/*
* Copyright 2017-2020 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_local.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)
{
#ifdef CHARSET_EBCDIC
const char dom_s[] = {0x53, 0x69, 0x67, 0x45,
0x64, 0x34, 0x34, 0x38, 0x00};
#else
const char dom_s[] = "SigEd448";
#endif
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_scalar_t challenge_scalar;
curve448_scalar_t response_scalar;
/* Order in little endian format */
static const uint8_t order[] = {
0xF3, 0x44, 0x58, 0xAB, 0x92, 0xC2, 0x78, 0x23, 0x55, 0x8F, 0xC5, 0x8D,
0x72, 0xC2, 0x6C, 0x21, 0x90, 0x36, 0xD6, 0xAE, 0x49, 0xDB, 0x4E, 0xC4,
0xE9, 0x23, 0xCA, 0x7C, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x3F, 0x00
};
int i;
/*
* Check that s (second 57 bytes of the sig) is less than the order. Both
* s and the order are in little-endian format. This can be done in
* variable time, since if this is not the case the signature if publicly
* invalid.
*/
for (i = EDDSA_448_PUBLIC_BYTES - 1; i >= 0; i--) {
if (signature[i + EDDSA_448_PUBLIC_BYTES] > order[i])
return C448_FAILURE;
if (signature[i + EDDSA_448_PUBLIC_BYTES] < order[i])
break;
}
if (i < 0)
return C448_FAILURE;
error =
curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point, pubkey);
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;
}