crypto/ec/curve448/eddsa.c

   1 /*
   2  * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
   3  * Copyright 2015-2016 Cryptography Research, Inc.
   4  *
   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
   9  *
  10  * Originally written by Mike Hamburg
  11  */
  12 #include <string.h>
  13 #include <openssl/crypto.h>
  14 #include <openssl/evp.h>
  15 #include "curve448_lcl.h"
  16 #include "word.h"
  17 #include "ed448.h"
  18 #include "internal/numbers.h"
  19
  20 #define COFACTOR 4
  21
  22 static c448_error_t oneshot_hash(uint8_t *out, size_t outlen,
  23                                  const uint8_t *in, size_t inlen)
  24 {
  25     EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
  26
  27     if (hashctx == NULL)
  28         return C448_FAILURE;
  29
  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);
  34         return C448_FAILURE;
  35     }
  36
  37     EVP_MD_CTX_free(hashctx);
  38     return C448_SUCCESS;
  39 }
  40
  41 static void clamp(uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES])
  42 {
  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;
  46 }
  47
  48 static c448_error_t hash_init_with_dom(EVP_MD_CTX *hashctx, uint8_t prehashed,
  49                                        uint8_t for_prehash,
  50                                        const uint8_t *context,
  51                                        size_t context_len)
  52 {
  53     const char *dom_s = "SigEd448";
  54     uint8_t dom[2];
  55
  56     if (context_len > UINT8_MAX)
  57         return C448_FAILURE;
  58
  59     dom[0] = (uint8_t)(2 - (prehashed == 0 ? 1 : 0)
  60                        - (for_prehash == 0 ? 1 : 0));
  61     dom[1] = (uint8_t)context_len;
  62
  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))
  67         return C448_FAILURE;
  68
  69     return C448_SUCCESS;
  70 }
  71
  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])
  76 {
  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);
  81 }
  82
  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])
  86 {
  87     /* only this much used for keygen */
  88     uint8_t secret_scalar_ser[EDDSA_448_PRIVATE_BYTES];
  89     curve448_scalar_t secret_scalar;
  90     unsigned int c;
  91     curve448_point_t p;
  92
  93     if (!oneshot_hash(secret_scalar_ser, sizeof(secret_scalar_ser), privkey,
  94                       EDDSA_448_PRIVATE_BYTES))
  95         return C448_FAILURE;
  96
  97     clamp(secret_scalar_ser);
  98
  99     curve448_scalar_decode_long(secret_scalar, secret_scalar_ser,
 100                                 sizeof(secret_scalar_ser));
 101
 102     /*
 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.
 109      */
 110     for (c = 1; c < C448_EDDSA_ENCODE_RATIO; c <<= 1)
 111         curve448_scalar_halve(secret_scalar, secret_scalar);
 112
 113     curve448_precomputed_scalarmul(p, curve448_precomputed_base, secret_scalar);
 114
 115     curve448_point_mul_by_ratio_and_encode_like_eddsa(pubkey, p);
 116
 117     /* Cleanup */
 118     curve448_scalar_destroy(secret_scalar);
 119     curve448_point_destroy(p);
 120     OPENSSL_cleanse(secret_scalar_ser, sizeof(secret_scalar_ser));
 121
 122     return C448_SUCCESS;
 123 }
 124
 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,
 131                         size_t context_len)
 132 {
 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 };
 138     unsigned int c;
 139     curve448_scalar_t challenge_scalar;
 140
 141     if (hashctx == NULL)
 142         return C448_FAILURE;
 143
 144     {
 145         /*
 146          * Schedule the secret key, First EDDSA_448_PRIVATE_BYTES is serialised
 147          * secret scalar,next EDDSA_448_PRIVATE_BYTES bytes is the seed.
 148          */
 149         uint8_t expanded[EDDSA_448_PRIVATE_BYTES * 2];
 150
 151         if (!oneshot_hash(expanded, sizeof(expanded), privkey,
 152                           EDDSA_448_PRIVATE_BYTES))
 153             goto err;
 154         clamp(expanded);
 155         curve448_scalar_decode_long(secret_scalar, expanded,
 156                                     EDDSA_448_PRIVATE_BYTES);
 157
 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));
 165             goto err;
 166         }
 167         OPENSSL_cleanse(expanded, sizeof(expanded));
 168     }
 169
 170     /* Decode the nonce */
 171     {
 172         uint8_t nonce[2 * EDDSA_448_PRIVATE_BYTES];
 173
 174         if (!EVP_DigestFinalXOF(hashctx, nonce, sizeof(nonce)))
 175             goto err;
 176         curve448_scalar_decode_long(nonce_scalar, nonce, sizeof(nonce));
 177         OPENSSL_cleanse(nonce, sizeof(nonce));
 178     }
 179
 180     {
 181         /* Scalarmul to create the nonce-point */
 182         curve448_scalar_t nonce_scalar_2;
 183         curve448_point_t p;
 184
 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);
 188
 189         curve448_precomputed_scalarmul(p, curve448_precomputed_base,
 190                                        nonce_scalar_2);
 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);
 194     }
 195
 196     {
 197         uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];
 198
 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)))
 205             goto err;
 206
 207         curve448_scalar_decode_long(challenge_scalar, challenge,
 208                                     sizeof(challenge));
 209         OPENSSL_cleanse(challenge, sizeof(challenge));
 210     }
 211
 212     curve448_scalar_mul(challenge_scalar, challenge_scalar, secret_scalar);
 213     curve448_scalar_add(challenge_scalar, challenge_scalar, nonce_scalar);
 214
 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],
 218                            challenge_scalar);
 219
 220     curve448_scalar_destroy(secret_scalar);
 221     curve448_scalar_destroy(nonce_scalar);
 222     curve448_scalar_destroy(challenge_scalar);
 223
 224     ret = C448_SUCCESS;
 225  err:
 226     EVP_MD_CTX_free(hashctx);
 227     return ret;
 228 }
 229
 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,
 235                         size_t context_len)
 236 {
 237     return c448_ed448_sign(signature, privkey, pubkey, hash, 64, 1, context,
 238                            context_len);
 239 }
 240
 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,
 246                     uint8_t context_len)
 247 {
 248     curve448_point_t pk_point, r_point;
 249     c448_error_t error =
 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;
 253
 254     if (C448_SUCCESS != error)
 255         return error;
 256
 257     error =
 258         curve448_point_decode_like_eddsa_and_mul_by_ratio(r_point, signature);
 259     if (C448_SUCCESS != error)
 260         return error;
 261
 262     {
 263         /* Compute the challenge */
 264         EVP_MD_CTX *hashctx = EVP_MD_CTX_new();
 265         uint8_t challenge[2 * EDDSA_448_PRIVATE_BYTES];
 266
 267         if (hashctx == NULL
 268                 || !hash_init_with_dom(hashctx, prehashed, 0, context,
 269                                        context_len)
 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);
 275             return C448_FAILURE;
 276         }
 277
 278         EVP_MD_CTX_free(hashctx);
 279         curve448_scalar_decode_long(challenge_scalar, challenge,
 280                                     sizeof(challenge));
 281         OPENSSL_cleanse(challenge, sizeof(challenge));
 282     }
 283     curve448_scalar_sub(challenge_scalar, curve448_scalar_zero,
 284                         challenge_scalar);
 285
 286     curve448_scalar_decode_long(response_scalar,
 287                                 &signature[EDDSA_448_PUBLIC_BYTES],
 288                                 EDDSA_448_PRIVATE_BYTES);
 289
 290     /* pk_point = -c(x(P)) + (cx + k)G = kG */
 291     curve448_base_double_scalarmul_non_secret(pk_point,
 292                                               response_scalar,
 293                                               pk_point, challenge_scalar);
 294     return c448_succeed_if(curve448_point_eq(pk_point, r_point));
 295 }
 296
 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,
 301                     uint8_t context_len)
 302 {
 303     return c448_ed448_verify(signature, pubkey, hash, 64, 1, context,
 304                              context_len);
 305 }
 306
 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)
 310 {
 311     return c448_ed448_sign(out_sig, private_key, public_key, message,
 312                            message_len, 0, context, context_len)
 313         == C448_SUCCESS;
 314 }
 315
 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)
 319 {
 320     return c448_ed448_verify(signature, public_key, message, message_len, 0,
 321                              context, (uint8_t)context_len) == C448_SUCCESS;
 322 }
 323
 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)
 327 {
 328     return c448_ed448_sign_prehash(out_sig, private_key, public_key, hash,
 329                                    context, context_len) == C448_SUCCESS;
 330
 331 }
 332
 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,
 335                    size_t context_len)
 336 {
 337     return c448_ed448_verify_prehash(signature, public_key, hash, context,
 338                                      (uint8_t)context_len) == C448_SUCCESS;
 339 }
 340
 341 int ED448_public_from_private(uint8_t out_public_key[57],
 342                               const uint8_t private_key[57])
 343 {
 344     return c448_ed448_derive_public_key(out_public_key, private_key)
 345         == C448_SUCCESS;
 346 }