466 lines
16 KiB
C
466 lines
16 KiB
C
/* ====================================================================
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* Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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*
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* 3. All advertising materials mentioning features or use of this
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* software must display the following acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
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*
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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* endorse or promote products derived from this software without
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* prior written permission. For written permission, please contact
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* openssl-core@OpenSSL.org.
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*
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* 5. Products derived from this software may not be called "OpenSSL"
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* nor may "OpenSSL" appear in their names without prior written
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* permission of the OpenSSL Project.
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*
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* 6. Redistributions of any form whatsoever must retain the following
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* acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
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*
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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* ====================================================================
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*
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* This product includes cryptographic software written by Eric Young
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* (eay@cryptsoft.com). This product includes software written by Tim
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* Hudson (tjh@cryptsoft.com). */
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#include <openssl/ecdsa.h>
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#include <assert.h>
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#include <string.h>
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#include <openssl/bn.h>
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#include <openssl/err.h>
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#include <openssl/mem.h>
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#include <openssl/sha.h>
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#include <openssl/type_check.h>
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#include "../bn/internal.h"
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#include "../ec/internal.h"
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#include "../../internal.h"
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// EC_LOOSE_SCALAR is like |EC_SCALAR| but is bounded by 2^|BN_num_bits(order)|
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// rather than |order|.
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typedef union {
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// bytes is the representation of the scalar in little-endian order.
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uint8_t bytes[EC_MAX_SCALAR_BYTES];
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BN_ULONG words[EC_MAX_SCALAR_WORDS];
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} EC_LOOSE_SCALAR;
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static void scalar_add_loose(const EC_GROUP *group, EC_LOOSE_SCALAR *r,
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const EC_LOOSE_SCALAR *a, const EC_SCALAR *b) {
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// Add and subtract one copy of |order| if necessary. We have:
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// |a| + |b| < 2^BN_num_bits(order) + order
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// so this leaves |r| < 2^BN_num_bits(order).
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const BIGNUM *order = &group->order;
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BN_ULONG carry = bn_add_words(r->words, a->words, b->words, order->top);
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EC_LOOSE_SCALAR tmp;
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BN_ULONG v = bn_sub_words(tmp.words, r->words, order->d, order->top) - carry;
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v = 0u - v;
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for (int i = 0; i < order->top; i++) {
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OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
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crypto_word_t_too_small);
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r->words[i] = constant_time_select_w(v, r->words[i], tmp.words[i]);
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}
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}
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static int scalar_mod_mul_montgomery(const EC_GROUP *group, EC_SCALAR *r,
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const EC_SCALAR *a, const EC_SCALAR *b) {
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const BIGNUM *order = &group->order;
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return bn_mod_mul_montgomery_small(r->words, order->top, a->words, order->top,
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b->words, order->top, group->order_mont);
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}
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static int scalar_mod_mul_montgomery_loose(const EC_GROUP *group, EC_SCALAR *r,
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const EC_LOOSE_SCALAR *a,
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const EC_SCALAR *b) {
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// Although |a| is loose, |bn_mod_mul_montgomery_small| only requires the
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// product not exceed R * |order|. |b| is fully reduced and |a| <
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// 2^BN_num_bits(order) <= R, so this holds.
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const BIGNUM *order = &group->order;
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return bn_mod_mul_montgomery_small(r->words, order->top, a->words, order->top,
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b->words, order->top, group->order_mont);
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}
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// digest_to_scalar interprets |digest_len| bytes from |digest| as a scalar for
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// ECDSA. Note this value is not fully reduced modulo the order, only the
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// correct number of bits.
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static void digest_to_scalar(const EC_GROUP *group, EC_LOOSE_SCALAR *out,
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const uint8_t *digest, size_t digest_len) {
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const BIGNUM *order = &group->order;
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size_t num_bits = BN_num_bits(order);
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// Need to truncate digest if it is too long: first truncate whole bytes.
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if (8 * digest_len > num_bits) {
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digest_len = (num_bits + 7) / 8;
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}
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OPENSSL_memset(out, 0, sizeof(EC_SCALAR));
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for (size_t i = 0; i < digest_len; i++) {
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out->bytes[i] = digest[digest_len - 1 - i];
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}
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// If still too long truncate remaining bits with a shift
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if (8 * digest_len > num_bits) {
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size_t shift = 8 - (num_bits & 0x7);
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for (int i = 0; i < order->top - 1; i++) {
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out->words[i] =
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(out->words[i] >> shift) | (out->words[i + 1] << (BN_BITS2 - shift));
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}
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out->words[order->top - 1] >>= shift;
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}
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}
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// field_element_to_scalar reduces |r| modulo |group->order|. |r| must
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// previously have been reduced modulo |group->field|.
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static int field_element_to_scalar(const EC_GROUP *group, BIGNUM *r) {
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// We must have p < 2×order, assuming p is not tiny (p >= 17). Thus rather we
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// can reduce by performing at most one subtraction.
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//
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// Proof: We only work with prime order curves, so the number of points on
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// the curve is the order. Thus Hasse's theorem gives:
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//
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// |order - (p + 1)| <= 2×sqrt(p)
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// p + 1 - order <= 2×sqrt(p)
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// p + 1 - 2×sqrt(p) <= order
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// p + 1 - 2×(p/4) < order (p/4 > sqrt(p) for p >= 17)
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// p/2 < p/2 + 1 < order
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// p < 2×order
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//
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// Additionally, one can manually check this property for built-in curves. It
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// is enforced for legacy custom curves in |EC_GROUP_set_generator|.
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//
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// TODO(davidben): Introduce |EC_FIELD_ELEMENT|, make this a function from
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// |EC_FIELD_ELEMENT| to |EC_SCALAR|, and cut out the |BIGNUM|. Does this need
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// to be constant-time for signing? |r| is the x-coordinate for kG, which is
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// public unless k was rerolled because |s| was zero.
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assert(!BN_is_negative(r));
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assert(BN_cmp(r, &group->field) < 0);
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if (BN_cmp(r, &group->order) >= 0 &&
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!BN_sub(r, r, &group->order)) {
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return 0;
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}
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assert(!BN_is_negative(r));
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assert(BN_cmp(r, &group->order) < 0);
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return 1;
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}
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ECDSA_SIG *ECDSA_SIG_new(void) {
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ECDSA_SIG *sig = OPENSSL_malloc(sizeof(ECDSA_SIG));
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if (sig == NULL) {
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return NULL;
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}
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sig->r = BN_new();
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sig->s = BN_new();
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if (sig->r == NULL || sig->s == NULL) {
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ECDSA_SIG_free(sig);
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return NULL;
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}
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return sig;
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}
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void ECDSA_SIG_free(ECDSA_SIG *sig) {
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if (sig == NULL) {
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return;
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}
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BN_free(sig->r);
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BN_free(sig->s);
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OPENSSL_free(sig);
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}
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void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **out_r,
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const BIGNUM **out_s) {
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if (out_r != NULL) {
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*out_r = sig->r;
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}
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if (out_s != NULL) {
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*out_s = sig->s;
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}
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}
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int ECDSA_SIG_set0(ECDSA_SIG *sig, BIGNUM *r, BIGNUM *s) {
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if (r == NULL || s == NULL) {
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return 0;
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}
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BN_free(sig->r);
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BN_free(sig->s);
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sig->r = r;
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sig->s = s;
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return 1;
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}
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int ECDSA_do_verify(const uint8_t *digest, size_t digest_len,
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const ECDSA_SIG *sig, const EC_KEY *eckey) {
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const EC_GROUP *group = EC_KEY_get0_group(eckey);
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const EC_POINT *pub_key = EC_KEY_get0_public_key(eckey);
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if (group == NULL || pub_key == NULL || sig == NULL) {
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OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_MISSING_PARAMETERS);
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return 0;
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}
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BN_CTX *ctx = BN_CTX_new();
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if (!ctx) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE);
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return 0;
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}
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int ret = 0;
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EC_POINT *point = NULL;
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BN_CTX_start(ctx);
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BIGNUM *X = BN_CTX_get(ctx);
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if (X == NULL) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB);
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goto err;
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}
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EC_SCALAR r, s, u1, u2, s_inv_mont;
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EC_LOOSE_SCALAR m;
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const BIGNUM *order = EC_GROUP_get0_order(group);
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if (BN_is_zero(sig->r) ||
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!ec_bignum_to_scalar(group, &r, sig->r) ||
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BN_is_zero(sig->s) ||
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!ec_bignum_to_scalar(group, &s, sig->s)) {
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OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_BAD_SIGNATURE);
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goto err;
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}
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// s_inv_mont = s^-1 mod order. We convert the result to Montgomery form for
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// the products below.
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int no_inverse;
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if (!BN_mod_inverse_odd(X, &no_inverse, sig->s, order, ctx) ||
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// TODO(davidben): Add a words version of |BN_mod_inverse_odd| and write
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// into |s_inv_mont| directly.
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!ec_bignum_to_scalar_unchecked(group, &s_inv_mont, X) ||
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!bn_to_montgomery_small(s_inv_mont.words, order->top, s_inv_mont.words,
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order->top, group->order_mont)) {
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goto err;
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}
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// u1 = m * s^-1 mod order
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// u2 = r * s^-1 mod order
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//
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// |s_inv_mont| is in Montgomery form while |m| and |r| are not, so |u1| and
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// |u2| will be taken out of Montgomery form, as desired.
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digest_to_scalar(group, &m, digest, digest_len);
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if (!scalar_mod_mul_montgomery_loose(group, &u1, &m, &s_inv_mont) ||
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!scalar_mod_mul_montgomery(group, &u2, &r, &s_inv_mont)) {
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goto err;
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}
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point = EC_POINT_new(group);
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if (point == NULL) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE);
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goto err;
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}
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if (!ec_point_mul_scalar_public(group, point, &u1, pub_key, &u2, ctx)) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB);
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goto err;
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}
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if (!EC_POINT_get_affine_coordinates_GFp(group, point, X, NULL, ctx)) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB);
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goto err;
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}
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if (!field_element_to_scalar(group, X)) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB);
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goto err;
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}
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// The signature is correct iff |X| is equal to |sig->r|.
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if (BN_ucmp(X, sig->r) != 0) {
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OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_BAD_SIGNATURE);
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goto err;
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}
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ret = 1;
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err:
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BN_CTX_end(ctx);
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BN_CTX_free(ctx);
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EC_POINT_free(point);
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return ret;
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}
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static int ecdsa_sign_setup(const EC_KEY *eckey, BN_CTX *ctx,
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EC_SCALAR *out_kinv_mont, BIGNUM **rp,
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const uint8_t *digest, size_t digest_len,
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const EC_SCALAR *priv_key) {
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EC_POINT *tmp_point = NULL;
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int ret = 0;
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EC_SCALAR k;
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BIGNUM *r = BN_new(); // this value is later returned in *rp
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if (r == NULL) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE);
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goto err;
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}
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const EC_GROUP *group = EC_KEY_get0_group(eckey);
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const BIGNUM *order = EC_GROUP_get0_order(group);
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tmp_point = EC_POINT_new(group);
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if (tmp_point == NULL) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB);
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goto err;
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}
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// Check that the size of the group order is FIPS compliant (FIPS 186-4
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// B.5.2).
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if (BN_num_bits(order) < 160) {
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OPENSSL_PUT_ERROR(ECDSA, EC_R_INVALID_GROUP_ORDER);
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goto err;
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}
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do {
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// Include the private key and message digest in the k generation.
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if (eckey->fixed_k != NULL) {
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if (!ec_bignum_to_scalar(group, &k, eckey->fixed_k)) {
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goto err;
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}
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} else {
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// Pass a SHA512 hash of the private key and digest as additional data
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// into the RBG. This is a hardening measure against entropy failure.
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OPENSSL_COMPILE_ASSERT(SHA512_DIGEST_LENGTH >= 32,
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additional_data_is_too_large_for_sha512);
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SHA512_CTX sha;
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uint8_t additional_data[SHA512_DIGEST_LENGTH];
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SHA512_Init(&sha);
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SHA512_Update(&sha, priv_key->words, order->top * sizeof(BN_ULONG));
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SHA512_Update(&sha, digest, digest_len);
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SHA512_Final(additional_data, &sha);
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if (!ec_random_nonzero_scalar(group, &k, additional_data)) {
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goto err;
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}
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}
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// Compute k^-1. We leave it in the Montgomery domain as an optimization for
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// later operations.
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if (!bn_to_montgomery_small(out_kinv_mont->words, order->top, k.words,
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order->top, group->order_mont) ||
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!bn_mod_inverse_prime_mont_small(out_kinv_mont->words, order->top,
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out_kinv_mont->words, order->top,
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group->order_mont)) {
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goto err;
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}
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// Compute r, the x-coordinate of generator * k.
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if (!ec_point_mul_scalar(group, tmp_point, &k, NULL, NULL, ctx) ||
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!EC_POINT_get_affine_coordinates_GFp(group, tmp_point, r, NULL,
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ctx)) {
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goto err;
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}
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if (!field_element_to_scalar(group, r)) {
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goto err;
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}
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} while (BN_is_zero(r));
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BN_clear_free(*rp);
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*rp = r;
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r = NULL;
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ret = 1;
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err:
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OPENSSL_cleanse(&k, sizeof(k));
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BN_clear_free(r);
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EC_POINT_free(tmp_point);
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return ret;
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}
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ECDSA_SIG *ECDSA_do_sign(const uint8_t *digest, size_t digest_len,
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const EC_KEY *eckey) {
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if (eckey->ecdsa_meth && eckey->ecdsa_meth->sign) {
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OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_NOT_IMPLEMENTED);
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return NULL;
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}
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const EC_GROUP *group = EC_KEY_get0_group(eckey);
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const BIGNUM *priv_key_bn = EC_KEY_get0_private_key(eckey);
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if (group == NULL || priv_key_bn == NULL) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_PASSED_NULL_PARAMETER);
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return NULL;
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}
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const BIGNUM *order = EC_GROUP_get0_order(group);
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int ok = 0;
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ECDSA_SIG *ret = ECDSA_SIG_new();
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BN_CTX *ctx = BN_CTX_new();
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EC_SCALAR kinv_mont, priv_key, r_mont, s;
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EC_LOOSE_SCALAR m, tmp;
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if (ret == NULL || ctx == NULL) {
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OPENSSL_PUT_ERROR(ECDSA, ERR_R_MALLOC_FAILURE);
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return NULL;
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}
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digest_to_scalar(group, &m, digest, digest_len);
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// TODO(davidben): Store the private key as an |EC_SCALAR| so this is obvious
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// via the type system.
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if (!ec_bignum_to_scalar_unchecked(group, &priv_key, priv_key_bn)) {
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goto err;
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}
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for (;;) {
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if (!ecdsa_sign_setup(eckey, ctx, &kinv_mont, &ret->r, digest, digest_len,
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&priv_key)) {
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goto err;
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}
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// Compute priv_key * r (mod order). Note if only one parameter is in the
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// Montgomery domain, |scalar_mod_mul_montgomery| will compute the answer in
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// the normal domain.
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if (!ec_bignum_to_scalar(group, &r_mont, ret->r) ||
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!bn_to_montgomery_small(r_mont.words, order->top, r_mont.words,
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order->top, group->order_mont) ||
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!scalar_mod_mul_montgomery(group, &s, &priv_key, &r_mont)) {
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goto err;
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}
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// Compute tmp = m + priv_key * r.
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scalar_add_loose(group, &tmp, &m, &s);
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// Finally, multiply s by k^-1. That was retained in Montgomery form, so the
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// same technique as the previous multiplication works.
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if (!scalar_mod_mul_montgomery_loose(group, &s, &tmp, &kinv_mont) ||
|
||
!bn_set_words(ret->s, s.words, order->top)) {
|
||
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(&priv_key, sizeof(priv_key));
|
||
OPENSSL_cleanse(&r_mont, sizeof(r_mont));
|
||
OPENSSL_cleanse(&s, sizeof(s));
|
||
OPENSSL_cleanse(&tmp, sizeof(tmp));
|
||
OPENSSL_cleanse(&m, sizeof(m));
|
||
return ret;
|
||
}
|