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[thirdparty/openssl.git] / crypto / ec / ecp_nistp256.c
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
50 typedef uint8_t u8;
51 typedef uint32_t u32;
52 typedef uint64_t u64;
53 typedef 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
60 typedef 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. */
64 static 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 /*-
88 * The representation of field elements.
89 * ------------------------------------
90 *
91 * We represent field elements with either four 128-bit values, eight 128-bit
92 * values, or four 64-bit values. The field element represented is:
93 * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192 (mod p)
94 * or:
95 * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512 (mod p)
96 *
97 * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits
98 * apart, but are 128-bits wide, the most significant bits of each limb overlap
99 * with the least significant bits of the next.
100 *
101 * A field element with four limbs is an 'felem'. One with eight limbs is a
102 * 'longfelem'
103 *
104 * A field element with four, 64-bit values is called a 'smallfelem'. Small
105 * values are used as intermediate values before multiplication.
106 */
107
108 #define NLIMBS 4
109
110 typedef uint128_t limb;
111 typedef limb felem[NLIMBS];
112 typedef limb longfelem[NLIMBS * 2];
113 typedef u64 smallfelem[NLIMBS];
114
115 /* This is the value of the prime as four 64-bit words, little-endian. */
116 static const u64 kPrime[4] = { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul };
117 static 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. */
121 static 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. */
131 static 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 */
140 static 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 */
148 static 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 */
174 static 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
186 static void smallfelem_one(smallfelem out)
187 {
188 out[0] = 1;
189 out[1] = 0;
190 out[2] = 0;
191 out[3] = 0;
192 }
193
194 static 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
202 static 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. */
211 static 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. */
220 static 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 */
229 static 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 */
238 static 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 */
255 static const felem zero105 = { two105m41m9, two105, two105m41p9, two105m41p9 };
256
257 /*-
258 * smallfelem_neg sets |out| to |-small|
259 * On exit:
260 * out[i] < out[i] + 2^105
261 */
262 static void smallfelem_neg(felem out, const smallfelem small)
263 {
264 /* In order to prevent underflow, we subtract from 0 mod p. */
265 out[0] = zero105[0] - small[0];
266 out[1] = zero105[1] - small[1];
267 out[2] = zero105[2] - small[2];
268 out[3] = zero105[3] - small[3];
269 }
270
271 /*-
272 * felem_diff subtracts |in| from |out|
273 * On entry:
274 * in[i] < 2^104
275 * On exit:
276 * out[i] < out[i] + 2^105
277 */
278 static void felem_diff(felem out, const felem in)
279 {
280 /* In order to prevent underflow, we add 0 mod p before subtracting. */
281 out[0] += zero105[0];
282 out[1] += zero105[1];
283 out[2] += zero105[2];
284 out[3] += zero105[3];
285
286 out[0] -= in[0];
287 out[1] -= in[1];
288 out[2] -= in[2];
289 out[3] -= in[3];
290 }
291
292 #define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11)
293 #define two107 (((limb)1) << 107)
294 #define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11)
295
296 /* zero107 is 0 mod p */
297 static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 };
298
299 /*-
300 * An alternative felem_diff for larger inputs |in|
301 * felem_diff_zero107 subtracts |in| from |out|
302 * On entry:
303 * in[i] < 2^106
304 * On exit:
305 * out[i] < out[i] + 2^107
306 */
307 static void felem_diff_zero107(felem out, const felem in)
308 {
309 /* In order to prevent underflow, we add 0 mod p before subtracting. */
310 out[0] += zero107[0];
311 out[1] += zero107[1];
312 out[2] += zero107[2];
313 out[3] += zero107[3];
314
315 out[0] -= in[0];
316 out[1] -= in[1];
317 out[2] -= in[2];
318 out[3] -= in[3];
319 }
320
321 /*-
322 * longfelem_diff subtracts |in| from |out|
323 * On entry:
324 * in[i] < 7*2^67
325 * On exit:
326 * out[i] < out[i] + 2^70 + 2^40
327 */
328 static void longfelem_diff(longfelem out, const longfelem in)
329 {
330 static const limb two70m8p6 = (((limb)1) << 70) - (((limb)1) << 8) + (((limb)1) << 6);
331 static const limb two70p40 = (((limb)1) << 70) + (((limb)1) << 40);
332 static const limb two70 = (((limb)1) << 70);
333 static const limb two70m40m38p6 = (((limb)1) << 70) - (((limb)1) << 40) - (((limb)1) << 38) + (((limb)1) << 6);
334 static const limb two70m6 = (((limb)1) << 70) - (((limb)1) << 6);
335
336 /* add 0 mod p to avoid underflow */
337 out[0] += two70m8p6;
338 out[1] += two70p40;
339 out[2] += two70;
340 out[3] += two70m40m38p6;
341 out[4] += two70m6;
342 out[5] += two70m6;
343 out[6] += two70m6;
344 out[7] += two70m6;
345
346 /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */
347 out[0] -= in[0];
348 out[1] -= in[1];
349 out[2] -= in[2];
350 out[3] -= in[3];
351 out[4] -= in[4];
352 out[5] -= in[5];
353 out[6] -= in[6];
354 out[7] -= in[7];
355 }
356
357 #define two64m0 (((limb)1) << 64) - 1
358 #define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1
359 #define two64m46 (((limb)1) << 64) - (((limb)1) << 46)
360 #define two64m32 (((limb)1) << 64) - (((limb)1) << 32)
361
362 /* zero110 is 0 mod p */
363 static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 };
364
365 /*-
366 * felem_shrink converts an felem into a smallfelem. The result isn't quite
367 * minimal as the value may be greater than p.
368 *
369 * On entry:
370 * in[i] < 2^109
371 * On exit:
372 * out[i] < 2^64
373 */
374 static void felem_shrink(smallfelem out, const felem in)
375 {
376 felem tmp;
377 u64 a, b, mask;
378 s64 high, low;
379 static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */
380
381 /* Carry 2->3 */
382 tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64));
383 /* tmp[3] < 2^110 */
384
385 tmp[2] = zero110[2] + (u64) in[2];
386 tmp[0] = zero110[0] + in[0];
387 tmp[1] = zero110[1] + in[1];
388 /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */
389
390 /* We perform two partial reductions where we eliminate the
391 * high-word of tmp[3]. We don't update the other words till the end.
392 */
393 a = tmp[3] >> 64; /* a < 2^46 */
394 tmp[3] = (u64) tmp[3];
395 tmp[3] -= a;
396 tmp[3] += ((limb)a) << 32;
397 /* tmp[3] < 2^79 */
398
399 b = a;
400 a = tmp[3] >> 64; /* a < 2^15 */
401 b += a; /* b < 2^46 + 2^15 < 2^47 */
402 tmp[3] = (u64) tmp[3];
403 tmp[3] -= a;
404 tmp[3] += ((limb)a) << 32;
405 /* tmp[3] < 2^64 + 2^47 */
406
407 /* This adjusts the other two words to complete the two partial
408 * reductions. */
409 tmp[0] += b;
410 tmp[1] -= (((limb)b) << 32);
411
412 /* In order to make space in tmp[3] for the carry from 2 -> 3, we
413 * conditionally subtract kPrime if tmp[3] is large enough. */
414 high = tmp[3] >> 64;
415 /* As tmp[3] < 2^65, high is either 1 or 0 */
416 high <<= 63;
417 high >>= 63;
418 /*-
419 * high is:
420 * all ones if the high word of tmp[3] is 1
421 * all zeros if the high word of tmp[3] if 0 */
422 low = tmp[3];
423 mask = low >> 63;
424 /*-
425 * mask is:
426 * all ones if the MSB of low is 1
427 * all zeros if the MSB of low if 0 */
428 low &= bottom63bits;
429 low -= kPrime3Test;
430 /* if low was greater than kPrime3Test then the MSB is zero */
431 low = ~low;
432 low >>= 63;
433 /*-
434 * low is:
435 * all ones if low was > kPrime3Test
436 * all zeros if low was <= kPrime3Test */
437 mask = (mask & low) | high;
438 tmp[0] -= mask & kPrime[0];
439 tmp[1] -= mask & kPrime[1];
440 /* kPrime[2] is zero, so omitted */
441 tmp[3] -= mask & kPrime[3];
442 /* tmp[3] < 2**64 - 2**32 + 1 */
443
444 tmp[1] += ((u64) (tmp[0] >> 64)); tmp[0] = (u64) tmp[0];
445 tmp[2] += ((u64) (tmp[1] >> 64)); tmp[1] = (u64) tmp[1];
446 tmp[3] += ((u64) (tmp[2] >> 64)); tmp[2] = (u64) tmp[2];
447 /* tmp[i] < 2^64 */
448
449 out[0] = tmp[0];
450 out[1] = tmp[1];
451 out[2] = tmp[2];
452 out[3] = tmp[3];
453 }
454
455 /* smallfelem_expand converts a smallfelem to an felem */
456 static void smallfelem_expand(felem out, const smallfelem in)
457 {
458 out[0] = in[0];
459 out[1] = in[1];
460 out[2] = in[2];
461 out[3] = in[3];
462 }
463
464 /*-
465 * smallfelem_square sets |out| = |small|^2
466 * On entry:
467 * small[i] < 2^64
468 * On exit:
469 * out[i] < 7 * 2^64 < 2^67
470 */
471 static void smallfelem_square(longfelem out, const smallfelem small)
472 {
473 limb a;
474 u64 high, low;
475
476 a = ((uint128_t) small[0]) * small[0];
477 low = a;
478 high = a >> 64;
479 out[0] = low;
480 out[1] = high;
481
482 a = ((uint128_t) small[0]) * small[1];
483 low = a;
484 high = a >> 64;
485 out[1] += low;
486 out[1] += low;
487 out[2] = high;
488
489 a = ((uint128_t) small[0]) * small[2];
490 low = a;
491 high = a >> 64;
492 out[2] += low;
493 out[2] *= 2;
494 out[3] = high;
495
496 a = ((uint128_t) small[0]) * small[3];
497 low = a;
498 high = a >> 64;
499 out[3] += low;
500 out[4] = high;
501
502 a = ((uint128_t) small[1]) * small[2];
503 low = a;
504 high = a >> 64;
505 out[3] += low;
506 out[3] *= 2;
507 out[4] += high;
508
509 a = ((uint128_t) small[1]) * small[1];
510 low = a;
511 high = a >> 64;
512 out[2] += low;
513 out[3] += high;
514
515 a = ((uint128_t) small[1]) * small[3];
516 low = a;
517 high = a >> 64;
518 out[4] += low;
519 out[4] *= 2;
520 out[5] = high;
521
522 a = ((uint128_t) small[2]) * small[3];
523 low = a;
524 high = a >> 64;
525 out[5] += low;
526 out[5] *= 2;
527 out[6] = high;
528 out[6] += high;
529
530 a = ((uint128_t) small[2]) * small[2];
531 low = a;
532 high = a >> 64;
533 out[4] += low;
534 out[5] += high;
535
536 a = ((uint128_t) small[3]) * small[3];
537 low = a;
538 high = a >> 64;
539 out[6] += low;
540 out[7] = high;
541 }
542
543 /*-
544 * felem_square sets |out| = |in|^2
545 * On entry:
546 * in[i] < 2^109
547 * On exit:
548 * out[i] < 7 * 2^64 < 2^67
549 */
550 static void felem_square(longfelem out, const felem in)
551 {
552 u64 small[4];
553 felem_shrink(small, in);
554 smallfelem_square(out, small);
555 }
556
557 /*-
558 * smallfelem_mul sets |out| = |small1| * |small2|
559 * On entry:
560 * small1[i] < 2^64
561 * small2[i] < 2^64
562 * On exit:
563 * out[i] < 7 * 2^64 < 2^67
564 */
565 static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2)
566 {
567 limb a;
568 u64 high, low;
569
570 a = ((uint128_t) small1[0]) * small2[0];
571 low = a;
572 high = a >> 64;
573 out[0] = low;
574 out[1] = high;
575
576
577 a = ((uint128_t) small1[0]) * small2[1];
578 low = a;
579 high = a >> 64;
580 out[1] += low;
581 out[2] = high;
582
583 a = ((uint128_t) small1[1]) * small2[0];
584 low = a;
585 high = a >> 64;
586 out[1] += low;
587 out[2] += high;
588
589
590 a = ((uint128_t) small1[0]) * small2[2];
591 low = a;
592 high = a >> 64;
593 out[2] += low;
594 out[3] = high;
595
596 a = ((uint128_t) small1[1]) * small2[1];
597 low = a;
598 high = a >> 64;
599 out[2] += low;
600 out[3] += high;
601
602 a = ((uint128_t) small1[2]) * small2[0];
603 low = a;
604 high = a >> 64;
605 out[2] += low;
606 out[3] += high;
607
608
609 a = ((uint128_t) small1[0]) * small2[3];
610 low = a;
611 high = a >> 64;
612 out[3] += low;
613 out[4] = high;
614
615 a = ((uint128_t) small1[1]) * small2[2];
616 low = a;
617 high = a >> 64;
618 out[3] += low;
619 out[4] += high;
620
621 a = ((uint128_t) small1[2]) * small2[1];
622 low = a;
623 high = a >> 64;
624 out[3] += low;
625 out[4] += high;
626
627 a = ((uint128_t) small1[3]) * small2[0];
628 low = a;
629 high = a >> 64;
630 out[3] += low;
631 out[4] += high;
632
633
634 a = ((uint128_t) small1[1]) * small2[3];
635 low = a;
636 high = a >> 64;
637 out[4] += low;
638 out[5] = high;
639
640 a = ((uint128_t) small1[2]) * small2[2];
641 low = a;
642 high = a >> 64;
643 out[4] += low;
644 out[5] += high;
645
646 a = ((uint128_t) small1[3]) * small2[1];
647 low = a;
648 high = a >> 64;
649 out[4] += low;
650 out[5] += high;
651
652
653 a = ((uint128_t) small1[2]) * small2[3];
654 low = a;
655 high = a >> 64;
656 out[5] += low;
657 out[6] = high;
658
659 a = ((uint128_t) small1[3]) * small2[2];
660 low = a;
661 high = a >> 64;
662 out[5] += low;
663 out[6] += high;
664
665
666 a = ((uint128_t) small1[3]) * small2[3];
667 low = a;
668 high = a >> 64;
669 out[6] += low;
670 out[7] = high;
671 }
672
673 /*-
674 * felem_mul sets |out| = |in1| * |in2|
675 * On entry:
676 * in1[i] < 2^109
677 * in2[i] < 2^109
678 * On exit:
679 * out[i] < 7 * 2^64 < 2^67
680 */
681 static void felem_mul(longfelem out, const felem in1, const felem in2)
682 {
683 smallfelem small1, small2;
684 felem_shrink(small1, in1);
685 felem_shrink(small2, in2);
686 smallfelem_mul(out, small1, small2);
687 }
688
689 /*-
690 * felem_small_mul sets |out| = |small1| * |in2|
691 * On entry:
692 * small1[i] < 2^64
693 * in2[i] < 2^109
694 * On exit:
695 * out[i] < 7 * 2^64 < 2^67
696 */
697 static void felem_small_mul(longfelem out, const smallfelem small1, const felem in2)
698 {
699 smallfelem small2;
700 felem_shrink(small2, in2);
701 smallfelem_mul(out, small1, small2);
702 }
703
704 #define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4)
705 #define two100 (((limb)1) << 100)
706 #define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4)
707 /* zero100 is 0 mod p */
708 static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 };
709
710 /*-
711 * Internal function for the different flavours of felem_reduce.
712 * felem_reduce_ reduces the higher coefficients in[4]-in[7].
713 * On entry:
714 * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7]
715 * out[1] >= in[7] + 2^32*in[4]
716 * out[2] >= in[5] + 2^32*in[5]
717 * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6]
718 * On exit:
719 * out[0] <= out[0] + in[4] + 2^32*in[5]
720 * out[1] <= out[1] + in[5] + 2^33*in[6]
721 * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7]
722 * out[3] <= out[3] + 2^32*in[4] + 3*in[7]
723 */
724 static void felem_reduce_(felem out, const longfelem in)
725 {
726 int128_t c;
727 /* combine common terms from below */
728 c = in[4] + (in[5] << 32);
729 out[0] += c;
730 out[3] -= c;
731
732 c = in[5] - in[7];
733 out[1] += c;
734 out[2] -= c;
735
736 /* the remaining terms */
737 /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */
738 out[1] -= (in[4] << 32);
739 out[3] += (in[4] << 32);
740
741 /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */
742 out[2] -= (in[5] << 32);
743
744 /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */
745 out[0] -= in[6];
746 out[0] -= (in[6] << 32);
747 out[1] += (in[6] << 33);
748 out[2] += (in[6] * 2);
749 out[3] -= (in[6] << 32);
750
751 /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */
752 out[0] -= in[7];
753 out[0] -= (in[7] << 32);
754 out[2] += (in[7] << 33);
755 out[3] += (in[7] * 3);
756 }
757
758 /*-
759 * felem_reduce converts a longfelem into an felem.
760 * To be called directly after felem_square or felem_mul.
761 * On entry:
762 * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64
763 * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64
764 * On exit:
765 * out[i] < 2^101
766 */
767 static void felem_reduce(felem out, const longfelem in)
768 {
769 out[0] = zero100[0] + in[0];
770 out[1] = zero100[1] + in[1];
771 out[2] = zero100[2] + in[2];
772 out[3] = zero100[3] + in[3];
773
774 felem_reduce_(out, in);
775
776 /*-
777 * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0
778 * out[1] > 2^100 - 2^64 - 7*2^96 > 0
779 * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0
780 * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0
781 *
782 * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101
783 * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101
784 * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101
785 * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101
786 */
787 }
788
789 /*-
790 * felem_reduce_zero105 converts a larger longfelem into an felem.
791 * On entry:
792 * in[0] < 2^71
793 * On exit:
794 * out[i] < 2^106
795 */
796 static void felem_reduce_zero105(felem out, const longfelem in)
797 {
798 out[0] = zero105[0] + in[0];
799 out[1] = zero105[1] + in[1];
800 out[2] = zero105[2] + in[2];
801 out[3] = zero105[3] + in[3];
802
803 felem_reduce_(out, in);
804
805 /*-
806 * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0
807 * out[1] > 2^105 - 2^71 - 2^103 > 0
808 * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0
809 * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0
810 *
811 * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106
812 * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106
813 * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106
814 * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106
815 */
816 }
817
818 /* subtract_u64 sets *result = *result - v and *carry to one if the subtraction
819 * underflowed. */
820 static void subtract_u64(u64* result, u64* carry, u64 v)
821 {
822 uint128_t r = *result;
823 r -= v;
824 *carry = (r >> 64) & 1;
825 *result = (u64) r;
826 }
827
828 /* felem_contract converts |in| to its unique, minimal representation.
829 * On entry:
830 * in[i] < 2^109
831 */
832 static void felem_contract(smallfelem out, const felem in)
833 {
834 unsigned i;
835 u64 all_equal_so_far = 0, result = 0, carry;
836
837 felem_shrink(out, in);
838 /* small is minimal except that the value might be > p */
839
840 all_equal_so_far--;
841 /* We are doing a constant time test if out >= kPrime. We need to
842 * compare each u64, from most-significant to least significant. For
843 * each one, if all words so far have been equal (m is all ones) then a
844 * non-equal result is the answer. Otherwise we continue. */
845 for (i = 3; i < 4; i--)
846 {
847 u64 equal;
848 uint128_t a = ((uint128_t) kPrime[i]) - out[i];
849 /* if out[i] > kPrime[i] then a will underflow and the high
850 * 64-bits will all be set. */
851 result |= all_equal_so_far & ((u64) (a >> 64));
852
853 /* if kPrime[i] == out[i] then |equal| will be all zeros and
854 * the decrement will make it all ones. */
855 equal = kPrime[i] ^ out[i];
856 equal--;
857 equal &= equal << 32;
858 equal &= equal << 16;
859 equal &= equal << 8;
860 equal &= equal << 4;
861 equal &= equal << 2;
862 equal &= equal << 1;
863 equal = ((s64) equal) >> 63;
864
865 all_equal_so_far &= equal;
866 }
867
868 /* if all_equal_so_far is still all ones then the two values are equal
869 * and so out >= kPrime is true. */
870 result |= all_equal_so_far;
871
872 /* if out >= kPrime then we subtract kPrime. */
873 subtract_u64(&out[0], &carry, result & kPrime[0]);
874 subtract_u64(&out[1], &carry, carry);
875 subtract_u64(&out[2], &carry, carry);
876 subtract_u64(&out[3], &carry, carry);
877
878 subtract_u64(&out[1], &carry, result & kPrime[1]);
879 subtract_u64(&out[2], &carry, carry);
880 subtract_u64(&out[3], &carry, carry);
881
882 subtract_u64(&out[2], &carry, result & kPrime[2]);
883 subtract_u64(&out[3], &carry, carry);
884
885 subtract_u64(&out[3], &carry, result & kPrime[3]);
886 }
887
888 static void smallfelem_square_contract(smallfelem out, const smallfelem in)
889 {
890 longfelem longtmp;
891 felem tmp;
892
893 smallfelem_square(longtmp, in);
894 felem_reduce(tmp, longtmp);
895 felem_contract(out, tmp);
896 }
897
898 static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2)
899 {
900 longfelem longtmp;
901 felem tmp;
902
903 smallfelem_mul(longtmp, in1, in2);
904 felem_reduce(tmp, longtmp);
905 felem_contract(out, tmp);
906 }
907
908 /*-
909 * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0
910 * otherwise.
911 * On entry:
912 * small[i] < 2^64
913 */
914 static limb smallfelem_is_zero(const smallfelem small)
915 {
916 limb result;
917 u64 is_p;
918
919 u64 is_zero = small[0] | small[1] | small[2] | small[3];
920 is_zero--;
921 is_zero &= is_zero << 32;
922 is_zero &= is_zero << 16;
923 is_zero &= is_zero << 8;
924 is_zero &= is_zero << 4;
925 is_zero &= is_zero << 2;
926 is_zero &= is_zero << 1;
927 is_zero = ((s64) is_zero) >> 63;
928
929 is_p = (small[0] ^ kPrime[0]) |
930 (small[1] ^ kPrime[1]) |
931 (small[2] ^ kPrime[2]) |
932 (small[3] ^ kPrime[3]);
933 is_p--;
934 is_p &= is_p << 32;
935 is_p &= is_p << 16;
936 is_p &= is_p << 8;
937 is_p &= is_p << 4;
938 is_p &= is_p << 2;
939 is_p &= is_p << 1;
940 is_p = ((s64) is_p) >> 63;
941
942 is_zero |= is_p;
943
944 result = is_zero;
945 result |= ((limb) is_zero) << 64;
946 return result;
947 }
948
949 static int smallfelem_is_zero_int(const smallfelem small)
950 {
951 return (int) (smallfelem_is_zero(small) & ((limb)1));
952 }
953
954 /*-
955 * felem_inv calculates |out| = |in|^{-1}
956 *
957 * Based on Fermat's Little Theorem:
958 * a^p = a (mod p)
959 * a^{p-1} = 1 (mod p)
960 * a^{p-2} = a^{-1} (mod p)
961 */
962 static void felem_inv(felem out, const felem in)
963 {
964 felem ftmp, ftmp2;
965 /* each e_I will hold |in|^{2^I - 1} */
966 felem e2, e4, e8, e16, e32, e64;
967 longfelem tmp;
968 unsigned i;
969
970 felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */
971 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */
972 felem_assign(e2, ftmp);
973 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */
974 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */
975 felem_mul(tmp, ftmp, e2); felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */
976 felem_assign(e4, ftmp);
977 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */
978 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */
979 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */
980 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */
981 felem_mul(tmp, ftmp, e4); felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */
982 felem_assign(e8, ftmp);
983 for (i = 0; i < 8; i++) {
984 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
985 } /* 2^16 - 2^8 */
986 felem_mul(tmp, ftmp, e8); felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */
987 felem_assign(e16, ftmp);
988 for (i = 0; i < 16; i++) {
989 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
990 } /* 2^32 - 2^16 */
991 felem_mul(tmp, ftmp, e16); felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */
992 felem_assign(e32, ftmp);
993 for (i = 0; i < 32; i++) {
994 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
995 } /* 2^64 - 2^32 */
996 felem_assign(e64, ftmp);
997 felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */
998 for (i = 0; i < 192; i++) {
999 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
1000 } /* 2^256 - 2^224 + 2^192 */
1001
1002 felem_mul(tmp, e64, e32); felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */
1003 for (i = 0; i < 16; i++) {
1004 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
1005 } /* 2^80 - 2^16 */
1006 felem_mul(tmp, ftmp2, e16); felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */
1007 for (i = 0; i < 8; i++) {
1008 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
1009 } /* 2^88 - 2^8 */
1010 felem_mul(tmp, ftmp2, e8); felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */
1011 for (i = 0; i < 4; i++) {
1012 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
1013 } /* 2^92 - 2^4 */
1014 felem_mul(tmp, ftmp2, e4); felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */
1015 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */
1016 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */
1017 felem_mul(tmp, ftmp2, e2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */
1018 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */
1019 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */
1020 felem_mul(tmp, ftmp2, in); felem_reduce(ftmp2, tmp); /* 2^96 - 3 */
1021
1022 felem_mul(tmp, ftmp2, ftmp); felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */
1023 }
1024
1025 static void smallfelem_inv_contract(smallfelem out, const smallfelem in)
1026 {
1027 felem tmp;
1028
1029 smallfelem_expand(tmp, in);
1030 felem_inv(tmp, tmp);
1031 felem_contract(out, tmp);
1032 }
1033
1034 /*-
1035 * Group operations
1036 * ----------------
1037 *
1038 * Building on top of the field operations we have the operations on the
1039 * elliptic curve group itself. Points on the curve are represented in Jacobian
1040 * coordinates */
1041
1042 /*-
1043 * point_double calculates 2*(x_in, y_in, z_in)
1044 *
1045 * The method is taken from:
1046 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
1047 *
1048 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed.
1049 * while x_out == y_in is not (maybe this works, but it's not tested). */
1050 static void
1051 point_double(felem x_out, felem y_out, felem z_out,
1052 const felem x_in, const felem y_in, const felem z_in)
1053 {
1054 longfelem tmp, tmp2;
1055 felem delta, gamma, beta, alpha, ftmp, ftmp2;
1056 smallfelem small1, small2;
1057
1058 felem_assign(ftmp, x_in);
1059 /* ftmp[i] < 2^106 */
1060 felem_assign(ftmp2, x_in);
1061 /* ftmp2[i] < 2^106 */
1062
1063 /* delta = z^2 */
1064 felem_square(tmp, z_in);
1065 felem_reduce(delta, tmp);
1066 /* delta[i] < 2^101 */
1067
1068 /* gamma = y^2 */
1069 felem_square(tmp, y_in);
1070 felem_reduce(gamma, tmp);
1071 /* gamma[i] < 2^101 */
1072 felem_shrink(small1, gamma);
1073
1074 /* beta = x*gamma */
1075 felem_small_mul(tmp, small1, x_in);
1076 felem_reduce(beta, tmp);
1077 /* beta[i] < 2^101 */
1078
1079 /* alpha = 3*(x-delta)*(x+delta) */
1080 felem_diff(ftmp, delta);
1081 /* ftmp[i] < 2^105 + 2^106 < 2^107 */
1082 felem_sum(ftmp2, delta);
1083 /* ftmp2[i] < 2^105 + 2^106 < 2^107 */
1084 felem_scalar(ftmp2, 3);
1085 /* ftmp2[i] < 3 * 2^107 < 2^109 */
1086 felem_mul(tmp, ftmp, ftmp2);
1087 felem_reduce(alpha, tmp);
1088 /* alpha[i] < 2^101 */
1089 felem_shrink(small2, alpha);
1090
1091 /* x' = alpha^2 - 8*beta */
1092 smallfelem_square(tmp, small2);
1093 felem_reduce(x_out, tmp);
1094 felem_assign(ftmp, beta);
1095 felem_scalar(ftmp, 8);
1096 /* ftmp[i] < 8 * 2^101 = 2^104 */
1097 felem_diff(x_out, ftmp);
1098 /* x_out[i] < 2^105 + 2^101 < 2^106 */
1099
1100 /* z' = (y + z)^2 - gamma - delta */
1101 felem_sum(delta, gamma);
1102 /* delta[i] < 2^101 + 2^101 = 2^102 */
1103 felem_assign(ftmp, y_in);
1104 felem_sum(ftmp, z_in);
1105 /* ftmp[i] < 2^106 + 2^106 = 2^107 */
1106 felem_square(tmp, ftmp);
1107 felem_reduce(z_out, tmp);
1108 felem_diff(z_out, delta);
1109 /* z_out[i] < 2^105 + 2^101 < 2^106 */
1110
1111 /* y' = alpha*(4*beta - x') - 8*gamma^2 */
1112 felem_scalar(beta, 4);
1113 /* beta[i] < 4 * 2^101 = 2^103 */
1114 felem_diff_zero107(beta, x_out);
1115 /* beta[i] < 2^107 + 2^103 < 2^108 */
1116 felem_small_mul(tmp, small2, beta);
1117 /* tmp[i] < 7 * 2^64 < 2^67 */
1118 smallfelem_square(tmp2, small1);
1119 /* tmp2[i] < 7 * 2^64 */
1120 longfelem_scalar(tmp2, 8);
1121 /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */
1122 longfelem_diff(tmp, tmp2);
1123 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
1124 felem_reduce_zero105(y_out, tmp);
1125 /* y_out[i] < 2^106 */
1126 }
1127
1128 /* point_double_small is the same as point_double, except that it operates on
1129 * smallfelems */
1130 static void
1131 point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out,
1132 const smallfelem x_in, const smallfelem y_in, const smallfelem z_in)
1133 {
1134 felem felem_x_out, felem_y_out, felem_z_out;
1135 felem felem_x_in, felem_y_in, felem_z_in;
1136
1137 smallfelem_expand(felem_x_in, x_in);
1138 smallfelem_expand(felem_y_in, y_in);
1139 smallfelem_expand(felem_z_in, z_in);
1140 point_double(felem_x_out, felem_y_out, felem_z_out,
1141 felem_x_in, felem_y_in, felem_z_in);
1142 felem_shrink(x_out, felem_x_out);
1143 felem_shrink(y_out, felem_y_out);
1144 felem_shrink(z_out, felem_z_out);
1145 }
1146
1147 /* copy_conditional copies in to out iff mask is all ones. */
1148 static void
1149 copy_conditional(felem out, const felem in, limb mask)
1150 {
1151 unsigned i;
1152 for (i = 0; i < NLIMBS; ++i)
1153 {
1154 const limb tmp = mask & (in[i] ^ out[i]);
1155 out[i] ^= tmp;
1156 }
1157 }
1158
1159 /* copy_small_conditional copies in to out iff mask is all ones. */
1160 static void
1161 copy_small_conditional(felem out, const smallfelem in, limb mask)
1162 {
1163 unsigned i;
1164 const u64 mask64 = mask;
1165 for (i = 0; i < NLIMBS; ++i)
1166 {
1167 out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask);
1168 }
1169 }
1170
1171 /*-
1172 * point_add calcuates (x1, y1, z1) + (x2, y2, z2)
1173 *
1174 * The method is taken from:
1175 * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl,
1176 * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity).
1177 *
1178 * This function includes a branch for checking whether the two input points
1179 * are equal, (while not equal to the point at infinity). This case never
1180 * happens during single point multiplication, so there is no timing leak for
1181 * ECDH or ECDSA signing. */
1182 static void point_add(felem x3, felem y3, felem z3,
1183 const felem x1, const felem y1, const felem z1,
1184 const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2)
1185 {
1186 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out;
1187 longfelem tmp, tmp2;
1188 smallfelem small1, small2, small3, small4, small5;
1189 limb x_equal, y_equal, z1_is_zero, z2_is_zero;
1190
1191 felem_shrink(small3, z1);
1192
1193 z1_is_zero = smallfelem_is_zero(small3);
1194 z2_is_zero = smallfelem_is_zero(z2);
1195
1196 /* ftmp = z1z1 = z1**2 */
1197 smallfelem_square(tmp, small3);
1198 felem_reduce(ftmp, tmp);
1199 /* ftmp[i] < 2^101 */
1200 felem_shrink(small1, ftmp);
1201
1202 if(!mixed)
1203 {
1204 /* ftmp2 = z2z2 = z2**2 */
1205 smallfelem_square(tmp, z2);
1206 felem_reduce(ftmp2, tmp);
1207 /* ftmp2[i] < 2^101 */
1208 felem_shrink(small2, ftmp2);
1209
1210 felem_shrink(small5, x1);
1211
1212 /* u1 = ftmp3 = x1*z2z2 */
1213 smallfelem_mul(tmp, small5, small2);
1214 felem_reduce(ftmp3, tmp);
1215 /* ftmp3[i] < 2^101 */
1216
1217 /* ftmp5 = z1 + z2 */
1218 felem_assign(ftmp5, z1);
1219 felem_small_sum(ftmp5, z2);
1220 /* ftmp5[i] < 2^107 */
1221
1222 /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */
1223 felem_square(tmp, ftmp5);
1224 felem_reduce(ftmp5, tmp);
1225 /* ftmp2 = z2z2 + z1z1 */
1226 felem_sum(ftmp2, ftmp);
1227 /* ftmp2[i] < 2^101 + 2^101 = 2^102 */
1228 felem_diff(ftmp5, ftmp2);
1229 /* ftmp5[i] < 2^105 + 2^101 < 2^106 */
1230
1231 /* ftmp2 = z2 * z2z2 */
1232 smallfelem_mul(tmp, small2, z2);
1233 felem_reduce(ftmp2, tmp);
1234
1235 /* s1 = ftmp2 = y1 * z2**3 */
1236 felem_mul(tmp, y1, ftmp2);
1237 felem_reduce(ftmp6, tmp);
1238 /* ftmp6[i] < 2^101 */
1239 }
1240 else
1241 {
1242 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
1243
1244 /* u1 = ftmp3 = x1*z2z2 */
1245 felem_assign(ftmp3, x1);
1246 /* ftmp3[i] < 2^106 */
1247
1248 /* ftmp5 = 2z1z2 */
1249 felem_assign(ftmp5, z1);
1250 felem_scalar(ftmp5, 2);
1251 /* ftmp5[i] < 2*2^106 = 2^107 */
1252
1253 /* s1 = ftmp2 = y1 * z2**3 */
1254 felem_assign(ftmp6, y1);
1255 /* ftmp6[i] < 2^106 */
1256 }
1257
1258 /* u2 = x2*z1z1 */
1259 smallfelem_mul(tmp, x2, small1);
1260 felem_reduce(ftmp4, tmp);
1261
1262 /* h = ftmp4 = u2 - u1 */
1263 felem_diff_zero107(ftmp4, ftmp3);
1264 /* ftmp4[i] < 2^107 + 2^101 < 2^108 */
1265 felem_shrink(small4, ftmp4);
1266
1267 x_equal = smallfelem_is_zero(small4);
1268
1269 /* z_out = ftmp5 * h */
1270 felem_small_mul(tmp, small4, ftmp5);
1271 felem_reduce(z_out, tmp);
1272 /* z_out[i] < 2^101 */
1273
1274 /* ftmp = z1 * z1z1 */
1275 smallfelem_mul(tmp, small1, small3);
1276 felem_reduce(ftmp, tmp);
1277
1278 /* s2 = tmp = y2 * z1**3 */
1279 felem_small_mul(tmp, y2, ftmp);
1280 felem_reduce(ftmp5, tmp);
1281
1282 /* r = ftmp5 = (s2 - s1)*2 */
1283 felem_diff_zero107(ftmp5, ftmp6);
1284 /* ftmp5[i] < 2^107 + 2^107 = 2^108*/
1285 felem_scalar(ftmp5, 2);
1286 /* ftmp5[i] < 2^109 */
1287 felem_shrink(small1, ftmp5);
1288 y_equal = smallfelem_is_zero(small1);
1289
1290 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero)
1291 {
1292 point_double(x3, y3, z3, x1, y1, z1);
1293 return;
1294 }
1295
1296 /* I = ftmp = (2h)**2 */
1297 felem_assign(ftmp, ftmp4);
1298 felem_scalar(ftmp, 2);
1299 /* ftmp[i] < 2*2^108 = 2^109 */
1300 felem_square(tmp, ftmp);
1301 felem_reduce(ftmp, tmp);
1302
1303 /* J = ftmp2 = h * I */
1304 felem_mul(tmp, ftmp4, ftmp);
1305 felem_reduce(ftmp2, tmp);
1306
1307 /* V = ftmp4 = U1 * I */
1308 felem_mul(tmp, ftmp3, ftmp);
1309 felem_reduce(ftmp4, tmp);
1310
1311 /* x_out = r**2 - J - 2V */
1312 smallfelem_square(tmp, small1);
1313 felem_reduce(x_out, tmp);
1314 felem_assign(ftmp3, ftmp4);
1315 felem_scalar(ftmp4, 2);
1316 felem_sum(ftmp4, ftmp2);
1317 /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */
1318 felem_diff(x_out, ftmp4);
1319 /* x_out[i] < 2^105 + 2^101 */
1320
1321 /* y_out = r(V-x_out) - 2 * s1 * J */
1322 felem_diff_zero107(ftmp3, x_out);
1323 /* ftmp3[i] < 2^107 + 2^101 < 2^108 */
1324 felem_small_mul(tmp, small1, ftmp3);
1325 felem_mul(tmp2, ftmp6, ftmp2);
1326 longfelem_scalar(tmp2, 2);
1327 /* tmp2[i] < 2*2^67 = 2^68 */
1328 longfelem_diff(tmp, tmp2);
1329 /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
1330 felem_reduce_zero105(y_out, tmp);
1331 /* y_out[i] < 2^106 */
1332
1333 copy_small_conditional(x_out, x2, z1_is_zero);
1334 copy_conditional(x_out, x1, z2_is_zero);
1335 copy_small_conditional(y_out, y2, z1_is_zero);
1336 copy_conditional(y_out, y1, z2_is_zero);
1337 copy_small_conditional(z_out, z2, z1_is_zero);
1338 copy_conditional(z_out, z1, z2_is_zero);
1339 felem_assign(x3, x_out);
1340 felem_assign(y3, y_out);
1341 felem_assign(z3, z_out);
1342 }
1343
1344 /* point_add_small is the same as point_add, except that it operates on
1345 * smallfelems */
1346 static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3,
1347 smallfelem x1, smallfelem y1, smallfelem z1,
1348 smallfelem x2, smallfelem y2, smallfelem z2)
1349 {
1350 felem felem_x3, felem_y3, felem_z3;
1351 felem felem_x1, felem_y1, felem_z1;
1352 smallfelem_expand(felem_x1, x1);
1353 smallfelem_expand(felem_y1, y1);
1354 smallfelem_expand(felem_z1, z1);
1355 point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, x2, y2, z2);
1356 felem_shrink(x3, felem_x3);
1357 felem_shrink(y3, felem_y3);
1358 felem_shrink(z3, felem_z3);
1359 }
1360
1361 /*-
1362 * Base point pre computation
1363 * --------------------------
1364 *
1365 * Two different sorts of precomputed tables are used in the following code.
1366 * Each contain various points on the curve, where each point is three field
1367 * elements (x, y, z).
1368 *
1369 * For the base point table, z is usually 1 (0 for the point at infinity).
1370 * This table has 2 * 16 elements, starting with the following:
1371 * index | bits | point
1372 * ------+---------+------------------------------
1373 * 0 | 0 0 0 0 | 0G
1374 * 1 | 0 0 0 1 | 1G
1375 * 2 | 0 0 1 0 | 2^64G
1376 * 3 | 0 0 1 1 | (2^64 + 1)G
1377 * 4 | 0 1 0 0 | 2^128G
1378 * 5 | 0 1 0 1 | (2^128 + 1)G
1379 * 6 | 0 1 1 0 | (2^128 + 2^64)G
1380 * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G
1381 * 8 | 1 0 0 0 | 2^192G
1382 * 9 | 1 0 0 1 | (2^192 + 1)G
1383 * 10 | 1 0 1 0 | (2^192 + 2^64)G
1384 * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G
1385 * 12 | 1 1 0 0 | (2^192 + 2^128)G
1386 * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G
1387 * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G
1388 * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G
1389 * followed by a copy of this with each element multiplied by 2^32.
1390 *
1391 * The reason for this is so that we can clock bits into four different
1392 * locations when doing simple scalar multiplies against the base point,
1393 * and then another four locations using the second 16 elements.
1394 *
1395 * Tables for other points have table[i] = iG for i in 0 .. 16. */
1396
1397 /* gmul is the table of precomputed base points */
1398 static const smallfelem gmul[2][16][3] =
1399 {{{{0, 0, 0, 0},
1400 {0, 0, 0, 0},
1401 {0, 0, 0, 0}},
1402 {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247},
1403 {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b},
1404 {1, 0, 0, 0}},
1405 {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5},
1406 {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d},
1407 {1, 0, 0, 0}},
1408 {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f},
1409 {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644},
1410 {1, 0, 0, 0}},
1411 {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67},
1412 {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee},
1413 {1, 0, 0, 0}},
1414 {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff},
1415 {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b},
1416 {1, 0, 0, 0}},
1417 {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8},
1418 {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851},
1419 {1, 0, 0, 0}},
1420 {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea},
1421 {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b},
1422 {1, 0, 0, 0}},
1423 {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276},
1424 {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816},
1425 {1, 0, 0, 0}},
1426 {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad},
1427 {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663},
1428 {1, 0, 0, 0}},
1429 {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d},
1430 {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321},
1431 {1, 0, 0, 0}},
1432 {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287},
1433 {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6},
1434 {1, 0, 0, 0}},
1435 {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466},
1436 {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20},
1437 {1, 0, 0, 0}},
1438 {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9},
1439 {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61},
1440 {1, 0, 0, 0}},
1441 {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a},
1442 {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc},
1443 {1, 0, 0, 0}},
1444 {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c},
1445 {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab},
1446 {1, 0, 0, 0}}},
1447 {{{0, 0, 0, 0},
1448 {0, 0, 0, 0},
1449 {0, 0, 0, 0}},
1450 {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89},
1451 {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624},
1452 {1, 0, 0, 0}},
1453 {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6},
1454 {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1},
1455 {1, 0, 0, 0}},
1456 {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a},
1457 {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593},
1458 {1, 0, 0, 0}},
1459 {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617},
1460 {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7},
1461 {1, 0, 0, 0}},
1462 {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276},
1463 {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a},
1464 {1, 0, 0, 0}},
1465 {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908},
1466 {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e},
1467 {1, 0, 0, 0}},
1468 {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7},
1469 {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec},
1470 {1, 0, 0, 0}},
1471 {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee},
1472 {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6},
1473 {1, 0, 0, 0}},
1474 {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109},
1475 {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5},
1476 {1, 0, 0, 0}},
1477 {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba},
1478 {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44},
1479 {1, 0, 0, 0}},
1480 {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b},
1481 {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc},
1482 {1, 0, 0, 0}},
1483 {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107},
1484 {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387},
1485 {1, 0, 0, 0}},
1486 {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503},
1487 {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be},
1488 {1, 0, 0, 0}},
1489 {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9},
1490 {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a},
1491 {1, 0, 0, 0}},
1492 {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6},
1493 {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81},
1494 {1, 0, 0, 0}}}};
1495
1496 /* select_point selects the |idx|th point from a precomputation table and
1497 * copies it to out. */
1498 static void select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3])
1499 {
1500 unsigned i, j;
1501 u64 *outlimbs = &out[0][0];
1502 memset(outlimbs, 0, 3 * sizeof(smallfelem));
1503
1504 for (i = 0; i < size; i++)
1505 {
1506 const u64 *inlimbs = (u64*) &pre_comp[i][0][0];
1507 u64 mask = i ^ idx;
1508 mask |= mask >> 4;
1509 mask |= mask >> 2;
1510 mask |= mask >> 1;
1511 mask &= 1;
1512 mask--;
1513 for (j = 0; j < NLIMBS * 3; j++)
1514 outlimbs[j] |= inlimbs[j] & mask;
1515 }
1516 }
1517
1518 /* get_bit returns the |i|th bit in |in| */
1519 static char get_bit(const felem_bytearray in, int i)
1520 {
1521 if ((i < 0) || (i >= 256))
1522 return 0;
1523 return (in[i >> 3] >> (i & 7)) & 1;
1524 }
1525
1526 /* Interleaved point multiplication using precomputed point multiples:
1527 * The small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[],
1528 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
1529 * of the generator, using certain (large) precomputed multiples in g_pre_comp.
1530 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
1531 static void batch_mul(felem x_out, felem y_out, felem z_out,
1532 const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar,
1533 const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3])
1534 {
1535 int i, skip;
1536 unsigned num, gen_mul = (g_scalar != NULL);
1537 felem nq[3], ftmp;
1538 smallfelem tmp[3];
1539 u64 bits;
1540 u8 sign, digit;
1541
1542 /* set nq to the point at infinity */
1543 memset(nq, 0, 3 * sizeof(felem));
1544
1545 /* Loop over all scalars msb-to-lsb, interleaving additions
1546 * of multiples of the generator (two in each of the last 32 rounds)
1547 * and additions of other points multiples (every 5th round).
1548 */
1549 skip = 1; /* save two point operations in the first round */
1550 for (i = (num_points ? 255 : 31); i >= 0; --i)
1551 {
1552 /* double */
1553 if (!skip)
1554 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
1555
1556 /* add multiples of the generator */
1557 if (gen_mul && (i <= 31))
1558 {
1559 /* first, look 32 bits upwards */
1560 bits = get_bit(g_scalar, i + 224) << 3;
1561 bits |= get_bit(g_scalar, i + 160) << 2;
1562 bits |= get_bit(g_scalar, i + 96) << 1;
1563 bits |= get_bit(g_scalar, i + 32);
1564 /* select the point to add, in constant time */
1565 select_point(bits, 16, g_pre_comp[1], tmp);
1566
1567 if (!skip)
1568 {
1569 point_add(nq[0], nq[1], nq[2],
1570 nq[0], nq[1], nq[2],
1571 1 /* mixed */, tmp[0], tmp[1], tmp[2]);
1572 }
1573 else
1574 {
1575 smallfelem_expand(nq[0], tmp[0]);
1576 smallfelem_expand(nq[1], tmp[1]);
1577 smallfelem_expand(nq[2], tmp[2]);
1578 skip = 0;
1579 }
1580
1581 /* second, look at the current position */
1582 bits = get_bit(g_scalar, i + 192) << 3;
1583 bits |= get_bit(g_scalar, i + 128) << 2;
1584 bits |= get_bit(g_scalar, i + 64) << 1;
1585 bits |= get_bit(g_scalar, i);
1586 /* select the point to add, in constant time */
1587 select_point(bits, 16, g_pre_comp[0], tmp);
1588 point_add(nq[0], nq[1], nq[2],
1589 nq[0], nq[1], nq[2],
1590 1 /* mixed */, tmp[0], tmp[1], tmp[2]);
1591 }
1592
1593 /* do other additions every 5 doublings */
1594 if (num_points && (i % 5 == 0))
1595 {
1596 /* loop over all scalars */
1597 for (num = 0; num < num_points; ++num)
1598 {
1599 bits = get_bit(scalars[num], i + 4) << 5;
1600 bits |= get_bit(scalars[num], i + 3) << 4;
1601 bits |= get_bit(scalars[num], i + 2) << 3;
1602 bits |= get_bit(scalars[num], i + 1) << 2;
1603 bits |= get_bit(scalars[num], i) << 1;
1604 bits |= get_bit(scalars[num], i - 1);
1605 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
1606
1607 /* select the point to add or subtract, in constant time */
1608 select_point(digit, 17, pre_comp[num], tmp);
1609 smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative point */
1610 copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1));
1611 felem_contract(tmp[1], ftmp);
1612
1613 if (!skip)
1614 {
1615 point_add(nq[0], nq[1], nq[2],
1616 nq[0], nq[1], nq[2],
1617 mixed, tmp[0], tmp[1], tmp[2]);
1618 }
1619 else
1620 {
1621 smallfelem_expand(nq[0], tmp[0]);
1622 smallfelem_expand(nq[1], tmp[1]);
1623 smallfelem_expand(nq[2], tmp[2]);
1624 skip = 0;
1625 }
1626 }
1627 }
1628 }
1629 felem_assign(x_out, nq[0]);
1630 felem_assign(y_out, nq[1]);
1631 felem_assign(z_out, nq[2]);
1632 }
1633
1634 /* Precomputation for the group generator. */
1635 typedef struct {
1636 smallfelem g_pre_comp[2][16][3];
1637 int references;
1638 } NISTP256_PRE_COMP;
1639
1640 const EC_METHOD *EC_GFp_nistp256_method(void)
1641 {
1642 static const EC_METHOD ret = {
1643 EC_FLAGS_DEFAULT_OCT,
1644 NID_X9_62_prime_field,
1645 ec_GFp_nistp256_group_init,
1646 ec_GFp_simple_group_finish,
1647 ec_GFp_simple_group_clear_finish,
1648 ec_GFp_nist_group_copy,
1649 ec_GFp_nistp256_group_set_curve,
1650 ec_GFp_simple_group_get_curve,
1651 ec_GFp_simple_group_get_degree,
1652 ec_GFp_simple_group_check_discriminant,
1653 ec_GFp_simple_point_init,
1654 ec_GFp_simple_point_finish,
1655 ec_GFp_simple_point_clear_finish,
1656 ec_GFp_simple_point_copy,
1657 ec_GFp_simple_point_set_to_infinity,
1658 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1659 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1660 ec_GFp_simple_point_set_affine_coordinates,
1661 ec_GFp_nistp256_point_get_affine_coordinates,
1662 0 /* point_set_compressed_coordinates */,
1663 0 /* point2oct */,
1664 0 /* oct2point */,
1665 ec_GFp_simple_add,
1666 ec_GFp_simple_dbl,
1667 ec_GFp_simple_invert,
1668 ec_GFp_simple_is_at_infinity,
1669 ec_GFp_simple_is_on_curve,
1670 ec_GFp_simple_cmp,
1671 ec_GFp_simple_make_affine,
1672 ec_GFp_simple_points_make_affine,
1673 ec_GFp_nistp256_points_mul,
1674 ec_GFp_nistp256_precompute_mult,
1675 ec_GFp_nistp256_have_precompute_mult,
1676 ec_GFp_nist_field_mul,
1677 ec_GFp_nist_field_sqr,
1678 0 /* field_div */,
1679 0 /* field_encode */,
1680 0 /* field_decode */,
1681 0 /* field_set_to_one */ };
1682
1683 return &ret;
1684 }
1685
1686 /******************************************************************************/
1687 /* FUNCTIONS TO MANAGE PRECOMPUTATION
1688 */
1689
1690 static NISTP256_PRE_COMP *nistp256_pre_comp_new()
1691 {
1692 NISTP256_PRE_COMP *ret = NULL;
1693 ret = (NISTP256_PRE_COMP *) OPENSSL_malloc(sizeof *ret);
1694 if (!ret)
1695 {
1696 ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1697 return ret;
1698 }
1699 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1700 ret->references = 1;
1701 return ret;
1702 }
1703
1704 static void *nistp256_pre_comp_dup(void *src_)
1705 {
1706 NISTP256_PRE_COMP *src = src_;
1707
1708 /* no need to actually copy, these objects never change! */
1709 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1710
1711 return src_;
1712 }
1713
1714 static void nistp256_pre_comp_free(void *pre_)
1715 {
1716 int i;
1717 NISTP256_PRE_COMP *pre = pre_;
1718
1719 if (!pre)
1720 return;
1721
1722 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1723 if (i > 0)
1724 return;
1725
1726 OPENSSL_free(pre);
1727 }
1728
1729 static void nistp256_pre_comp_clear_free(void *pre_)
1730 {
1731 int i;
1732 NISTP256_PRE_COMP *pre = pre_;
1733
1734 if (!pre)
1735 return;
1736
1737 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1738 if (i > 0)
1739 return;
1740
1741 OPENSSL_cleanse(pre, sizeof *pre);
1742 OPENSSL_free(pre);
1743 }
1744
1745 /******************************************************************************/
1746 /* OPENSSL EC_METHOD FUNCTIONS
1747 */
1748
1749 int ec_GFp_nistp256_group_init(EC_GROUP *group)
1750 {
1751 int ret;
1752 ret = ec_GFp_simple_group_init(group);
1753 group->a_is_minus3 = 1;
1754 return ret;
1755 }
1756
1757 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
1758 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1759 {
1760 int ret = 0;
1761 BN_CTX *new_ctx = NULL;
1762 BIGNUM *curve_p, *curve_a, *curve_b;
1763
1764 if (ctx == NULL)
1765 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1766 BN_CTX_start(ctx);
1767 if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1768 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1769 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err;
1770 BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p);
1771 BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a);
1772 BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b);
1773 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1774 (BN_cmp(curve_b, b)))
1775 {
1776 ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE,
1777 EC_R_WRONG_CURVE_PARAMETERS);
1778 goto err;
1779 }
1780 group->field_mod_func = BN_nist_mod_256;
1781 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1782 err:
1783 BN_CTX_end(ctx);
1784 if (new_ctx != NULL)
1785 BN_CTX_free(new_ctx);
1786 return ret;
1787 }
1788
1789 /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1790 * (X', Y') = (X/Z^2, Y/Z^3) */
1791 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
1792 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1793 {
1794 felem z1, z2, x_in, y_in;
1795 smallfelem x_out, y_out;
1796 longfelem tmp;
1797
1798 if (EC_POINT_is_at_infinity(group, point))
1799 {
1800 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
1801 EC_R_POINT_AT_INFINITY);
1802 return 0;
1803 }
1804 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1805 (!BN_to_felem(z1, &point->Z))) return 0;
1806 felem_inv(z2, z1);
1807 felem_square(tmp, z2); felem_reduce(z1, tmp);
1808 felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp);
1809 felem_contract(x_out, x_in);
1810 if (x != NULL)
1811 {
1812 if (!smallfelem_to_BN(x, x_out)) {
1813 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
1814 ERR_R_BN_LIB);
1815 return 0;
1816 }
1817 }
1818 felem_mul(tmp, z1, z2); felem_reduce(z1, tmp);
1819 felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp);
1820 felem_contract(y_out, y_in);
1821 if (y != NULL)
1822 {
1823 if (!smallfelem_to_BN(y, y_out))
1824 {
1825 ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES,
1826 ERR_R_BN_LIB);
1827 return 0;
1828 }
1829 }
1830 return 1;
1831 }
1832
1833 static void make_points_affine(size_t num, smallfelem points[/* num */][3], smallfelem tmp_smallfelems[/* num+1 */])
1834 {
1835 /* Runs in constant time, unless an input is the point at infinity
1836 * (which normally shouldn't happen). */
1837 ec_GFp_nistp_points_make_affine_internal(
1838 num,
1839 points,
1840 sizeof(smallfelem),
1841 tmp_smallfelems,
1842 (void (*)(void *)) smallfelem_one,
1843 (int (*)(const void *)) smallfelem_is_zero_int,
1844 (void (*)(void *, const void *)) smallfelem_assign,
1845 (void (*)(void *, const void *)) smallfelem_square_contract,
1846 (void (*)(void *, const void *, const void *)) smallfelem_mul_contract,
1847 (void (*)(void *, const void *)) smallfelem_inv_contract,
1848 (void (*)(void *, const void *)) smallfelem_assign /* nothing to contract */);
1849 }
1850
1851 /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1852 * Result is stored in r (r can equal one of the inputs). */
1853 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
1854 const BIGNUM *scalar, size_t num, const EC_POINT *points[],
1855 const BIGNUM *scalars[], BN_CTX *ctx)
1856 {
1857 int ret = 0;
1858 int j;
1859 int mixed = 0;
1860 BN_CTX *new_ctx = NULL;
1861 BIGNUM *x, *y, *z, *tmp_scalar;
1862 felem_bytearray g_secret;
1863 felem_bytearray *secrets = NULL;
1864 smallfelem (*pre_comp)[17][3] = NULL;
1865 smallfelem *tmp_smallfelems = NULL;
1866 felem_bytearray tmp;
1867 unsigned i, num_bytes;
1868 int have_pre_comp = 0;
1869 size_t num_points = num;
1870 smallfelem x_in, y_in, z_in;
1871 felem x_out, y_out, z_out;
1872 NISTP256_PRE_COMP *pre = NULL;
1873 const smallfelem (*g_pre_comp)[16][3] = NULL;
1874 EC_POINT *generator = NULL;
1875 const EC_POINT *p = NULL;
1876 const BIGNUM *p_scalar = NULL;
1877
1878 if (ctx == NULL)
1879 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1880 BN_CTX_start(ctx);
1881 if (((x = BN_CTX_get(ctx)) == NULL) ||
1882 ((y = BN_CTX_get(ctx)) == NULL) ||
1883 ((z = BN_CTX_get(ctx)) == NULL) ||
1884 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1885 goto err;
1886
1887 if (scalar != NULL)
1888 {
1889 pre = EC_EX_DATA_get_data(group->extra_data,
1890 nistp256_pre_comp_dup, nistp256_pre_comp_free,
1891 nistp256_pre_comp_clear_free);
1892 if (pre)
1893 /* we have precomputation, try to use it */
1894 g_pre_comp = (const smallfelem (*)[16][3]) pre->g_pre_comp;
1895 else
1896 /* try to use the standard precomputation */
1897 g_pre_comp = &gmul[0];
1898 generator = EC_POINT_new(group);
1899 if (generator == NULL)
1900 goto err;
1901 /* get the generator from precomputation */
1902 if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) ||
1903 !smallfelem_to_BN(y, g_pre_comp[0][1][1]) ||
1904 !smallfelem_to_BN(z, g_pre_comp[0][1][2]))
1905 {
1906 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
1907 goto err;
1908 }
1909 if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1910 generator, x, y, z, ctx))
1911 goto err;
1912 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1913 /* precomputation matches generator */
1914 have_pre_comp = 1;
1915 else
1916 /* we don't have valid precomputation:
1917 * treat the generator as a random point */
1918 num_points++;
1919 }
1920 if (num_points > 0)
1921 {
1922 if (num_points >= 3)
1923 {
1924 /* unless we precompute multiples for just one or two points,
1925 * converting those into affine form is time well spent */
1926 mixed = 1;
1927 }
1928 secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray));
1929 pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(smallfelem));
1930 if (mixed)
1931 tmp_smallfelems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(smallfelem));
1932 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL)))
1933 {
1934 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1935 goto err;
1936 }
1937
1938 /* we treat NULL scalars as 0, and NULL points as points at infinity,
1939 * i.e., they contribute nothing to the linear combination */
1940 memset(secrets, 0, num_points * sizeof(felem_bytearray));
1941 memset(pre_comp, 0, num_points * 17 * 3 * sizeof(smallfelem));
1942 for (i = 0; i < num_points; ++i)
1943 {
1944 if (i == num)
1945 /* we didn't have a valid precomputation, so we pick
1946 * the generator */
1947 {
1948 p = EC_GROUP_get0_generator(group);
1949 p_scalar = scalar;
1950 }
1951 else
1952 /* the i^th point */
1953 {
1954 p = points[i];
1955 p_scalar = scalars[i];
1956 }
1957 if ((p_scalar != NULL) && (p != NULL))
1958 {
1959 /* reduce scalar to 0 <= scalar < 2^256 */
1960 if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar)))
1961 {
1962 /* this is an unusual input, and we don't guarantee
1963 * constant-timeness */
1964 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx))
1965 {
1966 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
1967 goto err;
1968 }
1969 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1970 }
1971 else
1972 num_bytes = BN_bn2bin(p_scalar, tmp);
1973 flip_endian(secrets[i], tmp, num_bytes);
1974 /* precompute multiples */
1975 if ((!BN_to_felem(x_out, &p->X)) ||
1976 (!BN_to_felem(y_out, &p->Y)) ||
1977 (!BN_to_felem(z_out, &p->Z))) goto err;
1978 felem_shrink(pre_comp[i][1][0], x_out);
1979 felem_shrink(pre_comp[i][1][1], y_out);
1980 felem_shrink(pre_comp[i][1][2], z_out);
1981 for (j = 2; j <= 16; ++j)
1982 {
1983 if (j & 1)
1984 {
1985 point_add_small(
1986 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1987 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
1988 pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]);
1989 }
1990 else
1991 {
1992 point_double_small(
1993 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1994 pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]);
1995 }
1996 }
1997 }
1998 }
1999 if (mixed)
2000 make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems);
2001 }
2002
2003 /* the scalar for the generator */
2004 if ((scalar != NULL) && (have_pre_comp))
2005 {
2006 memset(g_secret, 0, sizeof(g_secret));
2007 /* reduce scalar to 0 <= scalar < 2^256 */
2008 if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar)))
2009 {
2010 /* this is an unusual input, and we don't guarantee
2011 * constant-timeness */
2012 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx))
2013 {
2014 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
2015 goto err;
2016 }
2017 num_bytes = BN_bn2bin(tmp_scalar, tmp);
2018 }
2019 else
2020 num_bytes = BN_bn2bin(scalar, tmp);
2021 flip_endian(g_secret, tmp, num_bytes);
2022 /* do the multiplication with generator precomputation*/
2023 batch_mul(x_out, y_out, z_out,
2024 (const felem_bytearray (*)) secrets, num_points,
2025 g_secret,
2026 mixed, (const smallfelem (*)[17][3]) pre_comp,
2027 g_pre_comp);
2028 }
2029 else
2030 /* do the multiplication without generator precomputation */
2031 batch_mul(x_out, y_out, z_out,
2032 (const felem_bytearray (*)) secrets, num_points,
2033 NULL, mixed, (const smallfelem (*)[17][3]) pre_comp, NULL);
2034 /* reduce the output to its unique minimal representation */
2035 felem_contract(x_in, x_out);
2036 felem_contract(y_in, y_out);
2037 felem_contract(z_in, z_out);
2038 if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) ||
2039 (!smallfelem_to_BN(z, z_in)))
2040 {
2041 ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB);
2042 goto err;
2043 }
2044 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
2045
2046 err:
2047 BN_CTX_end(ctx);
2048 if (generator != NULL)
2049 EC_POINT_free(generator);
2050 if (new_ctx != NULL)
2051 BN_CTX_free(new_ctx);
2052 if (secrets != NULL)
2053 OPENSSL_free(secrets);
2054 if (pre_comp != NULL)
2055 OPENSSL_free(pre_comp);
2056 if (tmp_smallfelems != NULL)
2057 OPENSSL_free(tmp_smallfelems);
2058 return ret;
2059 }
2060
2061 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
2062 {
2063 int ret = 0;
2064 NISTP256_PRE_COMP *pre = NULL;
2065 int i, j;
2066 BN_CTX *new_ctx = NULL;
2067 BIGNUM *x, *y;
2068 EC_POINT *generator = NULL;
2069 smallfelem tmp_smallfelems[32];
2070 felem x_tmp, y_tmp, z_tmp;
2071
2072 /* throw away old precomputation */
2073 EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup,
2074 nistp256_pre_comp_free, nistp256_pre_comp_clear_free);
2075 if (ctx == NULL)
2076 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
2077 BN_CTX_start(ctx);
2078 if (((x = BN_CTX_get(ctx)) == NULL) ||
2079 ((y = BN_CTX_get(ctx)) == NULL))
2080 goto err;
2081 /* get the generator */
2082 if (group->generator == NULL) goto err;
2083 generator = EC_POINT_new(group);
2084 if (generator == NULL)
2085 goto err;
2086 BN_bin2bn(nistp256_curve_params[3], sizeof (felem_bytearray), x);
2087 BN_bin2bn(nistp256_curve_params[4], sizeof (felem_bytearray), y);
2088 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
2089 goto err;
2090 if ((pre = nistp256_pre_comp_new()) == NULL)
2091 goto err;
2092 /* if the generator is the standard one, use built-in precomputation */
2093 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
2094 {
2095 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
2096 ret = 1;
2097 goto err;
2098 }
2099 if ((!BN_to_felem(x_tmp, &group->generator->X)) ||
2100 (!BN_to_felem(y_tmp, &group->generator->Y)) ||
2101 (!BN_to_felem(z_tmp, &group->generator->Z)))
2102 goto err;
2103 felem_shrink(pre->g_pre_comp[0][1][0], x_tmp);
2104 felem_shrink(pre->g_pre_comp[0][1][1], y_tmp);
2105 felem_shrink(pre->g_pre_comp[0][1][2], z_tmp);
2106 /* compute 2^64*G, 2^128*G, 2^192*G for the first table,
2107 * 2^32*G, 2^96*G, 2^160*G, 2^224*G for the second one
2108 */
2109 for (i = 1; i <= 8; i <<= 1)
2110 {
2111 point_double_small(
2112 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
2113 pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]);
2114 for (j = 0; j < 31; ++j)
2115 {
2116 point_double_small(
2117 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
2118 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
2119 }
2120 if (i == 8)
2121 break;
2122 point_double_small(
2123 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2],
2124 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
2125 for (j = 0; j < 31; ++j)
2126 {
2127 point_double_small(
2128 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2],
2129 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]);
2130 }
2131 }
2132 for (i = 0; i < 2; i++)
2133 {
2134 /* g_pre_comp[i][0] is the point at infinity */
2135 memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0]));
2136 /* the remaining multiples */
2137 /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */
2138 point_add_small(
2139 pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2],
2140 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2],
2141 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]);
2142 /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */
2143 point_add_small(
2144 pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2],
2145 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
2146 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]);
2147 /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */
2148 point_add_small(
2149 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
2150 pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
2151 pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]);
2152 /* 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G */
2153 point_add_small(
2154 pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2],
2155 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
2156 pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]);
2157 for (j = 1; j < 8; ++j)
2158 {
2159 /* odd multiples: add G resp. 2^32*G */
2160 point_add_small(
2161 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],
2162 pre->g_pre_comp[i][2*j][0], pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2],
2163 pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]);
2164 }
2165 }
2166 make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems);
2167
2168 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup,
2169 nistp256_pre_comp_free, nistp256_pre_comp_clear_free))
2170 goto err;
2171 ret = 1;
2172 pre = NULL;
2173 err:
2174 BN_CTX_end(ctx);
2175 if (generator != NULL)
2176 EC_POINT_free(generator);
2177 if (new_ctx != NULL)
2178 BN_CTX_free(new_ctx);
2179 if (pre)
2180 nistp256_pre_comp_free(pre);
2181 return ret;
2182 }
2183
2184 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group)
2185 {
2186 if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup,
2187 nistp256_pre_comp_free, nistp256_pre_comp_clear_free)
2188 != NULL)
2189 return 1;
2190 else
2191 return 0;
2192 }
2193 #else
2194 static void *dummy=&dummy;
2195 #endif
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