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3e00b4c9 BM |
1 | /* |
2 | * Written by Adam Langley (Google) for the OpenSSL project | |
3 | */ | |
4 | /* Copyright 2011 Google Inc. | |
5 | * | |
6 | * Licensed under the Apache License, Version 2.0 (the "License"); | |
7 | * | |
8 | * you may not use this file except in compliance with the License. | |
9 | * You may obtain a copy of the License at | |
10 | * | |
11 | * http://www.apache.org/licenses/LICENSE-2.0 | |
12 | * | |
13 | * Unless required by applicable law or agreed to in writing, software | |
14 | * distributed under the License is distributed on an "AS IS" BASIS, | |
15 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
16 | * See the License for the specific language governing permissions and | |
17 | * limitations under the License. | |
18 | */ | |
19 | ||
20 | /* | |
21 | * A 64-bit implementation of the NIST P-256 elliptic curve point multiplication | |
22 | * | |
23 | * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. | |
24 | * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 | |
25 | * work which got its smarts from Daniel J. Bernstein's work on the same. | |
26 | */ | |
27 | ||
e0d6132b | 28 | #include <openssl/opensslconf.h> |
effaf4de RS |
29 | #ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 |
30 | NON_EMPTY_TRANSLATION_UNIT | |
31 | #else | |
3e00b4c9 | 32 | |
0f113f3e MC |
33 | # include <stdint.h> |
34 | # include <string.h> | |
35 | # include <openssl/err.h> | |
36 | # include "ec_lcl.h" | |
3e00b4c9 | 37 | |
0f113f3e | 38 | # if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) |
3e00b4c9 | 39 | /* even with gcc, the typedef won't work for 32-bit platforms */ |
0f113f3e MC |
40 | typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit |
41 | * platforms */ | |
42 | typedef __int128_t int128_t; | |
43 | # else | |
44 | # error "Need GCC 3.1 or later to define type uint128_t" | |
45 | # endif | |
3e00b4c9 BM |
46 | |
47 | typedef uint8_t u8; | |
48 | typedef uint32_t u32; | |
49 | typedef uint64_t u64; | |
50 | typedef int64_t s64; | |
51 | ||
0f113f3e MC |
52 | /* |
53 | * The underlying field. P256 operates over GF(2^256-2^224+2^192+2^96-1). We | |
54 | * can serialise an element of this field into 32 bytes. We call this an | |
55 | * felem_bytearray. | |
56 | */ | |
3e00b4c9 BM |
57 | |
58 | typedef u8 felem_bytearray[32]; | |
59 | ||
0f113f3e MC |
60 | /* |
61 | * These are the parameters of P256, taken from FIPS 186-3, page 86. These | |
62 | * values are big-endian. | |
63 | */ | |
3e00b4c9 | 64 | static const felem_bytearray nistp256_curve_params[5] = { |
0f113f3e MC |
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} | |
3e00b4c9 BM |
85 | }; |
86 | ||
1d97c843 TH |
87 | /*- |
88 | * The representation of field elements. | |
3e00b4c9 BM |
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 | ||
0f113f3e | 108 | # define NLIMBS 4 |
3e00b4c9 BM |
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. */ | |
0f113f3e MC |
116 | static const u64 kPrime[4] = |
117 | { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; | |
3e00b4c9 BM |
118 | static const u64 bottom63bits = 0x7ffffffffffffffful; |
119 | ||
0f113f3e MC |
120 | /* |
121 | * bin32_to_felem takes a little-endian byte array and converts it into felem | |
122 | * form. This assumes that the CPU is little-endian. | |
123 | */ | |
3e00b4c9 | 124 | static void bin32_to_felem(felem out, const u8 in[32]) |
0f113f3e MC |
125 | { |
126 | out[0] = *((u64 *)&in[0]); | |
127 | out[1] = *((u64 *)&in[8]); | |
128 | out[2] = *((u64 *)&in[16]); | |
129 | out[3] = *((u64 *)&in[24]); | |
130 | } | |
131 | ||
132 | /* | |
133 | * smallfelem_to_bin32 takes a smallfelem and serialises into a little | |
134 | * endian, 32 byte array. This assumes that the CPU is little-endian. | |
135 | */ | |
3e00b4c9 | 136 | static void smallfelem_to_bin32(u8 out[32], const smallfelem in) |
0f113f3e MC |
137 | { |
138 | *((u64 *)&out[0]) = in[0]; | |
139 | *((u64 *)&out[8]) = in[1]; | |
140 | *((u64 *)&out[16]) = in[2]; | |
141 | *((u64 *)&out[24]) = in[3]; | |
142 | } | |
3e00b4c9 BM |
143 | |
144 | /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ | |
145 | static void flip_endian(u8 *out, const u8 *in, unsigned len) | |
0f113f3e MC |
146 | { |
147 | unsigned i; | |
148 | for (i = 0; i < len; ++i) | |
149 | out[i] = in[len - 1 - i]; | |
150 | } | |
3e00b4c9 BM |
151 | |
152 | /* BN_to_felem converts an OpenSSL BIGNUM into an felem */ | |
153 | static int BN_to_felem(felem out, const BIGNUM *bn) | |
0f113f3e MC |
154 | { |
155 | felem_bytearray b_in; | |
156 | felem_bytearray b_out; | |
157 | unsigned num_bytes; | |
158 | ||
159 | /* BN_bn2bin eats leading zeroes */ | |
16f8d4eb | 160 | memset(b_out, 0, sizeof(b_out)); |
0f113f3e MC |
161 | num_bytes = BN_num_bytes(bn); |
162 | if (num_bytes > sizeof b_out) { | |
163 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); | |
164 | return 0; | |
165 | } | |
166 | if (BN_is_negative(bn)) { | |
167 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); | |
168 | return 0; | |
169 | } | |
170 | num_bytes = BN_bn2bin(bn, b_in); | |
171 | flip_endian(b_out, b_in, num_bytes); | |
172 | bin32_to_felem(out, b_out); | |
173 | return 1; | |
174 | } | |
3e00b4c9 BM |
175 | |
176 | /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ | |
177 | static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) | |
0f113f3e MC |
178 | { |
179 | felem_bytearray b_in, b_out; | |
180 | smallfelem_to_bin32(b_in, in); | |
181 | flip_endian(b_out, b_in, sizeof b_out); | |
182 | return BN_bin2bn(b_out, sizeof b_out, out); | |
183 | } | |
3e00b4c9 | 184 | |
3a83462d MC |
185 | /*- |
186 | * Field operations | |
187 | * ---------------- | |
188 | */ | |
3e00b4c9 BM |
189 | |
190 | static void smallfelem_one(smallfelem out) | |
0f113f3e MC |
191 | { |
192 | out[0] = 1; | |
193 | out[1] = 0; | |
194 | out[2] = 0; | |
195 | out[3] = 0; | |
196 | } | |
3e00b4c9 BM |
197 | |
198 | static void smallfelem_assign(smallfelem out, const smallfelem in) | |
0f113f3e MC |
199 | { |
200 | out[0] = in[0]; | |
201 | out[1] = in[1]; | |
202 | out[2] = in[2]; | |
203 | out[3] = in[3]; | |
204 | } | |
3e00b4c9 BM |
205 | |
206 | static void felem_assign(felem out, const felem in) | |
0f113f3e MC |
207 | { |
208 | out[0] = in[0]; | |
209 | out[1] = in[1]; | |
210 | out[2] = in[2]; | |
211 | out[3] = in[3]; | |
212 | } | |
3e00b4c9 BM |
213 | |
214 | /* felem_sum sets out = out + in. */ | |
215 | static void felem_sum(felem out, const felem in) | |
0f113f3e MC |
216 | { |
217 | out[0] += in[0]; | |
218 | out[1] += in[1]; | |
219 | out[2] += in[2]; | |
220 | out[3] += in[3]; | |
221 | } | |
3e00b4c9 BM |
222 | |
223 | /* felem_small_sum sets out = out + in. */ | |
224 | static void felem_small_sum(felem out, const smallfelem in) | |
0f113f3e MC |
225 | { |
226 | out[0] += in[0]; | |
227 | out[1] += in[1]; | |
228 | out[2] += in[2]; | |
229 | out[3] += in[3]; | |
230 | } | |
3e00b4c9 BM |
231 | |
232 | /* felem_scalar sets out = out * scalar */ | |
233 | static void felem_scalar(felem out, const u64 scalar) | |
0f113f3e MC |
234 | { |
235 | out[0] *= scalar; | |
236 | out[1] *= scalar; | |
237 | out[2] *= scalar; | |
238 | out[3] *= scalar; | |
239 | } | |
3e00b4c9 BM |
240 | |
241 | /* longfelem_scalar sets out = out * scalar */ | |
242 | static void longfelem_scalar(longfelem out, const u64 scalar) | |
0f113f3e MC |
243 | { |
244 | out[0] *= scalar; | |
245 | out[1] *= scalar; | |
246 | out[2] *= scalar; | |
247 | out[3] *= scalar; | |
248 | out[4] *= scalar; | |
249 | out[5] *= scalar; | |
250 | out[6] *= scalar; | |
251 | out[7] *= scalar; | |
252 | } | |
253 | ||
254 | # define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) | |
255 | # define two105 (((limb)1) << 105) | |
256 | # define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) | |
3e00b4c9 BM |
257 | |
258 | /* zero105 is 0 mod p */ | |
0f113f3e MC |
259 | static const felem zero105 = |
260 | { two105m41m9, two105, two105m41p9, two105m41p9 }; | |
3e00b4c9 | 261 | |
1d97c843 TH |
262 | /*- |
263 | * smallfelem_neg sets |out| to |-small| | |
3e00b4c9 BM |
264 | * On exit: |
265 | * out[i] < out[i] + 2^105 | |
266 | */ | |
267 | static void smallfelem_neg(felem out, const smallfelem small) | |
0f113f3e MC |
268 | { |
269 | /* In order to prevent underflow, we subtract from 0 mod p. */ | |
270 | out[0] = zero105[0] - small[0]; | |
271 | out[1] = zero105[1] - small[1]; | |
272 | out[2] = zero105[2] - small[2]; | |
273 | out[3] = zero105[3] - small[3]; | |
274 | } | |
3e00b4c9 | 275 | |
1d97c843 TH |
276 | /*- |
277 | * felem_diff subtracts |in| from |out| | |
3e00b4c9 BM |
278 | * On entry: |
279 | * in[i] < 2^104 | |
280 | * On exit: | |
281 | * out[i] < out[i] + 2^105 | |
282 | */ | |
283 | static void felem_diff(felem out, const felem in) | |
0f113f3e MC |
284 | { |
285 | /* | |
286 | * In order to prevent underflow, we add 0 mod p before subtracting. | |
287 | */ | |
288 | out[0] += zero105[0]; | |
289 | out[1] += zero105[1]; | |
290 | out[2] += zero105[2]; | |
291 | out[3] += zero105[3]; | |
292 | ||
293 | out[0] -= in[0]; | |
294 | out[1] -= in[1]; | |
295 | out[2] -= in[2]; | |
296 | out[3] -= in[3]; | |
297 | } | |
298 | ||
299 | # define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) | |
300 | # define two107 (((limb)1) << 107) | |
301 | # define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) | |
3e00b4c9 BM |
302 | |
303 | /* zero107 is 0 mod p */ | |
0f113f3e MC |
304 | static const felem zero107 = |
305 | { two107m43m11, two107, two107m43p11, two107m43p11 }; | |
3e00b4c9 | 306 | |
1d97c843 TH |
307 | /*- |
308 | * An alternative felem_diff for larger inputs |in| | |
3e00b4c9 BM |
309 | * felem_diff_zero107 subtracts |in| from |out| |
310 | * On entry: | |
311 | * in[i] < 2^106 | |
312 | * On exit: | |
313 | * out[i] < out[i] + 2^107 | |
314 | */ | |
315 | static void felem_diff_zero107(felem out, const felem in) | |
0f113f3e MC |
316 | { |
317 | /* | |
318 | * In order to prevent underflow, we add 0 mod p before subtracting. | |
319 | */ | |
320 | out[0] += zero107[0]; | |
321 | out[1] += zero107[1]; | |
322 | out[2] += zero107[2]; | |
323 | out[3] += zero107[3]; | |
324 | ||
325 | out[0] -= in[0]; | |
326 | out[1] -= in[1]; | |
327 | out[2] -= in[2]; | |
328 | out[3] -= in[3]; | |
329 | } | |
3e00b4c9 | 330 | |
1d97c843 TH |
331 | /*- |
332 | * longfelem_diff subtracts |in| from |out| | |
3e00b4c9 BM |
333 | * On entry: |
334 | * in[i] < 7*2^67 | |
335 | * On exit: | |
336 | * out[i] < out[i] + 2^70 + 2^40 | |
337 | */ | |
338 | static void longfelem_diff(longfelem out, const longfelem in) | |
0f113f3e MC |
339 | { |
340 | static const limb two70m8p6 = | |
341 | (((limb) 1) << 70) - (((limb) 1) << 8) + (((limb) 1) << 6); | |
342 | static const limb two70p40 = (((limb) 1) << 70) + (((limb) 1) << 40); | |
343 | static const limb two70 = (((limb) 1) << 70); | |
344 | static const limb two70m40m38p6 = | |
345 | (((limb) 1) << 70) - (((limb) 1) << 40) - (((limb) 1) << 38) + | |
346 | (((limb) 1) << 6); | |
347 | static const limb two70m6 = (((limb) 1) << 70) - (((limb) 1) << 6); | |
348 | ||
349 | /* add 0 mod p to avoid underflow */ | |
350 | out[0] += two70m8p6; | |
351 | out[1] += two70p40; | |
352 | out[2] += two70; | |
353 | out[3] += two70m40m38p6; | |
354 | out[4] += two70m6; | |
355 | out[5] += two70m6; | |
356 | out[6] += two70m6; | |
357 | out[7] += two70m6; | |
358 | ||
359 | /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */ | |
360 | out[0] -= in[0]; | |
361 | out[1] -= in[1]; | |
362 | out[2] -= in[2]; | |
363 | out[3] -= in[3]; | |
364 | out[4] -= in[4]; | |
365 | out[5] -= in[5]; | |
366 | out[6] -= in[6]; | |
367 | out[7] -= in[7]; | |
368 | } | |
369 | ||
370 | # define two64m0 (((limb)1) << 64) - 1 | |
371 | # define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 | |
372 | # define two64m46 (((limb)1) << 64) - (((limb)1) << 46) | |
373 | # define two64m32 (((limb)1) << 64) - (((limb)1) << 32) | |
3e00b4c9 BM |
374 | |
375 | /* zero110 is 0 mod p */ | |
376 | static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; | |
377 | ||
1d97c843 TH |
378 | /*- |
379 | * felem_shrink converts an felem into a smallfelem. The result isn't quite | |
3e00b4c9 BM |
380 | * minimal as the value may be greater than p. |
381 | * | |
382 | * On entry: | |
383 | * in[i] < 2^109 | |
384 | * On exit: | |
385 | * out[i] < 2^64 | |
386 | */ | |
387 | static void felem_shrink(smallfelem out, const felem in) | |
0f113f3e MC |
388 | { |
389 | felem tmp; | |
390 | u64 a, b, mask; | |
391 | s64 high, low; | |
392 | static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ | |
393 | ||
394 | /* Carry 2->3 */ | |
395 | tmp[3] = zero110[3] + in[3] + ((u64)(in[2] >> 64)); | |
396 | /* tmp[3] < 2^110 */ | |
397 | ||
398 | tmp[2] = zero110[2] + (u64)in[2]; | |
399 | tmp[0] = zero110[0] + in[0]; | |
400 | tmp[1] = zero110[1] + in[1]; | |
401 | /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ | |
402 | ||
403 | /* | |
404 | * We perform two partial reductions where we eliminate the high-word of | |
405 | * tmp[3]. We don't update the other words till the end. | |
406 | */ | |
407 | a = tmp[3] >> 64; /* a < 2^46 */ | |
408 | tmp[3] = (u64)tmp[3]; | |
409 | tmp[3] -= a; | |
410 | tmp[3] += ((limb) a) << 32; | |
411 | /* tmp[3] < 2^79 */ | |
412 | ||
413 | b = a; | |
414 | a = tmp[3] >> 64; /* a < 2^15 */ | |
415 | b += a; /* b < 2^46 + 2^15 < 2^47 */ | |
416 | tmp[3] = (u64)tmp[3]; | |
417 | tmp[3] -= a; | |
418 | tmp[3] += ((limb) a) << 32; | |
419 | /* tmp[3] < 2^64 + 2^47 */ | |
420 | ||
421 | /* | |
422 | * This adjusts the other two words to complete the two partial | |
423 | * reductions. | |
424 | */ | |
425 | tmp[0] += b; | |
426 | tmp[1] -= (((limb) b) << 32); | |
427 | ||
428 | /* | |
429 | * In order to make space in tmp[3] for the carry from 2 -> 3, we | |
430 | * conditionally subtract kPrime if tmp[3] is large enough. | |
431 | */ | |
432 | high = tmp[3] >> 64; | |
433 | /* As tmp[3] < 2^65, high is either 1 or 0 */ | |
434 | high <<= 63; | |
435 | high >>= 63; | |
35a1cc90 MC |
436 | /*- |
437 | * high is: | |
438 | * all ones if the high word of tmp[3] is 1 | |
439 | * all zeros if the high word of tmp[3] if 0 */ | |
0f113f3e MC |
440 | low = tmp[3]; |
441 | mask = low >> 63; | |
35a1cc90 MC |
442 | /*- |
443 | * mask is: | |
444 | * all ones if the MSB of low is 1 | |
445 | * all zeros if the MSB of low if 0 */ | |
0f113f3e MC |
446 | low &= bottom63bits; |
447 | low -= kPrime3Test; | |
448 | /* if low was greater than kPrime3Test then the MSB is zero */ | |
449 | low = ~low; | |
450 | low >>= 63; | |
35a1cc90 MC |
451 | /*- |
452 | * low is: | |
453 | * all ones if low was > kPrime3Test | |
454 | * all zeros if low was <= kPrime3Test */ | |
0f113f3e MC |
455 | mask = (mask & low) | high; |
456 | tmp[0] -= mask & kPrime[0]; | |
457 | tmp[1] -= mask & kPrime[1]; | |
458 | /* kPrime[2] is zero, so omitted */ | |
459 | tmp[3] -= mask & kPrime[3]; | |
460 | /* tmp[3] < 2**64 - 2**32 + 1 */ | |
461 | ||
462 | tmp[1] += ((u64)(tmp[0] >> 64)); | |
463 | tmp[0] = (u64)tmp[0]; | |
464 | tmp[2] += ((u64)(tmp[1] >> 64)); | |
465 | tmp[1] = (u64)tmp[1]; | |
466 | tmp[3] += ((u64)(tmp[2] >> 64)); | |
467 | tmp[2] = (u64)tmp[2]; | |
468 | /* tmp[i] < 2^64 */ | |
469 | ||
470 | out[0] = tmp[0]; | |
471 | out[1] = tmp[1]; | |
472 | out[2] = tmp[2]; | |
473 | out[3] = tmp[3]; | |
474 | } | |
3e00b4c9 BM |
475 | |
476 | /* smallfelem_expand converts a smallfelem to an felem */ | |
477 | static void smallfelem_expand(felem out, const smallfelem in) | |
0f113f3e MC |
478 | { |
479 | out[0] = in[0]; | |
480 | out[1] = in[1]; | |
481 | out[2] = in[2]; | |
482 | out[3] = in[3]; | |
483 | } | |
484 | ||
485 | /*- | |
1d97c843 | 486 | * smallfelem_square sets |out| = |small|^2 |
3e00b4c9 BM |
487 | * On entry: |
488 | * small[i] < 2^64 | |
489 | * On exit: | |
490 | * out[i] < 7 * 2^64 < 2^67 | |
491 | */ | |
492 | static void smallfelem_square(longfelem out, const smallfelem small) | |
0f113f3e MC |
493 | { |
494 | limb a; | |
495 | u64 high, low; | |
496 | ||
497 | a = ((uint128_t) small[0]) * small[0]; | |
498 | low = a; | |
499 | high = a >> 64; | |
500 | out[0] = low; | |
501 | out[1] = high; | |
502 | ||
503 | a = ((uint128_t) small[0]) * small[1]; | |
504 | low = a; | |
505 | high = a >> 64; | |
506 | out[1] += low; | |
507 | out[1] += low; | |
508 | out[2] = high; | |
509 | ||
510 | a = ((uint128_t) small[0]) * small[2]; | |
511 | low = a; | |
512 | high = a >> 64; | |
513 | out[2] += low; | |
514 | out[2] *= 2; | |
515 | out[3] = high; | |
516 | ||
517 | a = ((uint128_t) small[0]) * small[3]; | |
518 | low = a; | |
519 | high = a >> 64; | |
520 | out[3] += low; | |
521 | out[4] = high; | |
522 | ||
523 | a = ((uint128_t) small[1]) * small[2]; | |
524 | low = a; | |
525 | high = a >> 64; | |
526 | out[3] += low; | |
527 | out[3] *= 2; | |
528 | out[4] += high; | |
529 | ||
530 | a = ((uint128_t) small[1]) * small[1]; | |
531 | low = a; | |
532 | high = a >> 64; | |
533 | out[2] += low; | |
534 | out[3] += high; | |
535 | ||
536 | a = ((uint128_t) small[1]) * small[3]; | |
537 | low = a; | |
538 | high = a >> 64; | |
539 | out[4] += low; | |
540 | out[4] *= 2; | |
541 | out[5] = high; | |
542 | ||
543 | a = ((uint128_t) small[2]) * small[3]; | |
544 | low = a; | |
545 | high = a >> 64; | |
546 | out[5] += low; | |
547 | out[5] *= 2; | |
548 | out[6] = high; | |
549 | out[6] += high; | |
550 | ||
551 | a = ((uint128_t) small[2]) * small[2]; | |
552 | low = a; | |
553 | high = a >> 64; | |
554 | out[4] += low; | |
555 | out[5] += high; | |
556 | ||
557 | a = ((uint128_t) small[3]) * small[3]; | |
558 | low = a; | |
559 | high = a >> 64; | |
560 | out[6] += low; | |
561 | out[7] = high; | |
562 | } | |
3e00b4c9 | 563 | |
1d97c843 TH |
564 | /*- |
565 | * felem_square sets |out| = |in|^2 | |
3e00b4c9 BM |
566 | * On entry: |
567 | * in[i] < 2^109 | |
568 | * On exit: | |
569 | * out[i] < 7 * 2^64 < 2^67 | |
570 | */ | |
571 | static void felem_square(longfelem out, const felem in) | |
0f113f3e MC |
572 | { |
573 | u64 small[4]; | |
574 | felem_shrink(small, in); | |
575 | smallfelem_square(out, small); | |
576 | } | |
3e00b4c9 | 577 | |
1d97c843 TH |
578 | /*- |
579 | * smallfelem_mul sets |out| = |small1| * |small2| | |
3e00b4c9 BM |
580 | * On entry: |
581 | * small1[i] < 2^64 | |
582 | * small2[i] < 2^64 | |
583 | * On exit: | |
584 | * out[i] < 7 * 2^64 < 2^67 | |
585 | */ | |
0f113f3e MC |
586 | static void smallfelem_mul(longfelem out, const smallfelem small1, |
587 | const smallfelem small2) | |
588 | { | |
589 | limb a; | |
590 | u64 high, low; | |
591 | ||
592 | a = ((uint128_t) small1[0]) * small2[0]; | |
593 | low = a; | |
594 | high = a >> 64; | |
595 | out[0] = low; | |
596 | out[1] = high; | |
597 | ||
598 | a = ((uint128_t) small1[0]) * small2[1]; | |
599 | low = a; | |
600 | high = a >> 64; | |
601 | out[1] += low; | |
602 | out[2] = high; | |
603 | ||
604 | a = ((uint128_t) small1[1]) * small2[0]; | |
605 | low = a; | |
606 | high = a >> 64; | |
607 | out[1] += low; | |
608 | out[2] += high; | |
609 | ||
610 | a = ((uint128_t) small1[0]) * small2[2]; | |
611 | low = a; | |
612 | high = a >> 64; | |
613 | out[2] += low; | |
614 | out[3] = high; | |
615 | ||
616 | a = ((uint128_t) small1[1]) * small2[1]; | |
617 | low = a; | |
618 | high = a >> 64; | |
619 | out[2] += low; | |
620 | out[3] += high; | |
621 | ||
622 | a = ((uint128_t) small1[2]) * small2[0]; | |
623 | low = a; | |
624 | high = a >> 64; | |
625 | out[2] += low; | |
626 | out[3] += high; | |
627 | ||
628 | a = ((uint128_t) small1[0]) * small2[3]; | |
629 | low = a; | |
630 | high = a >> 64; | |
631 | out[3] += low; | |
632 | out[4] = high; | |
633 | ||
634 | a = ((uint128_t) small1[1]) * small2[2]; | |
635 | low = a; | |
636 | high = a >> 64; | |
637 | out[3] += low; | |
638 | out[4] += high; | |
639 | ||
640 | a = ((uint128_t) small1[2]) * small2[1]; | |
641 | low = a; | |
642 | high = a >> 64; | |
643 | out[3] += low; | |
644 | out[4] += high; | |
645 | ||
646 | a = ((uint128_t) small1[3]) * small2[0]; | |
647 | low = a; | |
648 | high = a >> 64; | |
649 | out[3] += low; | |
650 | out[4] += high; | |
651 | ||
652 | a = ((uint128_t) small1[1]) * small2[3]; | |
653 | low = a; | |
654 | high = a >> 64; | |
655 | out[4] += low; | |
656 | out[5] = high; | |
657 | ||
658 | a = ((uint128_t) small1[2]) * small2[2]; | |
659 | low = a; | |
660 | high = a >> 64; | |
661 | out[4] += low; | |
662 | out[5] += high; | |
663 | ||
664 | a = ((uint128_t) small1[3]) * small2[1]; | |
665 | low = a; | |
666 | high = a >> 64; | |
667 | out[4] += low; | |
668 | out[5] += high; | |
669 | ||
670 | a = ((uint128_t) small1[2]) * small2[3]; | |
671 | low = a; | |
672 | high = a >> 64; | |
673 | out[5] += low; | |
674 | out[6] = high; | |
675 | ||
676 | a = ((uint128_t) small1[3]) * small2[2]; | |
677 | low = a; | |
678 | high = a >> 64; | |
679 | out[5] += low; | |
680 | out[6] += high; | |
681 | ||
682 | a = ((uint128_t) small1[3]) * small2[3]; | |
683 | low = a; | |
684 | high = a >> 64; | |
685 | out[6] += low; | |
686 | out[7] = high; | |
687 | } | |
3e00b4c9 | 688 | |
1d97c843 TH |
689 | /*- |
690 | * felem_mul sets |out| = |in1| * |in2| | |
3e00b4c9 BM |
691 | * On entry: |
692 | * in1[i] < 2^109 | |
693 | * in2[i] < 2^109 | |
694 | * On exit: | |
695 | * out[i] < 7 * 2^64 < 2^67 | |
696 | */ | |
697 | static void felem_mul(longfelem out, const felem in1, const felem in2) | |
0f113f3e MC |
698 | { |
699 | smallfelem small1, small2; | |
700 | felem_shrink(small1, in1); | |
701 | felem_shrink(small2, in2); | |
702 | smallfelem_mul(out, small1, small2); | |
703 | } | |
3e00b4c9 | 704 | |
1d97c843 TH |
705 | /*- |
706 | * felem_small_mul sets |out| = |small1| * |in2| | |
3e00b4c9 BM |
707 | * On entry: |
708 | * small1[i] < 2^64 | |
709 | * in2[i] < 2^109 | |
710 | * On exit: | |
711 | * out[i] < 7 * 2^64 < 2^67 | |
712 | */ | |
0f113f3e MC |
713 | static void felem_small_mul(longfelem out, const smallfelem small1, |
714 | const felem in2) | |
715 | { | |
716 | smallfelem small2; | |
717 | felem_shrink(small2, in2); | |
718 | smallfelem_mul(out, small1, small2); | |
719 | } | |
720 | ||
721 | # define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) | |
722 | # define two100 (((limb)1) << 100) | |
723 | # define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) | |
3e00b4c9 | 724 | /* zero100 is 0 mod p */ |
0f113f3e MC |
725 | static const felem zero100 = |
726 | { two100m36m4, two100, two100m36p4, two100m36p4 }; | |
3e00b4c9 | 727 | |
1d97c843 TH |
728 | /*- |
729 | * Internal function for the different flavours of felem_reduce. | |
3e00b4c9 BM |
730 | * felem_reduce_ reduces the higher coefficients in[4]-in[7]. |
731 | * On entry: | |
0f113f3e | 732 | * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] |
3e00b4c9 BM |
733 | * out[1] >= in[7] + 2^32*in[4] |
734 | * out[2] >= in[5] + 2^32*in[5] | |
735 | * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] | |
736 | * On exit: | |
737 | * out[0] <= out[0] + in[4] + 2^32*in[5] | |
738 | * out[1] <= out[1] + in[5] + 2^33*in[6] | |
739 | * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7] | |
740 | * out[3] <= out[3] + 2^32*in[4] + 3*in[7] | |
741 | */ | |
742 | static void felem_reduce_(felem out, const longfelem in) | |
0f113f3e MC |
743 | { |
744 | int128_t c; | |
745 | /* combine common terms from below */ | |
746 | c = in[4] + (in[5] << 32); | |
747 | out[0] += c; | |
748 | out[3] -= c; | |
749 | ||
750 | c = in[5] - in[7]; | |
751 | out[1] += c; | |
752 | out[2] -= c; | |
753 | ||
754 | /* the remaining terms */ | |
755 | /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */ | |
756 | out[1] -= (in[4] << 32); | |
757 | out[3] += (in[4] << 32); | |
758 | ||
759 | /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */ | |
760 | out[2] -= (in[5] << 32); | |
761 | ||
762 | /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */ | |
763 | out[0] -= in[6]; | |
764 | out[0] -= (in[6] << 32); | |
765 | out[1] += (in[6] << 33); | |
766 | out[2] += (in[6] * 2); | |
767 | out[3] -= (in[6] << 32); | |
768 | ||
769 | /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */ | |
770 | out[0] -= in[7]; | |
771 | out[0] -= (in[7] << 32); | |
772 | out[2] += (in[7] << 33); | |
773 | out[3] += (in[7] * 3); | |
774 | } | |
3e00b4c9 | 775 | |
1d97c843 TH |
776 | /*- |
777 | * felem_reduce converts a longfelem into an felem. | |
3e00b4c9 BM |
778 | * To be called directly after felem_square or felem_mul. |
779 | * On entry: | |
780 | * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64 | |
781 | * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64 | |
782 | * On exit: | |
783 | * out[i] < 2^101 | |
784 | */ | |
785 | static void felem_reduce(felem out, const longfelem in) | |
0f113f3e MC |
786 | { |
787 | out[0] = zero100[0] + in[0]; | |
788 | out[1] = zero100[1] + in[1]; | |
789 | out[2] = zero100[2] + in[2]; | |
790 | out[3] = zero100[3] + in[3]; | |
791 | ||
792 | felem_reduce_(out, in); | |
793 | ||
35a1cc90 MC |
794 | /*- |
795 | * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 | |
796 | * out[1] > 2^100 - 2^64 - 7*2^96 > 0 | |
797 | * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 | |
798 | * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 | |
799 | * | |
800 | * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 | |
801 | * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 | |
802 | * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 | |
803 | * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 | |
804 | */ | |
0f113f3e | 805 | } |
3e00b4c9 | 806 | |
1d97c843 TH |
807 | /*- |
808 | * felem_reduce_zero105 converts a larger longfelem into an felem. | |
3e00b4c9 BM |
809 | * On entry: |
810 | * in[0] < 2^71 | |
811 | * On exit: | |
812 | * out[i] < 2^106 | |
813 | */ | |
814 | static void felem_reduce_zero105(felem out, const longfelem in) | |
0f113f3e MC |
815 | { |
816 | out[0] = zero105[0] + in[0]; | |
817 | out[1] = zero105[1] + in[1]; | |
818 | out[2] = zero105[2] + in[2]; | |
819 | out[3] = zero105[3] + in[3]; | |
820 | ||
821 | felem_reduce_(out, in); | |
822 | ||
35a1cc90 MC |
823 | /*- |
824 | * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 | |
825 | * out[1] > 2^105 - 2^71 - 2^103 > 0 | |
826 | * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 | |
827 | * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 | |
828 | * | |
829 | * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 | |
830 | * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 | |
831 | * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 | |
832 | * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 | |
833 | */ | |
0f113f3e MC |
834 | } |
835 | ||
836 | /* | |
837 | * subtract_u64 sets *result = *result - v and *carry to one if the | |
838 | * subtraction underflowed. | |
839 | */ | |
840 | static void subtract_u64(u64 *result, u64 *carry, u64 v) | |
841 | { | |
842 | uint128_t r = *result; | |
843 | r -= v; | |
844 | *carry = (r >> 64) & 1; | |
845 | *result = (u64)r; | |
846 | } | |
847 | ||
848 | /* | |
849 | * felem_contract converts |in| to its unique, minimal representation. On | |
850 | * entry: in[i] < 2^109 | |
3e00b4c9 BM |
851 | */ |
852 | static void felem_contract(smallfelem out, const felem in) | |
0f113f3e MC |
853 | { |
854 | unsigned i; | |
855 | u64 all_equal_so_far = 0, result = 0, carry; | |
856 | ||
857 | felem_shrink(out, in); | |
858 | /* small is minimal except that the value might be > p */ | |
859 | ||
860 | all_equal_so_far--; | |
861 | /* | |
862 | * We are doing a constant time test if out >= kPrime. We need to compare | |
863 | * each u64, from most-significant to least significant. For each one, if | |
864 | * all words so far have been equal (m is all ones) then a non-equal | |
865 | * result is the answer. Otherwise we continue. | |
866 | */ | |
867 | for (i = 3; i < 4; i--) { | |
868 | u64 equal; | |
869 | uint128_t a = ((uint128_t) kPrime[i]) - out[i]; | |
870 | /* | |
871 | * if out[i] > kPrime[i] then a will underflow and the high 64-bits | |
872 | * will all be set. | |
873 | */ | |
874 | result |= all_equal_so_far & ((u64)(a >> 64)); | |
875 | ||
876 | /* | |
877 | * if kPrime[i] == out[i] then |equal| will be all zeros and the | |
878 | * decrement will make it all ones. | |
879 | */ | |
880 | equal = kPrime[i] ^ out[i]; | |
881 | equal--; | |
882 | equal &= equal << 32; | |
883 | equal &= equal << 16; | |
884 | equal &= equal << 8; | |
885 | equal &= equal << 4; | |
886 | equal &= equal << 2; | |
887 | equal &= equal << 1; | |
888 | equal = ((s64) equal) >> 63; | |
889 | ||
890 | all_equal_so_far &= equal; | |
891 | } | |
892 | ||
893 | /* | |
894 | * if all_equal_so_far is still all ones then the two values are equal | |
895 | * and so out >= kPrime is true. | |
896 | */ | |
897 | result |= all_equal_so_far; | |
898 | ||
899 | /* if out >= kPrime then we subtract kPrime. */ | |
900 | subtract_u64(&out[0], &carry, result & kPrime[0]); | |
901 | subtract_u64(&out[1], &carry, carry); | |
902 | subtract_u64(&out[2], &carry, carry); | |
903 | subtract_u64(&out[3], &carry, carry); | |
904 | ||
905 | subtract_u64(&out[1], &carry, result & kPrime[1]); | |
906 | subtract_u64(&out[2], &carry, carry); | |
907 | subtract_u64(&out[3], &carry, carry); | |
908 | ||
909 | subtract_u64(&out[2], &carry, result & kPrime[2]); | |
910 | subtract_u64(&out[3], &carry, carry); | |
911 | ||
912 | subtract_u64(&out[3], &carry, result & kPrime[3]); | |
913 | } | |
3e00b4c9 BM |
914 | |
915 | static void smallfelem_square_contract(smallfelem out, const smallfelem in) | |
0f113f3e MC |
916 | { |
917 | longfelem longtmp; | |
918 | felem tmp; | |
919 | ||
920 | smallfelem_square(longtmp, in); | |
921 | felem_reduce(tmp, longtmp); | |
922 | felem_contract(out, tmp); | |
923 | } | |
924 | ||
925 | static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, | |
926 | const smallfelem in2) | |
927 | { | |
928 | longfelem longtmp; | |
929 | felem tmp; | |
930 | ||
931 | smallfelem_mul(longtmp, in1, in2); | |
932 | felem_reduce(tmp, longtmp); | |
933 | felem_contract(out, tmp); | |
934 | } | |
3e00b4c9 | 935 | |
1d97c843 TH |
936 | /*- |
937 | * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 | |
3e00b4c9 BM |
938 | * otherwise. |
939 | * On entry: | |
940 | * small[i] < 2^64 | |
941 | */ | |
942 | static limb smallfelem_is_zero(const smallfelem small) | |
0f113f3e MC |
943 | { |
944 | limb result; | |
945 | u64 is_p; | |
946 | ||
947 | u64 is_zero = small[0] | small[1] | small[2] | small[3]; | |
948 | is_zero--; | |
949 | is_zero &= is_zero << 32; | |
950 | is_zero &= is_zero << 16; | |
951 | is_zero &= is_zero << 8; | |
952 | is_zero &= is_zero << 4; | |
953 | is_zero &= is_zero << 2; | |
954 | is_zero &= is_zero << 1; | |
955 | is_zero = ((s64) is_zero) >> 63; | |
956 | ||
957 | is_p = (small[0] ^ kPrime[0]) | | |
958 | (small[1] ^ kPrime[1]) | | |
959 | (small[2] ^ kPrime[2]) | (small[3] ^ kPrime[3]); | |
960 | is_p--; | |
961 | is_p &= is_p << 32; | |
962 | is_p &= is_p << 16; | |
963 | is_p &= is_p << 8; | |
964 | is_p &= is_p << 4; | |
965 | is_p &= is_p << 2; | |
966 | is_p &= is_p << 1; | |
967 | is_p = ((s64) is_p) >> 63; | |
968 | ||
969 | is_zero |= is_p; | |
970 | ||
971 | result = is_zero; | |
972 | result |= ((limb) is_zero) << 64; | |
973 | return result; | |
974 | } | |
3e00b4c9 BM |
975 | |
976 | static int smallfelem_is_zero_int(const smallfelem small) | |
0f113f3e MC |
977 | { |
978 | return (int)(smallfelem_is_zero(small) & ((limb) 1)); | |
979 | } | |
3e00b4c9 | 980 | |
1d97c843 TH |
981 | /*- |
982 | * felem_inv calculates |out| = |in|^{-1} | |
3e00b4c9 BM |
983 | * |
984 | * Based on Fermat's Little Theorem: | |
985 | * a^p = a (mod p) | |
986 | * a^{p-1} = 1 (mod p) | |
987 | * a^{p-2} = a^{-1} (mod p) | |
988 | */ | |
989 | static void felem_inv(felem out, const felem in) | |
0f113f3e MC |
990 | { |
991 | felem ftmp, ftmp2; | |
992 | /* each e_I will hold |in|^{2^I - 1} */ | |
993 | felem e2, e4, e8, e16, e32, e64; | |
994 | longfelem tmp; | |
995 | unsigned i; | |
996 | ||
997 | felem_square(tmp, in); | |
998 | felem_reduce(ftmp, tmp); /* 2^1 */ | |
999 | felem_mul(tmp, in, ftmp); | |
1000 | felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ | |
1001 | felem_assign(e2, ftmp); | |
1002 | felem_square(tmp, ftmp); | |
1003 | felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ | |
1004 | felem_square(tmp, ftmp); | |
1005 | felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ | |
1006 | felem_mul(tmp, ftmp, e2); | |
1007 | felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ | |
1008 | felem_assign(e4, ftmp); | |
1009 | felem_square(tmp, ftmp); | |
1010 | felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ | |
1011 | felem_square(tmp, ftmp); | |
1012 | felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ | |
1013 | felem_square(tmp, ftmp); | |
1014 | felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ | |
1015 | felem_square(tmp, ftmp); | |
1016 | felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ | |
1017 | felem_mul(tmp, ftmp, e4); | |
1018 | felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ | |
1019 | felem_assign(e8, ftmp); | |
1020 | for (i = 0; i < 8; i++) { | |
1021 | felem_square(tmp, ftmp); | |
1022 | felem_reduce(ftmp, tmp); | |
1023 | } /* 2^16 - 2^8 */ | |
1024 | felem_mul(tmp, ftmp, e8); | |
1025 | felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ | |
1026 | felem_assign(e16, ftmp); | |
1027 | for (i = 0; i < 16; i++) { | |
1028 | felem_square(tmp, ftmp); | |
1029 | felem_reduce(ftmp, tmp); | |
1030 | } /* 2^32 - 2^16 */ | |
1031 | felem_mul(tmp, ftmp, e16); | |
1032 | felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ | |
1033 | felem_assign(e32, ftmp); | |
1034 | for (i = 0; i < 32; i++) { | |
1035 | felem_square(tmp, ftmp); | |
1036 | felem_reduce(ftmp, tmp); | |
1037 | } /* 2^64 - 2^32 */ | |
1038 | felem_assign(e64, ftmp); | |
1039 | felem_mul(tmp, ftmp, in); | |
1040 | felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ | |
1041 | for (i = 0; i < 192; i++) { | |
1042 | felem_square(tmp, ftmp); | |
1043 | felem_reduce(ftmp, tmp); | |
1044 | } /* 2^256 - 2^224 + 2^192 */ | |
1045 | ||
1046 | felem_mul(tmp, e64, e32); | |
1047 | felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ | |
1048 | for (i = 0; i < 16; i++) { | |
1049 | felem_square(tmp, ftmp2); | |
1050 | felem_reduce(ftmp2, tmp); | |
1051 | } /* 2^80 - 2^16 */ | |
1052 | felem_mul(tmp, ftmp2, e16); | |
1053 | felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ | |
1054 | for (i = 0; i < 8; i++) { | |
1055 | felem_square(tmp, ftmp2); | |
1056 | felem_reduce(ftmp2, tmp); | |
1057 | } /* 2^88 - 2^8 */ | |
1058 | felem_mul(tmp, ftmp2, e8); | |
1059 | felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ | |
1060 | for (i = 0; i < 4; i++) { | |
1061 | felem_square(tmp, ftmp2); | |
1062 | felem_reduce(ftmp2, tmp); | |
1063 | } /* 2^92 - 2^4 */ | |
1064 | felem_mul(tmp, ftmp2, e4); | |
1065 | felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ | |
1066 | felem_square(tmp, ftmp2); | |
1067 | felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ | |
1068 | felem_square(tmp, ftmp2); | |
1069 | felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ | |
1070 | felem_mul(tmp, ftmp2, e2); | |
1071 | felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ | |
1072 | felem_square(tmp, ftmp2); | |
1073 | felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ | |
1074 | felem_square(tmp, ftmp2); | |
1075 | felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ | |
1076 | felem_mul(tmp, ftmp2, in); | |
1077 | felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ | |
1078 | ||
1079 | felem_mul(tmp, ftmp2, ftmp); | |
1080 | felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ | |
1081 | } | |
3e00b4c9 BM |
1082 | |
1083 | static void smallfelem_inv_contract(smallfelem out, const smallfelem in) | |
0f113f3e MC |
1084 | { |
1085 | felem tmp; | |
3e00b4c9 | 1086 | |
0f113f3e MC |
1087 | smallfelem_expand(tmp, in); |
1088 | felem_inv(tmp, tmp); | |
1089 | felem_contract(out, tmp); | |
1090 | } | |
3e00b4c9 | 1091 | |
1d97c843 TH |
1092 | /*- |
1093 | * Group operations | |
3e00b4c9 BM |
1094 | * ---------------- |
1095 | * | |
1096 | * Building on top of the field operations we have the operations on the | |
1097 | * elliptic curve group itself. Points on the curve are represented in Jacobian | |
35a1cc90 MC |
1098 | * coordinates |
1099 | */ | |
3e00b4c9 | 1100 | |
1d97c843 TH |
1101 | /*- |
1102 | * point_double calculates 2*(x_in, y_in, z_in) | |
3e00b4c9 BM |
1103 | * |
1104 | * The method is taken from: | |
1105 | * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b | |
1106 | * | |
1107 | * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. | |
35a1cc90 MC |
1108 | * while x_out == y_in is not (maybe this works, but it's not tested). |
1109 | */ | |
3e00b4c9 BM |
1110 | static void |
1111 | point_double(felem x_out, felem y_out, felem z_out, | |
0f113f3e MC |
1112 | const felem x_in, const felem y_in, const felem z_in) |
1113 | { | |
1114 | longfelem tmp, tmp2; | |
1115 | felem delta, gamma, beta, alpha, ftmp, ftmp2; | |
1116 | smallfelem small1, small2; | |
1117 | ||
1118 | felem_assign(ftmp, x_in); | |
1119 | /* ftmp[i] < 2^106 */ | |
1120 | felem_assign(ftmp2, x_in); | |
1121 | /* ftmp2[i] < 2^106 */ | |
1122 | ||
1123 | /* delta = z^2 */ | |
1124 | felem_square(tmp, z_in); | |
1125 | felem_reduce(delta, tmp); | |
1126 | /* delta[i] < 2^101 */ | |
1127 | ||
1128 | /* gamma = y^2 */ | |
1129 | felem_square(tmp, y_in); | |
1130 | felem_reduce(gamma, tmp); | |
1131 | /* gamma[i] < 2^101 */ | |
1132 | felem_shrink(small1, gamma); | |
1133 | ||
1134 | /* beta = x*gamma */ | |
1135 | felem_small_mul(tmp, small1, x_in); | |
1136 | felem_reduce(beta, tmp); | |
1137 | /* beta[i] < 2^101 */ | |
1138 | ||
1139 | /* alpha = 3*(x-delta)*(x+delta) */ | |
1140 | felem_diff(ftmp, delta); | |
1141 | /* ftmp[i] < 2^105 + 2^106 < 2^107 */ | |
1142 | felem_sum(ftmp2, delta); | |
1143 | /* ftmp2[i] < 2^105 + 2^106 < 2^107 */ | |
1144 | felem_scalar(ftmp2, 3); | |
1145 | /* ftmp2[i] < 3 * 2^107 < 2^109 */ | |
1146 | felem_mul(tmp, ftmp, ftmp2); | |
1147 | felem_reduce(alpha, tmp); | |
1148 | /* alpha[i] < 2^101 */ | |
1149 | felem_shrink(small2, alpha); | |
1150 | ||
1151 | /* x' = alpha^2 - 8*beta */ | |
1152 | smallfelem_square(tmp, small2); | |
1153 | felem_reduce(x_out, tmp); | |
1154 | felem_assign(ftmp, beta); | |
1155 | felem_scalar(ftmp, 8); | |
1156 | /* ftmp[i] < 8 * 2^101 = 2^104 */ | |
1157 | felem_diff(x_out, ftmp); | |
1158 | /* x_out[i] < 2^105 + 2^101 < 2^106 */ | |
1159 | ||
1160 | /* z' = (y + z)^2 - gamma - delta */ | |
1161 | felem_sum(delta, gamma); | |
1162 | /* delta[i] < 2^101 + 2^101 = 2^102 */ | |
1163 | felem_assign(ftmp, y_in); | |
1164 | felem_sum(ftmp, z_in); | |
1165 | /* ftmp[i] < 2^106 + 2^106 = 2^107 */ | |
1166 | felem_square(tmp, ftmp); | |
1167 | felem_reduce(z_out, tmp); | |
1168 | felem_diff(z_out, delta); | |
1169 | /* z_out[i] < 2^105 + 2^101 < 2^106 */ | |
1170 | ||
1171 | /* y' = alpha*(4*beta - x') - 8*gamma^2 */ | |
1172 | felem_scalar(beta, 4); | |
1173 | /* beta[i] < 4 * 2^101 = 2^103 */ | |
1174 | felem_diff_zero107(beta, x_out); | |
1175 | /* beta[i] < 2^107 + 2^103 < 2^108 */ | |
1176 | felem_small_mul(tmp, small2, beta); | |
1177 | /* tmp[i] < 7 * 2^64 < 2^67 */ | |
1178 | smallfelem_square(tmp2, small1); | |
1179 | /* tmp2[i] < 7 * 2^64 */ | |
1180 | longfelem_scalar(tmp2, 8); | |
1181 | /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */ | |
1182 | longfelem_diff(tmp, tmp2); | |
1183 | /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ | |
1184 | felem_reduce_zero105(y_out, tmp); | |
1185 | /* y_out[i] < 2^106 */ | |
1186 | } | |
1187 | ||
1188 | /* | |
1189 | * point_double_small is the same as point_double, except that it operates on | |
1190 | * smallfelems | |
1191 | */ | |
3e00b4c9 BM |
1192 | static void |
1193 | point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, | |
0f113f3e MC |
1194 | const smallfelem x_in, const smallfelem y_in, |
1195 | const smallfelem z_in) | |
1196 | { | |
1197 | felem felem_x_out, felem_y_out, felem_z_out; | |
1198 | felem felem_x_in, felem_y_in, felem_z_in; | |
1199 | ||
1200 | smallfelem_expand(felem_x_in, x_in); | |
1201 | smallfelem_expand(felem_y_in, y_in); | |
1202 | smallfelem_expand(felem_z_in, z_in); | |
1203 | point_double(felem_x_out, felem_y_out, felem_z_out, | |
1204 | felem_x_in, felem_y_in, felem_z_in); | |
1205 | felem_shrink(x_out, felem_x_out); | |
1206 | felem_shrink(y_out, felem_y_out); | |
1207 | felem_shrink(z_out, felem_z_out); | |
1208 | } | |
3e00b4c9 BM |
1209 | |
1210 | /* copy_conditional copies in to out iff mask is all ones. */ | |
0f113f3e MC |
1211 | static void copy_conditional(felem out, const felem in, limb mask) |
1212 | { | |
1213 | unsigned i; | |
1214 | for (i = 0; i < NLIMBS; ++i) { | |
1215 | const limb tmp = mask & (in[i] ^ out[i]); | |
1216 | out[i] ^= tmp; | |
1217 | } | |
1218 | } | |
3e00b4c9 BM |
1219 | |
1220 | /* copy_small_conditional copies in to out iff mask is all ones. */ | |
0f113f3e MC |
1221 | static void copy_small_conditional(felem out, const smallfelem in, limb mask) |
1222 | { | |
1223 | unsigned i; | |
1224 | const u64 mask64 = mask; | |
1225 | for (i = 0; i < NLIMBS; ++i) { | |
1226 | out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); | |
1227 | } | |
1228 | } | |
3e00b4c9 | 1229 | |
1d97c843 | 1230 | /*- |
0d4fb843 | 1231 | * point_add calculates (x1, y1, z1) + (x2, y2, z2) |
3e00b4c9 BM |
1232 | * |
1233 | * The method is taken from: | |
1234 | * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, | |
1235 | * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). | |
1236 | * | |
1237 | * This function includes a branch for checking whether the two input points | |
1238 | * are equal, (while not equal to the point at infinity). This case never | |
1239 | * happens during single point multiplication, so there is no timing leak for | |
35a1cc90 MC |
1240 | * ECDH or ECDSA signing. |
1241 | */ | |
3e00b4c9 | 1242 | static void point_add(felem x3, felem y3, felem z3, |
0f113f3e MC |
1243 | const felem x1, const felem y1, const felem z1, |
1244 | const int mixed, const smallfelem x2, | |
1245 | const smallfelem y2, const smallfelem z2) | |
1246 | { | |
1247 | felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; | |
1248 | longfelem tmp, tmp2; | |
1249 | smallfelem small1, small2, small3, small4, small5; | |
1250 | limb x_equal, y_equal, z1_is_zero, z2_is_zero; | |
1251 | ||
1252 | felem_shrink(small3, z1); | |
1253 | ||
1254 | z1_is_zero = smallfelem_is_zero(small3); | |
1255 | z2_is_zero = smallfelem_is_zero(z2); | |
1256 | ||
1257 | /* ftmp = z1z1 = z1**2 */ | |
1258 | smallfelem_square(tmp, small3); | |
1259 | felem_reduce(ftmp, tmp); | |
1260 | /* ftmp[i] < 2^101 */ | |
1261 | felem_shrink(small1, ftmp); | |
1262 | ||
1263 | if (!mixed) { | |
1264 | /* ftmp2 = z2z2 = z2**2 */ | |
1265 | smallfelem_square(tmp, z2); | |
1266 | felem_reduce(ftmp2, tmp); | |
1267 | /* ftmp2[i] < 2^101 */ | |
1268 | felem_shrink(small2, ftmp2); | |
1269 | ||
1270 | felem_shrink(small5, x1); | |
1271 | ||
1272 | /* u1 = ftmp3 = x1*z2z2 */ | |
1273 | smallfelem_mul(tmp, small5, small2); | |
1274 | felem_reduce(ftmp3, tmp); | |
1275 | /* ftmp3[i] < 2^101 */ | |
1276 | ||
1277 | /* ftmp5 = z1 + z2 */ | |
1278 | felem_assign(ftmp5, z1); | |
1279 | felem_small_sum(ftmp5, z2); | |
1280 | /* ftmp5[i] < 2^107 */ | |
1281 | ||
1282 | /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */ | |
1283 | felem_square(tmp, ftmp5); | |
1284 | felem_reduce(ftmp5, tmp); | |
1285 | /* ftmp2 = z2z2 + z1z1 */ | |
1286 | felem_sum(ftmp2, ftmp); | |
1287 | /* ftmp2[i] < 2^101 + 2^101 = 2^102 */ | |
1288 | felem_diff(ftmp5, ftmp2); | |
1289 | /* ftmp5[i] < 2^105 + 2^101 < 2^106 */ | |
1290 | ||
1291 | /* ftmp2 = z2 * z2z2 */ | |
1292 | smallfelem_mul(tmp, small2, z2); | |
1293 | felem_reduce(ftmp2, tmp); | |
1294 | ||
1295 | /* s1 = ftmp2 = y1 * z2**3 */ | |
1296 | felem_mul(tmp, y1, ftmp2); | |
1297 | felem_reduce(ftmp6, tmp); | |
1298 | /* ftmp6[i] < 2^101 */ | |
1299 | } else { | |
1300 | /* | |
1301 | * We'll assume z2 = 1 (special case z2 = 0 is handled later) | |
1302 | */ | |
1303 | ||
1304 | /* u1 = ftmp3 = x1*z2z2 */ | |
1305 | felem_assign(ftmp3, x1); | |
1306 | /* ftmp3[i] < 2^106 */ | |
1307 | ||
1308 | /* ftmp5 = 2z1z2 */ | |
1309 | felem_assign(ftmp5, z1); | |
1310 | felem_scalar(ftmp5, 2); | |
1311 | /* ftmp5[i] < 2*2^106 = 2^107 */ | |
1312 | ||
1313 | /* s1 = ftmp2 = y1 * z2**3 */ | |
1314 | felem_assign(ftmp6, y1); | |
1315 | /* ftmp6[i] < 2^106 */ | |
1316 | } | |
1317 | ||
1318 | /* u2 = x2*z1z1 */ | |
1319 | smallfelem_mul(tmp, x2, small1); | |
1320 | felem_reduce(ftmp4, tmp); | |
1321 | ||
1322 | /* h = ftmp4 = u2 - u1 */ | |
1323 | felem_diff_zero107(ftmp4, ftmp3); | |
1324 | /* ftmp4[i] < 2^107 + 2^101 < 2^108 */ | |
1325 | felem_shrink(small4, ftmp4); | |
1326 | ||
1327 | x_equal = smallfelem_is_zero(small4); | |
1328 | ||
1329 | /* z_out = ftmp5 * h */ | |
1330 | felem_small_mul(tmp, small4, ftmp5); | |
1331 | felem_reduce(z_out, tmp); | |
1332 | /* z_out[i] < 2^101 */ | |
1333 | ||
1334 | /* ftmp = z1 * z1z1 */ | |
1335 | smallfelem_mul(tmp, small1, small3); | |
1336 | felem_reduce(ftmp, tmp); | |
1337 | ||
1338 | /* s2 = tmp = y2 * z1**3 */ | |
1339 | felem_small_mul(tmp, y2, ftmp); | |
1340 | felem_reduce(ftmp5, tmp); | |
1341 | ||
1342 | /* r = ftmp5 = (s2 - s1)*2 */ | |
1343 | felem_diff_zero107(ftmp5, ftmp6); | |
1344 | /* ftmp5[i] < 2^107 + 2^107 = 2^108 */ | |
1345 | felem_scalar(ftmp5, 2); | |
1346 | /* ftmp5[i] < 2^109 */ | |
1347 | felem_shrink(small1, ftmp5); | |
1348 | y_equal = smallfelem_is_zero(small1); | |
1349 | ||
1350 | if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { | |
1351 | point_double(x3, y3, z3, x1, y1, z1); | |
1352 | return; | |
1353 | } | |
1354 | ||
1355 | /* I = ftmp = (2h)**2 */ | |
1356 | felem_assign(ftmp, ftmp4); | |
1357 | felem_scalar(ftmp, 2); | |
1358 | /* ftmp[i] < 2*2^108 = 2^109 */ | |
1359 | felem_square(tmp, ftmp); | |
1360 | felem_reduce(ftmp, tmp); | |
1361 | ||
1362 | /* J = ftmp2 = h * I */ | |
1363 | felem_mul(tmp, ftmp4, ftmp); | |
1364 | felem_reduce(ftmp2, tmp); | |
1365 | ||
1366 | /* V = ftmp4 = U1 * I */ | |
1367 | felem_mul(tmp, ftmp3, ftmp); | |
1368 | felem_reduce(ftmp4, tmp); | |
1369 | ||
1370 | /* x_out = r**2 - J - 2V */ | |
1371 | smallfelem_square(tmp, small1); | |
1372 | felem_reduce(x_out, tmp); | |
1373 | felem_assign(ftmp3, ftmp4); | |
1374 | felem_scalar(ftmp4, 2); | |
1375 | felem_sum(ftmp4, ftmp2); | |
1376 | /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */ | |
1377 | felem_diff(x_out, ftmp4); | |
1378 | /* x_out[i] < 2^105 + 2^101 */ | |
1379 | ||
1380 | /* y_out = r(V-x_out) - 2 * s1 * J */ | |
1381 | felem_diff_zero107(ftmp3, x_out); | |
1382 | /* ftmp3[i] < 2^107 + 2^101 < 2^108 */ | |
1383 | felem_small_mul(tmp, small1, ftmp3); | |
1384 | felem_mul(tmp2, ftmp6, ftmp2); | |
1385 | longfelem_scalar(tmp2, 2); | |
1386 | /* tmp2[i] < 2*2^67 = 2^68 */ | |
1387 | longfelem_diff(tmp, tmp2); | |
1388 | /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ | |
1389 | felem_reduce_zero105(y_out, tmp); | |
1390 | /* y_out[i] < 2^106 */ | |
1391 | ||
1392 | copy_small_conditional(x_out, x2, z1_is_zero); | |
1393 | copy_conditional(x_out, x1, z2_is_zero); | |
1394 | copy_small_conditional(y_out, y2, z1_is_zero); | |
1395 | copy_conditional(y_out, y1, z2_is_zero); | |
1396 | copy_small_conditional(z_out, z2, z1_is_zero); | |
1397 | copy_conditional(z_out, z1, z2_is_zero); | |
1398 | felem_assign(x3, x_out); | |
1399 | felem_assign(y3, y_out); | |
1400 | felem_assign(z3, z_out); | |
1401 | } | |
1402 | ||
1403 | /* | |
1404 | * point_add_small is the same as point_add, except that it operates on | |
1405 | * smallfelems | |
1406 | */ | |
3e00b4c9 | 1407 | static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, |
0f113f3e MC |
1408 | smallfelem x1, smallfelem y1, smallfelem z1, |
1409 | smallfelem x2, smallfelem y2, smallfelem z2) | |
1410 | { | |
1411 | felem felem_x3, felem_y3, felem_z3; | |
1412 | felem felem_x1, felem_y1, felem_z1; | |
1413 | smallfelem_expand(felem_x1, x1); | |
1414 | smallfelem_expand(felem_y1, y1); | |
1415 | smallfelem_expand(felem_z1, z1); | |
1416 | point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, | |
1417 | x2, y2, z2); | |
1418 | felem_shrink(x3, felem_x3); | |
1419 | felem_shrink(y3, felem_y3); | |
1420 | felem_shrink(z3, felem_z3); | |
1421 | } | |
3e00b4c9 | 1422 | |
1d97c843 TH |
1423 | /*- |
1424 | * Base point pre computation | |
3e00b4c9 BM |
1425 | * -------------------------- |
1426 | * | |
1427 | * Two different sorts of precomputed tables are used in the following code. | |
1428 | * Each contain various points on the curve, where each point is three field | |
1429 | * elements (x, y, z). | |
1430 | * | |
1431 | * For the base point table, z is usually 1 (0 for the point at infinity). | |
1432 | * This table has 2 * 16 elements, starting with the following: | |
1433 | * index | bits | point | |
1434 | * ------+---------+------------------------------ | |
1435 | * 0 | 0 0 0 0 | 0G | |
1436 | * 1 | 0 0 0 1 | 1G | |
1437 | * 2 | 0 0 1 0 | 2^64G | |
1438 | * 3 | 0 0 1 1 | (2^64 + 1)G | |
1439 | * 4 | 0 1 0 0 | 2^128G | |
1440 | * 5 | 0 1 0 1 | (2^128 + 1)G | |
1441 | * 6 | 0 1 1 0 | (2^128 + 2^64)G | |
1442 | * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G | |
1443 | * 8 | 1 0 0 0 | 2^192G | |
1444 | * 9 | 1 0 0 1 | (2^192 + 1)G | |
1445 | * 10 | 1 0 1 0 | (2^192 + 2^64)G | |
1446 | * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G | |
1447 | * 12 | 1 1 0 0 | (2^192 + 2^128)G | |
1448 | * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G | |
1449 | * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G | |
1450 | * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G | |
1451 | * followed by a copy of this with each element multiplied by 2^32. | |
1452 | * | |
1453 | * The reason for this is so that we can clock bits into four different | |
1454 | * locations when doing simple scalar multiplies against the base point, | |
1455 | * and then another four locations using the second 16 elements. | |
1456 | * | |
1457 | * Tables for other points have table[i] = iG for i in 0 .. 16. */ | |
1458 | ||
1459 | /* gmul is the table of precomputed base points */ | |
b853717f | 1460 | static const smallfelem gmul[2][16][3] = { |
0f113f3e MC |
1461 | {{{0, 0, 0, 0}, |
1462 | {0, 0, 0, 0}, | |
1463 | {0, 0, 0, 0}}, | |
1464 | {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, | |
1465 | 0x6b17d1f2e12c4247}, | |
1466 | {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, | |
1467 | 0x4fe342e2fe1a7f9b}, | |
1468 | {1, 0, 0, 0}}, | |
1469 | {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, | |
1470 | 0x0fa822bc2811aaa5}, | |
1471 | {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, | |
1472 | 0xbff44ae8f5dba80d}, | |
1473 | {1, 0, 0, 0}}, | |
1474 | {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, | |
1475 | 0x300a4bbc89d6726f}, | |
1476 | {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, | |
1477 | 0x72aac7e0d09b4644}, | |
1478 | {1, 0, 0, 0}}, | |
1479 | {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, | |
1480 | 0x447d739beedb5e67}, | |
1481 | {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, | |
1482 | 0x2d4825ab834131ee}, | |
1483 | {1, 0, 0, 0}}, | |
1484 | {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, | |
1485 | 0xef9519328a9c72ff}, | |
1486 | {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, | |
1487 | 0x611e9fc37dbb2c9b}, | |
1488 | {1, 0, 0, 0}}, | |
1489 | {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, | |
1490 | 0x550663797b51f5d8}, | |
1491 | {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, | |
1492 | 0x157164848aecb851}, | |
1493 | {1, 0, 0, 0}}, | |
1494 | {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, | |
1495 | 0xeb5d7745b21141ea}, | |
1496 | {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, | |
1497 | 0xeafd72ebdbecc17b}, | |
1498 | {1, 0, 0, 0}}, | |
1499 | {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, | |
1500 | 0xa6d39677a7849276}, | |
1501 | {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, | |
1502 | 0x674f84749b0b8816}, | |
1503 | {1, 0, 0, 0}}, | |
1504 | {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, | |
1505 | 0x4e769e7672c9ddad}, | |
1506 | {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, | |
1507 | 0x42b99082de830663}, | |
1508 | {1, 0, 0, 0}}, | |
1509 | {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, | |
1510 | 0x78878ef61c6ce04d}, | |
1511 | {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, | |
1512 | 0xb6cb3f5d7b72c321}, | |
1513 | {1, 0, 0, 0}}, | |
1514 | {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, | |
1515 | 0x0c88bc4d716b1287}, | |
1516 | {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, | |
1517 | 0xdd5ddea3f3901dc6}, | |
1518 | {1, 0, 0, 0}}, | |
1519 | {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, | |
1520 | 0x68f344af6b317466}, | |
1521 | {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, | |
1522 | 0x31b9c405f8540a20}, | |
1523 | {1, 0, 0, 0}}, | |
1524 | {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, | |
1525 | 0x4052bf4b6f461db9}, | |
1526 | {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, | |
1527 | 0xfecf4d5190b0fc61}, | |
1528 | {1, 0, 0, 0}}, | |
1529 | {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, | |
1530 | 0x1eddbae2c802e41a}, | |
1531 | {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, | |
1532 | 0x43104d86560ebcfc}, | |
1533 | {1, 0, 0, 0}}, | |
1534 | {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, | |
1535 | 0xb48e26b484f7a21c}, | |
1536 | {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, | |
1537 | 0xfac015404d4d3dab}, | |
1538 | {1, 0, 0, 0}}}, | |
1539 | {{{0, 0, 0, 0}, | |
1540 | {0, 0, 0, 0}, | |
1541 | {0, 0, 0, 0}}, | |
1542 | {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, | |
1543 | 0x7fe36b40af22af89}, | |
1544 | {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, | |
1545 | 0xe697d45825b63624}, | |
1546 | {1, 0, 0, 0}}, | |
1547 | {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, | |
1548 | 0x4a5b506612a677a6}, | |
1549 | {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, | |
1550 | 0xeb13461ceac089f1}, | |
1551 | {1, 0, 0, 0}}, | |
1552 | {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, | |
1553 | 0x0781b8291c6a220a}, | |
1554 | {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, | |
1555 | 0x690cde8df0151593}, | |
1556 | {1, 0, 0, 0}}, | |
1557 | {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, | |
1558 | 0x8a535f566ec73617}, | |
1559 | {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, | |
1560 | 0x0455c08468b08bd7}, | |
1561 | {1, 0, 0, 0}}, | |
1562 | {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, | |
1563 | 0x06bada7ab77f8276}, | |
1564 | {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, | |
1565 | 0x5b476dfd0e6cb18a}, | |
1566 | {1, 0, 0, 0}}, | |
1567 | {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, | |
1568 | 0x3e29864e8a2ec908}, | |
1569 | {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, | |
1570 | 0x239b90ea3dc31e7e}, | |
1571 | {1, 0, 0, 0}}, | |
1572 | {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, | |
1573 | 0x820f4dd949f72ff7}, | |
1574 | {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, | |
1575 | 0x140406ec783a05ec}, | |
1576 | {1, 0, 0, 0}}, | |
1577 | {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, | |
1578 | 0x68f6b8542783dfee}, | |
1579 | {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, | |
1580 | 0xcbe1feba92e40ce6}, | |
1581 | {1, 0, 0, 0}}, | |
1582 | {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, | |
1583 | 0xd0b2f94d2f420109}, | |
1584 | {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, | |
1585 | 0x971459828b0719e5}, | |
1586 | {1, 0, 0, 0}}, | |
1587 | {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, | |
1588 | 0x961610004a866aba}, | |
1589 | {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, | |
1590 | 0x7acb9fadcee75e44}, | |
1591 | {1, 0, 0, 0}}, | |
1592 | {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, | |
1593 | 0x24eb9acca333bf5b}, | |
1594 | {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, | |
1595 | 0x69f891c5acd079cc}, | |
1596 | {1, 0, 0, 0}}, | |
1597 | {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, | |
1598 | 0xe51f547c5972a107}, | |
1599 | {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, | |
1600 | 0x1c309a2b25bb1387}, | |
1601 | {1, 0, 0, 0}}, | |
1602 | {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, | |
1603 | 0x20b87b8aa2c4e503}, | |
1604 | {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, | |
1605 | 0xf5c6fa49919776be}, | |
1606 | {1, 0, 0, 0}}, | |
1607 | {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, | |
1608 | 0x1ed7d1b9332010b9}, | |
1609 | {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, | |
1610 | 0x3a2b03f03217257a}, | |
1611 | {1, 0, 0, 0}}, | |
1612 | {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, | |
1613 | 0x15fee545c78dd9f6}, | |
1614 | {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, | |
1615 | 0x4ab5b6b2b8753f81}, | |
1616 | {1, 0, 0, 0}}} | |
1617 | }; | |
1618 | ||
1619 | /* | |
1620 | * select_point selects the |idx|th point from a precomputation table and | |
1621 | * copies it to out. | |
1622 | */ | |
1623 | static void select_point(const u64 idx, unsigned int size, | |
1624 | const smallfelem pre_comp[16][3], smallfelem out[3]) | |
1625 | { | |
1626 | unsigned i, j; | |
1627 | u64 *outlimbs = &out[0][0]; | |
16f8d4eb | 1628 | |
88f4c6f3 | 1629 | memset(out, 0, sizeof(*out) * 3); |
0f113f3e MC |
1630 | |
1631 | for (i = 0; i < size; i++) { | |
1632 | const u64 *inlimbs = (u64 *)&pre_comp[i][0][0]; | |
1633 | u64 mask = i ^ idx; | |
1634 | mask |= mask >> 4; | |
1635 | mask |= mask >> 2; | |
1636 | mask |= mask >> 1; | |
1637 | mask &= 1; | |
1638 | mask--; | |
1639 | for (j = 0; j < NLIMBS * 3; j++) | |
1640 | outlimbs[j] |= inlimbs[j] & mask; | |
1641 | } | |
1642 | } | |
3e00b4c9 BM |
1643 | |
1644 | /* get_bit returns the |i|th bit in |in| */ | |
1645 | static char get_bit(const felem_bytearray in, int i) | |
0f113f3e MC |
1646 | { |
1647 | if ((i < 0) || (i >= 256)) | |
1648 | return 0; | |
1649 | return (in[i >> 3] >> (i & 7)) & 1; | |
1650 | } | |
1651 | ||
1652 | /* | |
1653 | * Interleaved point multiplication using precomputed point multiples: The | |
1654 | * small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[], the scalars | |
1655 | * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the | |
1656 | * generator, using certain (large) precomputed multiples in g_pre_comp. | |
1657 | * Output point (X, Y, Z) is stored in x_out, y_out, z_out | |
1658 | */ | |
3e00b4c9 | 1659 | static void batch_mul(felem x_out, felem y_out, felem z_out, |
0f113f3e MC |
1660 | const felem_bytearray scalars[], |
1661 | const unsigned num_points, const u8 *g_scalar, | |
1662 | const int mixed, const smallfelem pre_comp[][17][3], | |
1663 | const smallfelem g_pre_comp[2][16][3]) | |
1664 | { | |
1665 | int i, skip; | |
1666 | unsigned num, gen_mul = (g_scalar != NULL); | |
1667 | felem nq[3], ftmp; | |
1668 | smallfelem tmp[3]; | |
1669 | u64 bits; | |
1670 | u8 sign, digit; | |
1671 | ||
1672 | /* set nq to the point at infinity */ | |
16f8d4eb | 1673 | memset(nq, 0, sizeof(nq)); |
0f113f3e MC |
1674 | |
1675 | /* | |
1676 | * Loop over all scalars msb-to-lsb, interleaving additions of multiples | |
1677 | * of the generator (two in each of the last 32 rounds) and additions of | |
1678 | * other points multiples (every 5th round). | |
1679 | */ | |
1680 | skip = 1; /* save two point operations in the first | |
1681 | * round */ | |
1682 | for (i = (num_points ? 255 : 31); i >= 0; --i) { | |
1683 | /* double */ | |
1684 | if (!skip) | |
1685 | point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); | |
1686 | ||
1687 | /* add multiples of the generator */ | |
1688 | if (gen_mul && (i <= 31)) { | |
1689 | /* first, look 32 bits upwards */ | |
1690 | bits = get_bit(g_scalar, i + 224) << 3; | |
1691 | bits |= get_bit(g_scalar, i + 160) << 2; | |
1692 | bits |= get_bit(g_scalar, i + 96) << 1; | |
1693 | bits |= get_bit(g_scalar, i + 32); | |
1694 | /* select the point to add, in constant time */ | |
1695 | select_point(bits, 16, g_pre_comp[1], tmp); | |
1696 | ||
1697 | if (!skip) { | |
1698 | /* Arg 1 below is for "mixed" */ | |
1699 | point_add(nq[0], nq[1], nq[2], | |
1700 | nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); | |
1701 | } else { | |
1702 | smallfelem_expand(nq[0], tmp[0]); | |
1703 | smallfelem_expand(nq[1], tmp[1]); | |
1704 | smallfelem_expand(nq[2], tmp[2]); | |
1705 | skip = 0; | |
1706 | } | |
1707 | ||
1708 | /* second, look at the current position */ | |
1709 | bits = get_bit(g_scalar, i + 192) << 3; | |
1710 | bits |= get_bit(g_scalar, i + 128) << 2; | |
1711 | bits |= get_bit(g_scalar, i + 64) << 1; | |
1712 | bits |= get_bit(g_scalar, i); | |
1713 | /* select the point to add, in constant time */ | |
1714 | select_point(bits, 16, g_pre_comp[0], tmp); | |
1715 | /* Arg 1 below is for "mixed" */ | |
1716 | point_add(nq[0], nq[1], nq[2], | |
1717 | nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); | |
1718 | } | |
1719 | ||
1720 | /* do other additions every 5 doublings */ | |
1721 | if (num_points && (i % 5 == 0)) { | |
1722 | /* loop over all scalars */ | |
1723 | for (num = 0; num < num_points; ++num) { | |
1724 | bits = get_bit(scalars[num], i + 4) << 5; | |
1725 | bits |= get_bit(scalars[num], i + 3) << 4; | |
1726 | bits |= get_bit(scalars[num], i + 2) << 3; | |
1727 | bits |= get_bit(scalars[num], i + 1) << 2; | |
1728 | bits |= get_bit(scalars[num], i) << 1; | |
1729 | bits |= get_bit(scalars[num], i - 1); | |
1730 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); | |
1731 | ||
1732 | /* | |
1733 | * select the point to add or subtract, in constant time | |
1734 | */ | |
1735 | select_point(digit, 17, pre_comp[num], tmp); | |
1736 | smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative | |
1737 | * point */ | |
1738 | copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); | |
1739 | felem_contract(tmp[1], ftmp); | |
1740 | ||
1741 | if (!skip) { | |
1742 | point_add(nq[0], nq[1], nq[2], | |
1743 | nq[0], nq[1], nq[2], | |
1744 | mixed, tmp[0], tmp[1], tmp[2]); | |
1745 | } else { | |
1746 | smallfelem_expand(nq[0], tmp[0]); | |
1747 | smallfelem_expand(nq[1], tmp[1]); | |
1748 | smallfelem_expand(nq[2], tmp[2]); | |
1749 | skip = 0; | |
1750 | } | |
1751 | } | |
1752 | } | |
1753 | } | |
1754 | felem_assign(x_out, nq[0]); | |
1755 | felem_assign(y_out, nq[1]); | |
1756 | felem_assign(z_out, nq[2]); | |
1757 | } | |
3e00b4c9 BM |
1758 | |
1759 | /* Precomputation for the group generator. */ | |
3aef36ff | 1760 | struct nistp256_pre_comp_st { |
0f113f3e MC |
1761 | smallfelem g_pre_comp[2][16][3]; |
1762 | int references; | |
9b398ef2 | 1763 | CRYPTO_RWLOCK *lock; |
3aef36ff | 1764 | }; |
3e00b4c9 BM |
1765 | |
1766 | const EC_METHOD *EC_GFp_nistp256_method(void) | |
0f113f3e MC |
1767 | { |
1768 | static const EC_METHOD ret = { | |
1769 | EC_FLAGS_DEFAULT_OCT, | |
1770 | NID_X9_62_prime_field, | |
1771 | ec_GFp_nistp256_group_init, | |
1772 | ec_GFp_simple_group_finish, | |
1773 | ec_GFp_simple_group_clear_finish, | |
1774 | ec_GFp_nist_group_copy, | |
1775 | ec_GFp_nistp256_group_set_curve, | |
1776 | ec_GFp_simple_group_get_curve, | |
1777 | ec_GFp_simple_group_get_degree, | |
9ff9bccc | 1778 | ec_group_simple_order_bits, |
0f113f3e MC |
1779 | ec_GFp_simple_group_check_discriminant, |
1780 | ec_GFp_simple_point_init, | |
1781 | ec_GFp_simple_point_finish, | |
1782 | ec_GFp_simple_point_clear_finish, | |
1783 | ec_GFp_simple_point_copy, | |
1784 | ec_GFp_simple_point_set_to_infinity, | |
1785 | ec_GFp_simple_set_Jprojective_coordinates_GFp, | |
1786 | ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
1787 | ec_GFp_simple_point_set_affine_coordinates, | |
1788 | ec_GFp_nistp256_point_get_affine_coordinates, | |
1789 | 0 /* point_set_compressed_coordinates */ , | |
1790 | 0 /* point2oct */ , | |
1791 | 0 /* oct2point */ , | |
1792 | ec_GFp_simple_add, | |
1793 | ec_GFp_simple_dbl, | |
1794 | ec_GFp_simple_invert, | |
1795 | ec_GFp_simple_is_at_infinity, | |
1796 | ec_GFp_simple_is_on_curve, | |
1797 | ec_GFp_simple_cmp, | |
1798 | ec_GFp_simple_make_affine, | |
1799 | ec_GFp_simple_points_make_affine, | |
1800 | ec_GFp_nistp256_points_mul, | |
1801 | ec_GFp_nistp256_precompute_mult, | |
1802 | ec_GFp_nistp256_have_precompute_mult, | |
1803 | ec_GFp_nist_field_mul, | |
1804 | ec_GFp_nist_field_sqr, | |
1805 | 0 /* field_div */ , | |
1806 | 0 /* field_encode */ , | |
1807 | 0 /* field_decode */ , | |
9ff9bccc DSH |
1808 | 0, /* field_set_to_one */ |
1809 | ec_key_simple_priv2oct, | |
1810 | ec_key_simple_oct2priv, | |
1811 | 0, /* set private */ | |
1812 | ec_key_simple_generate_key, | |
1813 | ec_key_simple_check_key, | |
1814 | ec_key_simple_generate_public_key, | |
1815 | 0, /* keycopy */ | |
1816 | 0, /* keyfinish */ | |
1817 | ecdh_simple_compute_key | |
0f113f3e MC |
1818 | }; |
1819 | ||
1820 | return &ret; | |
1821 | } | |
3e00b4c9 BM |
1822 | |
1823 | /******************************************************************************/ | |
0f113f3e MC |
1824 | /* |
1825 | * FUNCTIONS TO MANAGE PRECOMPUTATION | |
3e00b4c9 BM |
1826 | */ |
1827 | ||
1828 | static NISTP256_PRE_COMP *nistp256_pre_comp_new() | |
0f113f3e | 1829 | { |
a2d0baa2 F |
1830 | NISTP256_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); |
1831 | ||
90945fa3 | 1832 | if (ret == NULL) { |
0f113f3e MC |
1833 | ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
1834 | return ret; | |
1835 | } | |
a2d0baa2 | 1836 | |
0f113f3e | 1837 | ret->references = 1; |
9b398ef2 AG |
1838 | |
1839 | ret->lock = CRYPTO_THREAD_lock_new(); | |
1840 | if (ret->lock == NULL) { | |
1841 | ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
1842 | OPENSSL_free(ret); | |
1843 | return NULL; | |
1844 | } | |
0f113f3e MC |
1845 | return ret; |
1846 | } | |
3e00b4c9 | 1847 | |
3aef36ff | 1848 | NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *p) |
0f113f3e | 1849 | { |
9b398ef2 | 1850 | int i; |
3aef36ff | 1851 | if (p != NULL) |
9b398ef2 | 1852 | CRYPTO_atomic_add(&p->references, 1, &i, p->lock); |
3aef36ff | 1853 | return p; |
0f113f3e | 1854 | } |
3e00b4c9 | 1855 | |
3aef36ff | 1856 | void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *pre) |
0f113f3e | 1857 | { |
9b398ef2 AG |
1858 | int i; |
1859 | ||
1860 | if (pre == NULL) | |
0f113f3e | 1861 | return; |
9b398ef2 AG |
1862 | |
1863 | CRYPTO_atomic_add(&pre->references, -1, &i, pre->lock); | |
1864 | REF_PRINT_COUNT("EC_nistp256", x); | |
1865 | if (i > 0) | |
1866 | return; | |
1867 | REF_ASSERT_ISNT(i < 0); | |
1868 | ||
1869 | CRYPTO_THREAD_lock_free(pre->lock); | |
0f113f3e MC |
1870 | OPENSSL_free(pre); |
1871 | } | |
3e00b4c9 | 1872 | |
3e00b4c9 | 1873 | /******************************************************************************/ |
0f113f3e MC |
1874 | /* |
1875 | * OPENSSL EC_METHOD FUNCTIONS | |
3e00b4c9 BM |
1876 | */ |
1877 | ||
1878 | int ec_GFp_nistp256_group_init(EC_GROUP *group) | |
0f113f3e MC |
1879 | { |
1880 | int ret; | |
1881 | ret = ec_GFp_simple_group_init(group); | |
1882 | group->a_is_minus3 = 1; | |
1883 | return ret; | |
1884 | } | |
3e00b4c9 BM |
1885 | |
1886 | int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, | |
0f113f3e MC |
1887 | const BIGNUM *a, const BIGNUM *b, |
1888 | BN_CTX *ctx) | |
1889 | { | |
1890 | int ret = 0; | |
1891 | BN_CTX *new_ctx = NULL; | |
1892 | BIGNUM *curve_p, *curve_a, *curve_b; | |
1893 | ||
1894 | if (ctx == NULL) | |
1895 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) | |
1896 | return 0; | |
1897 | BN_CTX_start(ctx); | |
1898 | if (((curve_p = BN_CTX_get(ctx)) == NULL) || | |
1899 | ((curve_a = BN_CTX_get(ctx)) == NULL) || | |
1900 | ((curve_b = BN_CTX_get(ctx)) == NULL)) | |
1901 | goto err; | |
1902 | BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); | |
1903 | BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); | |
1904 | BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b); | |
1905 | if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { | |
1906 | ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE, | |
1907 | EC_R_WRONG_CURVE_PARAMETERS); | |
1908 | goto err; | |
1909 | } | |
1910 | group->field_mod_func = BN_nist_mod_256; | |
1911 | ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); | |
1912 | err: | |
1913 | BN_CTX_end(ctx); | |
23a1d5e9 | 1914 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1915 | return ret; |
1916 | } | |
1917 | ||
1918 | /* | |
1919 | * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = | |
1920 | * (X/Z^2, Y/Z^3) | |
1921 | */ | |
3e00b4c9 | 1922 | int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, |
0f113f3e MC |
1923 | const EC_POINT *point, |
1924 | BIGNUM *x, BIGNUM *y, | |
1925 | BN_CTX *ctx) | |
1926 | { | |
1927 | felem z1, z2, x_in, y_in; | |
1928 | smallfelem x_out, y_out; | |
1929 | longfelem tmp; | |
1930 | ||
1931 | if (EC_POINT_is_at_infinity(group, point)) { | |
1932 | ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, | |
1933 | EC_R_POINT_AT_INFINITY); | |
1934 | return 0; | |
1935 | } | |
ace8f546 AP |
1936 | if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || |
1937 | (!BN_to_felem(z1, point->Z))) | |
0f113f3e MC |
1938 | return 0; |
1939 | felem_inv(z2, z1); | |
1940 | felem_square(tmp, z2); | |
1941 | felem_reduce(z1, tmp); | |
1942 | felem_mul(tmp, x_in, z1); | |
1943 | felem_reduce(x_in, tmp); | |
1944 | felem_contract(x_out, x_in); | |
1945 | if (x != NULL) { | |
1946 | if (!smallfelem_to_BN(x, x_out)) { | |
1947 | ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, | |
1948 | ERR_R_BN_LIB); | |
1949 | return 0; | |
1950 | } | |
1951 | } | |
1952 | felem_mul(tmp, z1, z2); | |
1953 | felem_reduce(z1, tmp); | |
1954 | felem_mul(tmp, y_in, z1); | |
1955 | felem_reduce(y_in, tmp); | |
1956 | felem_contract(y_out, y_in); | |
1957 | if (y != NULL) { | |
1958 | if (!smallfelem_to_BN(y, y_out)) { | |
1959 | ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, | |
1960 | ERR_R_BN_LIB); | |
1961 | return 0; | |
1962 | } | |
1963 | } | |
1964 | return 1; | |
1965 | } | |
3e00b4c9 | 1966 | |
b853717f | 1967 | /* points below is of size |num|, and tmp_smallfelems is of size |num+1| */ |
0f113f3e MC |
1968 | static void make_points_affine(size_t num, smallfelem points[][3], |
1969 | smallfelem tmp_smallfelems[]) | |
1970 | { | |
1971 | /* | |
1972 | * Runs in constant time, unless an input is the point at infinity (which | |
1973 | * normally shouldn't happen). | |
1974 | */ | |
1975 | ec_GFp_nistp_points_make_affine_internal(num, | |
1976 | points, | |
1977 | sizeof(smallfelem), | |
1978 | tmp_smallfelems, | |
1979 | (void (*)(void *))smallfelem_one, | |
1980 | (int (*)(const void *)) | |
1981 | smallfelem_is_zero_int, | |
1982 | (void (*)(void *, const void *)) | |
1983 | smallfelem_assign, | |
1984 | (void (*)(void *, const void *)) | |
1985 | smallfelem_square_contract, | |
1986 | (void (*) | |
1987 | (void *, const void *, | |
1988 | const void *)) | |
1989 | smallfelem_mul_contract, | |
1990 | (void (*)(void *, const void *)) | |
1991 | smallfelem_inv_contract, | |
1992 | /* nothing to contract */ | |
1993 | (void (*)(void *, const void *)) | |
1994 | smallfelem_assign); | |
1995 | } | |
1996 | ||
1997 | /* | |
1998 | * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL | |
1999 | * values Result is stored in r (r can equal one of the inputs). | |
2000 | */ | |
3e00b4c9 | 2001 | int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, |
0f113f3e MC |
2002 | const BIGNUM *scalar, size_t num, |
2003 | const EC_POINT *points[], | |
2004 | const BIGNUM *scalars[], BN_CTX *ctx) | |
2005 | { | |
2006 | int ret = 0; | |
2007 | int j; | |
2008 | int mixed = 0; | |
2009 | BN_CTX *new_ctx = NULL; | |
2010 | BIGNUM *x, *y, *z, *tmp_scalar; | |
2011 | felem_bytearray g_secret; | |
2012 | felem_bytearray *secrets = NULL; | |
16f8d4eb | 2013 | smallfelem (*pre_comp)[17][3] = NULL; |
0f113f3e MC |
2014 | smallfelem *tmp_smallfelems = NULL; |
2015 | felem_bytearray tmp; | |
2016 | unsigned i, num_bytes; | |
2017 | int have_pre_comp = 0; | |
2018 | size_t num_points = num; | |
2019 | smallfelem x_in, y_in, z_in; | |
2020 | felem x_out, y_out, z_out; | |
2021 | NISTP256_PRE_COMP *pre = NULL; | |
2022 | const smallfelem(*g_pre_comp)[16][3] = NULL; | |
2023 | EC_POINT *generator = NULL; | |
2024 | const EC_POINT *p = NULL; | |
2025 | const BIGNUM *p_scalar = NULL; | |
2026 | ||
2027 | if (ctx == NULL) | |
2028 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) | |
2029 | return 0; | |
2030 | BN_CTX_start(ctx); | |
2031 | if (((x = BN_CTX_get(ctx)) == NULL) || | |
2032 | ((y = BN_CTX_get(ctx)) == NULL) || | |
2033 | ((z = BN_CTX_get(ctx)) == NULL) || | |
2034 | ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) | |
2035 | goto err; | |
2036 | ||
2037 | if (scalar != NULL) { | |
3aef36ff | 2038 | pre = group->pre_comp.nistp256; |
0f113f3e MC |
2039 | if (pre) |
2040 | /* we have precomputation, try to use it */ | |
2041 | g_pre_comp = (const smallfelem(*)[16][3])pre->g_pre_comp; | |
2042 | else | |
2043 | /* try to use the standard precomputation */ | |
2044 | g_pre_comp = &gmul[0]; | |
2045 | generator = EC_POINT_new(group); | |
2046 | if (generator == NULL) | |
2047 | goto err; | |
2048 | /* get the generator from precomputation */ | |
2049 | if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || | |
2050 | !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || | |
2051 | !smallfelem_to_BN(z, g_pre_comp[0][1][2])) { | |
2052 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); | |
2053 | goto err; | |
2054 | } | |
2055 | if (!EC_POINT_set_Jprojective_coordinates_GFp(group, | |
2056 | generator, x, y, z, | |
2057 | ctx)) | |
2058 | goto err; | |
2059 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) | |
2060 | /* precomputation matches generator */ | |
2061 | have_pre_comp = 1; | |
2062 | else | |
2063 | /* | |
2064 | * we don't have valid precomputation: treat the generator as a | |
2065 | * random point | |
2066 | */ | |
2067 | num_points++; | |
2068 | } | |
2069 | if (num_points > 0) { | |
2070 | if (num_points >= 3) { | |
2071 | /* | |
2072 | * unless we precompute multiples for just one or two points, | |
2073 | * converting those into affine form is time well spent | |
2074 | */ | |
2075 | mixed = 1; | |
2076 | } | |
16f8d4eb RS |
2077 | secrets = OPENSSL_malloc(sizeof(*secrets) * num_points); |
2078 | pre_comp = OPENSSL_malloc(sizeof(*pre_comp) * num_points); | |
0f113f3e MC |
2079 | if (mixed) |
2080 | tmp_smallfelems = | |
16f8d4eb | 2081 | OPENSSL_malloc(sizeof(*tmp_smallfelems) * (num_points * 17 + 1)); |
0f113f3e MC |
2082 | if ((secrets == NULL) || (pre_comp == NULL) |
2083 | || (mixed && (tmp_smallfelems == NULL))) { | |
2084 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE); | |
2085 | goto err; | |
2086 | } | |
2087 | ||
2088 | /* | |
2089 | * we treat NULL scalars as 0, and NULL points as points at infinity, | |
2090 | * i.e., they contribute nothing to the linear combination | |
2091 | */ | |
16f8d4eb RS |
2092 | memset(secrets, 0, sizeof(*secrets) * num_points); |
2093 | memset(pre_comp, 0, sizeof(*pre_comp) * num_points); | |
0f113f3e MC |
2094 | for (i = 0; i < num_points; ++i) { |
2095 | if (i == num) | |
2096 | /* | |
2097 | * we didn't have a valid precomputation, so we pick the | |
2098 | * generator | |
2099 | */ | |
2100 | { | |
2101 | p = EC_GROUP_get0_generator(group); | |
2102 | p_scalar = scalar; | |
2103 | } else | |
2104 | /* the i^th point */ | |
2105 | { | |
2106 | p = points[i]; | |
2107 | p_scalar = scalars[i]; | |
2108 | } | |
2109 | if ((p_scalar != NULL) && (p != NULL)) { | |
2110 | /* reduce scalar to 0 <= scalar < 2^256 */ | |
2111 | if ((BN_num_bits(p_scalar) > 256) | |
2112 | || (BN_is_negative(p_scalar))) { | |
2113 | /* | |
2114 | * this is an unusual input, and we don't guarantee | |
2115 | * constant-timeness | |
2116 | */ | |
ace8f546 | 2117 | if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { |
0f113f3e MC |
2118 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); |
2119 | goto err; | |
2120 | } | |
2121 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
2122 | } else | |
2123 | num_bytes = BN_bn2bin(p_scalar, tmp); | |
2124 | flip_endian(secrets[i], tmp, num_bytes); | |
2125 | /* precompute multiples */ | |
ace8f546 AP |
2126 | if ((!BN_to_felem(x_out, p->X)) || |
2127 | (!BN_to_felem(y_out, p->Y)) || | |
2128 | (!BN_to_felem(z_out, p->Z))) | |
0f113f3e MC |
2129 | goto err; |
2130 | felem_shrink(pre_comp[i][1][0], x_out); | |
2131 | felem_shrink(pre_comp[i][1][1], y_out); | |
2132 | felem_shrink(pre_comp[i][1][2], z_out); | |
2133 | for (j = 2; j <= 16; ++j) { | |
2134 | if (j & 1) { | |
2135 | point_add_small(pre_comp[i][j][0], pre_comp[i][j][1], | |
2136 | pre_comp[i][j][2], pre_comp[i][1][0], | |
2137 | pre_comp[i][1][1], pre_comp[i][1][2], | |
2138 | pre_comp[i][j - 1][0], | |
2139 | pre_comp[i][j - 1][1], | |
2140 | pre_comp[i][j - 1][2]); | |
2141 | } else { | |
2142 | point_double_small(pre_comp[i][j][0], | |
2143 | pre_comp[i][j][1], | |
2144 | pre_comp[i][j][2], | |
2145 | pre_comp[i][j / 2][0], | |
2146 | pre_comp[i][j / 2][1], | |
2147 | pre_comp[i][j / 2][2]); | |
2148 | } | |
2149 | } | |
2150 | } | |
2151 | } | |
2152 | if (mixed) | |
2153 | make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems); | |
2154 | } | |
2155 | ||
2156 | /* the scalar for the generator */ | |
2157 | if ((scalar != NULL) && (have_pre_comp)) { | |
2158 | memset(g_secret, 0, sizeof(g_secret)); | |
2159 | /* reduce scalar to 0 <= scalar < 2^256 */ | |
2160 | if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) { | |
2161 | /* | |
2162 | * this is an unusual input, and we don't guarantee | |
2163 | * constant-timeness | |
2164 | */ | |
ace8f546 | 2165 | if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { |
0f113f3e MC |
2166 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); |
2167 | goto err; | |
2168 | } | |
2169 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
2170 | } else | |
2171 | num_bytes = BN_bn2bin(scalar, tmp); | |
2172 | flip_endian(g_secret, tmp, num_bytes); | |
2173 | /* do the multiplication with generator precomputation */ | |
2174 | batch_mul(x_out, y_out, z_out, | |
2175 | (const felem_bytearray(*))secrets, num_points, | |
2176 | g_secret, | |
2177 | mixed, (const smallfelem(*)[17][3])pre_comp, g_pre_comp); | |
2178 | } else | |
2179 | /* do the multiplication without generator precomputation */ | |
2180 | batch_mul(x_out, y_out, z_out, | |
2181 | (const felem_bytearray(*))secrets, num_points, | |
2182 | NULL, mixed, (const smallfelem(*)[17][3])pre_comp, NULL); | |
2183 | /* reduce the output to its unique minimal representation */ | |
2184 | felem_contract(x_in, x_out); | |
2185 | felem_contract(y_in, y_out); | |
2186 | felem_contract(z_in, z_out); | |
2187 | if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || | |
2188 | (!smallfelem_to_BN(z, z_in))) { | |
2189 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); | |
2190 | goto err; | |
2191 | } | |
2192 | ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); | |
2193 | ||
2194 | err: | |
2195 | BN_CTX_end(ctx); | |
8fdc3734 | 2196 | EC_POINT_free(generator); |
23a1d5e9 | 2197 | BN_CTX_free(new_ctx); |
b548a1f1 RS |
2198 | OPENSSL_free(secrets); |
2199 | OPENSSL_free(pre_comp); | |
2200 | OPENSSL_free(tmp_smallfelems); | |
0f113f3e MC |
2201 | return ret; |
2202 | } | |
3e00b4c9 BM |
2203 | |
2204 | int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) | |
0f113f3e MC |
2205 | { |
2206 | int ret = 0; | |
2207 | NISTP256_PRE_COMP *pre = NULL; | |
2208 | int i, j; | |
2209 | BN_CTX *new_ctx = NULL; | |
2210 | BIGNUM *x, *y; | |
2211 | EC_POINT *generator = NULL; | |
2212 | smallfelem tmp_smallfelems[32]; | |
2213 | felem x_tmp, y_tmp, z_tmp; | |
2214 | ||
2215 | /* throw away old precomputation */ | |
2c52ac9b | 2216 | EC_pre_comp_free(group); |
0f113f3e MC |
2217 | if (ctx == NULL) |
2218 | if ((ctx = new_ctx = BN_CTX_new()) == NULL) | |
2219 | return 0; | |
2220 | BN_CTX_start(ctx); | |
2221 | if (((x = BN_CTX_get(ctx)) == NULL) || ((y = BN_CTX_get(ctx)) == NULL)) | |
2222 | goto err; | |
2223 | /* get the generator */ | |
2224 | if (group->generator == NULL) | |
2225 | goto err; | |
2226 | generator = EC_POINT_new(group); | |
2227 | if (generator == NULL) | |
2228 | goto err; | |
2229 | BN_bin2bn(nistp256_curve_params[3], sizeof(felem_bytearray), x); | |
2230 | BN_bin2bn(nistp256_curve_params[4], sizeof(felem_bytearray), y); | |
2231 | if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) | |
2232 | goto err; | |
2233 | if ((pre = nistp256_pre_comp_new()) == NULL) | |
2234 | goto err; | |
2235 | /* | |
2236 | * if the generator is the standard one, use built-in precomputation | |
2237 | */ | |
2238 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { | |
2239 | memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); | |
615614c8 | 2240 | goto done; |
0f113f3e | 2241 | } |
ace8f546 AP |
2242 | if ((!BN_to_felem(x_tmp, group->generator->X)) || |
2243 | (!BN_to_felem(y_tmp, group->generator->Y)) || | |
2244 | (!BN_to_felem(z_tmp, group->generator->Z))) | |
0f113f3e MC |
2245 | goto err; |
2246 | felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); | |
2247 | felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); | |
2248 | felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); | |
2249 | /* | |
2250 | * compute 2^64*G, 2^128*G, 2^192*G for the first table, 2^32*G, 2^96*G, | |
2251 | * 2^160*G, 2^224*G for the second one | |
2252 | */ | |
2253 | for (i = 1; i <= 8; i <<= 1) { | |
2254 | point_double_small(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], | |
2255 | pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0], | |
2256 | pre->g_pre_comp[0][i][1], | |
2257 | pre->g_pre_comp[0][i][2]); | |
2258 | for (j = 0; j < 31; ++j) { | |
2259 | point_double_small(pre->g_pre_comp[1][i][0], | |
2260 | pre->g_pre_comp[1][i][1], | |
2261 | pre->g_pre_comp[1][i][2], | |
2262 | pre->g_pre_comp[1][i][0], | |
2263 | pre->g_pre_comp[1][i][1], | |
2264 | pre->g_pre_comp[1][i][2]); | |
2265 | } | |
2266 | if (i == 8) | |
2267 | break; | |
2268 | point_double_small(pre->g_pre_comp[0][2 * i][0], | |
2269 | pre->g_pre_comp[0][2 * i][1], | |
2270 | pre->g_pre_comp[0][2 * i][2], | |
2271 | pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], | |
2272 | pre->g_pre_comp[1][i][2]); | |
2273 | for (j = 0; j < 31; ++j) { | |
2274 | point_double_small(pre->g_pre_comp[0][2 * i][0], | |
2275 | pre->g_pre_comp[0][2 * i][1], | |
2276 | pre->g_pre_comp[0][2 * i][2], | |
2277 | pre->g_pre_comp[0][2 * i][0], | |
2278 | pre->g_pre_comp[0][2 * i][1], | |
2279 | pre->g_pre_comp[0][2 * i][2]); | |
2280 | } | |
2281 | } | |
2282 | for (i = 0; i < 2; i++) { | |
2283 | /* g_pre_comp[i][0] is the point at infinity */ | |
2284 | memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); | |
2285 | /* the remaining multiples */ | |
2286 | /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ | |
2287 | point_add_small(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], | |
2288 | pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], | |
2289 | pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], | |
2290 | pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
2291 | pre->g_pre_comp[i][2][2]); | |
2292 | /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ | |
2293 | point_add_small(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], | |
2294 | pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], | |
2295 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
2296 | pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
2297 | pre->g_pre_comp[i][2][2]); | |
2298 | /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ | |
2299 | point_add_small(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], | |
2300 | pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], | |
2301 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
2302 | pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], | |
2303 | pre->g_pre_comp[i][4][2]); | |
2304 | /* | |
2305 | * 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G | |
2306 | */ | |
2307 | point_add_small(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], | |
2308 | pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], | |
2309 | pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], | |
2310 | pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
2311 | pre->g_pre_comp[i][2][2]); | |
2312 | for (j = 1; j < 8; ++j) { | |
2313 | /* odd multiples: add G resp. 2^32*G */ | |
2314 | point_add_small(pre->g_pre_comp[i][2 * j + 1][0], | |
2315 | pre->g_pre_comp[i][2 * j + 1][1], | |
2316 | pre->g_pre_comp[i][2 * j + 1][2], | |
2317 | pre->g_pre_comp[i][2 * j][0], | |
2318 | pre->g_pre_comp[i][2 * j][1], | |
2319 | pre->g_pre_comp[i][2 * j][2], | |
2320 | pre->g_pre_comp[i][1][0], | |
2321 | pre->g_pre_comp[i][1][1], | |
2322 | pre->g_pre_comp[i][1][2]); | |
2323 | } | |
2324 | } | |
2325 | make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems); | |
2326 | ||
615614c8 | 2327 | done: |
3aef36ff | 2328 | SETPRECOMP(group, nistp256, pre); |
0f113f3e | 2329 | pre = NULL; |
3aef36ff RS |
2330 | ret = 1; |
2331 | ||
3e00b4c9 | 2332 | err: |
0f113f3e | 2333 | BN_CTX_end(ctx); |
8fdc3734 | 2334 | EC_POINT_free(generator); |
23a1d5e9 | 2335 | BN_CTX_free(new_ctx); |
3aef36ff | 2336 | EC_nistp256_pre_comp_free(pre); |
0f113f3e MC |
2337 | return ret; |
2338 | } | |
3e00b4c9 BM |
2339 | |
2340 | int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) | |
0f113f3e | 2341 | { |
3aef36ff | 2342 | return HAVEPRECOMP(group, nistp256); |
0f113f3e | 2343 | } |
3e00b4c9 | 2344 | #endif |