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3e00b4c9 | 1 | /* |
0d664759 | 2 | * Copyright 2011-2018 The OpenSSL Project Authors. All Rights Reserved. |
4f22f405 | 3 | * |
a7f182b7 | 4 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
4f22f405 RS |
5 | * this file except in compliance with the License. You can obtain a copy |
6 | * in the file LICENSE in the source distribution or at | |
7 | * https://www.openssl.org/source/license.html | |
3e00b4c9 | 8 | */ |
4f22f405 | 9 | |
3e00b4c9 BM |
10 | /* Copyright 2011 Google Inc. |
11 | * | |
12 | * Licensed under the Apache License, Version 2.0 (the "License"); | |
13 | * | |
14 | * you may not use this file except in compliance with the License. | |
15 | * You may obtain a copy of the License at | |
16 | * | |
17 | * http://www.apache.org/licenses/LICENSE-2.0 | |
18 | * | |
19 | * Unless required by applicable law or agreed to in writing, software | |
20 | * distributed under the License is distributed on an "AS IS" BASIS, | |
21 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
22 | * See the License for the specific language governing permissions and | |
23 | * limitations under the License. | |
24 | */ | |
25 | ||
26 | /* | |
27 | * A 64-bit implementation of the NIST P-256 elliptic curve point multiplication | |
28 | * | |
29 | * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. | |
30 | * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 | |
31 | * work which got its smarts from Daniel J. Bernstein's work on the same. | |
32 | */ | |
33 | ||
e0d6132b | 34 | #include <openssl/opensslconf.h> |
effaf4de RS |
35 | #ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 |
36 | NON_EMPTY_TRANSLATION_UNIT | |
37 | #else | |
3e00b4c9 | 38 | |
0f113f3e MC |
39 | # include <stdint.h> |
40 | # include <string.h> | |
41 | # include <openssl/err.h> | |
42 | # include "ec_lcl.h" | |
3e00b4c9 | 43 | |
6afed267 | 44 | # if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 |
3e00b4c9 | 45 | /* even with gcc, the typedef won't work for 32-bit platforms */ |
0f113f3e MC |
46 | typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit |
47 | * platforms */ | |
48 | typedef __int128_t int128_t; | |
49 | # else | |
8cc1dc36 | 50 | # error "Your compiler doesn't appear to support 128-bit integer types" |
0f113f3e | 51 | # endif |
3e00b4c9 BM |
52 | |
53 | typedef uint8_t u8; | |
54 | typedef uint32_t u32; | |
55 | typedef uint64_t u64; | |
3e00b4c9 | 56 | |
0f113f3e MC |
57 | /* |
58 | * The underlying field. P256 operates over GF(2^256-2^224+2^192+2^96-1). We | |
59 | * can serialise an element of this field into 32 bytes. We call this an | |
60 | * felem_bytearray. | |
61 | */ | |
3e00b4c9 BM |
62 | |
63 | typedef u8 felem_bytearray[32]; | |
64 | ||
0f113f3e MC |
65 | /* |
66 | * These are the parameters of P256, taken from FIPS 186-3, page 86. These | |
67 | * values are big-endian. | |
68 | */ | |
3e00b4c9 | 69 | static const felem_bytearray nistp256_curve_params[5] = { |
0f113f3e MC |
70 | {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */ |
71 | 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, | |
72 | 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, | |
73 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, | |
74 | {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */ | |
75 | 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, | |
76 | 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, | |
77 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */ | |
78 | {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7, | |
79 | 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc, | |
80 | 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6, | |
81 | 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b}, | |
82 | {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */ | |
83 | 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2, | |
84 | 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0, | |
85 | 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96}, | |
86 | {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */ | |
87 | 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16, | |
88 | 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce, | |
89 | 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5} | |
3e00b4c9 BM |
90 | }; |
91 | ||
1d97c843 TH |
92 | /*- |
93 | * The representation of field elements. | |
3e00b4c9 BM |
94 | * ------------------------------------ |
95 | * | |
96 | * We represent field elements with either four 128-bit values, eight 128-bit | |
97 | * values, or four 64-bit values. The field element represented is: | |
98 | * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192 (mod p) | |
99 | * or: | |
100 | * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512 (mod p) | |
101 | * | |
102 | * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits | |
103 | * apart, but are 128-bits wide, the most significant bits of each limb overlap | |
104 | * with the least significant bits of the next. | |
105 | * | |
106 | * A field element with four limbs is an 'felem'. One with eight limbs is a | |
107 | * 'longfelem' | |
108 | * | |
109 | * A field element with four, 64-bit values is called a 'smallfelem'. Small | |
110 | * values are used as intermediate values before multiplication. | |
111 | */ | |
112 | ||
0f113f3e | 113 | # define NLIMBS 4 |
3e00b4c9 BM |
114 | |
115 | typedef uint128_t limb; | |
116 | typedef limb felem[NLIMBS]; | |
117 | typedef limb longfelem[NLIMBS * 2]; | |
118 | typedef u64 smallfelem[NLIMBS]; | |
119 | ||
120 | /* This is the value of the prime as four 64-bit words, little-endian. */ | |
0f113f3e MC |
121 | static const u64 kPrime[4] = |
122 | { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; | |
3e00b4c9 BM |
123 | static const u64 bottom63bits = 0x7ffffffffffffffful; |
124 | ||
0f113f3e MC |
125 | /* |
126 | * bin32_to_felem takes a little-endian byte array and converts it into felem | |
127 | * form. This assumes that the CPU is little-endian. | |
128 | */ | |
3e00b4c9 | 129 | static void bin32_to_felem(felem out, const u8 in[32]) |
0f113f3e MC |
130 | { |
131 | out[0] = *((u64 *)&in[0]); | |
132 | out[1] = *((u64 *)&in[8]); | |
133 | out[2] = *((u64 *)&in[16]); | |
134 | out[3] = *((u64 *)&in[24]); | |
135 | } | |
136 | ||
137 | /* | |
138 | * smallfelem_to_bin32 takes a smallfelem and serialises into a little | |
139 | * endian, 32 byte array. This assumes that the CPU is little-endian. | |
140 | */ | |
3e00b4c9 | 141 | static void smallfelem_to_bin32(u8 out[32], const smallfelem in) |
0f113f3e MC |
142 | { |
143 | *((u64 *)&out[0]) = in[0]; | |
144 | *((u64 *)&out[8]) = in[1]; | |
145 | *((u64 *)&out[16]) = in[2]; | |
146 | *((u64 *)&out[24]) = in[3]; | |
147 | } | |
3e00b4c9 BM |
148 | |
149 | /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ | |
150 | static void flip_endian(u8 *out, const u8 *in, unsigned len) | |
0f113f3e MC |
151 | { |
152 | unsigned i; | |
153 | for (i = 0; i < len; ++i) | |
154 | out[i] = in[len - 1 - i]; | |
155 | } | |
3e00b4c9 BM |
156 | |
157 | /* BN_to_felem converts an OpenSSL BIGNUM into an felem */ | |
158 | static int BN_to_felem(felem out, const BIGNUM *bn) | |
0f113f3e MC |
159 | { |
160 | felem_bytearray b_in; | |
161 | felem_bytearray b_out; | |
162 | unsigned num_bytes; | |
163 | ||
164 | /* BN_bn2bin eats leading zeroes */ | |
16f8d4eb | 165 | memset(b_out, 0, sizeof(b_out)); |
0f113f3e | 166 | num_bytes = BN_num_bytes(bn); |
cbe29648 | 167 | if (num_bytes > sizeof(b_out)) { |
0f113f3e MC |
168 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); |
169 | return 0; | |
170 | } | |
171 | if (BN_is_negative(bn)) { | |
172 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); | |
173 | return 0; | |
174 | } | |
175 | num_bytes = BN_bn2bin(bn, b_in); | |
176 | flip_endian(b_out, b_in, num_bytes); | |
177 | bin32_to_felem(out, b_out); | |
178 | return 1; | |
179 | } | |
3e00b4c9 BM |
180 | |
181 | /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ | |
182 | static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) | |
0f113f3e MC |
183 | { |
184 | felem_bytearray b_in, b_out; | |
185 | smallfelem_to_bin32(b_in, in); | |
cbe29648 RS |
186 | flip_endian(b_out, b_in, sizeof(b_out)); |
187 | return BN_bin2bn(b_out, sizeof(b_out), out); | |
0f113f3e | 188 | } |
3e00b4c9 | 189 | |
3a83462d MC |
190 | /*- |
191 | * Field operations | |
192 | * ---------------- | |
193 | */ | |
3e00b4c9 BM |
194 | |
195 | static void smallfelem_one(smallfelem out) | |
0f113f3e MC |
196 | { |
197 | out[0] = 1; | |
198 | out[1] = 0; | |
199 | out[2] = 0; | |
200 | out[3] = 0; | |
201 | } | |
3e00b4c9 BM |
202 | |
203 | static void smallfelem_assign(smallfelem out, const smallfelem in) | |
0f113f3e MC |
204 | { |
205 | out[0] = in[0]; | |
206 | out[1] = in[1]; | |
207 | out[2] = in[2]; | |
208 | out[3] = in[3]; | |
209 | } | |
3e00b4c9 BM |
210 | |
211 | static void felem_assign(felem out, const felem in) | |
0f113f3e MC |
212 | { |
213 | out[0] = in[0]; | |
214 | out[1] = in[1]; | |
215 | out[2] = in[2]; | |
216 | out[3] = in[3]; | |
217 | } | |
3e00b4c9 BM |
218 | |
219 | /* felem_sum sets out = out + in. */ | |
220 | static void felem_sum(felem out, const felem in) | |
0f113f3e MC |
221 | { |
222 | out[0] += in[0]; | |
223 | out[1] += in[1]; | |
224 | out[2] += in[2]; | |
225 | out[3] += in[3]; | |
226 | } | |
3e00b4c9 BM |
227 | |
228 | /* felem_small_sum sets out = out + in. */ | |
229 | static void felem_small_sum(felem out, const smallfelem in) | |
0f113f3e MC |
230 | { |
231 | out[0] += in[0]; | |
232 | out[1] += in[1]; | |
233 | out[2] += in[2]; | |
234 | out[3] += in[3]; | |
235 | } | |
3e00b4c9 BM |
236 | |
237 | /* felem_scalar sets out = out * scalar */ | |
238 | static void felem_scalar(felem out, const u64 scalar) | |
0f113f3e MC |
239 | { |
240 | out[0] *= scalar; | |
241 | out[1] *= scalar; | |
242 | out[2] *= scalar; | |
243 | out[3] *= scalar; | |
244 | } | |
3e00b4c9 BM |
245 | |
246 | /* longfelem_scalar sets out = out * scalar */ | |
247 | static void longfelem_scalar(longfelem out, const u64 scalar) | |
0f113f3e MC |
248 | { |
249 | out[0] *= scalar; | |
250 | out[1] *= scalar; | |
251 | out[2] *= scalar; | |
252 | out[3] *= scalar; | |
253 | out[4] *= scalar; | |
254 | out[5] *= scalar; | |
255 | out[6] *= scalar; | |
256 | out[7] *= scalar; | |
257 | } | |
258 | ||
259 | # define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) | |
260 | # define two105 (((limb)1) << 105) | |
261 | # define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) | |
3e00b4c9 BM |
262 | |
263 | /* zero105 is 0 mod p */ | |
0f113f3e MC |
264 | static const felem zero105 = |
265 | { two105m41m9, two105, two105m41p9, two105m41p9 }; | |
3e00b4c9 | 266 | |
1d97c843 TH |
267 | /*- |
268 | * smallfelem_neg sets |out| to |-small| | |
3e00b4c9 BM |
269 | * On exit: |
270 | * out[i] < out[i] + 2^105 | |
271 | */ | |
272 | static void smallfelem_neg(felem out, const smallfelem small) | |
0f113f3e MC |
273 | { |
274 | /* In order to prevent underflow, we subtract from 0 mod p. */ | |
275 | out[0] = zero105[0] - small[0]; | |
276 | out[1] = zero105[1] - small[1]; | |
277 | out[2] = zero105[2] - small[2]; | |
278 | out[3] = zero105[3] - small[3]; | |
279 | } | |
3e00b4c9 | 280 | |
1d97c843 TH |
281 | /*- |
282 | * felem_diff subtracts |in| from |out| | |
3e00b4c9 BM |
283 | * On entry: |
284 | * in[i] < 2^104 | |
285 | * On exit: | |
286 | * out[i] < out[i] + 2^105 | |
287 | */ | |
288 | static void felem_diff(felem out, const felem in) | |
0f113f3e MC |
289 | { |
290 | /* | |
291 | * In order to prevent underflow, we add 0 mod p before subtracting. | |
292 | */ | |
293 | out[0] += zero105[0]; | |
294 | out[1] += zero105[1]; | |
295 | out[2] += zero105[2]; | |
296 | out[3] += zero105[3]; | |
297 | ||
298 | out[0] -= in[0]; | |
299 | out[1] -= in[1]; | |
300 | out[2] -= in[2]; | |
301 | out[3] -= in[3]; | |
302 | } | |
303 | ||
304 | # define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) | |
305 | # define two107 (((limb)1) << 107) | |
306 | # define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) | |
3e00b4c9 BM |
307 | |
308 | /* zero107 is 0 mod p */ | |
0f113f3e MC |
309 | static const felem zero107 = |
310 | { two107m43m11, two107, two107m43p11, two107m43p11 }; | |
3e00b4c9 | 311 | |
1d97c843 TH |
312 | /*- |
313 | * An alternative felem_diff for larger inputs |in| | |
3e00b4c9 BM |
314 | * felem_diff_zero107 subtracts |in| from |out| |
315 | * On entry: | |
316 | * in[i] < 2^106 | |
317 | * On exit: | |
318 | * out[i] < out[i] + 2^107 | |
319 | */ | |
320 | static void felem_diff_zero107(felem out, const felem in) | |
0f113f3e MC |
321 | { |
322 | /* | |
323 | * In order to prevent underflow, we add 0 mod p before subtracting. | |
324 | */ | |
325 | out[0] += zero107[0]; | |
326 | out[1] += zero107[1]; | |
327 | out[2] += zero107[2]; | |
328 | out[3] += zero107[3]; | |
329 | ||
330 | out[0] -= in[0]; | |
331 | out[1] -= in[1]; | |
332 | out[2] -= in[2]; | |
333 | out[3] -= in[3]; | |
334 | } | |
3e00b4c9 | 335 | |
1d97c843 TH |
336 | /*- |
337 | * longfelem_diff subtracts |in| from |out| | |
3e00b4c9 BM |
338 | * On entry: |
339 | * in[i] < 7*2^67 | |
340 | * On exit: | |
341 | * out[i] < out[i] + 2^70 + 2^40 | |
342 | */ | |
343 | static void longfelem_diff(longfelem out, const longfelem in) | |
0f113f3e MC |
344 | { |
345 | static const limb two70m8p6 = | |
346 | (((limb) 1) << 70) - (((limb) 1) << 8) + (((limb) 1) << 6); | |
347 | static const limb two70p40 = (((limb) 1) << 70) + (((limb) 1) << 40); | |
348 | static const limb two70 = (((limb) 1) << 70); | |
349 | static const limb two70m40m38p6 = | |
350 | (((limb) 1) << 70) - (((limb) 1) << 40) - (((limb) 1) << 38) + | |
351 | (((limb) 1) << 6); | |
352 | static const limb two70m6 = (((limb) 1) << 70) - (((limb) 1) << 6); | |
353 | ||
354 | /* add 0 mod p to avoid underflow */ | |
355 | out[0] += two70m8p6; | |
356 | out[1] += two70p40; | |
357 | out[2] += two70; | |
358 | out[3] += two70m40m38p6; | |
359 | out[4] += two70m6; | |
360 | out[5] += two70m6; | |
361 | out[6] += two70m6; | |
362 | out[7] += two70m6; | |
363 | ||
364 | /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */ | |
365 | out[0] -= in[0]; | |
366 | out[1] -= in[1]; | |
367 | out[2] -= in[2]; | |
368 | out[3] -= in[3]; | |
369 | out[4] -= in[4]; | |
370 | out[5] -= in[5]; | |
371 | out[6] -= in[6]; | |
372 | out[7] -= in[7]; | |
373 | } | |
374 | ||
375 | # define two64m0 (((limb)1) << 64) - 1 | |
376 | # define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 | |
377 | # define two64m46 (((limb)1) << 64) - (((limb)1) << 46) | |
378 | # define two64m32 (((limb)1) << 64) - (((limb)1) << 32) | |
3e00b4c9 BM |
379 | |
380 | /* zero110 is 0 mod p */ | |
381 | static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; | |
382 | ||
1d97c843 TH |
383 | /*- |
384 | * felem_shrink converts an felem into a smallfelem. The result isn't quite | |
3e00b4c9 BM |
385 | * minimal as the value may be greater than p. |
386 | * | |
387 | * On entry: | |
388 | * in[i] < 2^109 | |
389 | * On exit: | |
390 | * out[i] < 2^64 | |
391 | */ | |
392 | static void felem_shrink(smallfelem out, const felem in) | |
0f113f3e MC |
393 | { |
394 | felem tmp; | |
395 | u64 a, b, mask; | |
8af7e94d | 396 | u64 high, low; |
0f113f3e MC |
397 | static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ |
398 | ||
399 | /* Carry 2->3 */ | |
400 | tmp[3] = zero110[3] + in[3] + ((u64)(in[2] >> 64)); | |
401 | /* tmp[3] < 2^110 */ | |
402 | ||
403 | tmp[2] = zero110[2] + (u64)in[2]; | |
404 | tmp[0] = zero110[0] + in[0]; | |
405 | tmp[1] = zero110[1] + in[1]; | |
406 | /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ | |
407 | ||
408 | /* | |
409 | * We perform two partial reductions where we eliminate the high-word of | |
410 | * tmp[3]. We don't update the other words till the end. | |
411 | */ | |
412 | a = tmp[3] >> 64; /* a < 2^46 */ | |
413 | tmp[3] = (u64)tmp[3]; | |
414 | tmp[3] -= a; | |
415 | tmp[3] += ((limb) a) << 32; | |
416 | /* tmp[3] < 2^79 */ | |
417 | ||
418 | b = a; | |
419 | a = tmp[3] >> 64; /* a < 2^15 */ | |
420 | b += a; /* b < 2^46 + 2^15 < 2^47 */ | |
421 | tmp[3] = (u64)tmp[3]; | |
422 | tmp[3] -= a; | |
423 | tmp[3] += ((limb) a) << 32; | |
424 | /* tmp[3] < 2^64 + 2^47 */ | |
425 | ||
426 | /* | |
427 | * This adjusts the other two words to complete the two partial | |
428 | * reductions. | |
429 | */ | |
430 | tmp[0] += b; | |
431 | tmp[1] -= (((limb) b) << 32); | |
432 | ||
433 | /* | |
434 | * In order to make space in tmp[3] for the carry from 2 -> 3, we | |
435 | * conditionally subtract kPrime if tmp[3] is large enough. | |
436 | */ | |
8af7e94d | 437 | high = (u64)(tmp[3] >> 64); |
0f113f3e | 438 | /* As tmp[3] < 2^65, high is either 1 or 0 */ |
8af7e94d | 439 | high = 0 - high; |
35a1cc90 MC |
440 | /*- |
441 | * high is: | |
442 | * all ones if the high word of tmp[3] is 1 | |
8af7e94d AP |
443 | * all zeros if the high word of tmp[3] if 0 |
444 | */ | |
445 | low = (u64)tmp[3]; | |
446 | mask = 0 - (low >> 63); | |
35a1cc90 MC |
447 | /*- |
448 | * mask is: | |
449 | * all ones if the MSB of low is 1 | |
8af7e94d AP |
450 | * all zeros if the MSB of low if 0 |
451 | */ | |
0f113f3e MC |
452 | low &= bottom63bits; |
453 | low -= kPrime3Test; | |
454 | /* if low was greater than kPrime3Test then the MSB is zero */ | |
455 | low = ~low; | |
8af7e94d | 456 | low = 0 - (low >> 63); |
35a1cc90 MC |
457 | /*- |
458 | * low is: | |
459 | * all ones if low was > kPrime3Test | |
8af7e94d AP |
460 | * all zeros if low was <= kPrime3Test |
461 | */ | |
0f113f3e MC |
462 | mask = (mask & low) | high; |
463 | tmp[0] -= mask & kPrime[0]; | |
464 | tmp[1] -= mask & kPrime[1]; | |
465 | /* kPrime[2] is zero, so omitted */ | |
466 | tmp[3] -= mask & kPrime[3]; | |
467 | /* tmp[3] < 2**64 - 2**32 + 1 */ | |
468 | ||
469 | tmp[1] += ((u64)(tmp[0] >> 64)); | |
470 | tmp[0] = (u64)tmp[0]; | |
471 | tmp[2] += ((u64)(tmp[1] >> 64)); | |
472 | tmp[1] = (u64)tmp[1]; | |
473 | tmp[3] += ((u64)(tmp[2] >> 64)); | |
474 | tmp[2] = (u64)tmp[2]; | |
475 | /* tmp[i] < 2^64 */ | |
476 | ||
477 | out[0] = tmp[0]; | |
478 | out[1] = tmp[1]; | |
479 | out[2] = tmp[2]; | |
480 | out[3] = tmp[3]; | |
481 | } | |
3e00b4c9 BM |
482 | |
483 | /* smallfelem_expand converts a smallfelem to an felem */ | |
484 | static void smallfelem_expand(felem out, const smallfelem in) | |
0f113f3e MC |
485 | { |
486 | out[0] = in[0]; | |
487 | out[1] = in[1]; | |
488 | out[2] = in[2]; | |
489 | out[3] = in[3]; | |
490 | } | |
491 | ||
492 | /*- | |
1d97c843 | 493 | * smallfelem_square sets |out| = |small|^2 |
3e00b4c9 BM |
494 | * On entry: |
495 | * small[i] < 2^64 | |
496 | * On exit: | |
497 | * out[i] < 7 * 2^64 < 2^67 | |
498 | */ | |
499 | static void smallfelem_square(longfelem out, const smallfelem small) | |
0f113f3e MC |
500 | { |
501 | limb a; | |
502 | u64 high, low; | |
503 | ||
504 | a = ((uint128_t) small[0]) * small[0]; | |
505 | low = a; | |
506 | high = a >> 64; | |
507 | out[0] = low; | |
508 | out[1] = high; | |
509 | ||
510 | a = ((uint128_t) small[0]) * small[1]; | |
511 | low = a; | |
512 | high = a >> 64; | |
513 | out[1] += low; | |
514 | out[1] += low; | |
515 | out[2] = high; | |
516 | ||
517 | a = ((uint128_t) small[0]) * small[2]; | |
518 | low = a; | |
519 | high = a >> 64; | |
520 | out[2] += low; | |
521 | out[2] *= 2; | |
522 | out[3] = high; | |
523 | ||
524 | a = ((uint128_t) small[0]) * small[3]; | |
525 | low = a; | |
526 | high = a >> 64; | |
527 | out[3] += low; | |
528 | out[4] = high; | |
529 | ||
530 | a = ((uint128_t) small[1]) * small[2]; | |
531 | low = a; | |
532 | high = a >> 64; | |
533 | out[3] += low; | |
534 | out[3] *= 2; | |
535 | out[4] += high; | |
536 | ||
537 | a = ((uint128_t) small[1]) * small[1]; | |
538 | low = a; | |
539 | high = a >> 64; | |
540 | out[2] += low; | |
541 | out[3] += high; | |
542 | ||
543 | a = ((uint128_t) small[1]) * small[3]; | |
544 | low = a; | |
545 | high = a >> 64; | |
546 | out[4] += low; | |
547 | out[4] *= 2; | |
548 | out[5] = high; | |
549 | ||
550 | a = ((uint128_t) small[2]) * small[3]; | |
551 | low = a; | |
552 | high = a >> 64; | |
553 | out[5] += low; | |
554 | out[5] *= 2; | |
555 | out[6] = high; | |
556 | out[6] += high; | |
557 | ||
558 | a = ((uint128_t) small[2]) * small[2]; | |
559 | low = a; | |
560 | high = a >> 64; | |
561 | out[4] += low; | |
562 | out[5] += high; | |
563 | ||
564 | a = ((uint128_t) small[3]) * small[3]; | |
565 | low = a; | |
566 | high = a >> 64; | |
567 | out[6] += low; | |
568 | out[7] = high; | |
569 | } | |
3e00b4c9 | 570 | |
1d97c843 TH |
571 | /*- |
572 | * felem_square sets |out| = |in|^2 | |
3e00b4c9 BM |
573 | * On entry: |
574 | * in[i] < 2^109 | |
575 | * On exit: | |
576 | * out[i] < 7 * 2^64 < 2^67 | |
577 | */ | |
578 | static void felem_square(longfelem out, const felem in) | |
0f113f3e MC |
579 | { |
580 | u64 small[4]; | |
581 | felem_shrink(small, in); | |
582 | smallfelem_square(out, small); | |
583 | } | |
3e00b4c9 | 584 | |
1d97c843 TH |
585 | /*- |
586 | * smallfelem_mul sets |out| = |small1| * |small2| | |
3e00b4c9 BM |
587 | * On entry: |
588 | * small1[i] < 2^64 | |
589 | * small2[i] < 2^64 | |
590 | * On exit: | |
591 | * out[i] < 7 * 2^64 < 2^67 | |
592 | */ | |
0f113f3e MC |
593 | static void smallfelem_mul(longfelem out, const smallfelem small1, |
594 | const smallfelem small2) | |
595 | { | |
596 | limb a; | |
597 | u64 high, low; | |
598 | ||
599 | a = ((uint128_t) small1[0]) * small2[0]; | |
600 | low = a; | |
601 | high = a >> 64; | |
602 | out[0] = low; | |
603 | out[1] = high; | |
604 | ||
605 | a = ((uint128_t) small1[0]) * small2[1]; | |
606 | low = a; | |
607 | high = a >> 64; | |
608 | out[1] += low; | |
609 | out[2] = high; | |
610 | ||
611 | a = ((uint128_t) small1[1]) * small2[0]; | |
612 | low = a; | |
613 | high = a >> 64; | |
614 | out[1] += low; | |
615 | out[2] += high; | |
616 | ||
617 | a = ((uint128_t) small1[0]) * small2[2]; | |
618 | low = a; | |
619 | high = a >> 64; | |
620 | out[2] += low; | |
621 | out[3] = high; | |
622 | ||
623 | a = ((uint128_t) small1[1]) * small2[1]; | |
624 | low = a; | |
625 | high = a >> 64; | |
626 | out[2] += low; | |
627 | out[3] += high; | |
628 | ||
629 | a = ((uint128_t) small1[2]) * small2[0]; | |
630 | low = a; | |
631 | high = a >> 64; | |
632 | out[2] += low; | |
633 | out[3] += high; | |
634 | ||
635 | a = ((uint128_t) small1[0]) * small2[3]; | |
636 | low = a; | |
637 | high = a >> 64; | |
638 | out[3] += low; | |
639 | out[4] = high; | |
640 | ||
641 | a = ((uint128_t) small1[1]) * small2[2]; | |
642 | low = a; | |
643 | high = a >> 64; | |
644 | out[3] += low; | |
645 | out[4] += high; | |
646 | ||
647 | a = ((uint128_t) small1[2]) * small2[1]; | |
648 | low = a; | |
649 | high = a >> 64; | |
650 | out[3] += low; | |
651 | out[4] += high; | |
652 | ||
653 | a = ((uint128_t) small1[3]) * small2[0]; | |
654 | low = a; | |
655 | high = a >> 64; | |
656 | out[3] += low; | |
657 | out[4] += high; | |
658 | ||
659 | a = ((uint128_t) small1[1]) * small2[3]; | |
660 | low = a; | |
661 | high = a >> 64; | |
662 | out[4] += low; | |
663 | out[5] = high; | |
664 | ||
665 | a = ((uint128_t) small1[2]) * small2[2]; | |
666 | low = a; | |
667 | high = a >> 64; | |
668 | out[4] += low; | |
669 | out[5] += high; | |
670 | ||
671 | a = ((uint128_t) small1[3]) * small2[1]; | |
672 | low = a; | |
673 | high = a >> 64; | |
674 | out[4] += low; | |
675 | out[5] += high; | |
676 | ||
677 | a = ((uint128_t) small1[2]) * small2[3]; | |
678 | low = a; | |
679 | high = a >> 64; | |
680 | out[5] += low; | |
681 | out[6] = high; | |
682 | ||
683 | a = ((uint128_t) small1[3]) * small2[2]; | |
684 | low = a; | |
685 | high = a >> 64; | |
686 | out[5] += low; | |
687 | out[6] += high; | |
688 | ||
689 | a = ((uint128_t) small1[3]) * small2[3]; | |
690 | low = a; | |
691 | high = a >> 64; | |
692 | out[6] += low; | |
693 | out[7] = high; | |
694 | } | |
3e00b4c9 | 695 | |
1d97c843 TH |
696 | /*- |
697 | * felem_mul sets |out| = |in1| * |in2| | |
3e00b4c9 BM |
698 | * On entry: |
699 | * in1[i] < 2^109 | |
700 | * in2[i] < 2^109 | |
701 | * On exit: | |
702 | * out[i] < 7 * 2^64 < 2^67 | |
703 | */ | |
704 | static void felem_mul(longfelem out, const felem in1, const felem in2) | |
0f113f3e MC |
705 | { |
706 | smallfelem small1, small2; | |
707 | felem_shrink(small1, in1); | |
708 | felem_shrink(small2, in2); | |
709 | smallfelem_mul(out, small1, small2); | |
710 | } | |
3e00b4c9 | 711 | |
1d97c843 TH |
712 | /*- |
713 | * felem_small_mul sets |out| = |small1| * |in2| | |
3e00b4c9 BM |
714 | * On entry: |
715 | * small1[i] < 2^64 | |
716 | * in2[i] < 2^109 | |
717 | * On exit: | |
718 | * out[i] < 7 * 2^64 < 2^67 | |
719 | */ | |
0f113f3e MC |
720 | static void felem_small_mul(longfelem out, const smallfelem small1, |
721 | const felem in2) | |
722 | { | |
723 | smallfelem small2; | |
724 | felem_shrink(small2, in2); | |
725 | smallfelem_mul(out, small1, small2); | |
726 | } | |
727 | ||
728 | # define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) | |
729 | # define two100 (((limb)1) << 100) | |
730 | # define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) | |
3e00b4c9 | 731 | /* zero100 is 0 mod p */ |
0f113f3e MC |
732 | static const felem zero100 = |
733 | { two100m36m4, two100, two100m36p4, two100m36p4 }; | |
3e00b4c9 | 734 | |
1d97c843 TH |
735 | /*- |
736 | * Internal function for the different flavours of felem_reduce. | |
3e00b4c9 BM |
737 | * felem_reduce_ reduces the higher coefficients in[4]-in[7]. |
738 | * On entry: | |
0f113f3e | 739 | * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] |
3e00b4c9 BM |
740 | * out[1] >= in[7] + 2^32*in[4] |
741 | * out[2] >= in[5] + 2^32*in[5] | |
742 | * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] | |
743 | * On exit: | |
744 | * out[0] <= out[0] + in[4] + 2^32*in[5] | |
745 | * out[1] <= out[1] + in[5] + 2^33*in[6] | |
746 | * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7] | |
747 | * out[3] <= out[3] + 2^32*in[4] + 3*in[7] | |
748 | */ | |
749 | static void felem_reduce_(felem out, const longfelem in) | |
0f113f3e MC |
750 | { |
751 | int128_t c; | |
752 | /* combine common terms from below */ | |
753 | c = in[4] + (in[5] << 32); | |
754 | out[0] += c; | |
755 | out[3] -= c; | |
756 | ||
757 | c = in[5] - in[7]; | |
758 | out[1] += c; | |
759 | out[2] -= c; | |
760 | ||
761 | /* the remaining terms */ | |
762 | /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */ | |
763 | out[1] -= (in[4] << 32); | |
764 | out[3] += (in[4] << 32); | |
765 | ||
766 | /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */ | |
767 | out[2] -= (in[5] << 32); | |
768 | ||
769 | /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */ | |
770 | out[0] -= in[6]; | |
771 | out[0] -= (in[6] << 32); | |
772 | out[1] += (in[6] << 33); | |
773 | out[2] += (in[6] * 2); | |
774 | out[3] -= (in[6] << 32); | |
775 | ||
776 | /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */ | |
777 | out[0] -= in[7]; | |
778 | out[0] -= (in[7] << 32); | |
779 | out[2] += (in[7] << 33); | |
780 | out[3] += (in[7] * 3); | |
781 | } | |
3e00b4c9 | 782 | |
1d97c843 TH |
783 | /*- |
784 | * felem_reduce converts a longfelem into an felem. | |
3e00b4c9 BM |
785 | * To be called directly after felem_square or felem_mul. |
786 | * On entry: | |
787 | * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64 | |
788 | * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64 | |
789 | * On exit: | |
790 | * out[i] < 2^101 | |
791 | */ | |
792 | static void felem_reduce(felem out, const longfelem in) | |
0f113f3e MC |
793 | { |
794 | out[0] = zero100[0] + in[0]; | |
795 | out[1] = zero100[1] + in[1]; | |
796 | out[2] = zero100[2] + in[2]; | |
797 | out[3] = zero100[3] + in[3]; | |
798 | ||
799 | felem_reduce_(out, in); | |
800 | ||
35a1cc90 MC |
801 | /*- |
802 | * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 | |
803 | * out[1] > 2^100 - 2^64 - 7*2^96 > 0 | |
804 | * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 | |
805 | * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 | |
806 | * | |
807 | * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 | |
808 | * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 | |
809 | * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 | |
810 | * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 | |
811 | */ | |
0f113f3e | 812 | } |
3e00b4c9 | 813 | |
1d97c843 TH |
814 | /*- |
815 | * felem_reduce_zero105 converts a larger longfelem into an felem. | |
3e00b4c9 BM |
816 | * On entry: |
817 | * in[0] < 2^71 | |
818 | * On exit: | |
819 | * out[i] < 2^106 | |
820 | */ | |
821 | static void felem_reduce_zero105(felem out, const longfelem in) | |
0f113f3e MC |
822 | { |
823 | out[0] = zero105[0] + in[0]; | |
824 | out[1] = zero105[1] + in[1]; | |
825 | out[2] = zero105[2] + in[2]; | |
826 | out[3] = zero105[3] + in[3]; | |
827 | ||
828 | felem_reduce_(out, in); | |
829 | ||
35a1cc90 MC |
830 | /*- |
831 | * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 | |
832 | * out[1] > 2^105 - 2^71 - 2^103 > 0 | |
833 | * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 | |
834 | * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 | |
835 | * | |
836 | * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 | |
837 | * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 | |
838 | * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 | |
839 | * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 | |
840 | */ | |
0f113f3e MC |
841 | } |
842 | ||
843 | /* | |
844 | * subtract_u64 sets *result = *result - v and *carry to one if the | |
845 | * subtraction underflowed. | |
846 | */ | |
847 | static void subtract_u64(u64 *result, u64 *carry, u64 v) | |
848 | { | |
849 | uint128_t r = *result; | |
850 | r -= v; | |
851 | *carry = (r >> 64) & 1; | |
852 | *result = (u64)r; | |
853 | } | |
854 | ||
855 | /* | |
856 | * felem_contract converts |in| to its unique, minimal representation. On | |
857 | * entry: in[i] < 2^109 | |
3e00b4c9 BM |
858 | */ |
859 | static void felem_contract(smallfelem out, const felem in) | |
0f113f3e MC |
860 | { |
861 | unsigned i; | |
862 | u64 all_equal_so_far = 0, result = 0, carry; | |
863 | ||
864 | felem_shrink(out, in); | |
865 | /* small is minimal except that the value might be > p */ | |
866 | ||
867 | all_equal_so_far--; | |
868 | /* | |
869 | * We are doing a constant time test if out >= kPrime. We need to compare | |
870 | * each u64, from most-significant to least significant. For each one, if | |
871 | * all words so far have been equal (m is all ones) then a non-equal | |
872 | * result is the answer. Otherwise we continue. | |
873 | */ | |
874 | for (i = 3; i < 4; i--) { | |
875 | u64 equal; | |
876 | uint128_t a = ((uint128_t) kPrime[i]) - out[i]; | |
877 | /* | |
878 | * if out[i] > kPrime[i] then a will underflow and the high 64-bits | |
879 | * will all be set. | |
880 | */ | |
881 | result |= all_equal_so_far & ((u64)(a >> 64)); | |
882 | ||
883 | /* | |
884 | * if kPrime[i] == out[i] then |equal| will be all zeros and the | |
885 | * decrement will make it all ones. | |
886 | */ | |
887 | equal = kPrime[i] ^ out[i]; | |
888 | equal--; | |
889 | equal &= equal << 32; | |
890 | equal &= equal << 16; | |
891 | equal &= equal << 8; | |
892 | equal &= equal << 4; | |
893 | equal &= equal << 2; | |
894 | equal &= equal << 1; | |
8af7e94d | 895 | equal = 0 - (equal >> 63); |
0f113f3e MC |
896 | |
897 | all_equal_so_far &= equal; | |
898 | } | |
899 | ||
900 | /* | |
901 | * if all_equal_so_far is still all ones then the two values are equal | |
902 | * and so out >= kPrime is true. | |
903 | */ | |
904 | result |= all_equal_so_far; | |
905 | ||
906 | /* if out >= kPrime then we subtract kPrime. */ | |
907 | subtract_u64(&out[0], &carry, result & kPrime[0]); | |
908 | subtract_u64(&out[1], &carry, carry); | |
909 | subtract_u64(&out[2], &carry, carry); | |
910 | subtract_u64(&out[3], &carry, carry); | |
911 | ||
912 | subtract_u64(&out[1], &carry, result & kPrime[1]); | |
913 | subtract_u64(&out[2], &carry, carry); | |
914 | subtract_u64(&out[3], &carry, carry); | |
915 | ||
916 | subtract_u64(&out[2], &carry, result & kPrime[2]); | |
917 | subtract_u64(&out[3], &carry, carry); | |
918 | ||
919 | subtract_u64(&out[3], &carry, result & kPrime[3]); | |
920 | } | |
3e00b4c9 BM |
921 | |
922 | static void smallfelem_square_contract(smallfelem out, const smallfelem in) | |
0f113f3e MC |
923 | { |
924 | longfelem longtmp; | |
925 | felem tmp; | |
926 | ||
927 | smallfelem_square(longtmp, in); | |
928 | felem_reduce(tmp, longtmp); | |
929 | felem_contract(out, tmp); | |
930 | } | |
931 | ||
932 | static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, | |
933 | const smallfelem in2) | |
934 | { | |
935 | longfelem longtmp; | |
936 | felem tmp; | |
937 | ||
938 | smallfelem_mul(longtmp, in1, in2); | |
939 | felem_reduce(tmp, longtmp); | |
940 | felem_contract(out, tmp); | |
941 | } | |
3e00b4c9 | 942 | |
1d97c843 TH |
943 | /*- |
944 | * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 | |
3e00b4c9 BM |
945 | * otherwise. |
946 | * On entry: | |
947 | * small[i] < 2^64 | |
948 | */ | |
949 | static limb smallfelem_is_zero(const smallfelem small) | |
0f113f3e MC |
950 | { |
951 | limb result; | |
952 | u64 is_p; | |
953 | ||
954 | u64 is_zero = small[0] | small[1] | small[2] | small[3]; | |
955 | is_zero--; | |
956 | is_zero &= is_zero << 32; | |
957 | is_zero &= is_zero << 16; | |
958 | is_zero &= is_zero << 8; | |
959 | is_zero &= is_zero << 4; | |
960 | is_zero &= is_zero << 2; | |
961 | is_zero &= is_zero << 1; | |
8af7e94d | 962 | is_zero = 0 - (is_zero >> 63); |
0f113f3e MC |
963 | |
964 | is_p = (small[0] ^ kPrime[0]) | | |
965 | (small[1] ^ kPrime[1]) | | |
966 | (small[2] ^ kPrime[2]) | (small[3] ^ kPrime[3]); | |
967 | is_p--; | |
968 | is_p &= is_p << 32; | |
969 | is_p &= is_p << 16; | |
970 | is_p &= is_p << 8; | |
971 | is_p &= is_p << 4; | |
972 | is_p &= is_p << 2; | |
973 | is_p &= is_p << 1; | |
8af7e94d | 974 | is_p = 0 - (is_p >> 63); |
0f113f3e MC |
975 | |
976 | is_zero |= is_p; | |
977 | ||
978 | result = is_zero; | |
979 | result |= ((limb) is_zero) << 64; | |
980 | return result; | |
981 | } | |
3e00b4c9 | 982 | |
c55b786a | 983 | static int smallfelem_is_zero_int(const void *small) |
0f113f3e MC |
984 | { |
985 | return (int)(smallfelem_is_zero(small) & ((limb) 1)); | |
986 | } | |
3e00b4c9 | 987 | |
1d97c843 TH |
988 | /*- |
989 | * felem_inv calculates |out| = |in|^{-1} | |
3e00b4c9 BM |
990 | * |
991 | * Based on Fermat's Little Theorem: | |
992 | * a^p = a (mod p) | |
993 | * a^{p-1} = 1 (mod p) | |
994 | * a^{p-2} = a^{-1} (mod p) | |
995 | */ | |
996 | static void felem_inv(felem out, const felem in) | |
0f113f3e MC |
997 | { |
998 | felem ftmp, ftmp2; | |
999 | /* each e_I will hold |in|^{2^I - 1} */ | |
1000 | felem e2, e4, e8, e16, e32, e64; | |
1001 | longfelem tmp; | |
1002 | unsigned i; | |
1003 | ||
1004 | felem_square(tmp, in); | |
1005 | felem_reduce(ftmp, tmp); /* 2^1 */ | |
1006 | felem_mul(tmp, in, ftmp); | |
1007 | felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ | |
1008 | felem_assign(e2, ftmp); | |
1009 | felem_square(tmp, ftmp); | |
1010 | felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ | |
1011 | felem_square(tmp, ftmp); | |
1012 | felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ | |
1013 | felem_mul(tmp, ftmp, e2); | |
1014 | felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ | |
1015 | felem_assign(e4, ftmp); | |
1016 | felem_square(tmp, ftmp); | |
1017 | felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ | |
1018 | felem_square(tmp, ftmp); | |
1019 | felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ | |
1020 | felem_square(tmp, ftmp); | |
1021 | felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ | |
1022 | felem_square(tmp, ftmp); | |
1023 | felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ | |
1024 | felem_mul(tmp, ftmp, e4); | |
1025 | felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ | |
1026 | felem_assign(e8, ftmp); | |
1027 | for (i = 0; i < 8; i++) { | |
1028 | felem_square(tmp, ftmp); | |
1029 | felem_reduce(ftmp, tmp); | |
1030 | } /* 2^16 - 2^8 */ | |
1031 | felem_mul(tmp, ftmp, e8); | |
1032 | felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ | |
1033 | felem_assign(e16, ftmp); | |
1034 | for (i = 0; i < 16; i++) { | |
1035 | felem_square(tmp, ftmp); | |
1036 | felem_reduce(ftmp, tmp); | |
1037 | } /* 2^32 - 2^16 */ | |
1038 | felem_mul(tmp, ftmp, e16); | |
1039 | felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ | |
1040 | felem_assign(e32, ftmp); | |
1041 | for (i = 0; i < 32; i++) { | |
1042 | felem_square(tmp, ftmp); | |
1043 | felem_reduce(ftmp, tmp); | |
1044 | } /* 2^64 - 2^32 */ | |
1045 | felem_assign(e64, ftmp); | |
1046 | felem_mul(tmp, ftmp, in); | |
1047 | felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ | |
1048 | for (i = 0; i < 192; i++) { | |
1049 | felem_square(tmp, ftmp); | |
1050 | felem_reduce(ftmp, tmp); | |
1051 | } /* 2^256 - 2^224 + 2^192 */ | |
1052 | ||
1053 | felem_mul(tmp, e64, e32); | |
1054 | felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ | |
1055 | for (i = 0; i < 16; i++) { | |
1056 | felem_square(tmp, ftmp2); | |
1057 | felem_reduce(ftmp2, tmp); | |
1058 | } /* 2^80 - 2^16 */ | |
1059 | felem_mul(tmp, ftmp2, e16); | |
1060 | felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ | |
1061 | for (i = 0; i < 8; i++) { | |
1062 | felem_square(tmp, ftmp2); | |
1063 | felem_reduce(ftmp2, tmp); | |
1064 | } /* 2^88 - 2^8 */ | |
1065 | felem_mul(tmp, ftmp2, e8); | |
1066 | felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ | |
1067 | for (i = 0; i < 4; i++) { | |
1068 | felem_square(tmp, ftmp2); | |
1069 | felem_reduce(ftmp2, tmp); | |
1070 | } /* 2^92 - 2^4 */ | |
1071 | felem_mul(tmp, ftmp2, e4); | |
1072 | felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ | |
1073 | felem_square(tmp, ftmp2); | |
1074 | felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ | |
1075 | felem_square(tmp, ftmp2); | |
1076 | felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ | |
1077 | felem_mul(tmp, ftmp2, e2); | |
1078 | felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ | |
1079 | felem_square(tmp, ftmp2); | |
1080 | felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ | |
1081 | felem_square(tmp, ftmp2); | |
1082 | felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ | |
1083 | felem_mul(tmp, ftmp2, in); | |
1084 | felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ | |
1085 | ||
1086 | felem_mul(tmp, ftmp2, ftmp); | |
1087 | felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ | |
1088 | } | |
3e00b4c9 BM |
1089 | |
1090 | static void smallfelem_inv_contract(smallfelem out, const smallfelem in) | |
0f113f3e MC |
1091 | { |
1092 | felem tmp; | |
3e00b4c9 | 1093 | |
0f113f3e MC |
1094 | smallfelem_expand(tmp, in); |
1095 | felem_inv(tmp, tmp); | |
1096 | felem_contract(out, tmp); | |
1097 | } | |
3e00b4c9 | 1098 | |
1d97c843 TH |
1099 | /*- |
1100 | * Group operations | |
3e00b4c9 BM |
1101 | * ---------------- |
1102 | * | |
1103 | * Building on top of the field operations we have the operations on the | |
1104 | * elliptic curve group itself. Points on the curve are represented in Jacobian | |
35a1cc90 MC |
1105 | * coordinates |
1106 | */ | |
3e00b4c9 | 1107 | |
1d97c843 TH |
1108 | /*- |
1109 | * point_double calculates 2*(x_in, y_in, z_in) | |
3e00b4c9 BM |
1110 | * |
1111 | * The method is taken from: | |
1112 | * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b | |
1113 | * | |
1114 | * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. | |
35a1cc90 MC |
1115 | * while x_out == y_in is not (maybe this works, but it's not tested). |
1116 | */ | |
3e00b4c9 BM |
1117 | static void |
1118 | point_double(felem x_out, felem y_out, felem z_out, | |
0f113f3e MC |
1119 | const felem x_in, const felem y_in, const felem z_in) |
1120 | { | |
1121 | longfelem tmp, tmp2; | |
1122 | felem delta, gamma, beta, alpha, ftmp, ftmp2; | |
1123 | smallfelem small1, small2; | |
1124 | ||
1125 | felem_assign(ftmp, x_in); | |
1126 | /* ftmp[i] < 2^106 */ | |
1127 | felem_assign(ftmp2, x_in); | |
1128 | /* ftmp2[i] < 2^106 */ | |
1129 | ||
1130 | /* delta = z^2 */ | |
1131 | felem_square(tmp, z_in); | |
1132 | felem_reduce(delta, tmp); | |
1133 | /* delta[i] < 2^101 */ | |
1134 | ||
1135 | /* gamma = y^2 */ | |
1136 | felem_square(tmp, y_in); | |
1137 | felem_reduce(gamma, tmp); | |
1138 | /* gamma[i] < 2^101 */ | |
1139 | felem_shrink(small1, gamma); | |
1140 | ||
1141 | /* beta = x*gamma */ | |
1142 | felem_small_mul(tmp, small1, x_in); | |
1143 | felem_reduce(beta, tmp); | |
1144 | /* beta[i] < 2^101 */ | |
1145 | ||
1146 | /* alpha = 3*(x-delta)*(x+delta) */ | |
1147 | felem_diff(ftmp, delta); | |
1148 | /* ftmp[i] < 2^105 + 2^106 < 2^107 */ | |
1149 | felem_sum(ftmp2, delta); | |
1150 | /* ftmp2[i] < 2^105 + 2^106 < 2^107 */ | |
1151 | felem_scalar(ftmp2, 3); | |
1152 | /* ftmp2[i] < 3 * 2^107 < 2^109 */ | |
1153 | felem_mul(tmp, ftmp, ftmp2); | |
1154 | felem_reduce(alpha, tmp); | |
1155 | /* alpha[i] < 2^101 */ | |
1156 | felem_shrink(small2, alpha); | |
1157 | ||
1158 | /* x' = alpha^2 - 8*beta */ | |
1159 | smallfelem_square(tmp, small2); | |
1160 | felem_reduce(x_out, tmp); | |
1161 | felem_assign(ftmp, beta); | |
1162 | felem_scalar(ftmp, 8); | |
1163 | /* ftmp[i] < 8 * 2^101 = 2^104 */ | |
1164 | felem_diff(x_out, ftmp); | |
1165 | /* x_out[i] < 2^105 + 2^101 < 2^106 */ | |
1166 | ||
1167 | /* z' = (y + z)^2 - gamma - delta */ | |
1168 | felem_sum(delta, gamma); | |
1169 | /* delta[i] < 2^101 + 2^101 = 2^102 */ | |
1170 | felem_assign(ftmp, y_in); | |
1171 | felem_sum(ftmp, z_in); | |
1172 | /* ftmp[i] < 2^106 + 2^106 = 2^107 */ | |
1173 | felem_square(tmp, ftmp); | |
1174 | felem_reduce(z_out, tmp); | |
1175 | felem_diff(z_out, delta); | |
1176 | /* z_out[i] < 2^105 + 2^101 < 2^106 */ | |
1177 | ||
1178 | /* y' = alpha*(4*beta - x') - 8*gamma^2 */ | |
1179 | felem_scalar(beta, 4); | |
1180 | /* beta[i] < 4 * 2^101 = 2^103 */ | |
1181 | felem_diff_zero107(beta, x_out); | |
1182 | /* beta[i] < 2^107 + 2^103 < 2^108 */ | |
1183 | felem_small_mul(tmp, small2, beta); | |
1184 | /* tmp[i] < 7 * 2^64 < 2^67 */ | |
1185 | smallfelem_square(tmp2, small1); | |
1186 | /* tmp2[i] < 7 * 2^64 */ | |
1187 | longfelem_scalar(tmp2, 8); | |
1188 | /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */ | |
1189 | longfelem_diff(tmp, tmp2); | |
1190 | /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ | |
1191 | felem_reduce_zero105(y_out, tmp); | |
1192 | /* y_out[i] < 2^106 */ | |
1193 | } | |
1194 | ||
1195 | /* | |
1196 | * point_double_small is the same as point_double, except that it operates on | |
1197 | * smallfelems | |
1198 | */ | |
3e00b4c9 BM |
1199 | static void |
1200 | point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, | |
0f113f3e MC |
1201 | const smallfelem x_in, const smallfelem y_in, |
1202 | const smallfelem z_in) | |
1203 | { | |
1204 | felem felem_x_out, felem_y_out, felem_z_out; | |
1205 | felem felem_x_in, felem_y_in, felem_z_in; | |
1206 | ||
1207 | smallfelem_expand(felem_x_in, x_in); | |
1208 | smallfelem_expand(felem_y_in, y_in); | |
1209 | smallfelem_expand(felem_z_in, z_in); | |
1210 | point_double(felem_x_out, felem_y_out, felem_z_out, | |
1211 | felem_x_in, felem_y_in, felem_z_in); | |
1212 | felem_shrink(x_out, felem_x_out); | |
1213 | felem_shrink(y_out, felem_y_out); | |
1214 | felem_shrink(z_out, felem_z_out); | |
1215 | } | |
3e00b4c9 BM |
1216 | |
1217 | /* copy_conditional copies in to out iff mask is all ones. */ | |
0f113f3e MC |
1218 | static void copy_conditional(felem out, const felem in, limb mask) |
1219 | { | |
1220 | unsigned i; | |
1221 | for (i = 0; i < NLIMBS; ++i) { | |
1222 | const limb tmp = mask & (in[i] ^ out[i]); | |
1223 | out[i] ^= tmp; | |
1224 | } | |
1225 | } | |
3e00b4c9 BM |
1226 | |
1227 | /* copy_small_conditional copies in to out iff mask is all ones. */ | |
0f113f3e MC |
1228 | static void copy_small_conditional(felem out, const smallfelem in, limb mask) |
1229 | { | |
1230 | unsigned i; | |
1231 | const u64 mask64 = mask; | |
1232 | for (i = 0; i < NLIMBS; ++i) { | |
1233 | out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); | |
1234 | } | |
1235 | } | |
3e00b4c9 | 1236 | |
1d97c843 | 1237 | /*- |
0d4fb843 | 1238 | * point_add calculates (x1, y1, z1) + (x2, y2, z2) |
3e00b4c9 BM |
1239 | * |
1240 | * The method is taken from: | |
1241 | * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, | |
1242 | * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). | |
1243 | * | |
1244 | * This function includes a branch for checking whether the two input points | |
1245 | * are equal, (while not equal to the point at infinity). This case never | |
1246 | * happens during single point multiplication, so there is no timing leak for | |
35a1cc90 MC |
1247 | * ECDH or ECDSA signing. |
1248 | */ | |
3e00b4c9 | 1249 | static void point_add(felem x3, felem y3, felem z3, |
0f113f3e MC |
1250 | const felem x1, const felem y1, const felem z1, |
1251 | const int mixed, const smallfelem x2, | |
1252 | const smallfelem y2, const smallfelem z2) | |
1253 | { | |
1254 | felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; | |
1255 | longfelem tmp, tmp2; | |
1256 | smallfelem small1, small2, small3, small4, small5; | |
1257 | limb x_equal, y_equal, z1_is_zero, z2_is_zero; | |
1258 | ||
1259 | felem_shrink(small3, z1); | |
1260 | ||
1261 | z1_is_zero = smallfelem_is_zero(small3); | |
1262 | z2_is_zero = smallfelem_is_zero(z2); | |
1263 | ||
1264 | /* ftmp = z1z1 = z1**2 */ | |
1265 | smallfelem_square(tmp, small3); | |
1266 | felem_reduce(ftmp, tmp); | |
1267 | /* ftmp[i] < 2^101 */ | |
1268 | felem_shrink(small1, ftmp); | |
1269 | ||
1270 | if (!mixed) { | |
1271 | /* ftmp2 = z2z2 = z2**2 */ | |
1272 | smallfelem_square(tmp, z2); | |
1273 | felem_reduce(ftmp2, tmp); | |
1274 | /* ftmp2[i] < 2^101 */ | |
1275 | felem_shrink(small2, ftmp2); | |
1276 | ||
1277 | felem_shrink(small5, x1); | |
1278 | ||
1279 | /* u1 = ftmp3 = x1*z2z2 */ | |
1280 | smallfelem_mul(tmp, small5, small2); | |
1281 | felem_reduce(ftmp3, tmp); | |
1282 | /* ftmp3[i] < 2^101 */ | |
1283 | ||
1284 | /* ftmp5 = z1 + z2 */ | |
1285 | felem_assign(ftmp5, z1); | |
1286 | felem_small_sum(ftmp5, z2); | |
1287 | /* ftmp5[i] < 2^107 */ | |
1288 | ||
1289 | /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */ | |
1290 | felem_square(tmp, ftmp5); | |
1291 | felem_reduce(ftmp5, tmp); | |
1292 | /* ftmp2 = z2z2 + z1z1 */ | |
1293 | felem_sum(ftmp2, ftmp); | |
1294 | /* ftmp2[i] < 2^101 + 2^101 = 2^102 */ | |
1295 | felem_diff(ftmp5, ftmp2); | |
1296 | /* ftmp5[i] < 2^105 + 2^101 < 2^106 */ | |
1297 | ||
1298 | /* ftmp2 = z2 * z2z2 */ | |
1299 | smallfelem_mul(tmp, small2, z2); | |
1300 | felem_reduce(ftmp2, tmp); | |
1301 | ||
1302 | /* s1 = ftmp2 = y1 * z2**3 */ | |
1303 | felem_mul(tmp, y1, ftmp2); | |
1304 | felem_reduce(ftmp6, tmp); | |
1305 | /* ftmp6[i] < 2^101 */ | |
1306 | } else { | |
1307 | /* | |
1308 | * We'll assume z2 = 1 (special case z2 = 0 is handled later) | |
1309 | */ | |
1310 | ||
1311 | /* u1 = ftmp3 = x1*z2z2 */ | |
1312 | felem_assign(ftmp3, x1); | |
1313 | /* ftmp3[i] < 2^106 */ | |
1314 | ||
1315 | /* ftmp5 = 2z1z2 */ | |
1316 | felem_assign(ftmp5, z1); | |
1317 | felem_scalar(ftmp5, 2); | |
1318 | /* ftmp5[i] < 2*2^106 = 2^107 */ | |
1319 | ||
1320 | /* s1 = ftmp2 = y1 * z2**3 */ | |
1321 | felem_assign(ftmp6, y1); | |
1322 | /* ftmp6[i] < 2^106 */ | |
1323 | } | |
1324 | ||
1325 | /* u2 = x2*z1z1 */ | |
1326 | smallfelem_mul(tmp, x2, small1); | |
1327 | felem_reduce(ftmp4, tmp); | |
1328 | ||
1329 | /* h = ftmp4 = u2 - u1 */ | |
1330 | felem_diff_zero107(ftmp4, ftmp3); | |
1331 | /* ftmp4[i] < 2^107 + 2^101 < 2^108 */ | |
1332 | felem_shrink(small4, ftmp4); | |
1333 | ||
1334 | x_equal = smallfelem_is_zero(small4); | |
1335 | ||
1336 | /* z_out = ftmp5 * h */ | |
1337 | felem_small_mul(tmp, small4, ftmp5); | |
1338 | felem_reduce(z_out, tmp); | |
1339 | /* z_out[i] < 2^101 */ | |
1340 | ||
1341 | /* ftmp = z1 * z1z1 */ | |
1342 | smallfelem_mul(tmp, small1, small3); | |
1343 | felem_reduce(ftmp, tmp); | |
1344 | ||
1345 | /* s2 = tmp = y2 * z1**3 */ | |
1346 | felem_small_mul(tmp, y2, ftmp); | |
1347 | felem_reduce(ftmp5, tmp); | |
1348 | ||
1349 | /* r = ftmp5 = (s2 - s1)*2 */ | |
1350 | felem_diff_zero107(ftmp5, ftmp6); | |
1351 | /* ftmp5[i] < 2^107 + 2^107 = 2^108 */ | |
1352 | felem_scalar(ftmp5, 2); | |
1353 | /* ftmp5[i] < 2^109 */ | |
1354 | felem_shrink(small1, ftmp5); | |
1355 | y_equal = smallfelem_is_zero(small1); | |
1356 | ||
1357 | if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { | |
1358 | point_double(x3, y3, z3, x1, y1, z1); | |
1359 | return; | |
1360 | } | |
1361 | ||
1362 | /* I = ftmp = (2h)**2 */ | |
1363 | felem_assign(ftmp, ftmp4); | |
1364 | felem_scalar(ftmp, 2); | |
1365 | /* ftmp[i] < 2*2^108 = 2^109 */ | |
1366 | felem_square(tmp, ftmp); | |
1367 | felem_reduce(ftmp, tmp); | |
1368 | ||
1369 | /* J = ftmp2 = h * I */ | |
1370 | felem_mul(tmp, ftmp4, ftmp); | |
1371 | felem_reduce(ftmp2, tmp); | |
1372 | ||
1373 | /* V = ftmp4 = U1 * I */ | |
1374 | felem_mul(tmp, ftmp3, ftmp); | |
1375 | felem_reduce(ftmp4, tmp); | |
1376 | ||
1377 | /* x_out = r**2 - J - 2V */ | |
1378 | smallfelem_square(tmp, small1); | |
1379 | felem_reduce(x_out, tmp); | |
1380 | felem_assign(ftmp3, ftmp4); | |
1381 | felem_scalar(ftmp4, 2); | |
1382 | felem_sum(ftmp4, ftmp2); | |
1383 | /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */ | |
1384 | felem_diff(x_out, ftmp4); | |
1385 | /* x_out[i] < 2^105 + 2^101 */ | |
1386 | ||
1387 | /* y_out = r(V-x_out) - 2 * s1 * J */ | |
1388 | felem_diff_zero107(ftmp3, x_out); | |
1389 | /* ftmp3[i] < 2^107 + 2^101 < 2^108 */ | |
1390 | felem_small_mul(tmp, small1, ftmp3); | |
1391 | felem_mul(tmp2, ftmp6, ftmp2); | |
1392 | longfelem_scalar(tmp2, 2); | |
1393 | /* tmp2[i] < 2*2^67 = 2^68 */ | |
1394 | longfelem_diff(tmp, tmp2); | |
1395 | /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ | |
1396 | felem_reduce_zero105(y_out, tmp); | |
1397 | /* y_out[i] < 2^106 */ | |
1398 | ||
1399 | copy_small_conditional(x_out, x2, z1_is_zero); | |
1400 | copy_conditional(x_out, x1, z2_is_zero); | |
1401 | copy_small_conditional(y_out, y2, z1_is_zero); | |
1402 | copy_conditional(y_out, y1, z2_is_zero); | |
1403 | copy_small_conditional(z_out, z2, z1_is_zero); | |
1404 | copy_conditional(z_out, z1, z2_is_zero); | |
1405 | felem_assign(x3, x_out); | |
1406 | felem_assign(y3, y_out); | |
1407 | felem_assign(z3, z_out); | |
1408 | } | |
1409 | ||
1410 | /* | |
1411 | * point_add_small is the same as point_add, except that it operates on | |
1412 | * smallfelems | |
1413 | */ | |
3e00b4c9 | 1414 | static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, |
0f113f3e MC |
1415 | smallfelem x1, smallfelem y1, smallfelem z1, |
1416 | smallfelem x2, smallfelem y2, smallfelem z2) | |
1417 | { | |
1418 | felem felem_x3, felem_y3, felem_z3; | |
1419 | felem felem_x1, felem_y1, felem_z1; | |
1420 | smallfelem_expand(felem_x1, x1); | |
1421 | smallfelem_expand(felem_y1, y1); | |
1422 | smallfelem_expand(felem_z1, z1); | |
1423 | point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, | |
1424 | x2, y2, z2); | |
1425 | felem_shrink(x3, felem_x3); | |
1426 | felem_shrink(y3, felem_y3); | |
1427 | felem_shrink(z3, felem_z3); | |
1428 | } | |
3e00b4c9 | 1429 | |
1d97c843 TH |
1430 | /*- |
1431 | * Base point pre computation | |
3e00b4c9 BM |
1432 | * -------------------------- |
1433 | * | |
1434 | * Two different sorts of precomputed tables are used in the following code. | |
1435 | * Each contain various points on the curve, where each point is three field | |
1436 | * elements (x, y, z). | |
1437 | * | |
1438 | * For the base point table, z is usually 1 (0 for the point at infinity). | |
1439 | * This table has 2 * 16 elements, starting with the following: | |
1440 | * index | bits | point | |
1441 | * ------+---------+------------------------------ | |
1442 | * 0 | 0 0 0 0 | 0G | |
1443 | * 1 | 0 0 0 1 | 1G | |
1444 | * 2 | 0 0 1 0 | 2^64G | |
1445 | * 3 | 0 0 1 1 | (2^64 + 1)G | |
1446 | * 4 | 0 1 0 0 | 2^128G | |
1447 | * 5 | 0 1 0 1 | (2^128 + 1)G | |
1448 | * 6 | 0 1 1 0 | (2^128 + 2^64)G | |
1449 | * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G | |
1450 | * 8 | 1 0 0 0 | 2^192G | |
1451 | * 9 | 1 0 0 1 | (2^192 + 1)G | |
1452 | * 10 | 1 0 1 0 | (2^192 + 2^64)G | |
1453 | * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G | |
1454 | * 12 | 1 1 0 0 | (2^192 + 2^128)G | |
1455 | * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G | |
1456 | * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G | |
1457 | * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G | |
1458 | * followed by a copy of this with each element multiplied by 2^32. | |
1459 | * | |
1460 | * The reason for this is so that we can clock bits into four different | |
1461 | * locations when doing simple scalar multiplies against the base point, | |
1462 | * and then another four locations using the second 16 elements. | |
1463 | * | |
1464 | * Tables for other points have table[i] = iG for i in 0 .. 16. */ | |
1465 | ||
1466 | /* gmul is the table of precomputed base points */ | |
b853717f | 1467 | static const smallfelem gmul[2][16][3] = { |
0f113f3e MC |
1468 | {{{0, 0, 0, 0}, |
1469 | {0, 0, 0, 0}, | |
1470 | {0, 0, 0, 0}}, | |
1471 | {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, | |
1472 | 0x6b17d1f2e12c4247}, | |
1473 | {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, | |
1474 | 0x4fe342e2fe1a7f9b}, | |
1475 | {1, 0, 0, 0}}, | |
1476 | {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, | |
1477 | 0x0fa822bc2811aaa5}, | |
1478 | {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, | |
1479 | 0xbff44ae8f5dba80d}, | |
1480 | {1, 0, 0, 0}}, | |
1481 | {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, | |
1482 | 0x300a4bbc89d6726f}, | |
1483 | {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, | |
1484 | 0x72aac7e0d09b4644}, | |
1485 | {1, 0, 0, 0}}, | |
1486 | {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, | |
1487 | 0x447d739beedb5e67}, | |
1488 | {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, | |
1489 | 0x2d4825ab834131ee}, | |
1490 | {1, 0, 0, 0}}, | |
1491 | {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, | |
1492 | 0xef9519328a9c72ff}, | |
1493 | {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, | |
1494 | 0x611e9fc37dbb2c9b}, | |
1495 | {1, 0, 0, 0}}, | |
1496 | {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, | |
1497 | 0x550663797b51f5d8}, | |
1498 | {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, | |
1499 | 0x157164848aecb851}, | |
1500 | {1, 0, 0, 0}}, | |
1501 | {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, | |
1502 | 0xeb5d7745b21141ea}, | |
1503 | {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, | |
1504 | 0xeafd72ebdbecc17b}, | |
1505 | {1, 0, 0, 0}}, | |
1506 | {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, | |
1507 | 0xa6d39677a7849276}, | |
1508 | {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, | |
1509 | 0x674f84749b0b8816}, | |
1510 | {1, 0, 0, 0}}, | |
1511 | {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, | |
1512 | 0x4e769e7672c9ddad}, | |
1513 | {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, | |
1514 | 0x42b99082de830663}, | |
1515 | {1, 0, 0, 0}}, | |
1516 | {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, | |
1517 | 0x78878ef61c6ce04d}, | |
1518 | {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, | |
1519 | 0xb6cb3f5d7b72c321}, | |
1520 | {1, 0, 0, 0}}, | |
1521 | {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, | |
1522 | 0x0c88bc4d716b1287}, | |
1523 | {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, | |
1524 | 0xdd5ddea3f3901dc6}, | |
1525 | {1, 0, 0, 0}}, | |
1526 | {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, | |
1527 | 0x68f344af6b317466}, | |
1528 | {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, | |
1529 | 0x31b9c405f8540a20}, | |
1530 | {1, 0, 0, 0}}, | |
1531 | {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, | |
1532 | 0x4052bf4b6f461db9}, | |
1533 | {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, | |
1534 | 0xfecf4d5190b0fc61}, | |
1535 | {1, 0, 0, 0}}, | |
1536 | {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, | |
1537 | 0x1eddbae2c802e41a}, | |
1538 | {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, | |
1539 | 0x43104d86560ebcfc}, | |
1540 | {1, 0, 0, 0}}, | |
1541 | {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, | |
1542 | 0xb48e26b484f7a21c}, | |
1543 | {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, | |
1544 | 0xfac015404d4d3dab}, | |
1545 | {1, 0, 0, 0}}}, | |
1546 | {{{0, 0, 0, 0}, | |
1547 | {0, 0, 0, 0}, | |
1548 | {0, 0, 0, 0}}, | |
1549 | {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, | |
1550 | 0x7fe36b40af22af89}, | |
1551 | {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, | |
1552 | 0xe697d45825b63624}, | |
1553 | {1, 0, 0, 0}}, | |
1554 | {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, | |
1555 | 0x4a5b506612a677a6}, | |
1556 | {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, | |
1557 | 0xeb13461ceac089f1}, | |
1558 | {1, 0, 0, 0}}, | |
1559 | {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, | |
1560 | 0x0781b8291c6a220a}, | |
1561 | {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, | |
1562 | 0x690cde8df0151593}, | |
1563 | {1, 0, 0, 0}}, | |
1564 | {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, | |
1565 | 0x8a535f566ec73617}, | |
1566 | {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, | |
1567 | 0x0455c08468b08bd7}, | |
1568 | {1, 0, 0, 0}}, | |
1569 | {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, | |
1570 | 0x06bada7ab77f8276}, | |
1571 | {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, | |
1572 | 0x5b476dfd0e6cb18a}, | |
1573 | {1, 0, 0, 0}}, | |
1574 | {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, | |
1575 | 0x3e29864e8a2ec908}, | |
1576 | {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, | |
1577 | 0x239b90ea3dc31e7e}, | |
1578 | {1, 0, 0, 0}}, | |
1579 | {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, | |
1580 | 0x820f4dd949f72ff7}, | |
1581 | {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, | |
1582 | 0x140406ec783a05ec}, | |
1583 | {1, 0, 0, 0}}, | |
1584 | {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, | |
1585 | 0x68f6b8542783dfee}, | |
1586 | {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, | |
1587 | 0xcbe1feba92e40ce6}, | |
1588 | {1, 0, 0, 0}}, | |
1589 | {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, | |
1590 | 0xd0b2f94d2f420109}, | |
1591 | {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, | |
1592 | 0x971459828b0719e5}, | |
1593 | {1, 0, 0, 0}}, | |
1594 | {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, | |
1595 | 0x961610004a866aba}, | |
1596 | {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, | |
1597 | 0x7acb9fadcee75e44}, | |
1598 | {1, 0, 0, 0}}, | |
1599 | {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, | |
1600 | 0x24eb9acca333bf5b}, | |
1601 | {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, | |
1602 | 0x69f891c5acd079cc}, | |
1603 | {1, 0, 0, 0}}, | |
1604 | {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, | |
1605 | 0xe51f547c5972a107}, | |
1606 | {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, | |
1607 | 0x1c309a2b25bb1387}, | |
1608 | {1, 0, 0, 0}}, | |
1609 | {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, | |
1610 | 0x20b87b8aa2c4e503}, | |
1611 | {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, | |
1612 | 0xf5c6fa49919776be}, | |
1613 | {1, 0, 0, 0}}, | |
1614 | {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, | |
1615 | 0x1ed7d1b9332010b9}, | |
1616 | {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, | |
1617 | 0x3a2b03f03217257a}, | |
1618 | {1, 0, 0, 0}}, | |
1619 | {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, | |
1620 | 0x15fee545c78dd9f6}, | |
1621 | {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, | |
1622 | 0x4ab5b6b2b8753f81}, | |
1623 | {1, 0, 0, 0}}} | |
1624 | }; | |
1625 | ||
1626 | /* | |
1627 | * select_point selects the |idx|th point from a precomputation table and | |
1628 | * copies it to out. | |
1629 | */ | |
1630 | static void select_point(const u64 idx, unsigned int size, | |
1631 | const smallfelem pre_comp[16][3], smallfelem out[3]) | |
1632 | { | |
1633 | unsigned i, j; | |
1634 | u64 *outlimbs = &out[0][0]; | |
16f8d4eb | 1635 | |
88f4c6f3 | 1636 | memset(out, 0, sizeof(*out) * 3); |
0f113f3e MC |
1637 | |
1638 | for (i = 0; i < size; i++) { | |
1639 | const u64 *inlimbs = (u64 *)&pre_comp[i][0][0]; | |
1640 | u64 mask = i ^ idx; | |
1641 | mask |= mask >> 4; | |
1642 | mask |= mask >> 2; | |
1643 | mask |= mask >> 1; | |
1644 | mask &= 1; | |
1645 | mask--; | |
1646 | for (j = 0; j < NLIMBS * 3; j++) | |
1647 | outlimbs[j] |= inlimbs[j] & mask; | |
1648 | } | |
1649 | } | |
3e00b4c9 BM |
1650 | |
1651 | /* get_bit returns the |i|th bit in |in| */ | |
1652 | static char get_bit(const felem_bytearray in, int i) | |
0f113f3e MC |
1653 | { |
1654 | if ((i < 0) || (i >= 256)) | |
1655 | return 0; | |
1656 | return (in[i >> 3] >> (i & 7)) & 1; | |
1657 | } | |
1658 | ||
1659 | /* | |
1660 | * Interleaved point multiplication using precomputed point multiples: The | |
1661 | * small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[], the scalars | |
1662 | * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the | |
1663 | * generator, using certain (large) precomputed multiples in g_pre_comp. | |
1664 | * Output point (X, Y, Z) is stored in x_out, y_out, z_out | |
1665 | */ | |
3e00b4c9 | 1666 | static void batch_mul(felem x_out, felem y_out, felem z_out, |
0f113f3e MC |
1667 | const felem_bytearray scalars[], |
1668 | const unsigned num_points, const u8 *g_scalar, | |
1669 | const int mixed, const smallfelem pre_comp[][17][3], | |
1670 | const smallfelem g_pre_comp[2][16][3]) | |
1671 | { | |
1672 | int i, skip; | |
1673 | unsigned num, gen_mul = (g_scalar != NULL); | |
1674 | felem nq[3], ftmp; | |
1675 | smallfelem tmp[3]; | |
1676 | u64 bits; | |
1677 | u8 sign, digit; | |
1678 | ||
1679 | /* set nq to the point at infinity */ | |
16f8d4eb | 1680 | memset(nq, 0, sizeof(nq)); |
0f113f3e MC |
1681 | |
1682 | /* | |
1683 | * Loop over all scalars msb-to-lsb, interleaving additions of multiples | |
1684 | * of the generator (two in each of the last 32 rounds) and additions of | |
1685 | * other points multiples (every 5th round). | |
1686 | */ | |
1687 | skip = 1; /* save two point operations in the first | |
1688 | * round */ | |
1689 | for (i = (num_points ? 255 : 31); i >= 0; --i) { | |
1690 | /* double */ | |
1691 | if (!skip) | |
1692 | point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); | |
1693 | ||
1694 | /* add multiples of the generator */ | |
1695 | if (gen_mul && (i <= 31)) { | |
1696 | /* first, look 32 bits upwards */ | |
1697 | bits = get_bit(g_scalar, i + 224) << 3; | |
1698 | bits |= get_bit(g_scalar, i + 160) << 2; | |
1699 | bits |= get_bit(g_scalar, i + 96) << 1; | |
1700 | bits |= get_bit(g_scalar, i + 32); | |
1701 | /* select the point to add, in constant time */ | |
1702 | select_point(bits, 16, g_pre_comp[1], tmp); | |
1703 | ||
1704 | if (!skip) { | |
1705 | /* Arg 1 below is for "mixed" */ | |
1706 | point_add(nq[0], nq[1], nq[2], | |
1707 | nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); | |
1708 | } else { | |
1709 | smallfelem_expand(nq[0], tmp[0]); | |
1710 | smallfelem_expand(nq[1], tmp[1]); | |
1711 | smallfelem_expand(nq[2], tmp[2]); | |
1712 | skip = 0; | |
1713 | } | |
1714 | ||
1715 | /* second, look at the current position */ | |
1716 | bits = get_bit(g_scalar, i + 192) << 3; | |
1717 | bits |= get_bit(g_scalar, i + 128) << 2; | |
1718 | bits |= get_bit(g_scalar, i + 64) << 1; | |
1719 | bits |= get_bit(g_scalar, i); | |
1720 | /* select the point to add, in constant time */ | |
1721 | select_point(bits, 16, g_pre_comp[0], tmp); | |
1722 | /* Arg 1 below is for "mixed" */ | |
1723 | point_add(nq[0], nq[1], nq[2], | |
1724 | nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); | |
1725 | } | |
1726 | ||
1727 | /* do other additions every 5 doublings */ | |
1728 | if (num_points && (i % 5 == 0)) { | |
1729 | /* loop over all scalars */ | |
1730 | for (num = 0; num < num_points; ++num) { | |
1731 | bits = get_bit(scalars[num], i + 4) << 5; | |
1732 | bits |= get_bit(scalars[num], i + 3) << 4; | |
1733 | bits |= get_bit(scalars[num], i + 2) << 3; | |
1734 | bits |= get_bit(scalars[num], i + 1) << 2; | |
1735 | bits |= get_bit(scalars[num], i) << 1; | |
1736 | bits |= get_bit(scalars[num], i - 1); | |
1737 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); | |
1738 | ||
1739 | /* | |
1740 | * select the point to add or subtract, in constant time | |
1741 | */ | |
1742 | select_point(digit, 17, pre_comp[num], tmp); | |
1743 | smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative | |
1744 | * point */ | |
1745 | copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); | |
1746 | felem_contract(tmp[1], ftmp); | |
1747 | ||
1748 | if (!skip) { | |
1749 | point_add(nq[0], nq[1], nq[2], | |
1750 | nq[0], nq[1], nq[2], | |
1751 | mixed, tmp[0], tmp[1], tmp[2]); | |
1752 | } else { | |
1753 | smallfelem_expand(nq[0], tmp[0]); | |
1754 | smallfelem_expand(nq[1], tmp[1]); | |
1755 | smallfelem_expand(nq[2], tmp[2]); | |
1756 | skip = 0; | |
1757 | } | |
1758 | } | |
1759 | } | |
1760 | } | |
1761 | felem_assign(x_out, nq[0]); | |
1762 | felem_assign(y_out, nq[1]); | |
1763 | felem_assign(z_out, nq[2]); | |
1764 | } | |
3e00b4c9 BM |
1765 | |
1766 | /* Precomputation for the group generator. */ | |
3aef36ff | 1767 | struct nistp256_pre_comp_st { |
0f113f3e | 1768 | smallfelem g_pre_comp[2][16][3]; |
2f545ae4 | 1769 | CRYPTO_REF_COUNT references; |
9b398ef2 | 1770 | CRYPTO_RWLOCK *lock; |
3aef36ff | 1771 | }; |
3e00b4c9 BM |
1772 | |
1773 | const EC_METHOD *EC_GFp_nistp256_method(void) | |
0f113f3e MC |
1774 | { |
1775 | static const EC_METHOD ret = { | |
1776 | EC_FLAGS_DEFAULT_OCT, | |
1777 | NID_X9_62_prime_field, | |
1778 | ec_GFp_nistp256_group_init, | |
1779 | ec_GFp_simple_group_finish, | |
1780 | ec_GFp_simple_group_clear_finish, | |
1781 | ec_GFp_nist_group_copy, | |
1782 | ec_GFp_nistp256_group_set_curve, | |
1783 | ec_GFp_simple_group_get_curve, | |
1784 | ec_GFp_simple_group_get_degree, | |
9ff9bccc | 1785 | ec_group_simple_order_bits, |
0f113f3e MC |
1786 | ec_GFp_simple_group_check_discriminant, |
1787 | ec_GFp_simple_point_init, | |
1788 | ec_GFp_simple_point_finish, | |
1789 | ec_GFp_simple_point_clear_finish, | |
1790 | ec_GFp_simple_point_copy, | |
1791 | ec_GFp_simple_point_set_to_infinity, | |
1792 | ec_GFp_simple_set_Jprojective_coordinates_GFp, | |
1793 | ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
1794 | ec_GFp_simple_point_set_affine_coordinates, | |
1795 | ec_GFp_nistp256_point_get_affine_coordinates, | |
1796 | 0 /* point_set_compressed_coordinates */ , | |
1797 | 0 /* point2oct */ , | |
1798 | 0 /* oct2point */ , | |
1799 | ec_GFp_simple_add, | |
1800 | ec_GFp_simple_dbl, | |
1801 | ec_GFp_simple_invert, | |
1802 | ec_GFp_simple_is_at_infinity, | |
1803 | ec_GFp_simple_is_on_curve, | |
1804 | ec_GFp_simple_cmp, | |
1805 | ec_GFp_simple_make_affine, | |
1806 | ec_GFp_simple_points_make_affine, | |
1807 | ec_GFp_nistp256_points_mul, | |
1808 | ec_GFp_nistp256_precompute_mult, | |
1809 | ec_GFp_nistp256_have_precompute_mult, | |
1810 | ec_GFp_nist_field_mul, | |
1811 | ec_GFp_nist_field_sqr, | |
1812 | 0 /* field_div */ , | |
e0033efc | 1813 | ec_GFp_simple_field_inv, |
0f113f3e MC |
1814 | 0 /* field_encode */ , |
1815 | 0 /* field_decode */ , | |
9ff9bccc DSH |
1816 | 0, /* field_set_to_one */ |
1817 | ec_key_simple_priv2oct, | |
1818 | ec_key_simple_oct2priv, | |
1819 | 0, /* set private */ | |
1820 | ec_key_simple_generate_key, | |
1821 | ec_key_simple_check_key, | |
1822 | ec_key_simple_generate_public_key, | |
1823 | 0, /* keycopy */ | |
1824 | 0, /* keyfinish */ | |
37124360 | 1825 | ecdh_simple_compute_key, |
9bf682f6 PS |
1826 | ecdsa_simple_sign_setup, |
1827 | ecdsa_simple_sign_sig, | |
1828 | ecdsa_simple_verify_sig, | |
37124360 NT |
1829 | 0, /* field_inverse_mod_ord */ |
1830 | 0, /* blind_coordinates */ | |
1831 | 0, /* ladder_pre */ | |
1832 | 0, /* ladder_step */ | |
1833 | 0 /* ladder_post */ | |
0f113f3e MC |
1834 | }; |
1835 | ||
1836 | return &ret; | |
1837 | } | |
3e00b4c9 BM |
1838 | |
1839 | /******************************************************************************/ | |
0f113f3e MC |
1840 | /* |
1841 | * FUNCTIONS TO MANAGE PRECOMPUTATION | |
3e00b4c9 BM |
1842 | */ |
1843 | ||
3f5abab9 | 1844 | static NISTP256_PRE_COMP *nistp256_pre_comp_new(void) |
0f113f3e | 1845 | { |
a2d0baa2 F |
1846 | NISTP256_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); |
1847 | ||
90945fa3 | 1848 | if (ret == NULL) { |
0f113f3e MC |
1849 | ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
1850 | return ret; | |
1851 | } | |
a2d0baa2 | 1852 | |
0f113f3e | 1853 | ret->references = 1; |
9b398ef2 AG |
1854 | |
1855 | ret->lock = CRYPTO_THREAD_lock_new(); | |
1856 | if (ret->lock == NULL) { | |
1857 | ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
1858 | OPENSSL_free(ret); | |
1859 | return NULL; | |
1860 | } | |
0f113f3e MC |
1861 | return ret; |
1862 | } | |
3e00b4c9 | 1863 | |
3aef36ff | 1864 | NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *p) |
0f113f3e | 1865 | { |
9b398ef2 | 1866 | int i; |
3aef36ff | 1867 | if (p != NULL) |
2f545ae4 | 1868 | CRYPTO_UP_REF(&p->references, &i, p->lock); |
3aef36ff | 1869 | return p; |
0f113f3e | 1870 | } |
3e00b4c9 | 1871 | |
3aef36ff | 1872 | void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *pre) |
0f113f3e | 1873 | { |
9b398ef2 AG |
1874 | int i; |
1875 | ||
1876 | if (pre == NULL) | |
0f113f3e | 1877 | return; |
9b398ef2 | 1878 | |
2f545ae4 | 1879 | CRYPTO_DOWN_REF(&pre->references, &i, pre->lock); |
9b398ef2 AG |
1880 | REF_PRINT_COUNT("EC_nistp256", x); |
1881 | if (i > 0) | |
1882 | return; | |
1883 | REF_ASSERT_ISNT(i < 0); | |
1884 | ||
1885 | CRYPTO_THREAD_lock_free(pre->lock); | |
0f113f3e MC |
1886 | OPENSSL_free(pre); |
1887 | } | |
3e00b4c9 | 1888 | |
3e00b4c9 | 1889 | /******************************************************************************/ |
0f113f3e MC |
1890 | /* |
1891 | * OPENSSL EC_METHOD FUNCTIONS | |
3e00b4c9 BM |
1892 | */ |
1893 | ||
1894 | int ec_GFp_nistp256_group_init(EC_GROUP *group) | |
0f113f3e MC |
1895 | { |
1896 | int ret; | |
1897 | ret = ec_GFp_simple_group_init(group); | |
1898 | group->a_is_minus3 = 1; | |
1899 | return ret; | |
1900 | } | |
3e00b4c9 BM |
1901 | |
1902 | int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, | |
0f113f3e MC |
1903 | const BIGNUM *a, const BIGNUM *b, |
1904 | BN_CTX *ctx) | |
1905 | { | |
1906 | int ret = 0; | |
0f113f3e | 1907 | BIGNUM *curve_p, *curve_a, *curve_b; |
a9612d6c MC |
1908 | #ifndef FIPS_MODE |
1909 | BN_CTX *new_ctx = NULL; | |
0f113f3e MC |
1910 | |
1911 | if (ctx == NULL) | |
a6482df0 | 1912 | ctx = new_ctx = BN_CTX_new(); |
a9612d6c MC |
1913 | #endif |
1914 | if (ctx == NULL) | |
1915 | return 0; | |
1916 | ||
0f113f3e | 1917 | BN_CTX_start(ctx); |
edea42c6 PY |
1918 | curve_p = BN_CTX_get(ctx); |
1919 | curve_a = BN_CTX_get(ctx); | |
1920 | curve_b = BN_CTX_get(ctx); | |
1921 | if (curve_b == NULL) | |
0f113f3e MC |
1922 | goto err; |
1923 | BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); | |
1924 | BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); | |
1925 | BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b); | |
1926 | if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { | |
1927 | ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE, | |
1928 | EC_R_WRONG_CURVE_PARAMETERS); | |
1929 | goto err; | |
1930 | } | |
1931 | group->field_mod_func = BN_nist_mod_256; | |
1932 | ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); | |
1933 | err: | |
1934 | BN_CTX_end(ctx); | |
a9612d6c | 1935 | #ifndef FIPS_MODE |
23a1d5e9 | 1936 | BN_CTX_free(new_ctx); |
a9612d6c | 1937 | #endif |
0f113f3e MC |
1938 | return ret; |
1939 | } | |
1940 | ||
1941 | /* | |
1942 | * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = | |
1943 | * (X/Z^2, Y/Z^3) | |
1944 | */ | |
3e00b4c9 | 1945 | int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, |
0f113f3e MC |
1946 | const EC_POINT *point, |
1947 | BIGNUM *x, BIGNUM *y, | |
1948 | BN_CTX *ctx) | |
1949 | { | |
1950 | felem z1, z2, x_in, y_in; | |
1951 | smallfelem x_out, y_out; | |
1952 | longfelem tmp; | |
1953 | ||
1954 | if (EC_POINT_is_at_infinity(group, point)) { | |
1955 | ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, | |
1956 | EC_R_POINT_AT_INFINITY); | |
1957 | return 0; | |
1958 | } | |
ace8f546 AP |
1959 | if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || |
1960 | (!BN_to_felem(z1, point->Z))) | |
0f113f3e MC |
1961 | return 0; |
1962 | felem_inv(z2, z1); | |
1963 | felem_square(tmp, z2); | |
1964 | felem_reduce(z1, tmp); | |
1965 | felem_mul(tmp, x_in, z1); | |
1966 | felem_reduce(x_in, tmp); | |
1967 | felem_contract(x_out, x_in); | |
1968 | if (x != NULL) { | |
1969 | if (!smallfelem_to_BN(x, x_out)) { | |
1970 | ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, | |
1971 | ERR_R_BN_LIB); | |
1972 | return 0; | |
1973 | } | |
1974 | } | |
1975 | felem_mul(tmp, z1, z2); | |
1976 | felem_reduce(z1, tmp); | |
1977 | felem_mul(tmp, y_in, z1); | |
1978 | felem_reduce(y_in, tmp); | |
1979 | felem_contract(y_out, y_in); | |
1980 | if (y != NULL) { | |
1981 | if (!smallfelem_to_BN(y, y_out)) { | |
1982 | ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, | |
1983 | ERR_R_BN_LIB); | |
1984 | return 0; | |
1985 | } | |
1986 | } | |
1987 | return 1; | |
1988 | } | |
3e00b4c9 | 1989 | |
b853717f | 1990 | /* points below is of size |num|, and tmp_smallfelems is of size |num+1| */ |
0f113f3e MC |
1991 | static void make_points_affine(size_t num, smallfelem points[][3], |
1992 | smallfelem tmp_smallfelems[]) | |
1993 | { | |
1994 | /* | |
1995 | * Runs in constant time, unless an input is the point at infinity (which | |
1996 | * normally shouldn't happen). | |
1997 | */ | |
1998 | ec_GFp_nistp_points_make_affine_internal(num, | |
1999 | points, | |
2000 | sizeof(smallfelem), | |
2001 | tmp_smallfelems, | |
2002 | (void (*)(void *))smallfelem_one, | |
0f113f3e MC |
2003 | smallfelem_is_zero_int, |
2004 | (void (*)(void *, const void *)) | |
2005 | smallfelem_assign, | |
2006 | (void (*)(void *, const void *)) | |
2007 | smallfelem_square_contract, | |
2008 | (void (*) | |
2009 | (void *, const void *, | |
2010 | const void *)) | |
2011 | smallfelem_mul_contract, | |
2012 | (void (*)(void *, const void *)) | |
2013 | smallfelem_inv_contract, | |
2014 | /* nothing to contract */ | |
2015 | (void (*)(void *, const void *)) | |
2016 | smallfelem_assign); | |
2017 | } | |
2018 | ||
2019 | /* | |
2020 | * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL | |
2021 | * values Result is stored in r (r can equal one of the inputs). | |
2022 | */ | |
3e00b4c9 | 2023 | int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, |
0f113f3e MC |
2024 | const BIGNUM *scalar, size_t num, |
2025 | const EC_POINT *points[], | |
2026 | const BIGNUM *scalars[], BN_CTX *ctx) | |
2027 | { | |
2028 | int ret = 0; | |
2029 | int j; | |
2030 | int mixed = 0; | |
0f113f3e MC |
2031 | BIGNUM *x, *y, *z, *tmp_scalar; |
2032 | felem_bytearray g_secret; | |
2033 | felem_bytearray *secrets = NULL; | |
16f8d4eb | 2034 | smallfelem (*pre_comp)[17][3] = NULL; |
0f113f3e MC |
2035 | smallfelem *tmp_smallfelems = NULL; |
2036 | felem_bytearray tmp; | |
2037 | unsigned i, num_bytes; | |
2038 | int have_pre_comp = 0; | |
2039 | size_t num_points = num; | |
2040 | smallfelem x_in, y_in, z_in; | |
2041 | felem x_out, y_out, z_out; | |
2042 | NISTP256_PRE_COMP *pre = NULL; | |
2043 | const smallfelem(*g_pre_comp)[16][3] = NULL; | |
2044 | EC_POINT *generator = NULL; | |
2045 | const EC_POINT *p = NULL; | |
2046 | const BIGNUM *p_scalar = NULL; | |
2047 | ||
0f113f3e | 2048 | BN_CTX_start(ctx); |
edea42c6 PY |
2049 | x = BN_CTX_get(ctx); |
2050 | y = BN_CTX_get(ctx); | |
2051 | z = BN_CTX_get(ctx); | |
2052 | tmp_scalar = BN_CTX_get(ctx); | |
2053 | if (tmp_scalar == NULL) | |
0f113f3e MC |
2054 | goto err; |
2055 | ||
2056 | if (scalar != NULL) { | |
3aef36ff | 2057 | pre = group->pre_comp.nistp256; |
0f113f3e MC |
2058 | if (pre) |
2059 | /* we have precomputation, try to use it */ | |
2060 | g_pre_comp = (const smallfelem(*)[16][3])pre->g_pre_comp; | |
2061 | else | |
2062 | /* try to use the standard precomputation */ | |
2063 | g_pre_comp = &gmul[0]; | |
2064 | generator = EC_POINT_new(group); | |
2065 | if (generator == NULL) | |
2066 | goto err; | |
2067 | /* get the generator from precomputation */ | |
2068 | if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || | |
2069 | !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || | |
2070 | !smallfelem_to_BN(z, g_pre_comp[0][1][2])) { | |
2071 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); | |
2072 | goto err; | |
2073 | } | |
2074 | if (!EC_POINT_set_Jprojective_coordinates_GFp(group, | |
2075 | generator, x, y, z, | |
2076 | ctx)) | |
2077 | goto err; | |
2078 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) | |
2079 | /* precomputation matches generator */ | |
2080 | have_pre_comp = 1; | |
2081 | else | |
2082 | /* | |
2083 | * we don't have valid precomputation: treat the generator as a | |
2084 | * random point | |
2085 | */ | |
2086 | num_points++; | |
2087 | } | |
2088 | if (num_points > 0) { | |
2089 | if (num_points >= 3) { | |
2090 | /* | |
2091 | * unless we precompute multiples for just one or two points, | |
2092 | * converting those into affine form is time well spent | |
2093 | */ | |
2094 | mixed = 1; | |
2095 | } | |
16f8d4eb RS |
2096 | secrets = OPENSSL_malloc(sizeof(*secrets) * num_points); |
2097 | pre_comp = OPENSSL_malloc(sizeof(*pre_comp) * num_points); | |
0f113f3e MC |
2098 | if (mixed) |
2099 | tmp_smallfelems = | |
16f8d4eb | 2100 | OPENSSL_malloc(sizeof(*tmp_smallfelems) * (num_points * 17 + 1)); |
0f113f3e MC |
2101 | if ((secrets == NULL) || (pre_comp == NULL) |
2102 | || (mixed && (tmp_smallfelems == NULL))) { | |
2103 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE); | |
2104 | goto err; | |
2105 | } | |
2106 | ||
2107 | /* | |
2108 | * we treat NULL scalars as 0, and NULL points as points at infinity, | |
2109 | * i.e., they contribute nothing to the linear combination | |
2110 | */ | |
16f8d4eb RS |
2111 | memset(secrets, 0, sizeof(*secrets) * num_points); |
2112 | memset(pre_comp, 0, sizeof(*pre_comp) * num_points); | |
0f113f3e MC |
2113 | for (i = 0; i < num_points; ++i) { |
2114 | if (i == num) | |
2115 | /* | |
2116 | * we didn't have a valid precomputation, so we pick the | |
2117 | * generator | |
2118 | */ | |
2119 | { | |
2120 | p = EC_GROUP_get0_generator(group); | |
2121 | p_scalar = scalar; | |
2122 | } else | |
2123 | /* the i^th point */ | |
2124 | { | |
2125 | p = points[i]; | |
2126 | p_scalar = scalars[i]; | |
2127 | } | |
2128 | if ((p_scalar != NULL) && (p != NULL)) { | |
2129 | /* reduce scalar to 0 <= scalar < 2^256 */ | |
2130 | if ((BN_num_bits(p_scalar) > 256) | |
2131 | || (BN_is_negative(p_scalar))) { | |
2132 | /* | |
2133 | * this is an unusual input, and we don't guarantee | |
2134 | * constant-timeness | |
2135 | */ | |
ace8f546 | 2136 | if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { |
0f113f3e MC |
2137 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); |
2138 | goto err; | |
2139 | } | |
2140 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
2141 | } else | |
2142 | num_bytes = BN_bn2bin(p_scalar, tmp); | |
2143 | flip_endian(secrets[i], tmp, num_bytes); | |
2144 | /* precompute multiples */ | |
ace8f546 AP |
2145 | if ((!BN_to_felem(x_out, p->X)) || |
2146 | (!BN_to_felem(y_out, p->Y)) || | |
2147 | (!BN_to_felem(z_out, p->Z))) | |
0f113f3e MC |
2148 | goto err; |
2149 | felem_shrink(pre_comp[i][1][0], x_out); | |
2150 | felem_shrink(pre_comp[i][1][1], y_out); | |
2151 | felem_shrink(pre_comp[i][1][2], z_out); | |
2152 | for (j = 2; j <= 16; ++j) { | |
2153 | if (j & 1) { | |
2154 | point_add_small(pre_comp[i][j][0], pre_comp[i][j][1], | |
2155 | pre_comp[i][j][2], pre_comp[i][1][0], | |
2156 | pre_comp[i][1][1], pre_comp[i][1][2], | |
2157 | pre_comp[i][j - 1][0], | |
2158 | pre_comp[i][j - 1][1], | |
2159 | pre_comp[i][j - 1][2]); | |
2160 | } else { | |
2161 | point_double_small(pre_comp[i][j][0], | |
2162 | pre_comp[i][j][1], | |
2163 | pre_comp[i][j][2], | |
2164 | pre_comp[i][j / 2][0], | |
2165 | pre_comp[i][j / 2][1], | |
2166 | pre_comp[i][j / 2][2]); | |
2167 | } | |
2168 | } | |
2169 | } | |
2170 | } | |
2171 | if (mixed) | |
2172 | make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems); | |
2173 | } | |
2174 | ||
2175 | /* the scalar for the generator */ | |
2176 | if ((scalar != NULL) && (have_pre_comp)) { | |
2177 | memset(g_secret, 0, sizeof(g_secret)); | |
2178 | /* reduce scalar to 0 <= scalar < 2^256 */ | |
2179 | if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) { | |
2180 | /* | |
2181 | * this is an unusual input, and we don't guarantee | |
2182 | * constant-timeness | |
2183 | */ | |
ace8f546 | 2184 | if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { |
0f113f3e MC |
2185 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); |
2186 | goto err; | |
2187 | } | |
2188 | num_bytes = BN_bn2bin(tmp_scalar, tmp); | |
2189 | } else | |
2190 | num_bytes = BN_bn2bin(scalar, tmp); | |
2191 | flip_endian(g_secret, tmp, num_bytes); | |
2192 | /* do the multiplication with generator precomputation */ | |
2193 | batch_mul(x_out, y_out, z_out, | |
2194 | (const felem_bytearray(*))secrets, num_points, | |
2195 | g_secret, | |
2196 | mixed, (const smallfelem(*)[17][3])pre_comp, g_pre_comp); | |
2197 | } else | |
2198 | /* do the multiplication without generator precomputation */ | |
2199 | batch_mul(x_out, y_out, z_out, | |
2200 | (const felem_bytearray(*))secrets, num_points, | |
2201 | NULL, mixed, (const smallfelem(*)[17][3])pre_comp, NULL); | |
2202 | /* reduce the output to its unique minimal representation */ | |
2203 | felem_contract(x_in, x_out); | |
2204 | felem_contract(y_in, y_out); | |
2205 | felem_contract(z_in, z_out); | |
2206 | if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || | |
2207 | (!smallfelem_to_BN(z, z_in))) { | |
2208 | ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); | |
2209 | goto err; | |
2210 | } | |
2211 | ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); | |
2212 | ||
2213 | err: | |
2214 | BN_CTX_end(ctx); | |
8fdc3734 | 2215 | EC_POINT_free(generator); |
b548a1f1 RS |
2216 | OPENSSL_free(secrets); |
2217 | OPENSSL_free(pre_comp); | |
2218 | OPENSSL_free(tmp_smallfelems); | |
0f113f3e MC |
2219 | return ret; |
2220 | } | |
3e00b4c9 BM |
2221 | |
2222 | int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) | |
0f113f3e MC |
2223 | { |
2224 | int ret = 0; | |
2225 | NISTP256_PRE_COMP *pre = NULL; | |
2226 | int i, j; | |
0f113f3e MC |
2227 | BIGNUM *x, *y; |
2228 | EC_POINT *generator = NULL; | |
2229 | smallfelem tmp_smallfelems[32]; | |
2230 | felem x_tmp, y_tmp, z_tmp; | |
a9612d6c MC |
2231 | #ifndef FIPS_MODE |
2232 | BN_CTX *new_ctx = NULL; | |
2233 | #endif | |
0f113f3e MC |
2234 | |
2235 | /* throw away old precomputation */ | |
2c52ac9b | 2236 | EC_pre_comp_free(group); |
a9612d6c MC |
2237 | |
2238 | #ifndef FIPS_MODE | |
0f113f3e | 2239 | if (ctx == NULL) |
a6482df0 | 2240 | ctx = new_ctx = BN_CTX_new(); |
a9612d6c MC |
2241 | #endif |
2242 | if (ctx == NULL) | |
2243 | return 0; | |
2244 | ||
0f113f3e | 2245 | BN_CTX_start(ctx); |
edea42c6 PY |
2246 | x = BN_CTX_get(ctx); |
2247 | y = BN_CTX_get(ctx); | |
2248 | if (y == NULL) | |
0f113f3e MC |
2249 | goto err; |
2250 | /* get the generator */ | |
2251 | if (group->generator == NULL) | |
2252 | goto err; | |
2253 | generator = EC_POINT_new(group); | |
2254 | if (generator == NULL) | |
2255 | goto err; | |
2256 | BN_bin2bn(nistp256_curve_params[3], sizeof(felem_bytearray), x); | |
2257 | BN_bin2bn(nistp256_curve_params[4], sizeof(felem_bytearray), y); | |
9cc570d4 | 2258 | if (!EC_POINT_set_affine_coordinates(group, generator, x, y, ctx)) |
0f113f3e MC |
2259 | goto err; |
2260 | if ((pre = nistp256_pre_comp_new()) == NULL) | |
2261 | goto err; | |
2262 | /* | |
2263 | * if the generator is the standard one, use built-in precomputation | |
2264 | */ | |
2265 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { | |
2266 | memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); | |
615614c8 | 2267 | goto done; |
0f113f3e | 2268 | } |
ace8f546 AP |
2269 | if ((!BN_to_felem(x_tmp, group->generator->X)) || |
2270 | (!BN_to_felem(y_tmp, group->generator->Y)) || | |
2271 | (!BN_to_felem(z_tmp, group->generator->Z))) | |
0f113f3e MC |
2272 | goto err; |
2273 | felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); | |
2274 | felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); | |
2275 | felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); | |
2276 | /* | |
2277 | * compute 2^64*G, 2^128*G, 2^192*G for the first table, 2^32*G, 2^96*G, | |
2278 | * 2^160*G, 2^224*G for the second one | |
2279 | */ | |
2280 | for (i = 1; i <= 8; i <<= 1) { | |
2281 | point_double_small(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], | |
2282 | pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0], | |
2283 | pre->g_pre_comp[0][i][1], | |
2284 | pre->g_pre_comp[0][i][2]); | |
2285 | for (j = 0; j < 31; ++j) { | |
2286 | point_double_small(pre->g_pre_comp[1][i][0], | |
2287 | pre->g_pre_comp[1][i][1], | |
2288 | pre->g_pre_comp[1][i][2], | |
2289 | pre->g_pre_comp[1][i][0], | |
2290 | pre->g_pre_comp[1][i][1], | |
2291 | pre->g_pre_comp[1][i][2]); | |
2292 | } | |
2293 | if (i == 8) | |
2294 | break; | |
2295 | point_double_small(pre->g_pre_comp[0][2 * i][0], | |
2296 | pre->g_pre_comp[0][2 * i][1], | |
2297 | pre->g_pre_comp[0][2 * i][2], | |
2298 | pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], | |
2299 | pre->g_pre_comp[1][i][2]); | |
2300 | for (j = 0; j < 31; ++j) { | |
2301 | point_double_small(pre->g_pre_comp[0][2 * i][0], | |
2302 | pre->g_pre_comp[0][2 * i][1], | |
2303 | pre->g_pre_comp[0][2 * i][2], | |
2304 | pre->g_pre_comp[0][2 * i][0], | |
2305 | pre->g_pre_comp[0][2 * i][1], | |
2306 | pre->g_pre_comp[0][2 * i][2]); | |
2307 | } | |
2308 | } | |
2309 | for (i = 0; i < 2; i++) { | |
2310 | /* g_pre_comp[i][0] is the point at infinity */ | |
2311 | memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); | |
2312 | /* the remaining multiples */ | |
2313 | /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ | |
2314 | point_add_small(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], | |
2315 | pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], | |
2316 | pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], | |
2317 | pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
2318 | pre->g_pre_comp[i][2][2]); | |
2319 | /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ | |
2320 | point_add_small(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], | |
2321 | pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], | |
2322 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
2323 | pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
2324 | pre->g_pre_comp[i][2][2]); | |
2325 | /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ | |
2326 | point_add_small(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], | |
2327 | pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], | |
2328 | pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], | |
2329 | pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], | |
2330 | pre->g_pre_comp[i][4][2]); | |
2331 | /* | |
2332 | * 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G | |
2333 | */ | |
2334 | point_add_small(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], | |
2335 | pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], | |
2336 | pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], | |
2337 | pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], | |
2338 | pre->g_pre_comp[i][2][2]); | |
2339 | for (j = 1; j < 8; ++j) { | |
2340 | /* odd multiples: add G resp. 2^32*G */ | |
2341 | point_add_small(pre->g_pre_comp[i][2 * j + 1][0], | |
2342 | pre->g_pre_comp[i][2 * j + 1][1], | |
2343 | pre->g_pre_comp[i][2 * j + 1][2], | |
2344 | pre->g_pre_comp[i][2 * j][0], | |
2345 | pre->g_pre_comp[i][2 * j][1], | |
2346 | pre->g_pre_comp[i][2 * j][2], | |
2347 | pre->g_pre_comp[i][1][0], | |
2348 | pre->g_pre_comp[i][1][1], | |
2349 | pre->g_pre_comp[i][1][2]); | |
2350 | } | |
2351 | } | |
2352 | make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems); | |
2353 | ||
615614c8 | 2354 | done: |
3aef36ff | 2355 | SETPRECOMP(group, nistp256, pre); |
0f113f3e | 2356 | pre = NULL; |
3aef36ff RS |
2357 | ret = 1; |
2358 | ||
3e00b4c9 | 2359 | err: |
0f113f3e | 2360 | BN_CTX_end(ctx); |
8fdc3734 | 2361 | EC_POINT_free(generator); |
a9612d6c | 2362 | #ifndef FIPS_MODE |
23a1d5e9 | 2363 | BN_CTX_free(new_ctx); |
a9612d6c | 2364 | #endif |
3aef36ff | 2365 | EC_nistp256_pre_comp_free(pre); |
0f113f3e MC |
2366 | return ret; |
2367 | } | |
3e00b4c9 BM |
2368 | |
2369 | int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) | |
0f113f3e | 2370 | { |
3aef36ff | 2371 | return HAVEPRECOMP(group, nistp256); |
0f113f3e | 2372 | } |
3e00b4c9 | 2373 | #endif |