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
12 #include <openssl/crypto.h>
13 #include <openssl/evp.h>
15 #include "curve448_lcl.h"
19 #include "internal/numbers.h"
23 static c448_error_t oneshot_hash(uint8_t *out, size_t outlen,
24 const uint8_t *in, size_t inlen)
26 EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
31 if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
32 || !EVP_DigestUpdate(hashctx, in, inlen)
33 || !EVP_DigestFinalXOF(hashctx, out, outlen)) {
34 EVP_MD_CTX_free(hashctx);
38 EVP_MD_CTX_free(hashctx);
42 static void clamp(uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES])
44 uint8_t hibit = (1 << 0) >> 1;
47 secret_scalar_ser[0] &= -COFACTOR;
49 secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 1] = 0;
50 secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 2] |= 0x80;
52 secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 1] &= hibit - 1;
53 secret_scalar_ser[EDDSA_448_PRIVATE_BYTES - 1] |= hibit;
57 static c448_error_t hash_init_with_dom(EVP_MD_CTX *hashctx, uint8_t prehashed,
59 const uint8_t *context,
62 const char *dom_s = "SigEd448";
65 dom[0] = 2 + word_is_zero(prehashed) + word_is_zero(for_prehash);
66 dom[1] = (uint8_t)context_len;
68 if (context_len > UINT8_MAX)
71 if (!EVP_DigestInit_ex(hashctx, EVP_shake256(), NULL)
72 || !EVP_DigestUpdate(hashctx, dom_s, strlen(dom_s))
73 || !EVP_DigestUpdate(hashctx, dom, sizeof(dom))
74 || !EVP_DigestUpdate(hashctx, context, context_len))
80 /* In this file because it uses the hash */
81 c448_error_t c448_ed448_convert_private_key_to_x448(
82 uint8_t x[X448_PRIVATE_BYTES],
83 const uint8_t ed [EDDSA_448_PRIVATE_BYTES])
85 /* pass the private key through oneshot_hash function */
86 /* and keep the first X448_PRIVATE_BYTES bytes */
87 return oneshot_hash(x, X448_PRIVATE_BYTES, ed,
88 EDDSA_448_PRIVATE_BYTES);
91 c448_error_t c448_ed448_derive_public_key(
92 uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
93 const uint8_t privkey[EDDSA_448_PRIVATE_BYTES])
95 /* only this much used for keygen */
96 uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES];
97 curve448_scalar_t secret_scalar;
101 if (!oneshot_hash(secret_scalar_ser, sizeof(secret_scalar_ser), privkey,
102 EDDSA_448_PRIVATE_BYTES))
105 clamp(secret_scalar_ser);
107 curve448_scalar_decode_long(secret_scalar, secret_scalar_ser,
108 sizeof(secret_scalar_ser));
111 * Since we are going to mul_by_cofactor during encoding, divide by it
112 * here. However, the EdDSA base point is not the same as the decaf base
113 * point if the sigma isogeny is in use: the EdDSA base point is on
114 * Etwist_d/(1-d) and the decaf base point is on Etwist_d, and when
115 * converted it effectively picks up a factor of 2 from the isogenies. So
116 * we might start at 2 instead of 1.
118 for (c = 1; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
119 curve448_scalar_halve(secret_scalar, secret_scalar);
121 curve448_precomputed_scalarmul(p, curve448_precomputed_base, secret_scalar);
123 curve448_point_mul_by_ratio_and_encode_like_eddsa(pubkey, p);
126 curve448_scalar_destroy(secret_scalar);
127 curve448_point_destroy(p);
128 OPENSSL_cleanse(secret_scalar_ser, sizeof(secret_scalar_ser));
133 c448_error_t c448_ed448_sign(
134 uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
135 const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
136 const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
137 const uint8_t *message, size_t message_len,
138 uint8_t prehashed, const uint8_t *context,
141 curve448_scalar_t secret_scalar;
142 EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
143 c448_error_t ret = C448_FAILURE;
144 curve448_scalar_t nonce_scalar;
145 uint8_t nonce_point[EDDSA_448_PUBLIC_BYTES] = { 0 };
147 curve448_scalar_t challenge_scalar;
154 * Schedule the secret key, First EDDSA_448_PRIVATE_BYTES is serialised
155 * secret scalar,next EDDSA_448_PRIVATE_BYTES bytes is the seed.
157 uint8_t expanded[EDDSA_448_PRIVATE_BYTES * 2];
159 if (!oneshot_hash(expanded, sizeof(expanded), privkey,
160 EDDSA_448_PRIVATE_BYTES))
163 curve448_scalar_decode_long(secret_scalar, expanded,
164 EDDSA_448_PRIVATE_BYTES);
166 /* Hash to create the nonce */
167 if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
168 || !EVP_DigestUpdate(hashctx,
169 expanded + EDDSA_448_PRIVATE_BYTES,
170 EDDSA_448_PRIVATE_BYTES)
171 || !EVP_DigestUpdate(hashctx, message, message_len)) {
172 OPENSSL_cleanse(expanded, sizeof(expanded));
175 OPENSSL_cleanse(expanded, sizeof(expanded));
178 /* Decode the nonce */
180 uint8_t nonce[2 * EDDSA_448_PRIVATE_BYTES];
182 if (!EVP_DigestFinalXOF(hashctx, nonce, sizeof(nonce)))
184 curve448_scalar_decode_long(nonce_scalar, nonce, sizeof(nonce));
185 OPENSSL_cleanse(nonce, sizeof(nonce));
189 /* Scalarmul to create the nonce-point */
190 curve448_scalar_t nonce_scalar_2;
193 curve448_scalar_halve(nonce_scalar_2, nonce_scalar);
194 for (c = 2; c < C448_EDDSA_ENCODE_RATIO; c <<= 1) {
195 curve448_scalar_halve(nonce_scalar_2, nonce_scalar_2);
198 curve448_precomputed_scalarmul(p, curve448_precomputed_base,
200 curve448_point_mul_by_ratio_and_encode_like_eddsa(nonce_point, p);
201 curve448_point_destroy(p);
202 curve448_scalar_destroy(nonce_scalar_2);
206 uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];
208 /* Compute the challenge */
209 if (!hash_init_with_dom(hashctx, prehashed, 0, context, context_len)
210 || !EVP_DigestUpdate(hashctx, nonce_point, sizeof(nonce_point))
211 || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
212 || !EVP_DigestUpdate(hashctx, message, message_len)
213 || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge)))
216 curve448_scalar_decode_long(challenge_scalar, challenge,
218 OPENSSL_cleanse(challenge, sizeof(challenge));
221 curve448_scalar_mul(challenge_scalar, challenge_scalar, secret_scalar);
222 curve448_scalar_add(challenge_scalar, challenge_scalar, nonce_scalar);
224 OPENSSL_cleanse(signature, EDDSA_448_SIGNATURE_BYTES);
225 memcpy(signature, nonce_point, sizeof(nonce_point));
226 curve448_scalar_encode(&signature[EDDSA_448_PUBLIC_BYTES],
229 curve448_scalar_destroy(secret_scalar);
230 curve448_scalar_destroy(nonce_scalar);
231 curve448_scalar_destroy(challenge_scalar);
235 EVP_MD_CTX_free(hashctx);
239 c448_error_t c448_ed448_sign_prehash(
240 uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
241 const uint8_t privkey[EDDSA_448_PRIVATE_BYTES],
242 const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
243 const uint8_t hash[64], const uint8_t *context,
246 return c448_ed448_sign(signature, privkey, pubkey, hash, 64, 1, context,
250 c448_error_t c448_ed448_verify(
251 const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
252 const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
253 const uint8_t *message, size_t message_len,
254 uint8_t prehashed, const uint8_t *context,
257 curve448_point_t pk_point, r_point;
259 curve448_point_decode_like_eddsa_and_mul_by_ratio(pk_point, pubkey);
260 curve448_scalar_t challenge_scalar;
261 curve448_scalar_t response_scalar;
264 if (C448_SUCCESS != error)
268 curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point, signature);
269 if (C448_SUCCESS != error)
273 /* Compute the challenge */
274 EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
275 uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];
278 || !hash_init_with_dom(hashctx, prehashed, 0, context,
280 || !EVP_DigestUpdate(hashctx, signature, EDDSA_448_PUBLIC_BYTES)
281 || !EVP_DigestUpdate(hashctx, pubkey, EDDSA_448_PUBLIC_BYTES)
282 || !EVP_DigestUpdate(hashctx, message, message_len)
283 || !EVP_DigestFinalXOF(hashctx, challenge, sizeof(challenge))) {
284 EVP_MD_CTX_free(hashctx);
288 EVP_MD_CTX_free(hashctx);
289 curve448_scalar_decode_long(challenge_scalar, challenge,
291 OPENSSL_cleanse(challenge, sizeof(challenge));
293 curve448_scalar_sub(challenge_scalar, curve448_scalar_zero,
296 curve448_scalar_decode_long(response_scalar,
297 &signature[EDDSA_448_PUBLIC_BYTES],
298 EDDSA_448_PRIVATE_BYTES);
300 for (c = 1; c < C448_EDDSA_DECODE_RATIO; c <<= 1)
301 curve448_scalar_add(response_scalar, response_scalar, response_scalar);
303 /* pk_point = -c(x(P)) + (cx + k)G = kG */
304 curve448_base_double_scalarmul_non_secret(pk_point,
306 pk_point, challenge_scalar);
307 return c448_succeed_if(curve448_point_eq(pk_point, r_point));
310 c448_error_t c448_ed448_verify_prehash(
311 const uint8_t signature[EDDSA_448_SIGNATURE_BYTES],
312 const uint8_t pubkey[EDDSA_448_PUBLIC_BYTES],
313 const uint8_t hash[64], const uint8_t *context,
318 ret = c448_ed448_verify(signature, pubkey, hash, 64, 1, context,
324 int ED448_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
325 const uint8_t public_key[57], const uint8_t private_key[57],
326 const uint8_t *context, size_t context_len)
329 return c448_ed448_sign(out_sig, private_key, public_key, message,
330 message_len, 0, context, context_len)
334 int ED448_verify(const uint8_t *message, size_t message_len,
335 const uint8_t signature[114], const uint8_t public_key[57],
336 const uint8_t *context, size_t context_len)
338 return c448_ed448_verify(signature, public_key, message, message_len, 0,
339 context, (uint8_t)context_len) == C448_SUCCESS;
342 int ED448ph_sign(uint8_t *out_sig, const uint8_t hash[64],
343 const uint8_t public_key[57], const uint8_t private_key[57],
344 const uint8_t *context, size_t context_len)
346 return c448_ed448_sign_prehash(out_sig, private_key, public_key, hash,
347 context, context_len) == C448_SUCCESS;
351 int ED448ph_verify(const uint8_t hash[64], const uint8_t signature[114],
352 const uint8_t public_key[57], const uint8_t *context,
355 return c448_ed448_verify_prehash(signature, public_key, hash, context,
356 (uint8_t)context_len) == C448_SUCCESS;
359 int ED448_public_from_private(uint8_t out_public_key[57],
360 const uint8_t private_key[57])
362 return c448_ed448_derive_public_key(out_public_key, private_key)