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1 | /* -*-c-*- |
2 | * | |
3 | * Arithmetic modulo 2^255 - 19 | |
4 | * | |
5 | * (c) 2017 Straylight/Edgeware | |
6 | */ | |
7 | ||
8 | /*----- Licensing notice --------------------------------------------------* | |
9 | * | |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
16 | * | |
17 | * Catacomb is distributed in the hope that it will be useful, | |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
21 | * | |
22 | * You should have received a copy of the GNU Library General Public | |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
28 | /*----- Header files ------------------------------------------------------*/ | |
29 | ||
30 | #include "config.h" | |
31 | ||
32 | #include "f25519.h" | |
33 | ||
34 | /*----- Basic setup -------------------------------------------------------*/ | |
35 | ||
36 | #if F25519_IMPL == 26 | |
37 | /* Elements x of GF(2^255 - 19) are represented by ten signed integers x_i: x | |
38 | * = SUM_{0<=i<10} x_i 2^ceil(51i/2), mostly following Bernstein's original | |
39 | * paper. | |
40 | */ | |
41 | ||
42 | typedef int32 piece; typedef int64 dblpiece; | |
43 | typedef uint32 upiece; typedef uint64 udblpiece; | |
44 | #define P p26 | |
45 | #define PIECEWD(i) ((i)%2 ? 25 : 26) | |
46 | #define NPIECE 10 | |
47 | ||
48 | #define M26 0x03ffffffu | |
49 | #define M25 0x01ffffffu | |
50 | #define B26 0x04000000u | |
51 | #define B25 0x02000000u | |
52 | #define B24 0x01000000u | |
53 | ||
54 | #define PIECES(v) v##0, v##1, v##2, v##3, v##4, v##5, v##6, v##7, v##8, v##9 | |
55 | #define FETCH(v, w) do { \ | |
56 | v##0 = (w)->P[0]; v##1 = (w)->P[1]; \ | |
57 | v##2 = (w)->P[2]; v##3 = (w)->P[3]; \ | |
58 | v##4 = (w)->P[4]; v##5 = (w)->P[5]; \ | |
59 | v##6 = (w)->P[6]; v##7 = (w)->P[7]; \ | |
60 | v##8 = (w)->P[8]; v##9 = (w)->P[9]; \ | |
61 | } while (0) | |
62 | #define STASH(w, v) do { \ | |
63 | (w)->P[0] = v##0; (w)->P[1] = v##1; \ | |
64 | (w)->P[2] = v##2; (w)->P[3] = v##3; \ | |
65 | (w)->P[4] = v##4; (w)->P[5] = v##5; \ | |
66 | (w)->P[6] = v##6; (w)->P[7] = v##7; \ | |
67 | (w)->P[8] = v##8; (w)->P[9] = v##9; \ | |
68 | } while (0) | |
69 | ||
70 | #elif F25519_IMPL == 10 | |
71 | /* Elements x of GF(2^255 - 19) are represented by 26 signed integers x_i: x | |
72 | * = SUM_{0<=i<26} x_i 2^ceil(255i/26); i.e., most pieces are 10 bits wide, | |
73 | * except for pieces 5, 10, 15, 20, and 25 which have 9 bits. | |
74 | */ | |
75 | ||
76 | typedef int16 piece; typedef int32 dblpiece; | |
77 | typedef uint16 upiece; typedef uint32 udblpiece; | |
78 | #define P p10 | |
79 | #define PIECEWD(i) \ | |
80 | ((i) == 5 || (i) == 10 || (i) == 15 || (i) == 20 || (i) == 25 ? 9 : 10) | |
81 | #define NPIECE 26 | |
82 | ||
83 | #define B10 0x0400 | |
84 | #define B9 0x200 | |
85 | #define B8 0x100 | |
86 | #define M10 0x3ff | |
87 | #define M9 0x1ff | |
88 | ||
89 | #endif | |
90 | ||
91 | /*----- Debugging machinery -----------------------------------------------*/ | |
92 | ||
93 | #if defined(F25519_DEBUG) || defined(TEST_RIG) | |
94 | ||
95 | #include <stdio.h> | |
96 | ||
97 | #include "mp.h" | |
98 | #include "mptext.h" | |
99 | ||
100 | static mp *get_2p255m91(void) | |
101 | { | |
102 | mpw w19 = 19; | |
103 | mp *p = MP_NEW, m19; | |
104 | ||
105 | p = mp_setbit(p, MP_ZERO, 255); | |
106 | mp_build(&m19, &w19, &w19 + 1); | |
107 | p = mp_sub(p, p, &m19); | |
108 | return (p); | |
109 | } | |
110 | ||
111 | DEF_FDUMP(fdump, piece, PIECEWD, NPIECE, 32, get_2p255m91()) | |
112 | ||
113 | #endif | |
114 | ||
115 | /*----- Loading and storing -----------------------------------------------*/ | |
116 | ||
117 | /* --- @f25519_load@ --- * | |
118 | * | |
119 | * Arguments: @f25519 *z@ = where to store the result | |
120 | * @const octet xv[32]@ = source to read | |
121 | * | |
122 | * Returns: --- | |
123 | * | |
124 | * Use: Reads an element of %$\gf{2^{255} - 19}$% in external | |
125 | * representation from @xv@ and stores it in @z@. | |
126 | * | |
127 | * External representation is little-endian base-256. Some | |
128 | * elements have multiple encodings, which are not produced by | |
129 | * correct software; use of noncanonical encodings is not an | |
130 | * error, and toleration of them is considered a performance | |
131 | * feature. | |
132 | */ | |
133 | ||
134 | void f25519_load(f25519 *z, const octet xv[32]) | |
135 | { | |
136 | #if F25519_IMPL == 26 | |
137 | ||
138 | uint32 xw0 = LOAD32_L(xv + 0), xw1 = LOAD32_L(xv + 4), | |
139 | xw2 = LOAD32_L(xv + 8), xw3 = LOAD32_L(xv + 12), | |
140 | xw4 = LOAD32_L(xv + 16), xw5 = LOAD32_L(xv + 20), | |
141 | xw6 = LOAD32_L(xv + 24), xw7 = LOAD32_L(xv + 28); | |
142 | piece PIECES(x), b, c; | |
143 | ||
144 | /* First, split the 32-bit words into the irregularly-sized pieces we need | |
145 | * for the field representation. These pieces are all positive. We'll do | |
146 | * the sign correction afterwards. | |
147 | * | |
148 | * It may be that the top bit of the input is set. Avoid trouble by | |
149 | * folding that back round into the bottom piece of the representation. | |
150 | * | |
151 | * Here, we briefly have 0 <= x_0 < 2^26 + 19, but will resolve this later. | |
152 | * Otherwise, we have 0 <= x_{2i} < 2^26, and 0 <= x_{2i+1} < 2^25. | |
153 | */ | |
154 | x0 = ((xw0 << 0)&0x03ffffff) + 19*((xw7 >> 31)&0x00000001); | |
155 | x1 = ((xw1 << 6)&0x01ffffc0) | ((xw0 >> 26)&0x0000003f); | |
156 | x2 = ((xw2 << 13)&0x03ffe000) | ((xw1 >> 19)&0x00001fff); | |
157 | x3 = ((xw3 << 19)&0x01f80000) | ((xw2 >> 13)&0x0007ffff); | |
158 | x4 = ((xw3 >> 6)&0x03ffffff); | |
159 | x5 = (xw4 << 0)&0x01ffffff; | |
160 | x6 = ((xw5 << 7)&0x03ffff80) | ((xw4 >> 25)&0x0000007f); | |
161 | x7 = ((xw6 << 13)&0x01ffe000) | ((xw5 >> 19)&0x00001fff); | |
162 | x8 = ((xw7 << 20)&0x03f00000) | ((xw6 >> 12)&0x000fffff); | |
163 | x9 = ((xw7 >> 6)&0x01ffffff); | |
164 | ||
165 | /* Next, we convert these pieces into a roughly balanced signed | |
166 | * representation. For each piece, check to see if its top bit is set. If | |
167 | * it is, then lend a bit to the next piece over. For x_9, this needs to | |
168 | * be carried around, which is a little fiddly. In particular, we delay | |
169 | * the carry until after all of the pieces have been balanced. If we don't | |
170 | * do this, then we have to do a more expensive test for nonzeroness to | |
171 | * decide whether to lend a bit leftwards rather than just testing a single | |
172 | * bit. | |
173 | * | |
174 | * This fixes up the anomalous size of x_0: the loan of a bit becomes an | |
175 | * actual carry if x_0 >= 2^26. By the end, then, we have: | |
176 | * | |
177 | * { 2^25 if i even | |
178 | * |x_i| <= { | |
179 | * { 2^24 if i odd | |
180 | * | |
181 | * Note that we don't try for a canonical representation here: both upper | |
182 | * and lower bounds are achievable. | |
183 | * | |
184 | * All of the x_i at this point are positive, so we don't need to do | |
185 | * anything wierd when masking them. | |
186 | */ | |
187 | b = x9&B24; c = 19&((b >> 19) - (b >> 24)); x9 -= b << 1; | |
188 | b = x8&B25; x9 += b >> 25; x8 -= b << 1; | |
189 | b = x7&B24; x8 += b >> 24; x7 -= b << 1; | |
190 | b = x6&B25; x7 += b >> 25; x6 -= b << 1; | |
191 | b = x5&B24; x6 += b >> 24; x5 -= b << 1; | |
192 | b = x4&B25; x5 += b >> 25; x4 -= b << 1; | |
193 | b = x3&B24; x4 += b >> 24; x3 -= b << 1; | |
194 | b = x2&B25; x3 += b >> 25; x2 -= b << 1; | |
195 | b = x1&B24; x2 += b >> 24; x1 -= b << 1; | |
196 | b = x0&B25; x1 += (b >> 25) + (x0 >> 26); x0 = (x0&M26) - (b << 1); | |
197 | x0 += c; | |
198 | ||
199 | /* And with that, we're done. */ | |
200 | STASH(z, x); | |
201 | ||
202 | #elif F25519_IMPL == 10 | |
203 | ||
204 | piece x[NPIECE]; | |
205 | unsigned i, j, n, wd; | |
206 | uint32 a; | |
207 | int b, c; | |
208 | ||
209 | /* First, just get the content out of the buffer. */ | |
210 | for (i = j = a = n = 0, wd = 10; j < NPIECE; i++) { | |
211 | a |= (uint32)xv[i] << n; n += 8; | |
212 | if (n >= wd) { | |
213 | x[j++] = a&MASK(wd); | |
214 | a >>= wd; n -= wd; | |
215 | wd = PIECEWD(j); | |
216 | } | |
217 | } | |
218 | ||
219 | /* There's a little bit left over from the top byte. Carry it into the low | |
220 | * piece. | |
221 | */ | |
222 | x[0] += 19*(int)(a&MASK(n)); | |
223 | ||
224 | /* Next, convert the pieces into a roughly balanced signed representation. | |
225 | * If a piece's top bit is set, lend a bit to the next piece over. For | |
226 | * x_25, this needs to be carried around, which is a bit fiddly. | |
227 | */ | |
228 | b = x[NPIECE - 1]&B8; | |
229 | c = 19&((b >> 3) - (b >> 8)); | |
230 | x[NPIECE - 1] -= b << 1; | |
231 | for (i = NPIECE - 2; i > 0; i--) { | |
232 | wd = PIECEWD(i) - 1; | |
233 | b = x[i]&BIT(wd); | |
234 | x[i + 1] += b >> wd; | |
235 | x[i] -= b << 1; | |
236 | } | |
237 | b = x[0]&B9; | |
238 | x[1] += (b >> 9) + (x[0] >> 10); | |
239 | x[0] = (x[0]&M10) - (b << 1) + c; | |
240 | ||
241 | /* And we're done. */ | |
242 | for (i = 0; i < NPIECE; i++) z->P[i] = x[i]; | |
243 | ||
244 | #endif | |
245 | } | |
246 | ||
247 | /* --- @f25519_store@ --- * | |
248 | * | |
249 | * Arguments: @octet zv[32]@ = where to write the result | |
250 | * @const f25519 *x@ = the field element to write | |
251 | * | |
252 | * Returns: --- | |
253 | * | |
254 | * Use: Stores a field element in the given octet vector in external | |
255 | * representation. A canonical encoding is always stored, so, | |
256 | * in particular, the top bit of @xv[31]@ is always left clear. | |
257 | */ | |
258 | ||
259 | void f25519_store(octet zv[32], const f25519 *x) | |
260 | { | |
261 | #if F25519_IMPL == 26 | |
262 | ||
263 | piece PIECES(x), PIECES(y), c, d; | |
264 | uint32 zw0, zw1, zw2, zw3, zw4, zw5, zw6, zw7; | |
265 | mask32 m; | |
266 | ||
267 | FETCH(x, x); | |
268 | ||
269 | /* First, propagate the carries throughout the pieces. By the end of this, | |
270 | * we'll have all of the pieces canonically sized and positive, and maybe | |
271 | * there'll be (signed) carry out. The carry c is in { -1, 0, +1 }, and | |
272 | * the remaining value will be in the half-open interval [0, 2^255). The | |
273 | * whole represented value is then x + 2^255 c. | |
274 | * | |
275 | * It's worth paying careful attention to the bounds. We assume that we | |
276 | * start out with |x_i| <= 2^30. We start by cutting off and reducing the | |
277 | * carry c_9 from the topmost piece, x_9. This leaves 0 <= x_9 < 2^25; and | |
278 | * we'll have |c_9| <= 2^5. We multiply this by 19 and we'll add it onto | |
279 | * x_0 and propagate the carries: but what bounds can we calculate on x | |
280 | * before this? | |
281 | * | |
282 | * Let o_i = floor(51 i/2). We have X_i = SUM_{0<=j<i} x_j 2^{o_i}, so | |
283 | * x = X_10. We see, inductively, that |X_i| < 2^{31+o_{i-1}}: X_0 = 0; | |
284 | * |x_i| <= 2^30; and |X_{i+1}| = |X_i + x_i 2^{o_i}| <= |X_i| + 2^{30+o_i} | |
285 | * < 2^{31+o_i}. Then x = X_9 + 2^230 x_9, and we have better bounds for | |
286 | * x_9, so | |
287 | * | |
288 | * -2^235 < x + 19 c_9 < 2^255 + 2^235 | |
289 | * | |
290 | * Here, the x_i are signed, so we must be cautious about bithacking them. | |
291 | */ | |
292 | c = ASR(piece, x9, 25); x9 = (upiece)x9&M25; | |
293 | x0 += 19*c; c = ASR(piece, x0, 26); x0 = (upiece)x0&M26; | |
294 | x1 += c; c = ASR(piece, x1, 25); x1 = (upiece)x1&M25; | |
295 | x2 += c; c = ASR(piece, x2, 26); x2 = (upiece)x2&M26; | |
296 | x3 += c; c = ASR(piece, x3, 25); x3 = (upiece)x3&M25; | |
297 | x4 += c; c = ASR(piece, x4, 26); x4 = (upiece)x4&M26; | |
298 | x5 += c; c = ASR(piece, x5, 25); x5 = (upiece)x5&M25; | |
299 | x6 += c; c = ASR(piece, x6, 26); x6 = (upiece)x6&M26; | |
300 | x7 += c; c = ASR(piece, x7, 25); x7 = (upiece)x7&M25; | |
301 | x8 += c; c = ASR(piece, x8, 26); x8 = (upiece)x8&M26; | |
302 | x9 += c; c = ASR(piece, x9, 25); x9 = (upiece)x9&M25; | |
303 | ||
304 | /* Now we have a slightly fiddly job to do. If c = +1, or if c = 0 and | |
305 | * x >= 2^255 - 19, then we should subtract 2^255 - 19 from the whole | |
306 | * value; if c = -1 then we should add 2^255 - 19; and otherwise we should | |
307 | * do nothing. | |
308 | * | |
309 | * But conditional behaviour is bad, m'kay. So here's what we do instead. | |
310 | * | |
311 | * The first job is to sort out what we wanted to do. If c = -1 then we | |
312 | * want to (a) invert the constant addend and (b) feed in a carry-in; | |
313 | * otherwise, we don't. | |
314 | */ | |
315 | m = SIGN(c); | |
316 | d = m&1; | |
317 | ||
318 | /* Now do the addition/subtraction. Remember that all of the x_i are | |
319 | * nonnegative, so shifting and masking are safe and easy. | |
320 | */ | |
321 | d += x0 + (19 ^ (M26&m)); y0 = d&M26; d >>= 26; | |
322 | d += x1 + (M25&m); y1 = d&M25; d >>= 25; | |
323 | d += x2 + (M26&m); y2 = d&M26; d >>= 26; | |
324 | d += x3 + (M25&m); y3 = d&M25; d >>= 25; | |
325 | d += x4 + (M26&m); y4 = d&M26; d >>= 26; | |
326 | d += x5 + (M25&m); y5 = d&M25; d >>= 25; | |
327 | d += x6 + (M26&m); y6 = d&M26; d >>= 26; | |
328 | d += x7 + (M25&m); y7 = d&M25; d >>= 25; | |
329 | d += x8 + (M26&m); y8 = d&M26; d >>= 26; | |
330 | d += x9 + (M25&m); y9 = d&M25; d >>= 25; | |
331 | ||
332 | /* The final carry-out is in d; since we only did addition, and the x_i are | |
333 | * nonnegative, then d is in { 0, 1 }. We want to keep y, rather than x, | |
334 | * if (a) c /= 0 (in which case we know that the old value was | |
335 | * unsatisfactory), or (b) if d = 1 (in which case, if c = 0, we know that | |
336 | * the subtraction didn't cause a borrow, so we must be in the case where | |
337 | * 2^255 - 19 <= x < 2^255). | |
338 | */ | |
339 | m = NONZEROP(c) | ~NONZEROP(d - 1); | |
340 | x0 = (y0&m) | (x0&~m); x1 = (y1&m) | (x1&~m); | |
341 | x2 = (y2&m) | (x2&~m); x3 = (y3&m) | (x3&~m); | |
342 | x4 = (y4&m) | (x4&~m); x5 = (y5&m) | (x5&~m); | |
343 | x6 = (y6&m) | (x6&~m); x7 = (y7&m) | (x7&~m); | |
344 | x8 = (y8&m) | (x8&~m); x9 = (y9&m) | (x9&~m); | |
345 | ||
346 | /* Extract 32-bit words from the value. */ | |
347 | zw0 = ((x0 >> 0)&0x03ffffff) | (((uint32)x1 << 26)&0xfc000000); | |
348 | zw1 = ((x1 >> 6)&0x0007ffff) | (((uint32)x2 << 19)&0xfff80000); | |
349 | zw2 = ((x2 >> 13)&0x00001fff) | (((uint32)x3 << 13)&0xffffe000); | |
350 | zw3 = ((x3 >> 19)&0x0000003f) | (((uint32)x4 << 6)&0xffffffc0); | |
351 | zw4 = ((x5 >> 0)&0x01ffffff) | (((uint32)x6 << 25)&0xfe000000); | |
352 | zw5 = ((x6 >> 7)&0x0007ffff) | (((uint32)x7 << 19)&0xfff80000); | |
353 | zw6 = ((x7 >> 13)&0x00000fff) | (((uint32)x8 << 12)&0xfffff000); | |
354 | zw7 = ((x8 >> 20)&0x0000003f) | (((uint32)x9 << 6)&0x7fffffc0); | |
355 | ||
356 | /* Store the result as an octet string. */ | |
357 | STORE32_L(zv + 0, zw0); STORE32_L(zv + 4, zw1); | |
358 | STORE32_L(zv + 8, zw2); STORE32_L(zv + 12, zw3); | |
359 | STORE32_L(zv + 16, zw4); STORE32_L(zv + 20, zw5); | |
360 | STORE32_L(zv + 24, zw6); STORE32_L(zv + 28, zw7); | |
361 | ||
362 | #elif F25519_IMPL == 10 | |
363 | ||
364 | piece y[NPIECE], yy[NPIECE], c, d; | |
365 | unsigned i, j, n, wd; | |
366 | uint32 m, a; | |
367 | ||
368 | /* Before we do anything, copy the input so we can hack on it. */ | |
369 | for (i = 0; i < NPIECE; i++) y[i] = x->P[i]; | |
370 | ||
371 | /* First, propagate the carries throughout the pieces. | |
372 | * | |
373 | * It's worth paying careful attention to the bounds. We assume that we | |
374 | * start out with |y_i| <= 2^14. We start by cutting off and reducing the | |
375 | * carry c_25 from the topmost piece, y_25. This leaves 0 <= y_25 < 2^9; | |
376 | * and we'll have |c_25| <= 2^5. We multiply this by 19 and we'll ad it | |
377 | * onto y_0 and propagte the carries: but what bounds can we calculate on | |
378 | * y before this? | |
379 | * | |
380 | * Let o_i = floor(255 i/26). We have Y_i = SUM_{0<=j<i} y_j 2^{o_i}, so | |
381 | * y = Y_26. We see, inductively, that |Y_i| < 2^{31+o_{i-1}}: Y_0 = 0; | |
382 | * |y_i| <= 2^14; and |Y_{i+1}| = |Y_i + y_i 2^{o_i}| <= |Y_i| + 2^{14+o_i} | |
383 | * < 2^{15+o_i}. Then x = Y_25 + 2^246 y_25, and we have better bounds for | |
384 | * y_25, so | |
385 | * | |
386 | * -2^251 < y + 19 c_25 < 2^255 + 2^251 | |
387 | * | |
388 | * Here, the y_i are signed, so we must be cautious about bithacking them. | |
389 | * | |
390 | * (Rather closer than the 10-piece case above, but still doable in one | |
391 | * pass.) | |
392 | */ | |
393 | c = 19*ASR(piece, y[NPIECE - 1], 9); | |
394 | y[NPIECE - 1] = (upiece)y[NPIECE - 1]&M9; | |
395 | for (i = 0; i < NPIECE; i++) { | |
396 | wd = PIECEWD(i); | |
397 | y[i] += c; | |
398 | c = ASR(piece, y[i], wd); | |
399 | y[i] = (upiece)y[i]&MASK(wd); | |
400 | } | |
401 | ||
402 | /* Now the addition or subtraction. */ | |
403 | m = SIGN(c); | |
404 | d = m&1; | |
405 | ||
406 | d += y[0] + (19 ^ (M10&m)); | |
407 | yy[0] = d&M10; | |
408 | d >>= 10; | |
409 | for (i = 1; i < NPIECE; i++) { | |
410 | wd = PIECEWD(i); | |
411 | d += y[i] + (MASK(wd)&m); | |
412 | yy[i] = d&MASK(wd); | |
413 | d >>= wd; | |
414 | } | |
415 | ||
416 | /* Choose which value to keep. */ | |
417 | m = NONZEROP(c) | ~NONZEROP(d - 1); | |
418 | for (i = 0; i < NPIECE; i++) y[i] = (yy[i]&m) | (y[i]&~m); | |
419 | ||
420 | /* Store the result as an octet string. */ | |
421 | for (i = j = a = n = 0; i < NPIECE; i++) { | |
422 | a |= (upiece)y[i] << n; n += PIECEWD(i); | |
423 | while (n >= 8) { | |
424 | zv[j++] = a&0xff; | |
425 | a >>= 8; n -= 8; | |
426 | } | |
427 | } | |
428 | zv[j++] = a; | |
429 | ||
430 | #endif | |
431 | } | |
432 | ||
433 | /* --- @f25519_set@ --- * | |
434 | * | |
435 | * Arguments: @f25519 *z@ = where to write the result | |
436 | * @int a@ = a small-ish constant | |
437 | * | |
438 | * Returns: --- | |
439 | * | |
440 | * Use: Sets @z@ to equal @a@. | |
441 | */ | |
442 | ||
443 | void f25519_set(f25519 *x, int a) | |
444 | { | |
445 | unsigned i; | |
446 | ||
447 | x->P[0] = a; | |
448 | for (i = 1; i < NPIECE; i++) x->P[i] = 0; | |
449 | } | |
450 | ||
451 | /*----- Basic arithmetic --------------------------------------------------*/ | |
452 | ||
453 | /* --- @f25519_add@ --- * | |
454 | * | |
455 | * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@) | |
456 | * @const f25519 *x, *y@ = two operands | |
457 | * | |
458 | * Returns: --- | |
459 | * | |
460 | * Use: Set @z@ to the sum %$x + y$%. | |
461 | */ | |
462 | ||
463 | void f25519_add(f25519 *z, const f25519 *x, const f25519 *y) | |
464 | { | |
465 | #if F25519_IMPL == 26 | |
466 | z->P[0] = x->P[0] + y->P[0]; z->P[1] = x->P[1] + y->P[1]; | |
467 | z->P[2] = x->P[2] + y->P[2]; z->P[3] = x->P[3] + y->P[3]; | |
468 | z->P[4] = x->P[4] + y->P[4]; z->P[5] = x->P[5] + y->P[5]; | |
469 | z->P[6] = x->P[6] + y->P[6]; z->P[7] = x->P[7] + y->P[7]; | |
470 | z->P[8] = x->P[8] + y->P[8]; z->P[9] = x->P[9] + y->P[9]; | |
471 | #elif F25519_IMPL == 10 | |
472 | unsigned i; | |
473 | for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] + y->P[i]; | |
474 | #endif | |
475 | } | |
476 | ||
477 | /* --- @f25519_sub@ --- * | |
478 | * | |
479 | * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@) | |
480 | * @const f25519 *x, *y@ = two operands | |
481 | * | |
482 | * Returns: --- | |
483 | * | |
484 | * Use: Set @z@ to the difference %$x - y$%. | |
485 | */ | |
486 | ||
487 | void f25519_sub(f25519 *z, const f25519 *x, const f25519 *y) | |
488 | { | |
489 | #if F25519_IMPL == 26 | |
490 | z->P[0] = x->P[0] - y->P[0]; z->P[1] = x->P[1] - y->P[1]; | |
491 | z->P[2] = x->P[2] - y->P[2]; z->P[3] = x->P[3] - y->P[3]; | |
492 | z->P[4] = x->P[4] - y->P[4]; z->P[5] = x->P[5] - y->P[5]; | |
493 | z->P[6] = x->P[6] - y->P[6]; z->P[7] = x->P[7] - y->P[7]; | |
494 | z->P[8] = x->P[8] - y->P[8]; z->P[9] = x->P[9] - y->P[9]; | |
495 | #elif F25519_IMPL == 10 | |
496 | unsigned i; | |
497 | for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] - y->P[i]; | |
498 | #endif | |
499 | } | |
500 | ||
501 | /*----- Constant-time utilities -------------------------------------------*/ | |
502 | ||
503 | /* --- @f25519_condswap@ --- * | |
504 | * | |
505 | * Arguments: @f25519 *x, *y@ = two operands | |
506 | * @uint32 m@ = a mask | |
507 | * | |
508 | * Returns: --- | |
509 | * | |
510 | * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then | |
511 | * exchange @x@ and @y@. If @m@ has some other value, then | |
512 | * scramble @x@ and @y@ in an unhelpful way. | |
513 | */ | |
514 | ||
515 | void f25519_condswap(f25519 *x, f25519 *y, uint32 m) | |
516 | { | |
517 | mask32 mm = FIX_MASK32(m); | |
518 | ||
519 | #if F25519_IMPL == 26 | |
520 | CONDSWAP(x->P[0], y->P[0], mm); | |
521 | CONDSWAP(x->P[1], y->P[1], mm); | |
522 | CONDSWAP(x->P[2], y->P[2], mm); | |
523 | CONDSWAP(x->P[3], y->P[3], mm); | |
524 | CONDSWAP(x->P[4], y->P[4], mm); | |
525 | CONDSWAP(x->P[5], y->P[5], mm); | |
526 | CONDSWAP(x->P[6], y->P[6], mm); | |
527 | CONDSWAP(x->P[7], y->P[7], mm); | |
528 | CONDSWAP(x->P[8], y->P[8], mm); | |
529 | CONDSWAP(x->P[9], y->P[9], mm); | |
530 | #elif F25519_IMPL == 10 | |
531 | unsigned i; | |
532 | for (i = 0; i < NPIECE; i++) CONDSWAP(x->P[i], y->P[i], mm); | |
533 | #endif | |
534 | } | |
535 | ||
536 | /*----- Multiplication ----------------------------------------------------*/ | |
537 | ||
538 | #if F25519_IMPL == 26 | |
539 | ||
540 | /* Let B = 2^63 - 1 be the largest value such that +B and -B can be | |
541 | * represented in a double-precision piece. On entry, it must be the case | |
542 | * that |X_i| <= M <= B - 2^25 for some M. If this is the case, then, on | |
543 | * exit, we will have |Z_i| <= 2^25 + 19 M/2^25. | |
544 | */ | |
545 | #define CARRYSTEP(z, x, m, b, f, xx, n) do { \ | |
546 | (z) = (dblpiece)((udblpiece)(x)&(m)) - (b) + \ | |
547 | (f)*ASR(dblpiece, (xx), (n)); \ | |
548 | } while (0) | |
549 | #define CARRY_REDUCE(z, x) do { \ | |
550 | dblpiece PIECES(_t); \ | |
551 | \ | |
552 | /* Bias the input pieces. This keeps the carries and so on centred \ | |
553 | * around zero rather than biased positive. \ | |
554 | */ \ | |
555 | _t0 = (x##0) + B25; _t1 = (x##1) + B24; \ | |
556 | _t2 = (x##2) + B25; _t3 = (x##3) + B24; \ | |
557 | _t4 = (x##4) + B25; _t5 = (x##5) + B24; \ | |
558 | _t6 = (x##6) + B25; _t7 = (x##7) + B24; \ | |
559 | _t8 = (x##8) + B25; _t9 = (x##9) + B24; \ | |
560 | \ | |
561 | /* Calculate the reduced pieces. Careful with the bithacking. */ \ | |
562 | CARRYSTEP(z##0, _t0, M26, B25, 19, _t9, 25); \ | |
563 | CARRYSTEP(z##1, _t1, M25, B24, 1, _t0, 26); \ | |
564 | CARRYSTEP(z##2, _t2, M26, B25, 1, _t1, 25); \ | |
565 | CARRYSTEP(z##3, _t3, M25, B24, 1, _t2, 26); \ | |
566 | CARRYSTEP(z##4, _t4, M26, B25, 1, _t3, 25); \ | |
567 | CARRYSTEP(z##5, _t5, M25, B24, 1, _t4, 26); \ | |
568 | CARRYSTEP(z##6, _t6, M26, B25, 1, _t5, 25); \ | |
569 | CARRYSTEP(z##7, _t7, M25, B24, 1, _t6, 26); \ | |
570 | CARRYSTEP(z##8, _t8, M26, B25, 1, _t7, 25); \ | |
571 | CARRYSTEP(z##9, _t9, M25, B24, 1, _t8, 26); \ | |
572 | } while (0) | |
573 | ||
574 | #elif F25519_IMPL == 10 | |
575 | ||
576 | /* Perform carry propagation on X. */ | |
577 | static void carry_reduce(dblpiece x[NPIECE]) | |
578 | { | |
579 | /* Initial bounds: we assume |x_i| < 2^31 - 2^27. */ | |
580 | ||
581 | unsigned i, j; | |
582 | dblpiece c; | |
583 | ||
584 | /* The result is nearly canonical, because we do sequential carry | |
585 | * propagation, because smaller processors are more likely to prefer the | |
586 | * smaller working set than the instruction-level parallelism. | |
587 | * | |
588 | * Start at x_23; truncate it to 10 bits, and propagate the carry to x_24. | |
589 | * Truncate x_24 to 10 bits, and add the carry onto x_25. Truncate x_25 to | |
590 | * 9 bits, and add 19 times the carry onto x_0. And so on. | |
591 | * | |
592 | * Let c_i be the portion of x_i to be carried onto x_{i+1}. I claim that | |
593 | * |c_i| <= 2^22. Then the carry /into/ any x_i has magnitude at most | |
594 | * 19*2^22 < 2^27 (allowing for the reduction as we carry from x_25 to | |
595 | * x_0), and x_i after carry is bounded above by 2^31. Hence, the carry | |
596 | * out is at most 2^22, as claimed. | |
597 | * | |
598 | * Once we reach x_23 for the second time, we start with |x_23| <= 2^9. | |
599 | * The carry into x_23 is at most 2^27 as calculated above; so the carry | |
600 | * out into x_24 has magnitude at most 2^17. In turn, |x_24| <= 2^9 before | |
601 | * the carry, so is now no more than 2^18 in magnitude, and the carry out | |
602 | * into x_25 is at most 2^8. This leaves |x_25| < 2^9 after carry | |
603 | * propagation. | |
604 | * | |
605 | * Be careful with the bit hacking because the quantities involved are | |
606 | * signed. | |
607 | */ | |
608 | ||
609 | /*For each piece, we bias it so that floor division (as done by an | |
610 | * arithmetic right shift) and modulus (as done by bitwise-AND) does the | |
611 | * right thing. | |
612 | */ | |
613 | #define CARRY(i, wd, b, m) do { \ | |
614 | x[i] += (b); \ | |
615 | c = ASR(dblpiece, x[i], (wd)); \ | |
616 | x[i] = (dblpiece)((udblpiece)x[i]&(m)) - (b); \ | |
617 | } while (0) | |
618 | ||
619 | { CARRY(23, 10, B9, M10); } | |
620 | { x[24] += c; CARRY(24, 10, B9, M10); } | |
621 | { x[25] += c; CARRY(25, 9, B8, M9); } | |
622 | { x[0] += 19*c; CARRY( 0, 10, B9, M10); } | |
623 | for (i = 1; i < 21; ) { | |
624 | for (j = i + 4; i < j; ) { x[i] += c; CARRY( i, 10, B9, M10); i++; } | |
625 | { x[i] += c; CARRY( i, 9, B8, M9); i++; } | |
626 | } | |
627 | while (i < 25) { x[i] += c; CARRY( i, 10, B9, M10); i++; } | |
628 | x[25] += c; | |
629 | ||
630 | #undef CARRY | |
631 | } | |
632 | ||
633 | #endif | |
634 | ||
635 | /* --- @f25519_mulconst@ --- * | |
636 | * | |
637 | * Arguments: @f25519 *z@ = where to put the result (may alias @x@) | |
638 | * @const f25519 *x@ = an operand | |
639 | * @long a@ = a small-ish constant; %$|a| < 2^{20}$%. | |
640 | * | |
641 | * Returns: --- | |
642 | * | |
643 | * Use: Set @z@ to the product %$a x$%. | |
644 | */ | |
645 | ||
646 | void f25519_mulconst(f25519 *z, const f25519 *x, long a) | |
647 | { | |
648 | #if F25519_IMPL == 26 | |
649 | ||
650 | piece PIECES(x); | |
651 | dblpiece PIECES(z), aa = a; | |
652 | ||
653 | FETCH(x, x); | |
654 | ||
655 | /* Suppose that |x_i| <= 2^27, and |a| <= 2^23. Then we'll have | |
656 | * |z_i| <= 2^50. | |
657 | */ | |
658 | z0 = aa*x0; z1 = aa*x1; z2 = aa*x2; z3 = aa*x3; z4 = aa*x4; | |
659 | z5 = aa*x5; z6 = aa*x6; z7 = aa*x7; z8 = aa*x8; z9 = aa*x9; | |
660 | ||
661 | /* Following `CARRY_REDUCE', we'll have |z_i| <= 2^26. */ | |
662 | CARRY_REDUCE(z, z); | |
663 | STASH(z, z); | |
664 | ||
665 | #elif F25519_IMPL == 10 | |
666 | ||
667 | dblpiece y[NPIECE]; | |
668 | unsigned i; | |
669 | ||
670 | for (i = 0; i < NPIECE; i++) y[i] = a*x->P[i]; | |
671 | carry_reduce(y); | |
672 | for (i = 0; i < NPIECE; i++) z->P[i] = y[i]; | |
673 | ||
674 | #endif | |
675 | } | |
676 | ||
677 | /* --- @f25519_mul@ --- * | |
678 | * | |
679 | * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@) | |
680 | * @const f25519 *x, *y@ = two operands | |
681 | * | |
682 | * Returns: --- | |
683 | * | |
684 | * Use: Set @z@ to the product %$x y$%. | |
685 | */ | |
686 | ||
687 | void f25519_mul(f25519 *z, const f25519 *x, const f25519 *y) | |
688 | { | |
689 | #if F25519_IMPL == 26 | |
690 | ||
691 | piece PIECES(x), PIECES(y); | |
692 | dblpiece PIECES(z); | |
693 | unsigned i; | |
694 | ||
695 | FETCH(x, x); FETCH(y, y); | |
696 | ||
697 | /* Suppose that |x_i|, |y_i| <= 2^27. Then we'll have | |
698 | * | |
699 | * |z_0| <= 267*2^54 | |
700 | * |z_1| <= 154*2^54 | |
701 | * |z_2| <= 213*2^54 | |
702 | * |z_3| <= 118*2^54 | |
703 | * |z_4| <= 159*2^54 | |
704 | * |z_5| <= 82*2^54 | |
705 | * |z_6| <= 105*2^54 | |
706 | * |z_7| <= 46*2^54 | |
707 | * |z_8| <= 51*2^54 | |
708 | * |z_9| <= 10*2^54 | |
709 | * | |
710 | * all of which are less than 2^63 - 2^25. | |
711 | */ | |
712 | ||
713 | #define M(a, b) ((dblpiece)(a)*(b)) | |
714 | z0 = M(x0, y0) + | |
715 | 19*(M(x2, y8) + M(x4, y6) + M(x6, y4) + M(x8, y2)) + | |
716 | 38*(M(x1, y9) + M(x3, y7) + M(x5, y5) + M(x7, y3) + M(x9, y1)); | |
717 | z1 = M(x0, y1) + M(x1, y0) + | |
718 | 19*(M(x2, y9) + M(x3, y8) + M(x4, y7) + M(x5, y6) + | |
719 | M(x6, y5) + M(x7, y4) + M(x8, y3) + M(x9, y2)); | |
720 | z2 = M(x0, y2) + M(x2, y0) + | |
721 | 2* M(x1, y1) + | |
722 | 19*(M(x4, y8) + M(x6, y6) + M(x8, y4)) + | |
723 | 38*(M(x3, y9) + M(x5, y7) + M(x7, y5) + M(x9, y3)); | |
724 | z3 = M(x0, y3) + M(x1, y2) + M(x2, y1) + M(x3, y0) + | |
725 | 19*(M(x4, y9) + M(x5, y8) + M(x6, y7) + | |
726 | M(x7, y6) + M(x8, y5) + M(x9, y4)); | |
727 | z4 = M(x0, y4) + M(x2, y2) + M(x4, y0) + | |
728 | 2*(M(x1, y3) + M(x3, y1)) + | |
729 | 19*(M(x6, y8) + M(x8, y6)) + | |
730 | 38*(M(x5, y9) + M(x7, y7) + M(x9, y5)); | |
731 | z5 = M(x0, y5) + M(x1, y4) + M(x2, y3) + | |
732 | M(x3, y2) + M(x4, y1) + M(x5, y0) + | |
733 | 19*(M(x6, y9) + M(x7, y8) + M(x8, y7) + M(x9, y6)); | |
734 | z6 = M(x0, y6) + M(x2, y4) + M(x4, y2) + M(x6, y0) + | |
735 | 2*(M(x1, y5) + M(x3, y3) + M(x5, y1)) + | |
736 | 19* M(x8, y8) + | |
737 | 38*(M(x7, y9) + M(x9, y7)); | |
738 | z7 = M(x0, y7) + M(x1, y6) + M(x2, y5) + M(x3, y4) + | |
739 | M(x4, y3) + M(x5, y2) + M(x6, y1) + M(x7, y0) + | |
740 | 19*(M(x8, y9) + M(x9, y8)); | |
741 | z8 = M(x0, y8) + M(x2, y6) + M(x4, y4) + M(x6, y2) + M(x8, y0) + | |
742 | 2*(M(x1, y7) + M(x3, y5) + M(x5, y3) + M(x7, y1)) + | |
743 | 38* M(x9, y9); | |
744 | z9 = M(x0, y9) + M(x1, y8) + M(x2, y7) + M(x3, y6) + M(x4, y5) + | |
745 | M(x5, y4) + M(x6, y3) + M(x7, y2) + M(x8, y1) + M(x9, y0); | |
746 | #undef M | |
747 | ||
748 | /* From above, we have |z_i| <= 2^63 - 2^25. A pass of `CARRY_REDUCE' will | |
749 | * leave |z_i| <= 2^38 + 2^25; and a second pass will leave |z_i| <= 2^25 + | |
750 | * 2^13, which is comfortable for an addition prior to the next | |
751 | * multiplication. | |
752 | */ | |
753 | for (i = 0; i < 2; i++) CARRY_REDUCE(z, z); | |
754 | STASH(z, z); | |
755 | ||
756 | #elif F25519_IMPL == 10 | |
757 | ||
758 | dblpiece u[NPIECE], t, tt, p; | |
759 | unsigned i, j, k; | |
760 | ||
761 | /* This is unpleasant. Honestly, this table seems to be the best way of | |
762 | * doing it. | |
763 | */ | |
764 | static const unsigned short off[NPIECE] = { | |
765 | 0, 10, 20, 30, 40, 50, 59, 69, 79, 89, 99, 108, 118, | |
766 | 128, 138, 148, 157, 167, 177, 187, 197, 206, 216, 226, 236, 246 | |
767 | }; | |
768 | ||
769 | /* First pass: things we must multiply by 19 or 38. */ | |
770 | for (i = 0; i < NPIECE - 1; i++) { | |
771 | t = tt = 0; | |
772 | for (j = i + 1; j < NPIECE; j++) { | |
773 | k = NPIECE + i - j; p = (dblpiece)x->P[j]*y->P[k]; | |
774 | if (off[i] < off[j] + off[k] - 255) tt += p; | |
775 | else t += p; | |
776 | } | |
777 | u[i] = 19*(t + 2*tt); | |
778 | } | |
779 | u[NPIECE - 1] = 0; | |
780 | ||
781 | /* Second pass: things we must multiply by 1 or 2. */ | |
782 | for (i = 0; i < NPIECE; i++) { | |
783 | t = tt = 0; | |
784 | for (j = 0; j <= i; j++) { | |
785 | k = i - j; p = (dblpiece)x->P[j]*y->P[k]; | |
786 | if (off[i] < off[j] + off[k]) tt += p; | |
787 | else t += p; | |
788 | } | |
789 | u[i] += t + 2*tt; | |
790 | } | |
791 | ||
792 | /* And we're done. */ | |
793 | carry_reduce(u); | |
794 | for (i = 0; i < NPIECE; i++) z->P[i] = u[i]; | |
795 | ||
796 | #endif | |
797 | } | |
798 | ||
799 | /* --- @f25519_sqr@ --- * | |
800 | * | |
801 | * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@) | |
802 | * @const f25519 *x@ = an operand | |
803 | * | |
804 | * Returns: --- | |
805 | * | |
806 | * Use: Set @z@ to the square %$x^2$%. | |
807 | */ | |
808 | ||
809 | void f25519_sqr(f25519 *z, const f25519 *x) | |
810 | { | |
811 | #if F25519_IMPL == 26 | |
812 | ||
813 | piece PIECES(x); | |
814 | dblpiece PIECES(z); | |
815 | unsigned i; | |
816 | ||
817 | FETCH(x, x); | |
818 | ||
819 | /* See `f25519_mul' for bounds. */ | |
820 | ||
821 | #define M(a, b) ((dblpiece)(a)*(b)) | |
822 | z0 = M(x0, x0) + | |
823 | 38*(M(x2, x8) + M(x4, x6) + M(x5, x5)) + | |
824 | 76*(M(x1, x9) + M(x3, x7)); | |
825 | z1 = 2* M(x0, x1) + | |
826 | 38*(M(x2, x9) + M(x3, x8) + M(x4, x7) + M(x5, x6)); | |
827 | z2 = 2*(M(x0, x2) + M(x1, x1)) + | |
828 | 19* M(x6, x6) + | |
829 | 38* M(x4, x8) + | |
830 | 76*(M(x3, x9) + M(x5, x7)); | |
831 | z3 = 2*(M(x0, x3) + M(x1, x2)) + | |
832 | 38*(M(x4, x9) + M(x5, x8) + M(x6, x7)); | |
833 | z4 = M(x2, x2) + | |
834 | 2* M(x0, x4) + | |
835 | 4* M(x1, x3) + | |
836 | 38*(M(x6, x8) + M(x7, x7)) + | |
837 | 76* M(x5, x9); | |
838 | z5 = 2*(M(x0, x5) + M(x1, x4) + M(x2, x3)) + | |
839 | 38*(M(x6, x9) + M(x7, x8)); | |
840 | z6 = 2*(M(x0, x6) + M(x2, x4) + M(x3, x3)) + | |
841 | 4* M(x1, x5) + | |
842 | 19* M(x8, x8) + | |
843 | 76* M(x7, x9); | |
844 | z7 = 2*(M(x0, x7) + M(x1, x6) + M(x2, x5) + M(x3, x4)) + | |
845 | 38* M(x8, x9); | |
846 | z8 = M(x4, x4) + | |
847 | 2*(M(x0, x8) + M(x2, x6)) + | |
848 | 4*(M(x1, x7) + M(x3, x5)) + | |
849 | 38* M(x9, x9); | |
850 | z9 = 2*(M(x0, x9) + M(x1, x8) + M(x2, x7) + M(x3, x6) + M(x4, x5)); | |
851 | #undef M | |
852 | ||
853 | /* See `f25519_mul' for details. */ | |
854 | for (i = 0; i < 2; i++) CARRY_REDUCE(z, z); | |
855 | STASH(z, z); | |
856 | ||
857 | #elif F25519_IMPL == 10 | |
858 | f25519_mul(z, x, x); | |
859 | #endif | |
860 | } | |
861 | ||
862 | /*----- More complicated things -------------------------------------------*/ | |
863 | ||
864 | /* --- @f25519_inv@ --- * | |
865 | * | |
866 | * Arguments: @f25519 *z@ = where to put the result (may alias @x@) | |
867 | * @const f25519 *x@ = an operand | |
868 | * | |
869 | * Returns: --- | |
870 | * | |
871 | * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If | |
872 | * %$x = 0$% then @z@ is set to zero. This is considered a | |
873 | * feature. | |
874 | */ | |
875 | ||
876 | void f25519_inv(f25519 *z, const f25519 *x) | |
877 | { | |
878 | f25519 t, u, t2, t11, t2p10m1, t2p50m1; | |
879 | unsigned i; | |
880 | ||
881 | #define SQRN(z, x, n) do { \ | |
882 | f25519_sqr((z), (x)); \ | |
883 | for (i = 1; i < (n); i++) f25519_sqr((z), (z)); \ | |
884 | } while (0) | |
885 | ||
886 | /* Calculate x^-1 = x^(p - 2) = x^(2^255 - 21), which also handles x = 0 as | |
887 | * intended. The addition chain here is from Bernstein's implementation; I | |
888 | * couldn't find a better one. | |
889 | */ /* step | value */ | |
890 | f25519_sqr(&t2, x); /* 1 | 2 */ | |
891 | SQRN(&u, &t2, 2); /* 3 | 8 */ | |
892 | f25519_mul(&t, &u, x); /* 4 | 9 */ | |
893 | f25519_mul(&t11, &t, &t2); /* 5 | 11 = 2^5 - 21 */ | |
894 | f25519_sqr(&u, &t11); /* 6 | 22 */ | |
895 | f25519_mul(&t, &t, &u); /* 7 | 31 = 2^5 - 1 */ | |
896 | SQRN(&u, &t, 5); /* 12 | 2^10 - 2^5 */ | |
897 | f25519_mul(&t2p10m1, &t, &u); /* 13 | 2^10 - 1 */ | |
898 | SQRN(&u, &t2p10m1, 10); /* 23 | 2^20 - 2^10 */ | |
899 | f25519_mul(&t, &t2p10m1, &u); /* 24 | 2^20 - 1 */ | |
900 | SQRN(&u, &t, 20); /* 44 | 2^40 - 2^20 */ | |
901 | f25519_mul(&t, &t, &u); /* 45 | 2^40 - 1 */ | |
902 | SQRN(&u, &t, 10); /* 55 | 2^50 - 2^10 */ | |
903 | f25519_mul(&t2p50m1, &t2p10m1, &u); /* 56 | 2^50 - 1 */ | |
904 | SQRN(&u, &t2p50m1, 50); /* 106 | 2^100 - 2^50 */ | |
905 | f25519_mul(&t, &t2p50m1, &u); /* 107 | 2^100 - 1 */ | |
906 | SQRN(&u, &t, 100); /* 207 | 2^200 - 2^100 */ | |
907 | f25519_mul(&t, &t, &u); /* 208 | 2^200 - 1 */ | |
908 | SQRN(&u, &t, 50); /* 258 | 2^250 - 2^50 */ | |
909 | f25519_mul(&t, &t2p50m1, &u); /* 259 | 2^250 - 1 */ | |
910 | SQRN(&u, &t, 5); /* 264 | 2^255 - 2^5 */ | |
911 | f25519_mul(z, &u, &t11); /* 265 | 2^255 - 21 */ | |
912 | ||
913 | #undef SQRN | |
914 | } | |
915 | ||
916 | /*----- Test rig ----------------------------------------------------------*/ | |
917 | ||
918 | #ifdef TEST_RIG | |
919 | ||
920 | #include <mLib/report.h> | |
921 | #include <mLib/testrig.h> | |
922 | ||
923 | static void fixdstr(dstr *d) | |
924 | { | |
925 | if (d->len > 32) | |
926 | die(1, "invalid length for f25519"); | |
927 | else if (d->len < 32) { | |
928 | dstr_ensure(d, 32); | |
929 | memset(d->buf + d->len, 0, 32 - d->len); | |
930 | d->len = 32; | |
931 | } | |
932 | } | |
933 | ||
934 | static void cvt_f25519(const char *buf, dstr *d) | |
935 | { | |
936 | dstr dd = DSTR_INIT; | |
937 | ||
938 | type_hex.cvt(buf, &dd); fixdstr(&dd); | |
939 | dstr_ensure(d, sizeof(f25519)); d->len = sizeof(f25519); | |
940 | f25519_load((f25519 *)d->buf, (const octet *)dd.buf); | |
941 | dstr_destroy(&dd); | |
942 | } | |
943 | ||
944 | static void dump_f25519(dstr *d, FILE *fp) | |
945 | { fdump(stderr, "???", (const piece *)d->buf); } | |
946 | ||
947 | static void cvt_f25519_ref(const char *buf, dstr *d) | |
948 | { type_hex.cvt(buf, d); fixdstr(d); } | |
949 | ||
950 | static void dump_f25519_ref(dstr *d, FILE *fp) | |
951 | { | |
952 | f25519 x; | |
953 | ||
954 | f25519_load(&x, (const octet *)d->buf); | |
955 | fdump(stderr, "???", x.P); | |
956 | } | |
957 | ||
958 | static int eq(const f25519 *x, dstr *d) | |
959 | { octet b[32]; f25519_store(b, x); return (memcmp(b, d->buf, 32) == 0); } | |
960 | ||
961 | static const test_type | |
962 | type_f25519 = { cvt_f25519, dump_f25519 }, | |
963 | type_f25519_ref = { cvt_f25519_ref, dump_f25519_ref }; | |
964 | ||
965 | #define TEST_UNOP(op) \ | |
966 | static int vrf_##op(dstr dv[]) \ | |
967 | { \ | |
968 | f25519 *x = (f25519 *)dv[0].buf; \ | |
969 | f25519 z, zz; \ | |
970 | int ok = 1; \ | |
971 | \ | |
972 | f25519_##op(&z, x); \ | |
973 | if (!eq(&z, &dv[1])) { \ | |
974 | ok = 0; \ | |
975 | fprintf(stderr, "failed!\n"); \ | |
976 | fdump(stderr, "x", x->P); \ | |
977 | fdump(stderr, "calc", z.P); \ | |
978 | f25519_load(&zz, (const octet *)dv[1].buf); \ | |
979 | fdump(stderr, "z", zz.P); \ | |
980 | } \ | |
981 | \ | |
982 | return (ok); \ | |
983 | } | |
984 | ||
985 | TEST_UNOP(sqr) | |
986 | TEST_UNOP(inv) | |
987 | ||
988 | #define TEST_BINOP(op) \ | |
989 | static int vrf_##op(dstr dv[]) \ | |
990 | { \ | |
991 | f25519 *x = (f25519 *)dv[0].buf, *y = (f25519 *)dv[1].buf; \ | |
992 | f25519 z, zz; \ | |
993 | int ok = 1; \ | |
994 | \ | |
995 | f25519_##op(&z, x, y); \ | |
996 | if (!eq(&z, &dv[2])) { \ | |
997 | ok = 0; \ | |
998 | fprintf(stderr, "failed!\n"); \ | |
999 | fdump(stderr, "x", x->P); \ | |
1000 | fdump(stderr, "y", y->P); \ | |
1001 | fdump(stderr, "calc", z.P); \ | |
1002 | f25519_load(&zz, (const octet *)dv[2].buf); \ | |
1003 | fdump(stderr, "z", zz.P); \ | |
1004 | } \ | |
1005 | \ | |
1006 | return (ok); \ | |
1007 | } | |
1008 | ||
1009 | TEST_BINOP(add) | |
1010 | TEST_BINOP(sub) | |
1011 | TEST_BINOP(mul) | |
1012 | ||
1013 | static int vrf_mulc(dstr dv[]) | |
1014 | { | |
1015 | f25519 *x = (f25519 *)dv[0].buf; | |
1016 | long a = *(const long *)dv[1].buf; | |
1017 | f25519 z, zz; | |
1018 | int ok = 1; | |
1019 | ||
1020 | f25519_mulconst(&z, x, a); | |
1021 | if (!eq(&z, &dv[2])) { | |
1022 | ok = 0; | |
1023 | fprintf(stderr, "failed!\n"); | |
1024 | fdump(stderr, "x", x->P); | |
1025 | fprintf(stderr, "a = %ld\n", a); | |
1026 | fdump(stderr, "calc", z.P); | |
1027 | f25519_load(&zz, (const octet *)dv[2].buf); | |
1028 | fdump(stderr, "z", zz.P); | |
1029 | } | |
1030 | ||
1031 | return (ok); | |
1032 | } | |
1033 | ||
1034 | static int vrf_condswap(dstr dv[]) | |
1035 | { | |
1036 | f25519 *x = (f25519 *)dv[0].buf, *y = (f25519 *)dv[1].buf; | |
1037 | f25519 xx = *x, yy = *y; | |
1038 | uint32 m = *(uint32 *)dv[2].buf; | |
1039 | int ok = 1; | |
1040 | ||
1041 | f25519_condswap(&xx, &yy, m); | |
1042 | if (!eq(&xx, &dv[3]) || !eq(&yy, &dv[4])) { | |
1043 | ok = 0; | |
1044 | fprintf(stderr, "failed!\n"); | |
1045 | fdump(stderr, "x", x->P); | |
1046 | fdump(stderr, "y", y->P); | |
1047 | fprintf(stderr, "m = 0x%08lx\n", (unsigned long)m); | |
1048 | fdump(stderr, "calc xx", xx.P); | |
1049 | fdump(stderr, "calc yy", yy.P); | |
1050 | f25519_load(&xx, (const octet *)dv[3].buf); | |
1051 | f25519_load(&yy, (const octet *)dv[4].buf); | |
1052 | fdump(stderr, "want xx", xx.P); | |
1053 | fdump(stderr, "want yy", yy.P); | |
1054 | } | |
1055 | ||
1056 | return (ok); | |
1057 | } | |
1058 | ||
1059 | static int vrf_sub_mulc_add_sub_mul(dstr dv[]) | |
1060 | { | |
1061 | f25519 *u = (f25519 *)dv[0].buf, *v = (f25519 *)dv[1].buf, | |
1062 | *w = (f25519 *)dv[3].buf, *x = (f25519 *)dv[4].buf, | |
1063 | *y = (f25519 *)dv[5].buf; | |
1064 | long a = *(const long *)dv[2].buf; | |
1065 | f25519 umv, aumv, wpaumv, xmy, z, zz; | |
1066 | int ok = 1; | |
1067 | ||
1068 | f25519_sub(&umv, u, v); | |
1069 | f25519_mulconst(&aumv, &umv, a); | |
1070 | f25519_add(&wpaumv, w, &aumv); | |
1071 | f25519_sub(&xmy, x, y); | |
1072 | f25519_mul(&z, &wpaumv, &xmy); | |
1073 | ||
1074 | if (!eq(&z, &dv[6])) { | |
1075 | ok = 0; | |
1076 | fprintf(stderr, "failed!\n"); | |
1077 | fdump(stderr, "u", u->P); | |
1078 | fdump(stderr, "v", v->P); | |
1079 | fdump(stderr, "u - v", umv.P); | |
1080 | fprintf(stderr, "a = %ld\n", a); | |
1081 | fdump(stderr, "a (u - v)", aumv.P); | |
1082 | fdump(stderr, "w + a (u - v)", wpaumv.P); | |
1083 | fdump(stderr, "x", x->P); | |
1084 | fdump(stderr, "y", y->P); | |
1085 | fdump(stderr, "x - y", xmy.P); | |
1086 | fdump(stderr, "(x - y) (w + a (u - v))", z.P); | |
1087 | f25519_load(&zz, (const octet *)dv[6].buf); fdump(stderr, "z", zz.P); | |
1088 | } | |
1089 | ||
1090 | return (ok); | |
1091 | } | |
1092 | ||
1093 | static test_chunk tests[] = { | |
1094 | { "add", vrf_add, { &type_f25519, &type_f25519, &type_f25519_ref } }, | |
1095 | { "sub", vrf_sub, { &type_f25519, &type_f25519, &type_f25519_ref } }, | |
1096 | { "mul", vrf_mul, { &type_f25519, &type_f25519, &type_f25519_ref } }, | |
1097 | { "mulconst", vrf_mulc, { &type_f25519, &type_long, &type_f25519_ref } }, | |
1098 | { "condswap", vrf_condswap, | |
1099 | { &type_f25519, &type_f25519, &type_uint32, | |
1100 | &type_f25519_ref, &type_f25519_ref } }, | |
1101 | { "sqr", vrf_sqr, { &type_f25519, &type_f25519_ref } }, | |
1102 | { "inv", vrf_inv, { &type_f25519, &type_f25519_ref } }, | |
1103 | { "sub-mulc-add-sub-mul", vrf_sub_mulc_add_sub_mul, | |
1104 | { &type_f25519, &type_f25519, &type_long, &type_f25519, | |
1105 | &type_f25519, &type_f25519, &type_f25519_ref } }, | |
1106 | { 0, 0, { 0 } } | |
1107 | }; | |
1108 | ||
1109 | int main(int argc, char *argv[]) | |
1110 | { | |
1111 | test_run(argc, argv, tests, SRCDIR "/t/f25519"); | |
1112 | return (0); | |
1113 | } | |
1114 | ||
1115 | #endif | |
1116 | ||
1117 | /*----- That's all, folks -------------------------------------------------*/ |