| /* ==================================================================== |
| * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in |
| * the documentation and/or other materials provided with the |
| * distribution. |
| * |
| * 3. All advertising materials mentioning features or use of this |
| * software must display the following acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)" |
| * |
| * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| * endorse or promote products derived from this software without |
| * prior written permission. For written permission, please contact |
| * openssl-core@OpenSSL.org. |
| * |
| * 5. Products derived from this software may not be called "OpenSSL" |
| * nor may "OpenSSL" appear in their names without prior written |
| * permission of the OpenSSL Project. |
| * |
| * 6. Redistributions of any form whatsoever must retain the following |
| * acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| * OF THE POSSIBILITY OF SUCH DAMAGE. |
| * ==================================================================== |
| * |
| * This product includes cryptographic software written by Eric Young |
| * (eay@cryptsoft.com). This product includes software written by Tim |
| * Hudson (tjh@cryptsoft.com). */ |
| |
| #include <openssl/ecdsa.h> |
| |
| #include <assert.h> |
| #include <string.h> |
| |
| #include <openssl/bn.h> |
| #include <openssl/err.h> |
| #include <openssl/mem.h> |
| #include <openssl/sha.h> |
| #include <openssl/type_check.h> |
| |
| #include "../bn/internal.h" |
| #include "../ec/internal.h" |
| #include "../../internal.h" |
| |
| |
| // digest_to_scalar interprets |digest_len| bytes from |digest| as a scalar for |
| // ECDSA. Note this value is not fully reduced modulo the order, only the |
| // correct number of bits. |
| static void digest_to_scalar(const EC_GROUP *group, EC_SCALAR *out, |
| const uint8_t *digest, size_t digest_len) { |
| const BIGNUM *order = &group->order; |
| size_t num_bits = BN_num_bits(order); |
| // Need to truncate digest if it is too long: first truncate whole bytes. |
| size_t num_bytes = (num_bits + 7) / 8; |
| if (digest_len > num_bytes) { |
| digest_len = num_bytes; |
| } |
| OPENSSL_memset(out, 0, sizeof(EC_SCALAR)); |
| for (size_t i = 0; i < digest_len; i++) { |
| out->bytes[i] = digest[digest_len - 1 - i]; |
| } |
| |
| // If it is still too long, truncate remaining bits with a shift. |
| if (8 * digest_len > num_bits) { |
| bn_rshift_words(out->words, out->words, 8 - (num_bits & 0x7), order->width); |
| } |
| |
| // |out| now has the same bit width as |order|, but this only bounds by |
| // 2*|order|. Subtract the order if out of range. |
| // |
| // Montgomery multiplication accepts the looser bounds, so this isn't strictly |
| // necessary, but it is a cleaner abstraction and has no performance impact. |
| BN_ULONG tmp[EC_MAX_SCALAR_WORDS]; |
| bn_reduce_once_in_place(out->words, 0 /* no carry */, order->d, tmp, |
| order->width); |
| } |
| |
| // field_element_to_scalar reduces |r| modulo |group->order|. |r| must |
| // previously have been reduced modulo |group->field|. |
| static int field_element_to_scalar(const EC_GROUP *group, BIGNUM *r) { |
| // We must have p < 2×order, assuming p is not tiny (p >= 17). Thus rather we |
| // can reduce by performing at most one subtraction. |
| // |
| // Proof: We only work with prime order curves, so the number of points on |
| // the curve is the order. Thus Hasse's theorem gives: |
| // |
| // |order - (p + 1)| <= 2×sqrt(p) |
| // p + 1 - order <= 2×sqrt(p) |
| // p + 1 - 2×sqrt(p) <= order |
| // p + 1 - 2×(p/4) < order (p/4 > sqrt(p) for p >= 17) |
| // p/2 < p/2 + 1 < order |
| // p < 2×order |
| // |
| // Additionally, one can manually check this property for built-in curves. It |
| // is enforced for legacy custom curves in |EC_GROUP_set_generator|. |
| // |
| // TODO(davidben): Introduce |EC_FIELD_ELEMENT|, make this a function from |
| // |EC_FIELD_ELEMENT| to |EC_SCALAR|, and cut out the |BIGNUM|. Does this need |
| // to be constant-time for signing? |r| is the x-coordinate for kG, which is |
| // public unless k was rerolled because |s| was zero. |
| assert(!BN_is_negative(r)); |
| assert(BN_cmp(r, &group->field) < 0); |
| if (BN_cmp(r, &group->order) >= 0 && |
| !BN_sub(r, r, &group->order)) { |
| return 0; |
| } |
| assert(!BN_is_negative(r)); |
| assert(BN_cmp(r, &group->order) < 0); |
| return 1; |
| } |
| |
| ECDSA_SIG *ECDSA_SIG_new(void) { |
| ECDSA_SIG *sig = OPENSSL_malloc(sizeof(ECDSA_SIG)); |
| if (sig == NULL) { |
| return NULL; |
| } |
| sig->r = BN_new(); |
| sig->s = BN_new(); |
| if (sig->r == NULL || sig->s == NULL) { |
| ECDSA_SIG_free(sig); |
| return NULL; |
| } |
| return sig; |
| } |
| |
| void ECDSA_SIG_free(ECDSA_SIG *sig) { |
| if (sig == NULL) { |
| return; |
| } |
| |
| BN_free(sig->r); |
| BN_free(sig->s); |
| OPENSSL_free(sig); |
| } |
| |
| void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **out_r, |
| const BIGNUM **out_s) { |
| if (out_r != NULL) { |
| *out_r = sig->r; |
| } |
| if (out_s != NULL) { |
| *out_s = sig->s; |
| } |
| } |
| |
| int ECDSA_SIG_set0(ECDSA_SIG *sig, BIGNUM *r, BIGNUM *s) { |
| if (r == NULL || s == NULL) { |
| return 0; |
| } |
| BN_free(sig->r); |
| BN_free(sig->s); |
| sig->r = r; |
| sig->s = s; |
| return 1; |
| } |
| |
| int ECDSA_do_verify(const uint8_t *digest, size_t digest_len, |
| const ECDSA_SIG *sig, const EC_KEY *eckey) { |
| const EC_GROUP *group = EC_KEY_get0_group(eckey); |
| const EC_POINT *pub_key = EC_KEY_get0_public_key(eckey); |
| if (group == NULL || pub_key == NULL || sig == NULL) { |
| OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_MISSING_PARAMETERS); |
| return 0; |
| } |
| |
| BN_CTX *ctx = BN_CTX_new(); |
| if (!ctx) { |
| OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); |
| return 0; |
| } |
| int ret = 0; |
| EC_POINT *point = NULL; |
| BN_CTX_start(ctx); |
| BIGNUM *X = BN_CTX_get(ctx); |
| if (X == NULL) { |
| OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); |
| goto err; |
| } |
| |
| EC_SCALAR r, s, u1, u2, s_inv_mont, m; |
| if (BN_is_zero(sig->r) || |
| !ec_bignum_to_scalar(group, &r, sig->r) || |
| BN_is_zero(sig->s) || |
| !ec_bignum_to_scalar(group, &s, sig->s)) { |
| OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_BAD_SIGNATURE); |
| goto err; |
| } |
| |
| // s_inv_mont = s^-1 in the Montgomery domain. This is |
| // |ec_scalar_to_montgomery| followed by |ec_scalar_inv_montgomery|, but |
| // |ec_scalar_inv_montgomery| followed by |ec_scalar_from_montgomery| is |
| // equivalent and slightly more efficient. |
| ec_scalar_inv_montgomery(group, &s_inv_mont, &s); |
| ec_scalar_from_montgomery(group, &s_inv_mont, &s_inv_mont); |
| |
| // u1 = m * s^-1 mod order |
| // u2 = r * s^-1 mod order |
| // |
| // |s_inv_mont| is in Montgomery form while |m| and |r| are not, so |u1| and |
| // |u2| will be taken out of Montgomery form, as desired. |
| digest_to_scalar(group, &m, digest, digest_len); |
| ec_scalar_mul_montgomery(group, &u1, &m, &s_inv_mont); |
| ec_scalar_mul_montgomery(group, &u2, &r, &s_inv_mont); |
| |
| point = EC_POINT_new(group); |
| if (point == NULL) { |
| OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); |
| goto err; |
| } |
| if (!ec_point_mul_scalar_public(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 (!field_element_to_scalar(group, X)) { |
| OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB); |
| goto err; |
| } |
| // The signature is correct iff |X| is equal to |sig->r|. |
| if (BN_ucmp(X, 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; |
| } |
| |
| static int ecdsa_sign_setup(const EC_KEY *eckey, BN_CTX *ctx, |
| EC_SCALAR *out_kinv_mont, BIGNUM **rp, |
| const uint8_t *digest, size_t digest_len, |
| const EC_SCALAR *priv_key) { |
| EC_POINT *tmp_point = NULL; |
| int ret = 0; |
| EC_SCALAR k; |
| BIGNUM *r = BN_new(); // this value is later returned in *rp |
| if (r == NULL) { |
| OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); |
| goto err; |
| } |
| const EC_GROUP *group = EC_KEY_get0_group(eckey); |
| const BIGNUM *order = EC_GROUP_get0_order(group); |
| tmp_point = EC_POINT_new(group); |
| if (tmp_point == NULL) { |
| OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB); |
| goto err; |
| } |
| |
| // 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 { |
| // Include the private key and message digest in the k generation. |
| if (eckey->fixed_k != NULL) { |
| if (!ec_bignum_to_scalar(group, &k, eckey->fixed_k)) { |
| goto err; |
| } |
| } else { |
| // Pass a SHA512 hash of the private key and digest as additional data |
| // into the RBG. This is a hardening measure against entropy failure. |
| OPENSSL_COMPILE_ASSERT(SHA512_DIGEST_LENGTH >= 32, |
| additional_data_is_too_large_for_sha512); |
| SHA512_CTX sha; |
| uint8_t additional_data[SHA512_DIGEST_LENGTH]; |
| SHA512_Init(&sha); |
| SHA512_Update(&sha, priv_key->words, order->width * sizeof(BN_ULONG)); |
| SHA512_Update(&sha, digest, digest_len); |
| SHA512_Final(additional_data, &sha); |
| if (!ec_random_nonzero_scalar(group, &k, additional_data)) { |
| goto err; |
| } |
| } |
| |
| // Compute k^-1 in the Montgomery domain. This is |ec_scalar_to_montgomery| |
| // followed by |ec_scalar_inv_montgomery|, but |ec_scalar_inv_montgomery| |
| // followed by |ec_scalar_from_montgomery| is equivalent and slightly more |
| // efficient. |
| ec_scalar_inv_montgomery(group, out_kinv_mont, &k); |
| ec_scalar_from_montgomery(group, out_kinv_mont, out_kinv_mont); |
| |
| // Compute r, the x-coordinate of generator * k. |
| if (!ec_point_mul_scalar(group, tmp_point, &k, NULL, NULL, ctx) || |
| !EC_POINT_get_affine_coordinates_GFp(group, tmp_point, r, NULL, |
| ctx)) { |
| goto err; |
| } |
| |
| if (!field_element_to_scalar(group, r)) { |
| goto err; |
| } |
| } while (BN_is_zero(r)); |
| |
| BN_clear_free(*rp); |
| *rp = r; |
| r = NULL; |
| ret = 1; |
| |
| err: |
| OPENSSL_cleanse(&k, sizeof(k)); |
| BN_clear_free(r); |
| EC_POINT_free(tmp_point); |
| return ret; |
| } |
| |
| ECDSA_SIG *ECDSA_do_sign(const uint8_t *digest, size_t digest_len, |
| const EC_KEY *eckey) { |
| if (eckey->ecdsa_meth && eckey->ecdsa_meth->sign) { |
| OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_NOT_IMPLEMENTED); |
| return NULL; |
| } |
| |
| const EC_GROUP *group = EC_KEY_get0_group(eckey); |
| if (group == NULL || eckey->priv_key == NULL) { |
| OPENSSL_PUT_ERROR(ECDSA, ERR_R_PASSED_NULL_PARAMETER); |
| return NULL; |
| } |
| const BIGNUM *order = EC_GROUP_get0_order(group); |
| const EC_SCALAR *priv_key = &eckey->priv_key->scalar; |
| |
| int ok = 0; |
| ECDSA_SIG *ret = ECDSA_SIG_new(); |
| BN_CTX *ctx = BN_CTX_new(); |
| EC_SCALAR kinv_mont, r_mont, s, m, tmp; |
| if (ret == NULL || ctx == NULL) { |
| OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE); |
| return NULL; |
| } |
| |
| digest_to_scalar(group, &m, digest, digest_len); |
| for (;;) { |
| if (!ecdsa_sign_setup(eckey, ctx, &kinv_mont, &ret->r, digest, digest_len, |
| priv_key)) { |
| goto err; |
| } |
| |
| // Compute priv_key * r (mod order). Note if only one parameter is in the |
| // Montgomery domain, |scalar_mod_mul_montgomery| will compute the answer in |
| // the normal domain. |
| if (!ec_bignum_to_scalar(group, &r_mont, ret->r)) { |
| goto err; |
| } |
| ec_scalar_to_montgomery(group, &r_mont, &r_mont); |
| ec_scalar_mul_montgomery(group, &s, priv_key, &r_mont); |
| |
| // Compute tmp = m + priv_key * r. |
| ec_scalar_add(group, &tmp, &m, &s); |
| |
| // Finally, multiply s by k^-1. That was retained in Montgomery form, so the |
| // same technique as the previous multiplication works. |
| ec_scalar_mul_montgomery(group, &s, &tmp, &kinv_mont); |
| if (!bn_set_words(ret->s, s.words, order->width)) { |
| goto err; |
| } |
| if (!BN_is_zero(ret->s)) { |
| // s != 0 => we have a valid signature |
| break; |
| } |
| } |
| |
| ok = 1; |
| |
| err: |
| if (!ok) { |
| ECDSA_SIG_free(ret); |
| ret = NULL; |
| } |
| BN_CTX_free(ctx); |
| OPENSSL_cleanse(&kinv_mont, sizeof(kinv_mont)); |
| OPENSSL_cleanse(&r_mont, sizeof(r_mont)); |
| OPENSSL_cleanse(&s, sizeof(s)); |
| OPENSSL_cleanse(&tmp, sizeof(tmp)); |
| OPENSSL_cleanse(&m, sizeof(m)); |
| return ret; |
| } |