--- /dev/null
+/* ====================================================================
+ * 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"
+
+
+// EC_LOOSE_SCALAR is like |EC_SCALAR| but is bounded by 2^|BN_num_bits(order)|
+// rather than |order|.
+typedef union {
+ // bytes is the representation of the scalar in little-endian order.
+ uint8_t bytes[EC_MAX_SCALAR_BYTES];
+ BN_ULONG words[EC_MAX_SCALAR_WORDS];
+} EC_LOOSE_SCALAR;
+
+static void scalar_add_loose(const EC_GROUP *group, EC_LOOSE_SCALAR *r,
+ const EC_LOOSE_SCALAR *a, const EC_SCALAR *b) {
+ // Add and subtract one copy of |order| if necessary. We have:
+ // |a| + |b| < 2^BN_num_bits(order) + order
+ // so this leaves |r| < 2^BN_num_bits(order).
+ const BIGNUM *order = &group->order;
+ BN_ULONG carry = bn_add_words(r->words, a->words, b->words, order->width);
+ EC_LOOSE_SCALAR tmp;
+ BN_ULONG v =
+ bn_sub_words(tmp.words, r->words, order->d, order->width) - carry;
+ bn_select_words(r->words, 0u - v, r->words /* tmp < 0 */,
+ tmp.words /* tmp >= 0 */, order->width);
+}
+
+static int scalar_mod_mul_montgomery(const EC_GROUP *group, EC_SCALAR *r,
+ const EC_SCALAR *a, const EC_SCALAR *b) {
+ const BIGNUM *order = &group->order;
+ return bn_mod_mul_montgomery_small(r->words, order->width, a->words,
+ order->width, b->words, order->width,
+ group->order_mont);
+}
+
+static int scalar_mod_mul_montgomery_loose(const EC_GROUP *group, EC_SCALAR *r,
+ const EC_LOOSE_SCALAR *a,
+ const EC_SCALAR *b) {
+ // Although |a| is loose, |bn_mod_mul_montgomery_small| only requires the
+ // product not exceed R * |order|. |b| is fully reduced and |a| <
+ // 2^BN_num_bits(order) <= R, so this holds.
+ const BIGNUM *order = &group->order;
+ return bn_mod_mul_montgomery_small(r->words, order->width, a->words,
+ order->width, b->words, order->width,
+ group->order_mont);
+}
+
+// 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_LOOSE_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.
+ if (8 * digest_len > num_bits) {
+ digest_len = (num_bits + 7) / 8;
+ }
+ 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 still too long truncate remaining bits with a shift
+ if (8 * digest_len > num_bits) {
+ size_t shift = 8 - (num_bits & 0x7);
+ for (int i = 0; i < order->width - 1; i++) {
+ out->words[i] =
+ (out->words[i] >> shift) | (out->words[i + 1] << (BN_BITS2 - shift));
+ }
+ out->words[order->width - 1] >>= shift;
+ }
+}
+
+// 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;
+ EC_LOOSE_SCALAR m;
+ const BIGNUM *order = EC_GROUP_get0_order(group);
+ 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 mod order. We convert the result to Montgomery form for
+ // the products below.
+ int no_inverse;
+ if (!BN_mod_inverse_odd(X, &no_inverse, sig->s, order, ctx) ||
+ // TODO(davidben): Add a words version of |BN_mod_inverse_odd| and write
+ // into |s_inv_mont| directly.
+ !ec_bignum_to_scalar_unchecked(group, &s_inv_mont, X) ||
+ !bn_to_montgomery_small(s_inv_mont.words, order->width, s_inv_mont.words,
+ order->width, group->order_mont)) {
+ goto err;
+ }
+ // 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);
+ if (!scalar_mod_mul_montgomery_loose(group, &u1, &m, &s_inv_mont) ||
+ !scalar_mod_mul_montgomery(group, &u2, &r, &s_inv_mont)) {
+ goto err;
+ }
+
+ 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. We leave it in the Montgomery domain as an optimization for
+ // later operations.
+ if (!bn_to_montgomery_small(out_kinv_mont->words, order->width, k.words,
+ order->width, group->order_mont) ||
+ !bn_mod_inverse_prime_mont_small(out_kinv_mont->words, order->width,
+ out_kinv_mont->words, order->width,
+ group->order_mont)) {
+ goto err;
+ }
+
+ // 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;
+ EC_LOOSE_SCALAR 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) ||
+ !bn_to_montgomery_small(r_mont.words, order->width, r_mont.words,
+ order->width, group->order_mont) ||
+ !scalar_mod_mul_montgomery(group, &s, priv_key, &r_mont)) {
+ goto err;
+ }
+
+ // Compute tmp = m + priv_key * r.
+ scalar_add_loose(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.
+ if (!scalar_mod_mul_montgomery_loose(group, &s, &tmp, &kinv_mont) ||
+ !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;
+}
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