| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * The Ed25519 signature scheme |
| 4 | * |
| 5 | * (c) 2017 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 9 | * |
| 10 | * This file is part of secnet. |
| 11 | * See README for full list of copyright holders. |
| 12 | * |
| 13 | * secnet is free software; you can redistribute it and/or modify it |
| 14 | * under the terms of the GNU General Public License as published by |
| 15 | * the Free Software Foundation; either version d of the License, or |
| 16 | * (at your option) any later version. |
| 17 | * |
| 18 | * secnet is distributed in the hope that it will be useful, but |
| 19 | * WITHOUT ANY WARRANTY; without even the implied warranty of |
| 20 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| 21 | * General Public License for more details. |
| 22 | * |
| 23 | * You should have received a copy of the GNU General Public License |
| 24 | * version 3 along with secnet; if not, see |
| 25 | * https://www.gnu.org/licenses/gpl.html. |
| 26 | * |
| 27 | * This file was originally part of Catacomb, but has been automatically |
| 28 | * modified for incorporation into secnet: see `import-catacomb-crypto' |
| 29 | * for details. |
| 30 | * |
| 31 | * Catacomb is free software; you can redistribute it and/or modify |
| 32 | * it under the terms of the GNU Library General Public License as |
| 33 | * published by the Free Software Foundation; either version 2 of the |
| 34 | * License, or (at your option) any later version. |
| 35 | * |
| 36 | * Catacomb is distributed in the hope that it will be useful, |
| 37 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 38 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 39 | * GNU Library General Public License for more details. |
| 40 | * |
| 41 | * You should have received a copy of the GNU Library General Public |
| 42 | * License along with Catacomb; if not, write to the Free |
| 43 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 44 | * MA 02111-1307, USA. |
| 45 | */ |
| 46 | |
| 47 | /*----- Header files ------------------------------------------------------*/ |
| 48 | |
| 49 | #include <string.h> |
| 50 | |
| 51 | #include "f25519.h" |
| 52 | #include "ed25519.h" |
| 53 | #include "scaf.h" |
| 54 | #include "scmul.h" |
| 55 | #include "sha512.h" |
| 56 | |
| 57 | /*----- A number of magic numbers -----------------------------------------*/ |
| 58 | |
| 59 | # define PIECEWD 24 |
| 60 | static const scaf_piece l[] = { |
| 61 | 0xf5d3ed, 0x631a5c, 0xd65812, 0xa2f79c, 0xdef9de, 0x000014, |
| 62 | 0x000000, 0x000000, 0x000000, 0x000000, 0x001000 |
| 63 | }; |
| 64 | static const scaf_piece mu[] = { |
| 65 | 0x1b3994, 0x0a2c13, 0x9ce5a3, 0x29a7ed, 0x5d0863, 0x210621, |
| 66 | 0xffffeb, 0xffffff, 0xffffff, 0xffffff, 0xffffff, 0x000fff |
| 67 | }; |
| 68 | |
| 69 | #define NPIECE SCAF_NPIECE(255, PIECEWD) |
| 70 | |
| 71 | # define P p26 |
| 72 | static const f25519_piece bx_pieces[] = { |
| 73 | -14297830, -7645148, 16144683, -16471763, 27570974, |
| 74 | -2696100, -26142465, 8378389, 20764389, 8758491 |
| 75 | }, by_pieces[] = { |
| 76 | -26843541, -6710886, 13421773, -13421773, 26843546, |
| 77 | 6710886, -13421773, 13421773, -26843546, -6710886 |
| 78 | }, d_pieces[] = { |
| 79 | -10913610, 13857413, -15372611, 6949391, 114729, |
| 80 | -8787816, -6275908, -3247719, -18696448, -12055116 |
| 81 | }; |
| 82 | |
| 83 | static const f25519_piece bz_pieces[NPIECE] = { 1, 0, /* ... */ }; |
| 84 | #define BX ((const f25519 *)bx_pieces) |
| 85 | #define BY ((const f25519 *)by_pieces) |
| 86 | #define BZ ((const f25519 *)bz_pieces) |
| 87 | #define D ((const f25519 *)d_pieces) |
| 88 | |
| 89 | /*----- Point encoding and decoding ---------------------------------------*/ |
| 90 | |
| 91 | static void ptencode(octet q[32], |
| 92 | const f25519 *X, const f25519 *Y, const f25519 *Z) |
| 93 | { |
| 94 | f25519 x, y, t; |
| 95 | octet b[32]; |
| 96 | |
| 97 | f25519_inv(&t, Z); f25519_mul(&x, X, &t); f25519_mul(&y, Y, &t); |
| 98 | f25519_store(q, &y); f25519_store(b, &x); q[31] |= (b[0]&1u) << 7; |
| 99 | } |
| 100 | |
| 101 | static int ptdecode(f25519 *X, f25519 *Y, f25519 *Z, const octet q[32]) |
| 102 | { |
| 103 | octet b[32]; |
| 104 | unsigned i, a; |
| 105 | f25519 t, u; |
| 106 | uint32 m; |
| 107 | int rc = 0; |
| 108 | |
| 109 | /* Load the y-coordinate. */ |
| 110 | memcpy(b, q, 32); b[31] &= 0x7fu; f25519_load(Y, b); |
| 111 | |
| 112 | /* Check that the coordinate was in range. If we store it, we'll get a |
| 113 | * canonical version which we can compare against Q; be careful not to |
| 114 | * check the top bit. |
| 115 | */ |
| 116 | f25519_store(b, Y); |
| 117 | for (i = a = 0; i < 31; i++) a |= b[i] ^ q[i]; |
| 118 | a |= (b[31] ^ q[31])&0x7fu; |
| 119 | a = ((a - 1) >> 8)&0x01u; /* 0 |-> 1, non-0 |-> 0 */ |
| 120 | rc |= (int)a - 1; |
| 121 | |
| 122 | /* Decompress the x-coordinate. */ |
| 123 | f25519_sqr(&t, Y); f25519_mul(&u, &t, D); t.P[0] -= 1; u.P[0] += 1; |
| 124 | rc |= f25519_quosqrt(X, &t, &u); |
| 125 | f25519_store(b, X); m = -(uint32)(((q[31] >> 7) ^ b[0])&0x1u); |
| 126 | f25519_condneg(X, X, m); |
| 127 | |
| 128 | /* Set Z. */ |
| 129 | f25519_set(Z, 1); |
| 130 | |
| 131 | /* And we're done. */ |
| 132 | return (rc); |
| 133 | } |
| 134 | |
| 135 | /*----- Edwards curve arithmetic ------------------------------------------*/ |
| 136 | |
| 137 | static void ptadd(f25519 *X, f25519 *Y, f25519 *Z, |
| 138 | const f25519 *X0, const f25519 *Y0, const f25519 *Z0, |
| 139 | const f25519 *X1, const f25519 *Y1, const f25519 *Z1) |
| 140 | { |
| 141 | f25519 t0, t1, t2, t3; |
| 142 | |
| 143 | /* Bernstein, Birkner, Joye, Lange, and Peters, `Twisted Edwards Curves', |
| 144 | * 2008-03-13, https://cr.yp.to/newelliptic/twisted-20080313.pdf shows the |
| 145 | * formulae as: |
| 146 | * |
| 147 | * A = Z1 Z2; B = A^2; C = X1 X2; D = Y1 Y2; |
| 148 | * E = d C D; F = B - E; G = B + E; |
| 149 | * X3 = A F ((X1 + Y1) (X2 + Y2) - C - D); |
| 150 | * Y3 = A G (D - a C); Z3 = F G. |
| 151 | * |
| 152 | * Note that a = -1, which things easier. |
| 153 | */ |
| 154 | |
| 155 | f25519_mul(&t0, Z0, Z1); /* t0 = A = Z0 Z1 */ |
| 156 | f25519_add(&t1, X0, Y0); /* t1 = X0 + Y0 */ |
| 157 | f25519_add(&t2, X1, Y1); /* t2 = X1 + Y1 */ |
| 158 | f25519_mul(&t1, &t1, &t2); /* t1 = (X0 + Y0) (X1 + Y1) */ |
| 159 | f25519_mul(&t2, X0, X1); /* t2 = C = X0 X1 */ |
| 160 | f25519_mul(&t3, Y0, Y1); /* t3 = D = Y0 Y1 */ |
| 161 | f25519_add(Y, &t2, &t3); /* Y = C + D = D - a C */ |
| 162 | f25519_sub(X, &t1, Y); /* X = (X0 + Y0) (X1 + Y1) - C - D */ |
| 163 | f25519_mul(X, X, &t0); /* X = A ((X0 + Y0) (X1 + Y1) - C - D) */ |
| 164 | f25519_mul(Y, Y, &t0); /* Y = A (D - a C) */ |
| 165 | f25519_sqr(&t0, &t0); /* t0 = B = A^2 */ |
| 166 | f25519_mul(&t1, &t2, &t3); /* t1 = C D */ |
| 167 | f25519_mul(&t1, &t1, D); /* t1 = E = d C D */ |
| 168 | f25519_sub(&t2, &t0, &t1); /* t2 = F = B - E */ |
| 169 | f25519_add(&t1, &t0, &t1); /* t1 = G = B + E */ |
| 170 | f25519_mul(X, X, &t2); /* X = A F ((X0 + Y0) (X1 + Y1) - C - D) */ |
| 171 | f25519_mul(Y, Y, &t1); /* Y = A G (D - a C) */ |
| 172 | f25519_mul(Z, &t1, &t2); /* Z = F G */ |
| 173 | } |
| 174 | |
| 175 | static void ptdbl(f25519 *X, f25519 *Y, f25519 *Z, |
| 176 | const f25519 *X0, const f25519 *Y0, const f25519 *Z0) |
| 177 | { |
| 178 | f25519 t0, t1, t2; |
| 179 | |
| 180 | /* Bernstein, Birkner, Joye, Lange, and Peters, `Twisted Edwards Curves', |
| 181 | * 2008-03-13, https://cr.yp.to/newelliptic/twisted-20080313.pdf shows the |
| 182 | * formulae as: |
| 183 | * |
| 184 | * B = (X1 + Y1)^2; C = X1^2; D = Y1^2; E = a C; |
| 185 | * F = E + D; H = Z1^2; J = F - 2 H; |
| 186 | * X3 = (B - C - D) J; Y3 = F (E - D); Z3 = F J. |
| 187 | * |
| 188 | * Note that a = -1, which things easier. |
| 189 | */ |
| 190 | |
| 191 | f25519_add(&t0, X0, Y0); /* t0 = X0 + Y0 */ |
| 192 | f25519_sqr(&t0, &t0); /* t0 = B = (X0 + Y0)^2 */ |
| 193 | f25519_sqr(&t1, X0); /* t1 = C = X0^2 */ |
| 194 | f25519_sqr(&t2, Y0); /* t2 = D = Y0^2 */ |
| 195 | f25519_add(Y, &t1, &t2); /* Y = C + D = -(E - D) */ |
| 196 | f25519_sub(X, &t0, Y); /* X = B - C - D */ |
| 197 | /* (E = a C = -C) */ |
| 198 | f25519_sub(&t0, &t2, &t1); /* t0 = F = D - C = E + D */ |
| 199 | f25519_sqr(&t1, Z0); /* t1 = H = Z0^2 */ |
| 200 | f25519_add(&t1, &t1, &t1); /* t1 = 2 H */ |
| 201 | f25519_sub(&t1, &t0, &t1); /* t1 = J = F - 2 H */ |
| 202 | f25519_mul(X, X, &t1); /* X = (B - C - D) J */ |
| 203 | f25519_mul(Y, Y, &t0); /* Y = -F (E - D) */ |
| 204 | f25519_neg(Y, Y); /* Y = F (E - D) */ |
| 205 | f25519_mul(Z, &t0, &t1); /* Z = F J */ |
| 206 | } |
| 207 | |
| 208 | static DEFINE_SCMUL(ptmul, f25519, 4, PIECEWD, NPIECE, ptadd, ptdbl) |
| 209 | static DEFINE_SCSIMMUL(ptsimmul, f25519, 2, PIECEWD, NPIECE, ptadd, ptdbl) |
| 210 | |
| 211 | /*----- Key derivation utilities ------------------------------------------*/ |
| 212 | |
| 213 | static void unpack_key(scaf_piece a[NPIECE], octet h1[32], |
| 214 | const octet *k, size_t ksz) |
| 215 | { |
| 216 | struct sha512_ctx h; |
| 217 | octet b[SHA512_DIGEST_SIZE]; |
| 218 | |
| 219 | sha512_init_ctx(&h); sha512_process_bytes(k, ksz, &h); sha512_finish_ctx(&h, b); |
| 220 | b[0] &= 0xf8u; b[31] = (b[31]&0x3f) | 0x40; |
| 221 | scaf_load(a, b, 32, NPIECE, PIECEWD); |
| 222 | if (h1) memcpy(h1, b + 32, 32); |
| 223 | } |
| 224 | |
| 225 | #define PREFIX_BUFSZ 290 |
| 226 | static size_t prefix(octet b[PREFIX_BUFSZ], |
| 227 | int phflag, const octet *p, size_t psz) |
| 228 | { |
| 229 | if (phflag < 0) return (0); |
| 230 | memcpy(b, "SigEd25519 no Ed25519 collisions", 32); |
| 231 | b[32] = phflag; |
| 232 | assert(psz < ED25519_MAXPERSOSZ); b[33] = psz; memcpy(b + 34, p, psz); |
| 233 | return (psz + 34); |
| 234 | } |
| 235 | |
| 236 | /*----- Main code ---------------------------------------------------------*/ |
| 237 | |
| 238 | /* --- @ed25519_pubkey@ --- * |
| 239 | * |
| 240 | * Arguments: @octet K[ED25519_PUBSZ]@ = where to put the public key |
| 241 | * @const void *k@ = private key |
| 242 | * @size_t ksz@ = length of private key |
| 243 | * |
| 244 | * Returns: --- |
| 245 | * |
| 246 | * Use: Derives the public key from a private key. |
| 247 | */ |
| 248 | |
| 249 | void ed25519_pubkey(octet K[ED25519_PUBSZ], const void *k, size_t ksz) |
| 250 | { |
| 251 | scaf_piece a[NPIECE]; |
| 252 | f25519 AX, AY, AZ; |
| 253 | |
| 254 | unpack_key(a, 0, k, ksz); |
| 255 | ptmul(&AX, &AY, &AZ, a, BX, BY, BZ); |
| 256 | ptencode(K, &AX, &AY, &AZ); |
| 257 | } |
| 258 | |
| 259 | /* --- @ed25519_sign@, @ed25519ctx_sign@ --- * |
| 260 | * |
| 261 | * Arguments: @octet sig[ED25519_SIGSZ]@ = where to put the signature |
| 262 | * @const void *k@ = private key |
| 263 | * @size_t ksz@ = length of private key |
| 264 | * @const octet K[ED25519_PUBSZ]@ = public key |
| 265 | * @int phflag@ = whether the `message' has been hashed already |
| 266 | * @const void *p@ = personalization string |
| 267 | * @size_t psz@ = length of personalization string |
| 268 | * @const void *m@ = message to sign |
| 269 | * @size_t msz@ = length of message |
| 270 | * |
| 271 | * Returns: --- |
| 272 | * |
| 273 | * Use: Signs a message. |
| 274 | * |
| 275 | * In @ed25519ctx_sign@, if @phflag@ is @-1@ then you get plain |
| 276 | * old Ed25519: the personalization string pointer @p@ will be |
| 277 | * ignored. If @phflag > 0@ then the `message' @m@ should be a |
| 278 | * SHA512 hash of the actual message. |
| 279 | */ |
| 280 | |
| 281 | void ed25519ctx_sign(octet sig[ED25519_SIGSZ], |
| 282 | const void *k, size_t ksz, const octet K[ED25519_PUBSZ], |
| 283 | int phflag, const void *p, size_t psz, |
| 284 | const void *m, size_t msz) |
| 285 | { |
| 286 | struct sha512_ctx h; |
| 287 | scaf_piece a[NPIECE], r[NPIECE], t[NPIECE], scratch[3*NPIECE]; |
| 288 | scaf_dblpiece tt[2*NPIECE]; |
| 289 | f25519 RX, RY, RZ; |
| 290 | octet h1[32], pb[PREFIX_BUFSZ], rb[SHA512_DIGEST_SIZE]; |
| 291 | unsigned i; |
| 292 | |
| 293 | /* Get my private key. */ |
| 294 | unpack_key(a, h1, k, ksz); |
| 295 | |
| 296 | /* Determine the prefix string. */ |
| 297 | psz = prefix(pb, phflag, p, psz); |
| 298 | |
| 299 | /* Select the nonce and the vector part. */ |
| 300 | sha512_init_ctx(&h); |
| 301 | sha512_process_bytes(pb, psz, &h); |
| 302 | sha512_process_bytes(h1, 32, &h); |
| 303 | sha512_process_bytes(m, msz, &h); |
| 304 | sha512_finish_ctx(&h, rb); |
| 305 | scaf_loaddbl(tt, rb, 64, 2*NPIECE, PIECEWD); |
| 306 | scaf_reduce(r, tt, l, mu, NPIECE, PIECEWD, scratch); |
| 307 | ptmul(&RX, &RY, &RZ, r, BX, BY, BZ); |
| 308 | ptencode(sig, &RX, &RY, &RZ); |
| 309 | |
| 310 | /* Calculate the scalar part. */ |
| 311 | sha512_init_ctx(&h); |
| 312 | sha512_process_bytes(pb, psz, &h); |
| 313 | sha512_process_bytes(sig, 32, &h); |
| 314 | sha512_process_bytes(K, 32, &h); |
| 315 | sha512_process_bytes(m, msz, &h); |
| 316 | sha512_finish_ctx(&h, rb); |
| 317 | scaf_loaddbl(tt, rb, 64, 2*NPIECE, PIECEWD); |
| 318 | scaf_reduce(t, tt, l, mu, NPIECE, PIECEWD, scratch); |
| 319 | scaf_mul(tt, t, a, NPIECE); |
| 320 | for (i = 0; i < NPIECE; i++) tt[i] += r[i]; |
| 321 | scaf_reduce(t, tt, l, mu, NPIECE, PIECEWD, scratch); |
| 322 | scaf_store(sig + 32, 32, t, NPIECE, PIECEWD); |
| 323 | } |
| 324 | |
| 325 | void ed25519_sign(octet sig[ED25519_SIGSZ], |
| 326 | const void *k, size_t ksz, const octet K[ED25519_PUBSZ], |
| 327 | const void *m, size_t msz) |
| 328 | { ed25519ctx_sign(sig, k, ksz, K, -1, 0, 0, m, msz); } |
| 329 | |
| 330 | /* --- @ed25519_verify@, @ed25519ctx_verify@ --- * |
| 331 | * |
| 332 | * Arguments: @const octet K[ED25519_PUBSZ]@ = public key |
| 333 | * @int phflag@ = whether the `message' has been hashed already |
| 334 | * @const void *p@ = personalization string |
| 335 | * @size_t psz@ = length of personalization string |
| 336 | * @const void *m@ = message to sign |
| 337 | * @size_t msz@ = length of message |
| 338 | * @const octet sig[ED25519_SIGSZ]@ = signature |
| 339 | * |
| 340 | * Returns: Zero if OK, negative on failure. |
| 341 | * |
| 342 | * Use: Verify a signature. |
| 343 | * |
| 344 | * In @ed25519ctx_verify@, if @phflag@ is @-1@ then you get |
| 345 | * plain old Ed25519: the personalization string pointer @p@ |
| 346 | * will be ignored. If @phflag > 0@ then the `message' @m@ |
| 347 | * should be a SHA512 hash of the actual message. |
| 348 | */ |
| 349 | |
| 350 | int ed25519ctx_verify(const octet K[ED25519_PUBSZ], |
| 351 | int phflag, const void *p, size_t psz, |
| 352 | const void *m, size_t msz, |
| 353 | const octet sig[ED25519_SIGSZ]) |
| 354 | { |
| 355 | struct sha512_ctx h; |
| 356 | scaf_piece s[NPIECE], t[NPIECE], scratch[3*NPIECE]; |
| 357 | scaf_dblpiece tt[2*NPIECE]; |
| 358 | f25519 AX, AY, AZ, RX, RY, RZ; |
| 359 | octet b[PREFIX_BUFSZ]; |
| 360 | |
| 361 | /* Unpack the public key. Negate it: we're meant to subtract the term |
| 362 | * involving the public key point, and this is easier than negating the |
| 363 | * scalar. |
| 364 | */ |
| 365 | if (ptdecode(&AX, &AY, &AZ, K)) return (-1); |
| 366 | f25519_neg(&AX, &AX); |
| 367 | |
| 368 | /* Load the scalar and check that it's in range. The easy way is to store |
| 369 | * it again and see if the two match. |
| 370 | */ |
| 371 | scaf_loaddbl(tt, sig + 32, 32, 2*NPIECE, PIECEWD); |
| 372 | scaf_reduce(s, tt, l, mu, NPIECE, PIECEWD, scratch); |
| 373 | scaf_store(b, 32, s, NPIECE, PIECEWD); |
| 374 | if (memcmp(b, sig + 32, 32) != 0) return (-1); |
| 375 | |
| 376 | /* Check the signature. */ |
| 377 | psz = prefix(b, phflag, p, psz); |
| 378 | sha512_init_ctx(&h); |
| 379 | sha512_process_bytes(b, psz, &h); |
| 380 | sha512_process_bytes(sig, 32, &h); |
| 381 | sha512_process_bytes(K, 32, &h); |
| 382 | sha512_process_bytes(m, msz, &h); |
| 383 | sha512_finish_ctx(&h, b); |
| 384 | scaf_loaddbl(tt, b, 64, 2*NPIECE, PIECEWD); |
| 385 | scaf_reduce(t, tt, l, mu, NPIECE, PIECEWD, scratch); |
| 386 | ptsimmul(&RX, &RY, &RZ, s, BX, BY, BZ, t, &AX, &AY, &AZ); |
| 387 | ptencode(b, &RX, &RY, &RZ); |
| 388 | if (memcmp(b, sig, 32) != 0) return (-1); |
| 389 | |
| 390 | /* All is good. */ |
| 391 | return (0); |
| 392 | } |
| 393 | |
| 394 | int ed25519_verify(const octet K[ED25519_PUBSZ], |
| 395 | const void *m, size_t msz, |
| 396 | const octet sig[ED25519_SIGSZ]) |
| 397 | { return (ed25519ctx_verify(K, -1, 0, 0, m, msz, sig)); } |
| 398 | |
| 399 | /*----- That's all, folks -------------------------------------------------*/ |