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1/* $OpenBSD: ecp_nistp256.c,v 1.15 2015/02/08 22:25:03 miod Exp $ */
2/*
3 * Written by Adam Langley (Google) for the OpenSSL project
4 */
5/*
6 * Copyright (c) 2011 Google Inc.
7 *
8 * Permission to use, copy, modify, and distribute this software for any
9 * purpose with or without fee is hereby granted, provided that the above
10 * copyright notice and this permission notice appear in all copies.
11 *
12 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
13 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
14 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
15 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
16 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
17 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
18 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
19 */
20
21/*
22 * A 64-bit implementation of the NIST P-256 elliptic curve point multiplication
23 *
24 * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c.
25 * Otherwise based on Emilia's P224 work, which was inspired by my curve25519
26 * work which got its smarts from Daniel J. Bernstein's work on the same.
27 */
28
29#include <stdint.h>
30#include <string.h>
31
32#include <openssl/opensslconf.h>
33
34#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
35
36#include <openssl/err.h>
37#include "ec_lcl.h"
38
39#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
40 /* even with gcc, the typedef won't work for 32-bit platforms */
41 typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */
42 typedef __int128_t int128_t;
43#else
44 #error "Need GCC 3.1 or later to define type uint128_t"
45#endif
46
47typedef uint8_t u8;
48typedef uint32_t u32;
49typedef uint64_t u64;
50typedef int64_t s64;
51
52/* The underlying field.
53 *
54 * P256 operates over GF(2^256-2^224+2^192+2^96-1). We can serialise an element
55 * of this field into 32 bytes. We call this an felem_bytearray. */
56
57typedef u8 felem_bytearray[32];
58
59/* These are the parameters of P256, taken from FIPS 186-3, page 86. These
60 * values are big-endian. */
61static const felem_bytearray nistp256_curve_params[5] = {
62 {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */
63 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
64 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
65 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
66 {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */
67 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
68 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
69 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */
70 {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7,
71 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc,
72 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6,
73 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b},
74 {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */
75 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2,
76 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0,
77 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96},
78 {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */
79 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16,
80 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce,
81 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5}
82};
83
84/* The representation of field elements.
85 * ------------------------------------
86 *
87 * We represent field elements with either four 128-bit values, eight 128-bit
88 * values, or four 64-bit values. The field element represented is:
89 * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192 (mod p)
90 * or:
91 * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512 (mod p)
92 *
93 * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits
94 * apart, but are 128-bits wide, the most significant bits of each limb overlap
95 * with the least significant bits of the next.
96 *
97 * A field element with four limbs is an 'felem'. One with eight limbs is a
98 * 'longfelem'
99 *
100 * A field element with four, 64-bit values is called a 'smallfelem'. Small
101 * values are used as intermediate values before multiplication.
102 */
103
104#define NLIMBS 4
105
106typedef uint128_t limb;
107typedef limb felem[NLIMBS];
108typedef limb longfelem[NLIMBS * 2];
109typedef u64 smallfelem[NLIMBS];
110
111/* This is the value of the prime as four 64-bit words, little-endian. */
112static const u64 kPrime[4] = {0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul};
113static const limb bottom32bits = 0xffffffff;
114static const u64 bottom63bits = 0x7ffffffffffffffful;
115
116/* bin32_to_felem takes a little-endian byte array and converts it into felem
117 * form. This assumes that the CPU is little-endian. */
118static void
119bin32_to_felem(felem out, const u8 in[32])
120{
121 out[0] = *((u64 *) & in[0]);
122 out[1] = *((u64 *) & in[8]);
123 out[2] = *((u64 *) & in[16]);
124 out[3] = *((u64 *) & in[24]);
125}
126
127/* smallfelem_to_bin32 takes a smallfelem and serialises into a little endian,
128 * 32 byte array. This assumes that the CPU is little-endian. */
129static void
130smallfelem_to_bin32(u8 out[32], const smallfelem in)
131{
132 *((u64 *) & out[0]) = in[0];
133 *((u64 *) & out[8]) = in[1];
134 *((u64 *) & out[16]) = in[2];
135 *((u64 *) & out[24]) = in[3];
136}
137
138/* To preserve endianness when using BN_bn2bin and BN_bin2bn */
139static void
140flip_endian(u8 * out, const u8 * in, unsigned len)
141{
142 unsigned i;
143 for (i = 0; i < len; ++i)
144 out[i] = in[len - 1 - i];
145}
146
147/* BN_to_felem converts an OpenSSL BIGNUM into an felem */
148static int
149BN_to_felem(felem out, const BIGNUM * bn)
150{
151 felem_bytearray b_in;
152 felem_bytearray b_out;
153 unsigned num_bytes;
154
155 /* BN_bn2bin eats leading zeroes */
156 memset(b_out, 0, sizeof b_out);
157 num_bytes = BN_num_bytes(bn);
158 if (num_bytes > sizeof b_out) {
159 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
160 return 0;
161 }
162 if (BN_is_negative(bn)) {
163 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
164 return 0;
165 }
166 num_bytes = BN_bn2bin(bn, b_in);
167 flip_endian(b_out, b_in, num_bytes);
168 bin32_to_felem(out, b_out);
169 return 1;
170}
171
172/* felem_to_BN converts an felem into an OpenSSL BIGNUM */
173static BIGNUM *
174smallfelem_to_BN(BIGNUM * out, const smallfelem in)
175{
176 felem_bytearray b_in, b_out;
177 smallfelem_to_bin32(b_in, in);
178 flip_endian(b_out, b_in, sizeof b_out);
179 return BN_bin2bn(b_out, sizeof b_out, out);
180}
181
182
183/* Field operations
184 * ---------------- */
185
186static void
187smallfelem_one(smallfelem out)
188{
189 out[0] = 1;
190 out[1] = 0;
191 out[2] = 0;
192 out[3] = 0;
193}
194
195static void
196smallfelem_assign(smallfelem out, const smallfelem in)
197{
198 out[0] = in[0];
199 out[1] = in[1];
200 out[2] = in[2];
201 out[3] = in[3];
202}
203
204static void
205felem_assign(felem out, const felem in)
206{
207 out[0] = in[0];
208 out[1] = in[1];
209 out[2] = in[2];
210 out[3] = in[3];
211}
212
213/* felem_sum sets out = out + in. */
214static void
215felem_sum(felem out, const felem in)
216{
217 out[0] += in[0];
218 out[1] += in[1];
219 out[2] += in[2];
220 out[3] += in[3];
221}
222
223/* felem_small_sum sets out = out + in. */
224static void
225felem_small_sum(felem out, const smallfelem in)
226{
227 out[0] += in[0];
228 out[1] += in[1];
229 out[2] += in[2];
230 out[3] += in[3];
231}
232
233/* felem_scalar sets out = out * scalar */
234static void
235felem_scalar(felem out, const u64 scalar)
236{
237 out[0] *= scalar;
238 out[1] *= scalar;
239 out[2] *= scalar;
240 out[3] *= scalar;
241}
242
243/* longfelem_scalar sets out = out * scalar */
244static void
245longfelem_scalar(longfelem out, const u64 scalar)
246{
247 out[0] *= scalar;
248 out[1] *= scalar;
249 out[2] *= scalar;
250 out[3] *= scalar;
251 out[4] *= scalar;
252 out[5] *= scalar;
253 out[6] *= scalar;
254 out[7] *= scalar;
255}
256
257#define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9)
258#define two105 (((limb)1) << 105)
259#define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9)
260
261/* zero105 is 0 mod p */
262static const felem zero105 = {two105m41m9, two105, two105m41p9, two105m41p9};
263
264/* smallfelem_neg sets |out| to |-small|
265 * On exit:
266 * out[i] < out[i] + 2^105
267 */
268static void
269smallfelem_neg(felem out, const smallfelem small)
270{
271 /* In order to prevent underflow, we subtract from 0 mod p. */
272 out[0] = zero105[0] - small[0];
273 out[1] = zero105[1] - small[1];
274 out[2] = zero105[2] - small[2];
275 out[3] = zero105[3] - small[3];
276}
277
278/* felem_diff subtracts |in| from |out|
279 * On entry:
280 * in[i] < 2^104
281 * On exit:
282 * out[i] < out[i] + 2^105
283 */
284static void
285felem_diff(felem out, const felem in)
286{
287 /* In order to prevent underflow, we add 0 mod p before subtracting. */
288 out[0] += zero105[0];
289 out[1] += zero105[1];
290 out[2] += zero105[2];
291 out[3] += zero105[3];
292
293 out[0] -= in[0];
294 out[1] -= in[1];
295 out[2] -= in[2];
296 out[3] -= in[3];
297}
298
299#define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11)
300#define two107 (((limb)1) << 107)
301#define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11)
302
303/* zero107 is 0 mod p */
304static const felem zero107 = {two107m43m11, two107, two107m43p11, two107m43p11};
305
306/* An alternative felem_diff for larger inputs |in|
307 * felem_diff_zero107 subtracts |in| from |out|
308 * On entry:
309 * in[i] < 2^106
310 * On exit:
311 * out[i] < out[i] + 2^107
312 */
313static void
314felem_diff_zero107(felem out, const felem in)
315{
316 /* In order to prevent underflow, we add 0 mod p before subtracting. */
317 out[0] += zero107[0];
318 out[1] += zero107[1];
319 out[2] += zero107[2];
320 out[3] += zero107[3];
321
322 out[0] -= in[0];
323 out[1] -= in[1];
324 out[2] -= in[2];
325 out[3] -= in[3];
326}
327
328/* longfelem_diff subtracts |in| from |out|
329 * On entry:
330 * in[i] < 7*2^67
331 * On exit:
332 * out[i] < out[i] + 2^70 + 2^40
333 */
334static void
335longfelem_diff(longfelem out, const longfelem in)
336{
337 static const limb two70m8p6 = (((limb) 1) << 70) - (((limb) 1) << 8) + (((limb) 1) << 6);
338 static const limb two70p40 = (((limb) 1) << 70) + (((limb) 1) << 40);
339 static const limb two70 = (((limb) 1) << 70);
340 static const limb two70m40m38p6 = (((limb) 1) << 70) - (((limb) 1) << 40) - (((limb) 1) << 38) + (((limb) 1) << 6);
341 static const limb two70m6 = (((limb) 1) << 70) - (((limb) 1) << 6);
342
343 /* add 0 mod p to avoid underflow */
344 out[0] += two70m8p6;
345 out[1] += two70p40;
346 out[2] += two70;
347 out[3] += two70m40m38p6;
348 out[4] += two70m6;
349 out[5] += two70m6;
350 out[6] += two70m6;
351 out[7] += two70m6;
352
353 /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */
354 out[0] -= in[0];
355 out[1] -= in[1];
356 out[2] -= in[2];
357 out[3] -= in[3];
358 out[4] -= in[4];
359 out[5] -= in[5];
360 out[6] -= in[6];
361 out[7] -= in[7];
362}
363
364#define two64m0 (((limb)1) << 64) - 1
365#define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1
366#define two64m46 (((limb)1) << 64) - (((limb)1) << 46)
367#define two64m32 (((limb)1) << 64) - (((limb)1) << 32)
368
369/* zero110 is 0 mod p */
370static const felem zero110 = {two64m0, two110p32m0, two64m46, two64m32};
371
372/* felem_shrink converts an felem into a smallfelem. The result isn't quite
373 * minimal as the value may be greater than p.
374 *
375 * On entry:
376 * in[i] < 2^109
377 * On exit:
378 * out[i] < 2^64
379 */
380static void
381felem_shrink(smallfelem out, const felem in)
382{
383 felem tmp;
384 u64 a, b, mask;
385 s64 high, low;
386 static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */
387
388 /* Carry 2->3 */
389 tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64));
390 /* tmp[3] < 2^110 */
391
392 tmp[2] = zero110[2] + (u64) in[2];
393 tmp[0] = zero110[0] + in[0];
394 tmp[1] = zero110[1] + in[1];
395 /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */
396
397 /*
398 * We perform two partial reductions where we eliminate the high-word
399 * of tmp[3]. We don't update the other words till the end.
400 */
401 a = tmp[3] >> 64; /* a < 2^46 */
402 tmp[3] = (u64) tmp[3];
403 tmp[3] -= a;
404 tmp[3] += ((limb) a) << 32;
405 /* tmp[3] < 2^79 */
406
407 b = a;
408 a = tmp[3] >> 64; /* a < 2^15 */
409 b += a; /* b < 2^46 + 2^15 < 2^47 */
410 tmp[3] = (u64) tmp[3];
411 tmp[3] -= a;
412 tmp[3] += ((limb) a) << 32;
413 /* tmp[3] < 2^64 + 2^47 */
414
415 /*
416 * This adjusts the other two words to complete the two partial
417 * reductions.
418 */
419 tmp[0] += b;
420 tmp[1] -= (((limb) b) << 32);
421
422 /*
423 * In order to make space in tmp[3] for the carry from 2 -> 3, we
424 * conditionally subtract kPrime if tmp[3] is large enough.
425 */
426 high = tmp[3] >> 64;
427 /* As tmp[3] < 2^65, high is either 1 or 0 */
428 high <<= 63;
429 high >>= 63;
430 /*
431 * high is: all ones if the high word of tmp[3] is 1 all zeros if
432 * the high word of tmp[3] if 0
433 */
434 low = tmp[3];
435 mask = low >> 63;
436 /*
437 * mask is: all ones if the MSB of low is 1 all zeros if the MSB
438 * of low if 0
439 */
440 low &= bottom63bits;
441 low -= kPrime3Test;
442 /* if low was greater than kPrime3Test then the MSB is zero */
443 low = ~low;
444 low >>= 63;
445 /*
446 * low is: all ones if low was > kPrime3Test all zeros if low was
447 * <= kPrime3Test
448 */
449 mask = (mask & low) | high;
450 tmp[0] -= mask & kPrime[0];
451 tmp[1] -= mask & kPrime[1];
452 /* kPrime[2] is zero, so omitted */
453 tmp[3] -= mask & kPrime[3];
454 /* tmp[3] < 2**64 - 2**32 + 1 */
455
456 tmp[1] += ((u64) (tmp[0] >> 64));
457 tmp[0] = (u64) tmp[0];
458 tmp[2] += ((u64) (tmp[1] >> 64));
459 tmp[1] = (u64) tmp[1];
460 tmp[3] += ((u64) (tmp[2] >> 64));
461 tmp[2] = (u64) tmp[2];
462 /* tmp[i] < 2^64 */
463
464 out[0] = tmp[0];
465 out[1] = tmp[1];
466 out[2] = tmp[2];
467 out[3] = tmp[3];
468}
469
470/* smallfelem_expand converts a smallfelem to an felem */
471static void
472smallfelem_expand(felem out, const smallfelem in)
473{
474 out[0] = in[0];
475 out[1] = in[1];
476 out[2] = in[2];
477 out[3] = in[3];
478}
479
480/* smallfelem_square sets |out| = |small|^2
481 * On entry:
482 * small[i] < 2^64
483 * On exit:
484 * out[i] < 7 * 2^64 < 2^67
485 */
486static void
487smallfelem_square(longfelem out, const smallfelem small)
488{
489 limb a;
490 u64 high, low;
491
492 a = ((uint128_t) small[0]) * small[0];
493 low = a;
494 high = a >> 64;
495 out[0] = low;
496 out[1] = high;
497
498 a = ((uint128_t) small[0]) * small[1];
499 low = a;
500 high = a >> 64;
501 out[1] += low;
502 out[1] += low;
503 out[2] = high;
504
505 a = ((uint128_t) small[0]) * small[2];
506 low = a;
507 high = a >> 64;
508 out[2] += low;
509 out[2] *= 2;
510 out[3] = high;
511
512 a = ((uint128_t) small[0]) * small[3];
513 low = a;
514 high = a >> 64;
515 out[3] += low;
516 out[4] = high;
517
518 a = ((uint128_t) small[1]) * small[2];
519 low = a;
520 high = a >> 64;
521 out[3] += low;
522 out[3] *= 2;
523 out[4] += high;
524
525 a = ((uint128_t) small[1]) * small[1];
526 low = a;
527 high = a >> 64;
528 out[2] += low;
529 out[3] += high;
530
531 a = ((uint128_t) small[1]) * small[3];
532 low = a;
533 high = a >> 64;
534 out[4] += low;
535 out[4] *= 2;
536 out[5] = high;
537
538 a = ((uint128_t) small[2]) * small[3];
539 low = a;
540 high = a >> 64;
541 out[5] += low;
542 out[5] *= 2;
543 out[6] = high;
544 out[6] += high;
545
546 a = ((uint128_t) small[2]) * small[2];
547 low = a;
548 high = a >> 64;
549 out[4] += low;
550 out[5] += high;
551
552 a = ((uint128_t) small[3]) * small[3];
553 low = a;
554 high = a >> 64;
555 out[6] += low;
556 out[7] = high;
557}
558
559/* felem_square sets |out| = |in|^2
560 * On entry:
561 * in[i] < 2^109
562 * On exit:
563 * out[i] < 7 * 2^64 < 2^67
564 */
565static void
566felem_square(longfelem out, const felem in)
567{
568 u64 small[4];
569 felem_shrink(small, in);
570 smallfelem_square(out, small);
571}
572
573/* smallfelem_mul sets |out| = |small1| * |small2|
574 * On entry:
575 * small1[i] < 2^64
576 * small2[i] < 2^64
577 * On exit:
578 * out[i] < 7 * 2^64 < 2^67
579 */
580static void
581smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2)
582{
583 limb a;
584 u64 high, low;
585
586 a = ((uint128_t) small1[0]) * small2[0];
587 low = a;
588 high = a >> 64;
589 out[0] = low;
590 out[1] = high;
591
592
593 a = ((uint128_t) small1[0]) * small2[1];
594 low = a;
595 high = a >> 64;
596 out[1] += low;
597 out[2] = high;
598
599 a = ((uint128_t) small1[1]) * small2[0];
600 low = a;
601 high = a >> 64;
602 out[1] += low;
603 out[2] += high;
604
605
606 a = ((uint128_t) small1[0]) * small2[2];
607 low = a;
608 high = a >> 64;
609 out[2] += low;
610 out[3] = high;
611
612 a = ((uint128_t) small1[1]) * small2[1];
613 low = a;
614 high = a >> 64;
615 out[2] += low;
616 out[3] += high;
617
618 a = ((uint128_t) small1[2]) * small2[0];
619 low = a;
620 high = a >> 64;
621 out[2] += low;
622 out[3] += high;
623
624
625 a = ((uint128_t) small1[0]) * small2[3];
626 low = a;
627 high = a >> 64;
628 out[3] += low;
629 out[4] = high;
630
631 a = ((uint128_t) small1[1]) * small2[2];
632 low = a;
633 high = a >> 64;
634 out[3] += low;
635 out[4] += high;
636
637 a = ((uint128_t) small1[2]) * small2[1];
638 low = a;
639 high = a >> 64;
640 out[3] += low;
641 out[4] += high;
642
643 a = ((uint128_t) small1[3]) * small2[0];
644 low = a;
645 high = a >> 64;
646 out[3] += low;
647 out[4] += high;
648
649
650 a = ((uint128_t) small1[1]) * small2[3];
651 low = a;
652 high = a >> 64;
653 out[4] += low;
654 out[5] = high;
655
656 a = ((uint128_t) small1[2]) * small2[2];
657 low = a;
658 high = a >> 64;
659 out[4] += low;
660 out[5] += high;
661
662 a = ((uint128_t) small1[3]) * small2[1];
663 low = a;
664 high = a >> 64;
665 out[4] += low;
666 out[5] += high;
667
668
669 a = ((uint128_t) small1[2]) * small2[3];
670 low = a;
671 high = a >> 64;
672 out[5] += low;
673 out[6] = high;
674
675 a = ((uint128_t) small1[3]) * small2[2];
676 low = a;
677 high = a >> 64;
678 out[5] += low;
679 out[6] += high;
680
681
682 a = ((uint128_t) small1[3]) * small2[3];
683 low = a;
684 high = a >> 64;
685 out[6] += low;
686 out[7] = high;
687}
688
689/* felem_mul sets |out| = |in1| * |in2|
690 * On entry:
691 * in1[i] < 2^109
692 * in2[i] < 2^109
693 * On exit:
694 * out[i] < 7 * 2^64 < 2^67
695 */
696static void
697felem_mul(longfelem out, const felem in1, const felem in2)
698{
699 smallfelem small1, small2;
700 felem_shrink(small1, in1);
701 felem_shrink(small2, in2);
702 smallfelem_mul(out, small1, small2);
703}
704
705/* felem_small_mul sets |out| = |small1| * |in2|
706 * On entry:
707 * small1[i] < 2^64
708 * in2[i] < 2^109
709 * On exit:
710 * out[i] < 7 * 2^64 < 2^67
711 */
712static void
713felem_small_mul(longfelem out, const smallfelem small1, const felem in2)
714{
715 smallfelem small2;
716 felem_shrink(small2, in2);
717 smallfelem_mul(out, small1, small2);
718}
719
720#define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4)
721#define two100 (((limb)1) << 100)
722#define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4)
723/* zero100 is 0 mod p */
724static const felem zero100 = {two100m36m4, two100, two100m36p4, two100m36p4};
725
726/* Internal function for the different flavours of felem_reduce.
727 * felem_reduce_ reduces the higher coefficients in[4]-in[7].
728 * On entry:
729 * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7]
730 * out[1] >= in[7] + 2^32*in[4]
731 * out[2] >= in[5] + 2^32*in[5]
732 * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6]
733 * On exit:
734 * out[0] <= out[0] + in[4] + 2^32*in[5]
735 * out[1] <= out[1] + in[5] + 2^33*in[6]
736 * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7]
737 * out[3] <= out[3] + 2^32*in[4] + 3*in[7]
738 */
739static void
740felem_reduce_(felem out, const longfelem in)
741{
742 int128_t c;
743 /* combine common terms from below */
744 c = in[4] + (in[5] << 32);
745 out[0] += c;
746 out[3] -= c;
747
748 c = in[5] - in[7];
749 out[1] += c;
750 out[2] -= c;
751
752 /* the remaining terms */
753 /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */
754 out[1] -= (in[4] << 32);
755 out[3] += (in[4] << 32);
756
757 /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */
758 out[2] -= (in[5] << 32);
759
760 /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */
761 out[0] -= in[6];
762 out[0] -= (in[6] << 32);
763 out[1] += (in[6] << 33);
764 out[2] += (in[6] * 2);
765 out[3] -= (in[6] << 32);
766
767 /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */
768 out[0] -= in[7];
769 out[0] -= (in[7] << 32);
770 out[2] += (in[7] << 33);
771 out[3] += (in[7] * 3);
772}
773
774/* felem_reduce converts a longfelem into an felem.
775 * To be called directly after felem_square or felem_mul.
776 * On entry:
777 * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64
778 * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64
779 * On exit:
780 * out[i] < 2^101
781 */
782static void
783felem_reduce(felem out, const longfelem in)
784{
785 out[0] = zero100[0] + in[0];
786 out[1] = zero100[1] + in[1];
787 out[2] = zero100[2] + in[2];
788 out[3] = zero100[3] + in[3];
789
790 felem_reduce_(out, in);
791
792 /*
793 * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0
794 * out[1] > 2^100 - 2^64 - 7*2^96 > 0 out[2] > 2^100 - 2^36 + 2^4 -
795 * 5*2^64 - 5*2^96 > 0 out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96
796 * - 3*2^96 > 0
797 *
798 * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 out[1] < 2^100 +
799 * 3*2^64 + 5*2^64 + 3*2^97 < 2^101 out[2] < 2^100 + 5*2^64 + 2^64 +
800 * 3*2^65 + 2^97 < 2^101 out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 <
801 * 2^101
802 */
803}
804
805/* felem_reduce_zero105 converts a larger longfelem into an felem.
806 * On entry:
807 * in[0] < 2^71
808 * On exit:
809 * out[i] < 2^106
810 */
811static void
812felem_reduce_zero105(felem out, const longfelem in)
813{
814 out[0] = zero105[0] + in[0];
815 out[1] = zero105[1] + in[1];
816 out[2] = zero105[2] + in[2];
817 out[3] = zero105[3] + in[3];
818
819 felem_reduce_(out, in);
820
821 /*
822 * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0
823 * out[1] > 2^105 - 2^71 - 2^103 > 0 out[2] > 2^105 - 2^41 + 2^9 -
824 * 2^71 - 2^103 > 0 out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 -
825 * 2^103 > 0
826 *
827 * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 out[1] < 2^105 + 2^71 +
828 * 2^71 + 2^103 < 2^106 out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 <
829 * 2^106 out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106
830 */
831}
832
833/* subtract_u64 sets *result = *result - v and *carry to one if the subtraction
834 * underflowed. */
835static void
836subtract_u64(u64 * result, u64 * carry, u64 v)
837{
838 uint128_t r = *result;
839 r -= v;
840 *carry = (r >> 64) & 1;
841 *result = (u64) r;
842}
843
844/* felem_contract converts |in| to its unique, minimal representation.
845 * On entry:
846 * in[i] < 2^109
847 */
848static void
849felem_contract(smallfelem out, const felem in)
850{
851 unsigned i;
852 u64 all_equal_so_far = 0, result = 0, carry;
853
854 felem_shrink(out, in);
855 /* small is minimal except that the value might be > p */
856
857 all_equal_so_far--;
858 /*
859 * We are doing a constant time test if out >= kPrime. We need to
860 * compare each u64, from most-significant to least significant. For
861 * each one, if all words so far have been equal (m is all ones) then
862 * a non-equal result is the answer. Otherwise we continue.
863 */
864 for (i = 3; i < 4; i--) {
865 u64 equal;
866 uint128_t a = ((uint128_t) kPrime[i]) - out[i];
867 /*
868 * if out[i] > kPrime[i] then a will underflow and the high
869 * 64-bits will all be set.
870 */
871 result |= all_equal_so_far & ((u64) (a >> 64));
872
873 /*
874 * if kPrime[i] == out[i] then |equal| will be all zeros and
875 * the decrement will make it all ones.
876 */
877 equal = kPrime[i] ^ out[i];
878 equal--;
879 equal &= equal << 32;
880 equal &= equal << 16;
881 equal &= equal << 8;
882 equal &= equal << 4;
883 equal &= equal << 2;
884 equal &= equal << 1;
885 equal = ((s64) equal) >> 63;
886
887 all_equal_so_far &= equal;
888 }
889
890 /*
891 * if all_equal_so_far is still all ones then the two values are
892 * equal and so out >= kPrime is true.
893 */
894 result |= all_equal_so_far;
895
896 /* if out >= kPrime then we subtract kPrime. */
897 subtract_u64(&out[0], &carry, result & kPrime[0]);
898 subtract_u64(&out[1], &carry, carry);
899 subtract_u64(&out[2], &carry, carry);
900 subtract_u64(&out[3], &carry, carry);
901
902 subtract_u64(&out[1], &carry, result & kPrime[1]);
903 subtract_u64(&out[2], &carry, carry);
904 subtract_u64(&out[3], &carry, carry);
905
906 subtract_u64(&out[2], &carry, result & kPrime[2]);
907 subtract_u64(&out[3], &carry, carry);
908
909 subtract_u64(&out[3], &carry, result & kPrime[3]);
910}
911
912static void
913smallfelem_square_contract(smallfelem out, const smallfelem in)
914{
915 longfelem longtmp;
916 felem tmp;
917
918 smallfelem_square(longtmp, in);
919 felem_reduce(tmp, longtmp);
920 felem_contract(out, tmp);
921}
922
923static void
924smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2)
925{
926 longfelem longtmp;
927 felem tmp;
928
929 smallfelem_mul(longtmp, in1, in2);
930 felem_reduce(tmp, longtmp);
931 felem_contract(out, tmp);
932}
933
934/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0
935 * otherwise.
936 * On entry:
937 * small[i] < 2^64
938 */
939static limb
940smallfelem_is_zero(const smallfelem small)
941{
942 limb result;
943 u64 is_p;
944
945 u64 is_zero = small[0] | small[1] | small[2] | small[3];
946 is_zero--;
947 is_zero &= is_zero << 32;
948 is_zero &= is_zero << 16;
949 is_zero &= is_zero << 8;
950 is_zero &= is_zero << 4;
951 is_zero &= is_zero << 2;
952 is_zero &= is_zero << 1;
953 is_zero = ((s64) is_zero) >> 63;
954
955 is_p = (small[0] ^ kPrime[0]) |
956 (small[1] ^ kPrime[1]) |
957 (small[2] ^ kPrime[2]) |
958 (small[3] ^ kPrime[3]);
959 is_p--;
960 is_p &= is_p << 32;
961 is_p &= is_p << 16;
962 is_p &= is_p << 8;
963 is_p &= is_p << 4;
964 is_p &= is_p << 2;
965 is_p &= is_p << 1;
966 is_p = ((s64) is_p) >> 63;
967
968 is_zero |= is_p;
969
970 result = is_zero;
971 result |= ((limb) is_zero) << 64;
972 return result;
973}
974
975static int
976smallfelem_is_zero_int(const smallfelem small)
977{
978 return (int) (smallfelem_is_zero(small) & ((limb) 1));
979}
980
981/* felem_inv calculates |out| = |in|^{-1}
982 *
983 * Based on Fermat's Little Theorem:
984 * a^p = a (mod p)
985 * a^{p-1} = 1 (mod p)
986 * a^{p-2} = a^{-1} (mod p)
987 */
988static void
989felem_inv(felem out, const felem in)
990{
991 felem ftmp, ftmp2;
992 /* each e_I will hold |in|^{2^I - 1} */
993 felem e2, e4, e8, e16, e32, e64;
994 longfelem tmp;
995 unsigned i;
996
997 felem_square(tmp, in);
998 felem_reduce(ftmp, tmp);/* 2^1 */
999 felem_mul(tmp, in, ftmp);
1000 felem_reduce(ftmp, tmp);/* 2^2 - 2^0 */
1001 felem_assign(e2, ftmp);
1002 felem_square(tmp, ftmp);
1003 felem_reduce(ftmp, tmp);/* 2^3 - 2^1 */
1004 felem_square(tmp, ftmp);
1005 felem_reduce(ftmp, tmp);/* 2^4 - 2^2 */
1006 felem_mul(tmp, ftmp, e2);
1007 felem_reduce(ftmp, tmp);/* 2^4 - 2^0 */
1008 felem_assign(e4, ftmp);
1009 felem_square(tmp, ftmp);
1010 felem_reduce(ftmp, tmp);/* 2^5 - 2^1 */
1011 felem_square(tmp, ftmp);
1012 felem_reduce(ftmp, tmp);/* 2^6 - 2^2 */
1013 felem_square(tmp, ftmp);
1014 felem_reduce(ftmp, tmp);/* 2^7 - 2^3 */
1015 felem_square(tmp, ftmp);
1016 felem_reduce(ftmp, tmp);/* 2^8 - 2^4 */
1017 felem_mul(tmp, ftmp, e4);
1018 felem_reduce(ftmp, tmp);/* 2^8 - 2^0 */
1019 felem_assign(e8, ftmp);
1020 for (i = 0; i < 8; i++) {
1021 felem_square(tmp, ftmp);
1022 felem_reduce(ftmp, tmp);
1023 } /* 2^16 - 2^8 */
1024 felem_mul(tmp, ftmp, e8);
1025 felem_reduce(ftmp, tmp);/* 2^16 - 2^0 */
1026 felem_assign(e16, ftmp);
1027 for (i = 0; i < 16; i++) {
1028 felem_square(tmp, ftmp);
1029 felem_reduce(ftmp, tmp);
1030 } /* 2^32 - 2^16 */
1031 felem_mul(tmp, ftmp, e16);
1032 felem_reduce(ftmp, tmp);/* 2^32 - 2^0 */
1033 felem_assign(e32, ftmp);
1034 for (i = 0; i < 32; i++) {
1035 felem_square(tmp, ftmp);
1036 felem_reduce(ftmp, tmp);
1037 } /* 2^64 - 2^32 */
1038 felem_assign(e64, ftmp);
1039 felem_mul(tmp, ftmp, in);
1040 felem_reduce(ftmp, tmp);/* 2^64 - 2^32 + 2^0 */
1041 for (i = 0; i < 192; i++) {
1042 felem_square(tmp, ftmp);
1043 felem_reduce(ftmp, tmp);
1044 } /* 2^256 - 2^224 + 2^192 */
1045
1046 felem_mul(tmp, e64, e32);
1047 felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */
1048 for (i = 0; i < 16; i++) {
1049 felem_square(tmp, ftmp2);
1050 felem_reduce(ftmp2, tmp);
1051 } /* 2^80 - 2^16 */
1052 felem_mul(tmp, ftmp2, e16);
1053 felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */
1054 for (i = 0; i < 8; i++) {
1055 felem_square(tmp, ftmp2);
1056 felem_reduce(ftmp2, tmp);
1057 } /* 2^88 - 2^8 */
1058 felem_mul(tmp, ftmp2, e8);
1059 felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */
1060 for (i = 0; i < 4; i++) {
1061 felem_square(tmp, ftmp2);
1062 felem_reduce(ftmp2, tmp);
1063 } /* 2^92 - 2^4 */
1064 felem_mul(tmp, ftmp2, e4);
1065 felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */
1066 felem_square(tmp, ftmp2);
1067 felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */
1068 felem_square(tmp, ftmp2);
1069 felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */
1070 felem_mul(tmp, ftmp2, e2);
1071 felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */
1072 felem_square(tmp, ftmp2);
1073 felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */
1074 felem_square(tmp, ftmp2);
1075 felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */
1076 felem_mul(tmp, ftmp2, in);
1077 felem_reduce(ftmp2, tmp); /* 2^96 - 3 */
1078
1079 felem_mul(tmp, ftmp2, ftmp);
1080 felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */
1081}
1082
1083static void
1084smallfelem_inv_contract(smallfelem out, const smallfelem in)
1085{
1086 felem tmp;
1087
1088 smallfelem_expand(tmp, in);
1089 felem_inv(tmp, tmp);
1090 felem_contract(out, tmp);
1091}
1092
1093/* Group operations
1094 * ----------------
1095 *
1096 * Building on top of the field operations we have the operations on the
1097 * elliptic curve group itself. Points on the curve are represented in Jacobian
1098 * coordinates */
1099
1100/* point_double calculates 2*(x_in, y_in, z_in)
1101 *
1102 * The method is taken from:
1103 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
1104 *
1105 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed.
1106 * while x_out == y_in is not (maybe this works, but it's not tested). */
1107static void
1108point_double(felem x_out, felem y_out, felem z_out,
1109 const felem x_in, const felem y_in, const felem z_in)
1110{
1111 longfelem tmp, tmp2;
1112 felem delta, gamma, beta, alpha, ftmp, ftmp2;
1113 smallfelem small1, small2;
1114
1115 felem_assign(ftmp, x_in);
1116 /* ftmp[i] < 2^106 */
1117 felem_assign(ftmp2, x_in);
1118 /* ftmp2[i] < 2^106 */
1119
1120 /* delta = z^2 */
1121 felem_square(tmp, z_in);
1122 felem_reduce(delta, tmp);
1123 /* delta[i] < 2^101 */
1124
1125 /* gamma = y^2 */
1126 felem_square(tmp, y_in);
1127 felem_reduce(gamma, tmp);
1128 /* gamma[i] < 2^101 */
1129 felem_shrink(small1, gamma);
1130
1131 /* beta = x*gamma */
1132 felem_small_mul(tmp, small1, x_in);
1133 felem_reduce(beta, tmp);
1134 /* beta[i] < 2^101 */
1135
1136 /* alpha = 3*(x-delta)*(x+delta) */
1137 felem_diff(ftmp, delta);
1138 /* ftmp[i] < 2^105 + 2^106 < 2^107 */
1139 felem_sum(ftmp2, delta);
1140 /* ftmp2[i] < 2^105 + 2^106 < 2^107 */
1141 felem_scalar(ftmp2, 3);
1142 /* ftmp2[i] < 3 * 2^107 < 2^109 */
1143 felem_mul(tmp, ftmp, ftmp2);
1144 felem_reduce(alpha, tmp);
1145 /* alpha[i] < 2^101 */
1146 felem_shrink(small2, alpha);
1147
1148 /* x' = alpha^2 - 8*beta */
1149 smallfelem_square(tmp, small2);
1150 felem_reduce(x_out, tmp);
1151 felem_assign(ftmp, beta);
1152 felem_scalar(ftmp, 8);
1153 /* ftmp[i] < 8 * 2^101 = 2^104 */
1154 felem_diff(x_out, ftmp);
1155 /* x_out[i] < 2^105 + 2^101 < 2^106 */
1156
1157 /* z' = (y + z)^2 - gamma - delta */
1158 felem_sum(delta, gamma);
1159 /* delta[i] < 2^101 + 2^101 = 2^102 */
1160 felem_assign(ftmp, y_in);
1161 felem_sum(ftmp, z_in);
1162 /* ftmp[i] < 2^106 + 2^106 = 2^107 */
1163 felem_square(tmp, ftmp);
1164 felem_reduce(z_out, tmp);
1165 felem_diff(z_out, delta);
1166 /* z_out[i] < 2^105 + 2^101 < 2^106 */
1167
1168 /* y' = alpha*(4*beta - x') - 8*gamma^2 */
1169 felem_scalar(beta, 4);
1170 /* beta[i] < 4 * 2^101 = 2^103 */
1171 felem_diff_zero107(beta, x_out);
1172 /* beta[i] < 2^107 + 2^103 < 2^108 */
1173 felem_small_mul(tmp, small2, beta);
1174 /* tmp[i] < 7 * 2^64 < 2^67 */
1175 smallfelem_square(tmp2, small1);
1176 /* tmp2[i] < 7 * 2^64 */
1177 longfelem_scalar(tmp2, 8);
1178 /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */
1179 longfelem_diff(tmp, tmp2);
1180 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
1181 felem_reduce_zero105(y_out, tmp);
1182 /* y_out[i] < 2^106 */
1183}
1184
1185/* point_double_small is the same as point_double, except that it operates on
1186 * smallfelems */
1187static void
1188point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out,
1189 const smallfelem x_in, const smallfelem y_in, const smallfelem z_in)
1190{
1191 felem felem_x_out, felem_y_out, felem_z_out;
1192 felem felem_x_in, felem_y_in, felem_z_in;
1193
1194 smallfelem_expand(felem_x_in, x_in);
1195 smallfelem_expand(felem_y_in, y_in);
1196 smallfelem_expand(felem_z_in, z_in);
1197 point_double(felem_x_out, felem_y_out, felem_z_out,
1198 felem_x_in, felem_y_in, felem_z_in);
1199 felem_shrink(x_out, felem_x_out);
1200 felem_shrink(y_out, felem_y_out);
1201 felem_shrink(z_out, felem_z_out);
1202}
1203
1204/* copy_conditional copies in to out iff mask is all ones. */
1205static void
1206copy_conditional(felem out, const felem in, limb mask)
1207{
1208 unsigned i;
1209 for (i = 0; i < NLIMBS; ++i) {
1210 const limb tmp = mask & (in[i] ^ out[i]);
1211 out[i] ^= tmp;
1212 }
1213}
1214
1215/* copy_small_conditional copies in to out iff mask is all ones. */
1216static void
1217copy_small_conditional(felem out, const smallfelem in, limb mask)
1218{
1219 unsigned i;
1220 const u64 mask64 = mask;
1221 for (i = 0; i < NLIMBS; ++i) {
1222 out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask);
1223 }
1224}
1225
1226/* point_add calcuates (x1, y1, z1) + (x2, y2, z2)
1227 *
1228 * The method is taken from:
1229 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl,
1230 * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity).
1231 *
1232 * This function includes a branch for checking whether the two input points
1233 * are equal, (while not equal to the point at infinity). This case never
1234 * happens during single point multiplication, so there is no timing leak for
1235 * ECDH or ECDSA signing. */
1236static void
1237point_add(felem x3, felem y3, felem z3,
1238 const felem x1, const felem y1, const felem z1,
1239 const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2)
1240{
1241 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out;
1242 longfelem tmp, tmp2;
1243 smallfelem small1, small2, small3, small4, small5;
1244 limb x_equal, y_equal, z1_is_zero, z2_is_zero;
1245
1246 felem_shrink(small3, z1);
1247
1248 z1_is_zero = smallfelem_is_zero(small3);
1249 z2_is_zero = smallfelem_is_zero(z2);
1250
1251 /* ftmp = z1z1 = z1**2 */
1252 smallfelem_square(tmp, small3);
1253 felem_reduce(ftmp, tmp);
1254 /* ftmp[i] < 2^101 */
1255 felem_shrink(small1, ftmp);
1256
1257 if (!mixed) {
1258 /* ftmp2 = z2z2 = z2**2 */
1259 smallfelem_square(tmp, z2);
1260 felem_reduce(ftmp2, tmp);
1261 /* ftmp2[i] < 2^101 */
1262 felem_shrink(small2, ftmp2);
1263
1264 felem_shrink(small5, x1);
1265
1266 /* u1 = ftmp3 = x1*z2z2 */
1267 smallfelem_mul(tmp, small5, small2);
1268 felem_reduce(ftmp3, tmp);
1269 /* ftmp3[i] < 2^101 */
1270
1271 /* ftmp5 = z1 + z2 */
1272 felem_assign(ftmp5, z1);
1273 felem_small_sum(ftmp5, z2);
1274 /* ftmp5[i] < 2^107 */
1275
1276 /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */
1277 felem_square(tmp, ftmp5);
1278 felem_reduce(ftmp5, tmp);
1279 /* ftmp2 = z2z2 + z1z1 */
1280 felem_sum(ftmp2, ftmp);
1281 /* ftmp2[i] < 2^101 + 2^101 = 2^102 */
1282 felem_diff(ftmp5, ftmp2);
1283 /* ftmp5[i] < 2^105 + 2^101 < 2^106 */
1284
1285 /* ftmp2 = z2 * z2z2 */
1286 smallfelem_mul(tmp, small2, z2);
1287 felem_reduce(ftmp2, tmp);
1288
1289 /* s1 = ftmp2 = y1 * z2**3 */
1290 felem_mul(tmp, y1, ftmp2);
1291 felem_reduce(ftmp6, tmp);
1292 /* ftmp6[i] < 2^101 */
1293 } else {
1294 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
1295
1296 /* u1 = ftmp3 = x1*z2z2 */
1297 felem_assign(ftmp3, x1);
1298 /* ftmp3[i] < 2^106 */
1299
1300 /* ftmp5 = 2z1z2 */
1301 felem_assign(ftmp5, z1);
1302 felem_scalar(ftmp5, 2);
1303 /* ftmp5[i] < 2*2^106 = 2^107 */
1304
1305 /* s1 = ftmp2 = y1 * z2**3 */
1306 felem_assign(ftmp6, y1);
1307 /* ftmp6[i] < 2^106 */
1308 }
1309
1310 /* u2 = x2*z1z1 */
1311 smallfelem_mul(tmp, x2, small1);
1312 felem_reduce(ftmp4, tmp);
1313
1314 /* h = ftmp4 = u2 - u1 */
1315 felem_diff_zero107(ftmp4, ftmp3);
1316 /* ftmp4[i] < 2^107 + 2^101 < 2^108 */
1317 felem_shrink(small4, ftmp4);
1318
1319 x_equal = smallfelem_is_zero(small4);
1320
1321 /* z_out = ftmp5 * h */
1322 felem_small_mul(tmp, small4, ftmp5);
1323 felem_reduce(z_out, tmp);
1324 /* z_out[i] < 2^101 */
1325
1326 /* ftmp = z1 * z1z1 */
1327 smallfelem_mul(tmp, small1, small3);
1328 felem_reduce(ftmp, tmp);
1329
1330 /* s2 = tmp = y2 * z1**3 */
1331 felem_small_mul(tmp, y2, ftmp);
1332 felem_reduce(ftmp5, tmp);
1333
1334 /* r = ftmp5 = (s2 - s1)*2 */
1335 felem_diff_zero107(ftmp5, ftmp6);
1336 /* ftmp5[i] < 2^107 + 2^107 = 2^108 */
1337 felem_scalar(ftmp5, 2);
1338 /* ftmp5[i] < 2^109 */
1339 felem_shrink(small1, ftmp5);
1340 y_equal = smallfelem_is_zero(small1);
1341
1342 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
1343 point_double(x3, y3, z3, x1, y1, z1);
1344 return;
1345 }
1346 /* I = ftmp = (2h)**2 */
1347 felem_assign(ftmp, ftmp4);
1348 felem_scalar(ftmp, 2);
1349 /* ftmp[i] < 2*2^108 = 2^109 */
1350 felem_square(tmp, ftmp);
1351 felem_reduce(ftmp, tmp);
1352
1353 /* J = ftmp2 = h * I */
1354 felem_mul(tmp, ftmp4, ftmp);
1355 felem_reduce(ftmp2, tmp);
1356
1357 /* V = ftmp4 = U1 * I */
1358 felem_mul(tmp, ftmp3, ftmp);
1359 felem_reduce(ftmp4, tmp);
1360
1361 /* x_out = r**2 - J - 2V */
1362 smallfelem_square(tmp, small1);
1363 felem_reduce(x_out, tmp);
1364 felem_assign(ftmp3, ftmp4);
1365 felem_scalar(ftmp4, 2);
1366 felem_sum(ftmp4, ftmp2);
1367 /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */
1368 felem_diff(x_out, ftmp4);
1369 /* x_out[i] < 2^105 + 2^101 */
1370
1371 /* y_out = r(V-x_out) - 2 * s1 * J */
1372 felem_diff_zero107(ftmp3, x_out);
1373 /* ftmp3[i] < 2^107 + 2^101 < 2^108 */
1374 felem_small_mul(tmp, small1, ftmp3);
1375 felem_mul(tmp2, ftmp6, ftmp2);
1376 longfelem_scalar(tmp2, 2);
1377 /* tmp2[i] < 2*2^67 = 2^68 */
1378 longfelem_diff(tmp, tmp2);
1379 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
1380 felem_reduce_zero105(y_out, tmp);
1381 /* y_out[i] < 2^106 */
1382
1383 copy_small_conditional(x_out, x2, z1_is_zero);
1384 copy_conditional(x_out, x1, z2_is_zero);
1385 copy_small_conditional(y_out, y2, z1_is_zero);
1386 copy_conditional(y_out, y1, z2_is_zero);
1387 copy_small_conditional(z_out, z2, z1_is_zero);
1388 copy_conditional(z_out, z1, z2_is_zero);
1389 felem_assign(x3, x_out);
1390 felem_assign(y3, y_out);
1391 felem_assign(z3, z_out);
1392}
1393
1394/* point_add_small is the same as point_add, except that it operates on
1395 * smallfelems */
1396static void
1397point_add_small(smallfelem x3, smallfelem y3, smallfelem z3,
1398 smallfelem x1, smallfelem y1, smallfelem z1,
1399 smallfelem x2, smallfelem y2, smallfelem z2)
1400{
1401 felem felem_x3, felem_y3, felem_z3;
1402 felem felem_x1, felem_y1, felem_z1;
1403 smallfelem_expand(felem_x1, x1);
1404 smallfelem_expand(felem_y1, y1);
1405 smallfelem_expand(felem_z1, z1);
1406 point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, x2, y2, z2);
1407 felem_shrink(x3, felem_x3);
1408 felem_shrink(y3, felem_y3);
1409 felem_shrink(z3, felem_z3);
1410}
1411
1412/* Base point pre computation
1413 * --------------------------
1414 *
1415 * Two different sorts of precomputed tables are used in the following code.
1416 * Each contain various points on the curve, where each point is three field
1417 * elements (x, y, z).
1418 *
1419 * For the base point table, z is usually 1 (0 for the point at infinity).
1420 * This table has 2 * 16 elements, starting with the following:
1421 * index | bits | point
1422 * ------+---------+------------------------------
1423 * 0 | 0 0 0 0 | 0G
1424 * 1 | 0 0 0 1 | 1G
1425 * 2 | 0 0 1 0 | 2^64G
1426 * 3 | 0 0 1 1 | (2^64 + 1)G
1427 * 4 | 0 1 0 0 | 2^128G
1428 * 5 | 0 1 0 1 | (2^128 + 1)G
1429 * 6 | 0 1 1 0 | (2^128 + 2^64)G
1430 * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G
1431 * 8 | 1 0 0 0 | 2^192G
1432 * 9 | 1 0 0 1 | (2^192 + 1)G
1433 * 10 | 1 0 1 0 | (2^192 + 2^64)G
1434 * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G
1435 * 12 | 1 1 0 0 | (2^192 + 2^128)G
1436 * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G
1437 * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G
1438 * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G
1439 * followed by a copy of this with each element multiplied by 2^32.
1440 *
1441 * The reason for this is so that we can clock bits into four different
1442 * locations when doing simple scalar multiplies against the base point,
1443 * and then another four locations using the second 16 elements.
1444 *
1445 * Tables for other points have table[i] = iG for i in 0 .. 16. */
1446
1447/* gmul is the table of precomputed base points */
1448static const smallfelem gmul[2][16][3] =
1449{{{{0, 0, 0, 0},
1450{0, 0, 0, 0},
1451{0, 0, 0, 0}},
1452{{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247},
1453{0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b},
1454{1, 0, 0, 0}},
1455{{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5},
1456{0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d},
1457{1, 0, 0, 0}},
1458{{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f},
1459{0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644},
1460{1, 0, 0, 0}},
1461{{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67},
1462{0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee},
1463{1, 0, 0, 0}},
1464{{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff},
1465{0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b},
1466{1, 0, 0, 0}},
1467{{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8},
1468{0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851},
1469{1, 0, 0, 0}},
1470{{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea},
1471{0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b},
1472{1, 0, 0, 0}},
1473{{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276},
1474{0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816},
1475{1, 0, 0, 0}},
1476{{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad},
1477{0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663},
1478{1, 0, 0, 0}},
1479{{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d},
1480{0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321},
1481{1, 0, 0, 0}},
1482{{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287},
1483{0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6},
1484{1, 0, 0, 0}},
1485{{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466},
1486{0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20},
1487{1, 0, 0, 0}},
1488{{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9},
1489{0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61},
1490{1, 0, 0, 0}},
1491{{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a},
1492{0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc},
1493{1, 0, 0, 0}},
1494{{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c},
1495{0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab},
1496{1, 0, 0, 0}}},
1497{{{0, 0, 0, 0},
1498{0, 0, 0, 0},
1499{0, 0, 0, 0}},
1500{{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89},
1501{0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624},
1502{1, 0, 0, 0}},
1503{{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6},
1504{0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1},
1505{1, 0, 0, 0}},
1506{{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a},
1507{0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593},
1508{1, 0, 0, 0}},
1509{{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617},
1510{0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7},
1511{1, 0, 0, 0}},
1512{{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276},
1513{0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a},
1514{1, 0, 0, 0}},
1515{{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908},
1516{0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e},
1517{1, 0, 0, 0}},
1518{{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7},
1519{0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec},
1520{1, 0, 0, 0}},
1521{{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee},
1522{0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6},
1523{1, 0, 0, 0}},
1524{{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109},
1525{0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5},
1526{1, 0, 0, 0}},
1527{{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba},
1528{0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44},
1529{1, 0, 0, 0}},
1530{{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b},
1531{0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc},
1532{1, 0, 0, 0}},
1533{{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107},
1534{0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387},
1535{1, 0, 0, 0}},
1536{{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503},
1537{0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be},
1538{1, 0, 0, 0}},
1539{{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9},
1540{0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a},
1541{1, 0, 0, 0}},
1542{{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6},
1543{0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81},
1544{1, 0, 0, 0}}}};
1545
1546/* select_point selects the |idx|th point from a precomputation table and
1547 * copies it to out. */
1548static void
1549select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3])
1550{
1551 unsigned i, j;
1552 u64 *outlimbs = &out[0][0];
1553 memset(outlimbs, 0, 3 * sizeof(smallfelem));
1554
1555 for (i = 0; i < size; i++) {
1556 const u64 *inlimbs = (u64 *) & pre_comp[i][0][0];
1557 u64 mask = i ^ idx;
1558 mask |= mask >> 4;
1559 mask |= mask >> 2;
1560 mask |= mask >> 1;
1561 mask &= 1;
1562 mask--;
1563 for (j = 0; j < NLIMBS * 3; j++)
1564 outlimbs[j] |= inlimbs[j] & mask;
1565 }
1566}
1567
1568/* get_bit returns the |i|th bit in |in| */
1569static char
1570get_bit(const felem_bytearray in, int i)
1571{
1572 if ((i < 0) || (i >= 256))
1573 return 0;
1574 return (in[i >> 3] >> (i & 7)) & 1;
1575}
1576
1577/* Interleaved point multiplication using precomputed point multiples:
1578 * The small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[],
1579 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
1580 * of the generator, using certain (large) precomputed multiples in g_pre_comp.
1581 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
1582static void
1583batch_mul(felem x_out, felem y_out, felem z_out,
1584 const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar,
1585 const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3])
1586{
1587 int i, skip;
1588 unsigned num, gen_mul = (g_scalar != NULL);
1589 felem nq[3], ftmp;
1590 smallfelem tmp[3];
1591 u64 bits;
1592 u8 sign, digit;
1593
1594 /* set nq to the point at infinity */
1595 memset(nq, 0, 3 * sizeof(felem));
1596
1597 /*
1598 * Loop over all scalars msb-to-lsb, interleaving additions of
1599 * multiples of the generator (two in each of the last 32 rounds) and
1600 * additions of other points multiples (every 5th round).
1601 */
1602 skip = 1; /* save two point operations in the first
1603 * round */
1604 for (i = (num_points ? 255 : 31); i >= 0; --i) {
1605 /* double */
1606 if (!skip)
1607 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
1608
1609 /* add multiples of the generator */
1610 if (gen_mul && (i <= 31)) {
1611 /* first, look 32 bits upwards */
1612 bits = get_bit(g_scalar, i + 224) << 3;
1613 bits |= get_bit(g_scalar, i + 160) << 2;
1614 bits |= get_bit(g_scalar, i + 96) << 1;
1615 bits |= get_bit(g_scalar, i + 32);
1616 /* select the point to add, in constant time */
1617 select_point(bits, 16, g_pre_comp[1], tmp);
1618
1619 if (!skip) {
1620 point_add(nq[0], nq[1], nq[2],
1621 nq[0], nq[1], nq[2],
1622 1 /* mixed */ , tmp[0], tmp[1], tmp[2]);
1623 } else {
1624 smallfelem_expand(nq[0], tmp[0]);
1625 smallfelem_expand(nq[1], tmp[1]);
1626 smallfelem_expand(nq[2], tmp[2]);
1627 skip = 0;
1628 }
1629
1630 /* second, look at the current position */
1631 bits = get_bit(g_scalar, i + 192) << 3;
1632 bits |= get_bit(g_scalar, i + 128) << 2;
1633 bits |= get_bit(g_scalar, i + 64) << 1;
1634 bits |= get_bit(g_scalar, i);
1635 /* select the point to add, in constant time */
1636 select_point(bits, 16, g_pre_comp[0], tmp);
1637 point_add(nq[0], nq[1], nq[2],
1638 nq[0], nq[1], nq[2],
1639 1 /* mixed */ , tmp[0], tmp[1], tmp[2]);
1640 }
1641 /* do other additions every 5 doublings */
1642 if (num_points && (i % 5 == 0)) {
1643 /* loop over all scalars */
1644 for (num = 0; num < num_points; ++num) {
1645 bits = get_bit(scalars[num], i + 4) << 5;
1646 bits |= get_bit(scalars[num], i + 3) << 4;
1647 bits |= get_bit(scalars[num], i + 2) << 3;
1648 bits |= get_bit(scalars[num], i + 1) << 2;
1649 bits |= get_bit(scalars[num], i) << 1;
1650 bits |= get_bit(scalars[num], i - 1);
1651 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
1652
1653 /*
1654 * select the point to add or subtract, in
1655 * constant time
1656 */
1657 select_point(digit, 17, pre_comp[num], tmp);
1658 smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the
1659 * negative point */
1660 copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1));
1661 felem_contract(tmp[1], ftmp);
1662
1663 if (!skip) {
1664 point_add(nq[0], nq[1], nq[2],
1665 nq[0], nq[1], nq[2],
1666 mixed, tmp[0], tmp[1], tmp[2]);
1667 } else {
1668 smallfelem_expand(nq[0], tmp[0]);
1669 smallfelem_expand(nq[1], tmp[1]);
1670 smallfelem_expand(nq[2], tmp[2]);
1671 skip = 0;
1672 }
1673 }
1674 }
1675 }
1676 felem_assign(x_out, nq[0]);
1677 felem_assign(y_out, nq[1]);
1678 felem_assign(z_out, nq[2]);
1679}
1680
1681/* Precomputation for the group generator. */
1682typedef struct {
1683 smallfelem g_pre_comp[2][16][3];
1684 int references;
1685} NISTP256_PRE_COMP;
1686
1687const EC_METHOD *
1688EC_GFp_nistp256_method(void)
1689{
1690 static const EC_METHOD ret = {
1691 .flags = EC_FLAGS_DEFAULT_OCT,
1692 .field_type = NID_X9_62_prime_field,
1693 .group_init = ec_GFp_nistp256_group_init,
1694 .group_finish = ec_GFp_simple_group_finish,
1695 .group_clear_finish = ec_GFp_simple_group_clear_finish,
1696 .group_copy = ec_GFp_nist_group_copy,
1697 .group_set_curve = ec_GFp_nistp256_group_set_curve,
1698 .group_get_curve = ec_GFp_simple_group_get_curve,
1699 .group_get_degree = ec_GFp_simple_group_get_degree,
1700 .group_check_discriminant =
1701 ec_GFp_simple_group_check_discriminant,
1702 .point_init = ec_GFp_simple_point_init,
1703 .point_finish = ec_GFp_simple_point_finish,
1704 .point_clear_finish = ec_GFp_simple_point_clear_finish,
1705 .point_copy = ec_GFp_simple_point_copy,
1706 .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity,
1707 .point_set_Jprojective_coordinates_GFp =
1708 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1709 .point_get_Jprojective_coordinates_GFp =
1710 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1711 .point_set_affine_coordinates =
1712 ec_GFp_simple_point_set_affine_coordinates,
1713 .point_get_affine_coordinates =
1714 ec_GFp_nistp256_point_get_affine_coordinates,
1715 .add = ec_GFp_simple_add,
1716 .dbl = ec_GFp_simple_dbl,
1717 .invert = ec_GFp_simple_invert,
1718 .is_at_infinity = ec_GFp_simple_is_at_infinity,
1719 .is_on_curve = ec_GFp_simple_is_on_curve,
1720 .point_cmp = ec_GFp_simple_cmp,
1721 .make_affine = ec_GFp_simple_make_affine,
1722 .points_make_affine = ec_GFp_simple_points_make_affine,
1723 .mul = ec_GFp_nistp256_points_mul,
1724 .precompute_mult = ec_GFp_nistp256_precompute_mult,
1725 .have_precompute_mult = ec_GFp_nistp256_have_precompute_mult,
1726 .field_mul = ec_GFp_nist_field_mul,
1727 .field_sqr = ec_GFp_nist_field_sqr
1728 };
1729
1730 return &ret;
1731}
1732
1733/******************************************************************************/
1734/* FUNCTIONS TO MANAGE PRECOMPUTATION
1735 */
1736
1737static NISTP256_PRE_COMP *
1738nistp256_pre_comp_new()
1739{
1740 NISTP256_PRE_COMP *ret = NULL;
1741 ret = malloc(sizeof *ret);
1742 if (!ret) {
1743 ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1744 return ret;
1745 }
1746 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1747 ret->references = 1;
1748 return ret;
1749}
1750
1751static void *
1752nistp256_pre_comp_dup(void *src_)
1753{
1754 NISTP256_PRE_COMP *src = src_;
1755
1756 /* no need to actually copy, these objects never change! */
1757 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1758
1759 return src_;
1760}
1761
1762static void
1763nistp256_pre_comp_free(void *pre_)
1764{
1765 int i;
1766 NISTP256_PRE_COMP *pre = pre_;
1767
1768 if (!pre)
1769 return;
1770
1771 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1772 if (i > 0)
1773 return;
1774
1775 free(pre);
1776}
1777
1778static void
1779nistp256_pre_comp_clear_free(void *pre_)
1780{
1781 int i;
1782 NISTP256_PRE_COMP *pre = pre_;
1783
1784 if (!pre)
1785 return;
1786
1787 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1788 if (i > 0)
1789 return;
1790
1791 OPENSSL_cleanse(pre, sizeof *pre);
1792 free(pre);
1793}
1794
1795/******************************************************************************/
1796/* OPENSSL EC_METHOD FUNCTIONS
1797 */
1798
1799int
1800ec_GFp_nistp256_group_init(EC_GROUP * group)
1801{
1802 int ret;
1803 ret = ec_GFp_simple_group_init(group);
1804 group->a_is_minus3 = 1;
1805 return ret;
1806}
1807
1808int
1809ec_GFp_nistp256_group_set_curve(EC_GROUP * group, const BIGNUM * p,
1810 const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx)
1811{
1812 int ret = 0;
1813 BN_CTX *new_ctx = NULL;
1814 BIGNUM *curve_p, *curve_a, *curve_b;
1815
1816 if (ctx == NULL)
1817 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1818 return 0;
1819 BN_CTX_start(ctx);
1820 if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1821 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1822 ((curve_b = BN_CTX_get(ctx)) == NULL))
1823 goto err;
1824 BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p);
1825 BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a);
1826 BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b);
1827 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1828 (BN_cmp(curve_b, b))) {
1829 ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE,
1830 EC_R_WRONG_CURVE_PARAMETERS);
1831 goto err;
1832 }
1833 group->field_mod_func = BN_nist_mod_256;
1834 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1835err:
1836 BN_CTX_end(ctx);
1837 BN_CTX_free(new_ctx);
1838 return ret;
1839}
1840
1841/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1842 * (X', Y') = (X/Z^2, Y/Z^3) */
1843int
1844ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP * group,
1845 const EC_POINT * point, BIGNUM * x, BIGNUM * y, BN_CTX * ctx)
1846{
1847 felem z1, z2, x_in, y_in;
1848 smallfelem x_out, y_out;
1849 longfelem tmp;
1850
1851 if (EC_POINT_is_at_infinity(group, point) > 0) {
1852 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
1853 EC_R_POINT_AT_INFINITY);
1854 return 0;
1855 }
1856 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1857 (!BN_to_felem(z1, &point->Z)))
1858 return 0;
1859 felem_inv(z2, z1);
1860 felem_square(tmp, z2);
1861 felem_reduce(z1, tmp);
1862 felem_mul(tmp, x_in, z1);
1863 felem_reduce(x_in, tmp);
1864 felem_contract(x_out, x_in);
1865 if (x != NULL) {
1866 if (!smallfelem_to_BN(x, x_out)) {
1867 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
1868 ERR_R_BN_LIB);
1869 return 0;
1870 }
1871 }
1872 felem_mul(tmp, z1, z2);
1873 felem_reduce(z1, tmp);
1874 felem_mul(tmp, y_in, z1);
1875 felem_reduce(y_in, tmp);
1876 felem_contract(y_out, y_in);
1877 if (y != NULL) {
1878 if (!smallfelem_to_BN(y, y_out)) {
1879 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
1880 ERR_R_BN_LIB);
1881 return 0;
1882 }
1883 }
1884 return 1;
1885}
1886
1887static void
1888make_points_affine(size_t num, smallfelem points[ /* num */ ][3], smallfelem tmp_smallfelems[ /* num+1 */ ])
1889{
1890 /*
1891 * Runs in constant time, unless an input is the point at infinity
1892 * (which normally shouldn't happen).
1893 */
1894 ec_GFp_nistp_points_make_affine_internal(
1895 num,
1896 points,
1897 sizeof(smallfelem),
1898 tmp_smallfelems,
1899 (void (*) (void *)) smallfelem_one,
1900 (int (*) (const void *)) smallfelem_is_zero_int,
1901 (void (*) (void *, const void *)) smallfelem_assign,
1902 (void (*) (void *, const void *)) smallfelem_square_contract,
1903 (void (*) (void *, const void *, const void *)) smallfelem_mul_contract,
1904 (void (*) (void *, const void *)) smallfelem_inv_contract,
1905 (void (*) (void *, const void *)) smallfelem_assign /* nothing to contract */ );
1906}
1907
1908/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1909 * Result is stored in r (r can equal one of the inputs). */
1910int
1911ec_GFp_nistp256_points_mul(const EC_GROUP * group, EC_POINT * r,
1912 const BIGNUM * scalar, size_t num, const EC_POINT * points[],
1913 const BIGNUM * scalars[], BN_CTX * ctx)
1914{
1915 int ret = 0;
1916 int j;
1917 int mixed = 0;
1918 BN_CTX *new_ctx = NULL;
1919 BIGNUM *x, *y, *z, *tmp_scalar;
1920 felem_bytearray g_secret;
1921 felem_bytearray *secrets = NULL;
1922 smallfelem(*pre_comp)[17][3] = NULL;
1923 smallfelem *tmp_smallfelems = NULL;
1924 felem_bytearray tmp;
1925 unsigned i, num_bytes;
1926 int have_pre_comp = 0;
1927 size_t num_points = num;
1928 smallfelem x_in, y_in, z_in;
1929 felem x_out, y_out, z_out;
1930 NISTP256_PRE_COMP *pre = NULL;
1931 const smallfelem(*g_pre_comp)[16][3] = NULL;
1932 EC_POINT *generator = NULL;
1933 const EC_POINT *p = NULL;
1934 const BIGNUM *p_scalar = NULL;
1935
1936 if (ctx == NULL)
1937 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1938 return 0;
1939 BN_CTX_start(ctx);
1940 if (((x = BN_CTX_get(ctx)) == NULL) ||
1941 ((y = BN_CTX_get(ctx)) == NULL) ||
1942 ((z = BN_CTX_get(ctx)) == NULL) ||
1943 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1944 goto err;
1945
1946 if (scalar != NULL) {
1947 pre = EC_EX_DATA_get_data(group->extra_data,
1948 nistp256_pre_comp_dup, nistp256_pre_comp_free,
1949 nistp256_pre_comp_clear_free);
1950 if (pre)
1951 /* we have precomputation, try to use it */
1952 g_pre_comp = (const smallfelem(*)[16][3]) pre->g_pre_comp;
1953 else
1954 /* try to use the standard precomputation */
1955 g_pre_comp = &gmul[0];
1956 generator = EC_POINT_new(group);
1957 if (generator == NULL)
1958 goto err;
1959 /* get the generator from precomputation */
1960 if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) ||
1961 !smallfelem_to_BN(y, g_pre_comp[0][1][1]) ||
1962 !smallfelem_to_BN(z, g_pre_comp[0][1][2])) {
1963 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
1964 goto err;
1965 }
1966 if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1967 generator, x, y, z, ctx))
1968 goto err;
1969 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1970 /* precomputation matches generator */
1971 have_pre_comp = 1;
1972 else
1973 /*
1974 * we don't have valid precomputation: treat the
1975 * generator as a random point
1976 */
1977 num_points++;
1978 }
1979 if (num_points > 0) {
1980 if (num_points >= 3) {
1981 /*
1982 * unless we precompute multiples for just one or two
1983 * points, converting those into affine form is time
1984 * well spent
1985 */
1986 mixed = 1;
1987 }
1988 secrets = calloc(num_points, sizeof(felem_bytearray));
1989 pre_comp = calloc(num_points, 17 * 3 * sizeof(smallfelem));
1990 if (mixed) {
1991 /* XXX should do more int overflow checking */
1992 tmp_smallfelems = reallocarray(NULL,
1993 (num_points * 17 + 1), sizeof(smallfelem));
1994 }
1995 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) {
1996 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1997 goto err;
1998 }
1999 /*
2000 * we treat NULL scalars as 0, and NULL points as points at
2001 * infinity, i.e., they contribute nothing to the linear
2002 * combination
2003 */
2004 for (i = 0; i < num_points; ++i) {
2005 if (i == num)
2006 /*
2007 * we didn't have a valid precomputation, so
2008 * we pick the generator
2009 */
2010 {
2011 p = EC_GROUP_get0_generator(group);
2012 p_scalar = scalar;
2013 } else
2014 /* the i^th point */
2015 {
2016 p = points[i];
2017 p_scalar = scalars[i];
2018 }
2019 if ((p_scalar != NULL) && (p != NULL)) {
2020 /* reduce scalar to 0 <= scalar < 2^256 */
2021 if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar))) {
2022 /*
2023 * this is an unusual input, and we
2024 * don't guarantee constant-timeness
2025 */
2026 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) {
2027 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
2028 goto err;
2029 }
2030 num_bytes = BN_bn2bin(tmp_scalar, tmp);
2031 } else
2032 num_bytes = BN_bn2bin(p_scalar, tmp);
2033 flip_endian(secrets[i], tmp, num_bytes);
2034 /* precompute multiples */
2035 if ((!BN_to_felem(x_out, &p->X)) ||
2036 (!BN_to_felem(y_out, &p->Y)) ||
2037 (!BN_to_felem(z_out, &p->Z)))
2038 goto err;
2039 felem_shrink(pre_comp[i][1][0], x_out);
2040 felem_shrink(pre_comp[i][1][1], y_out);
2041 felem_shrink(pre_comp[i][1][2], z_out);
2042 for (j = 2; j <= 16; ++j) {
2043 if (j & 1) {
2044 point_add_small(
2045 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
2046 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
2047 pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]);
2048 } else {
2049 point_double_small(
2050 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
2051 pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]);
2052 }
2053 }
2054 }
2055 }
2056 if (mixed)
2057 make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems);
2058 }
2059 /* the scalar for the generator */
2060 if ((scalar != NULL) && (have_pre_comp)) {
2061 memset(g_secret, 0, sizeof(g_secret));
2062 /* reduce scalar to 0 <= scalar < 2^256 */
2063 if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) {
2064 /*
2065 * this is an unusual input, and we don't guarantee
2066 * constant-timeness
2067 */
2068 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) {
2069 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
2070 goto err;
2071 }
2072 num_bytes = BN_bn2bin(tmp_scalar, tmp);
2073 } else
2074 num_bytes = BN_bn2bin(scalar, tmp);
2075 flip_endian(g_secret, tmp, num_bytes);
2076 /* do the multiplication with generator precomputation */
2077 batch_mul(x_out, y_out, z_out,
2078 (const felem_bytearray(*)) secrets, num_points,
2079 g_secret,
2080 mixed, (const smallfelem(*)[17][3]) pre_comp,
2081 g_pre_comp);
2082 } else
2083 /* do the multiplication without generator precomputation */
2084 batch_mul(x_out, y_out, z_out,
2085 (const felem_bytearray(*)) secrets, num_points,
2086 NULL, mixed, (const smallfelem(*)[17][3]) pre_comp, NULL);
2087 /* reduce the output to its unique minimal representation */
2088 felem_contract(x_in, x_out);
2089 felem_contract(y_in, y_out);
2090 felem_contract(z_in, z_out);
2091 if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) ||
2092 (!smallfelem_to_BN(z, z_in))) {
2093 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
2094 goto err;
2095 }
2096 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
2097
2098err:
2099 BN_CTX_end(ctx);
2100 EC_POINT_free(generator);
2101 BN_CTX_free(new_ctx);
2102 free(secrets);
2103 free(pre_comp);
2104 free(tmp_smallfelems);
2105 return ret;
2106}
2107
2108int
2109ec_GFp_nistp256_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
2110{
2111 int ret = 0;
2112 NISTP256_PRE_COMP *pre = NULL;
2113 int i, j;
2114 BN_CTX *new_ctx = NULL;
2115 BIGNUM *x, *y;
2116 EC_POINT *generator = NULL;
2117 smallfelem tmp_smallfelems[32];
2118 felem x_tmp, y_tmp, z_tmp;
2119
2120 /* throw away old precomputation */
2121 EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup,
2122 nistp256_pre_comp_free, nistp256_pre_comp_clear_free);
2123 if (ctx == NULL)
2124 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
2125 return 0;
2126 BN_CTX_start(ctx);
2127 if (((x = BN_CTX_get(ctx)) == NULL) ||
2128 ((y = BN_CTX_get(ctx)) == NULL))
2129 goto err;
2130 /* get the generator */
2131 if (group->generator == NULL)
2132 goto err;
2133 generator = EC_POINT_new(group);
2134 if (generator == NULL)
2135 goto err;
2136 BN_bin2bn(nistp256_curve_params[3], sizeof(felem_bytearray), x);
2137 BN_bin2bn(nistp256_curve_params[4], sizeof(felem_bytearray), y);
2138 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
2139 goto err;
2140 if ((pre = nistp256_pre_comp_new()) == NULL)
2141 goto err;
2142 /* if the generator is the standard one, use built-in precomputation */
2143 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) {
2144 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
2145 ret = 1;
2146 goto err;
2147 }
2148 if ((!BN_to_felem(x_tmp, &group->generator->X)) ||
2149 (!BN_to_felem(y_tmp, &group->generator->Y)) ||
2150 (!BN_to_felem(z_tmp, &group->generator->Z)))
2151 goto err;
2152 felem_shrink(pre->g_pre_comp[0][1][0], x_tmp);
2153 felem_shrink(pre->g_pre_comp[0][1][1], y_tmp);
2154 felem_shrink(pre->g_pre_comp[0][1][2], z_tmp);
2155 /*
2156 * compute 2^64*G, 2^128*G, 2^192*G for the first table, 2^32*G,
2157 * 2^96*G, 2^160*G, 2^224*G for the second one
2158 */
2159 for (i = 1; i <= 8; i <<= 1) {
2160 point_double_small(
2161 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
2162 pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]);
2163 for (j = 0; j < 31; ++j) {
2164 point_double_small(
2165 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
2166 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
2167 }
2168 if (i == 8)
2169 break;
2170 point_double_small(
2171 pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2],
2172 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
2173 for (j = 0; j < 31; ++j) {
2174 point_double_small(
2175 pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2],
2176 pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2]);
2177 }
2178 }
2179 for (i = 0; i < 2; i++) {
2180 /* g_pre_comp[i][0] is the point at infinity */
2181 memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0]));
2182 /* the remaining multiples */
2183 /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */
2184 point_add_small(
2185 pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2],
2186 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2],
2187 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]);
2188 /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */
2189 point_add_small(
2190 pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2],
2191 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
2192 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]);
2193 /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */
2194 point_add_small(
2195 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
2196 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
2197 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]);
2198 /*
2199 * 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G +
2200 * 2^224*G
2201 */
2202 point_add_small(
2203 pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2],
2204 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
2205 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]);
2206 for (j = 1; j < 8; ++j) {
2207 /* odd multiples: add G resp. 2^32*G */
2208 point_add_small(
2209 pre->g_pre_comp[i][2 * j + 1][0], pre->g_pre_comp[i][2 * j + 1][1], pre->g_pre_comp[i][2 * j + 1][2],
2210 pre->g_pre_comp[i][2 * j][0], pre->g_pre_comp[i][2 * j][1], pre->g_pre_comp[i][2 * j][2],
2211 pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]);
2212 }
2213 }
2214 make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems);
2215
2216 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup,
2217 nistp256_pre_comp_free, nistp256_pre_comp_clear_free))
2218 goto err;
2219 ret = 1;
2220 pre = NULL;
2221err:
2222 BN_CTX_end(ctx);
2223 EC_POINT_free(generator);
2224 BN_CTX_free(new_ctx);
2225 nistp256_pre_comp_free(pre);
2226 return ret;
2227}
2228
2229int
2230ec_GFp_nistp256_have_precompute_mult(const EC_GROUP * group)
2231{
2232 if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup,
2233 nistp256_pre_comp_free, nistp256_pre_comp_clear_free)
2234 != NULL)
2235 return 1;
2236 else
2237 return 0;
2238}
2239#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-08-15 02:32:10 +0000