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New "i62" code for big integers with 64x64->128 opcodes; also improved "i31" modular...
[BearSSL] / src / ec / ec_c25519_m15.c
1 /*
2 * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
7 * without limitation the rights to use, copy, modify, merge, publish,
8 * distribute, sublicense, and/or sell copies of the Software, and to
9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
11 *
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
14 *
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22 * SOFTWARE.
23 */
24
25 #include "inner.h"
26
27 /* obsolete
28 #include <stdio.h>
29 #include <stdlib.h>
30 static void
31 print_int(const char *name, const uint32_t *x)
32 {
33 size_t u;
34 unsigned char tmp[36];
35
36 printf("%s = ", name);
37 for (u = 0; u < 20; u ++) {
38 if (x[u] > 0x1FFF) {
39 printf("INVALID:");
40 for (u = 0; u < 20; u ++) {
41 printf(" %04X", x[u]);
42 }
43 printf("\n");
44 return;
45 }
46 }
47 memset(tmp, 0, sizeof tmp);
48 for (u = 0; u < 20; u ++) {
49 uint32_t w;
50 int j, k;
51
52 w = x[u];
53 j = 13 * (int)u;
54 k = j & 7;
55 if (k != 0) {
56 w <<= k;
57 j -= k;
58 }
59 k = j >> 3;
60 tmp[35 - k] |= (unsigned char)w;
61 tmp[34 - k] |= (unsigned char)(w >> 8);
62 tmp[33 - k] |= (unsigned char)(w >> 16);
63 tmp[32 - k] |= (unsigned char)(w >> 24);
64 }
65 for (u = 4; u < 36; u ++) {
66 printf("%02X", tmp[u]);
67 }
68 printf("\n");
69 }
70 */
71
72 /*
73 * If BR_NO_ARITH_SHIFT is undefined, or defined to 0, then we _assume_
74 * that right-shifting a signed negative integer copies the sign bit
75 * (arithmetic right-shift). This is "implementation-defined behaviour",
76 * i.e. it is not undefined, but it may differ between compilers. Each
77 * compiler is supposed to document its behaviour in that respect. GCC
78 * explicitly defines that an arithmetic right shift is used. We expect
79 * all other compilers to do the same, because underlying CPU offer an
80 * arithmetic right shift opcode that could not be used otherwise.
81 */
82 #if BR_NO_ARITH_SHIFT
83 #define ARSH(x, n) (((uint32_t)(x) >> (n)) \
84 | ((-((uint32_t)(x) >> 31)) << (32 - (n))))
85 #else
86 #define ARSH(x, n) ((*(int32_t *)&(x)) >> (n))
87 #endif
88
89 /*
90 * Convert an integer from unsigned little-endian encoding to a sequence of
91 * 13-bit words in little-endian order. The final "partial" word is
92 * returned.
93 */
94 static uint32_t
95 le8_to_le13(uint32_t *dst, const unsigned char *src, size_t len)
96 {
97 uint32_t acc;
98 int acc_len;
99
100 acc = 0;
101 acc_len = 0;
102 while (len -- > 0) {
103 acc |= (uint32_t)(*src ++) << acc_len;
104 acc_len += 8;
105 if (acc_len >= 13) {
106 *dst ++ = acc & 0x1FFF;
107 acc >>= 13;
108 acc_len -= 13;
109 }
110 }
111 return acc;
112 }
113
114 /*
115 * Convert an integer (13-bit words, little-endian) to unsigned
116 * little-endian encoding. The total encoding length is provided; all
117 * the destination bytes will be filled.
118 */
119 static void
120 le13_to_le8(unsigned char *dst, size_t len, const uint32_t *src)
121 {
122 uint32_t acc;
123 int acc_len;
124
125 acc = 0;
126 acc_len = 0;
127 while (len -- > 0) {
128 if (acc_len < 8) {
129 acc |= (*src ++) << acc_len;
130 acc_len += 13;
131 }
132 *dst ++ = (unsigned char)acc;
133 acc >>= 8;
134 acc_len -= 8;
135 }
136 }
137
138 /*
139 * Normalise an array of words to a strict 13 bits per word. Returned
140 * value is the resulting carry. The source (w) and destination (d)
141 * arrays may be identical, but shall not overlap partially.
142 */
143 static inline uint32_t
144 norm13(uint32_t *d, const uint32_t *w, size_t len)
145 {
146 size_t u;
147 uint32_t cc;
148
149 cc = 0;
150 for (u = 0; u < len; u ++) {
151 int32_t z;
152
153 z = w[u] + cc;
154 d[u] = z & 0x1FFF;
155 cc = ARSH(z, 13);
156 }
157 return cc;
158 }
159
160 /*
161 * mul20() multiplies two 260-bit integers together. Each word must fit
162 * on 13 bits; source operands use 20 words, destination operand
163 * receives 40 words. All overlaps allowed.
164 *
165 * square20() computes the square of a 260-bit integer. Each word must
166 * fit on 13 bits; source operand uses 20 words, destination operand
167 * receives 40 words. All overlaps allowed.
168 */
169
170 #if BR_SLOW_MUL15
171
172 static void
173 mul20(uint32_t *d, const uint32_t *a, const uint32_t *b)
174 {
175 /*
176 * Two-level Karatsuba: turns a 20x20 multiplication into
177 * nine 5x5 multiplications. We use 13-bit words but do not
178 * propagate carries immediately, so words may expand:
179 *
180 * - First Karatsuba decomposition turns the 20x20 mul on
181 * 13-bit words into three 10x10 muls, two on 13-bit words
182 * and one on 14-bit words.
183 *
184 * - Second Karatsuba decomposition further splits these into:
185 *
186 * * four 5x5 muls on 13-bit words
187 * * four 5x5 muls on 14-bit words
188 * * one 5x5 mul on 15-bit words
189 *
190 * Highest word value is 8191, 16382 or 32764, for 13-bit, 14-bit
191 * or 15-bit words, respectively.
192 */
193 uint32_t u[45], v[45], w[90];
194 uint32_t cc;
195 int i;
196
197 #define ZADD(dw, d_off, s1w, s1_off, s2w, s2_off) do { \
198 (dw)[5 * (d_off) + 0] = (s1w)[5 * (s1_off) + 0] \
199 + (s2w)[5 * (s2_off) + 0]; \
200 (dw)[5 * (d_off) + 1] = (s1w)[5 * (s1_off) + 1] \
201 + (s2w)[5 * (s2_off) + 1]; \
202 (dw)[5 * (d_off) + 2] = (s1w)[5 * (s1_off) + 2] \
203 + (s2w)[5 * (s2_off) + 2]; \
204 (dw)[5 * (d_off) + 3] = (s1w)[5 * (s1_off) + 3] \
205 + (s2w)[5 * (s2_off) + 3]; \
206 (dw)[5 * (d_off) + 4] = (s1w)[5 * (s1_off) + 4] \
207 + (s2w)[5 * (s2_off) + 4]; \
208 } while (0)
209
210 #define ZADDT(dw, d_off, sw, s_off) do { \
211 (dw)[5 * (d_off) + 0] += (sw)[5 * (s_off) + 0]; \
212 (dw)[5 * (d_off) + 1] += (sw)[5 * (s_off) + 1]; \
213 (dw)[5 * (d_off) + 2] += (sw)[5 * (s_off) + 2]; \
214 (dw)[5 * (d_off) + 3] += (sw)[5 * (s_off) + 3]; \
215 (dw)[5 * (d_off) + 4] += (sw)[5 * (s_off) + 4]; \
216 } while (0)
217
218 #define ZSUB2F(dw, d_off, s1w, s1_off, s2w, s2_off) do { \
219 (dw)[5 * (d_off) + 0] -= (s1w)[5 * (s1_off) + 0] \
220 + (s2w)[5 * (s2_off) + 0]; \
221 (dw)[5 * (d_off) + 1] -= (s1w)[5 * (s1_off) + 1] \
222 + (s2w)[5 * (s2_off) + 1]; \
223 (dw)[5 * (d_off) + 2] -= (s1w)[5 * (s1_off) + 2] \
224 + (s2w)[5 * (s2_off) + 2]; \
225 (dw)[5 * (d_off) + 3] -= (s1w)[5 * (s1_off) + 3] \
226 + (s2w)[5 * (s2_off) + 3]; \
227 (dw)[5 * (d_off) + 4] -= (s1w)[5 * (s1_off) + 4] \
228 + (s2w)[5 * (s2_off) + 4]; \
229 } while (0)
230
231 #define CPR1(w, cprcc) do { \
232 uint32_t cprz = (w) + cprcc; \
233 (w) = cprz & 0x1FFF; \
234 cprcc = cprz >> 13; \
235 } while (0)
236
237 #define CPR(dw, d_off) do { \
238 uint32_t cprcc; \
239 cprcc = 0; \
240 CPR1((dw)[(d_off) + 0], cprcc); \
241 CPR1((dw)[(d_off) + 1], cprcc); \
242 CPR1((dw)[(d_off) + 2], cprcc); \
243 CPR1((dw)[(d_off) + 3], cprcc); \
244 CPR1((dw)[(d_off) + 4], cprcc); \
245 CPR1((dw)[(d_off) + 5], cprcc); \
246 CPR1((dw)[(d_off) + 6], cprcc); \
247 CPR1((dw)[(d_off) + 7], cprcc); \
248 CPR1((dw)[(d_off) + 8], cprcc); \
249 (dw)[(d_off) + 9] = cprcc; \
250 } while (0)
251
252 memcpy(u, a, 20 * sizeof *a);
253 ZADD(u, 4, a, 0, a, 1);
254 ZADD(u, 5, a, 2, a, 3);
255 ZADD(u, 6, a, 0, a, 2);
256 ZADD(u, 7, a, 1, a, 3);
257 ZADD(u, 8, u, 6, u, 7);
258
259 memcpy(v, b, 20 * sizeof *b);
260 ZADD(v, 4, b, 0, b, 1);
261 ZADD(v, 5, b, 2, b, 3);
262 ZADD(v, 6, b, 0, b, 2);
263 ZADD(v, 7, b, 1, b, 3);
264 ZADD(v, 8, v, 6, v, 7);
265
266 /*
267 * Do the eight first 8x8 muls. Source words are at most 16382
268 * each, so we can add product results together "as is" in 32-bit
269 * words.
270 */
271 for (i = 0; i < 40; i += 5) {
272 w[(i << 1) + 0] = MUL15(u[i + 0], v[i + 0]);
273 w[(i << 1) + 1] = MUL15(u[i + 0], v[i + 1])
274 + MUL15(u[i + 1], v[i + 0]);
275 w[(i << 1) + 2] = MUL15(u[i + 0], v[i + 2])
276 + MUL15(u[i + 1], v[i + 1])
277 + MUL15(u[i + 2], v[i + 0]);
278 w[(i << 1) + 3] = MUL15(u[i + 0], v[i + 3])
279 + MUL15(u[i + 1], v[i + 2])
280 + MUL15(u[i + 2], v[i + 1])
281 + MUL15(u[i + 3], v[i + 0]);
282 w[(i << 1) + 4] = MUL15(u[i + 0], v[i + 4])
283 + MUL15(u[i + 1], v[i + 3])
284 + MUL15(u[i + 2], v[i + 2])
285 + MUL15(u[i + 3], v[i + 1])
286 + MUL15(u[i + 4], v[i + 0]);
287 w[(i << 1) + 5] = MUL15(u[i + 1], v[i + 4])
288 + MUL15(u[i + 2], v[i + 3])
289 + MUL15(u[i + 3], v[i + 2])
290 + MUL15(u[i + 4], v[i + 1]);
291 w[(i << 1) + 6] = MUL15(u[i + 2], v[i + 4])
292 + MUL15(u[i + 3], v[i + 3])
293 + MUL15(u[i + 4], v[i + 2]);
294 w[(i << 1) + 7] = MUL15(u[i + 3], v[i + 4])
295 + MUL15(u[i + 4], v[i + 3]);
296 w[(i << 1) + 8] = MUL15(u[i + 4], v[i + 4]);
297 w[(i << 1) + 9] = 0;
298 }
299
300 /*
301 * For the 9th multiplication, source words are up to 32764,
302 * so we must do some carry propagation. If we add up to
303 * 4 products and the carry is no more than 524224, then the
304 * result fits in 32 bits, and the next carry will be no more
305 * than 524224 (because 4*(32764^2)+524224 < 8192*524225).
306 *
307 * We thus just skip one of the products in the middle word,
308 * then do a carry propagation (this reduces words to 13 bits
309 * each, except possibly the last, which may use up to 17 bits
310 * or so), then add the missing product.
311 */
312 w[80 + 0] = MUL15(u[40 + 0], v[40 + 0]);
313 w[80 + 1] = MUL15(u[40 + 0], v[40 + 1])
314 + MUL15(u[40 + 1], v[40 + 0]);
315 w[80 + 2] = MUL15(u[40 + 0], v[40 + 2])
316 + MUL15(u[40 + 1], v[40 + 1])
317 + MUL15(u[40 + 2], v[40 + 0]);
318 w[80 + 3] = MUL15(u[40 + 0], v[40 + 3])
319 + MUL15(u[40 + 1], v[40 + 2])
320 + MUL15(u[40 + 2], v[40 + 1])
321 + MUL15(u[40 + 3], v[40 + 0]);
322 w[80 + 4] = MUL15(u[40 + 0], v[40 + 4])
323 + MUL15(u[40 + 1], v[40 + 3])
324 + MUL15(u[40 + 2], v[40 + 2])
325 + MUL15(u[40 + 3], v[40 + 1]);
326 /* + MUL15(u[40 + 4], v[40 + 0]) */
327 w[80 + 5] = MUL15(u[40 + 1], v[40 + 4])
328 + MUL15(u[40 + 2], v[40 + 3])
329 + MUL15(u[40 + 3], v[40 + 2])
330 + MUL15(u[40 + 4], v[40 + 1]);
331 w[80 + 6] = MUL15(u[40 + 2], v[40 + 4])
332 + MUL15(u[40 + 3], v[40 + 3])
333 + MUL15(u[40 + 4], v[40 + 2]);
334 w[80 + 7] = MUL15(u[40 + 3], v[40 + 4])
335 + MUL15(u[40 + 4], v[40 + 3]);
336 w[80 + 8] = MUL15(u[40 + 4], v[40 + 4]);
337
338 CPR(w, 80);
339
340 w[80 + 4] += MUL15(u[40 + 4], v[40 + 0]);
341
342 /*
343 * The products on 14-bit words in slots 6 and 7 yield values
344 * up to 5*(16382^2) each, and we need to subtract two such
345 * values from the higher word. We need the subtraction to fit
346 * in a _signed_ 32-bit integer, i.e. 31 bits + a sign bit.
347 * However, 10*(16382^2) does not fit. So we must perform a
348 * bit of reduction here.
349 */
350 CPR(w, 60);
351 CPR(w, 70);
352
353 /*
354 * Recompose results.
355 */
356
357 /* 0..1*0..1 into 0..3 */
358 ZSUB2F(w, 8, w, 0, w, 2);
359 ZSUB2F(w, 9, w, 1, w, 3);
360 ZADDT(w, 1, w, 8);
361 ZADDT(w, 2, w, 9);
362
363 /* 2..3*2..3 into 4..7 */
364 ZSUB2F(w, 10, w, 4, w, 6);
365 ZSUB2F(w, 11, w, 5, w, 7);
366 ZADDT(w, 5, w, 10);
367 ZADDT(w, 6, w, 11);
368
369 /* (0..1+2..3)*(0..1+2..3) into 12..15 */
370 ZSUB2F(w, 16, w, 12, w, 14);
371 ZSUB2F(w, 17, w, 13, w, 15);
372 ZADDT(w, 13, w, 16);
373 ZADDT(w, 14, w, 17);
374
375 /* first-level recomposition */
376 ZSUB2F(w, 12, w, 0, w, 4);
377 ZSUB2F(w, 13, w, 1, w, 5);
378 ZSUB2F(w, 14, w, 2, w, 6);
379 ZSUB2F(w, 15, w, 3, w, 7);
380 ZADDT(w, 2, w, 12);
381 ZADDT(w, 3, w, 13);
382 ZADDT(w, 4, w, 14);
383 ZADDT(w, 5, w, 15);
384
385 /*
386 * Perform carry propagation to bring all words down to 13 bits.
387 */
388 cc = norm13(d, w, 40);
389 d[39] += (cc << 13);
390
391 #undef ZADD
392 #undef ZADDT
393 #undef ZSUB2F
394 #undef CPR1
395 #undef CPR
396 }
397
398 static inline void
399 square20(uint32_t *d, const uint32_t *a)
400 {
401 mul20(d, a, a);
402 }
403
404 #else
405
406 static void
407 mul20(uint32_t *d, const uint32_t *a, const uint32_t *b)
408 {
409 uint32_t t[39];
410
411 t[ 0] = MUL15(a[ 0], b[ 0]);
412 t[ 1] = MUL15(a[ 0], b[ 1])
413 + MUL15(a[ 1], b[ 0]);
414 t[ 2] = MUL15(a[ 0], b[ 2])
415 + MUL15(a[ 1], b[ 1])
416 + MUL15(a[ 2], b[ 0]);
417 t[ 3] = MUL15(a[ 0], b[ 3])
418 + MUL15(a[ 1], b[ 2])
419 + MUL15(a[ 2], b[ 1])
420 + MUL15(a[ 3], b[ 0]);
421 t[ 4] = MUL15(a[ 0], b[ 4])
422 + MUL15(a[ 1], b[ 3])
423 + MUL15(a[ 2], b[ 2])
424 + MUL15(a[ 3], b[ 1])
425 + MUL15(a[ 4], b[ 0]);
426 t[ 5] = MUL15(a[ 0], b[ 5])
427 + MUL15(a[ 1], b[ 4])
428 + MUL15(a[ 2], b[ 3])
429 + MUL15(a[ 3], b[ 2])
430 + MUL15(a[ 4], b[ 1])
431 + MUL15(a[ 5], b[ 0]);
432 t[ 6] = MUL15(a[ 0], b[ 6])
433 + MUL15(a[ 1], b[ 5])
434 + MUL15(a[ 2], b[ 4])
435 + MUL15(a[ 3], b[ 3])
436 + MUL15(a[ 4], b[ 2])
437 + MUL15(a[ 5], b[ 1])
438 + MUL15(a[ 6], b[ 0]);
439 t[ 7] = MUL15(a[ 0], b[ 7])
440 + MUL15(a[ 1], b[ 6])
441 + MUL15(a[ 2], b[ 5])
442 + MUL15(a[ 3], b[ 4])
443 + MUL15(a[ 4], b[ 3])
444 + MUL15(a[ 5], b[ 2])
445 + MUL15(a[ 6], b[ 1])
446 + MUL15(a[ 7], b[ 0]);
447 t[ 8] = MUL15(a[ 0], b[ 8])
448 + MUL15(a[ 1], b[ 7])
449 + MUL15(a[ 2], b[ 6])
450 + MUL15(a[ 3], b[ 5])
451 + MUL15(a[ 4], b[ 4])
452 + MUL15(a[ 5], b[ 3])
453 + MUL15(a[ 6], b[ 2])
454 + MUL15(a[ 7], b[ 1])
455 + MUL15(a[ 8], b[ 0]);
456 t[ 9] = MUL15(a[ 0], b[ 9])
457 + MUL15(a[ 1], b[ 8])
458 + MUL15(a[ 2], b[ 7])
459 + MUL15(a[ 3], b[ 6])
460 + MUL15(a[ 4], b[ 5])
461 + MUL15(a[ 5], b[ 4])
462 + MUL15(a[ 6], b[ 3])
463 + MUL15(a[ 7], b[ 2])
464 + MUL15(a[ 8], b[ 1])
465 + MUL15(a[ 9], b[ 0]);
466 t[10] = MUL15(a[ 0], b[10])
467 + MUL15(a[ 1], b[ 9])
468 + MUL15(a[ 2], b[ 8])
469 + MUL15(a[ 3], b[ 7])
470 + MUL15(a[ 4], b[ 6])
471 + MUL15(a[ 5], b[ 5])
472 + MUL15(a[ 6], b[ 4])
473 + MUL15(a[ 7], b[ 3])
474 + MUL15(a[ 8], b[ 2])
475 + MUL15(a[ 9], b[ 1])
476 + MUL15(a[10], b[ 0]);
477 t[11] = MUL15(a[ 0], b[11])
478 + MUL15(a[ 1], b[10])
479 + MUL15(a[ 2], b[ 9])
480 + MUL15(a[ 3], b[ 8])
481 + MUL15(a[ 4], b[ 7])
482 + MUL15(a[ 5], b[ 6])
483 + MUL15(a[ 6], b[ 5])
484 + MUL15(a[ 7], b[ 4])
485 + MUL15(a[ 8], b[ 3])
486 + MUL15(a[ 9], b[ 2])
487 + MUL15(a[10], b[ 1])
488 + MUL15(a[11], b[ 0]);
489 t[12] = MUL15(a[ 0], b[12])
490 + MUL15(a[ 1], b[11])
491 + MUL15(a[ 2], b[10])
492 + MUL15(a[ 3], b[ 9])
493 + MUL15(a[ 4], b[ 8])
494 + MUL15(a[ 5], b[ 7])
495 + MUL15(a[ 6], b[ 6])
496 + MUL15(a[ 7], b[ 5])
497 + MUL15(a[ 8], b[ 4])
498 + MUL15(a[ 9], b[ 3])
499 + MUL15(a[10], b[ 2])
500 + MUL15(a[11], b[ 1])
501 + MUL15(a[12], b[ 0]);
502 t[13] = MUL15(a[ 0], b[13])
503 + MUL15(a[ 1], b[12])
504 + MUL15(a[ 2], b[11])
505 + MUL15(a[ 3], b[10])
506 + MUL15(a[ 4], b[ 9])
507 + MUL15(a[ 5], b[ 8])
508 + MUL15(a[ 6], b[ 7])
509 + MUL15(a[ 7], b[ 6])
510 + MUL15(a[ 8], b[ 5])
511 + MUL15(a[ 9], b[ 4])
512 + MUL15(a[10], b[ 3])
513 + MUL15(a[11], b[ 2])
514 + MUL15(a[12], b[ 1])
515 + MUL15(a[13], b[ 0]);
516 t[14] = MUL15(a[ 0], b[14])
517 + MUL15(a[ 1], b[13])
518 + MUL15(a[ 2], b[12])
519 + MUL15(a[ 3], b[11])
520 + MUL15(a[ 4], b[10])
521 + MUL15(a[ 5], b[ 9])
522 + MUL15(a[ 6], b[ 8])
523 + MUL15(a[ 7], b[ 7])
524 + MUL15(a[ 8], b[ 6])
525 + MUL15(a[ 9], b[ 5])
526 + MUL15(a[10], b[ 4])
527 + MUL15(a[11], b[ 3])
528 + MUL15(a[12], b[ 2])
529 + MUL15(a[13], b[ 1])
530 + MUL15(a[14], b[ 0]);
531 t[15] = MUL15(a[ 0], b[15])
532 + MUL15(a[ 1], b[14])
533 + MUL15(a[ 2], b[13])
534 + MUL15(a[ 3], b[12])
535 + MUL15(a[ 4], b[11])
536 + MUL15(a[ 5], b[10])
537 + MUL15(a[ 6], b[ 9])
538 + MUL15(a[ 7], b[ 8])
539 + MUL15(a[ 8], b[ 7])
540 + MUL15(a[ 9], b[ 6])
541 + MUL15(a[10], b[ 5])
542 + MUL15(a[11], b[ 4])
543 + MUL15(a[12], b[ 3])
544 + MUL15(a[13], b[ 2])
545 + MUL15(a[14], b[ 1])
546 + MUL15(a[15], b[ 0]);
547 t[16] = MUL15(a[ 0], b[16])
548 + MUL15(a[ 1], b[15])
549 + MUL15(a[ 2], b[14])
550 + MUL15(a[ 3], b[13])
551 + MUL15(a[ 4], b[12])
552 + MUL15(a[ 5], b[11])
553 + MUL15(a[ 6], b[10])
554 + MUL15(a[ 7], b[ 9])
555 + MUL15(a[ 8], b[ 8])
556 + MUL15(a[ 9], b[ 7])
557 + MUL15(a[10], b[ 6])
558 + MUL15(a[11], b[ 5])
559 + MUL15(a[12], b[ 4])
560 + MUL15(a[13], b[ 3])
561 + MUL15(a[14], b[ 2])
562 + MUL15(a[15], b[ 1])
563 + MUL15(a[16], b[ 0]);
564 t[17] = MUL15(a[ 0], b[17])
565 + MUL15(a[ 1], b[16])
566 + MUL15(a[ 2], b[15])
567 + MUL15(a[ 3], b[14])
568 + MUL15(a[ 4], b[13])
569 + MUL15(a[ 5], b[12])
570 + MUL15(a[ 6], b[11])
571 + MUL15(a[ 7], b[10])
572 + MUL15(a[ 8], b[ 9])
573 + MUL15(a[ 9], b[ 8])
574 + MUL15(a[10], b[ 7])
575 + MUL15(a[11], b[ 6])
576 + MUL15(a[12], b[ 5])
577 + MUL15(a[13], b[ 4])
578 + MUL15(a[14], b[ 3])
579 + MUL15(a[15], b[ 2])
580 + MUL15(a[16], b[ 1])
581 + MUL15(a[17], b[ 0]);
582 t[18] = MUL15(a[ 0], b[18])
583 + MUL15(a[ 1], b[17])
584 + MUL15(a[ 2], b[16])
585 + MUL15(a[ 3], b[15])
586 + MUL15(a[ 4], b[14])
587 + MUL15(a[ 5], b[13])
588 + MUL15(a[ 6], b[12])
589 + MUL15(a[ 7], b[11])
590 + MUL15(a[ 8], b[10])
591 + MUL15(a[ 9], b[ 9])
592 + MUL15(a[10], b[ 8])
593 + MUL15(a[11], b[ 7])
594 + MUL15(a[12], b[ 6])
595 + MUL15(a[13], b[ 5])
596 + MUL15(a[14], b[ 4])
597 + MUL15(a[15], b[ 3])
598 + MUL15(a[16], b[ 2])
599 + MUL15(a[17], b[ 1])
600 + MUL15(a[18], b[ 0]);
601 t[19] = MUL15(a[ 0], b[19])
602 + MUL15(a[ 1], b[18])
603 + MUL15(a[ 2], b[17])
604 + MUL15(a[ 3], b[16])
605 + MUL15(a[ 4], b[15])
606 + MUL15(a[ 5], b[14])
607 + MUL15(a[ 6], b[13])
608 + MUL15(a[ 7], b[12])
609 + MUL15(a[ 8], b[11])
610 + MUL15(a[ 9], b[10])
611 + MUL15(a[10], b[ 9])
612 + MUL15(a[11], b[ 8])
613 + MUL15(a[12], b[ 7])
614 + MUL15(a[13], b[ 6])
615 + MUL15(a[14], b[ 5])
616 + MUL15(a[15], b[ 4])
617 + MUL15(a[16], b[ 3])
618 + MUL15(a[17], b[ 2])
619 + MUL15(a[18], b[ 1])
620 + MUL15(a[19], b[ 0]);
621 t[20] = MUL15(a[ 1], b[19])
622 + MUL15(a[ 2], b[18])
623 + MUL15(a[ 3], b[17])
624 + MUL15(a[ 4], b[16])
625 + MUL15(a[ 5], b[15])
626 + MUL15(a[ 6], b[14])
627 + MUL15(a[ 7], b[13])
628 + MUL15(a[ 8], b[12])
629 + MUL15(a[ 9], b[11])
630 + MUL15(a[10], b[10])
631 + MUL15(a[11], b[ 9])
632 + MUL15(a[12], b[ 8])
633 + MUL15(a[13], b[ 7])
634 + MUL15(a[14], b[ 6])
635 + MUL15(a[15], b[ 5])
636 + MUL15(a[16], b[ 4])
637 + MUL15(a[17], b[ 3])
638 + MUL15(a[18], b[ 2])
639 + MUL15(a[19], b[ 1]);
640 t[21] = MUL15(a[ 2], b[19])
641 + MUL15(a[ 3], b[18])
642 + MUL15(a[ 4], b[17])
643 + MUL15(a[ 5], b[16])
644 + MUL15(a[ 6], b[15])
645 + MUL15(a[ 7], b[14])
646 + MUL15(a[ 8], b[13])
647 + MUL15(a[ 9], b[12])
648 + MUL15(a[10], b[11])
649 + MUL15(a[11], b[10])
650 + MUL15(a[12], b[ 9])
651 + MUL15(a[13], b[ 8])
652 + MUL15(a[14], b[ 7])
653 + MUL15(a[15], b[ 6])
654 + MUL15(a[16], b[ 5])
655 + MUL15(a[17], b[ 4])
656 + MUL15(a[18], b[ 3])
657 + MUL15(a[19], b[ 2]);
658 t[22] = MUL15(a[ 3], b[19])
659 + MUL15(a[ 4], b[18])
660 + MUL15(a[ 5], b[17])
661 + MUL15(a[ 6], b[16])
662 + MUL15(a[ 7], b[15])
663 + MUL15(a[ 8], b[14])
664 + MUL15(a[ 9], b[13])
665 + MUL15(a[10], b[12])
666 + MUL15(a[11], b[11])
667 + MUL15(a[12], b[10])
668 + MUL15(a[13], b[ 9])
669 + MUL15(a[14], b[ 8])
670 + MUL15(a[15], b[ 7])
671 + MUL15(a[16], b[ 6])
672 + MUL15(a[17], b[ 5])
673 + MUL15(a[18], b[ 4])
674 + MUL15(a[19], b[ 3]);
675 t[23] = MUL15(a[ 4], b[19])
676 + MUL15(a[ 5], b[18])
677 + MUL15(a[ 6], b[17])
678 + MUL15(a[ 7], b[16])
679 + MUL15(a[ 8], b[15])
680 + MUL15(a[ 9], b[14])
681 + MUL15(a[10], b[13])
682 + MUL15(a[11], b[12])
683 + MUL15(a[12], b[11])
684 + MUL15(a[13], b[10])
685 + MUL15(a[14], b[ 9])
686 + MUL15(a[15], b[ 8])
687 + MUL15(a[16], b[ 7])
688 + MUL15(a[17], b[ 6])
689 + MUL15(a[18], b[ 5])
690 + MUL15(a[19], b[ 4]);
691 t[24] = MUL15(a[ 5], b[19])
692 + MUL15(a[ 6], b[18])
693 + MUL15(a[ 7], b[17])
694 + MUL15(a[ 8], b[16])
695 + MUL15(a[ 9], b[15])
696 + MUL15(a[10], b[14])
697 + MUL15(a[11], b[13])
698 + MUL15(a[12], b[12])
699 + MUL15(a[13], b[11])
700 + MUL15(a[14], b[10])
701 + MUL15(a[15], b[ 9])
702 + MUL15(a[16], b[ 8])
703 + MUL15(a[17], b[ 7])
704 + MUL15(a[18], b[ 6])
705 + MUL15(a[19], b[ 5]);
706 t[25] = MUL15(a[ 6], b[19])
707 + MUL15(a[ 7], b[18])
708 + MUL15(a[ 8], b[17])
709 + MUL15(a[ 9], b[16])
710 + MUL15(a[10], b[15])
711 + MUL15(a[11], b[14])
712 + MUL15(a[12], b[13])
713 + MUL15(a[13], b[12])
714 + MUL15(a[14], b[11])
715 + MUL15(a[15], b[10])
716 + MUL15(a[16], b[ 9])
717 + MUL15(a[17], b[ 8])
718 + MUL15(a[18], b[ 7])
719 + MUL15(a[19], b[ 6]);
720 t[26] = MUL15(a[ 7], b[19])
721 + MUL15(a[ 8], b[18])
722 + MUL15(a[ 9], b[17])
723 + MUL15(a[10], b[16])
724 + MUL15(a[11], b[15])
725 + MUL15(a[12], b[14])
726 + MUL15(a[13], b[13])
727 + MUL15(a[14], b[12])
728 + MUL15(a[15], b[11])
729 + MUL15(a[16], b[10])
730 + MUL15(a[17], b[ 9])
731 + MUL15(a[18], b[ 8])
732 + MUL15(a[19], b[ 7]);
733 t[27] = MUL15(a[ 8], b[19])
734 + MUL15(a[ 9], b[18])
735 + MUL15(a[10], b[17])
736 + MUL15(a[11], b[16])
737 + MUL15(a[12], b[15])
738 + MUL15(a[13], b[14])
739 + MUL15(a[14], b[13])
740 + MUL15(a[15], b[12])
741 + MUL15(a[16], b[11])
742 + MUL15(a[17], b[10])
743 + MUL15(a[18], b[ 9])
744 + MUL15(a[19], b[ 8]);
745 t[28] = MUL15(a[ 9], b[19])
746 + MUL15(a[10], b[18])
747 + MUL15(a[11], b[17])
748 + MUL15(a[12], b[16])
749 + MUL15(a[13], b[15])
750 + MUL15(a[14], b[14])
751 + MUL15(a[15], b[13])
752 + MUL15(a[16], b[12])
753 + MUL15(a[17], b[11])
754 + MUL15(a[18], b[10])
755 + MUL15(a[19], b[ 9]);
756 t[29] = MUL15(a[10], b[19])
757 + MUL15(a[11], b[18])
758 + MUL15(a[12], b[17])
759 + MUL15(a[13], b[16])
760 + MUL15(a[14], b[15])
761 + MUL15(a[15], b[14])
762 + MUL15(a[16], b[13])
763 + MUL15(a[17], b[12])
764 + MUL15(a[18], b[11])
765 + MUL15(a[19], b[10]);
766 t[30] = MUL15(a[11], b[19])
767 + MUL15(a[12], b[18])
768 + MUL15(a[13], b[17])
769 + MUL15(a[14], b[16])
770 + MUL15(a[15], b[15])
771 + MUL15(a[16], b[14])
772 + MUL15(a[17], b[13])
773 + MUL15(a[18], b[12])
774 + MUL15(a[19], b[11]);
775 t[31] = MUL15(a[12], b[19])
776 + MUL15(a[13], b[18])
777 + MUL15(a[14], b[17])
778 + MUL15(a[15], b[16])
779 + MUL15(a[16], b[15])
780 + MUL15(a[17], b[14])
781 + MUL15(a[18], b[13])
782 + MUL15(a[19], b[12]);
783 t[32] = MUL15(a[13], b[19])
784 + MUL15(a[14], b[18])
785 + MUL15(a[15], b[17])
786 + MUL15(a[16], b[16])
787 + MUL15(a[17], b[15])
788 + MUL15(a[18], b[14])
789 + MUL15(a[19], b[13]);
790 t[33] = MUL15(a[14], b[19])
791 + MUL15(a[15], b[18])
792 + MUL15(a[16], b[17])
793 + MUL15(a[17], b[16])
794 + MUL15(a[18], b[15])
795 + MUL15(a[19], b[14]);
796 t[34] = MUL15(a[15], b[19])
797 + MUL15(a[16], b[18])
798 + MUL15(a[17], b[17])
799 + MUL15(a[18], b[16])
800 + MUL15(a[19], b[15]);
801 t[35] = MUL15(a[16], b[19])
802 + MUL15(a[17], b[18])
803 + MUL15(a[18], b[17])
804 + MUL15(a[19], b[16]);
805 t[36] = MUL15(a[17], b[19])
806 + MUL15(a[18], b[18])
807 + MUL15(a[19], b[17]);
808 t[37] = MUL15(a[18], b[19])
809 + MUL15(a[19], b[18]);
810 t[38] = MUL15(a[19], b[19]);
811
812 d[39] = norm13(d, t, 39);
813 }
814
815 static void
816 square20(uint32_t *d, const uint32_t *a)
817 {
818 uint32_t t[39];
819
820 t[ 0] = MUL15(a[ 0], a[ 0]);
821 t[ 1] = ((MUL15(a[ 0], a[ 1])) << 1);
822 t[ 2] = MUL15(a[ 1], a[ 1])
823 + ((MUL15(a[ 0], a[ 2])) << 1);
824 t[ 3] = ((MUL15(a[ 0], a[ 3])
825 + MUL15(a[ 1], a[ 2])) << 1);
826 t[ 4] = MUL15(a[ 2], a[ 2])
827 + ((MUL15(a[ 0], a[ 4])
828 + MUL15(a[ 1], a[ 3])) << 1);
829 t[ 5] = ((MUL15(a[ 0], a[ 5])
830 + MUL15(a[ 1], a[ 4])
831 + MUL15(a[ 2], a[ 3])) << 1);
832 t[ 6] = MUL15(a[ 3], a[ 3])
833 + ((MUL15(a[ 0], a[ 6])
834 + MUL15(a[ 1], a[ 5])
835 + MUL15(a[ 2], a[ 4])) << 1);
836 t[ 7] = ((MUL15(a[ 0], a[ 7])
837 + MUL15(a[ 1], a[ 6])
838 + MUL15(a[ 2], a[ 5])
839 + MUL15(a[ 3], a[ 4])) << 1);
840 t[ 8] = MUL15(a[ 4], a[ 4])
841 + ((MUL15(a[ 0], a[ 8])
842 + MUL15(a[ 1], a[ 7])
843 + MUL15(a[ 2], a[ 6])
844 + MUL15(a[ 3], a[ 5])) << 1);
845 t[ 9] = ((MUL15(a[ 0], a[ 9])
846 + MUL15(a[ 1], a[ 8])
847 + MUL15(a[ 2], a[ 7])
848 + MUL15(a[ 3], a[ 6])
849 + MUL15(a[ 4], a[ 5])) << 1);
850 t[10] = MUL15(a[ 5], a[ 5])
851 + ((MUL15(a[ 0], a[10])
852 + MUL15(a[ 1], a[ 9])
853 + MUL15(a[ 2], a[ 8])
854 + MUL15(a[ 3], a[ 7])
855 + MUL15(a[ 4], a[ 6])) << 1);
856 t[11] = ((MUL15(a[ 0], a[11])
857 + MUL15(a[ 1], a[10])
858 + MUL15(a[ 2], a[ 9])
859 + MUL15(a[ 3], a[ 8])
860 + MUL15(a[ 4], a[ 7])
861 + MUL15(a[ 5], a[ 6])) << 1);
862 t[12] = MUL15(a[ 6], a[ 6])
863 + ((MUL15(a[ 0], a[12])
864 + MUL15(a[ 1], a[11])
865 + MUL15(a[ 2], a[10])
866 + MUL15(a[ 3], a[ 9])
867 + MUL15(a[ 4], a[ 8])
868 + MUL15(a[ 5], a[ 7])) << 1);
869 t[13] = ((MUL15(a[ 0], a[13])
870 + MUL15(a[ 1], a[12])
871 + MUL15(a[ 2], a[11])
872 + MUL15(a[ 3], a[10])
873 + MUL15(a[ 4], a[ 9])
874 + MUL15(a[ 5], a[ 8])
875 + MUL15(a[ 6], a[ 7])) << 1);
876 t[14] = MUL15(a[ 7], a[ 7])
877 + ((MUL15(a[ 0], a[14])
878 + MUL15(a[ 1], a[13])
879 + MUL15(a[ 2], a[12])
880 + MUL15(a[ 3], a[11])
881 + MUL15(a[ 4], a[10])
882 + MUL15(a[ 5], a[ 9])
883 + MUL15(a[ 6], a[ 8])) << 1);
884 t[15] = ((MUL15(a[ 0], a[15])
885 + MUL15(a[ 1], a[14])
886 + MUL15(a[ 2], a[13])
887 + MUL15(a[ 3], a[12])
888 + MUL15(a[ 4], a[11])
889 + MUL15(a[ 5], a[10])
890 + MUL15(a[ 6], a[ 9])
891 + MUL15(a[ 7], a[ 8])) << 1);
892 t[16] = MUL15(a[ 8], a[ 8])
893 + ((MUL15(a[ 0], a[16])
894 + MUL15(a[ 1], a[15])
895 + MUL15(a[ 2], a[14])
896 + MUL15(a[ 3], a[13])
897 + MUL15(a[ 4], a[12])
898 + MUL15(a[ 5], a[11])
899 + MUL15(a[ 6], a[10])
900 + MUL15(a[ 7], a[ 9])) << 1);
901 t[17] = ((MUL15(a[ 0], a[17])
902 + MUL15(a[ 1], a[16])
903 + MUL15(a[ 2], a[15])
904 + MUL15(a[ 3], a[14])
905 + MUL15(a[ 4], a[13])
906 + MUL15(a[ 5], a[12])
907 + MUL15(a[ 6], a[11])
908 + MUL15(a[ 7], a[10])
909 + MUL15(a[ 8], a[ 9])) << 1);
910 t[18] = MUL15(a[ 9], a[ 9])
911 + ((MUL15(a[ 0], a[18])
912 + MUL15(a[ 1], a[17])
913 + MUL15(a[ 2], a[16])
914 + MUL15(a[ 3], a[15])
915 + MUL15(a[ 4], a[14])
916 + MUL15(a[ 5], a[13])
917 + MUL15(a[ 6], a[12])
918 + MUL15(a[ 7], a[11])
919 + MUL15(a[ 8], a[10])) << 1);
920 t[19] = ((MUL15(a[ 0], a[19])
921 + MUL15(a[ 1], a[18])
922 + MUL15(a[ 2], a[17])
923 + MUL15(a[ 3], a[16])
924 + MUL15(a[ 4], a[15])
925 + MUL15(a[ 5], a[14])
926 + MUL15(a[ 6], a[13])
927 + MUL15(a[ 7], a[12])
928 + MUL15(a[ 8], a[11])
929 + MUL15(a[ 9], a[10])) << 1);
930 t[20] = MUL15(a[10], a[10])
931 + ((MUL15(a[ 1], a[19])
932 + MUL15(a[ 2], a[18])
933 + MUL15(a[ 3], a[17])
934 + MUL15(a[ 4], a[16])
935 + MUL15(a[ 5], a[15])
936 + MUL15(a[ 6], a[14])
937 + MUL15(a[ 7], a[13])
938 + MUL15(a[ 8], a[12])
939 + MUL15(a[ 9], a[11])) << 1);
940 t[21] = ((MUL15(a[ 2], a[19])
941 + MUL15(a[ 3], a[18])
942 + MUL15(a[ 4], a[17])
943 + MUL15(a[ 5], a[16])
944 + MUL15(a[ 6], a[15])
945 + MUL15(a[ 7], a[14])
946 + MUL15(a[ 8], a[13])
947 + MUL15(a[ 9], a[12])
948 + MUL15(a[10], a[11])) << 1);
949 t[22] = MUL15(a[11], a[11])
950 + ((MUL15(a[ 3], a[19])
951 + MUL15(a[ 4], a[18])
952 + MUL15(a[ 5], a[17])
953 + MUL15(a[ 6], a[16])
954 + MUL15(a[ 7], a[15])
955 + MUL15(a[ 8], a[14])
956 + MUL15(a[ 9], a[13])
957 + MUL15(a[10], a[12])) << 1);
958 t[23] = ((MUL15(a[ 4], a[19])
959 + MUL15(a[ 5], a[18])
960 + MUL15(a[ 6], a[17])
961 + MUL15(a[ 7], a[16])
962 + MUL15(a[ 8], a[15])
963 + MUL15(a[ 9], a[14])
964 + MUL15(a[10], a[13])
965 + MUL15(a[11], a[12])) << 1);
966 t[24] = MUL15(a[12], a[12])
967 + ((MUL15(a[ 5], a[19])
968 + MUL15(a[ 6], a[18])
969 + MUL15(a[ 7], a[17])
970 + MUL15(a[ 8], a[16])
971 + MUL15(a[ 9], a[15])
972 + MUL15(a[10], a[14])
973 + MUL15(a[11], a[13])) << 1);
974 t[25] = ((MUL15(a[ 6], a[19])
975 + MUL15(a[ 7], a[18])
976 + MUL15(a[ 8], a[17])
977 + MUL15(a[ 9], a[16])
978 + MUL15(a[10], a[15])
979 + MUL15(a[11], a[14])
980 + MUL15(a[12], a[13])) << 1);
981 t[26] = MUL15(a[13], a[13])
982 + ((MUL15(a[ 7], a[19])
983 + MUL15(a[ 8], a[18])
984 + MUL15(a[ 9], a[17])
985 + MUL15(a[10], a[16])
986 + MUL15(a[11], a[15])
987 + MUL15(a[12], a[14])) << 1);
988 t[27] = ((MUL15(a[ 8], a[19])
989 + MUL15(a[ 9], a[18])
990 + MUL15(a[10], a[17])
991 + MUL15(a[11], a[16])
992 + MUL15(a[12], a[15])
993 + MUL15(a[13], a[14])) << 1);
994 t[28] = MUL15(a[14], a[14])
995 + ((MUL15(a[ 9], a[19])
996 + MUL15(a[10], a[18])
997 + MUL15(a[11], a[17])
998 + MUL15(a[12], a[16])
999 + MUL15(a[13], a[15])) << 1);
1000 t[29] = ((MUL15(a[10], a[19])
1001 + MUL15(a[11], a[18])
1002 + MUL15(a[12], a[17])
1003 + MUL15(a[13], a[16])
1004 + MUL15(a[14], a[15])) << 1);
1005 t[30] = MUL15(a[15], a[15])
1006 + ((MUL15(a[11], a[19])
1007 + MUL15(a[12], a[18])
1008 + MUL15(a[13], a[17])
1009 + MUL15(a[14], a[16])) << 1);
1010 t[31] = ((MUL15(a[12], a[19])
1011 + MUL15(a[13], a[18])
1012 + MUL15(a[14], a[17])
1013 + MUL15(a[15], a[16])) << 1);
1014 t[32] = MUL15(a[16], a[16])
1015 + ((MUL15(a[13], a[19])
1016 + MUL15(a[14], a[18])
1017 + MUL15(a[15], a[17])) << 1);
1018 t[33] = ((MUL15(a[14], a[19])
1019 + MUL15(a[15], a[18])
1020 + MUL15(a[16], a[17])) << 1);
1021 t[34] = MUL15(a[17], a[17])
1022 + ((MUL15(a[15], a[19])
1023 + MUL15(a[16], a[18])) << 1);
1024 t[35] = ((MUL15(a[16], a[19])
1025 + MUL15(a[17], a[18])) << 1);
1026 t[36] = MUL15(a[18], a[18])
1027 + ((MUL15(a[17], a[19])) << 1);
1028 t[37] = ((MUL15(a[18], a[19])) << 1);
1029 t[38] = MUL15(a[19], a[19]);
1030
1031 d[39] = norm13(d, t, 39);
1032 }
1033
1034 #endif
1035
1036 /*
1037 * Perform a "final reduction" in field F255 (field for Curve25519)
1038 * The source value must be less than twice the modulus. If the value
1039 * is not lower than the modulus, then the modulus is subtracted and
1040 * this function returns 1; otherwise, it leaves it untouched and it
1041 * returns 0.
1042 */
1043 static uint32_t
1044 reduce_final_f255(uint32_t *d)
1045 {
1046 uint32_t t[20];
1047 uint32_t cc;
1048 int i;
1049
1050 memcpy(t, d, sizeof t);
1051 cc = 19;
1052 for (i = 0; i < 20; i ++) {
1053 uint32_t w;
1054
1055 w = t[i] + cc;
1056 cc = w >> 13;
1057 t[i] = w & 0x1FFF;
1058 }
1059 cc = t[19] >> 8;
1060 t[19] &= 0xFF;
1061 CCOPY(cc, d, t, sizeof t);
1062 return cc;
1063 }
1064
1065 static void
1066 f255_mulgen(uint32_t *d, const uint32_t *a, const uint32_t *b, int square)
1067 {
1068 uint32_t t[40], cc, w;
1069
1070 /*
1071 * Compute raw multiplication. All result words fit in 13 bits
1072 * each; upper word (t[39]) must fit on 5 bits, since the product
1073 * of two 256-bit integers must fit on 512 bits.
1074 */
1075 if (square) {
1076 square20(t, a);
1077 } else {
1078 mul20(t, a, b);
1079 }
1080
1081 /*
1082 * Modular reduction: each high word is added where necessary.
1083 * Since the modulus is 2^255-19 and word 20 corresponds to
1084 * offset 20*13 = 260, word 20+k must be added to word k with
1085 * a factor of 19*2^5 = 608. The extra bits in word 19 are also
1086 * added that way.
1087 */
1088 cc = MUL15(t[19] >> 8, 19);
1089 t[19] &= 0xFF;
1090
1091 #define MM1(x) do { \
1092 w = t[x] + cc + MUL15(t[(x) + 20], 608); \
1093 t[x] = w & 0x1FFF; \
1094 cc = w >> 13; \
1095 } while (0)
1096
1097 MM1( 0);
1098 MM1( 1);
1099 MM1( 2);
1100 MM1( 3);
1101 MM1( 4);
1102 MM1( 5);
1103 MM1( 6);
1104 MM1( 7);
1105 MM1( 8);
1106 MM1( 9);
1107 MM1(10);
1108 MM1(11);
1109 MM1(12);
1110 MM1(13);
1111 MM1(14);
1112 MM1(15);
1113 MM1(16);
1114 MM1(17);
1115 MM1(18);
1116 MM1(19);
1117
1118 #undef MM1
1119
1120 cc = MUL15(w >> 8, 19);
1121 t[19] &= 0xFF;
1122
1123 #define MM2(x) do { \
1124 w = t[x] + cc; \
1125 d[x] = w & 0x1FFF; \
1126 cc = w >> 13; \
1127 } while (0)
1128
1129 MM2( 0);
1130 MM2( 1);
1131 MM2( 2);
1132 MM2( 3);
1133 MM2( 4);
1134 MM2( 5);
1135 MM2( 6);
1136 MM2( 7);
1137 MM2( 8);
1138 MM2( 9);
1139 MM2(10);
1140 MM2(11);
1141 MM2(12);
1142 MM2(13);
1143 MM2(14);
1144 MM2(15);
1145 MM2(16);
1146 MM2(17);
1147 MM2(18);
1148 MM2(19);
1149
1150 #undef MM2
1151 }
1152
1153 /*
1154 * Perform a multiplication of two integers modulo 2^255-19.
1155 * Operands are arrays of 20 words, each containing 13 bits of data, in
1156 * little-endian order. Input value may be up to 2^256-1; on output, value
1157 * fits on 256 bits and is lower than twice the modulus.
1158 *
1159 * f255_mul() is the general multiplication, f255_square() is specialised
1160 * for squarings.
1161 */
1162 #define f255_mul(d, a, b) f255_mulgen(d, a, b, 0)
1163 #define f255_square(d, a) f255_mulgen(d, a, a, 1)
1164
1165 /*
1166 * Add two values in F255. Partial reduction is performed (down to less
1167 * than twice the modulus).
1168 */
1169 static void
1170 f255_add(uint32_t *d, const uint32_t *a, const uint32_t *b)
1171 {
1172 int i;
1173 uint32_t cc, w;
1174
1175 cc = 0;
1176 for (i = 0; i < 20; i ++) {
1177 w = a[i] + b[i] + cc;
1178 d[i] = w & 0x1FFF;
1179 cc = w >> 13;
1180 }
1181 cc = MUL15(w >> 8, 19);
1182 d[19] &= 0xFF;
1183 for (i = 0; i < 20; i ++) {
1184 w = d[i] + cc;
1185 d[i] = w & 0x1FFF;
1186 cc = w >> 13;
1187 }
1188 }
1189
1190 /*
1191 * Subtract one value from another in F255. Partial reduction is
1192 * performed (down to less than twice the modulus).
1193 */
1194 static void
1195 f255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b)
1196 {
1197 /*
1198 * We actually compute a - b + 2*p, so that the final value is
1199 * necessarily positive.
1200 */
1201 int i;
1202 uint32_t cc, w;
1203
1204 cc = (uint32_t)-38;
1205 for (i = 0; i < 20; i ++) {
1206 w = a[i] - b[i] + cc;
1207 d[i] = w & 0x1FFF;
1208 cc = ARSH(w, 13);
1209 }
1210 cc = MUL15((w + 0x200) >> 8, 19);
1211 d[19] &= 0xFF;
1212 for (i = 0; i < 20; i ++) {
1213 w = d[i] + cc;
1214 d[i] = w & 0x1FFF;
1215 cc = w >> 13;
1216 }
1217 }
1218
1219 /*
1220 * Multiply an integer by the 'A24' constant (121665). Partial reduction
1221 * is performed (down to less than twice the modulus).
1222 */
1223 static void
1224 f255_mul_a24(uint32_t *d, const uint32_t *a)
1225 {
1226 int i;
1227 uint32_t cc, w;
1228
1229 cc = 0;
1230 for (i = 0; i < 20; i ++) {
1231 w = MUL15(a[i], 121665) + cc;
1232 d[i] = w & 0x1FFF;
1233 cc = w >> 13;
1234 }
1235 cc = MUL15(w >> 8, 19);
1236 d[19] &= 0xFF;
1237 for (i = 0; i < 20; i ++) {
1238 w = d[i] + cc;
1239 d[i] = w & 0x1FFF;
1240 cc = w >> 13;
1241 }
1242 }
1243
1244 static const unsigned char GEN[] = {
1245 0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
1246 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
1247 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
1248 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
1249 };
1250
1251 static const unsigned char ORDER[] = {
1252 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
1253 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
1254 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
1255 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
1256 };
1257
1258 static const unsigned char *
1259 api_generator(int curve, size_t *len)
1260 {
1261 (void)curve;
1262 *len = 32;
1263 return GEN;
1264 }
1265
1266 static const unsigned char *
1267 api_order(int curve, size_t *len)
1268 {
1269 (void)curve;
1270 *len = 32;
1271 return ORDER;
1272 }
1273
1274 static size_t
1275 api_xoff(int curve, size_t *len)
1276 {
1277 (void)curve;
1278 *len = 32;
1279 return 0;
1280 }
1281
1282 static void
1283 cswap(uint32_t *a, uint32_t *b, uint32_t ctl)
1284 {
1285 int i;
1286
1287 ctl = -ctl;
1288 for (i = 0; i < 20; i ++) {
1289 uint32_t aw, bw, tw;
1290
1291 aw = a[i];
1292 bw = b[i];
1293 tw = ctl & (aw ^ bw);
1294 a[i] = aw ^ tw;
1295 b[i] = bw ^ tw;
1296 }
1297 }
1298
1299 static uint32_t
1300 api_mul(unsigned char *G, size_t Glen,
1301 const unsigned char *kb, size_t kblen, int curve)
1302 {
1303 uint32_t x1[20], x2[20], x3[20], z2[20], z3[20];
1304 uint32_t a[20], aa[20], b[20], bb[20];
1305 uint32_t c[20], d[20], e[20], da[20], cb[20];
1306 unsigned char k[32];
1307 uint32_t swap;
1308 int i;
1309
1310 (void)curve;
1311
1312 /*
1313 * Points are encoded over exactly 32 bytes. Multipliers must fit
1314 * in 32 bytes as well.
1315 * RFC 7748 mandates that the high bit of the last point byte must
1316 * be ignored/cleared.
1317 */
1318 if (Glen != 32 || kblen > 32) {
1319 return 0;
1320 }
1321 G[31] &= 0x7F;
1322
1323 /*
1324 * Initialise variables x1, x2, z2, x3 and z3. We set all of them
1325 * into Montgomery representation.
1326 */
1327 x1[19] = le8_to_le13(x1, G, 32);
1328 memcpy(x3, x1, sizeof x1);
1329 memset(z2, 0, sizeof z2);
1330 memset(x2, 0, sizeof x2);
1331 x2[0] = 1;
1332 memset(z3, 0, sizeof z3);
1333 z3[0] = 1;
1334
1335 memcpy(k, kb, kblen);
1336 memset(k + kblen, 0, (sizeof k) - kblen);
1337 k[0] &= 0xF8;
1338 k[31] &= 0x7F;
1339 k[31] |= 0x40;
1340
1341 /* obsolete
1342 print_int("x1", x1);
1343 */
1344
1345 swap = 0;
1346 for (i = 254; i >= 0; i --) {
1347 uint32_t kt;
1348
1349 kt = (k[i >> 3] >> (i & 7)) & 1;
1350 swap ^= kt;
1351 cswap(x2, x3, swap);
1352 cswap(z2, z3, swap);
1353 swap = kt;
1354
1355 /* obsolete
1356 print_int("x2", x2);
1357 print_int("z2", z2);
1358 print_int("x3", x3);
1359 print_int("z3", z3);
1360 */
1361
1362 f255_add(a, x2, z2);
1363 f255_square(aa, a);
1364 f255_sub(b, x2, z2);
1365 f255_square(bb, b);
1366 f255_sub(e, aa, bb);
1367 f255_add(c, x3, z3);
1368 f255_sub(d, x3, z3);
1369 f255_mul(da, d, a);
1370 f255_mul(cb, c, b);
1371
1372 /* obsolete
1373 print_int("a ", a);
1374 print_int("aa", aa);
1375 print_int("b ", b);
1376 print_int("bb", bb);
1377 print_int("e ", e);
1378 print_int("c ", c);
1379 print_int("d ", d);
1380 print_int("da", da);
1381 print_int("cb", cb);
1382 */
1383
1384 f255_add(x3, da, cb);
1385 f255_square(x3, x3);
1386 f255_sub(z3, da, cb);
1387 f255_square(z3, z3);
1388 f255_mul(z3, z3, x1);
1389 f255_mul(x2, aa, bb);
1390 f255_mul_a24(z2, e);
1391 f255_add(z2, z2, aa);
1392 f255_mul(z2, e, z2);
1393
1394 /* obsolete
1395 print_int("x2", x2);
1396 print_int("z2", z2);
1397 print_int("x3", x3);
1398 print_int("z3", z3);
1399 */
1400 }
1401 cswap(x2, x3, swap);
1402 cswap(z2, z3, swap);
1403
1404 /*
1405 * Inverse z2 with a modular exponentiation. This is a simple
1406 * square-and-multiply algorithm; we mutualise most non-squarings
1407 * since the exponent contains almost only ones.
1408 */
1409 memcpy(a, z2, sizeof z2);
1410 for (i = 0; i < 15; i ++) {
1411 f255_square(a, a);
1412 f255_mul(a, a, z2);
1413 }
1414 memcpy(b, a, sizeof a);
1415 for (i = 0; i < 14; i ++) {
1416 int j;
1417
1418 for (j = 0; j < 16; j ++) {
1419 f255_square(b, b);
1420 }
1421 f255_mul(b, b, a);
1422 }
1423 for (i = 14; i >= 0; i --) {
1424 f255_square(b, b);
1425 if ((0xFFEB >> i) & 1) {
1426 f255_mul(b, z2, b);
1427 }
1428 }
1429 f255_mul(x2, x2, b);
1430 reduce_final_f255(x2);
1431 le13_to_le8(G, 32, x2);
1432 return 1;
1433 }
1434
1435 static size_t
1436 api_mulgen(unsigned char *R,
1437 const unsigned char *x, size_t xlen, int curve)
1438 {
1439 const unsigned char *G;
1440 size_t Glen;
1441
1442 G = api_generator(curve, &Glen);
1443 memcpy(R, G, Glen);
1444 api_mul(R, Glen, x, xlen, curve);
1445 return Glen;
1446 }
1447
1448 static uint32_t
1449 api_muladd(unsigned char *A, const unsigned char *B, size_t len,
1450 const unsigned char *x, size_t xlen,
1451 const unsigned char *y, size_t ylen, int curve)
1452 {
1453 /*
1454 * We don't implement this method, since it is used for ECDSA
1455 * only, and there is no ECDSA over Curve25519 (which instead
1456 * uses EdDSA).
1457 */
1458 (void)A;
1459 (void)B;
1460 (void)len;
1461 (void)x;
1462 (void)xlen;
1463 (void)y;
1464 (void)ylen;
1465 (void)curve;
1466 return 0;
1467 }
1468
1469 /* see bearssl_ec.h */
1470 const br_ec_impl br_ec_c25519_m15 = {
1471 (uint32_t)0x20000000,
1472 &api_generator,
1473 &api_order,
1474 &api_xoff,
1475 &api_mul,
1476 &api_mulgen,
1477 &api_muladd
1478 };
The BearSSL library and tools.