Mercurial > dropbear
view libtommath/bn_mp_sqrtmod_prime.c @ 1723:5386011b740d
Disable toom and karatsuba for new libtommath
author | Matt Johnston <matt@ucc.asn.au> |
---|---|
date | Thu, 18 Jun 2020 19:12:07 +0800 |
parents | 1051e4eea25a |
children |
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#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