * 2) != MP_OKAY) {
|
|
goto X0Y0;
|
|
}
|
|
|
|
/* 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;
|
|
|
|
tmpx = x0.dp;
|
|
tmpy = y0.dp;
|
|
for (x = 0; x < B; x++) {
|
|
*tmpx++ = *tmpa++;
|
|
*tmpy++ = *tmpb++;
|
|
}
|
|
|
|
tmpx = x1.dp;
|
|
for (x = B; x < a->used; x++) {
|
|
*tmpx++ = *tmpa++;
|
|
}
|
|
|
|
tmpy = y1.dp;
|
|
for (x = B; x < b->used; x++) {
|
|
*tmpy++ = *tmpb++;
|
|
}
|
|
}
|
|
|
|
/* only need to clamp the lower words since by definition the
|
|
* upper words x1/y1 must have a known number of digits
|
|
*/
|
|
mp_clamp(&x0);
|
|
mp_clamp(&y0);
|
|
|
|
/* now calc the products x0y0 and x1y1 */
|
|
/* after this x0 is no longer required, free temp [x0==t2]! */
|
|
if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) {
|
|
goto X1Y1; /* x0y0 = x0*y0 */
|
|
}
|
|
if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) {
|
|
goto X1Y1; /* x1y1 = x1*y1 */
|
|
}
|
|
|
|
/* now calc x1+x0 and y1+y0 */
|
|
if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = x1 - x0 */
|
|
}
|
|
if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) {
|
|
goto X1Y1; /* t2 = y1 - y0 */
|
|
}
|
|
if (mp_mul(&t1, &x0, &t1) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
|
|
}
|
|
|
|
/* add x0y0 */
|
|
if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) {
|
|
goto X1Y1; /* t2 = x0y0 + x1y1 */
|
|
}
|
|
if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
|
|
}
|
|
|
|
/* shift by B */
|
|
if (mp_lshd(&t1, B) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
|
|
}
|
|
if (mp_lshd(&x1y1, B * 2) != MP_OKAY) {
|
|
goto X1Y1; /* x1y1 = x1y1 << 2*B */
|
|
}
|
|
|
|
if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = x0y0 + t1 */
|
|
}
|
|
if (mp_add(&t1, &x1y1, c) != MP_OKAY) {
|
|
goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
|
|
}
|
|
|
|
/* Algorithm succeeded set the return code to MP_OKAY */
|
|
err = MP_OKAY;
|
|
|
|
X1Y1:
|
|
mp_clear(&x1y1);
|
|
X0Y0:
|
|
mp_clear(&x0y0);
|
|
T1:
|
|
mp_clear(&t1);
|
|
Y1:
|
|
mp_clear(&y1);
|
|
Y0:
|
|
mp_clear(&y0);
|
|
X1:
|
|
mp_clear(&x1);
|
|
X0:
|
|
mp_clear(&x0);
|
|
LBL_ERR:
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_karatsuba_mul.c */
|
|
|
|
/* Start: bn_s_mp_karatsuba_sqr.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_KARATSUBA_SQR_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
* tuned to perform recursive squarings.
|
|
*/
|
|
mp_err s_mp_karatsuba_sqr(const mp_int *a, mp_int *b)
|
|
{
|
|
mp_int x0, x1, t1, t2, x0x0, x1x1;
|
|
int B;
|
|
mp_err err = MP_MEM;
|
|
|
|
/* min # of digits */
|
|
B = a->used;
|
|
|
|
/* now divide in two */
|
|
B = B >> 1;
|
|
|
|
/* init copy all the temps */
|
|
if (mp_init_size(&x0, B) != MP_OKAY)
|
|
goto LBL_ERR;
|
|
if (mp_init_size(&x1, a->used - B) != MP_OKAY)
|
|
goto X0;
|
|
|
|
/* init temps */
|
|
if (mp_init_size(&t1, a->used * 2) != MP_OKAY)
|
|
goto X1;
|
|
if (mp_init_size(&t2, a->used * 2) != MP_OKAY)
|
|
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++;
|
|
}
|
|
|
|
dst = x1.dp;
|
|
for (x = B; x < a->used; x++) {
|
|
*dst++ = *src++;
|
|
}
|
|
}
|
|
|
|
x0.used = B;
|
|
x1.used = a->used - B;
|
|
|
|
mp_clamp(&x0);
|
|
|
|
/* now calc the products x0*x0 and x1*x1 */
|
|
if (mp_sqr(&x0, &x0x0) != MP_OKAY)
|
|
goto X1X1; /* x0x0 = x0*x0 */
|
|
if (mp_sqr(&x1, &x1x1) != MP_OKAY)
|
|
goto X1X1; /* x1x1 = x1*x1 */
|
|
|
|
/* now calc (x1+x0)**2 */
|
|
if (s_mp_add(&x1, &x0, &t1) != MP_OKAY)
|
|
goto X1X1; /* t1 = x1 - x0 */
|
|
if (mp_sqr(&t1, &t1) != MP_OKAY)
|
|
goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
|
|
|
|
/* add x0y0 */
|
|
if (s_mp_add(&x0x0, &x1x1, &t2) != MP_OKAY)
|
|
goto X1X1; /* t2 = x0x0 + x1x1 */
|
|
if (s_mp_sub(&t1, &t2, &t1) != MP_OKAY)
|
|
goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
|
|
|
|
/* shift by B */
|
|
if (mp_lshd(&t1, B) != MP_OKAY)
|
|
goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
|
|
if (mp_lshd(&x1x1, B * 2) != MP_OKAY)
|
|
goto X1X1; /* x1x1 = x1x1 << 2*B */
|
|
|
|
if (mp_add(&x0x0, &t1, &t1) != MP_OKAY)
|
|
goto X1X1; /* t1 = x0x0 + t1 */
|
|
if (mp_add(&t1, &x1x1, b) != MP_OKAY)
|
|
goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
|
|
|
|
err = MP_OKAY;
|
|
|
|
X1X1:
|
|
mp_clear(&x1x1);
|
|
X0X0:
|
|
mp_clear(&x0x0);
|
|
T2:
|
|
mp_clear(&t2);
|
|
T1:
|
|
mp_clear(&t1);
|
|
X1:
|
|
mp_clear(&x1);
|
|
X0:
|
|
mp_clear(&x0);
|
|
LBL_ERR:
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_karatsuba_sqr.c */
|
|
|
|
/* Start: bn_s_mp_montgomery_reduce_fast.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_MONTGOMERY_REDUCE_FAST_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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.
|
|
*
|
|
* Based on Algorithm 14.32 on pp.601 of HAC.
|
|
*/
|
|
mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho)
|
|
{
|
|
int ix, olduse;
|
|
mp_err err;
|
|
mp_word W[MP_WARRAY];
|
|
|
|
if (x->used > MP_WARRAY) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* get old used count */
|
|
olduse = x->used;
|
|
|
|
/* grow a as required */
|
|
if (x->alloc < (n->used + 1)) {
|
|
if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* 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] */
|
|
if (ix < ((n->used * 2) + 1)) {
|
|
MP_ZERO_BUFFER(_W, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix));
|
|
}
|
|
}
|
|
|
|
/* 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 = ((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.
|
|
*
|
|
* Note the comba method normally doesn't handle carries in the
|
|
* inner loop In this case we fix the carry from the previous
|
|
* 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;
|
|
|
|
/* inner loop */
|
|
for (iy = 0; iy < n->used; iy++) {
|
|
*_W++ += (mp_word)mu * (mp_word)*tmpn++;
|
|
}
|
|
}
|
|
|
|
/* now fix carry for next digit, W[ix+1] */
|
|
W[ix + 1] += W[ix] >> (mp_word)MP_DIGIT_BIT;
|
|
}
|
|
|
|
/* 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)MP_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
|
|
* we just copy them in the right order
|
|
*/
|
|
|
|
/* 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++ = *_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
|
|
*/
|
|
MP_ZERO_DIGITS(tmpx, olduse - ix);
|
|
}
|
|
|
|
/* set the max used and clamp */
|
|
x->used = n->used + 1;
|
|
mp_clamp(x);
|
|
|
|
/* 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
|
|
|
|
/* End: bn_s_mp_montgomery_reduce_fast.c */
|
|
|
|
/* Start: bn_s_mp_mul_digs.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_MUL_DIGS_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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.
|
|
*/
|
|
mp_err s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
|
|
{
|
|
mp_int t;
|
|
mp_err err;
|
|
int 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) &&
|
|
(MP_MIN(a->used, b->used) < MP_MAXFAST)) {
|
|
return s_mp_mul_digs_fast(a, b, c, digs);
|
|
}
|
|
|
|
if ((err = mp_init_size(&t, digs)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
t.used = digs;
|
|
|
|
/* compute the digits of the product directly */
|
|
pa = a->used;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* set the carry to zero */
|
|
u = 0;
|
|
|
|
/* limit ourselves to making digs digits of output */
|
|
pb = MP_MIN(b->used, digs - ix);
|
|
|
|
/* setup some aliases */
|
|
/* copy of the digit from a used within the nested loop */
|
|
tmpx = a->dp[ix];
|
|
|
|
/* an alias for the destination shifted ix places */
|
|
tmpt = t.dp + ix;
|
|
|
|
/* 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)MP_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
|
|
|
|
/* End: bn_s_mp_mul_digs.c */
|
|
|
|
/* Start: bn_s_mp_mul_digs_fast.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_MUL_DIGS_FAST_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
* of making the nested loops that compute the columns very
|
|
* simple and schedulable on super-scalar processors.
|
|
*
|
|
* This has been modified to produce a variable number of
|
|
* digits of output so if say only a half-product is required
|
|
* you don't have to compute the upper half (a feature
|
|
* required for fast Barrett reduction).
|
|
*
|
|
* Based on Algorithm 14.12 on pp.595 of HAC.
|
|
*
|
|
*/
|
|
mp_err s_mp_mul_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs)
|
|
{
|
|
int olduse, pa, ix, iz;
|
|
mp_err err;
|
|
mp_digit W[MP_WARRAY];
|
|
mp_word _W;
|
|
|
|
/* grow the destination as required */
|
|
if (c->alloc < digs) {
|
|
if ((err = mp_grow(c, digs)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
pa = MP_MIN(digs, a->used + b->used);
|
|
|
|
/* clear the carry */
|
|
_W = 0;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
int tx, ty;
|
|
int iy;
|
|
mp_digit *tmpx, *tmpy;
|
|
|
|
/* get offsets into the two bignums */
|
|
ty = MP_MIN(b->used-1, ix);
|
|
tx = ix - ty;
|
|
|
|
/* setup temp aliases */
|
|
tmpx = a->dp + tx;
|
|
tmpy = b->dp + ty;
|
|
|
|
/* this is the number of times the loop will iterrate, essentially
|
|
while (tx++ < a->used && ty-- >= 0) { ... }
|
|
*/
|
|
iy = MP_MIN(a->used-tx, ty+1);
|
|
|
|
/* execute loop */
|
|
for (iz = 0; iz < iy; ++iz) {
|
|
_W += (mp_word)*tmpx++ * (mp_word)*tmpy--;
|
|
|
|
}
|
|
|
|
/* store term */
|
|
W[ix] = (mp_digit)_W & MP_MASK;
|
|
|
|
/* make next carry */
|
|
_W = _W >> (mp_word)MP_DIGIT_BIT;
|
|
}
|
|
|
|
/* setup dest */
|
|
olduse = c->used;
|
|
c->used = pa;
|
|
|
|
{
|
|
mp_digit *tmpc;
|
|
tmpc = c->dp;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* now extract the previous digit [below the carry] */
|
|
*tmpc++ = W[ix];
|
|
}
|
|
|
|
/* clear unused digits [that existed in the old copy of c] */
|
|
MP_ZERO_DIGITS(tmpc, olduse - ix);
|
|
}
|
|
mp_clamp(c);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_mul_digs_fast.c */
|
|
|
|
/* Start: bn_s_mp_mul_high_digs.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* multiplies |a| * |b| and does not compute the lower digs digits
|
|
* [meant to get the higher part of the product]
|
|
*/
|
|
mp_err s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
|
|
{
|
|
mp_int t;
|
|
int pa, pb, ix, iy;
|
|
mp_err err;
|
|
mp_digit u;
|
|
mp_word r;
|
|
mp_digit tmpx, *tmpt, *tmpy;
|
|
|
|
/* can we use the fast multiplier? */
|
|
if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST)
|
|
&& ((a->used + b->used + 1) < MP_WARRAY)
|
|
&& (MP_MIN(a->used, b->used) < MP_MAXFAST)) {
|
|
return s_mp_mul_high_digs_fast(a, b, c, digs);
|
|
}
|
|
|
|
if ((err = mp_init_size(&t, a->used + b->used + 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
t.used = a->used + b->used + 1;
|
|
|
|
pa = a->used;
|
|
pb = b->used;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* clear the carry */
|
|
u = 0;
|
|
|
|
/* left hand side of A[ix] * B[iy] */
|
|
tmpx = a->dp[ix];
|
|
|
|
/* alias to the address of where the digits will be stored */
|
|
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)MP_DIGIT_BIT);
|
|
}
|
|
*tmpt = u;
|
|
}
|
|
mp_clamp(&t);
|
|
mp_exch(&t, c);
|
|
mp_clear(&t);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_mul_high_digs.c */
|
|
|
|
/* Start: bn_s_mp_mul_high_digs_fast.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_MUL_HIGH_DIGS_FAST_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
* only the higher digits were needed. This essentially halves the work.
|
|
*
|
|
* Based on Algorithm 14.12 on pp.595 of HAC.
|
|
*/
|
|
mp_err s_mp_mul_high_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs)
|
|
{
|
|
int olduse, pa, ix, iz;
|
|
mp_err err;
|
|
mp_digit W[MP_WARRAY];
|
|
mp_word _W;
|
|
|
|
/* grow the destination as required */
|
|
pa = a->used + b->used;
|
|
if (c->alloc < pa) {
|
|
if ((err = mp_grow(c, pa)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
pa = a->used + b->used;
|
|
_W = 0;
|
|
for (ix = digs; ix < pa; ix++) {
|
|
int tx, ty, iy;
|
|
mp_digit *tmpx, *tmpy;
|
|
|
|
/* get offsets into the two bignums */
|
|
ty = MP_MIN(b->used-1, ix);
|
|
tx = ix - ty;
|
|
|
|
/* setup temp aliases */
|
|
tmpx = a->dp + tx;
|
|
tmpy = b->dp + ty;
|
|
|
|
/* this is the number of times the loop will iterrate, essentially its
|
|
while (tx++ < a->used && ty-- >= 0) { ... }
|
|
*/
|
|
iy = MP_MIN(a->used-tx, ty+1);
|
|
|
|
/* execute loop */
|
|
for (iz = 0; iz < iy; iz++) {
|
|
_W += (mp_word)*tmpx++ * (mp_word)*tmpy--;
|
|
}
|
|
|
|
/* store term */
|
|
W[ix] = (mp_digit)_W & MP_MASK;
|
|
|
|
/* make next carry */
|
|
_W = _W >> (mp_word)MP_DIGIT_BIT;
|
|
}
|
|
|
|
/* 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];
|
|
}
|
|
|
|
/* clear unused digits [that existed in the old copy of c] */
|
|
MP_ZERO_DIGITS(tmpc, olduse - ix);
|
|
}
|
|
mp_clamp(c);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_mul_high_digs_fast.c */
|
|
|
|
/* Start: bn_s_mp_prime_is_divisible.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_PRIME_IS_DIVISIBLE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
*/
|
|
mp_err s_mp_prime_is_divisible(const mp_int *a, mp_bool *result)
|
|
{
|
|
int ix;
|
|
mp_err err;
|
|
mp_digit res;
|
|
|
|
/* default to not */
|
|
*result = MP_NO;
|
|
|
|
for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) {
|
|
/* what is a mod LBL_prime_tab[ix] */
|
|
if ((err = mp_mod_d(a, s_mp_prime_tab[ix], &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* is the residue zero? */
|
|
if (res == 0u) {
|
|
*result = MP_YES;
|
|
return MP_OKAY;
|
|
}
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_prime_is_divisible.c */
|
|
|
|
/* Start: bn_s_mp_rand_jenkins.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_RAND_JENKINS_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* Bob Jenkins' http://burtleburtle.net/bob/rand/smallprng.html */
|
|
/* Chosen for speed and a good "mix" */
|
|
typedef struct {
|
|
uint64_t a;
|
|
uint64_t b;
|
|
uint64_t c;
|
|
uint64_t d;
|
|
} ranctx;
|
|
|
|
static ranctx jenkins_x;
|
|
|
|
#define rot(x,k) (((x)<<(k))|((x)>>(64-(k))))
|
|
static uint64_t s_rand_jenkins_val(void)
|
|
{
|
|
uint64_t e = jenkins_x.a - rot(jenkins_x.b, 7);
|
|
jenkins_x.a = jenkins_x.b ^ rot(jenkins_x.c, 13);
|
|
jenkins_x.b = jenkins_x.c + rot(jenkins_x.d, 37);
|
|
jenkins_x.c = jenkins_x.d + e;
|
|
jenkins_x.d = e + jenkins_x.a;
|
|
return jenkins_x.d;
|
|
}
|
|
|
|
void s_mp_rand_jenkins_init(uint64_t seed)
|
|
{
|
|
uint64_t i;
|
|
jenkins_x.a = 0xf1ea5eedULL;
|
|
jenkins_x.b = jenkins_x.c = jenkins_x.d = seed;
|
|
for (i = 0uLL; i < 20uLL; ++i) {
|
|
(void)s_rand_jenkins_val();
|
|
}
|
|
}
|
|
|
|
mp_err s_mp_rand_jenkins(void *p, size_t n)
|
|
{
|
|
char *q = (char *)p;
|
|
while (n > 0u) {
|
|
int i;
|
|
uint64_t x = s_rand_jenkins_val();
|
|
for (i = 0; (i < 8) && (n > 0u); ++i, --n) {
|
|
*q++ = (char)(x & 0xFFuLL);
|
|
x >>= 8;
|
|
}
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_s_mp_rand_jenkins.c */
|
|
|
|
/* Start: bn_s_mp_rand_platform.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_RAND_PLATFORM_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* First the OS-specific special cases
|
|
* - *BSD
|
|
* - Windows
|
|
*/
|
|
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
|
|
#define BN_S_READ_ARC4RANDOM_C
|
|
static mp_err s_read_arc4random(void *p, size_t n)
|
|
{
|
|
arc4random_buf(p, n);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
#if defined(_WIN32) || defined(_WIN32_WCE)
|
|
#define BN_S_READ_WINCSP_C
|
|
|
|
#ifndef _WIN32_WINNT
|
|
#define _WIN32_WINNT 0x0400
|
|
#endif
|
|
#ifdef _WIN32_WCE
|
|
#define UNDER_CE
|
|
#define ARM
|
|
#endif
|
|
|
|
#define WIN32_LEAN_AND_MEAN
|
|
#include <windows.h>
|
|
#include <wincrypt.h>
|
|
|
|
static mp_err s_read_wincsp(void *p, size_t n)
|
|
{
|
|
static HCRYPTPROV hProv = 0;
|
|
if (hProv == 0) {
|
|
HCRYPTPROV h = 0;
|
|
if (!CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL,
|
|
(CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET)) &&
|
|
!CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL,
|
|
CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET | CRYPT_NEWKEYSET)) {
|
|
return MP_ERR;
|
|
}
|
|
hProv = h;
|
|
}
|
|
return CryptGenRandom(hProv, (DWORD)n, (BYTE *)p) == TRUE ? MP_OKAY : MP_ERR;
|
|
}
|
|
#endif /* WIN32 */
|
|
|
|
#if !defined(BN_S_READ_WINCSP_C) && defined(__linux__) && defined(__GLIBC_PREREQ)
|
|
#if __GLIBC_PREREQ(2, 25)
|
|
#define BN_S_READ_GETRANDOM_C
|
|
#include <sys/random.h>
|
|
#include <errno.h>
|
|
|
|
static mp_err s_read_getrandom(void *p, size_t n)
|
|
{
|
|
char *q = (char *)p;
|
|
while (n > 0u) {
|
|
ssize_t ret = getrandom(q, n, 0);
|
|
if (ret < 0) {
|
|
if (errno == EINTR) {
|
|
continue;
|
|
}
|
|
return MP_ERR;
|
|
}
|
|
q += ret;
|
|
n -= (size_t)ret;
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
#endif
|
|
|
|
/* We assume all platforms besides windows provide "/dev/urandom".
|
|
* In case yours doesn't, define MP_NO_DEV_URANDOM at compile-time.
|
|
*/
|
|
#if !defined(BN_S_READ_WINCSP_C) && !defined(MP_NO_DEV_URANDOM)
|
|
#define BN_S_READ_URANDOM_C
|
|
#ifndef MP_DEV_URANDOM
|
|
#define MP_DEV_URANDOM "/dev/urandom"
|
|
#endif
|
|
#include <fcntl.h>
|
|
#include <errno.h>
|
|
#include <unistd.h>
|
|
|
|
static mp_err s_read_urandom(void *p, size_t n)
|
|
{
|
|
int fd;
|
|
char *q = (char *)p;
|
|
|
|
do {
|
|
fd = open(MP_DEV_URANDOM, O_RDONLY);
|
|
} while ((fd == -1) && (errno == EINTR));
|
|
if (fd == -1) return MP_ERR;
|
|
|
|
while (n > 0u) {
|
|
ssize_t ret = read(fd, p, n);
|
|
if (ret < 0) {
|
|
if (errno == EINTR) {
|
|
continue;
|
|
}
|
|
close(fd);
|
|
return MP_ERR;
|
|
}
|
|
q += ret;
|
|
n -= (size_t)ret;
|
|
}
|
|
|
|
close(fd);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
#if defined(MP_PRNG_ENABLE_LTM_RNG)
|
|
#define BN_S_READ_LTM_RNG
|
|
unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void));
|
|
void (*ltm_rng_callback)(void);
|
|
|
|
static mp_err s_read_ltm_rng(void *p, size_t n)
|
|
{
|
|
unsigned long res;
|
|
if (ltm_rng == NULL) return MP_ERR;
|
|
res = ltm_rng(p, n, ltm_rng_callback);
|
|
if (res != n) return MP_ERR;
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
mp_err s_read_arc4random(void *p, size_t n);
|
|
mp_err s_read_wincsp(void *p, size_t n);
|
|
mp_err s_read_getrandom(void *p, size_t n);
|
|
mp_err s_read_urandom(void *p, size_t n);
|
|
mp_err s_read_ltm_rng(void *p, size_t n);
|
|
|
|
mp_err s_mp_rand_platform(void *p, size_t n)
|
|
{
|
|
mp_err err = MP_ERR;
|
|
if ((err != MP_OKAY) && MP_HAS(S_READ_ARC4RANDOM)) err = s_read_arc4random(p, n);
|
|
if ((err != MP_OKAY) && MP_HAS(S_READ_WINCSP)) err = s_read_wincsp(p, n);
|
|
if ((err != MP_OKAY) && MP_HAS(S_READ_GETRANDOM)) err = s_read_getrandom(p, n);
|
|
if ((err != MP_OKAY) && MP_HAS(S_READ_URANDOM)) err = s_read_urandom(p, n);
|
|
if ((err != MP_OKAY) && MP_HAS(S_READ_LTM_RNG)) err = s_read_ltm_rng(p, n);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_s_mp_rand_platform.c */
|
|
|
|
/* Start: bn_s_mp_reverse.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_REVERSE_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* reverse an array, used for radix code */
|
|
void s_mp_reverse(unsigned char *s, size_t len)
|
|
{
|
|
size_t ix, iy;
|
|
unsigned char t;
|
|
|
|
ix = 0u;
|
|
iy = len - 1u;
|
|
while (ix < iy) {
|
|
t = s[ix];
|
|
s[ix] = s[iy];
|
|
s[iy] = t;
|
|
++ix;
|
|
--iy;
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_reverse.c */
|
|
|
|
/* Start: bn_s_mp_sqr.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_SQR_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
|
|
mp_err s_mp_sqr(const mp_int *a, mp_int *b)
|
|
{
|
|
mp_int t;
|
|
int ix, iy, pa;
|
|
mp_err err;
|
|
mp_word r;
|
|
mp_digit u, tmpx, *tmpt;
|
|
|
|
pa = a->used;
|
|
if ((err = mp_init_size(&t, (2 * pa) + 1)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* 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)MP_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
|
|
*/
|
|
r = (mp_word)*tmpt + r + r + (mp_word)u;
|
|
|
|
/* store lower part */
|
|
*tmpt++ = (mp_digit)(r & (mp_word)MP_MASK);
|
|
|
|
/* get carry */
|
|
u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
|
|
}
|
|
/* propagate upwards */
|
|
while (u != 0uL) {
|
|
r = (mp_word)*tmpt + (mp_word)u;
|
|
*tmpt++ = (mp_digit)(r & (mp_word)MP_MASK);
|
|
u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
|
|
}
|
|
}
|
|
|
|
mp_clamp(&t);
|
|
mp_exch(&t, b);
|
|
mp_clear(&t);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_sqr.c */
|
|
|
|
/* Start: bn_s_mp_sqr_fast.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_SQR_FAST_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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
|
|
* you add in the inner loop
|
|
|
|
After that loop you do the squares and add them in.
|
|
*/
|
|
|
|
mp_err s_mp_sqr_fast(const mp_int *a, mp_int *b)
|
|
{
|
|
int olduse, pa, ix, iz;
|
|
mp_digit W[MP_WARRAY], *tmpx;
|
|
mp_word W1;
|
|
mp_err err;
|
|
|
|
/* grow the destination as required */
|
|
pa = a->used + a->used;
|
|
if (b->alloc < pa) {
|
|
if ((err = mp_grow(b, pa)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
W1 = 0;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
int tx, ty, iy;
|
|
mp_word _W;
|
|
mp_digit *tmpy;
|
|
|
|
/* clear counter */
|
|
_W = 0;
|
|
|
|
/* get offsets into the two bignums */
|
|
ty = MP_MIN(a->used-1, ix);
|
|
tx = ix - ty;
|
|
|
|
/* setup temp aliases */
|
|
tmpx = a->dp + tx;
|
|
tmpy = a->dp + ty;
|
|
|
|
/* this is the number of times the loop will iterrate, essentially
|
|
while (tx++ < a->used && ty-- >= 0) { ... }
|
|
*/
|
|
iy = MP_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 = MP_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 */
|
|
_W = _W + _W + W1;
|
|
|
|
/* even columns have the square term in them */
|
|
if (((unsigned)ix & 1u) == 0u) {
|
|
_W += (mp_word)a->dp[ix>>1] * (mp_word)a->dp[ix>>1];
|
|
}
|
|
|
|
/* store it */
|
|
W[ix] = (mp_digit)_W & MP_MASK;
|
|
|
|
/* make next carry */
|
|
W1 = _W >> (mp_word)MP_DIGIT_BIT;
|
|
}
|
|
|
|
/* setup dest */
|
|
olduse = b->used;
|
|
b->used = a->used+a->used;
|
|
|
|
{
|
|
mp_digit *tmpb;
|
|
tmpb = b->dp;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
*tmpb++ = W[ix] & MP_MASK;
|
|
}
|
|
|
|
/* clear unused digits [that existed in the old copy of c] */
|
|
MP_ZERO_DIGITS(tmpb, olduse - ix);
|
|
}
|
|
mp_clamp(b);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
/* End: bn_s_mp_sqr_fast.c */
|
|
|
|
/* Start: bn_s_mp_sub.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_SUB_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
|
|
mp_err s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
int olduse, min, max;
|
|
mp_err err;
|
|
|
|
/* find sizes */
|
|
min = b->used;
|
|
max = a->used;
|
|
|
|
/* init result */
|
|
if (c->alloc < max) {
|
|
if ((err = mp_grow(c, max)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
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_SIZEOF_BITS(mp_digit) - 1u);
|
|
|
|
/* 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_SIZEOF_BITS(mp_digit) - 1u);
|
|
|
|
/* Clear carry from T[i] */
|
|
*tmpc++ &= MP_MASK;
|
|
}
|
|
|
|
/* clear digits above used (since we may not have grown result above) */
|
|
MP_ZERO_DIGITS(tmpc, olduse - c->used);
|
|
}
|
|
|
|
mp_clamp(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_s_mp_sub.c */
|
|
|
|
/* Start: bn_s_mp_toom_mul.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_TOOM_MUL_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* 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...).
|
|
*/
|
|
|
|
/*
|
|
This file contains code from J. Arndt's book "Matters Computational"
|
|
and the accompanying FXT-library with permission of the author.
|
|
*/
|
|
|
|
/*
|
|
Setup from
|
|
|
|
Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
|
|
18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.
|
|
|
|
The interpolation from above needed one temporary variable more
|
|
than the interpolation here:
|
|
|
|
Bodrato, Marco, and Alberto Zanoni. "What about Toom-Cook matrices optimality."
|
|
Centro Vito Volterra Universita di Roma Tor Vergata (2006)
|
|
*/
|
|
|
|
mp_err s_mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c)
|
|
{
|
|
mp_int S1, S2, T1, a0, a1, a2, b0, b1, b2;
|
|
int B, count;
|
|
mp_err err;
|
|
|
|
/* init temps */
|
|
if ((err = mp_init_multi(&S1, &S2, &T1, NULL)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* B */
|
|
B = MP_MIN(a->used, b->used) / 3;
|
|
|
|
/** a = a2 * x^2 + a1 * x + a0; */
|
|
if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0;
|
|
|
|
for (count = 0; count < B; count++) {
|
|
a0.dp[count] = a->dp[count];
|
|
a0.used++;
|
|
}
|
|
mp_clamp(&a0);
|
|
if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1;
|
|
for (; count < (2 * B); count++) {
|
|
a1.dp[count - B] = a->dp[count];
|
|
a1.used++;
|
|
}
|
|
mp_clamp(&a1);
|
|
if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2;
|
|
for (; count < a->used; count++) {
|
|
a2.dp[count - (2 * B)] = a->dp[count];
|
|
a2.used++;
|
|
}
|
|
mp_clamp(&a2);
|
|
|
|
/** b = b2 * x^2 + b1 * x + b0; */
|
|
if ((err = mp_init_size(&b0, B)) != MP_OKAY) goto LBL_ERRb0;
|
|
for (count = 0; count < B; count++) {
|
|
b0.dp[count] = b->dp[count];
|
|
b0.used++;
|
|
}
|
|
mp_clamp(&b0);
|
|
if ((err = mp_init_size(&b1, B)) != MP_OKAY) goto LBL_ERRb1;
|
|
for (; count < (2 * B); count++) {
|
|
b1.dp[count - B] = b->dp[count];
|
|
b1.used++;
|
|
}
|
|
mp_clamp(&b1);
|
|
if ((err = mp_init_size(&b2, B + (b->used - (3 * B)))) != MP_OKAY) goto LBL_ERRb2;
|
|
for (; count < b->used; count++) {
|
|
b2.dp[count - (2 * B)] = b->dp[count];
|
|
b2.used++;
|
|
}
|
|
mp_clamp(&b2);
|
|
|
|
/** \\ S1 = (a2+a1+a0) * (b2+b1+b0); */
|
|
/** T1 = a2 + a1; */
|
|
if ((err = mp_add(&a2, &a1, &T1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S2 = T1 + a0; */
|
|
if ((err = mp_add(&T1, &a0, &S2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** c = b2 + b1; */
|
|
if ((err = mp_add(&b2, &b1, c)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S1 = c + b0; */
|
|
if ((err = mp_add(c, &b0, &S1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S1 = S1 * S2; */
|
|
if ((err = mp_mul(&S1, &S2, &S1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** \\S2 = (4*a2+2*a1+a0) * (4*b2+2*b1+b0); */
|
|
/** T1 = T1 + a2; */
|
|
if ((err = mp_add(&T1, &a2, &T1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** T1 = T1 << 1; */
|
|
if ((err = mp_mul_2(&T1, &T1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** T1 = T1 + a0; */
|
|
if ((err = mp_add(&T1, &a0, &T1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** c = c + b2; */
|
|
if ((err = mp_add(c, &b2, c)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** c = c << 1; */
|
|
if ((err = mp_mul_2(c, c)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** c = c + b0; */
|
|
if ((err = mp_add(c, &b0, c)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S2 = T1 * c; */
|
|
if ((err = mp_mul(&T1, c, &S2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** \\S3 = (a2-a1+a0) * (b2-b1+b0); */
|
|
/** a1 = a2 - a1; */
|
|
if ((err = mp_sub(&a2, &a1, &a1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** a1 = a1 + a0; */
|
|
if ((err = mp_add(&a1, &a0, &a1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** b1 = b2 - b1; */
|
|
if ((err = mp_sub(&b2, &b1, &b1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** b1 = b1 + b0; */
|
|
if ((err = mp_add(&b1, &b0, &b1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** a1 = a1 * b1; */
|
|
if ((err = mp_mul(&a1, &b1, &a1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** b1 = a2 * b2; */
|
|
if ((err = mp_mul(&a2, &b2, &b1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** \\S2 = (S2 - S3)/3; */
|
|
/** S2 = S2 - a1; */
|
|
if ((err = mp_sub(&S2, &a1, &S2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S2 = S2 / 3; \\ this is an exact division */
|
|
if ((err = mp_div_3(&S2, &S2, NULL)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** a1 = S1 - a1; */
|
|
if ((err = mp_sub(&S1, &a1, &a1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** a1 = a1 >> 1; */
|
|
if ((err = mp_div_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** a0 = a0 * b0; */
|
|
if ((err = mp_mul(&a0, &b0, &a0)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S1 = S1 - a0; */
|
|
if ((err = mp_sub(&S1, &a0, &S1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S2 = S2 - S1; */
|
|
if ((err = mp_sub(&S2, &S1, &S2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S2 = S2 >> 1; */
|
|
if ((err = mp_div_2(&S2, &S2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S1 = S1 - a1; */
|
|
if ((err = mp_sub(&S1, &a1, &S1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S1 = S1 - b1; */
|
|
if ((err = mp_sub(&S1, &b1, &S1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** T1 = b1 << 1; */
|
|
if ((err = mp_mul_2(&b1, &T1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** S2 = S2 - T1; */
|
|
if ((err = mp_sub(&S2, &T1, &S2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** a1 = a1 - S2; */
|
|
if ((err = mp_sub(&a1, &S2, &a1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
|
|
/** P = b1*x^4+ S2*x^3+ S1*x^2+ a1*x + a0; */
|
|
if ((err = mp_lshd(&b1, 4 * B)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_lshd(&S2, 3 * B)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_add(&b1, &S2, &b1)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_lshd(&S1, 2 * B)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_add(&b1, &S1, &b1)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_lshd(&a1, 1 * B)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_add(&b1, &a1, &b1)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_add(&b1, &a0, c)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** a * b - P */
|
|
|
|
|
|
LBL_ERR:
|
|
mp_clear(&b2);
|
|
LBL_ERRb2:
|
|
mp_clear(&b1);
|
|
LBL_ERRb1:
|
|
mp_clear(&b0);
|
|
LBL_ERRb0:
|
|
mp_clear(&a2);
|
|
LBL_ERRa2:
|
|
mp_clear(&a1);
|
|
LBL_ERRa1:
|
|
mp_clear(&a0);
|
|
LBL_ERRa0:
|
|
mp_clear_multi(&S1, &S2, &T1, NULL);
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_s_mp_toom_mul.c */
|
|
|
|
/* Start: bn_s_mp_toom_sqr.c */
|
|
#include "tommath_private.h"
|
|
#ifdef BN_S_MP_TOOM_SQR_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* squaring using Toom-Cook 3-way algorithm */
|
|
|
|
/*
|
|
This file contains code from J. Arndt's book "Matters Computational"
|
|
and the accompanying FXT-library with permission of the author.
|
|
*/
|
|
|
|
/* squaring using Toom-Cook 3-way algorithm */
|
|
/*
|
|
Setup and interpolation from algorithm SQR_3 in
|
|
|
|
Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
|
|
18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.
|
|
|
|
*/
|
|
mp_err s_mp_toom_sqr(const mp_int *a, mp_int *b)
|
|
{
|
|
mp_int S0, a0, a1, a2;
|
|
mp_digit *tmpa, *tmpc;
|
|
int B, count;
|
|
mp_err err;
|
|
|
|
|
|
/* init temps */
|
|
if ((err = mp_init(&S0)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* B */
|
|
B = a->used / 3;
|
|
|
|
/** a = a2 * x^2 + a1 * x + a0; */
|
|
if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0;
|
|
|
|
a0.used = B;
|
|
if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1;
|
|
a1.used = B;
|
|
if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2;
|
|
|
|
tmpa = a->dp;
|
|
tmpc = a0.dp;
|
|
for (count = 0; count < B; count++) {
|
|
*tmpc++ = *tmpa++;
|
|
}
|
|
tmpc = a1.dp;
|
|
for (; count < (2 * B); count++) {
|
|
*tmpc++ = *tmpa++;
|
|
}
|
|
tmpc = a2.dp;
|
|
for (; count < a->used; count++) {
|
|
*tmpc++ = *tmpa++;
|
|
a2.used++;
|
|
}
|
|
mp_clamp(&a0);
|
|
mp_clamp(&a1);
|
|
mp_clamp(&a2);
|
|
|
|
/** S0 = a0^2; */
|
|
if ((err = mp_sqr(&a0, &S0)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** \\S1 = (a2 + a1 + a0)^2 */
|
|
/** \\S2 = (a2 - a1 + a0)^2 */
|
|
/** \\S1 = a0 + a2; */
|
|
/** a0 = a0 + a2; */
|
|
if ((err = mp_add(&a0, &a2, &a0)) != MP_OKAY) goto LBL_ERR;
|
|
/** \\S2 = S1 - a1; */
|
|
/** b = a0 - a1; */
|
|
if ((err = mp_sub(&a0, &a1, b)) != MP_OKAY) goto LBL_ERR;
|
|
/** \\S1 = S1 + a1; */
|
|
/** a0 = a0 + a1; */
|
|
if ((err = mp_add(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR;
|
|
/** \\S1 = S1^2; */
|
|
/** a0 = a0^2; */
|
|
if ((err = mp_sqr(&a0, &a0)) != MP_OKAY) goto LBL_ERR;
|
|
/** \\S2 = S2^2; */
|
|
/** b = b^2; */
|
|
if ((err = mp_sqr(b, b)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** \\ S3 = 2 * a1 * a2 */
|
|
/** \\S3 = a1 * a2; */
|
|
/** a1 = a1 * a2; */
|
|
if ((err = mp_mul(&a1, &a2, &a1)) != MP_OKAY) goto LBL_ERR;
|
|
/** \\S3 = S3 << 1; */
|
|
/** a1 = a1 << 1; */
|
|
if ((err = mp_mul_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** \\S4 = a2^2; */
|
|
/** a2 = a2^2; */
|
|
if ((err = mp_sqr(&a2, &a2)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** \\ tmp = (S1 + S2)/2 */
|
|
/** \\tmp = S1 + S2; */
|
|
/** b = a0 + b; */
|
|
if ((err = mp_add(&a0, b, b)) != MP_OKAY) goto LBL_ERR;
|
|
/** \\tmp = tmp >> 1; */
|
|
/** b = b >> 1; */
|
|
if ((err = mp_div_2(b, b)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** \\ S1 = S1 - tmp - S3 */
|
|
/** \\S1 = S1 - tmp; */
|
|
/** a0 = a0 - b; */
|
|
if ((err = mp_sub(&a0, b, &a0)) != MP_OKAY) goto LBL_ERR;
|
|
/** \\S1 = S1 - S3; */
|
|
/** a0 = a0 - a1; */
|
|
if ((err = mp_sub(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
/** \\S2 = tmp - S4 -S0 */
|
|
/** \\S2 = tmp - S4; */
|
|
/** b = b - a2; */
|
|
if ((err = mp_sub(b, &a2, b)) != MP_OKAY) goto LBL_ERR;
|
|
/** \\S2 = S2 - S0; */
|
|
/** b = b - S0; */
|
|
if ((err = mp_sub(b, &S0, b)) != MP_OKAY) goto LBL_ERR;
|
|
|
|
|
|
/** \\P = S4*x^4 + S3*x^3 + S2*x^2 + S1*x + S0; */
|
|
/** P = a2*x^4 + a1*x^3 + b*x^2 + a0*x + S0; */
|
|
|
|
if ((err = mp_lshd(&a2, 4 * B)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_lshd(&a1, 3 * B)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_lshd(b, 2 * B)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_lshd(&a0, 1 * B)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_add(&a2, &a1, &a2)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_add(&a2, b, b)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_add(b, &a0, b)) != MP_OKAY) goto LBL_ERR;
|
|
if ((err = mp_add(b, &S0, b)) != MP_OKAY) goto LBL_ERR;
|
|
/** a^2 - P */
|
|
|
|
|
|
LBL_ERR:
|
|
mp_clear(&a2);
|
|
LBL_ERRa2:
|
|
mp_clear(&a1);
|
|
LBL_ERRa1:
|
|
mp_clear(&a0);
|
|
LBL_ERRa0:
|
|
mp_clear(&S0);
|
|
|
|
return err;
|
|
}
|
|
|
|
#endif
|
|
|
|
/* End: bn_s_mp_toom_sqr.c */
|
|
|
|
|
|
/* EOF */
|