2 * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright 2015-2016 Cryptography Research, Inc.
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
10 * Originally written by Mike Hamburg
13 #include <openssl/crypto.h>
14 #include <openssl/evp.h>
15 #include "curve448_lcl.h"
18 #include "internal/numbers.h"
22 static c448_error_t oneshot_hash(uint8_t *out, size_t outlen,
23 const uint8_t *in, size_t inlen)
25 EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
30 if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
31 || !EVP_DigestUpdate(hashctx, in, inlen)
32 || !EVP_DigestFinalXOF(hashctx, out, outlen)) {
33 EVP_MD_CTX_free(hashctx);
37 EVP_MD_CTX_free(hashctx);
41 static void clamp(uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES])
43 secret_scalar_ser[0] &= -COFACTOR;
44 secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 1] = 0;
45 secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 2] |= 0x80;
48 static c448_error_t hash_init_with_dom(EVP_MD_CTX *hashctx, uint8_t prehashed,
50 const uint8_t *context,
53 const char *dom_s = "SigEd448";
56 if (context_len > UINT8_MAX)
59 dom[0] = (uint8_t)(2 - (prehashed == 0 ? 1 : 0)
60 - (for_prehash == 0 ? 1 : 0));
61 dom[1] = (uint8_t)context_len;
63 if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
64 || !EVP_DigestUpdate(hashctx, dom_s, strlen(dom_s))
65 || !EVP_DigestUpdate(hashctx, dom, sizeof(dom))
66 || !EVP_DigestUpdate(hashctx, context, context_len))
72 /* In this file because it uses the hash */
73 c448_error_t c448_ed448_convert_private_key_to_x448(
74 uint8_t x[X448_PRIVATE_BYTES],
75 const uint8_t ed [EDDSA_448_PRIVATE_BYTES])
77 /* pass the private key through oneshot_hash function */
78 /* and keep the first X448_PRIVATE_BYTES bytes */
79 return oneshot_hash(x, X448_PRIVATE_BYTES, ed,
80 EDDSA_448_PRIVATE_BYTES);
83 c448_error_t c448_ed448_derive_public_key(
84 uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
85 const uint8_t privkey[EDDSA_448_PRIVATE_BYTES])
87 /* only this much used for keygen */
88 uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES];
89 curve448_scalar_t secret_scalar;
93 if (!oneshot_hash(secret_scalar_ser, sizeof(secret_scalar_ser), privkey,
94 EDDSA_448_PRIVATE_BYTES))
97 clamp(secret_scalar_ser);
99 curve448_scalar_decode_long(secret_scalar, secret_scalar_ser,
100 sizeof(secret_scalar_ser));
103 * Since we are going to mul_by_cofactor during encoding, divide by it
104 * here. However, the EdDSA base point is not the same as the decaf base
105 * point if the sigma isogeny is in use: the EdDSA base point is on
106 * Etwist_d/(1-d) and the decaf base point is on Etwist_d, and when
107 * converted it effectively picks up a factor of 2 from the isogenies. So
108 * we might start at 2 instead of 1.
110 for (c = 1; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
111 curve448_scalar_halve(secret_scalar, secret_scalar);
113 curve448_precomputed_scalarmul(p, curve448_precomputed_base, secret_scalar);
115 curve448_point_mul_by_ratio_and_encode_like_eddsa(pubkey, p);
118 curve448_scalar_destroy(secret_scalar);
119 curve448_point_destroy(p);
120 OPENSSL_cleanse(secret_scalar_ser, sizeof(secret_scalar_ser));
125 c448_error_t c448_ed448_sign(
126 uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
127 const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
128 const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
129 const uint8_t *message, size_t message_len,
130 uint8_t prehashed, const uint8_t *context,
133 curve448_scalar_t secret_scalar;
134 EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
135 c448_error_t ret = C448_FAILURE;
136 curve448_scalar_t nonce_scalar;
137 uint8_t nonce_point[EDDSA_448_PUBLIC_BYTES] = { 0 };
139 curve448_scalar_t challenge_scalar;
146 * Schedule the secret key, First EDDSA_448_PRIVATE_BYTES is serialised
147 * secret scalar,next EDDSA_448_PRIVATE_BYTES bytes is the seed.
149 uint8_t expanded[EDDSA_448_PRIVATE_BYTES * 2];
151 if (!oneshot_hash(expanded, sizeof(expanded), privkey,
152 EDDSA_448_PRIVATE_BYTES))
155 curve448_scalar_decode_long(secret_scalar, expanded,
156 EDDSA_448_PRIVATE_BYTES);
158 /* Hash to create the nonce */
159 if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
160 || !EVP_DigestUpdate(hashctx,
161 expanded + EDDSA_448_PRIVATE_BYTES,
162 EDDSA_448_PRIVATE_BYTES)
163 || !EVP_DigestUpdate(hashctx, message, message_len)) {
164 OPENSSL_cleanse(expanded, sizeof(expanded));
167 OPENSSL_cleanse(expanded, sizeof(expanded));
170 /* Decode the nonce */
172 uint8_t nonce[2 * EDDSA_448_PRIVATE_BYTES];
174 if (!EVP_DigestFinalXOF(hashctx, nonce, sizeof(nonce)))
176 curve448_scalar_decode_long(nonce_scalar, nonce, sizeof(nonce));
177 OPENSSL_cleanse(nonce, sizeof(nonce));
181 /* Scalarmul to create the nonce-point */
182 curve448_scalar_t nonce_scalar_2;
185 curve448_scalar_halve(nonce_scalar_2, nonce_scalar);
186 for (c = 2; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
187 curve448_scalar_halve(nonce_scalar_2, nonce_scalar_2);
189 curve448_precomputed_scalarmul(p, curve448_precomputed_base,
191 curve448_point_mul_by_ratio_and_encode_like_eddsa(nonce_point, p);
192 curve448_point_destroy(p);
193 curve448_scalar_destroy(nonce_scalar_2);
197 uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];
199 /* Compute the challenge */
200 if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
201 || !EVP_DigestUpdate(hashctx, nonce_point, sizeof(nonce_point))
202 || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
203 || !EVP_DigestUpdate(hashctx, message, message_len)
204 || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge)))
207 curve448_scalar_decode_long(challenge_scalar, challenge,
209 OPENSSL_cleanse(challenge, sizeof(challenge));
212 curve448_scalar_mul(challenge_scalar, challenge_scalar, secret_scalar);
213 curve448_scalar_add(challenge_scalar, challenge_scalar, nonce_scalar);
215 OPENSSL_cleanse(signature, EDDSA_448_SIGNATURE_BYTES);
216 memcpy(signature, nonce_point, sizeof(nonce_point));
217 curve448_scalar_encode(&signature[EDDSA_448_PUBLIC_BYTES],
220 curve448_scalar_destroy(secret_scalar);
221 curve448_scalar_destroy(nonce_scalar);
222 curve448_scalar_destroy(challenge_scalar);
226 EVP_MD_CTX_free(hashctx);
230 c448_error_t c448_ed448_sign_prehash(
231 uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
232 const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
233 const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
234 const uint8_t hash[64], const uint8_t *context,
237 return c448_ed448_sign(signature, privkey, pubkey, hash, 64, 1, context,
241 c448_error_t c448_ed448_verify(
242 const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
243 const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
244 const uint8_t *message, size_t message_len,
245 uint8_t prehashed, const uint8_t *context,
248 curve448_point_t pk_point, r_point;
250 curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point, pubkey);
251 curve448_scalar_t challenge_scalar;
252 curve448_scalar_t response_scalar;
254 if (C448_SUCCESS != error)
258 curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point, signature);
259 if (C448_SUCCESS != error)
263 /* Compute the challenge */
264 EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
265 uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];
268 || !hash_init_with_dom(hashctx, prehashed, 0, context,
270 || !EVP_DigestUpdate(hashctx, signature, EDDSA_448_PUBLIC_BYTES)
271 || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
272 || !EVP_DigestUpdate(hashctx, message, message_len)
273 || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) {
274 EVP_MD_CTX_free(hashctx);
278 EVP_MD_CTX_free(hashctx);
279 curve448_scalar_decode_long(challenge_scalar, challenge,
281 OPENSSL_cleanse(challenge, sizeof(challenge));
283 curve448_scalar_sub(challenge_scalar, curve448_scalar_zero,
286 curve448_scalar_decode_long(response_scalar,
287 &signature[EDDSA_448_PUBLIC_BYTES],
288 EDDSA_448_PRIVATE_BYTES);
290 /* pk_point = -c(x(P)) + (cx + k)G = kG */
291 curve448_base_double_scalarmul_non_secret(pk_point,
293 pk_point, challenge_scalar);
294 return c448_succeed_if(curve448_point_eq(pk_point, r_point));
297 c448_error_t c448_ed448_verify_prehash(
298 const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
299 const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
300 const uint8_t hash[64], const uint8_t *context,
303 return c448_ed448_verify(signature, pubkey, hash, 64, 1, context,
307 int ED448_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
308 const uint8_t public_key[57], const uint8_t private_key[57],
309 const uint8_t *context, size_t context_len)
311 return c448_ed448_sign(out_sig, private_key, public_key, message,
312 message_len, 0, context, context_len)
316 int ED448_verify(const uint8_t *message, size_t message_len,
317 const uint8_t signature[114], const uint8_t public_key[57],
318 const uint8_t *context, size_t context_len)
320 return c448_ed448_verify(signature, public_key, message, message_len, 0,
321 context, (uint8_t)context_len) == C448_SUCCESS;
324 int ED448ph_sign(uint8_t *out_sig, const uint8_t hash[64],
325 const uint8_t public_key[57], const uint8_t private_key[57],
326 const uint8_t *context, size_t context_len)
328 return c448_ed448_sign_prehash(out_sig, private_key, public_key, hash,
329 context, context_len) == C448_SUCCESS;
333 int ED448ph_verify(const uint8_t hash[64], const uint8_t signature[114],
334 const uint8_t public_key[57], const uint8_t *context,
337 return c448_ed448_verify_prehash(signature, public_key, hash, context,
338 (uint8_t)context_len) == C448_SUCCESS;
341 int ED448_public_from_private(uint8_t out_public_key[57],
342 const uint8_t private_key[57])
344 return c448_ed448_derive_public_key(out_public_key, private_key)