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1/* crypto/ec/ecp_nistp256.c */
2/*
3 * Written by Adam Langley (Google) for the OpenSSL project
4 */
5/* Copyright 2011 Google Inc.
6 *
7 * Licensed under the Apache License, Version 2.0 (the "License");
8 *
9 * you may not use this file except in compliance with the License.
10 * You may obtain a copy of the License at
11 *
12 * http://www.apache.org/licenses/LICENSE-2.0
13 *
14 * Unless required by applicable law or agreed to in writing, software
15 * distributed under the License is distributed on an "AS IS" BASIS,
16 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
17 * See the License for the specific language governing permissions and
18 * limitations under the License.
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 <openssl/opensslconf.h>
30#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
31
32#ifndef OPENSSL_SYS_VMS
33#include <stdint.h>
34#else
35#include <inttypes.h>
36#endif
37
38#include <string.h>
39#include <openssl/err.h>
40#include "ec_lcl.h"
41
42#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
43 /* even with gcc, the typedef won't work for 32-bit platforms */
44 typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */
45 typedef __int128_t int128_t;
46#else
47 #error "Need GCC 3.1 or later to define type uint128_t"
48#endif
49
50typedef uint8_t u8;
51typedef uint32_t u32;
52typedef uint64_t u64;
53typedef int64_t s64;
54
55/* The underlying field.
56 *
57 * P256 operates over GF(2^256-2^224+2^192+2^96-1). We can serialise an element
58 * of this field into 32 bytes. We call this an felem_bytearray. */
59
60typedef u8 felem_bytearray[32];
61
62/* These are the parameters of P256, taken from FIPS 186-3, page 86. These
63 * values are big-endian. */
64static const felem_bytearray nistp256_curve_params[5] = {
65 {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */
66 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
67 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
68 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
69 {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */
70 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
71 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
72 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */
73 {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7,
74 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc,
75 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6,
76 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b},
77 {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */
78 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2,
79 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0,
80 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96},
81 {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */
82 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16,
83 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce,
84 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5}
85};
86
87/* The representation of field elements.
88 * ------------------------------------
89 *
90 * We represent field elements with either four 128-bit values, eight 128-bit
91 * values, or four 64-bit values. The field element represented is:
92 * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192 (mod p)
93 * or:
94 * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512 (mod p)
95 *
96 * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits
97 * apart, but are 128-bits wide, the most significant bits of each limb overlap
98 * with the least significant bits of the next.
99 *
100 * A field element with four limbs is an 'felem'. One with eight limbs is a
101 * 'longfelem'
102 *
103 * A field element with four, 64-bit values is called a 'smallfelem'. Small
104 * values are used as intermediate values before multiplication.
105 */
106
107#define NLIMBS 4
108
109typedef uint128_t limb;
110typedef limb felem[NLIMBS];
111typedef limb longfelem[NLIMBS * 2];
112typedef u64 smallfelem[NLIMBS];
113
114/* This is the value of the prime as four 64-bit words, little-endian. */
115static const u64 kPrime[4] = { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul };
116static const limb bottom32bits = 0xffffffff;
117static const u64 bottom63bits = 0x7ffffffffffffffful;
118
119/* bin32_to_felem takes a little-endian byte array and converts it into felem
120 * form. This assumes that the CPU is little-endian. */
121static void bin32_to_felem(felem out, const u8 in[32])
122 {
123 out[0] = *((u64*) &in[0]);
124 out[1] = *((u64*) &in[8]);
125 out[2] = *((u64*) &in[16]);
126 out[3] = *((u64*) &in[24]);
127 }
128
129/* smallfelem_to_bin32 takes a smallfelem and serialises into a little endian,
130 * 32 byte array. This assumes that the CPU is little-endian. */
131static void smallfelem_to_bin32(u8 out[32], const smallfelem in)
132 {
133 *((u64*) &out[0]) = in[0];
134 *((u64*) &out[8]) = in[1];
135 *((u64*) &out[16]) = in[2];
136 *((u64*) &out[24]) = in[3];
137 }
138
139/* To preserve endianness when using BN_bn2bin and BN_bin2bn */
140static void flip_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 BN_to_felem(felem out, const BIGNUM *bn)
149 {
150 felem_bytearray b_in;
151 felem_bytearray b_out;
152 unsigned num_bytes;
153
154 /* BN_bn2bin eats leading zeroes */
155 memset(b_out, 0, sizeof b_out);
156 num_bytes = BN_num_bytes(bn);
157 if (num_bytes > sizeof b_out)
158 {
159 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
160 return 0;
161 }
162 if (BN_is_negative(bn))
163 {
164 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
165 return 0;
166 }
167 num_bytes = BN_bn2bin(bn, b_in);
168 flip_endian(b_out, b_in, num_bytes);
169 bin32_to_felem(out, b_out);
170 return 1;
171 }
172
173/* felem_to_BN converts an felem into an OpenSSL BIGNUM */
174static BIGNUM *smallfelem_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 smallfelem_one(smallfelem out)
187 {
188 out[0] = 1;
189 out[1] = 0;
190 out[2] = 0;
191 out[3] = 0;
192 }
193
194static void smallfelem_assign(smallfelem out, const smallfelem in)
195 {
196 out[0] = in[0];
197 out[1] = in[1];
198 out[2] = in[2];
199 out[3] = in[3];
200 }
201
202static void felem_assign(felem out, const felem in)
203 {
204 out[0] = in[0];
205 out[1] = in[1];
206 out[2] = in[2];
207 out[3] = in[3];
208 }
209
210/* felem_sum sets out = out + in. */
211static void felem_sum(felem out, const felem in)
212 {
213 out[0] += in[0];
214 out[1] += in[1];
215 out[2] += in[2];
216 out[3] += in[3];
217 }
218
219/* felem_small_sum sets out = out + in. */
220static void felem_small_sum(felem out, const smallfelem in)
221 {
222 out[0] += in[0];
223 out[1] += in[1];
224 out[2] += in[2];
225 out[3] += in[3];
226 }
227
228/* felem_scalar sets out = out * scalar */
229static void felem_scalar(felem out, const u64 scalar)
230 {
231 out[0] *= scalar;
232 out[1] *= scalar;
233 out[2] *= scalar;
234 out[3] *= scalar;
235 }
236
237/* longfelem_scalar sets out = out * scalar */
238static void longfelem_scalar(longfelem out, const u64 scalar)
239 {
240 out[0] *= scalar;
241 out[1] *= scalar;
242 out[2] *= scalar;
243 out[3] *= scalar;
244 out[4] *= scalar;
245 out[5] *= scalar;
246 out[6] *= scalar;
247 out[7] *= scalar;
248 }
249
250#define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9)
251#define two105 (((limb)1) << 105)
252#define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9)
253
254/* zero105 is 0 mod p */
255static const felem zero105 = { two105m41m9, two105, two105m41p9, two105m41p9 };
256
257/* smallfelem_neg sets |out| to |-small|
258 * On exit:
259 * out[i] < out[i] + 2^105
260 */
261static void smallfelem_neg(felem out, const smallfelem small)
262 {
263 /* In order to prevent underflow, we subtract from 0 mod p. */
264 out[0] = zero105[0] - small[0];
265 out[1] = zero105[1] - small[1];
266 out[2] = zero105[2] - small[2];
267 out[3] = zero105[3] - small[3];
268 }
269
270/* felem_diff subtracts |in| from |out|
271 * On entry:
272 * in[i] < 2^104
273 * On exit:
274 * out[i] < out[i] + 2^105
275 */
276static void felem_diff(felem out, const felem in)
277 {
278 /* In order to prevent underflow, we add 0 mod p before subtracting. */
279 out[0] += zero105[0];
280 out[1] += zero105[1];
281 out[2] += zero105[2];
282 out[3] += zero105[3];
283
284 out[0] -= in[0];
285 out[1] -= in[1];
286 out[2] -= in[2];
287 out[3] -= in[3];
288 }
289
290#define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11)
291#define two107 (((limb)1) << 107)
292#define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11)
293
294/* zero107 is 0 mod p */
295static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 };
296
297/* An alternative felem_diff for larger inputs |in|
298 * felem_diff_zero107 subtracts |in| from |out|
299 * On entry:
300 * in[i] < 2^106
301 * On exit:
302 * out[i] < out[i] + 2^107
303 */
304static void felem_diff_zero107(felem out, const felem in)
305 {
306 /* In order to prevent underflow, we add 0 mod p before subtracting. */
307 out[0] += zero107[0];
308 out[1] += zero107[1];
309 out[2] += zero107[2];
310 out[3] += zero107[3];
311
312 out[0] -= in[0];
313 out[1] -= in[1];
314 out[2] -= in[2];
315 out[3] -= in[3];
316 }
317
318/* longfelem_diff subtracts |in| from |out|
319 * On entry:
320 * in[i] < 7*2^67
321 * On exit:
322 * out[i] < out[i] + 2^70 + 2^40
323 */
324static void longfelem_diff(longfelem out, const longfelem in)
325 {
326 static const limb two70m8p6 = (((limb)1) << 70) - (((limb)1) << 8) + (((limb)1) << 6);
327 static const limb two70p40 = (((limb)1) << 70) + (((limb)1) << 40);
328 static const limb two70 = (((limb)1) << 70);
329 static const limb two70m40m38p6 = (((limb)1) << 70) - (((limb)1) << 40) - (((limb)1) << 38) + (((limb)1) << 6);
330 static const limb two70m6 = (((limb)1) << 70) - (((limb)1) << 6);
331
332 /* add 0 mod p to avoid underflow */
333 out[0] += two70m8p6;
334 out[1] += two70p40;
335 out[2] += two70;
336 out[3] += two70m40m38p6;
337 out[4] += two70m6;
338 out[5] += two70m6;
339 out[6] += two70m6;
340 out[7] += two70m6;
341
342 /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */
343 out[0] -= in[0];
344 out[1] -= in[1];
345 out[2] -= in[2];
346 out[3] -= in[3];
347 out[4] -= in[4];
348 out[5] -= in[5];
349 out[6] -= in[6];
350 out[7] -= in[7];
351 }
352
353#define two64m0 (((limb)1) << 64) - 1
354#define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1
355#define two64m46 (((limb)1) << 64) - (((limb)1) << 46)
356#define two64m32 (((limb)1) << 64) - (((limb)1) << 32)
357
358/* zero110 is 0 mod p */
359static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 };
360
361/* felem_shrink converts an felem into a smallfelem. The result isn't quite
362 * minimal as the value may be greater than p.
363 *
364 * On entry:
365 * in[i] < 2^109
366 * On exit:
367 * out[i] < 2^64
368 */
369static void felem_shrink(smallfelem out, const felem in)
370 {
371 felem tmp;
372 u64 a, b, mask;
373 s64 high, low;
374 static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */
375
376 /* Carry 2->3 */
377 tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64));
378 /* tmp[3] < 2^110 */
379
380 tmp[2] = zero110[2] + (u64) in[2];
381 tmp[0] = zero110[0] + in[0];
382 tmp[1] = zero110[1] + in[1];
383 /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */
384
385 /* We perform two partial reductions where we eliminate the
386 * high-word of tmp[3]. We don't update the other words till the end.
387 */
388 a = tmp[3] >> 64; /* a < 2^46 */
389 tmp[3] = (u64) tmp[3];
390 tmp[3] -= a;
391 tmp[3] += ((limb)a) << 32;
392 /* tmp[3] < 2^79 */
393
394 b = a;
395 a = tmp[3] >> 64; /* a < 2^15 */
396 b += a; /* b < 2^46 + 2^15 < 2^47 */
397 tmp[3] = (u64) tmp[3];
398 tmp[3] -= a;
399 tmp[3] += ((limb)a) << 32;
400 /* tmp[3] < 2^64 + 2^47 */
401
402 /* This adjusts the other two words to complete the two partial
403 * reductions. */
404 tmp[0] += b;
405 tmp[1] -= (((limb)b) << 32);
406
407 /* In order to make space in tmp[3] for the carry from 2 -> 3, we
408 * conditionally subtract kPrime if tmp[3] is large enough. */
409 high = tmp[3] >> 64;
410 /* As tmp[3] < 2^65, high is either 1 or 0 */
411 high <<= 63;
412 high >>= 63;
413 /* high is:
414 * all ones if the high word of tmp[3] is 1
415 * all zeros if the high word of tmp[3] if 0 */
416 low = tmp[3];
417 mask = low >> 63;
418 /* mask is:
419 * all ones if the MSB of low is 1
420 * all zeros if the MSB of low if 0 */
421 low &= bottom63bits;
422 low -= kPrime3Test;
423 /* if low was greater than kPrime3Test then the MSB is zero */
424 low = ~low;
425 low >>= 63;
426 /* low is:
427 * all ones if low was > kPrime3Test
428 * all zeros if low was <= kPrime3Test */
429 mask = (mask & low) | high;
430 tmp[0] -= mask & kPrime[0];
431 tmp[1] -= mask & kPrime[1];
432 /* kPrime[2] is zero, so omitted */
433 tmp[3] -= mask & kPrime[3];
434 /* tmp[3] < 2**64 - 2**32 + 1 */
435
436 tmp[1] += ((u64) (tmp[0] >> 64)); tmp[0] = (u64) tmp[0];
437 tmp[2] += ((u64) (tmp[1] >> 64)); tmp[1] = (u64) tmp[1];
438 tmp[3] += ((u64) (tmp[2] >> 64)); tmp[2] = (u64) tmp[2];
439 /* tmp[i] < 2^64 */
440
441 out[0] = tmp[0];
442 out[1] = tmp[1];
443 out[2] = tmp[2];
444 out[3] = tmp[3];
445 }
446
447/* smallfelem_expand converts a smallfelem to an felem */
448static void smallfelem_expand(felem out, const smallfelem in)
449 {
450 out[0] = in[0];
451 out[1] = in[1];
452 out[2] = in[2];
453 out[3] = in[3];
454 }
455
456/* smallfelem_square sets |out| = |small|^2
457 * On entry:
458 * small[i] < 2^64
459 * On exit:
460 * out[i] < 7 * 2^64 < 2^67
461 */
462static void smallfelem_square(longfelem out, const smallfelem small)
463 {
464 limb a;
465 u64 high, low;
466
467 a = ((uint128_t) small[0]) * small[0];
468 low = a;
469 high = a >> 64;
470 out[0] = low;
471 out[1] = high;
472
473 a = ((uint128_t) small[0]) * small[1];
474 low = a;
475 high = a >> 64;
476 out[1] += low;
477 out[1] += low;
478 out[2] = high;
479
480 a = ((uint128_t) small[0]) * small[2];
481 low = a;
482 high = a >> 64;
483 out[2] += low;
484 out[2] *= 2;
485 out[3] = high;
486
487 a = ((uint128_t) small[0]) * small[3];
488 low = a;
489 high = a >> 64;
490 out[3] += low;
491 out[4] = high;
492
493 a = ((uint128_t) small[1]) * small[2];
494 low = a;
495 high = a >> 64;
496 out[3] += low;
497 out[3] *= 2;
498 out[4] += high;
499
500 a = ((uint128_t) small[1]) * small[1];
501 low = a;
502 high = a >> 64;
503 out[2] += low;
504 out[3] += high;
505
506 a = ((uint128_t) small[1]) * small[3];
507 low = a;
508 high = a >> 64;
509 out[4] += low;
510 out[4] *= 2;
511 out[5] = high;
512
513 a = ((uint128_t) small[2]) * small[3];
514 low = a;
515 high = a >> 64;
516 out[5] += low;
517 out[5] *= 2;
518 out[6] = high;
519 out[6] += high;
520
521 a = ((uint128_t) small[2]) * small[2];
522 low = a;
523 high = a >> 64;
524 out[4] += low;
525 out[5] += high;
526
527 a = ((uint128_t) small[3]) * small[3];
528 low = a;
529 high = a >> 64;
530 out[6] += low;
531 out[7] = high;
532 }
533
534/* felem_square sets |out| = |in|^2
535 * On entry:
536 * in[i] < 2^109
537 * On exit:
538 * out[i] < 7 * 2^64 < 2^67
539 */
540static void felem_square(longfelem out, const felem in)
541 {
542 u64 small[4];
543 felem_shrink(small, in);
544 smallfelem_square(out, small);
545 }
546
547/* smallfelem_mul sets |out| = |small1| * |small2|
548 * On entry:
549 * small1[i] < 2^64
550 * small2[i] < 2^64
551 * On exit:
552 * out[i] < 7 * 2^64 < 2^67
553 */
554static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2)
555 {
556 limb a;
557 u64 high, low;
558
559 a = ((uint128_t) small1[0]) * small2[0];
560 low = a;
561 high = a >> 64;
562 out[0] = low;
563 out[1] = high;
564
565
566 a = ((uint128_t) small1[0]) * small2[1];
567 low = a;
568 high = a >> 64;
569 out[1] += low;
570 out[2] = high;
571
572 a = ((uint128_t) small1[1]) * small2[0];
573 low = a;
574 high = a >> 64;
575 out[1] += low;
576 out[2] += high;
577
578
579 a = ((uint128_t) small1[0]) * small2[2];
580 low = a;
581 high = a >> 64;
582 out[2] += low;
583 out[3] = high;
584
585 a = ((uint128_t) small1[1]) * small2[1];
586 low = a;
587 high = a >> 64;
588 out[2] += low;
589 out[3] += high;
590
591 a = ((uint128_t) small1[2]) * small2[0];
592 low = a;
593 high = a >> 64;
594 out[2] += low;
595 out[3] += high;
596
597
598 a = ((uint128_t) small1[0]) * small2[3];
599 low = a;
600 high = a >> 64;
601 out[3] += low;
602 out[4] = high;
603
604 a = ((uint128_t) small1[1]) * small2[2];
605 low = a;
606 high = a >> 64;
607 out[3] += low;
608 out[4] += high;
609
610 a = ((uint128_t) small1[2]) * small2[1];
611 low = a;
612 high = a >> 64;
613 out[3] += low;
614 out[4] += high;
615
616 a = ((uint128_t) small1[3]) * small2[0];
617 low = a;
618 high = a >> 64;
619 out[3] += low;
620 out[4] += high;
621
622
623 a = ((uint128_t) small1[1]) * small2[3];
624 low = a;
625 high = a >> 64;
626 out[4] += low;
627 out[5] = high;
628
629 a = ((uint128_t) small1[2]) * small2[2];
630 low = a;
631 high = a >> 64;
632 out[4] += low;
633 out[5] += high;
634
635 a = ((uint128_t) small1[3]) * small2[1];
636 low = a;
637 high = a >> 64;
638 out[4] += low;
639 out[5] += high;
640
641
642 a = ((uint128_t) small1[2]) * small2[3];
643 low = a;
644 high = a >> 64;
645 out[5] += low;
646 out[6] = high;
647
648 a = ((uint128_t) small1[3]) * small2[2];
649 low = a;
650 high = a >> 64;
651 out[5] += low;
652 out[6] += high;
653
654
655 a = ((uint128_t) small1[3]) * small2[3];
656 low = a;
657 high = a >> 64;
658 out[6] += low;
659 out[7] = high;
660 }
661
662/* felem_mul sets |out| = |in1| * |in2|
663 * On entry:
664 * in1[i] < 2^109
665 * in2[i] < 2^109
666 * On exit:
667 * out[i] < 7 * 2^64 < 2^67
668 */
669static void felem_mul(longfelem out, const felem in1, const felem in2)
670 {
671 smallfelem small1, small2;
672 felem_shrink(small1, in1);
673 felem_shrink(small2, in2);
674 smallfelem_mul(out, small1, small2);
675 }
676
677/* felem_small_mul sets |out| = |small1| * |in2|
678 * On entry:
679 * small1[i] < 2^64
680 * in2[i] < 2^109
681 * On exit:
682 * out[i] < 7 * 2^64 < 2^67
683 */
684static void felem_small_mul(longfelem out, const smallfelem small1, const felem in2)
685 {
686 smallfelem small2;
687 felem_shrink(small2, in2);
688 smallfelem_mul(out, small1, small2);
689 }
690
691#define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4)
692#define two100 (((limb)1) << 100)
693#define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4)
694/* zero100 is 0 mod p */
695static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 };
696
697/* Internal function for the different flavours of felem_reduce.
698 * felem_reduce_ reduces the higher coefficients in[4]-in[7].
699 * On entry:
700 * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7]
701 * out[1] >= in[7] + 2^32*in[4]
702 * out[2] >= in[5] + 2^32*in[5]
703 * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6]
704 * On exit:
705 * out[0] <= out[0] + in[4] + 2^32*in[5]
706 * out[1] <= out[1] + in[5] + 2^33*in[6]
707 * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7]
708 * out[3] <= out[3] + 2^32*in[4] + 3*in[7]
709 */
710static void felem_reduce_(felem out, const longfelem in)
711 {
712 int128_t c;
713 /* combine common terms from below */
714 c = in[4] + (in[5] << 32);
715 out[0] += c;
716 out[3] -= c;
717
718 c = in[5] - in[7];
719 out[1] += c;
720 out[2] -= c;
721
722 /* the remaining terms */
723 /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */
724 out[1] -= (in[4] << 32);
725 out[3] += (in[4] << 32);
726
727 /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */
728 out[2] -= (in[5] << 32);
729
730 /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */
731 out[0] -= in[6];
732 out[0] -= (in[6] << 32);
733 out[1] += (in[6] << 33);
734 out[2] += (in[6] * 2);
735 out[3] -= (in[6] << 32);
736
737 /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */
738 out[0] -= in[7];
739 out[0] -= (in[7] << 32);
740 out[2] += (in[7] << 33);
741 out[3] += (in[7] * 3);
742 }
743
744/* felem_reduce converts a longfelem into an felem.
745 * To be called directly after felem_square or felem_mul.
746 * On entry:
747 * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64
748 * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64
749 * On exit:
750 * out[i] < 2^101
751 */
752static void felem_reduce(felem out, const longfelem in)
753 {
754 out[0] = zero100[0] + in[0];
755 out[1] = zero100[1] + in[1];
756 out[2] = zero100[2] + in[2];
757 out[3] = zero100[3] + in[3];
758
759 felem_reduce_(out, in);
760
761 /* out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0
762 * out[1] > 2^100 - 2^64 - 7*2^96 > 0
763 * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0
764 * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0
765 *
766 * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101
767 * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101
768 * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101
769 * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101
770 */
771 }
772
773/* felem_reduce_zero105 converts a larger longfelem into an felem.
774 * On entry:
775 * in[0] < 2^71
776 * On exit:
777 * out[i] < 2^106
778 */
779static void felem_reduce_zero105(felem out, const longfelem in)
780 {
781 out[0] = zero105[0] + in[0];
782 out[1] = zero105[1] + in[1];
783 out[2] = zero105[2] + in[2];
784 out[3] = zero105[3] + in[3];
785
786 felem_reduce_(out, in);
787
788 /* out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0
789 * out[1] > 2^105 - 2^71 - 2^103 > 0
790 * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0
791 * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0
792 *
793 * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106
794 * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106
795 * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106
796 * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106
797 */
798 }
799
800/* subtract_u64 sets *result = *result - v and *carry to one if the subtraction
801 * underflowed. */
802static void subtract_u64(u64* result, u64* carry, u64 v)
803 {
804 uint128_t r = *result;
805 r -= v;
806 *carry = (r >> 64) & 1;
807 *result = (u64) r;
808 }
809
810/* felem_contract converts |in| to its unique, minimal representation.
811 * On entry:
812 * in[i] < 2^109
813 */
814static void felem_contract(smallfelem out, const felem in)
815 {
816 unsigned i;
817 u64 all_equal_so_far = 0, result = 0, carry;
818
819 felem_shrink(out, in);
820 /* small is minimal except that the value might be > p */
821
822 all_equal_so_far--;
823 /* We are doing a constant time test if out >= kPrime. We need to
824 * compare each u64, from most-significant to least significant. For
825 * each one, if all words so far have been equal (m is all ones) then a
826 * non-equal result is the answer. Otherwise we continue. */
827 for (i = 3; i < 4; i--)
828 {
829 u64 equal;
830 uint128_t a = ((uint128_t) kPrime[i]) - out[i];
831 /* if out[i] > kPrime[i] then a will underflow and the high
832 * 64-bits will all be set. */
833 result |= all_equal_so_far & ((u64) (a >> 64));
834
835 /* if kPrime[i] == out[i] then |equal| will be all zeros and
836 * the decrement will make it all ones. */
837 equal = kPrime[i] ^ out[i];
838 equal--;
839 equal &= equal << 32;
840 equal &= equal << 16;
841 equal &= equal << 8;
842 equal &= equal << 4;
843 equal &= equal << 2;
844 equal &= equal << 1;
845 equal = ((s64) equal) >> 63;
846
847 all_equal_so_far &= equal;
848 }
849
850 /* if all_equal_so_far is still all ones then the two values are equal
851 * and so out >= kPrime is true. */
852 result |= all_equal_so_far;
853
854 /* if out >= kPrime then we subtract kPrime. */
855 subtract_u64(&out[0], &carry, result & kPrime[0]);
856 subtract_u64(&out[1], &carry, carry);
857 subtract_u64(&out[2], &carry, carry);
858 subtract_u64(&out[3], &carry, carry);
859
860 subtract_u64(&out[1], &carry, result & kPrime[1]);
861 subtract_u64(&out[2], &carry, carry);
862 subtract_u64(&out[3], &carry, carry);
863
864 subtract_u64(&out[2], &carry, result & kPrime[2]);
865 subtract_u64(&out[3], &carry, carry);
866
867 subtract_u64(&out[3], &carry, result & kPrime[3]);
868 }
869
870static void smallfelem_square_contract(smallfelem out, const smallfelem in)
871 {
872 longfelem longtmp;
873 felem tmp;
874
875 smallfelem_square(longtmp, in);
876 felem_reduce(tmp, longtmp);
877 felem_contract(out, tmp);
878 }
879
880static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2)
881 {
882 longfelem longtmp;
883 felem tmp;
884
885 smallfelem_mul(longtmp, in1, in2);
886 felem_reduce(tmp, longtmp);
887 felem_contract(out, tmp);
888 }
889
890/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0
891 * otherwise.
892 * On entry:
893 * small[i] < 2^64
894 */
895static limb smallfelem_is_zero(const smallfelem small)
896 {
897 limb result;
898 u64 is_p;
899
900 u64 is_zero = small[0] | small[1] | small[2] | small[3];
901 is_zero--;
902 is_zero &= is_zero << 32;
903 is_zero &= is_zero << 16;
904 is_zero &= is_zero << 8;
905 is_zero &= is_zero << 4;
906 is_zero &= is_zero << 2;
907 is_zero &= is_zero << 1;
908 is_zero = ((s64) is_zero) >> 63;
909
910 is_p = (small[0] ^ kPrime[0]) |
911 (small[1] ^ kPrime[1]) |
912 (small[2] ^ kPrime[2]) |
913 (small[3] ^ kPrime[3]);
914 is_p--;
915 is_p &= is_p << 32;
916 is_p &= is_p << 16;
917 is_p &= is_p << 8;
918 is_p &= is_p << 4;
919 is_p &= is_p << 2;
920 is_p &= is_p << 1;
921 is_p = ((s64) is_p) >> 63;
922
923 is_zero |= is_p;
924
925 result = is_zero;
926 result |= ((limb) is_zero) << 64;
927 return result;
928 }
929
930static int smallfelem_is_zero_int(const smallfelem small)
931 {
932 return (int) (smallfelem_is_zero(small) & ((limb)1));
933 }
934
935/* felem_inv calculates |out| = |in|^{-1}
936 *
937 * Based on Fermat's Little Theorem:
938 * a^p = a (mod p)
939 * a^{p-1} = 1 (mod p)
940 * a^{p-2} = a^{-1} (mod p)
941 */
942static void felem_inv(felem out, const felem in)
943 {
944 felem ftmp, ftmp2;
945 /* each e_I will hold |in|^{2^I - 1} */
946 felem e2, e4, e8, e16, e32, e64;
947 longfelem tmp;
948 unsigned i;
949
950 felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */
951 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */
952 felem_assign(e2, ftmp);
953 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */
954 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */
955 felem_mul(tmp, ftmp, e2); felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */
956 felem_assign(e4, ftmp);
957 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */
958 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */
959 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */
960 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */
961 felem_mul(tmp, ftmp, e4); felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */
962 felem_assign(e8, ftmp);
963 for (i = 0; i < 8; i++) {
964 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
965 } /* 2^16 - 2^8 */
966 felem_mul(tmp, ftmp, e8); felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */
967 felem_assign(e16, ftmp);
968 for (i = 0; i < 16; i++) {
969 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
970 } /* 2^32 - 2^16 */
971 felem_mul(tmp, ftmp, e16); felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */
972 felem_assign(e32, ftmp);
973 for (i = 0; i < 32; i++) {
974 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
975 } /* 2^64 - 2^32 */
976 felem_assign(e64, ftmp);
977 felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */
978 for (i = 0; i < 192; i++) {
979 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
980 } /* 2^256 - 2^224 + 2^192 */
981
982 felem_mul(tmp, e64, e32); felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */
983 for (i = 0; i < 16; i++) {
984 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
985 } /* 2^80 - 2^16 */
986 felem_mul(tmp, ftmp2, e16); felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */
987 for (i = 0; i < 8; i++) {
988 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
989 } /* 2^88 - 2^8 */
990 felem_mul(tmp, ftmp2, e8); felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */
991 for (i = 0; i < 4; i++) {
992 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
993 } /* 2^92 - 2^4 */
994 felem_mul(tmp, ftmp2, e4); felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */
995 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */
996 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */
997 felem_mul(tmp, ftmp2, e2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */
998 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */
999 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */
1000 felem_mul(tmp, ftmp2, in); felem_reduce(ftmp2, tmp); /* 2^96 - 3 */
1001
1002 felem_mul(tmp, ftmp2, ftmp); felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */
1003 }
1004
1005static void smallfelem_inv_contract(smallfelem out, const smallfelem in)
1006 {
1007 felem tmp;
1008
1009 smallfelem_expand(tmp, in);
1010 felem_inv(tmp, tmp);
1011 felem_contract(out, tmp);
1012 }
1013
1014/* Group operations
1015 * ----------------
1016 *
1017 * Building on top of the field operations we have the operations on the
1018 * elliptic curve group itself. Points on the curve are represented in Jacobian
1019 * coordinates */
1020
1021/* point_double calculates 2*(x_in, y_in, z_in)
1022 *
1023 * The method is taken from:
1024 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
1025 *
1026 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed.
1027 * while x_out == y_in is not (maybe this works, but it's not tested). */
1028static void
1029point_double(felem x_out, felem y_out, felem z_out,
1030 const felem x_in, const felem y_in, const felem z_in)
1031 {
1032 longfelem tmp, tmp2;
1033 felem delta, gamma, beta, alpha, ftmp, ftmp2;
1034 smallfelem small1, small2;
1035
1036 felem_assign(ftmp, x_in);
1037 /* ftmp[i] < 2^106 */
1038 felem_assign(ftmp2, x_in);
1039 /* ftmp2[i] < 2^106 */
1040
1041 /* delta = z^2 */
1042 felem_square(tmp, z_in);
1043 felem_reduce(delta, tmp);
1044 /* delta[i] < 2^101 */
1045
1046 /* gamma = y^2 */
1047 felem_square(tmp, y_in);
1048 felem_reduce(gamma, tmp);
1049 /* gamma[i] < 2^101 */
1050 felem_shrink(small1, gamma);
1051
1052 /* beta = x*gamma */
1053 felem_small_mul(tmp, small1, x_in);
1054 felem_reduce(beta, tmp);
1055 /* beta[i] < 2^101 */
1056
1057 /* alpha = 3*(x-delta)*(x+delta) */
1058 felem_diff(ftmp, delta);
1059 /* ftmp[i] < 2^105 + 2^106 < 2^107 */
1060 felem_sum(ftmp2, delta);
1061 /* ftmp2[i] < 2^105 + 2^106 < 2^107 */
1062 felem_scalar(ftmp2, 3);
1063 /* ftmp2[i] < 3 * 2^107 < 2^109 */
1064 felem_mul(tmp, ftmp, ftmp2);
1065 felem_reduce(alpha, tmp);
1066 /* alpha[i] < 2^101 */
1067 felem_shrink(small2, alpha);
1068
1069 /* x' = alpha^2 - 8*beta */
1070 smallfelem_square(tmp, small2);
1071 felem_reduce(x_out, tmp);
1072 felem_assign(ftmp, beta);
1073 felem_scalar(ftmp, 8);
1074 /* ftmp[i] < 8 * 2^101 = 2^104 */
1075 felem_diff(x_out, ftmp);
1076 /* x_out[i] < 2^105 + 2^101 < 2^106 */
1077
1078 /* z' = (y + z)^2 - gamma - delta */
1079 felem_sum(delta, gamma);
1080 /* delta[i] < 2^101 + 2^101 = 2^102 */
1081 felem_assign(ftmp, y_in);
1082 felem_sum(ftmp, z_in);
1083 /* ftmp[i] < 2^106 + 2^106 = 2^107 */
1084 felem_square(tmp, ftmp);
1085 felem_reduce(z_out, tmp);
1086 felem_diff(z_out, delta);
1087 /* z_out[i] < 2^105 + 2^101 < 2^106 */
1088
1089 /* y' = alpha*(4*beta - x') - 8*gamma^2 */
1090 felem_scalar(beta, 4);
1091 /* beta[i] < 4 * 2^101 = 2^103 */
1092 felem_diff_zero107(beta, x_out);
1093 /* beta[i] < 2^107 + 2^103 < 2^108 */
1094 felem_small_mul(tmp, small2, beta);
1095 /* tmp[i] < 7 * 2^64 < 2^67 */
1096 smallfelem_square(tmp2, small1);
1097 /* tmp2[i] < 7 * 2^64 */
1098 longfelem_scalar(tmp2, 8);
1099 /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */
1100 longfelem_diff(tmp, tmp2);
1101 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
1102 felem_reduce_zero105(y_out, tmp);
1103 /* y_out[i] < 2^106 */
1104 }
1105
1106/* point_double_small is the same as point_double, except that it operates on
1107 * smallfelems */
1108static void
1109point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out,
1110 const smallfelem x_in, const smallfelem y_in, const smallfelem z_in)
1111 {
1112 felem felem_x_out, felem_y_out, felem_z_out;
1113 felem felem_x_in, felem_y_in, felem_z_in;
1114
1115 smallfelem_expand(felem_x_in, x_in);
1116 smallfelem_expand(felem_y_in, y_in);
1117 smallfelem_expand(felem_z_in, z_in);
1118 point_double(felem_x_out, felem_y_out, felem_z_out,
1119 felem_x_in, felem_y_in, felem_z_in);
1120 felem_shrink(x_out, felem_x_out);
1121 felem_shrink(y_out, felem_y_out);
1122 felem_shrink(z_out, felem_z_out);
1123 }
1124
1125/* copy_conditional copies in to out iff mask is all ones. */
1126static void
1127copy_conditional(felem out, const felem in, limb mask)
1128 {
1129 unsigned i;
1130 for (i = 0; i < NLIMBS; ++i)
1131 {
1132 const limb tmp = mask & (in[i] ^ out[i]);
1133 out[i] ^= tmp;
1134 }
1135 }
1136
1137/* copy_small_conditional copies in to out iff mask is all ones. */
1138static void
1139copy_small_conditional(felem out, const smallfelem in, limb mask)
1140 {
1141 unsigned i;
1142 const u64 mask64 = mask;
1143 for (i = 0; i < NLIMBS; ++i)
1144 {
1145 out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask);
1146 }
1147 }
1148
1149/* point_add calcuates (x1, y1, z1) + (x2, y2, z2)
1150 *
1151 * The method is taken from:
1152 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl,
1153 * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity).
1154 *
1155 * This function includes a branch for checking whether the two input points
1156 * are equal, (while not equal to the point at infinity). This case never
1157 * happens during single point multiplication, so there is no timing leak for
1158 * ECDH or ECDSA signing. */
1159static void point_add(felem x3, felem y3, felem z3,
1160 const felem x1, const felem y1, const felem z1,
1161 const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2)
1162 {
1163 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out;
1164 longfelem tmp, tmp2;
1165 smallfelem small1, small2, small3, small4, small5;
1166 limb x_equal, y_equal, z1_is_zero, z2_is_zero;
1167
1168 felem_shrink(small3, z1);
1169
1170 z1_is_zero = smallfelem_is_zero(small3);
1171 z2_is_zero = smallfelem_is_zero(z2);
1172
1173 /* ftmp = z1z1 = z1**2 */
1174 smallfelem_square(tmp, small3);
1175 felem_reduce(ftmp, tmp);
1176 /* ftmp[i] < 2^101 */
1177 felem_shrink(small1, ftmp);
1178
1179 if(!mixed)
1180 {
1181 /* ftmp2 = z2z2 = z2**2 */
1182 smallfelem_square(tmp, z2);
1183 felem_reduce(ftmp2, tmp);
1184 /* ftmp2[i] < 2^101 */
1185 felem_shrink(small2, ftmp2);
1186
1187 felem_shrink(small5, x1);
1188
1189 /* u1 = ftmp3 = x1*z2z2 */
1190 smallfelem_mul(tmp, small5, small2);
1191 felem_reduce(ftmp3, tmp);
1192 /* ftmp3[i] < 2^101 */
1193
1194 /* ftmp5 = z1 + z2 */
1195 felem_assign(ftmp5, z1);
1196 felem_small_sum(ftmp5, z2);
1197 /* ftmp5[i] < 2^107 */
1198
1199 /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */
1200 felem_square(tmp, ftmp5);
1201 felem_reduce(ftmp5, tmp);
1202 /* ftmp2 = z2z2 + z1z1 */
1203 felem_sum(ftmp2, ftmp);
1204 /* ftmp2[i] < 2^101 + 2^101 = 2^102 */
1205 felem_diff(ftmp5, ftmp2);
1206 /* ftmp5[i] < 2^105 + 2^101 < 2^106 */
1207
1208 /* ftmp2 = z2 * z2z2 */
1209 smallfelem_mul(tmp, small2, z2);
1210 felem_reduce(ftmp2, tmp);
1211
1212 /* s1 = ftmp2 = y1 * z2**3 */
1213 felem_mul(tmp, y1, ftmp2);
1214 felem_reduce(ftmp6, tmp);
1215 /* ftmp6[i] < 2^101 */
1216 }
1217 else
1218 {
1219 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
1220
1221 /* u1 = ftmp3 = x1*z2z2 */
1222 felem_assign(ftmp3, x1);
1223 /* ftmp3[i] < 2^106 */
1224
1225 /* ftmp5 = 2z1z2 */
1226 felem_assign(ftmp5, z1);
1227 felem_scalar(ftmp5, 2);
1228 /* ftmp5[i] < 2*2^106 = 2^107 */
1229
1230 /* s1 = ftmp2 = y1 * z2**3 */
1231 felem_assign(ftmp6, y1);
1232 /* ftmp6[i] < 2^106 */
1233 }
1234
1235 /* u2 = x2*z1z1 */
1236 smallfelem_mul(tmp, x2, small1);
1237 felem_reduce(ftmp4, tmp);
1238
1239 /* h = ftmp4 = u2 - u1 */
1240 felem_diff_zero107(ftmp4, ftmp3);
1241 /* ftmp4[i] < 2^107 + 2^101 < 2^108 */
1242 felem_shrink(small4, ftmp4);
1243
1244 x_equal = smallfelem_is_zero(small4);
1245
1246 /* z_out = ftmp5 * h */
1247 felem_small_mul(tmp, small4, ftmp5);
1248 felem_reduce(z_out, tmp);
1249 /* z_out[i] < 2^101 */
1250
1251 /* ftmp = z1 * z1z1 */
1252 smallfelem_mul(tmp, small1, small3);
1253 felem_reduce(ftmp, tmp);
1254
1255 /* s2 = tmp = y2 * z1**3 */
1256 felem_small_mul(tmp, y2, ftmp);
1257 felem_reduce(ftmp5, tmp);
1258
1259 /* r = ftmp5 = (s2 - s1)*2 */
1260 felem_diff_zero107(ftmp5, ftmp6);
1261 /* ftmp5[i] < 2^107 + 2^107 = 2^108*/
1262 felem_scalar(ftmp5, 2);
1263 /* ftmp5[i] < 2^109 */
1264 felem_shrink(small1, ftmp5);
1265 y_equal = smallfelem_is_zero(small1);
1266
1267 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero)
1268 {
1269 point_double(x3, y3, z3, x1, y1, z1);
1270 return;
1271 }
1272
1273 /* I = ftmp = (2h)**2 */
1274 felem_assign(ftmp, ftmp4);
1275 felem_scalar(ftmp, 2);
1276 /* ftmp[i] < 2*2^108 = 2^109 */
1277 felem_square(tmp, ftmp);
1278 felem_reduce(ftmp, tmp);
1279
1280 /* J = ftmp2 = h * I */
1281 felem_mul(tmp, ftmp4, ftmp);
1282 felem_reduce(ftmp2, tmp);
1283
1284 /* V = ftmp4 = U1 * I */
1285 felem_mul(tmp, ftmp3, ftmp);
1286 felem_reduce(ftmp4, tmp);
1287
1288 /* x_out = r**2 - J - 2V */
1289 smallfelem_square(tmp, small1);
1290 felem_reduce(x_out, tmp);
1291 felem_assign(ftmp3, ftmp4);
1292 felem_scalar(ftmp4, 2);
1293 felem_sum(ftmp4, ftmp2);
1294 /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */
1295 felem_diff(x_out, ftmp4);
1296 /* x_out[i] < 2^105 + 2^101 */
1297
1298 /* y_out = r(V-x_out) - 2 * s1 * J */
1299 felem_diff_zero107(ftmp3, x_out);
1300 /* ftmp3[i] < 2^107 + 2^101 < 2^108 */
1301 felem_small_mul(tmp, small1, ftmp3);
1302 felem_mul(tmp2, ftmp6, ftmp2);
1303 longfelem_scalar(tmp2, 2);
1304 /* tmp2[i] < 2*2^67 = 2^68 */
1305 longfelem_diff(tmp, tmp2);
1306 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
1307 felem_reduce_zero105(y_out, tmp);
1308 /* y_out[i] < 2^106 */
1309
1310 copy_small_conditional(x_out, x2, z1_is_zero);
1311 copy_conditional(x_out, x1, z2_is_zero);
1312 copy_small_conditional(y_out, y2, z1_is_zero);
1313 copy_conditional(y_out, y1, z2_is_zero);
1314 copy_small_conditional(z_out, z2, z1_is_zero);
1315 copy_conditional(z_out, z1, z2_is_zero);
1316 felem_assign(x3, x_out);
1317 felem_assign(y3, y_out);
1318 felem_assign(z3, z_out);
1319 }
1320
1321/* point_add_small is the same as point_add, except that it operates on
1322 * smallfelems */
1323static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3,
1324 smallfelem x1, smallfelem y1, smallfelem z1,
1325 smallfelem x2, smallfelem y2, smallfelem z2)
1326 {
1327 felem felem_x3, felem_y3, felem_z3;
1328 felem felem_x1, felem_y1, felem_z1;
1329 smallfelem_expand(felem_x1, x1);
1330 smallfelem_expand(felem_y1, y1);
1331 smallfelem_expand(felem_z1, z1);
1332 point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, x2, y2, z2);
1333 felem_shrink(x3, felem_x3);
1334 felem_shrink(y3, felem_y3);
1335 felem_shrink(z3, felem_z3);
1336 }
1337
1338/* Base point pre computation
1339 * --------------------------
1340 *
1341 * Two different sorts of precomputed tables are used in the following code.
1342 * Each contain various points on the curve, where each point is three field
1343 * elements (x, y, z).
1344 *
1345 * For the base point table, z is usually 1 (0 for the point at infinity).
1346 * This table has 2 * 16 elements, starting with the following:
1347 * index | bits | point
1348 * ------+---------+------------------------------
1349 * 0 | 0 0 0 0 | 0G
1350 * 1 | 0 0 0 1 | 1G
1351 * 2 | 0 0 1 0 | 2^64G
1352 * 3 | 0 0 1 1 | (2^64 + 1)G
1353 * 4 | 0 1 0 0 | 2^128G
1354 * 5 | 0 1 0 1 | (2^128 + 1)G
1355 * 6 | 0 1 1 0 | (2^128 + 2^64)G
1356 * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G
1357 * 8 | 1 0 0 0 | 2^192G
1358 * 9 | 1 0 0 1 | (2^192 + 1)G
1359 * 10 | 1 0 1 0 | (2^192 + 2^64)G
1360 * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G
1361 * 12 | 1 1 0 0 | (2^192 + 2^128)G
1362 * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G
1363 * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G
1364 * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G
1365 * followed by a copy of this with each element multiplied by 2^32.
1366 *
1367 * The reason for this is so that we can clock bits into four different
1368 * locations when doing simple scalar multiplies against the base point,
1369 * and then another four locations using the second 16 elements.
1370 *
1371 * Tables for other points have table[i] = iG for i in 0 .. 16. */
1372
1373/* gmul is the table of precomputed base points */
1374static const smallfelem gmul[2][16][3] =
1375{{{{0, 0, 0, 0},
1376 {0, 0, 0, 0},
1377 {0, 0, 0, 0}},
1378 {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247},
1379 {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b},
1380 {1, 0, 0, 0}},
1381 {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5},
1382 {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d},
1383 {1, 0, 0, 0}},
1384 {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f},
1385 {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644},
1386 {1, 0, 0, 0}},
1387 {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67},
1388 {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee},
1389 {1, 0, 0, 0}},
1390 {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff},
1391 {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b},
1392 {1, 0, 0, 0}},
1393 {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8},
1394 {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851},
1395 {1, 0, 0, 0}},
1396 {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea},
1397 {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b},
1398 {1, 0, 0, 0}},
1399 {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276},
1400 {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816},
1401 {1, 0, 0, 0}},
1402 {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad},
1403 {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663},
1404 {1, 0, 0, 0}},
1405 {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d},
1406 {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321},
1407 {1, 0, 0, 0}},
1408 {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287},
1409 {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6},
1410 {1, 0, 0, 0}},
1411 {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466},
1412 {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20},
1413 {1, 0, 0, 0}},
1414 {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9},
1415 {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61},
1416 {1, 0, 0, 0}},
1417 {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a},
1418 {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc},
1419 {1, 0, 0, 0}},
1420 {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c},
1421 {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab},
1422 {1, 0, 0, 0}}},
1423 {{{0, 0, 0, 0},
1424 {0, 0, 0, 0},
1425 {0, 0, 0, 0}},
1426 {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89},
1427 {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624},
1428 {1, 0, 0, 0}},
1429 {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6},
1430 {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1},
1431 {1, 0, 0, 0}},
1432 {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a},
1433 {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593},
1434 {1, 0, 0, 0}},
1435 {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617},
1436 {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7},
1437 {1, 0, 0, 0}},
1438 {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276},
1439 {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a},
1440 {1, 0, 0, 0}},
1441 {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908},
1442 {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e},
1443 {1, 0, 0, 0}},
1444 {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7},
1445 {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec},
1446 {1, 0, 0, 0}},
1447 {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee},
1448 {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6},
1449 {1, 0, 0, 0}},
1450 {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109},
1451 {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5},
1452 {1, 0, 0, 0}},
1453 {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba},
1454 {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44},
1455 {1, 0, 0, 0}},
1456 {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b},
1457 {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc},
1458 {1, 0, 0, 0}},
1459 {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107},
1460 {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387},
1461 {1, 0, 0, 0}},
1462 {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503},
1463 {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be},
1464 {1, 0, 0, 0}},
1465 {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9},
1466 {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a},
1467 {1, 0, 0, 0}},
1468 {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6},
1469 {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81},
1470 {1, 0, 0, 0}}}};
1471
1472/* select_point selects the |idx|th point from a precomputation table and
1473 * copies it to out. */
1474static void select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3])
1475 {
1476 unsigned i, j;
1477 u64 *outlimbs = &out[0][0];
1478 memset(outlimbs, 0, 3 * sizeof(smallfelem));
1479
1480 for (i = 0; i < size; i++)
1481 {
1482 const u64 *inlimbs = (u64*) &pre_comp[i][0][0];
1483 u64 mask = i ^ idx;
1484 mask |= mask >> 4;
1485 mask |= mask >> 2;
1486 mask |= mask >> 1;
1487 mask &= 1;
1488 mask--;
1489 for (j = 0; j < NLIMBS * 3; j++)
1490 outlimbs[j] |= inlimbs[j] & mask;
1491 }
1492 }
1493
1494/* get_bit returns the |i|th bit in |in| */
1495static char get_bit(const felem_bytearray in, int i)
1496 {
1497 if ((i < 0) || (i >= 256))
1498 return 0;
1499 return (in[i >> 3] >> (i & 7)) & 1;
1500 }
1501
1502/* Interleaved point multiplication using precomputed point multiples:
1503 * The small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[],
1504 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
1505 * of the generator, using certain (large) precomputed multiples in g_pre_comp.
1506 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
1507static void batch_mul(felem x_out, felem y_out, felem z_out,
1508 const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar,
1509 const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3])
1510 {
1511 int i, skip;
1512 unsigned num, gen_mul = (g_scalar != NULL);
1513 felem nq[3], ftmp;
1514 smallfelem tmp[3];
1515 u64 bits;
1516 u8 sign, digit;
1517
1518 /* set nq to the point at infinity */
1519 memset(nq, 0, 3 * sizeof(felem));
1520
1521 /* Loop over all scalars msb-to-lsb, interleaving additions
1522 * of multiples of the generator (two in each of the last 32 rounds)
1523 * and additions of other points multiples (every 5th round).
1524 */
1525 skip = 1; /* save two point operations in the first round */
1526 for (i = (num_points ? 255 : 31); i >= 0; --i)
1527 {
1528 /* double */
1529 if (!skip)
1530 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
1531
1532 /* add multiples of the generator */
1533 if (gen_mul && (i <= 31))
1534 {
1535 /* first, look 32 bits upwards */
1536 bits = get_bit(g_scalar, i + 224) << 3;
1537 bits |= get_bit(g_scalar, i + 160) << 2;
1538 bits |= get_bit(g_scalar, i + 96) << 1;
1539 bits |= get_bit(g_scalar, i + 32);
1540 /* select the point to add, in constant time */
1541 select_point(bits, 16, g_pre_comp[1], tmp);
1542
1543 if (!skip)
1544 {
1545 point_add(nq[0], nq[1], nq[2],
1546 nq[0], nq[1], nq[2],
1547 1 /* mixed */, tmp[0], tmp[1], tmp[2]);
1548 }
1549 else
1550 {
1551 smallfelem_expand(nq[0], tmp[0]);
1552 smallfelem_expand(nq[1], tmp[1]);
1553 smallfelem_expand(nq[2], tmp[2]);
1554 skip = 0;
1555 }
1556
1557 /* second, look at the current position */
1558 bits = get_bit(g_scalar, i + 192) << 3;
1559 bits |= get_bit(g_scalar, i + 128) << 2;
1560 bits |= get_bit(g_scalar, i + 64) << 1;
1561 bits |= get_bit(g_scalar, i);
1562 /* select the point to add, in constant time */
1563 select_point(bits, 16, g_pre_comp[0], tmp);
1564 point_add(nq[0], nq[1], nq[2],
1565 nq[0], nq[1], nq[2],
1566 1 /* mixed */, tmp[0], tmp[1], tmp[2]);
1567 }
1568
1569 /* do other additions every 5 doublings */
1570 if (num_points && (i % 5 == 0))
1571 {
1572 /* loop over all scalars */
1573 for (num = 0; num < num_points; ++num)
1574 {
1575 bits = get_bit(scalars[num], i + 4) << 5;
1576 bits |= get_bit(scalars[num], i + 3) << 4;
1577 bits |= get_bit(scalars[num], i + 2) << 3;
1578 bits |= get_bit(scalars[num], i + 1) << 2;
1579 bits |= get_bit(scalars[num], i) << 1;
1580 bits |= get_bit(scalars[num], i - 1);
1581 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
1582
1583 /* select the point to add or subtract, in constant time */
1584 select_point(digit, 17, pre_comp[num], tmp);
1585 smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative point */
1586 copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1));
1587 felem_contract(tmp[1], ftmp);
1588
1589 if (!skip)
1590 {
1591 point_add(nq[0], nq[1], nq[2],
1592 nq[0], nq[1], nq[2],
1593 mixed, tmp[0], tmp[1], tmp[2]);
1594 }
1595 else
1596 {
1597 smallfelem_expand(nq[0], tmp[0]);
1598 smallfelem_expand(nq[1], tmp[1]);
1599 smallfelem_expand(nq[2], tmp[2]);
1600 skip = 0;
1601 }
1602 }
1603 }
1604 }
1605 felem_assign(x_out, nq[0]);
1606 felem_assign(y_out, nq[1]);
1607 felem_assign(z_out, nq[2]);
1608 }
1609
1610/* Precomputation for the group generator. */
1611typedef struct {
1612 smallfelem g_pre_comp[2][16][3];
1613 int references;
1614} NISTP256_PRE_COMP;
1615
1616const EC_METHOD *EC_GFp_nistp256_method(void)
1617 {
1618 static const EC_METHOD ret = {
1619 EC_FLAGS_DEFAULT_OCT,
1620 NID_X9_62_prime_field,
1621 ec_GFp_nistp256_group_init,
1622 ec_GFp_simple_group_finish,
1623 ec_GFp_simple_group_clear_finish,
1624 ec_GFp_nist_group_copy,
1625 ec_GFp_nistp256_group_set_curve,
1626 ec_GFp_simple_group_get_curve,
1627 ec_GFp_simple_group_get_degree,
1628 ec_GFp_simple_group_check_discriminant,
1629 ec_GFp_simple_point_init,
1630 ec_GFp_simple_point_finish,
1631 ec_GFp_simple_point_clear_finish,
1632 ec_GFp_simple_point_copy,
1633 ec_GFp_simple_point_set_to_infinity,
1634 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1635 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1636 ec_GFp_simple_point_set_affine_coordinates,
1637 ec_GFp_nistp256_point_get_affine_coordinates,
1638 0 /* point_set_compressed_coordinates */,
1639 0 /* point2oct */,
1640 0 /* oct2point */,
1641 ec_GFp_simple_add,
1642 ec_GFp_simple_dbl,
1643 ec_GFp_simple_invert,
1644 ec_GFp_simple_is_at_infinity,
1645 ec_GFp_simple_is_on_curve,
1646 ec_GFp_simple_cmp,
1647 ec_GFp_simple_make_affine,
1648 ec_GFp_simple_points_make_affine,
1649 ec_GFp_nistp256_points_mul,
1650 ec_GFp_nistp256_precompute_mult,
1651 ec_GFp_nistp256_have_precompute_mult,
1652 ec_GFp_nist_field_mul,
1653 ec_GFp_nist_field_sqr,
1654 0 /* field_div */,
1655 0 /* field_encode */,
1656 0 /* field_decode */,
1657 0 /* field_set_to_one */ };
1658
1659 return &ret;
1660 }
1661
1662/******************************************************************************/
1663/* FUNCTIONS TO MANAGE PRECOMPUTATION
1664 */
1665
1666static NISTP256_PRE_COMP *nistp256_pre_comp_new()
1667 {
1668 NISTP256_PRE_COMP *ret = NULL;
1669 ret = (NISTP256_PRE_COMP *) OPENSSL_malloc(sizeof *ret);
1670 if (!ret)
1671 {
1672 ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1673 return ret;
1674 }
1675 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1676 ret->references = 1;
1677 return ret;
1678 }
1679
1680static void *nistp256_pre_comp_dup(void *src_)
1681 {
1682 NISTP256_PRE_COMP *src = src_;
1683
1684 /* no need to actually copy, these objects never change! */
1685 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1686
1687 return src_;
1688 }
1689
1690static void nistp256_pre_comp_free(void *pre_)
1691 {
1692 int i;
1693 NISTP256_PRE_COMP *pre = pre_;
1694
1695 if (!pre)
1696 return;
1697
1698 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1699 if (i > 0)
1700 return;
1701
1702 OPENSSL_free(pre);
1703 }
1704
1705static void nistp256_pre_comp_clear_free(void *pre_)
1706 {
1707 int i;
1708 NISTP256_PRE_COMP *pre = pre_;
1709
1710 if (!pre)
1711 return;
1712
1713 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1714 if (i > 0)
1715 return;
1716
1717 OPENSSL_cleanse(pre, sizeof *pre);
1718 OPENSSL_free(pre);
1719 }
1720
1721/******************************************************************************/
1722/* OPENSSL EC_METHOD FUNCTIONS
1723 */
1724
1725int ec_GFp_nistp256_group_init(EC_GROUP *group)
1726 {
1727 int ret;
1728 ret = ec_GFp_simple_group_init(group);
1729 group->a_is_minus3 = 1;
1730 return ret;
1731 }
1732
1733int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
1734 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1735 {
1736 int ret = 0;
1737 BN_CTX *new_ctx = NULL;
1738 BIGNUM *curve_p, *curve_a, *curve_b;
1739
1740 if (ctx == NULL)
1741 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1742 BN_CTX_start(ctx);
1743 if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1744 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1745 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err;
1746 BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p);
1747 BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a);
1748 BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b);
1749 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1750 (BN_cmp(curve_b, b)))
1751 {
1752 ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE,
1753 EC_R_WRONG_CURVE_PARAMETERS);
1754 goto err;
1755 }
1756 group->field_mod_func = BN_nist_mod_256;
1757 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1758err:
1759 BN_CTX_end(ctx);
1760 if (new_ctx != NULL)
1761 BN_CTX_free(new_ctx);
1762 return ret;
1763 }
1764
1765/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1766 * (X', Y') = (X/Z^2, Y/Z^3) */
1767int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
1768 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1769 {
1770 felem z1, z2, x_in, y_in;
1771 smallfelem x_out, y_out;
1772 longfelem tmp;
1773
1774 if (EC_POINT_is_at_infinity(group, point))
1775 {
1776 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
1777 EC_R_POINT_AT_INFINITY);
1778 return 0;
1779 }
1780 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1781 (!BN_to_felem(z1, &point->Z))) return 0;
1782 felem_inv(z2, z1);
1783 felem_square(tmp, z2); felem_reduce(z1, tmp);
1784 felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp);
1785 felem_contract(x_out, x_in);
1786 if (x != NULL)
1787 {
1788 if (!smallfelem_to_BN(x, x_out)) {
1789 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
1790 ERR_R_BN_LIB);
1791 return 0;
1792 }
1793 }
1794 felem_mul(tmp, z1, z2); felem_reduce(z1, tmp);
1795 felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp);
1796 felem_contract(y_out, y_in);
1797 if (y != NULL)
1798 {
1799 if (!smallfelem_to_BN(y, y_out))
1800 {
1801 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
1802 ERR_R_BN_LIB);
1803 return 0;
1804 }
1805 }
1806 return 1;
1807 }
1808
1809static void make_points_affine(size_t num, smallfelem points[/* num */][3], smallfelem tmp_smallfelems[/* num+1 */])
1810 {
1811 /* Runs in constant time, unless an input is the point at infinity
1812 * (which normally shouldn't happen). */
1813 ec_GFp_nistp_points_make_affine_internal(
1814 num,
1815 points,
1816 sizeof(smallfelem),
1817 tmp_smallfelems,
1818 (void (*)(void *)) smallfelem_one,
1819 (int (*)(const void *)) smallfelem_is_zero_int,
1820 (void (*)(void *, const void *)) smallfelem_assign,
1821 (void (*)(void *, const void *)) smallfelem_square_contract,
1822 (void (*)(void *, const void *, const void *)) smallfelem_mul_contract,
1823 (void (*)(void *, const void *)) smallfelem_inv_contract,
1824 (void (*)(void *, const void *)) smallfelem_assign /* nothing to contract */);
1825 }
1826
1827/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1828 * Result is stored in r (r can equal one of the inputs). */
1829int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
1830 const BIGNUM *scalar, size_t num, const EC_POINT *points[],
1831 const BIGNUM *scalars[], BN_CTX *ctx)
1832 {
1833 int ret = 0;
1834 int j;
1835 int mixed = 0;
1836 BN_CTX *new_ctx = NULL;
1837 BIGNUM *x, *y, *z, *tmp_scalar;
1838 felem_bytearray g_secret;
1839 felem_bytearray *secrets = NULL;
1840 smallfelem (*pre_comp)[17][3] = NULL;
1841 smallfelem *tmp_smallfelems = NULL;
1842 felem_bytearray tmp;
1843 unsigned i, num_bytes;
1844 int have_pre_comp = 0;
1845 size_t num_points = num;
1846 smallfelem x_in, y_in, z_in;
1847 felem x_out, y_out, z_out;
1848 NISTP256_PRE_COMP *pre = NULL;
1849 const smallfelem (*g_pre_comp)[16][3] = NULL;
1850 EC_POINT *generator = NULL;
1851 const EC_POINT *p = NULL;
1852 const BIGNUM *p_scalar = NULL;
1853
1854 if (ctx == NULL)
1855 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1856 BN_CTX_start(ctx);
1857 if (((x = BN_CTX_get(ctx)) == NULL) ||
1858 ((y = BN_CTX_get(ctx)) == NULL) ||
1859 ((z = BN_CTX_get(ctx)) == NULL) ||
1860 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1861 goto err;
1862
1863 if (scalar != NULL)
1864 {
1865 pre = EC_EX_DATA_get_data(group->extra_data,
1866 nistp256_pre_comp_dup, nistp256_pre_comp_free,
1867 nistp256_pre_comp_clear_free);
1868 if (pre)
1869 /* we have precomputation, try to use it */
1870 g_pre_comp = (const smallfelem (*)[16][3]) pre->g_pre_comp;
1871 else
1872 /* try to use the standard precomputation */
1873 g_pre_comp = &gmul[0];
1874 generator = EC_POINT_new(group);
1875 if (generator == NULL)
1876 goto err;
1877 /* get the generator from precomputation */
1878 if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) ||
1879 !smallfelem_to_BN(y, g_pre_comp[0][1][1]) ||
1880 !smallfelem_to_BN(z, g_pre_comp[0][1][2]))
1881 {
1882 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
1883 goto err;
1884 }
1885 if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1886 generator, x, y, z, ctx))
1887 goto err;
1888 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1889 /* precomputation matches generator */
1890 have_pre_comp = 1;
1891 else
1892 /* we don't have valid precomputation:
1893 * treat the generator as a random point */
1894 num_points++;
1895 }
1896 if (num_points > 0)
1897 {
1898 if (num_points >= 3)
1899 {
1900 /* unless we precompute multiples for just one or two points,
1901 * converting those into affine form is time well spent */
1902 mixed = 1;
1903 }
1904 secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray));
1905 pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(smallfelem));
1906 if (mixed)
1907 tmp_smallfelems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(smallfelem));
1908 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL)))
1909 {
1910 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1911 goto err;
1912 }
1913
1914 /* we treat NULL scalars as 0, and NULL points as points at infinity,
1915 * i.e., they contribute nothing to the linear combination */
1916 memset(secrets, 0, num_points * sizeof(felem_bytearray));
1917 memset(pre_comp, 0, num_points * 17 * 3 * sizeof(smallfelem));
1918 for (i = 0; i < num_points; ++i)
1919 {
1920 if (i == num)
1921 /* we didn't have a valid precomputation, so we pick
1922 * the generator */
1923 {
1924 p = EC_GROUP_get0_generator(group);
1925 p_scalar = scalar;
1926 }
1927 else
1928 /* the i^th point */
1929 {
1930 p = points[i];
1931 p_scalar = scalars[i];
1932 }
1933 if ((p_scalar != NULL) && (p != NULL))
1934 {
1935 /* reduce scalar to 0 <= scalar < 2^256 */
1936 if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar)))
1937 {
1938 /* this is an unusual input, and we don't guarantee
1939 * constant-timeness */
1940 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx))
1941 {
1942 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
1943 goto err;
1944 }
1945 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1946 }
1947 else
1948 num_bytes = BN_bn2bin(p_scalar, tmp);
1949 flip_endian(secrets[i], tmp, num_bytes);
1950 /* precompute multiples */
1951 if ((!BN_to_felem(x_out, &p->X)) ||
1952 (!BN_to_felem(y_out, &p->Y)) ||
1953 (!BN_to_felem(z_out, &p->Z))) goto err;
1954 felem_shrink(pre_comp[i][1][0], x_out);
1955 felem_shrink(pre_comp[i][1][1], y_out);
1956 felem_shrink(pre_comp[i][1][2], z_out);
1957 for (j = 2; j <= 16; ++j)
1958 {
1959 if (j & 1)
1960 {
1961 point_add_small(
1962 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1963 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
1964 pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]);
1965 }
1966 else
1967 {
1968 point_double_small(
1969 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1970 pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]);
1971 }
1972 }
1973 }
1974 }
1975 if (mixed)
1976 make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems);
1977 }
1978
1979 /* the scalar for the generator */
1980 if ((scalar != NULL) && (have_pre_comp))
1981 {
1982 memset(g_secret, 0, sizeof(g_secret));
1983 /* reduce scalar to 0 <= scalar < 2^256 */
1984 if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar)))
1985 {
1986 /* this is an unusual input, and we don't guarantee
1987 * constant-timeness */
1988 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx))
1989 {
1990 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
1991 goto err;
1992 }
1993 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1994 }
1995 else
1996 num_bytes = BN_bn2bin(scalar, tmp);
1997 flip_endian(g_secret, tmp, num_bytes);
1998 /* do the multiplication with generator precomputation*/
1999 batch_mul(x_out, y_out, z_out,
2000 (const felem_bytearray (*)) secrets, num_points,
2001 g_secret,
2002 mixed, (const smallfelem (*)[17][3]) pre_comp,
2003 g_pre_comp);
2004 }
2005 else
2006 /* do the multiplication without generator precomputation */
2007 batch_mul(x_out, y_out, z_out,
2008 (const felem_bytearray (*)) secrets, num_points,
2009 NULL, mixed, (const smallfelem (*)[17][3]) pre_comp, NULL);
2010 /* reduce the output to its unique minimal representation */
2011 felem_contract(x_in, x_out);
2012 felem_contract(y_in, y_out);
2013 felem_contract(z_in, z_out);
2014 if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) ||
2015 (!smallfelem_to_BN(z, z_in)))
2016 {
2017 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
2018 goto err;
2019 }
2020 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
2021
2022err:
2023 BN_CTX_end(ctx);
2024 if (generator != NULL)
2025 EC_POINT_free(generator);
2026 if (new_ctx != NULL)
2027 BN_CTX_free(new_ctx);
2028 if (secrets != NULL)
2029 OPENSSL_free(secrets);
2030 if (pre_comp != NULL)
2031 OPENSSL_free(pre_comp);
2032 if (tmp_smallfelems != NULL)
2033 OPENSSL_free(tmp_smallfelems);
2034 return ret;
2035 }
2036
2037int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
2038 {
2039 int ret = 0;
2040 NISTP256_PRE_COMP *pre = NULL;
2041 int i, j;
2042 BN_CTX *new_ctx = NULL;
2043 BIGNUM *x, *y;
2044 EC_POINT *generator = NULL;
2045 smallfelem tmp_smallfelems[32];
2046 felem x_tmp, y_tmp, z_tmp;
2047
2048 /* throw away old precomputation */
2049 EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup,
2050 nistp256_pre_comp_free, nistp256_pre_comp_clear_free);
2051 if (ctx == NULL)
2052 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
2053 BN_CTX_start(ctx);
2054 if (((x = BN_CTX_get(ctx)) == NULL) ||
2055 ((y = BN_CTX_get(ctx)) == NULL))
2056 goto err;
2057 /* get the generator */
2058 if (group->generator == NULL) goto err;
2059 generator = EC_POINT_new(group);
2060 if (generator == NULL)
2061 goto err;
2062 BN_bin2bn(nistp256_curve_params[3], sizeof (felem_bytearray), x);
2063 BN_bin2bn(nistp256_curve_params[4], sizeof (felem_bytearray), y);
2064 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
2065 goto err;
2066 if ((pre = nistp256_pre_comp_new()) == NULL)
2067 goto err;
2068 /* if the generator is the standard one, use built-in precomputation */
2069 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
2070 {
2071 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
2072 ret = 1;
2073 goto err;
2074 }
2075 if ((!BN_to_felem(x_tmp, &group->generator->X)) ||
2076 (!BN_to_felem(y_tmp, &group->generator->Y)) ||
2077 (!BN_to_felem(z_tmp, &group->generator->Z)))
2078 goto err;
2079 felem_shrink(pre->g_pre_comp[0][1][0], x_tmp);
2080 felem_shrink(pre->g_pre_comp[0][1][1], y_tmp);
2081 felem_shrink(pre->g_pre_comp[0][1][2], z_tmp);
2082 /* compute 2^64*G, 2^128*G, 2^192*G for the first table,
2083 * 2^32*G, 2^96*G, 2^160*G, 2^224*G for the second one
2084 */
2085 for (i = 1; i <= 8; i <<= 1)
2086 {
2087 point_double_small(
2088 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
2089 pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]);
2090 for (j = 0; j < 31; ++j)
2091 {
2092 point_double_small(
2093 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
2094 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
2095 }
2096 if (i == 8)
2097 break;
2098 point_double_small(
2099 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2],
2100 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
2101 for (j = 0; j < 31; ++j)
2102 {
2103 point_double_small(
2104 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2],
2105 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]);
2106 }
2107 }
2108 for (i = 0; i < 2; i++)
2109 {
2110 /* g_pre_comp[i][0] is the point at infinity */
2111 memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0]));
2112 /* the remaining multiples */
2113 /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */
2114 point_add_small(
2115 pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2],
2116 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2],
2117 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]);
2118 /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */
2119 point_add_small(
2120 pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2],
2121 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
2122 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]);
2123 /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */
2124 point_add_small(
2125 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
2126 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
2127 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]);
2128 /* 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G */
2129 point_add_small(
2130 pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2],
2131 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
2132 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]);
2133 for (j = 1; j < 8; ++j)
2134 {
2135 /* odd multiples: add G resp. 2^32*G */
2136 point_add_small(
2137 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],
2138 pre->g_pre_comp[i][2*j][0], pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2],
2139 pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]);
2140 }
2141 }
2142 make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems);
2143
2144 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup,
2145 nistp256_pre_comp_free, nistp256_pre_comp_clear_free))
2146 goto err;
2147 ret = 1;
2148 pre = NULL;
2149 err:
2150 BN_CTX_end(ctx);
2151 if (generator != NULL)
2152 EC_POINT_free(generator);
2153 if (new_ctx != NULL)
2154 BN_CTX_free(new_ctx);
2155 if (pre)
2156 nistp256_pre_comp_free(pre);
2157 return ret;
2158 }
2159
2160int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group)
2161 {
2162 if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup,
2163 nistp256_pre_comp_free, nistp256_pre_comp_clear_free)
2164 != NULL)
2165 return 1;
2166 else
2167 return 0;
2168 }
2169#else
2170static void *dummy=&dummy;
2171#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-08-04 16:33:25 +0000