crypto/fipsmodule/ecdsa/ecdsa.c - boringssl.git - Git at Google

 /* ====================================================================
  * 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 "../../internal.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_WORDS];
   bn_reduce_once_in_place(out->words, 0 /* no carry */, order->d, tmp,
                           order->width);
 }

 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);
 }

 const BIGNUM *ECDSA_SIG_get0_r(const ECDSA_SIG *sig) {
   return sig->r;
 }

 const BIGNUM *ECDSA_SIG_get0_s(const ECDSA_SIG *sig) {
   return sig->s;
 }

 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;
   }

   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);
     return 0;
   }

   // s_inv_mont = s^-1 in the Montgomery domain.
   if (!ec_scalar_to_montgomery_inv_vartime(group, &s_inv_mont, &s)) {
     OPENSSL_PUT_ERROR(ECDSA, ERR_R_INTERNAL_ERROR);
     return 0;
   }

   // 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);

   EC_RAW_POINT point;
   if (!ec_point_mul_scalar_public(group, &point, &u1, &pub_key->raw, &u2)) {
     OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB);
     return 0;
   }

   if (!ec_cmp_x_coordinate(group, &point, &r)) {
     OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_BAD_SIGNATURE);
     return 0;
   }

   return 1;
 }

 static ECDSA_SIG *ecdsa_sign_impl(const EC_GROUP *group, int *out_retry,
                                   const EC_SCALAR *priv_key, const EC_SCALAR *k,
                                   const uint8_t *digest, size_t digest_len) {
   *out_retry = 0;

   // Check that the size of the group order is FIPS compliant (FIPS 186-4
   // B.5.2).
   const BIGNUM *order = EC_GROUP_get0_order(group);
   if (BN_num_bits(order) < 160) {
     OPENSSL_PUT_ERROR(ECDSA, EC_R_INVALID_GROUP_ORDER);
     return NULL;
   }

   // Compute r, the x-coordinate of k * generator.
   EC_RAW_POINT tmp_point;
   EC_SCALAR r;
   if (!ec_point_mul_scalar_base(group, &tmp_point, k) ||
       !ec_get_x_coordinate_as_scalar(group, &r, &tmp_point)) {
     return NULL;
   }

   if (ec_scalar_is_zero(group, &r)) {
     *out_retry = 1;
     return NULL;
   }

   // s = priv_key * r. Note if only one parameter is in the Montgomery domain,
   // |ec_scalar_mod_mul_montgomery| will compute the answer in the normal
   // domain.
   EC_SCALAR s;
   ec_scalar_to_montgomery(group, &s, &r);
   ec_scalar_mul_montgomery(group, &s, priv_key, &s);

   // s = m + priv_key * r.
   EC_SCALAR tmp;
   digest_to_scalar(group, &tmp, digest, digest_len);
   ec_scalar_add(group, &s, &s, &tmp);

   // s = k^-1 * (m + priv_key * r). First, we compute k^-1 in the Montgomery
   // domain. This is |ec_scalar_to_montgomery| followed by
   // |ec_scalar_inv0_montgomery|, but |ec_scalar_inv0_montgomery| followed by
   // |ec_scalar_from_montgomery| is equivalent and slightly more efficient.
   // Then, as above, only one parameter is in the Montgomery domain, so the
   // result is in the normal domain. Finally, note k is non-zero (or computing r
   // would fail), so the inverse must exist.
   ec_scalar_inv0_montgomery(group, &tmp, k);     // tmp = k^-1 R^2
   ec_scalar_from_montgomery(group, &tmp, &tmp);  // tmp = k^-1 R
   ec_scalar_mul_montgomery(group, &s, &s, &tmp);
   if (ec_scalar_is_zero(group, &s)) {
     *out_retry = 1;
     return NULL;
   }

   ECDSA_SIG *ret = ECDSA_SIG_new();
   if (ret == NULL ||  //
       !bn_set_words(ret->r, r.words, order->width) ||
       !bn_set_words(ret->s, s.words, order->width)) {
     ECDSA_SIG_free(ret);
     return NULL;
   }
   return ret;
 }

 ECDSA_SIG *ecdsa_sign_with_nonce_for_known_answer_test(const uint8_t *digest,
                                                        size_t digest_len,
                                                        const EC_KEY *eckey,
                                                        const uint8_t *nonce,
                                                        size_t nonce_len) {
   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 EC_SCALAR *priv_key = &eckey->priv_key->scalar;

   EC_SCALAR k;
   if (!ec_scalar_from_bytes(group, &k, nonce, nonce_len)) {
     return NULL;
   }
   int retry_ignored;
   return ecdsa_sign_impl(group, &retry_ignored, priv_key, &k, digest,
                          digest_len);
 }

 // This function is only exported for testing and is not called in production
 // code.
 ECDSA_SIG *ECDSA_sign_with_nonce_and_leak_private_key_for_testing(
     const uint8_t *digest, size_t digest_len, const EC_KEY *eckey,
     const uint8_t *nonce, size_t nonce_len) {
   return ecdsa_sign_with_nonce_for_known_answer_test(digest, digest_len, eckey,
                                                      nonce, nonce_len);
 }

 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;

   // 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_STATIC_ASSERT(SHA512_DIGEST_LENGTH >= 32,
                         "additional_data is too large for SHA-512");
   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);

   for (;;) {
     EC_SCALAR k;
     if (!ec_random_nonzero_scalar(group, &k, additional_data)) {
       return NULL;
     }

     int retry;
     ECDSA_SIG *sig =
         ecdsa_sign_impl(group, &retry, priv_key, &k, digest, digest_len);
     if (sig != NULL || !retry) {
       return sig;
     }
   }
 }
	/* ====================================================================
	* 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 "../../internal.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_WORDS];
	bn_reduce_once_in_place(out->words, 0 /* no carry */, order->d, tmp,
	order->width);
	}

	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);
	}

	const BIGNUM ECDSA_SIG_get0_r(const ECDSA_SIG sig) {
	return sig->r;
	}

	const BIGNUM ECDSA_SIG_get0_s(const ECDSA_SIG sig) {
	return sig->s;
	}

	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;
	}

	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);
	return 0;
	}

	// s_inv_mont = s^-1 in the Montgomery domain.
	if (!ec_scalar_to_montgomery_inv_vartime(group, &s_inv_mont, &s)) {
	OPENSSL_PUT_ERROR(ECDSA, ERR_R_INTERNAL_ERROR);
	return 0;
	}

	// 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);

	EC_RAW_POINT point;
	if (!ec_point_mul_scalar_public(group, &point, &u1, &pub_key->raw, &u2)) {
	OPENSSL_PUT_ERROR(ECDSA, ERR_R_EC_LIB);
	return 0;
	}

	if (!ec_cmp_x_coordinate(group, &point, &r)) {
	OPENSSL_PUT_ERROR(ECDSA, ECDSA_R_BAD_SIGNATURE);
	return 0;
	}

	return 1;
	}

	static ECDSA_SIG ecdsa_sign_impl(const EC_GROUP group, int *out_retry,
	const EC_SCALAR priv_key, const EC_SCALAR k,
	const uint8_t *digest, size_t digest_len) {
	*out_retry = 0;

	// Check that the size of the group order is FIPS compliant (FIPS 186-4
	// B.5.2).
	const BIGNUM *order = EC_GROUP_get0_order(group);
	if (BN_num_bits(order) < 160) {
	OPENSSL_PUT_ERROR(ECDSA, EC_R_INVALID_GROUP_ORDER);
	return NULL;
	}

	// Compute r, the x-coordinate of k * generator.
	EC_RAW_POINT tmp_point;
	EC_SCALAR r;
	if (!ec_point_mul_scalar_base(group, &tmp_point, k) \|\|
	!ec_get_x_coordinate_as_scalar(group, &r, &tmp_point)) {
	return NULL;
	}

	if (ec_scalar_is_zero(group, &r)) {
	*out_retry = 1;
	return NULL;
	}

	// s = priv_key * r. Note if only one parameter is in the Montgomery domain,
	// \|ec_scalar_mod_mul_montgomery\| will compute the answer in the normal
	// domain.
	EC_SCALAR s;
	ec_scalar_to_montgomery(group, &s, &r);
	ec_scalar_mul_montgomery(group, &s, priv_key, &s);

	// s = m + priv_key * r.
	EC_SCALAR tmp;
	digest_to_scalar(group, &tmp, digest, digest_len);
	ec_scalar_add(group, &s, &s, &tmp);

	// s = k^-1 * (m + priv_key * r). First, we compute k^-1 in the Montgomery
	// domain. This is \|ec_scalar_to_montgomery\| followed by
	// \|ec_scalar_inv0_montgomery\|, but \|ec_scalar_inv0_montgomery\| followed by
	// \|ec_scalar_from_montgomery\| is equivalent and slightly more efficient.
	// Then, as above, only one parameter is in the Montgomery domain, so the
	// result is in the normal domain. Finally, note k is non-zero (or computing r
	// would fail), so the inverse must exist.
	ec_scalar_inv0_montgomery(group, &tmp, k); // tmp = k^-1 R^2
	ec_scalar_from_montgomery(group, &tmp, &tmp); // tmp = k^-1 R
	ec_scalar_mul_montgomery(group, &s, &s, &tmp);
	if (ec_scalar_is_zero(group, &s)) {
	*out_retry = 1;
	return NULL;
	}

	ECDSA_SIG *ret = ECDSA_SIG_new();
	if (ret == NULL \|\| //
	!bn_set_words(ret->r, r.words, order->width) \|\|
	!bn_set_words(ret->s, s.words, order->width)) {
	ECDSA_SIG_free(ret);
	return NULL;
	}
	return ret;
	}

	ECDSA_SIG ecdsa_sign_with_nonce_for_known_answer_test(const uint8_t digest,
	size_t digest_len,
	const EC_KEY *eckey,
	const uint8_t *nonce,
	size_t nonce_len) {
	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 EC_SCALAR *priv_key = &eckey->priv_key->scalar;

	EC_SCALAR k;
	if (!ec_scalar_from_bytes(group, &k, nonce, nonce_len)) {
	return NULL;
	}
	int retry_ignored;
	return ecdsa_sign_impl(group, &retry_ignored, priv_key, &k, digest,
	digest_len);
	}

	// This function is only exported for testing and is not called in production
	// code.
	ECDSA_SIG *ECDSA_sign_with_nonce_and_leak_private_key_for_testing(
	const uint8_t digest, size_t digest_len, const EC_KEY eckey,
	const uint8_t *nonce, size_t nonce_len) {
	return ecdsa_sign_with_nonce_for_known_answer_test(digest, digest_len, eckey,
	nonce, nonce_len);
	}

	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;

	// 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_STATIC_ASSERT(SHA512_DIGEST_LENGTH >= 32,
	"additional_data is too large for SHA-512");
	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);

	for (;;) {
	EC_SCALAR k;
	if (!ec_random_nonzero_scalar(group, &k, additional_data)) {
	return NULL;
	}

	int retry;
	ECDSA_SIG *sig =
	ecdsa_sign_impl(group, &retry, priv_key, &k, digest, digest_len);
	if (sig != NULL \|\| !retry) {
	return sig;
	}
	}
	}