/*- * Set s := p, r := 2p. * * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve * multiplication resistant against side channel attacks" appendix, as described * at * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2 * * The input point p will be in randomized Jacobian projective coords: * x = X/Z**2, y=Y/Z**3 * * The output points p, s, and r are converted to standard (homogeneous) * projective coords: * x = X/Z, y=Y/Z */ int ec_GFp_simple_ladder_pre(const EC_GROUP *group, EC_POINT *r, EC_POINT *s, EC_POINT *p, BN_CTX *ctx) { BIGNUM *t1, *t2, *t3, *t4, *t5, *t6 = NULL; t1 = r->Z; t2 = r->Y; t3 = s->X; t4 = r->X; t5 = s->Y; t6 = s->Z; /* convert p: (X,Y,Z) -> (XZ,Y,Z**3) */ if (!group->meth->field_mul(group, p->X, p->X, p->Z, ctx) || !group->meth->field_sqr(group, t1, p->Z, ctx) || !group->meth->field_mul(group, p->Z, p->Z, t1, ctx) /* r := 2p */ || !group->meth->field_sqr(group, t2, p->X, ctx) || !group->meth->field_sqr(group, t3, p->Z, ctx) || !group->meth->field_mul(group, t4, t3, group->a, ctx) || !BN_mod_sub_quick(t5, t2, t4, group->field) || !BN_mod_add_quick(t2, t2, t4, group->field) || !group->meth->field_sqr(group, t5, t5, ctx) || !group->meth->field_mul(group, t6, t3, group->b, ctx) || !group->meth->field_mul(group, t1, p->X, p->Z, ctx) || !group->meth->field_mul(group, t4, t1, t6, ctx) || !BN_mod_lshift_quick(t4, t4, 3, group->field) /* r->X coord output */ || !BN_mod_sub_quick(r->X, t5, t4, group->field) || !group->meth->field_mul(group, t1, t1, t2, ctx) || !group->meth->field_mul(group, t2, t3, t6, ctx) || !BN_mod_add_quick(t1, t1, t2, group->field) /* r->Z coord output */ || !BN_mod_lshift_quick(r->Z, t1, 2, group->field) || !EC_POINT_copy(s, p)) return 0; r->Z_is_one = 0; s->Z_is_one = 0; p->Z_is_one = 0; return 1; }
void CSignerECDSA::SignFast(const uint256 &hash, unsigned char Signature[65]) { CBigNum m; BN_bin2bn((uint8_t*)&hash, 256/8, &m); // Spread-FIXME: replace with fixed-size arithmetic. CBigNum s; BN_mod_add_quick(&s, &pmr, &m, &order); BN_mod_mul(&s, &s, &kinv, &order, ctx); int nBitsS = BN_num_bits(&s); memset(Signature + 33, 0, 32); BN_bn2bin(&s, &Signature[65-(nBitsS+7)/8]); }
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 ECDSA_SIG *ecdsa_do_sign(const unsigned char *dgst, int dgst_len, const BIGNUM *in_kinv, const BIGNUM *in_r, EC_KEY *eckey) { int ok = 0, i; BIGNUM *kinv=NULL, *s, *m=NULL,*tmp=NULL,*order=NULL; const BIGNUM *ckinv; BN_CTX *ctx = NULL; const EC_GROUP *group; ECDSA_SIG *ret; ECDSA_DATA *ecdsa; const BIGNUM *priv_key; ecdsa = ecdsa_check(eckey); group = EC_KEY_get0_group(eckey); priv_key = EC_KEY_get0_private_key(eckey); if (group == NULL || priv_key == NULL || ecdsa == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_PASSED_NULL_PARAMETER); return NULL; } #ifdef OPENSSL_FIPS if (!fips_check_ec_prng(eckey)) return NULL; #endif ret = ECDSA_SIG_new(); if (!ret) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE); return NULL; } s = ret->s; if ((ctx = BN_CTX_new()) == NULL || (order = BN_new()) == NULL || (tmp = BN_new()) == NULL || (m = BN_new()) == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE); goto err; } if (!EC_GROUP_get_order(group, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_EC_LIB); goto err; } 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_SIGN, 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_SIGN, ERR_R_BN_LIB); goto err; } do { if (in_kinv == NULL || in_r == NULL) { if (!ecdsa->meth->ecdsa_sign_setup(eckey, ctx, &kinv, &ret->r)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN,ERR_R_ECDSA_LIB); goto err; } ckinv = kinv; } else { ckinv = in_kinv; if (BN_copy(ret->r, in_r) == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE); goto err; } } if (!BN_mod_mul(tmp, priv_key, ret->r, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } if (!BN_mod_add_quick(s, tmp, m, order)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } if (!BN_mod_mul(s, s, ckinv, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } if (BN_is_zero(s)) { /* if kinv and r have been supplied by the caller * don't to generate new kinv and r values */ if (in_kinv != NULL && in_r != NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ECDSA_R_NEED_NEW_SETUP_VALUES); goto err; } } else /* s != 0 => we have a valid signature */ break; } while (1); ok = 1; err: if (!ok) { ECDSA_SIG_free(ret); ret = NULL; } if (ctx) BN_CTX_free(ctx); if (m) BN_clear_free(m); if (tmp) BN_clear_free(tmp); if (order) BN_free(order); if (kinv) BN_clear_free(kinv); return ret; }
static ECDSA_SIG *ecdsa_do_sign(const unsigned char *dgst, int dgst_len, const BIGNUM *in_kinv, const BIGNUM *in_r, EC_KEY *eckey) { int ok = 0; BIGNUM *kinv=NULL, *s, *m=NULL,*tmp=NULL,*order=NULL; const BIGNUM *ckinv; BN_CTX *ctx = NULL; const EC_GROUP *group; ECDSA_SIG *ret; ECDSA_DATA *ecdsa; const BIGNUM *priv_key; ecdsa = ecdsa_check(eckey); group = EC_KEY_get0_group(eckey); priv_key = EC_KEY_get0_private_key(eckey); if (group == NULL || priv_key == NULL || ecdsa == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_PASSED_NULL_PARAMETER); return NULL; } ret = ECDSA_SIG_new(); if (!ret) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE); return NULL; } s = ret->s; if ((ctx = BN_CTX_new()) == NULL || (order = BN_new()) == NULL || (tmp = BN_new()) == NULL || (m = BN_new()) == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE); goto err; } if (!EC_GROUP_get_order(group, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, 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_SIGN, ECDSA_R_DATA_TOO_LARGE_FOR_KEY_SIZE); goto err; } if (!BN_bin2bn(dgst, dgst_len, m)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } do { if (in_kinv == NULL || in_r == NULL) { if (!ECDSA_sign_setup(eckey, ctx, &kinv, &ret->r)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN,ERR_R_ECDSA_LIB); goto err; } ckinv = kinv; } else { ckinv = in_kinv; if (BN_copy(ret->r, in_r) == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE); goto err; } } if (!BN_mod_mul(tmp, priv_key, ret->r, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } if (!BN_mod_add_quick(s, tmp, m, order)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } if (!BN_mod_mul(s, s, ckinv, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } if (BN_is_zero(s)) { /* if kinv and r have been supplied by the caller * don't to generate new kinv and r values */ if (in_kinv != NULL && in_r != NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ECDSA_R_NEED_NEW_SETUP_VALUES); goto err; } } else /* s != 0 => we have a valid signature */ break; } while (1); ok = 1; err: if (!ok) { ECDSA_SIG_free(ret); ret = NULL; } if (ctx) BN_CTX_free(ctx); if (m) BN_clear_free(m); if (tmp) BN_clear_free(tmp); if (order) BN_free(order); if (kinv) BN_clear_free(kinv); return ret; }
int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) { int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *rh, *tmp, *Z4, *Z6; int ret = -1; if (EC_POINT_is_at_infinity(group, point)) return 1; field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = group->field; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; } BN_CTX_start(ctx); rh = BN_CTX_get(ctx); tmp = BN_CTX_get(ctx); Z4 = BN_CTX_get(ctx); Z6 = BN_CTX_get(ctx); if (Z6 == NULL) goto err; /*- * We have a curve defined by a Weierstrass equation * y^2 = x^3 + a*x + b. * The point to consider is given in Jacobian projective coordinates * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). * Substituting this and multiplying by Z^6 transforms the above equation into * Y^2 = X^3 + a*X*Z^4 + b*Z^6. * To test this, we add up the right-hand side in 'rh'. */ /* rh := X^2 */ if (!field_sqr(group, rh, point->X, ctx)) goto err; if (!point->Z_is_one) { if (!field_sqr(group, tmp, point->Z, ctx)) goto err; if (!field_sqr(group, Z4, tmp, ctx)) goto err; if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err; /* rh := (rh + a*Z^4)*X */ if (group->a_is_minus3) { if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err; if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err; if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err; if (!field_mul(group, rh, rh, point->X, ctx)) goto err; } else { if (!field_mul(group, tmp, Z4, group->a, ctx)) goto err; if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; if (!field_mul(group, rh, rh, point->X, ctx)) goto err; } /* rh := rh + b*Z^6 */ if (!field_mul(group, tmp, group->b, Z6, ctx)) goto err; if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; } else { /* point->Z_is_one */ /* rh := (rh + a)*X */ if (!BN_mod_add_quick(rh, rh, group->a, p)) goto err; if (!field_mul(group, rh, rh, point->X, ctx)) goto err; /* rh := rh + b */ if (!BN_mod_add_quick(rh, rh, group->b, p)) goto err; } /* 'lh' := Y^2 */ if (!field_sqr(group, tmp, point->Y, ctx)) goto err; ret = (0 == BN_ucmp(tmp, rh)); err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; }
int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) { int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *n0, *n1, *n2, *n3; int ret = 0; if (EC_POINT_is_at_infinity(group, a)) { BN_zero(r->Z); r->Z_is_one = 0; return 1; } field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = group->field; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); n0 = BN_CTX_get(ctx); n1 = BN_CTX_get(ctx); n2 = BN_CTX_get(ctx); n3 = BN_CTX_get(ctx); if (n3 == NULL) goto err; /* * Note that in this function we must not read components of 'a' once we * have written the corresponding components of 'r'. ('r' might the same * as 'a'.) */ /* n1 */ if (a->Z_is_one) { if (!field_sqr(group, n0, a->X, ctx)) goto err; if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; if (!BN_mod_add_quick(n1, n0, group->a, p)) goto err; /* n1 = 3 * X_a^2 + a_curve */ } else if (group->a_is_minus3) { if (!field_sqr(group, n1, a->Z, ctx)) goto err; if (!BN_mod_add_quick(n0, a->X, n1, p)) goto err; if (!BN_mod_sub_quick(n2, a->X, n1, p)) goto err; if (!field_mul(group, n1, n0, n2, ctx)) goto err; if (!BN_mod_lshift1_quick(n0, n1, p)) goto err; if (!BN_mod_add_quick(n1, n0, n1, p)) goto err; /*- * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) * = 3 * X_a^2 - 3 * Z_a^4 */ } else { if (!field_sqr(group, n0, a->X, ctx)) goto err; if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; if (!field_sqr(group, n1, a->Z, ctx)) goto err; if (!field_sqr(group, n1, n1, ctx)) goto err; if (!field_mul(group, n1, n1, group->a, ctx)) goto err; if (!BN_mod_add_quick(n1, n1, n0, p)) goto err; /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ } /* Z_r */ if (a->Z_is_one) { if (!BN_copy(n0, a->Y)) goto err; } else { if (!field_mul(group, n0, a->Y, a->Z, ctx)) goto err; } if (!BN_mod_lshift1_quick(r->Z, n0, p)) goto err; r->Z_is_one = 0; /* Z_r = 2 * Y_a * Z_a */ /* n2 */ if (!field_sqr(group, n3, a->Y, ctx)) goto err; if (!field_mul(group, n2, a->X, n3, ctx)) goto err; if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err; /* n2 = 4 * X_a * Y_a^2 */ /* X_r */ if (!BN_mod_lshift1_quick(n0, n2, p)) goto err; if (!field_sqr(group, r->X, n1, ctx)) goto err; if (!BN_mod_sub_quick(r->X, r->X, n0, p)) goto err; /* X_r = n1^2 - 2 * n2 */ /* n3 */ if (!field_sqr(group, n0, n3, ctx)) goto err; if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err; /* n3 = 8 * Y_a^4 */ /* Y_r */ if (!BN_mod_sub_quick(n0, n2, r->X, p)) goto err; if (!field_mul(group, n0, n1, n0, ctx)) goto err; if (!BN_mod_sub_quick(r->Y, n0, n3, p)) goto err; /* Y_r = n1 * (n2 - X_r) - n3 */ ret = 1; err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; }
int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; int ret = 0; if (a == b) return EC_POINT_dbl(group, r, a, ctx); if (EC_POINT_is_at_infinity(group, a)) return EC_POINT_copy(r, b); if (EC_POINT_is_at_infinity(group, b)) return EC_POINT_copy(r, a); field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = group->field; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); n0 = BN_CTX_get(ctx); n1 = BN_CTX_get(ctx); n2 = BN_CTX_get(ctx); n3 = BN_CTX_get(ctx); n4 = BN_CTX_get(ctx); n5 = BN_CTX_get(ctx); n6 = BN_CTX_get(ctx); if (n6 == NULL) goto end; /* * Note that in this function we must not read components of 'a' or 'b' * once we have written the corresponding components of 'r'. ('r' might * be one of 'a' or 'b'.) */ /* n1, n2 */ if (b->Z_is_one) { if (!BN_copy(n1, a->X)) goto end; if (!BN_copy(n2, a->Y)) goto end; /* n1 = X_a */ /* n2 = Y_a */ } else { if (!field_sqr(group, n0, b->Z, ctx)) goto end; if (!field_mul(group, n1, a->X, n0, ctx)) goto end; /* n1 = X_a * Z_b^2 */ if (!field_mul(group, n0, n0, b->Z, ctx)) goto end; if (!field_mul(group, n2, a->Y, n0, ctx)) goto end; /* n2 = Y_a * Z_b^3 */ } /* n3, n4 */ if (a->Z_is_one) { if (!BN_copy(n3, b->X)) goto end; if (!BN_copy(n4, b->Y)) goto end; /* n3 = X_b */ /* n4 = Y_b */ } else { if (!field_sqr(group, n0, a->Z, ctx)) goto end; if (!field_mul(group, n3, b->X, n0, ctx)) goto end; /* n3 = X_b * Z_a^2 */ if (!field_mul(group, n0, n0, a->Z, ctx)) goto end; if (!field_mul(group, n4, b->Y, n0, ctx)) goto end; /* n4 = Y_b * Z_a^3 */ } /* n5, n6 */ if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end; if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end; /* n5 = n1 - n3 */ /* n6 = n2 - n4 */ if (BN_is_zero(n5)) { if (BN_is_zero(n6)) { /* a is the same point as b */ BN_CTX_end(ctx); ret = EC_POINT_dbl(group, r, a, ctx); ctx = NULL; goto end; } else { /* a is the inverse of b */ BN_zero(r->Z); r->Z_is_one = 0; ret = 1; goto end; } } /* 'n7', 'n8' */ if (!BN_mod_add_quick(n1, n1, n3, p)) goto end; if (!BN_mod_add_quick(n2, n2, n4, p)) goto end; /* 'n7' = n1 + n3 */ /* 'n8' = n2 + n4 */ /* Z_r */ if (a->Z_is_one && b->Z_is_one) { if (!BN_copy(r->Z, n5)) goto end; } else { if (a->Z_is_one) { if (!BN_copy(n0, b->Z)) goto end; } else if (b->Z_is_one) { if (!BN_copy(n0, a->Z)) goto end; } else { if (!field_mul(group, n0, a->Z, b->Z, ctx)) goto end; } if (!field_mul(group, r->Z, n0, n5, ctx)) goto end; } r->Z_is_one = 0; /* Z_r = Z_a * Z_b * n5 */ /* X_r */ if (!field_sqr(group, n0, n6, ctx)) goto end; if (!field_sqr(group, n4, n5, ctx)) goto end; if (!field_mul(group, n3, n1, n4, ctx)) goto end; if (!BN_mod_sub_quick(r->X, n0, n3, p)) goto end; /* X_r = n6^2 - n5^2 * 'n7' */ /* 'n9' */ if (!BN_mod_lshift1_quick(n0, r->X, p)) goto end; if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end; /* n9 = n5^2 * 'n7' - 2 * X_r */ /* Y_r */ if (!field_mul(group, n0, n0, n6, ctx)) goto end; if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */ if (!field_mul(group, n1, n2, n5, ctx)) goto end; if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end; if (BN_is_odd(n0)) if (!BN_add(n0, n0, p)) goto end; /* now 0 <= n0 < 2*p, and n0 is even */ if (!BN_rshift1(r->Y, n0)) goto end; /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ ret = 1; end: if (ctx) /* otherwise we already called BN_CTX_end */ BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; }
/*- * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass * Elliptic Curves and Side-Channel Attacks", modified to work in projective * coordinates and return r in Jacobian projective coordinates. * * X4 = two*Y1*X2*Z3*Z2*Z1; * Y4 = two*b*Z3*SQR(Z2*Z1) + Z3*(a*Z2*Z1+X1*X2)*(X1*Z2+X2*Z1) - X3*SQR(X1*Z2-X2*Z1); * Z4 = two*Y1*Z3*SQR(Z2)*Z1; * * Z4 != 0 because: * - Z1==0 implies p is at infinity, which would have caused an early exit in * the caller; * - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch); * - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch); * - Y1==0 implies p has order 2, so either r or s are infinity and handled by * one of the BN_is_zero(...) branches. */ int ec_GFp_simple_ladder_post(const EC_GROUP *group, EC_POINT *r, EC_POINT *s, EC_POINT *p, BN_CTX *ctx) { int ret = 0; BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL; if (BN_is_zero(r->Z)) return EC_POINT_set_to_infinity(group, r); if (BN_is_zero(s->Z)) { /* (X,Y,Z) -> (XZ,YZ**2,Z) */ if (!group->meth->field_mul(group, r->X, p->X, p->Z, ctx) || !group->meth->field_sqr(group, r->Z, p->Z, ctx) || !group->meth->field_mul(group, r->Y, p->Y, r->Z, ctx) || !BN_copy(r->Z, p->Z) || !EC_POINT_invert(group, r, ctx)) return 0; return 1; } BN_CTX_start(ctx); t0 = BN_CTX_get(ctx); t1 = BN_CTX_get(ctx); t2 = BN_CTX_get(ctx); t3 = BN_CTX_get(ctx); t4 = BN_CTX_get(ctx); t5 = BN_CTX_get(ctx); t6 = BN_CTX_get(ctx); if (t6 == NULL || !BN_mod_lshift1_quick(t0, p->Y, group->field) || !group->meth->field_mul(group, t1, r->X, p->Z, ctx) || !group->meth->field_mul(group, t2, r->Z, s->Z, ctx) || !group->meth->field_mul(group, t2, t1, t2, ctx) || !group->meth->field_mul(group, t3, t2, t0, ctx) || !group->meth->field_mul(group, t2, r->Z, p->Z, ctx) || !group->meth->field_sqr(group, t4, t2, ctx) || !BN_mod_lshift1_quick(t5, group->b, group->field) || !group->meth->field_mul(group, t4, t4, t5, ctx) || !group->meth->field_mul(group, t6, t2, group->a, ctx) || !group->meth->field_mul(group, t5, r->X, p->X, ctx) || !BN_mod_add_quick(t5, t6, t5, group->field) || !group->meth->field_mul(group, t6, r->Z, p->X, ctx) || !BN_mod_add_quick(t2, t6, t1, group->field) || !group->meth->field_mul(group, t5, t5, t2, ctx) || !BN_mod_sub_quick(t6, t6, t1, group->field) || !group->meth->field_sqr(group, t6, t6, ctx) || !group->meth->field_mul(group, t6, t6, s->X, ctx) || !BN_mod_add_quick(t4, t5, t4, group->field) || !group->meth->field_mul(group, t4, t4, s->Z, ctx) || !BN_mod_sub_quick(t4, t4, t6, group->field) || !group->meth->field_sqr(group, t5, r->Z, ctx) || !group->meth->field_mul(group, r->Z, p->Z, s->Z, ctx) || !group->meth->field_mul(group, r->Z, t5, r->Z, ctx) || !group->meth->field_mul(group, r->Z, r->Z, t0, ctx) /* t3 := X, t4 := Y */ /* (X,Y,Z) -> (XZ,YZ**2,Z) */ || !group->meth->field_mul(group, r->X, t3, r->Z, ctx) || !group->meth->field_sqr(group, t3, r->Z, ctx) || !group->meth->field_mul(group, r->Y, t4, t3, ctx)) goto err; ret = 1; err: BN_CTX_end(ctx); return ret; }
/*- * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi * "A fast parallel elliptic curve multiplication resistant against side channel * attacks", as described at * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-4 */ int ec_GFp_simple_ladder_step(const EC_GROUP *group, EC_POINT *r, EC_POINT *s, EC_POINT *p, BN_CTX *ctx) { int ret = 0; BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6, *t7 = NULL; BN_CTX_start(ctx); t0 = BN_CTX_get(ctx); t1 = BN_CTX_get(ctx); t2 = BN_CTX_get(ctx); t3 = BN_CTX_get(ctx); t4 = BN_CTX_get(ctx); t5 = BN_CTX_get(ctx); t6 = BN_CTX_get(ctx); t7 = BN_CTX_get(ctx); if (t7 == NULL || !group->meth->field_mul(group, t0, r->X, s->X, ctx) || !group->meth->field_mul(group, t1, r->Z, s->Z, ctx) || !group->meth->field_mul(group, t2, r->X, s->Z, ctx) || !group->meth->field_mul(group, t3, r->Z, s->X, ctx) || !group->meth->field_mul(group, t4, group->a, t1, ctx) || !BN_mod_add_quick(t0, t0, t4, group->field) || !BN_mod_add_quick(t4, t3, t2, group->field) || !group->meth->field_mul(group, t0, t4, t0, ctx) || !group->meth->field_sqr(group, t1, t1, ctx) || !BN_mod_lshift_quick(t7, group->b, 2, group->field) || !group->meth->field_mul(group, t1, t7, t1, ctx) || !BN_mod_lshift1_quick(t0, t0, group->field) || !BN_mod_add_quick(t0, t1, t0, group->field) || !BN_mod_sub_quick(t1, t2, t3, group->field) || !group->meth->field_sqr(group, t1, t1, ctx) || !group->meth->field_mul(group, t3, t1, p->X, ctx) || !group->meth->field_mul(group, t0, p->Z, t0, ctx) /* s->X coord output */ || !BN_mod_sub_quick(s->X, t0, t3, group->field) /* s->Z coord output */ || !group->meth->field_mul(group, s->Z, p->Z, t1, ctx) || !group->meth->field_sqr(group, t3, r->X, ctx) || !group->meth->field_sqr(group, t2, r->Z, ctx) || !group->meth->field_mul(group, t4, t2, group->a, ctx) || !BN_mod_add_quick(t5, r->X, r->Z, group->field) || !group->meth->field_sqr(group, t5, t5, ctx) || !BN_mod_sub_quick(t5, t5, t3, group->field) || !BN_mod_sub_quick(t5, t5, t2, group->field) || !BN_mod_sub_quick(t6, t3, t4, group->field) || !group->meth->field_sqr(group, t6, t6, ctx) || !group->meth->field_mul(group, t0, t2, t5, ctx) || !group->meth->field_mul(group, t0, t7, t0, ctx) /* r->X coord output */ || !BN_mod_sub_quick(r->X, t6, t0, group->field) || !BN_mod_add_quick(t6, t3, t4, group->field) || !group->meth->field_sqr(group, t3, t2, ctx) || !group->meth->field_mul(group, t7, t3, t7, ctx) || !group->meth->field_mul(group, t5, t5, t6, ctx) || !BN_mod_lshift1_quick(t5, t5, group->field) /* r->Z coord output */ || !BN_mod_add_quick(r->Z, t7, t5, group->field)) goto err; ret = 1; err: BN_CTX_end(ctx); return ret; }
ECDSA_SIG *ECDSA_do_sign_ex(const uint8_t *digest, size_t digest_len, const BIGNUM *in_kinv, const BIGNUM *in_r, const EC_KEY *eckey) { int ok = 0; BIGNUM *kinv = NULL, *s, *m = NULL, *tmp = NULL; const BIGNUM *ckinv; BN_CTX *ctx = NULL; const EC_GROUP *group; ECDSA_SIG *ret; const BIGNUM *priv_key; if (eckey->ecdsa_meth && eckey->ecdsa_meth->sign) { OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_NOT_IMPLEMENTED); return NULL; } group = EC_KEY_get0_group(eckey); priv_key = EC_KEY_get0_private_key(eckey); if (group == NULL || priv_key == NULL) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_PASSED_NULL_PARAMETER); return NULL; } ret = ECDSA_SIG_new(); if (!ret) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); return NULL; } s = ret->s; if ((ctx = BN_CTX_new()) == NULL || (tmp = BN_new()) == NULL || (m = BN_new()) == NULL) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); goto err; } const BIGNUM *order = EC_GROUP_get0_order(group); if (!digest_to_bn(m, digest, digest_len, order)) { goto err; } for (;;) { if (in_kinv == NULL || in_r == NULL) { if (!ecdsa_sign_setup(eckey, ctx, &kinv, &ret->r, digest, digest_len)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_ECDSA_LIB); goto err; } ckinv = kinv; } else { ckinv = in_kinv; if (BN_copy(ret->r, in_r) == NULL) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); goto err; } } if (!BN_mod_mul(tmp, priv_key, ret->r, order, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } if (!BN_mod_add_quick(s, tmp, m, order)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } if (!BN_mod_mul(s, s, ckinv, order, ctx)) { OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); goto err; } if (BN_is_zero(s)) { // if kinv and r have been supplied by the caller // don't to generate new kinv and r values if (in_kinv != NULL && in_r != NULL) { OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_NEED_NEW_SETUP_VALUES); goto err; } } else { // s != 0 => we have a valid signature break; } } ok = 1; err: if (!ok) { ECDSA_SIG_free(ret); ret = NULL; } BN_CTX_free(ctx); BN_clear_free(m); BN_clear_free(tmp); BN_clear_free(kinv); return ret; }
static ECDSA_SIG *ecdsa_do_sign(const unsigned char *dgst, int dgst_len, const BIGNUM *in_kinv, const BIGNUM *in_r, EC_KEY *eckey) { int ok = 0; BIGNUM *kinv=NULL, *s, *m=NULL,*tmp=NULL,*order=NULL; const BIGNUM *ckinv; BN_CTX *ctx = NULL; const EC_GROUP *group; ECDSA_SIG *ret; ECDSA_DATA *ecdsa; const BIGNUM *priv_key; ecdsa = ecdsa_check(eckey); group = EC_KEY_get0_group(eckey); priv_key = EC_KEY_get0_private_key(eckey); if (group == NULL || priv_key == NULL || ecdsa == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_PASSED_NULL_PARAMETER); return NULL; } ret = ECDSA_SIG_new(); if (!ret) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE); return NULL; } s = ret->s; if ((ctx = BN_CTX_new()) == NULL || (order = BN_new()) == NULL || (tmp = BN_new()) == NULL || (m = BN_new()) == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE); goto err; } if (!EC_GROUP_get_order(group, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_EC_LIB); goto err; } if (dgst_len > BN_num_bytes(order)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ECDSA_R_DATA_TOO_LARGE_FOR_KEY_SIZE); goto err; } if (!BN_bin2bn(dgst, dgst_len, m)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } do { if (in_kinv == NULL || in_r == NULL) { if (!ECDSA_sign_setup(eckey, ctx, &kinv, &ret->r)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN,ERR_R_ECDSA_LIB); goto err; } ckinv = kinv; } else { ckinv = in_kinv; if (BN_copy(ret->r, in_r) == NULL) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE); goto err; } } if (!BN_mod_mul(tmp, priv_key, ret->r, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } if (!BN_mod_add_quick(s, tmp, m, order)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } if (!BN_mod_mul(s, s, ckinv, order, ctx)) { ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB); goto err; } } while (BN_is_zero(s)); ok = 1; err: if (!ok) { ECDSA_SIG_free(ret); ret = NULL; } if (ctx) BN_CTX_free(ctx); if (m) BN_clear_free(m); if (tmp) BN_clear_free(tmp); if (order) BN_free(order); if (kinv) BN_clear_free(kinv); return ret; }
int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) { int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *n0, *n1, *n2, *n3; int ret = 0; if (EC_POINT_is_at_infinity(group, a)) { BN_zero(&r->Z); return 1; } field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = &group->field; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) { return 0; } } BN_CTX_start(ctx); n0 = BN_CTX_get(ctx); n1 = BN_CTX_get(ctx); n2 = BN_CTX_get(ctx); n3 = BN_CTX_get(ctx); if (n3 == NULL) { goto err; } /* Note that in this function we must not read components of 'a' * once we have written the corresponding components of 'r'. * ('r' might the same as 'a'.) */ /* n1 */ if (BN_cmp(&a->Z, &group->one) == 0) { if (!field_sqr(group, n0, &a->X, ctx) || !BN_mod_lshift1_quick(n1, n0, p) || !BN_mod_add_quick(n0, n0, n1, p) || !BN_mod_add_quick(n1, n0, &group->a, p)) { goto err; } /* n1 = 3 * X_a^2 + a_curve */ } else { /* ring: This assumes a == -3. */ if (!field_sqr(group, n1, &a->Z, ctx) || !BN_mod_add_quick(n0, &a->X, n1, p) || !BN_mod_sub_quick(n2, &a->X, n1, p) || !field_mul(group, n1, n0, n2, ctx) || !BN_mod_lshift1_quick(n0, n1, p) || !BN_mod_add_quick(n1, n0, n1, p)) { goto err; } /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) * = 3 * X_a^2 - 3 * Z_a^4 */ } /* Z_r */ if (BN_cmp(&a->Z, &group->one) == 0) { if (!BN_copy(n0, &a->Y)) { goto err; } } else if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) { goto err; } if (!BN_mod_lshift1_quick(&r->Z, n0, p)) { goto err; } /* Z_r = 2 * Y_a * Z_a */ /* n2 */ if (!field_sqr(group, n3, &a->Y, ctx) || !field_mul(group, n2, &a->X, n3, ctx) || !BN_mod_lshift_quick(n2, n2, 2, p)) { goto err; } /* n2 = 4 * X_a * Y_a^2 */ /* X_r */ if (!BN_mod_lshift1_quick(n0, n2, p) || !field_sqr(group, &r->X, n1, ctx) || !BN_mod_sub_quick(&r->X, &r->X, n0, p)) { goto err; } /* X_r = n1^2 - 2 * n2 */ /* n3 */ if (!field_sqr(group, n0, n3, ctx) || !BN_mod_lshift_quick(n3, n0, 3, p)) { goto err; } /* n3 = 8 * Y_a^4 */ /* Y_r */ if (!BN_mod_sub_quick(n0, n2, &r->X, p) || !field_mul(group, n0, n1, n0, ctx) || !BN_mod_sub_quick(&r->Y, n0, n3, p)) { goto err; } /* Y_r = n1 * (n2 - X_r) - n3 */ ret = 1; err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; }
ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len, const BIGNUM *in_kinv, const BIGNUM *in_r, EC_KEY *eckey) { int ok = 0, i; BIGNUM *kinv = NULL, *s, *m = NULL, *tmp = NULL; const BIGNUM *order, *ckinv; BN_CTX *ctx = NULL; const EC_GROUP *group; ECDSA_SIG *ret; const BIGNUM *priv_key; group = EC_KEY_get0_group(eckey); priv_key = EC_KEY_get0_private_key(eckey); if (group == NULL || priv_key == NULL) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_PASSED_NULL_PARAMETER); return NULL; } if (!EC_KEY_can_sign(eckey)) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, EC_R_CURVE_DOES_NOT_SUPPORT_SIGNING); return NULL; } ret = ECDSA_SIG_new(); if (ret == NULL) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE); return NULL; } ret->r = BN_new(); ret->s = BN_new(); if (ret->r == NULL || ret->s == NULL) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE); goto err; } s = ret->s; if ((ctx = BN_CTX_new()) == NULL || (tmp = BN_new()) == NULL || (m = BN_new()) == NULL) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE); goto err; } order = EC_GROUP_get0_order(group); if (order == NULL) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_EC_LIB); goto err; } 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)) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, 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))) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB); goto err; } do { if (in_kinv == NULL || in_r == NULL) { if (!ecdsa_sign_setup(eckey, ctx, &kinv, &ret->r, dgst, dgst_len)) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_ECDSA_LIB); goto err; } ckinv = kinv; } else { ckinv = in_kinv; if (BN_copy(ret->r, in_r) == NULL) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE); goto err; } } if (!BN_mod_mul(tmp, priv_key, ret->r, order, ctx)) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB); goto err; } if (!BN_mod_add_quick(s, tmp, m, order)) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB); goto err; } if (!BN_mod_mul(s, s, ckinv, order, ctx)) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB); goto err; } if (BN_is_zero(s)) { /* * if kinv and r have been supplied by the caller don't to * generate new kinv and r values */ if (in_kinv != NULL && in_r != NULL) { ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, EC_R_NEED_NEW_SETUP_VALUES); goto err; } } else /* s != 0 => we have a valid signature */ break; } while (1); ok = 1; err: if (!ok) { ECDSA_SIG_free(ret); ret = NULL; } BN_CTX_free(ctx); BN_clear_free(m); BN_clear_free(tmp); BN_clear_free(kinv); return ret; }