vendor/openssl-src/openssl/crypto/ec/curve448/eddsa.c - toolchain/rustc - Git at Google

 /*
  * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
  * Copyright 2015-2016 Cryptography Research, Inc.
  *
  * Licensed under the OpenSSL license (the "License").  You may not use
  * this file except in compliance with the License.  You can obtain a copy
  * in the file LICENSE in the source distribution or at
  * https://www.openssl.org/source/license.html
  *
  * Originally written by Mike Hamburg
  */
 #include <string.h>
 #include <openssl/crypto.h>
 #include <openssl/evp.h>
 #include "curve448_lcl.h"
 #include "word.h"
 #include "ed448.h"
 #include "internal/numbers.h"

 #define COFACTOR 4

 static c448_error_t oneshot_hash(uint8_t *out, size_t outlen,
                                  const uint8_t *in, size_t inlen)
 {
     EVP_MD_CTX *hashctx = EVP_MD_CTX_new();

     if (hashctx == NULL)
         return C448_FAILURE;

     if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
             || !EVP_DigestUpdate(hashctx, in, inlen)
             || !EVP_DigestFinalXOF(hashctx, out, outlen)) {
         EVP_MD_CTX_free(hashctx);
         return C448_FAILURE;
     }

     EVP_MD_CTX_free(hashctx);
     return C448_SUCCESS;
 }

 static void clamp(uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES])
 {
     secret_scalar_ser[0] &= -COFACTOR;
     secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 1] = 0;
     secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 2] |= 0x80;
 }

 static c448_error_t hash_init_with_dom(EVP_MD_CTX *hashctx, uint8_t prehashed,
                                        uint8_t for_prehash,
                                        const uint8_t *context,
                                        size_t context_len)
 {
     const char *dom_s = "SigEd448";
     uint8_t dom[2];

     if (context_len > UINT8_MAX)
         return C448_FAILURE;

     dom[0] = (uint8_t)(2 - (prehashed == 0 ? 1 : 0)
                        - (for_prehash == 0 ? 1 : 0));
     dom[1] = (uint8_t)context_len;

     if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
             || !EVP_DigestUpdate(hashctx, dom_s, strlen(dom_s))
             || !EVP_DigestUpdate(hashctx, dom, sizeof(dom))
             || !EVP_DigestUpdate(hashctx, context, context_len))
         return C448_FAILURE;

     return C448_SUCCESS;
 }

 /* In this file because it uses the hash */
 c448_error_t c448_ed448_convert_private_key_to_x448(
                             uint8_t x[X448_PRIVATE_BYTES],
                             const uint8_t ed [EDDSA_448_PRIVATE_BYTES])
 {
     /* pass the private key through oneshot_hash function */
     /* and keep the first X448_PRIVATE_BYTES bytes */
     return oneshot_hash(x, X448_PRIVATE_BYTES, ed,
                         EDDSA_448_PRIVATE_BYTES);
 }

 c448_error_t c448_ed448_derive_public_key(
                         uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
                         const uint8_t privkey[EDDSA_448_PRIVATE_BYTES])
 {
     /* only this much used for keygen */
     uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES];
     curve448_scalar_t secret_scalar;
     unsigned int c;
     curve448_point_t p;

     if (!oneshot_hash(secret_scalar_ser, sizeof(secret_scalar_ser), privkey,
                       EDDSA_448_PRIVATE_BYTES))
         return C448_FAILURE;

     clamp(secret_scalar_ser);

     curve448_scalar_decode_long(secret_scalar, secret_scalar_ser,
                                 sizeof(secret_scalar_ser));

     /*
      * Since we are going to mul_by_cofactor during encoding, divide by it
      * here. However, the EdDSA base point is not the same as the decaf base
      * point if the sigma isogeny is in use: the EdDSA base point is on
      * Etwist_d/(1-d) and the decaf base point is on Etwist_d, and when
      * converted it effectively picks up a factor of 2 from the isogenies.  So
      * we might start at 2 instead of 1.
      */
     for (c = 1; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
         curve448_scalar_halve(secret_scalar, secret_scalar);

     curve448_precomputed_scalarmul(p, curve448_precomputed_base, secret_scalar);

     curve448_point_mul_by_ratio_and_encode_like_eddsa(pubkey, p);

     /* Cleanup */
     curve448_scalar_destroy(secret_scalar);
     curve448_point_destroy(p);
     OPENSSL_cleanse(secret_scalar_ser, sizeof(secret_scalar_ser));

     return C448_SUCCESS;
 }

 c448_error_t c448_ed448_sign(
                         uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
                         const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
                         const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
                         const uint8_t *message, size_t message_len,
                         uint8_t prehashed, const uint8_t *context,
                         size_t context_len)
 {
     curve448_scalar_t secret_scalar;
     EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
     c448_error_t ret = C448_FAILURE;
     curve448_scalar_t nonce_scalar;
     uint8_t nonce_point[EDDSA_448_PUBLIC_BYTES] = { 0 };
     unsigned int c;
     curve448_scalar_t challenge_scalar;

     if (hashctx == NULL)
         return C448_FAILURE;

     {
         /*
          * Schedule the secret key, First EDDSA_448_PRIVATE_BYTES is serialised
          * secret scalar,next EDDSA_448_PRIVATE_BYTES bytes is the seed.
          */
         uint8_t expanded[EDDSA_448_PRIVATE_BYTES * 2];

         if (!oneshot_hash(expanded, sizeof(expanded), privkey,
                           EDDSA_448_PRIVATE_BYTES))
             goto err;
         clamp(expanded);
         curve448_scalar_decode_long(secret_scalar, expanded,
                                     EDDSA_448_PRIVATE_BYTES);

         /* Hash to create the nonce */
         if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
                 || !EVP_DigestUpdate(hashctx,
                                      expanded + EDDSA_448_PRIVATE_BYTES,
                                      EDDSA_448_PRIVATE_BYTES)
                 || !EVP_DigestUpdate(hashctx, message, message_len)) {
             OPENSSL_cleanse(expanded, sizeof(expanded));
             goto err;
         }
         OPENSSL_cleanse(expanded, sizeof(expanded));
     }

     /* Decode the nonce */
     {
         uint8_t nonce[2 * EDDSA_448_PRIVATE_BYTES];

         if (!EVP_DigestFinalXOF(hashctx, nonce, sizeof(nonce)))
             goto err;
         curve448_scalar_decode_long(nonce_scalar, nonce, sizeof(nonce));
         OPENSSL_cleanse(nonce, sizeof(nonce));
     }

     {
         /* Scalarmul to create the nonce-point */
         curve448_scalar_t nonce_scalar_2;
         curve448_point_t p;

         curve448_scalar_halve(nonce_scalar_2, nonce_scalar);
         for (c = 2; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
             curve448_scalar_halve(nonce_scalar_2, nonce_scalar_2);

         curve448_precomputed_scalarmul(p, curve448_precomputed_base,
                                        nonce_scalar_2);
         curve448_point_mul_by_ratio_and_encode_like_eddsa(nonce_point, p);
         curve448_point_destroy(p);
         curve448_scalar_destroy(nonce_scalar_2);
     }

     {
         uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];

         /* Compute the challenge */
         if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
                 || !EVP_DigestUpdate(hashctx, nonce_point, sizeof(nonce_point))
                 || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
                 || !EVP_DigestUpdate(hashctx, message, message_len)
                 || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge)))
             goto err;

         curve448_scalar_decode_long(challenge_scalar, challenge,
                                     sizeof(challenge));
         OPENSSL_cleanse(challenge, sizeof(challenge));
     }

     curve448_scalar_mul(challenge_scalar, challenge_scalar, secret_scalar);
     curve448_scalar_add(challenge_scalar, challenge_scalar, nonce_scalar);

     OPENSSL_cleanse(signature, EDDSA_448_SIGNATURE_BYTES);
     memcpy(signature, nonce_point, sizeof(nonce_point));
     curve448_scalar_encode(&signature[EDDSA_448_PUBLIC_BYTES],
                            challenge_scalar);

     curve448_scalar_destroy(secret_scalar);
     curve448_scalar_destroy(nonce_scalar);
     curve448_scalar_destroy(challenge_scalar);

     ret = C448_SUCCESS;
  err:
     EVP_MD_CTX_free(hashctx);
     return ret;
 }

 c448_error_t c448_ed448_sign_prehash(
                         uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
                         const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
                         const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
                         const uint8_t hash[64], const uint8_t *context,
                         size_t context_len)
 {
     return c448_ed448_sign(signature, privkey, pubkey, hash, 64, 1, context,
                            context_len);
 }

 c448_error_t c448_ed448_verify(
                     const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
                     const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
                     const uint8_t *message, size_t message_len,
                     uint8_t prehashed, const uint8_t *context,
                     uint8_t context_len)
 {
     curve448_point_t pk_point, r_point;
     c448_error_t error =
         curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point, pubkey);
     curve448_scalar_t challenge_scalar;
     curve448_scalar_t response_scalar;

     if (C448_SUCCESS != error)
         return error;

     error =
         curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point, signature);
     if (C448_SUCCESS != error)
         return error;

     {
         /* Compute the challenge */
         EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
         uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];

         if (hashctx == NULL
                 || !hash_init_with_dom(hashctx, prehashed, 0, context,
                                        context_len)
                 || !EVP_DigestUpdate(hashctx, signature, EDDSA_448_PUBLIC_BYTES)
                 || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
                 || !EVP_DigestUpdate(hashctx, message, message_len)
                 || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) {
             EVP_MD_CTX_free(hashctx);
             return C448_FAILURE;
         }

         EVP_MD_CTX_free(hashctx);
         curve448_scalar_decode_long(challenge_scalar, challenge,
                                     sizeof(challenge));
         OPENSSL_cleanse(challenge, sizeof(challenge));
     }
     curve448_scalar_sub(challenge_scalar, curve448_scalar_zero,
                         challenge_scalar);

     curve448_scalar_decode_long(response_scalar,
                                 &signature[EDDSA_448_PUBLIC_BYTES],
                                 EDDSA_448_PRIVATE_BYTES);

     /* pk_point = -c(x(P)) + (cx + k)G = kG */
     curve448_base_double_scalarmul_non_secret(pk_point,
                                               response_scalar,
                                               pk_point, challenge_scalar);
     return c448_succeed_if(curve448_point_eq(pk_point, r_point));
 }

 c448_error_t c448_ed448_verify_prehash(
                     const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
                     const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
                     const uint8_t hash[64], const uint8_t *context,
                     uint8_t context_len)
 {
     return c448_ed448_verify(signature, pubkey, hash, 64, 1, context,
                              context_len);
 }

 int ED448_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
                const uint8_t public_key[57], const uint8_t private_key[57],
                const uint8_t *context, size_t context_len)
 {
     return c448_ed448_sign(out_sig, private_key, public_key, message,
                            message_len, 0, context, context_len)
         == C448_SUCCESS;
 }

 int ED448_verify(const uint8_t *message, size_t message_len,
                  const uint8_t signature[114], const uint8_t public_key[57],
                  const uint8_t *context, size_t context_len)
 {
     return c448_ed448_verify(signature, public_key, message, message_len, 0,
                              context, (uint8_t)context_len) == C448_SUCCESS;
 }

 int ED448ph_sign(uint8_t *out_sig, const uint8_t hash[64],
                  const uint8_t public_key[57], const uint8_t private_key[57],
                  const uint8_t *context, size_t context_len)
 {
     return c448_ed448_sign_prehash(out_sig, private_key, public_key, hash,
                                    context, context_len) == C448_SUCCESS;

 }

 int ED448ph_verify(const uint8_t hash[64], const uint8_t signature[114],
                    const uint8_t public_key[57], const uint8_t *context,
                    size_t context_len)
 {
     return c448_ed448_verify_prehash(signature, public_key, hash, context,
                                      (uint8_t)context_len) == C448_SUCCESS;
 }

 int ED448_public_from_private(uint8_t out_public_key[57],
                               const uint8_t private_key[57])
 {
     return c448_ed448_derive_public_key(out_public_key, private_key)
         == C448_SUCCESS;
 }
	/*
	* Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
	* Copyright 2015-2016 Cryptography Research, Inc.
	*
	* Licensed under the OpenSSL license (the "License"). You may not use
	* this file except in compliance with the License. You can obtain a copy
	* in the file LICENSE in the source distribution or at
	* https://www.openssl.org/source/license.html
	*
	* Originally written by Mike Hamburg
	*/
	#include <string.h>
	#include <openssl/crypto.h>
	#include <openssl/evp.h>
	#include "curve448_lcl.h"
	#include "word.h"
	#include "ed448.h"
	#include "internal/numbers.h"

	#define COFACTOR 4

	static c448_error_t oneshot_hash(uint8_t *out, size_t outlen,
	const uint8_t *in, size_t inlen)
	{
	EVP_MD_CTX *hashctx = EVP_MD_CTX_new();

	if (hashctx == NULL)
	return C448_FAILURE;

	if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
	\|\| !EVP_DigestUpdate(hashctx, in, inlen)
	\|\| !EVP_DigestFinalXOF(hashctx, out, outlen)) {
	EVP_MD_CTX_free(hashctx);
	return C448_FAILURE;
	}

	EVP_MD_CTX_free(hashctx);
	return C448_SUCCESS;
	}

	static void clamp(uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES])
	{
	secret_scalar_ser[0] &= -COFACTOR;
	secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 1] = 0;
	secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 2] \|= 0x80;
	}

	static c448_error_t hash_init_with_dom(EVP_MD_CTX *hashctx, uint8_t prehashed,
	uint8_t for_prehash,
	const uint8_t *context,
	size_t context_len)
	{
	const char *dom_s = "SigEd448";
	uint8_t dom[2];

	if (context_len > UINT8_MAX)
	return C448_FAILURE;

	dom[0] = (uint8_t)(2 - (prehashed == 0 ? 1 : 0)
	- (for_prehash == 0 ? 1 : 0));
	dom[1] = (uint8_t)context_len;

	if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
	\|\| !EVP_DigestUpdate(hashctx, dom_s, strlen(dom_s))
	\|\| !EVP_DigestUpdate(hashctx, dom, sizeof(dom))
	\|\| !EVP_DigestUpdate(hashctx, context, context_len))
	return C448_FAILURE;

	return C448_SUCCESS;
	}

	/* In this file because it uses the hash */
	c448_error_t c448_ed448_convert_private_key_to_x448(
	uint8_t x[X448_PRIVATE_BYTES],
	const uint8_t ed [EDDSA_448_PRIVATE_BYTES])
	{
	/* pass the private key through oneshot_hash function */
	/* and keep the first X448_PRIVATE_BYTES bytes */
	return oneshot_hash(x, X448_PRIVATE_BYTES, ed,
	EDDSA_448_PRIVATE_BYTES);
	}

	c448_error_t c448_ed448_derive_public_key(
	uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
	const uint8_t privkey[EDDSA_448_PRIVATE_BYTES])
	{
	/* only this much used for keygen */
	uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES];
	curve448_scalar_t secret_scalar;
	unsigned int c;
	curve448_point_t p;

	if (!oneshot_hash(secret_scalar_ser, sizeof(secret_scalar_ser), privkey,
	EDDSA_448_PRIVATE_BYTES))
	return C448_FAILURE;

	clamp(secret_scalar_ser);

	curve448_scalar_decode_long(secret_scalar, secret_scalar_ser,
	sizeof(secret_scalar_ser));

	/*
	* Since we are going to mul_by_cofactor during encoding, divide by it
	* here. However, the EdDSA base point is not the same as the decaf base
	* point if the sigma isogeny is in use: the EdDSA base point is on
	* Etwist_d/(1-d) and the decaf base point is on Etwist_d, and when
	* converted it effectively picks up a factor of 2 from the isogenies. So
	* we might start at 2 instead of 1.
	*/
	for (c = 1; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
	curve448_scalar_halve(secret_scalar, secret_scalar);

	curve448_precomputed_scalarmul(p, curve448_precomputed_base, secret_scalar);

	curve448_point_mul_by_ratio_and_encode_like_eddsa(pubkey, p);

	/* Cleanup */
	curve448_scalar_destroy(secret_scalar);
	curve448_point_destroy(p);
	OPENSSL_cleanse(secret_scalar_ser, sizeof(secret_scalar_ser));

	return C448_SUCCESS;
	}

	c448_error_t c448_ed448_sign(
	uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
	const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
	const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
	const uint8_t *message, size_t message_len,
	uint8_t prehashed, const uint8_t *context,
	size_t context_len)
	{
	curve448_scalar_t secret_scalar;
	EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
	c448_error_t ret = C448_FAILURE;
	curve448_scalar_t nonce_scalar;
	uint8_t nonce_point[EDDSA_448_PUBLIC_BYTES] = { 0 };
	unsigned int c;
	curve448_scalar_t challenge_scalar;

	if (hashctx == NULL)
	return C448_FAILURE;

	{
	/*
	* Schedule the secret key, First EDDSA_448_PRIVATE_BYTES is serialised
	* secret scalar,next EDDSA_448_PRIVATE_BYTES bytes is the seed.
	*/
	uint8_t expanded[EDDSA_448_PRIVATE_BYTES * 2];

	if (!oneshot_hash(expanded, sizeof(expanded), privkey,
	EDDSA_448_PRIVATE_BYTES))
	goto err;
	clamp(expanded);
	curve448_scalar_decode_long(secret_scalar, expanded,
	EDDSA_448_PRIVATE_BYTES);

	/* Hash to create the nonce */
	if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
	\|\| !EVP_DigestUpdate(hashctx,
	expanded + EDDSA_448_PRIVATE_BYTES,
	EDDSA_448_PRIVATE_BYTES)
	\|\| !EVP_DigestUpdate(hashctx, message, message_len)) {
	OPENSSL_cleanse(expanded, sizeof(expanded));
	goto err;
	}
	OPENSSL_cleanse(expanded, sizeof(expanded));
	}

	/* Decode the nonce */
	{
	uint8_t nonce[2 * EDDSA_448_PRIVATE_BYTES];

	if (!EVP_DigestFinalXOF(hashctx, nonce, sizeof(nonce)))
	goto err;
	curve448_scalar_decode_long(nonce_scalar, nonce, sizeof(nonce));
	OPENSSL_cleanse(nonce, sizeof(nonce));
	}

	{
	/* Scalarmul to create the nonce-point */
	curve448_scalar_t nonce_scalar_2;
	curve448_point_t p;

	curve448_scalar_halve(nonce_scalar_2, nonce_scalar);
	for (c = 2; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
	curve448_scalar_halve(nonce_scalar_2, nonce_scalar_2);

	curve448_precomputed_scalarmul(p, curve448_precomputed_base,
	nonce_scalar_2);
	curve448_point_mul_by_ratio_and_encode_like_eddsa(nonce_point, p);
	curve448_point_destroy(p);
	curve448_scalar_destroy(nonce_scalar_2);
	}

	{
	uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];

	/* Compute the challenge */
	if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
	\|\| !EVP_DigestUpdate(hashctx, nonce_point, sizeof(nonce_point))
	\|\| !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
	\|\| !EVP_DigestUpdate(hashctx, message, message_len)
	\|\| !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge)))
	goto err;

	curve448_scalar_decode_long(challenge_scalar, challenge,
	sizeof(challenge));
	OPENSSL_cleanse(challenge, sizeof(challenge));
	}

	curve448_scalar_mul(challenge_scalar, challenge_scalar, secret_scalar);
	curve448_scalar_add(challenge_scalar, challenge_scalar, nonce_scalar);

	OPENSSL_cleanse(signature, EDDSA_448_SIGNATURE_BYTES);
	memcpy(signature, nonce_point, sizeof(nonce_point));
	curve448_scalar_encode(&signature[EDDSA_448_PUBLIC_BYTES],
	challenge_scalar);

	curve448_scalar_destroy(secret_scalar);
	curve448_scalar_destroy(nonce_scalar);
	curve448_scalar_destroy(challenge_scalar);

	ret = C448_SUCCESS;
	err:
	EVP_MD_CTX_free(hashctx);
	return ret;
	}

	c448_error_t c448_ed448_sign_prehash(
	uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
	const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
	const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
	const uint8_t hash[64], const uint8_t *context,
	size_t context_len)
	{
	return c448_ed448_sign(signature, privkey, pubkey, hash, 64, 1, context,
	context_len);
	}

	c448_error_t c448_ed448_verify(
	const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
	const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
	const uint8_t *message, size_t message_len,
	uint8_t prehashed, const uint8_t *context,
	uint8_t context_len)
	{
	curve448_point_t pk_point, r_point;
	c448_error_t error =
	curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point, pubkey);
	curve448_scalar_t challenge_scalar;
	curve448_scalar_t response_scalar;

	if (C448_SUCCESS != error)
	return error;

	error =
	curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point, signature);
	if (C448_SUCCESS != error)
	return error;

	{
	/* Compute the challenge */
	EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
	uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];

	if (hashctx == NULL
	\|\| !hash_init_with_dom(hashctx, prehashed, 0, context,
	context_len)
	\|\| !EVP_DigestUpdate(hashctx, signature, EDDSA_448_PUBLIC_BYTES)
	\|\| !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
	\|\| !EVP_DigestUpdate(hashctx, message, message_len)
	\|\| !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) {
	EVP_MD_CTX_free(hashctx);
	return C448_FAILURE;
	}

	EVP_MD_CTX_free(hashctx);
	curve448_scalar_decode_long(challenge_scalar, challenge,
	sizeof(challenge));
	OPENSSL_cleanse(challenge, sizeof(challenge));
	}
	curve448_scalar_sub(challenge_scalar, curve448_scalar_zero,
	challenge_scalar);

	curve448_scalar_decode_long(response_scalar,
	&signature[EDDSA_448_PUBLIC_BYTES],
	EDDSA_448_PRIVATE_BYTES);

	/* pk_point = -c(x(P)) + (cx + k)G = kG */
	curve448_base_double_scalarmul_non_secret(pk_point,
	response_scalar,
	pk_point, challenge_scalar);
	return c448_succeed_if(curve448_point_eq(pk_point, r_point));
	}

	c448_error_t c448_ed448_verify_prehash(
	const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
	const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
	const uint8_t hash[64], const uint8_t *context,
	uint8_t context_len)
	{
	return c448_ed448_verify(signature, pubkey, hash, 64, 1, context,
	context_len);
	}

	int ED448_sign(uint8_t out_sig, const uint8_t message, size_t message_len,
	const uint8_t public_key[57], const uint8_t private_key[57],
	const uint8_t *context, size_t context_len)
	{
	return c448_ed448_sign(out_sig, private_key, public_key, message,
	message_len, 0, context, context_len)
	== C448_SUCCESS;
	}

	int ED448_verify(const uint8_t *message, size_t message_len,
	const uint8_t signature[114], const uint8_t public_key[57],
	const uint8_t *context, size_t context_len)
	{
	return c448_ed448_verify(signature, public_key, message, message_len, 0,
	context, (uint8_t)context_len) == C448_SUCCESS;
	}

	int ED448ph_sign(uint8_t *out_sig, const uint8_t hash[64],
	const uint8_t public_key[57], const uint8_t private_key[57],
	const uint8_t *context, size_t context_len)
	{
	return c448_ed448_sign_prehash(out_sig, private_key, public_key, hash,
	context, context_len) == C448_SUCCESS;

	}

	int ED448ph_verify(const uint8_t hash[64], const uint8_t signature[114],
	const uint8_t public_key[57], const uint8_t *context,
	size_t context_len)
	{
	return c448_ed448_verify_prehash(signature, public_key, hash, context,
	(uint8_t)context_len) == C448_SUCCESS;
	}

	int ED448_public_from_private(uint8_t out_public_key[57],
	const uint8_t private_key[57])
	{
	return c448_ed448_derive_public_key(out_public_key, private_key)
	== C448_SUCCESS;
	}