int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) { BN_CTX *new_ctx = NULL; int ret = 0; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } if (x != NULL) { if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err; if (group->meth->field_encode) { if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err; } } if (y != NULL) { if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err; if (group->meth->field_encode) { if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err; } } if (z != NULL) { int Z_is_one; if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err; Z_is_one = BN_is_one(&point->Z); if (group->meth->field_encode) { if (Z_is_one && (group->meth->field_set_to_one != 0)) { if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err; } else { if (!group-> meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err; } } point->Z_is_one = Z_is_one; } ret = 1; err: if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; }
int ec_GFp_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *tmp_a; /* p must be a prime > 3 */ if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); return 0; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); tmp_a = BN_CTX_get(ctx); if (tmp_a == NULL) goto err; /* group->field */ if (!BN_copy(&group->field, p)) goto err; BN_set_negative(&group->field, 0); /* group->a */ if (!BN_nnmod(tmp_a, a, p, ctx)) goto err; if (group->meth->field_encode) { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; } else if (!BN_copy(&group->a, tmp_a)) goto err; /* group->b */ if (!BN_nnmod(&group->b, b, p, ctx)) goto err; if (group->meth->field_encode) if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err; /* group->a_is_minus3 */ if (!BN_add_word(tmp_a, 3)) goto err; group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); ret = 1; err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; }
/* slow but works */ int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx) { BIGNUM *t; int ret = 0; bn_check_top(a); bn_check_top(b); bn_check_top(m); BN_CTX_start(ctx); if ((t = BN_CTX_get(ctx)) == NULL) goto err; if (a == b) { if (!BN_sqr(t, a, ctx)) goto err; } else { if (!BN_mul(t, a,b, ctx)) goto err; } if (!BN_nnmod(r, t,m, ctx)) goto err; bn_check_top(r); ret = 1; err: BN_CTX_end(ctx); return (ret); }
int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx) { if (!BN_sub(r, a, b)) return 0; return BN_nnmod(r, r, m, ctx); }
int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) { if (!BN_lshift1(r, a)) return 0; bn_check_top(r); return BN_nnmod(r, r, m, ctx); }
/* The secret integers s0 and s1 must be in the range 0 < s < n for some n, and must be relatively prime to that n. We know a priori that n is of the form 2**k * p for some small integer k and prime p. Therefore, it suffices to choose a random integer in the range [0, n/2), multiply by two and add one (enforcing oddness), and then reject values which are divisible by p. */ static BIGNUM * random_s(const BIGNUM *n, const BIGNUM *p, BN_CTX *c) { BIGNUM h, m, *r; BN_init(&h); BN_init(&m); FAILZ(r = BN_new()); FAILZ(BN_copy(&h, n)); FAILZ(BN_rshift1(&h, &h)); do { FAILZ(BN_rand_range(r, &h)); FAILZ(BN_lshift1(r, r)); FAILZ(BN_add(r, r, BN_value_one())); FAILZ(BN_nnmod(&m, r, p, c)); } while (BN_is_zero(&m)); BN_clear(&h); BN_clear(&m); return r; fail: BN_clear(&h); BN_clear(&m); if (r) BN_clear_free(r); return 0; }
bool CECKey::TweakSecret(unsigned char vchSecretOut[32], const unsigned char vchSecretIn[32], const unsigned char vchTweak[32]) { bool ret = true; BN_CTX *ctx = BN_CTX_new(); BN_CTX_start(ctx); BIGNUM *bnSecret = BN_CTX_get(ctx); BIGNUM *bnTweak = BN_CTX_get(ctx); BIGNUM *bnOrder = BN_CTX_get(ctx); EC_GROUP *group = EC_GROUP_new_by_curve_name(NID_secp256k1); EC_GROUP_get_order(group, bnOrder, ctx); // what a grossly inefficient way to get the (constant) group order... BN_bin2bn(vchTweak, 32, bnTweak); if (BN_cmp(bnTweak, bnOrder) >= 0) ret = false; // extremely unlikely BN_bin2bn(vchSecretIn, 32, bnSecret); BN_add(bnSecret, bnSecret, bnTweak); BN_nnmod(bnSecret, bnSecret, bnOrder, ctx); if (BN_is_zero(bnSecret)) ret = false; // ridiculously unlikely int nBits = BN_num_bits(bnSecret); memset(vchSecretOut, 0, 32); BN_bn2bin(bnSecret, &vchSecretOut[32-(nBits+7)/8]); EC_GROUP_free(group); BN_CTX_end(ctx); BN_CTX_free(ctx); return ret; }
CSignerECDSA::CSignerECDSA(const uint8_t PrivData[32], unsigned char Signature[65]) { order.setuint256(g_Order); EC_KEY* pkey = EC_KEY_new_by_curve_name(NID_secp256k1); const EC_GROUP *group = EC_KEY_get0_group(pkey); CBigNum privkey; BN_bin2bn(PrivData, 32, &privkey); EC_KEY_regenerate_key(pkey, &privkey); EC_POINT *tmp_point = EC_POINT_new(group); EC_POINT *test_point = EC_POINT_new(group); CBigNum r, X, Y; bool which = false; do { // get random k do BN_rand_range(&kinv, &order); while (!kinv); /* We do not want timing information to leak the length of k, * so we compute G*k using an equivalent scalar of fixed * bit-length. */ kinv += order; if (BN_num_bits(&kinv) <= 256) kinv += order; // compute r the x-coordinate of generator * k EC_POINT_mul(group, tmp_point, &kinv, NULL, NULL, ctx); EC_POINT_get_affine_coordinates_GFp(group, tmp_point, &X, &Y, ctx); EC_POINT_set_compressed_coordinates_GFp(group, test_point, &X, 0, ctx); which = !!EC_POINT_cmp(group, tmp_point, test_point, ctx); BN_nnmod(&r, &X, &order, ctx); } while (!r); // compute the inverse of k BN_mod_inverse(&kinv, &kinv, &order, ctx); BN_mod_mul(&pmr, &privkey, &r, &order, ctx); BN_mod_mul(&prk, &pmr, &kinv, &order, ctx); memset(Signature, 0, 65); int nBitsR = BN_num_bits(&r); BN_bn2bin(&r, &Signature[33-(nBitsR+7)/8]); Signature[0] = 27 + which; EC_POINT_free(tmp_point); EC_POINT_free(test_point); EC_KEY_free(pkey); }
int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx) { BIGNUM *abs_m = NULL; int ret; if (!BN_nnmod(r, a, m, ctx)) return 0; if (m->neg) { abs_m = BN_dup(m); if (abs_m == NULL) return 0; abs_m->neg = 0; } ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m)); if (abs_m) BN_free(abs_m); return ret; }
int SRP_Verify_B_mod_N(BIGNUM *B, BIGNUM *N) { BIGNUM *r; BN_CTX *bn_ctx; int ret = 0; if (B == NULL || N == NULL || (bn_ctx = BN_CTX_new()) == NULL) return 0; if ((r = BN_new()) == NULL) goto err; /* Checks if B % N == 0 */ if (!BN_nnmod(r, B, N, bn_ctx)) goto err; ret = !BN_is_zero(r); err: BN_CTX_free(bn_ctx); BN_free(r); return ret; }
int test_mont(BIO *bp, BN_CTX *ctx) { BIGNUM a,b,c,d,A,B; BIGNUM n; int i; BN_MONT_CTX *mont; BN_init(&a); BN_init(&b); BN_init(&c); BN_init(&d); BN_init(&A); BN_init(&B); BN_init(&n); mont=BN_MONT_CTX_new(); BN_bntest_rand(&a,100,0,0); /**/ BN_bntest_rand(&b,100,0,0); /**/ for (i=0; i<num2; i++) { int bits = (200*(i+1))/num2; if (bits == 0) continue; BN_bntest_rand(&n,bits,0,1); BN_MONT_CTX_set(mont,&n,ctx); BN_nnmod(&a,&a,&n,ctx); BN_nnmod(&b,&b,&n,ctx); BN_to_montgomery(&A,&a,mont,ctx); BN_to_montgomery(&B,&b,mont,ctx); BN_mod_mul_montgomery(&c,&A,&B,mont,ctx);/**/ BN_from_montgomery(&A,&c,mont,ctx);/**/ if (bp != NULL) { if (!results) { #ifdef undef fprintf(stderr,"%d * %d %% %d\n", BN_num_bits(&a), BN_num_bits(&b), BN_num_bits(mont->N)); #endif BN_print(bp,&a); BIO_puts(bp," * "); BN_print(bp,&b); BIO_puts(bp," % "); BN_print(bp,&(mont->N)); BIO_puts(bp," - "); } BN_print(bp,&A); BIO_puts(bp,"\n"); } BN_mod_mul(&d,&a,&b,&n,ctx); BN_sub(&d,&d,&A); if(!BN_is_zero(&d)) { fprintf(stderr,"Montgomery multiplication test failed!\n"); return 0; } } BN_MONT_CTX_free(mont); BN_free(&a); BN_free(&b); BN_free(&c); BN_free(&d); BN_free(&A); BN_free(&B); BN_free(&n); return(1); }
static int ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, BIGNUM **rp, const unsigned char *dgst, int dlen) { BN_CTX *ctx = NULL; BIGNUM *k = NULL, *r = NULL, *order = NULL, *X = NULL; EC_POINT *tmp_point = NULL; const EC_GROUP *group; int ret = 0; if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_PASSED_NULL_PARAMETER); return 0; } if (ctx_in == NULL) { if ((ctx = BN_CTX_new()) == NULL) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE); return 0; } } else ctx = ctx_in; k = BN_new(); /* this value is later returned in *kinvp */ r = BN_new(); /* this value is later returned in *rp */ order = BN_new(); X = BN_new(); if (k == NULL || r == NULL || order == NULL || X == NULL) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE); goto err; } if ((tmp_point = EC_POINT_new(group)) == NULL) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } if (!EC_GROUP_get_order(group, order, ctx)) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } do { /* get random k */ do if (dgst != NULL) { if (!BN_generate_dsa_nonce (k, order, EC_KEY_get0_private_key(eckey), dgst, dlen, ctx)) { ECerr(EC_F_ECDSA_SIGN_SETUP, EC_R_RANDOM_NUMBER_GENERATION_FAILED); goto err; } } else { if (!BN_rand_range(k, order)) { ECerr(EC_F_ECDSA_SIGN_SETUP, EC_R_RANDOM_NUMBER_GENERATION_FAILED); goto err; } } while (BN_is_zero(k)); /* * We do not want timing information to leak the length of k, so we * compute G*k using an equivalent scalar of fixed bit-length. */ if (!BN_add(k, k, order)) goto err; if (BN_num_bits(k) <= BN_num_bits(order)) if (!BN_add(k, k, order)) goto err; /* compute r the x-coordinate of generator * k */ if (!EC_POINT_mul(group, tmp_point, k, NULL, NULL, ctx)) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == NID_X9_62_prime_field) { if (!EC_POINT_get_affine_coordinates_GFp (group, tmp_point, X, NULL, ctx)) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } } #ifndef OPENSSL_NO_EC2M else { /* NID_X9_62_characteristic_two_field */ if (!EC_POINT_get_affine_coordinates_GF2m(group, tmp_point, X, NULL, ctx)) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } } #endif if (!BN_nnmod(r, X, order, ctx)) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } } while (BN_is_zero(r)); /* compute the inverse of k */ if (EC_GROUP_get_mont_data(group) != NULL) { /* * We want inverse in constant time, therefore we utilize the fact * order must be prime and use Fermats Little Theorem instead. */ if (!BN_set_word(X, 2)) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } if (!BN_mod_sub(X, order, X, order, ctx)) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } BN_set_flags(X, BN_FLG_CONSTTIME); if (!BN_mod_exp_mont_consttime (k, k, X, order, ctx, EC_GROUP_get_mont_data(group))) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } } else { if (!BN_mod_inverse(k, k, order, ctx)) { ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } } /* clear old values if necessary */ BN_clear_free(*rp); BN_clear_free(*kinvp); /* save the pre-computed values */ *rp = r; *kinvp = k; ret = 1; err: if (!ret) { BN_clear_free(k); BN_clear_free(r); } if (ctx != ctx_in) BN_CTX_free(ctx); BN_free(order); EC_POINT_free(tmp_point); BN_clear_free(X); return (ret); }
/* Returns -2 for errors because both -1 and 0 are valid results. */ int BN_kronecker (const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) { int i; int ret = -2; /* avoid 'uninitialized' warning */ int err = 0; BIGNUM *A, *B, *tmp; /* In 'tab', only odd-indexed entries are relevant: * For any odd BIGNUM n, * tab[BN_lsw(n) & 7] * is $(-1)^{(n^2-1)/8}$ (using TeX notation). * Note that the sign of n does not matter. */ static const int tab[8] = { 0, 1, 0, -1, 0, -1, 0, 1 }; bn_check_top (a); bn_check_top (b); BN_CTX_start (ctx); A = BN_CTX_get (ctx); B = BN_CTX_get (ctx); if (B == NULL) goto end; err = !BN_copy (A, a); if (err) goto end; err = !BN_copy (B, b); if (err) goto end; /* * Kronecker symbol, imlemented according to Henri Cohen, * "A Course in Computational Algebraic Number Theory" * (algorithm 1.4.10). */ /* Cohen's step 1: */ if (BN_is_zero (B)) { ret = BN_abs_is_word (A, 1); goto end; } /* Cohen's step 2: */ if (!BN_is_odd (A) && !BN_is_odd (B)) { ret = 0; goto end; } /* now B is non-zero */ i = 0; while (!BN_is_bit_set (B, i)) i++; err = !BN_rshift (B, B, i); if (err) goto end; if (i & 1) { /* i is odd */ /* (thus B was even, thus A must be odd!) */ /* set 'ret' to $(-1)^{(A^2-1)/8}$ */ ret = tab[BN_lsw (A) & 7]; } else { /* i is even */ ret = 1; } if (B->neg) { B->neg = 0; if (A->neg) ret = -ret; } /* now B is positive and odd, so what remains to be done is * to compute the Jacobi symbol (A/B) and multiply it by 'ret' */ while (1) { /* Cohen's step 3: */ /* B is positive and odd */ if (BN_is_zero (A)) { ret = BN_is_one (B) ? ret : 0; goto end; } /* now A is non-zero */ i = 0; while (!BN_is_bit_set (A, i)) i++; err = !BN_rshift (A, A, i); if (err) goto end; if (i & 1) { /* i is odd */ /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */ ret = ret * tab[BN_lsw (B) & 7]; } /* Cohen's step 4: */ /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */ if ((A->neg ? ~BN_lsw (A) : BN_lsw (A)) & BN_lsw (B) & 2) ret = -ret; /* (A, B) := (B mod |A|, |A|) */ err = !BN_nnmod (B, B, A, ctx); if (err) goto end; tmp = A; A = B; B = tmp; tmp->neg = 0; } end: BN_CTX_end (ctx); if (err) return -2; else return ret; }
static int ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, BIGNUM **rp) { BN_CTX *ctx = NULL; BIGNUM *k = NULL, *r = NULL, *order = NULL, *X = NULL; EC_POINT *tmp_point = NULL; const EC_GROUP *group; int ret = 0; int order_bits; if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_PASSED_NULL_PARAMETER); return 0; } if (ctx_in == NULL) { if ((ctx = BN_CTX_new()) == NULL) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE); return 0; } } else ctx = ctx_in; k = BN_new(); /* this value is later returned in *kinvp */ r = BN_new(); /* this value is later returned in *rp */ order = BN_new(); X = BN_new(); if (!k || !r || !order || !X) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE); goto err; } if ((tmp_point = EC_POINT_new(group)) == NULL) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } if (!EC_GROUP_get_order(group, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } /* Preallocate space */ order_bits = BN_num_bits(order); if (!BN_set_bit(k, order_bits) || !BN_set_bit(r, order_bits) || !BN_set_bit(X, order_bits)) goto err; do { /* get random k */ do if (!BN_rand_range(k, order)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ECDSA_R_RANDOM_NUMBER_GENERATION_FAILED); goto err; } while (BN_is_zero(k)) ; /* * We do not want timing information to leak the length of k, so we * compute G*k using an equivalent scalar of fixed bit-length. * * We unconditionally perform both of these additions to prevent a * small timing information leakage. We then choose the sum that is * one bit longer than the order. This guarantees the code * path used in the constant time implementations elsewhere. * * TODO: revisit the BN_copy aiming for a memory access agnostic * conditional copy. */ if (!BN_add(r, k, order) || !BN_add(X, r, order) || !BN_copy(k, BN_num_bits(r) > order_bits ? r : X)) goto err; /* compute r the x-coordinate of generator * k */ if (!EC_POINT_mul(group, tmp_point, k, NULL, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == NID_X9_62_prime_field) { if (!EC_POINT_get_affine_coordinates_GFp (group, tmp_point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } } #ifndef OPENSSL_NO_EC2M else { /* NID_X9_62_characteristic_two_field */ if (!EC_POINT_get_affine_coordinates_GF2m(group, tmp_point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } } #endif if (!BN_nnmod(r, X, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } } while (BN_is_zero(r)); /* compute the inverse of k */ if (EC_GROUP_get_mont_data(group) != NULL) { /* * We want inverse in constant time, therefore we utilize the fact * order must be prime and use Fermats Little Theorem instead. */ if (!BN_set_word(X, 2)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } if (!BN_mod_sub(X, order, X, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } BN_set_flags(X, BN_FLG_CONSTTIME); if (!BN_mod_exp_mont_consttime (k, k, X, order, ctx, EC_GROUP_get_mont_data(group))) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } } else { if (!BN_mod_inverse(k, k, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } } /* clear old values if necessary */ if (*rp != NULL) BN_clear_free(*rp); if (*kinvp != NULL) BN_clear_free(*kinvp); /* save the pre-computed values */ *rp = r; *kinvp = k; ret = 1; err: if (!ret) { if (k != NULL) BN_clear_free(k); if (r != NULL) BN_clear_free(r); } if (ctx_in == NULL) BN_CTX_free(ctx); if (order != NULL) BN_free(order); if (tmp_point != NULL) EC_POINT_free(tmp_point); if (X) BN_clear_free(X); return (ret); }
static int ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, BIGNUM **rp) { BN_CTX *ctx = NULL; BIGNUM *k = NULL, *r = NULL, *order = NULL, *X = NULL; EC_POINT *tmp_point=NULL; const EC_GROUP *group; int ret = 0; if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_PASSED_NULL_PARAMETER); return 0; } if (ctx_in == NULL) { if ((ctx = BN_CTX_new()) == NULL) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP,ERR_R_MALLOC_FAILURE); return 0; } } else ctx = ctx_in; k = BN_new(); /* this value is later returned in *kinvp */ r = BN_new(); /* this value is later returned in *rp */ order = BN_new(); X = BN_new(); if (!k || !r || !order || !X) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE); goto err; } if ((tmp_point = EC_POINT_new(group)) == NULL) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } if (!EC_GROUP_get_order(group, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } #ifdef OPENSSL_FIPS if (!fips_check_ec_prng(eckey)) goto err; #endif do { /* get random k */ do if (!BN_rand_range(k, order)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ECDSA_R_RANDOM_NUMBER_GENERATION_FAILED); goto err; } while (BN_is_zero(k)); #ifdef ECDSA_POINT_MUL_NO_CONSTTIME /* We do not want timing information to leak the length of k, * so we compute G*k using an equivalent scalar of fixed * bit-length. */ if (!BN_add(k, k, order)) goto err; if (BN_num_bits(k) <= BN_num_bits(order)) if (!BN_add(k, k, order)) goto err; #endif /* def(ECDSA_POINT_MUL_NO_CONSTTIME) */ /* compute r the x-coordinate of generator * k */ if (!EC_POINT_mul(group, tmp_point, k, NULL, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == NID_X9_62_prime_field) { if (!EC_POINT_get_affine_coordinates_GFp(group, tmp_point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP,ERR_R_EC_LIB); goto err; } } #ifndef OPENSSL_NO_EC2M else /* NID_X9_62_characteristic_two_field */ { if (!EC_POINT_get_affine_coordinates_GF2m(group, tmp_point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP,ERR_R_EC_LIB); goto err; } } #endif if (!BN_nnmod(r, X, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } } while (BN_is_zero(r)); /* compute the inverse of k */ if (!BN_mod_inverse(k, k, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } /* clear old values if necessary */ if (*rp != NULL) BN_clear_free(*rp); if (*kinvp != NULL) BN_clear_free(*kinvp); /* save the pre-computed values */ *rp = r; *kinvp = k; ret = 1; err: if (!ret) { if (k != NULL) BN_clear_free(k); if (r != NULL) BN_clear_free(r); } if (ctx_in == NULL) BN_CTX_free(ctx); if (order != NULL) BN_free(order); if (tmp_point != NULL) EC_POINT_free(tmp_point); if (X) BN_clear_free(X); return(ret); }
/* BN_mod_inverse_no_branch is a special version of BN_mod_inverse. * It does not contain branches that may leak sensitive information. */ static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx) { BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL; BIGNUM local_A, local_B; BIGNUM *pA, *pB; BIGNUM *ret=NULL; int sign; bn_check_top(a); bn_check_top(n); BN_CTX_start(ctx); A = BN_CTX_get(ctx); B = BN_CTX_get(ctx); X = BN_CTX_get(ctx); D = BN_CTX_get(ctx); M = BN_CTX_get(ctx); Y = BN_CTX_get(ctx); T = BN_CTX_get(ctx); if (T == NULL) goto err; if (in == NULL) R=BN_new(); else R=in; if (R == NULL) goto err; BN_one(X); BN_zero(Y); if (BN_copy(B,a) == NULL) goto err; if (BN_copy(A,n) == NULL) goto err; A->neg = 0; if (B->neg || (BN_ucmp(B, A) >= 0)) { /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked, * BN_div_no_branch will be called eventually. */ pB = &local_B; BN_with_flags(pB, B, BN_FLG_CONSTTIME); if (!BN_nnmod(B, pB, A, ctx)) goto err; } sign = -1; /* From B = a mod |n|, A = |n| it follows that * * 0 <= B < A, * -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|). */ while (!BN_is_zero(B)) { BIGNUM *tmp; /* * 0 < B < A, * (*) -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|) */ /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked, * BN_div_no_branch will be called eventually. */ pA = &local_A; BN_with_flags(pA, A, BN_FLG_CONSTTIME); /* (D, M) := (A/B, A%B) ... */ if (!BN_div(D,M,pA,B,ctx)) goto err; /* Now * A = D*B + M; * thus we have * (**) sign*Y*a == D*B + M (mod |n|). */ tmp=A; /* keep the BIGNUM object, the value does not matter */ /* (A, B) := (B, A mod B) ... */ A=B; B=M; /* ... so we have 0 <= B < A again */ /* Since the former M is now B and the former B is now A, * (**) translates into * sign*Y*a == D*A + B (mod |n|), * i.e. * sign*Y*a - D*A == B (mod |n|). * Similarly, (*) translates into * -sign*X*a == A (mod |n|). * * Thus, * sign*Y*a + D*sign*X*a == B (mod |n|), * i.e. * sign*(Y + D*X)*a == B (mod |n|). * * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at * -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|). * Note that X and Y stay non-negative all the time. */ if (!BN_mul(tmp,D,X,ctx)) goto err; if (!BN_add(tmp,tmp,Y)) goto err; M=Y; /* keep the BIGNUM object, the value does not matter */ Y=X; X=tmp; sign = -sign; } /* * The while loop (Euclid's algorithm) ends when * A == gcd(a,n); * we have * sign*Y*a == A (mod |n|), * where Y is non-negative. */ if (sign < 0) { if (!BN_sub(Y,n,Y)) goto err; } /* Now Y*a == A (mod |n|). */ if (BN_is_one(A)) { /* Y*a == 1 (mod |n|) */ if (!Y->neg && BN_ucmp(Y,n) < 0) { if (!BN_copy(R,Y)) goto err; } else { if (!BN_nnmod(R,Y,n,ctx)) goto err; } } else { BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH,BN_R_NO_INVERSE); goto err; } ret=R; err: if ((ret == NULL) && (in == NULL)) BN_free(R); BN_CTX_end(ctx); bn_check_top(ret); return(ret); }
static int ecdsa_do_verify(const unsigned char *dgst, int dgst_len, const ECDSA_SIG *sig, EC_KEY *eckey) { int ret = -1; BN_CTX *ctx; BIGNUM *order, *u1, *u2, *m, *X; EC_POINT *point = NULL; const EC_GROUP *group; const EC_POINT *pub_key; /* check input values */ if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL || (pub_key = EC_KEY_get0_public_key(eckey)) == NULL || sig == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ECDSA_R_MISSING_PARAMETERS); return -1; } ctx = BN_CTX_new(); if (!ctx) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_MALLOC_FAILURE); return -1; } BN_CTX_start(ctx); order = BN_CTX_get(ctx); u1 = BN_CTX_get(ctx); u2 = BN_CTX_get(ctx); m = BN_CTX_get(ctx); X = BN_CTX_get(ctx); if (!X) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } if (!EC_GROUP_get_order(group, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_EC_LIB); goto err; } if (8 * dgst_len > BN_num_bits(order)) { /* XXX * * Should provide for optional hash truncation: * Keep the BN_num_bits(order) leftmost bits of dgst * (see March 2006 FIPS 186-3 draft, which has a few * confusing errors in this part though) */ ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ECDSA_R_DATA_TOO_LARGE_FOR_KEY_SIZE); ret = 0; goto err; } if (BN_is_zero(sig->r) || BN_is_negative(sig->r) || BN_ucmp(sig->r, order) >= 0 || BN_is_zero(sig->s) || BN_is_negative(sig->s) || BN_ucmp(sig->s, order) >= 0) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ECDSA_R_BAD_SIGNATURE); ret = 0; /* signature is invalid */ goto err; } /* calculate tmp1 = inv(S) mod order */ if (!BN_mod_inverse(u2, sig->s, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } /* digest -> m */ if (!BN_bin2bn(dgst, dgst_len, m)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } /* u1 = m * tmp mod order */ if (!BN_mod_mul(u1, m, u2, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } /* u2 = r * w mod q */ if (!BN_mod_mul(u2, sig->r, u2, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } if ((point = EC_POINT_new(group)) == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_MALLOC_FAILURE); goto err; } if (!EC_POINT_mul(group, point, u1, pub_key, u2, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_EC_LIB); goto err; } if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == NID_X9_62_prime_field) { if (!EC_POINT_get_affine_coordinates_GFp(group, point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_EC_LIB); goto err; } } else /* NID_X9_62_characteristic_two_field */ { if (!EC_POINT_get_affine_coordinates_GF2m(group, point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_EC_LIB); goto err; } } if (!BN_nnmod(u1, X, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } /* if the signature is correct u1 is equal to sig->r */ ret = (BN_ucmp(u1, sig->r) == 0); err: BN_CTX_end(ctx); BN_CTX_free(ctx); if (point) EC_POINT_free(point); return ret; }
/** * Reconstruct secret using the provided shares * * @param shares Shares used to reconstruct secret (should contain t entries) * @param t Threshold used to reconstruct the secret * @param prime Prime for finite field arithmetic * @param s Pointer for storage of calculated secred */ static int reconstructSecret(secret_share_t *shares, unsigned char t, const BIGNUM prime, BIGNUM *s) { unsigned char i; unsigned char j; // Array representing the polynomial a(x) = s + a_1 * x + ... + a_n-1 * x^n-1 mod p BIGNUM **bValue = malloc(t * sizeof(BIGNUM *)); BIGNUM **pbValue; BIGNUM numerator; BIGNUM denominator; BIGNUM temp; secret_share_t *sp_i; secret_share_t *sp_j; BN_CTX *ctx; // Initialize pbValue = bValue; for (i = 0; i < t; i++) { *pbValue = BN_new(); BN_init(*pbValue); pbValue++; } BN_init(&numerator); BN_init(&denominator); BN_init(&temp); // Create context for temporary variables of engine ctx = BN_CTX_new(); BN_CTX_init(ctx); pbValue = bValue; sp_i = shares; for (i = 0; i < t; i++) { BN_one(&numerator); BN_one(&denominator); sp_j = shares; for (j = 0; j < t; j++) { if (i == j) { sp_j++; continue; } BN_mul(&numerator, &numerator, &(sp_j->x), ctx); BN_sub(&temp, &(sp_j->x), &(sp_i->x)); BN_mul(&denominator, &denominator, &temp, ctx); sp_j++; } /* * Use the modular inverse value of the denominator for the * multiplication */ if (BN_mod_inverse(&denominator, &denominator, &prime, ctx) == NULL ) { return -1; } BN_mod_mul(*pbValue, &numerator, &denominator, &prime, ctx); pbValue++; sp_i++; } /* * Calculate the secret by multiplying all y-values with their * corresponding intermediate values */ pbValue = bValue; sp_i = shares; BN_zero(s); for (i = 0; i < t; i++) { BN_mul(&temp, &(sp_i->y), *pbValue, ctx); BN_add(s, s, &temp); pbValue++; sp_i++; } // Perform modulo operation and copy result BN_nnmod(&temp, s, &prime, ctx); BN_copy(s, &temp); BN_clear_free(&numerator); BN_clear_free(&denominator); BN_clear_free(&temp); BN_CTX_free(ctx); // Deallocate the resource of the polynomial pbValue = bValue; for (i = 0; i < t; i++) { BN_clear_free(*pbValue); pbValue++; } free(bValue); return 0; }
int ec_GFp_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *tmp_a; /* p must be a prime > 3 */ if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FIELD); return 0; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) { return 0; } } BN_CTX_start(ctx); tmp_a = BN_CTX_get(ctx); if (tmp_a == NULL) { goto err; } /* group->field */ if (!BN_copy(&group->field, p)) { goto err; } BN_set_negative(&group->field, 0); /* group->a */ if (!BN_nnmod(tmp_a, a, p, ctx)) { goto err; } if (group->meth->field_encode) { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) { goto err; } } else if (!BN_copy(&group->a, tmp_a)) { goto err; } /* group->b */ if (!BN_nnmod(&group->b, b, p, ctx)) { goto err; } if (group->meth->field_encode && !group->meth->field_encode(group, &group->b, &group->b, ctx)) { goto err; } #if !defined(NDEBUG) /* ring: assert a == -3. */ if (!BN_add_word(tmp_a, 3)) { goto err; } assert(0 == BN_cmp(tmp_a, &group->field)); #endif ret = 1; err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; }
int ec_GFp_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { int ret = 0; BN_CTX *new_ctx = NULL; BIGNUM *tmp_a; // p must be a prime > 3 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FIELD); return 0; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) { return 0; } } BN_CTX_start(ctx); tmp_a = BN_CTX_get(ctx); if (tmp_a == NULL) { goto err; } // group->field if (!BN_copy(&group->field, p)) { goto err; } BN_set_negative(&group->field, 0); // Store the field in minimal form, so it can be used with |BN_ULONG| arrays. bn_set_minimal_width(&group->field); // group->a if (!BN_nnmod(tmp_a, a, &group->field, ctx)) { goto err; } if (group->meth->field_encode) { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) { goto err; } } else if (!BN_copy(&group->a, tmp_a)) { goto err; } // group->b if (!BN_nnmod(&group->b, b, &group->field, ctx)) { goto err; } if (group->meth->field_encode && !group->meth->field_encode(group, &group->b, &group->b, ctx)) { goto err; } // group->a_is_minus3 if (!BN_add_word(tmp_a, 3)) { goto err; } group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); if (group->meth->field_encode != NULL) { if (!group->meth->field_encode(group, &group->one, BN_value_one(), ctx)) { goto err; } } else if (!BN_copy(&group->one, BN_value_one())) { goto err; } ret = 1; err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; }
BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) /* Returns 'ret' such that * ret^2 == a (mod p), * using the Tonelli/Shanks algorithm (cf. Henri Cohen, "A Course * in Algebraic Computational Number Theory", algorithm 1.5.1). * 'p' must be prime! */ { BIGNUM *ret = in; int err = 1; int r; BIGNUM *A, *b, *q, *t, *x, *y; int e, i, j; if (!BN_is_odd(p) || BN_abs_is_word(p, 1)) { if (BN_abs_is_word(p, 2)) { if (ret == NULL) ret = BN_new(); if (ret == NULL) goto end; if (!BN_set_word(ret, BN_is_bit_set(a, 0))) { if (ret != in) BN_free(ret); return NULL; } bn_check_top(ret); return ret; } BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME); return(NULL); } if (BN_is_zero(a) || BN_is_one(a)) { if (ret == NULL) ret = BN_new(); if (ret == NULL) goto end; if (!BN_set_word(ret, BN_is_one(a))) { if (ret != in) BN_free(ret); return NULL; } bn_check_top(ret); return ret; } BN_CTX_start(ctx); A = BN_CTX_get(ctx); b = BN_CTX_get(ctx); q = BN_CTX_get(ctx); t = BN_CTX_get(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); if (y == NULL) goto end; if (ret == NULL) ret = BN_new(); if (ret == NULL) goto end; /* A = a mod p */ if (!BN_nnmod(A, a, p, ctx)) goto end; /* now write |p| - 1 as 2^e*q where q is odd */ e = 1; while (!BN_is_bit_set(p, e)) e++; /* we'll set q later (if needed) */ if (e == 1) { /* The easy case: (|p|-1)/2 is odd, so 2 has an inverse * modulo (|p|-1)/2, and square roots can be computed * directly by modular exponentiation. * We have * 2 * (|p|+1)/4 == 1 (mod (|p|-1)/2), * so we can use exponent (|p|+1)/4, i.e. (|p|-3)/4 + 1. */ if (!BN_rshift(q, p, 2)) goto end; q->neg = 0; if (!BN_add_word(q, 1)) goto end; if (!BN_mod_exp(ret, A, q, p, ctx)) goto end; err = 0; goto vrfy; } if (e == 2) { /* |p| == 5 (mod 8) * * In this case 2 is always a non-square since * Legendre(2,p) = (-1)^((p^2-1)/8) for any odd prime. * So if a really is a square, then 2*a is a non-square. * Thus for * b := (2*a)^((|p|-5)/8), * i := (2*a)*b^2 * we have * i^2 = (2*a)^((1 + (|p|-5)/4)*2) * = (2*a)^((p-1)/2) * = -1; * so if we set * x := a*b*(i-1), * then * x^2 = a^2 * b^2 * (i^2 - 2*i + 1) * = a^2 * b^2 * (-2*i) * = a*(-i)*(2*a*b^2) * = a*(-i)*i * = a. * * (This is due to A.O.L. Atkin, * <URL: http://listserv.nodak.edu/scripts/wa.exe?A2=ind9211&L=nmbrthry&O=T&P=562>, * November 1992.) */ /* t := 2*a */ if (!BN_mod_lshift1_quick(t, A, p)) goto end; /* b := (2*a)^((|p|-5)/8) */ if (!BN_rshift(q, p, 3)) goto end; q->neg = 0; if (!BN_mod_exp(b, t, q, p, ctx)) goto end; /* y := b^2 */ if (!BN_mod_sqr(y, b, p, ctx)) goto end; /* t := (2*a)*b^2 - 1*/ if (!BN_mod_mul(t, t, y, p, ctx)) goto end; if (!BN_sub_word(t, 1)) goto end; /* x = a*b*t */ if (!BN_mod_mul(x, A, b, p, ctx)) goto end; if (!BN_mod_mul(x, x, t, p, ctx)) goto end; if (!BN_copy(ret, x)) goto end; err = 0; goto vrfy; } /* e > 2, so we really have to use the Tonelli/Shanks algorithm. * First, find some y that is not a square. */ if (!BN_copy(q, p)) goto end; /* use 'q' as temp */ q->neg = 0; i = 2; do { /* For efficiency, try small numbers first; * if this fails, try random numbers. */ if (i < 22) { if (!BN_set_word(y, i)) goto end; } else { if (!BN_pseudo_rand(y, BN_num_bits(p), 0, 0)) goto end; if (BN_ucmp(y, p) >= 0) { if (!(p->neg ? BN_add : BN_sub)(y, y, p)) goto end; } /* now 0 <= y < |p| */ if (BN_is_zero(y)) if (!BN_set_word(y, i)) goto end; } r = BN_kronecker(y, q, ctx); /* here 'q' is |p| */ if (r < -1) goto end; if (r == 0) { /* m divides p */ BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME); goto end; } } while (r == 1 && ++i < 82); if (r != -1) { /* Many rounds and still no non-square -- this is more likely * a bug than just bad luck. * Even if p is not prime, we should have found some y * such that r == -1. */ BNerr(BN_F_BN_MOD_SQRT, BN_R_TOO_MANY_ITERATIONS); goto end; } /* Here's our actual 'q': */ if (!BN_rshift(q, q, e)) goto end; /* Now that we have some non-square, we can find an element * of order 2^e by computing its q'th power. */ if (!BN_mod_exp(y, y, q, p, ctx)) goto end; if (BN_is_one(y)) { BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME); goto end; } /* Now we know that (if p is indeed prime) there is an integer * k, 0 <= k < 2^e, such that * * a^q * y^k == 1 (mod p). * * As a^q is a square and y is not, k must be even. * q+1 is even, too, so there is an element * * X := a^((q+1)/2) * y^(k/2), * * and it satisfies * * X^2 = a^q * a * y^k * = a, * * so it is the square root that we are looking for. */ /* t := (q-1)/2 (note that q is odd) */ if (!BN_rshift1(t, q)) goto end; /* x := a^((q-1)/2) */ if (BN_is_zero(t)) /* special case: p = 2^e + 1 */ { if (!BN_nnmod(t, A, p, ctx)) goto end; if (BN_is_zero(t)) { /* special case: a == 0 (mod p) */ BN_zero(ret); err = 0; goto end; } else if (!BN_one(x)) goto end; } else { if (!BN_mod_exp(x, A, t, p, ctx)) goto end; if (BN_is_zero(x)) { /* special case: a == 0 (mod p) */ BN_zero(ret); err = 0; goto end; } } /* b := a*x^2 (= a^q) */ if (!BN_mod_sqr(b, x, p, ctx)) goto end; if (!BN_mod_mul(b, b, A, p, ctx)) goto end; /* x := a*x (= a^((q+1)/2)) */ if (!BN_mod_mul(x, x, A, p, ctx)) goto end; while (1) { /* Now b is a^q * y^k for some even k (0 <= k < 2^E * where E refers to the original value of e, which we * don't keep in a variable), and x is a^((q+1)/2) * y^(k/2). * * We have a*b = x^2, * y^2^(e-1) = -1, * b^2^(e-1) = 1. */ if (BN_is_one(b)) { if (!BN_copy(ret, x)) goto end; err = 0; goto vrfy; } /* find smallest i such that b^(2^i) = 1 */ i = 1; if (!BN_mod_sqr(t, b, p, ctx)) goto end; while (!BN_is_one(t)) { i++; if (i == e) { BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE); goto end; } if (!BN_mod_mul(t, t, t, p, ctx)) goto end; } /* t := y^2^(e - i - 1) */ if (!BN_copy(t, y)) goto end; for (j = e - i - 1; j > 0; j--) { if (!BN_mod_sqr(t, t, p, ctx)) goto end; } if (!BN_mod_mul(y, t, t, p, ctx)) goto end; if (!BN_mod_mul(x, x, t, p, ctx)) goto end; if (!BN_mod_mul(b, b, y, p, ctx)) goto end; e = i; } vrfy: if (!err) { /* verify the result -- the input might have been not a square * (test added in 0.9.8) */ if (!BN_mod_sqr(x, ret, p, ctx)) err = 1; if (!err && 0 != BN_cmp(x, A)) { BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE); err = 1; } } end: if (err) { if (ret != NULL && ret != in) { BN_clear_free(ret); } ret = NULL; } BN_CTX_end(ctx); bn_check_top(ret); return ret; }
int test_sqrt(BIO *bp, BN_CTX *ctx) { BIGNUM *a,*p,*r; int i, j; int ret = 0; a = BN_new(); p = BN_new(); r = BN_new(); if (a == NULL || p == NULL || r == NULL) goto err; for (i = 0; i < 16; i++) { if (i < 8) { unsigned primes[8] = { 2, 3, 5, 7, 11, 13, 17, 19 }; if (!BN_set_word(p, primes[i])) goto err; } else { if (!BN_set_word(a, 32)) goto err; if (!BN_set_word(r, 2*i + 1)) goto err; if (!BN_generate_prime(p, 256, 0, a, r, genprime_cb, NULL)) goto err; putc('\n', stderr); } p->neg = rand_neg(); for (j = 0; j < num2; j++) { /* construct 'a' such that it is a square modulo p, * but in general not a proper square and not reduced modulo p */ if (!BN_bntest_rand(r, 256, 0, 3)) goto err; if (!BN_nnmod(r, r, p, ctx)) goto err; if (!BN_mod_sqr(r, r, p, ctx)) goto err; if (!BN_bntest_rand(a, 256, 0, 3)) goto err; if (!BN_nnmod(a, a, p, ctx)) goto err; if (!BN_mod_sqr(a, a, p, ctx)) goto err; if (!BN_mul(a, a, r, ctx)) goto err; if (rand_neg()) if (!BN_sub(a, a, p)) goto err; if (!BN_mod_sqrt(r, a, p, ctx)) goto err; if (!BN_mod_sqr(r, r, p, ctx)) goto err; if (!BN_nnmod(a, a, p, ctx)) goto err; if (BN_cmp(a, r) != 0) { fprintf(stderr, "BN_mod_sqrt failed: a = "); BN_print_fp(stderr, a); fprintf(stderr, ", r = "); BN_print_fp(stderr, r); fprintf(stderr, ", p = "); BN_print_fp(stderr, p); fprintf(stderr, "\n"); goto err; } putc('.', stderr); fflush(stderr); } putc('\n', stderr); fflush(stderr); } ret = 1; err: if (a != NULL) BN_free(a); if (p != NULL) BN_free(p); if (r != NULL) BN_free(r); return ret; }
static int ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, BIGNUM **rp) { BN_CTX *ctx = NULL; BIGNUM *k = NULL, *r = NULL, *order = NULL, *X = NULL; EC_POINT *tmp_point=NULL; const EC_GROUP *group; int ret = 0; if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_PASSED_NULL_PARAMETER); return 0; } if (ctx_in == NULL) { if ((ctx = BN_CTX_new()) == NULL) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP,ERR_R_MALLOC_FAILURE); return 0; } } else ctx = ctx_in; k = BN_new(); /* this value is later returned in *kinvp */ r = BN_new(); /* this value is later returned in *rp */ order = BN_new(); X = BN_new(); if (!k || !r || !order || !X) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE); goto err; } if ((tmp_point = EC_POINT_new(group)) == NULL) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } if (!EC_GROUP_get_order(group, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } do { /* get random k */ do if (!BN_rand_range(k, order)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ECDSA_R_RANDOM_NUMBER_GENERATION_FAILED); goto err; } while (BN_is_zero(k)); /* compute r the x-coordinate of generator * k */ if (!EC_POINT_mul(group, tmp_point, k, NULL, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); goto err; } if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == NID_X9_62_prime_field) { if (!EC_POINT_get_affine_coordinates_GFp(group, tmp_point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP,ERR_R_EC_LIB); goto err; } } else /* NID_X9_62_characteristic_two_field */ { if (!EC_POINT_get_affine_coordinates_GF2m(group, tmp_point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP,ERR_R_EC_LIB); goto err; } } if (!BN_nnmod(r, X, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } } while (BN_is_zero(r)); /* compute the inverse of k */ if (!BN_mod_inverse(k, k, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); goto err; } /* clear old values if necessary */ if (*rp != NULL) BN_clear_free(*rp); if (*kinvp != NULL) BN_clear_free(*kinvp); /* save the pre-computed values */ *rp = r; *kinvp = k; ret = 1; err: if (!ret) { if (k != NULL) BN_clear_free(k); if (r != NULL) BN_clear_free(r); } if (ctx_in == NULL) BN_CTX_free(ctx); if (order != NULL) BN_free(order); if (tmp_point != NULL) EC_POINT_free(tmp_point); if (X) BN_clear_free(X); return(ret); }
/* * Computes gost2001 signature as DSA_SIG structure * * */ DSA_SIG *gost2001_do_sign(const unsigned char *dgst,int dlen, EC_KEY *eckey) { DSA_SIG *newsig = NULL; BIGNUM *md = hashsum2bn(dgst); BIGNUM *order = NULL; const EC_GROUP *group; const BIGNUM *priv_key; BIGNUM *r=NULL,*s=NULL,*X=NULL,*tmp=NULL,*tmp2=NULL, *k=NULL,*e=NULL; EC_POINT *C=NULL; BN_CTX *ctx = BN_CTX_new(); BN_CTX_start(ctx); OPENSSL_assert(dlen==32); newsig=DSA_SIG_new(); if (!newsig) { GOSTerr(GOST_F_GOST2001_DO_SIGN,GOST_R_NO_MEMORY); goto err; } group = EC_KEY_get0_group(eckey); order=BN_CTX_get(ctx); EC_GROUP_get_order(group,order,ctx); priv_key = EC_KEY_get0_private_key(eckey); e = BN_CTX_get(ctx); BN_mod(e,md,order,ctx); #ifdef DEBUG_SIGN fprintf(stderr,"digest as bignum="); BN_print_fp(stderr,md); fprintf(stderr,"\ndigest mod q="); BN_print_fp(stderr,e); fprintf(stderr,"\n"); #endif if (BN_is_zero(e)) { BN_one(e); } k =BN_CTX_get(ctx); C=EC_POINT_new(group); do { do { if (!BN_rand_range(k,order)) { GOSTerr(GOST_F_GOST2001_DO_SIGN,GOST_R_RANDOM_NUMBER_GENERATOR_FAILED); DSA_SIG_free(newsig); goto err; } if (!EC_POINT_mul(group,C,k,NULL,NULL,ctx)) { GOSTerr(GOST_F_GOST2001_DO_SIGN,ERR_R_EC_LIB); DSA_SIG_free(newsig); goto err; } if (!X) X=BN_CTX_get(ctx); if (!EC_POINT_get_affine_coordinates_GFp(group,C,X,NULL,ctx)) { GOSTerr(GOST_F_GOST2001_DO_SIGN,ERR_R_EC_LIB); DSA_SIG_free(newsig); goto err; } if (!r) r=BN_CTX_get(ctx); BN_nnmod(r,X,order,ctx); } while (BN_is_zero(r)); /* s = (r*priv_key+k*e) mod order */ if (!tmp) tmp = BN_CTX_get(ctx); BN_mod_mul(tmp,priv_key,r,order,ctx); if (!tmp2) tmp2 = BN_CTX_get(ctx); BN_mod_mul(tmp2,k,e,order,ctx); if (!s) s=BN_CTX_get(ctx); BN_mod_add(s,tmp,tmp2,order,ctx); } while (BN_is_zero(s)); newsig->s=BN_dup(s); newsig->r=BN_dup(r); err: BN_CTX_end(ctx); BN_CTX_free(ctx); EC_POINT_free(C); BN_free(md); return newsig; }
BIGNUM *BN_mod_inverse(BIGNUM *in, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx) { BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL; BIGNUM *ret=NULL; int sign; if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0)) { return BN_mod_inverse_no_branch(in, a, n, ctx); } bn_check_top(a); bn_check_top(n); BN_CTX_start(ctx); A = BN_CTX_get(ctx); B = BN_CTX_get(ctx); X = BN_CTX_get(ctx); D = BN_CTX_get(ctx); M = BN_CTX_get(ctx); Y = BN_CTX_get(ctx); T = BN_CTX_get(ctx); if (T == NULL) goto err; if (in == NULL) R=BN_new(); else R=in; if (R == NULL) goto err; BN_one(X); BN_zero(Y); if (BN_copy(B,a) == NULL) goto err; if (BN_copy(A,n) == NULL) goto err; A->neg = 0; if (B->neg || (BN_ucmp(B, A) >= 0)) { if (!BN_nnmod(B, B, A, ctx)) goto err; } sign = -1; /* From B = a mod |n|, A = |n| it follows that * * 0 <= B < A, * -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|). */ if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048))) { /* Binary inversion algorithm; requires odd modulus. * This is faster than the general algorithm if the modulus * is sufficiently small (about 400 .. 500 bits on 32-bit * sytems, but much more on 64-bit systems) */ int shift; while (!BN_is_zero(B)) { /* * 0 < B < |n|, * 0 < A <= |n|, * (1) -sign*X*a == B (mod |n|), * (2) sign*Y*a == A (mod |n|) */ /* Now divide B by the maximum possible power of two in the integers, * and divide X by the same value mod |n|. * When we're done, (1) still holds. */ shift = 0; while (!BN_is_bit_set(B, shift)) /* note that 0 < B */ { shift++; if (BN_is_odd(X)) { if (!BN_uadd(X, X, n)) goto err; } /* now X is even, so we can easily divide it by two */ if (!BN_rshift1(X, X)) goto err; } if (shift > 0) { if (!BN_rshift(B, B, shift)) goto err; } /* Same for A and Y. Afterwards, (2) still holds. */ shift = 0; while (!BN_is_bit_set(A, shift)) /* note that 0 < A */ { shift++; if (BN_is_odd(Y)) { if (!BN_uadd(Y, Y, n)) goto err; } /* now Y is even */ if (!BN_rshift1(Y, Y)) goto err; } if (shift > 0) { if (!BN_rshift(A, A, shift)) goto err; } /* We still have (1) and (2). * Both A and B are odd. * The following computations ensure that * * 0 <= B < |n|, * 0 < A < |n|, * (1) -sign*X*a == B (mod |n|), * (2) sign*Y*a == A (mod |n|), * * and that either A or B is even in the next iteration. */ if (BN_ucmp(B, A) >= 0) { /* -sign*(X + Y)*a == B - A (mod |n|) */ if (!BN_uadd(X, X, Y)) goto err; /* NB: we could use BN_mod_add_quick(X, X, Y, n), but that * actually makes the algorithm slower */ if (!BN_usub(B, B, A)) goto err; } else { /* sign*(X + Y)*a == A - B (mod |n|) */ if (!BN_uadd(Y, Y, X)) goto err; /* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */ if (!BN_usub(A, A, B)) goto err; } } } else { /* general inversion algorithm */ while (!BN_is_zero(B)) { BIGNUM *tmp; /* * 0 < B < A, * (*) -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|) */ /* (D, M) := (A/B, A%B) ... */ if (BN_num_bits(A) == BN_num_bits(B)) { if (!BN_one(D)) goto err; if (!BN_sub(M,A,B)) goto err; } else if (BN_num_bits(A) == BN_num_bits(B) + 1) { /* A/B is 1, 2, or 3 */ if (!BN_lshift1(T,B)) goto err; if (BN_ucmp(A,T) < 0) { /* A < 2*B, so D=1 */ if (!BN_one(D)) goto err; if (!BN_sub(M,A,B)) goto err; } else { /* A >= 2*B, so D=2 or D=3 */ if (!BN_sub(M,A,T)) goto err; if (!BN_add(D,T,B)) goto err; /* use D (:= 3*B) as temp */ if (BN_ucmp(A,D) < 0) { /* A < 3*B, so D=2 */ if (!BN_set_word(D,2)) goto err; /* M (= A - 2*B) already has the correct value */ } else { /* only D=3 remains */ if (!BN_set_word(D,3)) goto err; /* currently M = A - 2*B, but we need M = A - 3*B */ if (!BN_sub(M,M,B)) goto err; } } } else { if (!BN_div(D,M,A,B,ctx)) goto err; } /* Now * A = D*B + M; * thus we have * (**) sign*Y*a == D*B + M (mod |n|). */ tmp=A; /* keep the BIGNUM object, the value does not matter */ /* (A, B) := (B, A mod B) ... */ A=B; B=M; /* ... so we have 0 <= B < A again */ /* Since the former M is now B and the former B is now A, * (**) translates into * sign*Y*a == D*A + B (mod |n|), * i.e. * sign*Y*a - D*A == B (mod |n|). * Similarly, (*) translates into * -sign*X*a == A (mod |n|). * * Thus, * sign*Y*a + D*sign*X*a == B (mod |n|), * i.e. * sign*(Y + D*X)*a == B (mod |n|). * * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at * -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|). * Note that X and Y stay non-negative all the time. */ /* most of the time D is very small, so we can optimize tmp := D*X+Y */ if (BN_is_one(D)) { if (!BN_add(tmp,X,Y)) goto err; } else { if (BN_is_word(D,2)) { if (!BN_lshift1(tmp,X)) goto err; } else if (BN_is_word(D,4)) { if (!BN_lshift(tmp,X,2)) goto err; } else if (D->top == 1) { if (!BN_copy(tmp,X)) goto err; if (!BN_mul_word(tmp,D->d[0])) goto err; } else { if (!BN_mul(tmp,D,X,ctx)) goto err; } if (!BN_add(tmp,tmp,Y)) goto err; } M=Y; /* keep the BIGNUM object, the value does not matter */ Y=X; X=tmp; sign = -sign; } } /* * The while loop (Euclid's algorithm) ends when * A == gcd(a,n); * we have * sign*Y*a == A (mod |n|), * where Y is non-negative. */ if (sign < 0) { if (!BN_sub(Y,n,Y)) goto err; } /* Now Y*a == A (mod |n|). */ if (BN_is_one(A)) { /* Y*a == 1 (mod |n|) */ if (!Y->neg && BN_ucmp(Y,n) < 0) { if (!BN_copy(R,Y)) goto err; } else { if (!BN_nnmod(R,Y,n,ctx)) goto err; } } else { BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE); goto err; } ret=R; err: if ((ret == NULL) && (in == NULL)) BN_free(R); BN_CTX_end(ctx); bn_check_top(ret); return(ret); }
/* * Computes gost_ec signature as DSA_SIG structure * */ DSA_SIG *gost_ec_sign(const unsigned char *dgst, int dlen, EC_KEY *eckey) { DSA_SIG *newsig = NULL, *ret = NULL; BIGNUM *md = NULL; BIGNUM *order = NULL; const EC_GROUP *group; const BIGNUM *priv_key; BIGNUM *r = NULL, *s = NULL, *X = NULL, *tmp = NULL, *tmp2 = NULL, *k = NULL, *e = NULL; EC_POINT *C = NULL; BN_CTX *ctx; OPENSSL_assert(dgst != NULL && eckey != NULL); if (!(ctx = BN_CTX_new())) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_MALLOC_FAILURE); return NULL; } BN_CTX_start(ctx); OPENSSL_assert(dlen == 32 || dlen == 64); md = hashsum2bn(dgst, dlen); newsig = DSA_SIG_new(); if (!newsig || !md) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_MALLOC_FAILURE); goto err; } group = EC_KEY_get0_group(eckey); if (!group) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_INTERNAL_ERROR); goto err; } order = BN_CTX_get(ctx); if (!order || !EC_GROUP_get_order(group, order, ctx)) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_INTERNAL_ERROR); goto err; } priv_key = EC_KEY_get0_private_key(eckey); if (!priv_key) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_INTERNAL_ERROR); goto err; } e = BN_CTX_get(ctx); if (!e || !BN_mod(e, md, order, ctx)) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_INTERNAL_ERROR); goto err; } #ifdef DEBUG_SIGN fprintf(stderr, "digest as bignum="); BN_print_fp(stderr, md); fprintf(stderr, "\ndigest mod q="); BN_print_fp(stderr, e); fprintf(stderr, "\n"); #endif if (BN_is_zero(e)) { BN_one(e); } k = BN_CTX_get(ctx); C = EC_POINT_new(group); if (!k || !C) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_MALLOC_FAILURE); goto err; } do { do { if (!BN_rand_range(k, order)) { GOSTerr(GOST_F_GOST_EC_SIGN, GOST_R_RNG_ERROR); goto err; } /* * To avoid timing information leaking the length of k, * compute C*k using an equivalent scalar of fixed bit-length */ if (!BN_add(k, k, order) || (BN_num_bits(k) <= BN_num_bits(order) && !BN_add(k, k, order))) { goto err; } if (!EC_POINT_mul(group, C, k, NULL, NULL, ctx)) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_EC_LIB); goto err; } if (!X) X = BN_CTX_get(ctx); if (!r) r = BN_CTX_get(ctx); if (!X || !r) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_MALLOC_FAILURE); goto err; } if (!EC_POINT_get_affine_coordinates_GFp(group, C, X, NULL, ctx)) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_EC_LIB); goto err; } if (!BN_nnmod(r, X, order, ctx)) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_INTERNAL_ERROR); goto err; } } while (BN_is_zero(r)); /* s = (r*priv_key+k*e) mod order */ if (!tmp) tmp = BN_CTX_get(ctx); if (!tmp2) tmp2 = BN_CTX_get(ctx); if (!s) s = BN_CTX_get(ctx); if (!tmp || !tmp2 || !s) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_MALLOC_FAILURE); goto err; } if (!BN_mod_mul(tmp, priv_key, r, order, ctx) || !BN_mod_mul(tmp2, k, e, order, ctx) || !BN_mod_add(s, tmp, tmp2, order, ctx)) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_INTERNAL_ERROR); goto err; } } while (BN_is_zero(s)); newsig->s = BN_dup(s); newsig->r = BN_dup(r); if (!newsig->s || !newsig->r) { GOSTerr(GOST_F_GOST_EC_SIGN, ERR_R_MALLOC_FAILURE); goto err; } ret = newsig; err: BN_CTX_end(ctx); BN_CTX_free(ctx); if (C) EC_POINT_free(C); if (md) BN_free(md); if (!ret && newsig) { DSA_SIG_free(newsig); } return ret; }
static int ecdsa_do_verify(const unsigned char *dgst, int dgst_len, const ECDSA_SIG *sig, EC_KEY *eckey) { int ret = -1, i; BN_CTX *ctx; BIGNUM *order, *u1, *u2, *m, *X; EC_POINT *point = NULL; const EC_GROUP *group; const EC_POINT *pub_key; /* check input values */ if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL || (pub_key = EC_KEY_get0_public_key(eckey)) == NULL || sig == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ECDSA_R_MISSING_PARAMETERS); return -1; } ctx = BN_CTX_new(); if (!ctx) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_MALLOC_FAILURE); return -1; } BN_CTX_start(ctx); order = BN_CTX_get(ctx); u1 = BN_CTX_get(ctx); u2 = BN_CTX_get(ctx); m = BN_CTX_get(ctx); X = BN_CTX_get(ctx); if (!X) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } if (!EC_GROUP_get_order(group, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_EC_LIB); goto err; } if (BN_is_zero(sig->r) || BN_is_negative(sig->r) || BN_ucmp(sig->r, order) >= 0 || BN_is_zero(sig->s) || BN_is_negative(sig->s) || BN_ucmp(sig->s, order) >= 0) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ECDSA_R_BAD_SIGNATURE); ret = 0; /* signature is invalid */ goto err; } /* calculate tmp1 = inv(S) mod order */ if (!BN_mod_inverse(u2, sig->s, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } /* digest -> m */ i = BN_num_bits(order); /* Need to truncate digest if it is too long: first truncate whole * bytes. */ if (8 * dgst_len > i) dgst_len = (i + 7)/8; if (!BN_bin2bn(dgst, dgst_len, m)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } /* If still too long truncate remaining bits with a shift */ if ((8 * dgst_len > i) && !BN_rshift(m, m, 8 - (i & 0x7))) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } /* u1 = m * tmp mod order */ if (!BN_mod_mul(u1, m, u2, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } /* u2 = r * w mod q */ if (!BN_mod_mul(u2, sig->r, u2, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } if ((point = EC_POINT_new(group)) == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_MALLOC_FAILURE); goto err; } if (!EC_POINT_mul(group, point, u1, pub_key, u2, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_EC_LIB); goto err; } if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == NID_X9_62_prime_field) { if (!EC_POINT_get_affine_coordinates_GFp(group, point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_EC_LIB); goto err; } } #ifndef OPENSSL_NO_EC2M else /* NID_X9_62_characteristic_two_field */ { if (!EC_POINT_get_affine_coordinates_GF2m(group, point, X, NULL, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_EC_LIB); goto err; } } #endif if (!BN_nnmod(u1, X, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_VERIFY, ERR_R_BN_LIB); goto err; } /* if the signature is correct u1 is equal to sig->r */ ret = (BN_ucmp(u1, sig->r) == 0); err: BN_CTX_end(ctx); BN_CTX_free(ctx); if (point) EC_POINT_free(point); return ret; }
int ECDSA_do_verify(const uint8_t *digest, size_t digest_len, const ECDSA_SIG *sig, const EC_KEY *eckey) { int ret = 0; BN_CTX *ctx; BIGNUM *u1, *u2, *m, *X; EC_POINT *point = NULL; const EC_GROUP *group; const EC_POINT *pub_key; // check input values if ((group = EC_KEY_get0_group(eckey)) == NULL || (pub_key = EC_KEY_get0_public_key(eckey)) == NULL || sig == NULL) { OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_MISSING_PARAMETERS); return 0; } ctx = BN_CTX_new(); if (!ctx) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); return 0; } BN_CTX_start(ctx); u1 = BN_CTX_get(ctx); u2 = BN_CTX_get(ctx); m = BN_CTX_get(ctx); X = BN_CTX_get(ctx); if (u1 == NULL || u2 == NULL || m == NULL || X == NULL) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } const BIGNUM *order = EC_GROUP_get0_order(group); if (BN_is_zero(sig->r) || BN_is_negative(sig->r) || BN_ucmp(sig->r, order) >= 0 || BN_is_zero(sig->s) || BN_is_negative(sig->s) || BN_ucmp(sig->s, order) >= 0) { OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_BAD_SIGNATURE); goto err; } // calculate tmp1 = inv(S) mod order int no_inverse; if (!BN_mod_inverse_odd(u2, &no_inverse, sig->s, order, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } if (!digest_to_bn(m, digest, digest_len, order)) { goto err; } // u1 = m * tmp mod order if (!BN_mod_mul(u1, m, u2, order, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } // u2 = r * w mod q if (!BN_mod_mul(u2, sig->r, u2, order, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } point = EC_POINT_new(group); if (point == NULL) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); goto err; } if (!EC_POINT_mul(group, point, u1, pub_key, u2, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB); goto err; } if (!EC_POINT_get_affine_coordinates_GFp(group, point, X, NULL, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB); goto err; } if (!BN_nnmod(u1, X, order, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } // if the signature is correct u1 is equal to sig->r if (BN_ucmp(u1, sig->r) != 0) { OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_BAD_SIGNATURE); goto err; } ret = 1; err: BN_CTX_end(ctx); BN_CTX_free(ctx); EC_POINT_free(point); return ret; }
int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x_, int y_bit, BN_CTX *ctx) { BN_CTX *new_ctx = NULL; BIGNUM *tmp1, *tmp2, *x, *y; int ret = 0; ERR_clear_error(); if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) { return 0; } } y_bit = (y_bit != 0); BN_CTX_start(ctx); tmp1 = BN_CTX_get(ctx); tmp2 = BN_CTX_get(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); if (y == NULL) { goto err; } /* Recover y. We have a Weierstrass equation * y^2 = x^3 + a*x + b, * so y is one of the square roots of x^3 + a*x + b. */ /* tmp1 := x^3 */ if (!BN_nnmod(x, x_, &group->field, ctx)) { goto err; } if (group->meth->field_decode == 0) { /* field_{sqr,mul} work on standard representation */ if (!group->meth->field_sqr(group, tmp2, x_, ctx) || !group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) { goto err; } } else { if (!BN_mod_sqr(tmp2, x_, &group->field, ctx) || !BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) { goto err; } } /* tmp1 := tmp1 + a*x */ if (group->a_is_minus3) { if (!BN_mod_lshift1_quick(tmp2, x, &group->field) || !BN_mod_add_quick(tmp2, tmp2, x, &group->field) || !BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) { goto err; } } else { if (group->meth->field_decode) { if (!group->meth->field_decode(group, tmp2, &group->a, ctx) || !BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) { goto err; } } else { /* field_mul works on standard representation */ if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) { goto err; } } if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) { goto err; } } /* tmp1 := tmp1 + b */ if (group->meth->field_decode) { if (!group->meth->field_decode(group, tmp2, &group->b, ctx) || !BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) { goto err; } } else { if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) { goto err; } } if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) { unsigned long err = ERR_peek_last_error(); if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) { ERR_clear_error(); OPENSSL_PUT_ERROR(EC, ec_GFp_simple_set_compressed_coordinates, EC_R_INVALID_COMPRESSED_POINT); } else { OPENSSL_PUT_ERROR(EC, ec_GFp_simple_set_compressed_coordinates, ERR_R_BN_LIB); } goto err; } if (y_bit != BN_is_odd(y)) { if (BN_is_zero(y)) { int kron; kron = BN_kronecker(x, &group->field, ctx); if (kron == -2) { goto err; } if (kron == 1) { OPENSSL_PUT_ERROR(EC, ec_GFp_simple_set_compressed_coordinates, EC_R_INVALID_COMPRESSION_BIT); } else { /* BN_mod_sqrt() should have cought this error (not a square) */ OPENSSL_PUT_ERROR(EC, ec_GFp_simple_set_compressed_coordinates, EC_R_INVALID_COMPRESSED_POINT); } goto err; } if (!BN_usub(y, &group->field, y)) { goto err; } } if (y_bit != BN_is_odd(y)) { OPENSSL_PUT_ERROR(EC, ec_GFp_simple_set_compressed_coordinates, ERR_R_INTERNAL_ERROR); goto err; } if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; ret = 1; err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; }
static int ecdsa_sign_setup(const EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, BIGNUM **rp, const uint8_t *digest, size_t digest_len) { BN_CTX *ctx = NULL; BIGNUM *k = NULL, *kinv = NULL, *r = NULL, *tmp = NULL; EC_POINT *tmp_point = NULL; const EC_GROUP *group; int ret = 0; if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_PASSED_NULL_PARAMETER); return 0; } if (ctx_in == NULL) { if ((ctx = BN_CTX_new()) == NULL) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); return 0; } } else { ctx = ctx_in; } k = BN_new(); kinv = BN_new(); // this value is later returned in *kinvp r = BN_new(); // this value is later returned in *rp tmp = BN_new(); if (k == NULL || kinv == NULL || r == NULL || tmp == NULL) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); goto err; } tmp_point = EC_POINT_new(group); if (tmp_point == NULL) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB); goto err; } const BIGNUM *order = EC_GROUP_get0_order(group); // Check that the size of the group order is FIPS compliant (FIPS 186-4 // B.5.2). if (BN_num_bits(order) < 160) { OPENSSL_PUT_ERROR(ECDSA, EC_R_INVALID_GROUP_ORDER); goto err; } do { // If possible, we'll include the private key and message digest in the k // generation. The |digest| argument is only empty if |ECDSA_sign_setup| is // being used. if (eckey->fixed_k != NULL) { if (!BN_copy(k, eckey->fixed_k)) { goto err; } } else if (digest_len > 0) { do { if (!BN_generate_dsa_nonce(k, order, EC_KEY_get0_private_key(eckey), digest, digest_len, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_RANDOM_NUMBER_GENERATION_FAILED); goto err; } } while (BN_is_zero(k)); } else if (!BN_rand_range_ex(k, 1, order)) { OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_RANDOM_NUMBER_GENERATION_FAILED); goto err; } // Compute the inverse of k. The order is a prime, so use Fermat's Little // Theorem. Note |ec_group_get_order_mont| may return NULL but // |bn_mod_inverse_prime| allows this. if (!bn_mod_inverse_prime(kinv, k, order, ctx, ec_group_get_order_mont(group))) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } // We do not want timing information to leak the length of k, // so we compute G*k using an equivalent scalar of fixed // bit-length. if (!BN_add(k, k, order)) { goto err; } if (BN_num_bits(k) <= BN_num_bits(order)) { if (!BN_add(k, k, order)) { goto err; } } // compute r the x-coordinate of generator * k if (!EC_POINT_mul(group, tmp_point, k, NULL, NULL, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB); goto err; } if (!EC_POINT_get_affine_coordinates_GFp(group, tmp_point, tmp, NULL, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB); goto err; } if (!BN_nnmod(r, tmp, order, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } } while (BN_is_zero(r)); // clear old values if necessary BN_clear_free(*rp); BN_clear_free(*kinvp); // save the pre-computed values *rp = r; *kinvp = kinv; ret = 1; err: BN_clear_free(k); if (!ret) { BN_clear_free(kinv); BN_clear_free(r); } if (ctx_in == NULL) { BN_CTX_free(ctx); } EC_POINT_free(tmp_point); BN_clear_free(tmp); return ret; }