Commit | Line | Data |
---|---|---|
a1a6042e MW |
1 | /* -*-c-*- |
2 | * | |
3 | * The Ed448 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 "fgoldi.h" | |
52 | #include "ed448.h" | |
53 | #include "scaf.h" | |
54 | #include "scmul.h" | |
55 | #include "sha3.h" | |
56 | ||
57 | /*----- A number of magic numbers -----------------------------------------*/ | |
58 | ||
59 | # define PIECEWD 24 | |
60 | static const scaf_piece l[] = { | |
61 | 0x5844f3, 0xc292ab, 0x552378, 0x8dc58f, 0x6cc272, | |
62 | 0x369021, 0x49aed6, 0xc44edb, 0xca23e9, 0xffff7c, | |
63 | 0xffffff, 0xffffff, 0xffffff, 0xffffff, 0xffffff, | |
64 | 0xffffff, 0xffffff, 0xffffff, 0x003fff | |
65 | }; | |
66 | static const scaf_piece mu[] = { | |
67 | 0xe0d00a, 0x4a7bb0, 0x73d6d5, 0x0aadc8, 0xd723a7, | |
68 | 0xe933d8, 0x9c96fd, 0x4b6512, 0x63bb12, 0x335dc1, | |
69 | 0x000008, 0x000000, 0x000000, 0x000000, 0x000000, | |
70 | 0x000000, 0x000000, 0x000000, 0x000000, 0x000400 | |
71 | }; | |
72 | ||
73 | #define NPIECE SCAF_NPIECE(448, PIECEWD) | |
74 | ||
75 | # define P p28 | |
76 | static const fgoldi_piece bx_pieces[] = { | |
77 | 118276190, 40534716, 9670182, -133293904, | |
78 | 85017404, -9262234, 68333083, -96650682, | |
79 | -93461723, 15824511, 73756743, 57518561, | |
80 | 94773951, -19783215, 107736334, 82941708 | |
81 | }, by_pieces[] = { | |
82 | 36764180, 8885695, 130592152, 20104429, | |
83 | -104530499, 30304196, 121295871, 5901357, | |
84 | 125344798, -96893944, -93097107, -59366209, | |
85 | 3626698, 38307682, 24032956, 110359655 | |
86 | }; | |
87 | ||
88 | static const fgoldi_piece bz_pieces[NPIECE] = { 1, 0, /* ... */ }; | |
89 | #define BX ((const fgoldi *)bx_pieces) | |
90 | #define BY ((const fgoldi *)by_pieces) | |
91 | #define BZ ((const fgoldi *)bz_pieces) | |
92 | #define D (-39081) | |
93 | ||
94 | /*----- Point encoding and decoding ---------------------------------------*/ | |
95 | ||
96 | static void ptencode(octet q[57], | |
97 | const fgoldi *X, const fgoldi *Y, const fgoldi *Z) | |
98 | { | |
99 | fgoldi x, y, t; | |
100 | octet b[56]; | |
101 | ||
102 | fgoldi_inv(&t, Z); fgoldi_mul(&x, X, &t); fgoldi_mul(&y, Y, &t); | |
103 | fgoldi_store(q, &y); fgoldi_store(b, &x); q[56] = (b[0]&1u) << 7; | |
104 | } | |
105 | ||
106 | static int ptdecode(fgoldi *X, fgoldi *Y, fgoldi *Z, const octet q[57]) | |
107 | { | |
108 | octet b[56]; | |
109 | unsigned i, a; | |
110 | fgoldi t, u; | |
111 | uint32 m; | |
112 | int rc = 0; | |
113 | ||
114 | /* Load the y-coordinate. */ | |
115 | fgoldi_load(Y, q); | |
116 | ||
117 | /* Check that the coordinate was in range. If we store it, we'll get a | |
118 | * canonical version which we can compare against Q. Also, check that the | |
119 | * extra bits in the top byte are zero. | |
120 | */ | |
121 | fgoldi_store(b, Y); | |
122 | for (i = a = 0; i < 56; i++) a |= b[i] ^ q[i]; | |
123 | a |= q[56]&0x7fu; | |
124 | a = ((a - 1) >> 8)&0x01u; /* 0 |-> 1, non-0 |-> 0 */ | |
125 | rc |= (int)a - 1; | |
126 | ||
127 | /* Decompress the x-coordinate. */ | |
128 | fgoldi_sqr(&t, Y); fgoldi_mulconst(&u, &t, D); t.P[0] -= 1; u.P[0] -= 1; | |
129 | rc |= fgoldi_quosqrt(X, &t, &u); | |
130 | fgoldi_store(b, X); m = -(uint32)(((q[56] >> 7) ^ b[0])&0x1u); | |
131 | fgoldi_condneg(X, X, m); | |
132 | ||
133 | /* Set Z. */ | |
134 | fgoldi_set(Z, 1); | |
135 | ||
136 | /* And we're done. */ | |
137 | return (rc); | |
138 | } | |
139 | ||
140 | /*----- Edwards curve arithmetic ------------------------------------------*/ | |
141 | ||
142 | static void ptadd(fgoldi *X, fgoldi *Y, fgoldi *Z, | |
143 | const fgoldi *X0, const fgoldi *Y0, const fgoldi *Z0, | |
144 | const fgoldi *X1, const fgoldi *Y1, const fgoldi *Z1) | |
145 | { | |
146 | fgoldi t0, t1, t2, t3; | |
147 | ||
148 | /* Bernstein and Lange, `Faster addition and doubling on elliptic curves', | |
149 | * 2007-09-06, https://cr.yp.to/newelliptic/newelliptic-20070906.pdf shows | |
150 | * the formulae as: | |
151 | * | |
152 | * A = Z1 Z2; B = A^2; C = X1 X2; D = Y1 Y2; | |
153 | * E = d C D; F = B - E; G = B + E; | |
154 | * X3 = A F ((X1 + Y1) (X2 + Y2) - C - D); | |
155 | * Y3 = A G (D - C); Z3 = c F G. | |
156 | * | |
157 | * But c = 1 here. | |
158 | */ | |
159 | ||
160 | fgoldi_mul(&t0, Z0, Z1); /* t0 = A = Z0 Z1 */ | |
161 | fgoldi_add(&t1, X0, Y0); /* t1 = X0 + Y0 */ | |
162 | fgoldi_add(&t2, X1, Y1); /* t2 = X1 + Y1 */ | |
163 | fgoldi_mul(&t1, &t1, &t2); /* t1 = (X0 + Y0) (X1 + Y1) */ | |
164 | fgoldi_mul(&t2, X0, X1); /* t2 = C = X0 X1 */ | |
165 | fgoldi_mul(&t3, Y0, Y1); /* t3 = D = Y0 Y1 */ | |
166 | fgoldi_sub(X, &t1, &t2); /* X = (X0 + Y0) (X1 + Y1) - C */ | |
167 | fgoldi_sub(X, X, &t3); /* X = (X0 + Y0) (X1 + Y1) - C - D */ | |
168 | fgoldi_sub(Y, &t3, &t2); /* Y = D - C */ | |
169 | fgoldi_mul(X, X, &t0); /* X = A ((X0 + Y0) (X1 + Y1) - C - D) */ | |
170 | fgoldi_mul(Y, Y, &t0); /* Y = A (D - C) */ | |
171 | fgoldi_sqr(&t0, &t0); /* t0 = B = A^2 */ | |
172 | fgoldi_mul(&t1, &t2, &t3); /* t1 = C D */ | |
173 | fgoldi_mulconst(&t1, &t1, D); /* t1 = E = d C D */ | |
174 | fgoldi_sub(&t2, &t0, &t1); /* t2 = F = B - E */ | |
175 | fgoldi_add(&t1, &t0, &t1); /* t1 = G = B + E */ | |
176 | fgoldi_mul(X, X, &t2); /* X = A F ((X0 + Y0) (X1 + Y1) - C - D) */ | |
177 | fgoldi_mul(Y, Y, &t1); /* Y = A G (D - C) */ | |
178 | fgoldi_mul(Z, &t1, &t2); /* Z = c F G */ | |
179 | } | |
180 | ||
181 | static void ptdbl(fgoldi *X, fgoldi *Y, fgoldi *Z, | |
182 | const fgoldi *X0, const fgoldi *Y0, const fgoldi *Z0) | |
183 | { | |
184 | fgoldi t0, t1, t2; | |
185 | ||
186 | /* Bernstein and Lange, `Faster addition and doubling on elliptic curves', | |
187 | * 2007-09-06, https://cr.yp.to/newelliptic/newelliptic-20070906.pdf shows | |
188 | * the formulae as: | |
189 | * | |
190 | * B = (X1 + Y1)^2; C = X1^2; D = Y1^2; | |
191 | * E = C + D; H = (c Z1)^2; J = E - 2 H; | |
192 | * X3 = c (B - E) J; Y3 = c E (C - D); Z3 = E J | |
193 | * | |
194 | * But c = 1 here. | |
195 | */ | |
196 | ||
197 | fgoldi_add(&t0, X0, Y0); /* t0 = X0 + Y0 */ | |
198 | fgoldi_sqr(&t0, &t0); /* t0 = B = (X0 + Y0)^2 */ | |
199 | fgoldi_sqr(&t1, X0); /* t1 = C = X0^2 */ | |
200 | fgoldi_sqr(&t2, Y0); /* t2 = D = Y0^2 */ | |
201 | fgoldi_add(Y, &t1, &t2); /* Y = E = C + D */ | |
202 | fgoldi_sub(&t1, &t1, &t2); /* t1 = C - D */ | |
203 | fgoldi_sub(X, &t0, Y); /* X = c (B - E) */ | |
204 | fgoldi_sqr(&t0, Z0); /* t0 = H = (c Z0)^2 */ | |
205 | fgoldi_add(&t0, &t0, &t0); /* t0 = 2 H */ | |
206 | fgoldi_sub(&t0, Y, &t0); /* t0 = J = E - 2 H */ | |
207 | fgoldi_mul(X, X, &t0); /* X = c (B - E) J */ | |
208 | fgoldi_mul(Z, Y, &t0); /* Z = E J */ | |
209 | fgoldi_mul(Y, Y, &t1); /* Y = c E (C - D) */ | |
210 | } | |
211 | ||
212 | static DEFINE_SCMUL(ptmul, fgoldi, 4, PIECEWD, NPIECE, ptadd, ptdbl) | |
213 | static DEFINE_SCSIMMUL(ptsimmul, fgoldi, 2, PIECEWD, NPIECE, ptadd, ptdbl) | |
214 | ||
215 | /*----- Key derivation utilities ------------------------------------------*/ | |
216 | ||
217 | static void unpack_key(scaf_piece a[NPIECE], octet h1[57], | |
218 | const octet *k, size_t ksz) | |
219 | { | |
220 | shake_ctx h; | |
221 | octet b[57]; | |
222 | ||
223 | shake256_init(&h); shake_hash(&h, k, ksz); | |
224 | shake_xof(&h); shake_get(&h, b, sizeof(b)); | |
225 | b[0] &= 0xfcu; b[55] |= 0x80u; scaf_load(a, b, 56, NPIECE, PIECEWD); | |
226 | if (h1) shake_get(&h, h1, 57); | |
227 | } | |
228 | ||
229 | #define PREFIX_BUFSZ 266 | |
230 | static size_t prefix(octet b[PREFIX_BUFSZ], | |
231 | int phflag, const octet *p, size_t psz) | |
232 | { | |
233 | memcpy(b, "SigEd448", 8); | |
234 | b[8] = phflag; | |
235 | assert(psz <= ED448_MAXPERSOSZ); b[9] = psz; memcpy(b + 10, p, psz); | |
236 | return (psz + 10); | |
237 | } | |
238 | ||
239 | /*----- Main code ---------------------------------------------------------*/ | |
240 | ||
241 | /* --- @ed448_pubkey@ --- * | |
242 | * | |
243 | * Arguments: @octet K[ED448_PUBSZ]@ = where to put the public key | |
244 | * @const void *k@ = private key | |
245 | * @size_t ksz@ = length of private key | |
246 | * | |
247 | * Returns: --- | |
248 | * | |
249 | * Use: Derives the public key from a private key. | |
250 | */ | |
251 | ||
252 | void ed448_pubkey(octet K[ED448_PUBSZ], const void *k, size_t ksz) | |
253 | { | |
254 | scaf_piece a[NPIECE]; | |
255 | fgoldi AX, AY, AZ; | |
256 | ||
257 | unpack_key(a, 0, k, ksz); | |
258 | ptmul(&AX, &AY, &AZ, a, BX, BY, BZ); | |
259 | ptencode(K, &AX, &AY, &AZ); | |
260 | } | |
261 | ||
262 | /* --- @ed448_sign@ --- * | |
263 | * | |
264 | * Arguments: @octet sig[ED448_SIGSZ]@ = where to put the signature | |
265 | * @const void *k@ = private key | |
266 | * @size_t ksz@ = length of private key | |
267 | * @const octet K[ED448_PUBSZ]@ = public key | |
268 | * @int phflag@ = whether the `message' has been hashed already | |
269 | * @const void *p@ = personalization string | |
270 | * @size_t psz@ = length of personalization string | |
271 | * @const void *m@ = message to sign | |
272 | * @size_t msz@ = length of message | |
273 | * | |
274 | * Returns: --- | |
275 | * | |
276 | * Use: Signs a message. | |
277 | */ | |
278 | ||
279 | void ed448_sign(octet sig[ED448_SIGSZ], | |
280 | const void *k, size_t ksz, const octet K[ED448_PUBSZ], | |
281 | int phflag, const void *p, size_t psz, | |
282 | const void *m, size_t msz) | |
283 | { | |
284 | shake_ctx h; | |
285 | scaf_piece a[NPIECE], r[NPIECE], t[NPIECE], scratch[3*NPIECE]; | |
286 | scaf_dblpiece tt[2*NPIECE]; | |
287 | fgoldi RX, RY, RZ; | |
288 | octet h1[57], pb[PREFIX_BUFSZ], rb[114]; | |
289 | unsigned i; | |
290 | ||
291 | /* Get my private key. */ | |
292 | unpack_key(a, h1, k, ksz); | |
293 | ||
294 | /* Determine the prefix string. */ | |
295 | psz = prefix(pb, phflag, p, psz); | |
296 | ||
297 | /* Select the nonce and the vector part. */ | |
298 | shake256_init(&h); | |
299 | shake_hash(&h, pb, psz); | |
300 | shake_hash(&h, h1, sizeof(h1)); | |
301 | shake_hash(&h, m, msz); | |
302 | shake_done(&h, rb, 114); | |
303 | scaf_loaddbl(tt, rb, 114, 2*NPIECE, PIECEWD); | |
304 | scaf_reduce(r, tt, l, mu, NPIECE, PIECEWD, scratch); | |
305 | ptmul(&RX, &RY, &RZ, r, BX, BY, BZ); | |
306 | ptencode(sig, &RX, &RY, &RZ); | |
307 | ||
308 | /* Calculate the scalar part. */ | |
309 | shake256_init(&h); | |
310 | shake_hash(&h, pb, psz); | |
311 | shake_hash(&h, sig, 57); | |
312 | shake_hash(&h, K, 57); | |
313 | shake_hash(&h, m, msz); | |
314 | shake_done(&h, rb, 114); | |
315 | scaf_loaddbl(tt, rb, 114, 2*NPIECE, PIECEWD); | |
316 | scaf_reduce(t, tt, l, mu, NPIECE, PIECEWD, scratch); | |
317 | scaf_mul(tt, t, a, NPIECE); | |
318 | for (i = 0; i < NPIECE; i++) tt[i] += r[i]; | |
319 | scaf_reduce(t, tt, l, mu, NPIECE, PIECEWD, scratch); | |
320 | scaf_store(sig + 57, 57, t, NPIECE, PIECEWD); | |
321 | } | |
322 | ||
323 | /* --- @ed448_verify@ --- * | |
324 | * | |
325 | * Arguments: @const octet K[ED448_PUBSZ]@ = public key | |
326 | * @const void *m@ = message to sign | |
327 | * @int phflag@ = whether the `message' has been hashed already | |
328 | * @const void *p@ = personalization string | |
329 | * @size_t psz@ = length of personalization string | |
330 | * @size_t msz@ = length of message | |
331 | * @const octet sig[ED448_SIGSZ]@ = signature | |
332 | * | |
333 | * Returns: Zero if OK, negative on failure. | |
334 | * | |
335 | * Use: Verify a signature. | |
336 | */ | |
337 | ||
338 | int ed448_verify(const octet K[ED448_PUBSZ], | |
339 | int phflag, const void *p, size_t psz, | |
340 | const void *m, size_t msz, | |
341 | const octet sig[ED448_SIGSZ]) | |
342 | { | |
343 | shake_ctx h; | |
344 | scaf_piece s[NPIECE], t[NPIECE], scratch[3*NPIECE]; | |
345 | scaf_dblpiece tt[2*NPIECE]; | |
346 | fgoldi AX, AY, AZ, RX, RY, RZ; | |
347 | octet b[PREFIX_BUFSZ]; | |
348 | ||
349 | /* Unpack the public key. Negate it: we're meant to subtract the term | |
350 | * involving the public key point, and this is easier than negating the | |
351 | * scalar. | |
352 | */ | |
353 | if (ptdecode(&AX, &AY, &AZ, K)) return (-1); | |
354 | fgoldi_neg(&AX, &AX); | |
355 | ||
356 | /* Load the scalar and check that it's in range. The easy way is to store | |
357 | * it again and see if the two match. | |
358 | */ | |
359 | scaf_loaddbl(tt, sig + 57, 57, 2*NPIECE, PIECEWD); | |
360 | scaf_reduce(s, tt, l, mu, NPIECE, PIECEWD, scratch); | |
361 | scaf_store(b, 57, s, NPIECE, PIECEWD); | |
362 | if (memcmp(b, sig + 57, 57) != 0) return (-1); | |
363 | ||
364 | /* Check the signature. */ | |
365 | psz = prefix(b, phflag, p, psz); | |
366 | shake256_init(&h); | |
367 | shake_hash(&h, b, psz); | |
368 | shake_hash(&h, sig, 57); | |
369 | shake_hash(&h, K, ED448_PUBSZ); | |
370 | shake_hash(&h, m, msz); | |
371 | shake_done(&h, b, 114); | |
372 | scaf_loaddbl(tt, b, 114, 2*NPIECE, PIECEWD); | |
373 | scaf_reduce(t, tt, l, mu, NPIECE, PIECEWD, scratch); | |
374 | ptsimmul(&RX, &RY, &RZ, s, BX, BY, BZ, t, &AX, &AY, &AZ); | |
375 | ptencode(b, &RX, &RY, &RZ); | |
376 | if (memcmp(b, sig, 57) != 0) return (-1); | |
377 | ||
378 | /* All is good. */ | |
379 | return (0); | |
380 | } | |
381 | ||
382 | /*----- That's all, folks -------------------------------------------------*/ |