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3e00b4c9 | 1 | /* |
33388b44 | 2 | * Copyright 2011-2020 The OpenSSL Project Authors. All Rights Reserved. |
aa6bb135 | 3 | * |
a7f182b7 | 4 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
aa6bb135 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 | */ |
aa6bb135 | 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 | ||
579422c8 P |
26 | /* |
27 | * ECDSA low level APIs are deprecated for public use, but still ok for | |
28 | * internal use. | |
29 | */ | |
30 | #include "internal/deprecated.h" | |
31 | ||
3e00b4c9 BM |
32 | /* |
33 | * A 64-bit implementation of the NIST P-521 elliptic curve point multiplication | |
34 | * | |
35 | * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. | |
36 | * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 | |
37 | * work which got its smarts from Daniel J. Bernstein's work on the same. | |
38 | */ | |
39 | ||
74a011eb | 40 | #include <openssl/e_os2.h> |
3e00b4c9 | 41 | |
705536e2 RS |
42 | #include <string.h> |
43 | #include <openssl/err.h> | |
44 | #include "ec_local.h" | |
3e00b4c9 | 45 | |
705536e2 | 46 | #if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 |
3e00b4c9 | 47 | /* even with gcc, the typedef won't work for 32-bit platforms */ |
0f113f3e MC |
48 | typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit |
49 | * platforms */ | |
705536e2 RS |
50 | #else |
51 | # error "Your compiler doesn't appear to support 128-bit integer types" | |
52 | #endif | |
3e00b4c9 BM |
53 | |
54 | typedef uint8_t u8; | |
55 | typedef uint64_t u64; | |
3e00b4c9 | 56 | |
0f113f3e MC |
57 | /* |
58 | * The underlying field. P521 operates over GF(2^521-1). We can serialise an | |
59 | * element of this field into 66 bytes where the most significant byte | |
60 | * contains only a single bit. We call this an felem_bytearray. | |
61 | */ | |
3e00b4c9 BM |
62 | |
63 | typedef u8 felem_bytearray[66]; | |
64 | ||
0f113f3e MC |
65 | /* |
66 | * These are the parameters of P521, taken from FIPS 186-3, section D.1.2.5. | |
67 | * These values are big-endian. | |
68 | */ | |
69 | static const felem_bytearray nistp521_curve_params[5] = { | |
70 | {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* p */ | |
71 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
72 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
73 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
74 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
75 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
76 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
77 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
78 | 0xff, 0xff}, | |
79 | {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* a = -3 */ | |
80 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
81 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
82 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
83 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
84 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
85 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
86 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, | |
87 | 0xff, 0xfc}, | |
88 | {0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, /* b */ | |
89 | 0x9a, 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, | |
90 | 0x40, 0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3, | |
91 | 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, | |
92 | 0x09, 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, | |
93 | 0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1, | |
94 | 0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, | |
95 | 0x34, 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, | |
96 | 0x3f, 0x00}, | |
97 | {0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, /* x */ | |
98 | 0xe9, 0xcd, 0x9e, 0x3e, 0xcb, 0x66, 0x23, 0x95, | |
99 | 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f, | |
100 | 0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, | |
101 | 0x3d, 0xba, 0xa1, 0x4b, 0x5e, 0x77, 0xef, 0xe7, | |
102 | 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff, | |
103 | 0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, | |
104 | 0x42, 0x9b, 0xf9, 0x7e, 0x7e, 0x31, 0xc2, 0xe5, | |
105 | 0xbd, 0x66}, | |
106 | {0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, /* y */ | |
107 | 0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, | |
108 | 0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, | |
109 | 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e, | |
110 | 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, | |
111 | 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, | |
112 | 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, | |
113 | 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, | |
114 | 0x66, 0x50} | |
115 | }; | |
3e00b4c9 | 116 | |
1d97c843 TH |
117 | /*- |
118 | * The representation of field elements. | |
3e00b4c9 BM |
119 | * ------------------------------------ |
120 | * | |
121 | * We represent field elements with nine values. These values are either 64 or | |
122 | * 128 bits and the field element represented is: | |
123 | * v[0]*2^0 + v[1]*2^58 + v[2]*2^116 + ... + v[8]*2^464 (mod p) | |
124 | * Each of the nine values is called a 'limb'. Since the limbs are spaced only | |
125 | * 58 bits apart, but are greater than 58 bits in length, the most significant | |
126 | * bits of each limb overlap with the least significant bits of the next. | |
127 | * | |
128 | * A field element with 64-bit limbs is an 'felem'. One with 128-bit limbs is a | |
129 | * 'largefelem' */ | |
130 | ||
705536e2 | 131 | #define NLIMBS 9 |
3e00b4c9 BM |
132 | |
133 | typedef uint64_t limb; | |
134 | typedef limb felem[NLIMBS]; | |
135 | typedef uint128_t largefelem[NLIMBS]; | |
136 | ||
137 | static const limb bottom57bits = 0x1ffffffffffffff; | |
138 | static const limb bottom58bits = 0x3ffffffffffffff; | |
139 | ||
0f113f3e MC |
140 | /* |
141 | * bin66_to_felem takes a little-endian byte array and converts it into felem | |
142 | * form. This assumes that the CPU is little-endian. | |
143 | */ | |
3e00b4c9 | 144 | static void bin66_to_felem(felem out, const u8 in[66]) |
0f113f3e MC |
145 | { |
146 | out[0] = (*((limb *) & in[0])) & bottom58bits; | |
147 | out[1] = (*((limb *) & in[7]) >> 2) & bottom58bits; | |
148 | out[2] = (*((limb *) & in[14]) >> 4) & bottom58bits; | |
149 | out[3] = (*((limb *) & in[21]) >> 6) & bottom58bits; | |
150 | out[4] = (*((limb *) & in[29])) & bottom58bits; | |
151 | out[5] = (*((limb *) & in[36]) >> 2) & bottom58bits; | |
152 | out[6] = (*((limb *) & in[43]) >> 4) & bottom58bits; | |
153 | out[7] = (*((limb *) & in[50]) >> 6) & bottom58bits; | |
154 | out[8] = (*((limb *) & in[58])) & bottom57bits; | |
155 | } | |
156 | ||
157 | /* | |
158 | * felem_to_bin66 takes an felem and serialises into a little endian, 66 byte | |
159 | * array. This assumes that the CPU is little-endian. | |
160 | */ | |
3e00b4c9 | 161 | static void felem_to_bin66(u8 out[66], const felem in) |
0f113f3e MC |
162 | { |
163 | memset(out, 0, 66); | |
164 | (*((limb *) & out[0])) = in[0]; | |
165 | (*((limb *) & out[7])) |= in[1] << 2; | |
166 | (*((limb *) & out[14])) |= in[2] << 4; | |
167 | (*((limb *) & out[21])) |= in[3] << 6; | |
168 | (*((limb *) & out[29])) = in[4]; | |
169 | (*((limb *) & out[36])) |= in[5] << 2; | |
170 | (*((limb *) & out[43])) |= in[6] << 4; | |
171 | (*((limb *) & out[50])) |= in[7] << 6; | |
172 | (*((limb *) & out[58])) = in[8]; | |
173 | } | |
3e00b4c9 | 174 | |
3e00b4c9 BM |
175 | /* BN_to_felem converts an OpenSSL BIGNUM into an felem */ |
176 | static int BN_to_felem(felem out, const BIGNUM *bn) | |
0f113f3e | 177 | { |
0f113f3e | 178 | felem_bytearray b_out; |
e0b660c2 | 179 | int num_bytes; |
0f113f3e | 180 | |
e0b660c2 | 181 | if (BN_is_negative(bn)) { |
0f113f3e MC |
182 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); |
183 | return 0; | |
184 | } | |
e0b660c2 NT |
185 | num_bytes = BN_bn2lebinpad(bn, b_out, sizeof(b_out)); |
186 | if (num_bytes < 0) { | |
0f113f3e MC |
187 | ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); |
188 | return 0; | |
189 | } | |
0f113f3e MC |
190 | bin66_to_felem(out, b_out); |
191 | return 1; | |
192 | } | |
3e00b4c9 BM |
193 | |
194 | /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ | |
195 | static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) | |
0f113f3e | 196 | { |
e0b660c2 NT |
197 | felem_bytearray b_out; |
198 | felem_to_bin66(b_out, in); | |
199 | return BN_lebin2bn(b_out, sizeof(b_out), out); | |
0f113f3e | 200 | } |
3e00b4c9 | 201 | |
3a83462d MC |
202 | /*- |
203 | * Field operations | |
204 | * ---------------- | |
205 | */ | |
3e00b4c9 BM |
206 | |
207 | static void felem_one(felem out) | |
0f113f3e MC |
208 | { |
209 | out[0] = 1; | |
210 | out[1] = 0; | |
211 | out[2] = 0; | |
212 | out[3] = 0; | |
213 | out[4] = 0; | |
214 | out[5] = 0; | |
215 | out[6] = 0; | |
216 | out[7] = 0; | |
217 | out[8] = 0; | |
218 | } | |
3e00b4c9 BM |
219 | |
220 | static void felem_assign(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 | out[4] = in[4]; | |
227 | out[5] = in[5]; | |
228 | out[6] = in[6]; | |
229 | out[7] = in[7]; | |
230 | out[8] = in[8]; | |
231 | } | |
3e00b4c9 BM |
232 | |
233 | /* felem_sum64 sets out = out + in. */ | |
234 | static void felem_sum64(felem out, const felem in) | |
0f113f3e MC |
235 | { |
236 | out[0] += in[0]; | |
237 | out[1] += in[1]; | |
238 | out[2] += in[2]; | |
239 | out[3] += in[3]; | |
240 | out[4] += in[4]; | |
241 | out[5] += in[5]; | |
242 | out[6] += in[6]; | |
243 | out[7] += in[7]; | |
244 | out[8] += in[8]; | |
245 | } | |
3e00b4c9 BM |
246 | |
247 | /* felem_scalar sets out = in * scalar */ | |
248 | static void felem_scalar(felem out, const felem in, limb scalar) | |
0f113f3e MC |
249 | { |
250 | out[0] = in[0] * scalar; | |
251 | out[1] = in[1] * scalar; | |
252 | out[2] = in[2] * scalar; | |
253 | out[3] = in[3] * scalar; | |
254 | out[4] = in[4] * scalar; | |
255 | out[5] = in[5] * scalar; | |
256 | out[6] = in[6] * scalar; | |
257 | out[7] = in[7] * scalar; | |
258 | out[8] = in[8] * scalar; | |
259 | } | |
3e00b4c9 BM |
260 | |
261 | /* felem_scalar64 sets out = out * scalar */ | |
262 | static void felem_scalar64(felem out, limb scalar) | |
0f113f3e MC |
263 | { |
264 | out[0] *= scalar; | |
265 | out[1] *= scalar; | |
266 | out[2] *= scalar; | |
267 | out[3] *= scalar; | |
268 | out[4] *= scalar; | |
269 | out[5] *= scalar; | |
270 | out[6] *= scalar; | |
271 | out[7] *= scalar; | |
272 | out[8] *= scalar; | |
273 | } | |
3e00b4c9 BM |
274 | |
275 | /* felem_scalar128 sets out = out * scalar */ | |
276 | static void felem_scalar128(largefelem out, limb scalar) | |
0f113f3e MC |
277 | { |
278 | out[0] *= scalar; | |
279 | out[1] *= scalar; | |
280 | out[2] *= scalar; | |
281 | out[3] *= scalar; | |
282 | out[4] *= scalar; | |
283 | out[5] *= scalar; | |
284 | out[6] *= scalar; | |
285 | out[7] *= scalar; | |
286 | out[8] *= scalar; | |
287 | } | |
3e00b4c9 | 288 | |
1d97c843 TH |
289 | /*- |
290 | * felem_neg sets |out| to |-in| | |
3e00b4c9 BM |
291 | * On entry: |
292 | * in[i] < 2^59 + 2^14 | |
293 | * On exit: | |
294 | * out[i] < 2^62 | |
295 | */ | |
296 | static void felem_neg(felem out, const felem in) | |
0f113f3e MC |
297 | { |
298 | /* In order to prevent underflow, we subtract from 0 mod p. */ | |
299 | static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); | |
300 | static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); | |
301 | ||
302 | out[0] = two62m3 - in[0]; | |
303 | out[1] = two62m2 - in[1]; | |
304 | out[2] = two62m2 - in[2]; | |
305 | out[3] = two62m2 - in[3]; | |
306 | out[4] = two62m2 - in[4]; | |
307 | out[5] = two62m2 - in[5]; | |
308 | out[6] = two62m2 - in[6]; | |
309 | out[7] = two62m2 - in[7]; | |
310 | out[8] = two62m2 - in[8]; | |
311 | } | |
3e00b4c9 | 312 | |
1d97c843 TH |
313 | /*- |
314 | * felem_diff64 subtracts |in| from |out| | |
3e00b4c9 BM |
315 | * On entry: |
316 | * in[i] < 2^59 + 2^14 | |
317 | * On exit: | |
318 | * out[i] < out[i] + 2^62 | |
319 | */ | |
320 | static void felem_diff64(felem out, const felem in) | |
0f113f3e MC |
321 | { |
322 | /* | |
323 | * In order to prevent underflow, we add 0 mod p before subtracting. | |
324 | */ | |
325 | static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); | |
326 | static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); | |
327 | ||
328 | out[0] += two62m3 - in[0]; | |
329 | out[1] += two62m2 - in[1]; | |
330 | out[2] += two62m2 - in[2]; | |
331 | out[3] += two62m2 - in[3]; | |
332 | out[4] += two62m2 - in[4]; | |
333 | out[5] += two62m2 - in[5]; | |
334 | out[6] += two62m2 - in[6]; | |
335 | out[7] += two62m2 - in[7]; | |
336 | out[8] += two62m2 - in[8]; | |
337 | } | |
3e00b4c9 | 338 | |
1d97c843 TH |
339 | /*- |
340 | * felem_diff_128_64 subtracts |in| from |out| | |
3e00b4c9 BM |
341 | * On entry: |
342 | * in[i] < 2^62 + 2^17 | |
343 | * On exit: | |
344 | * out[i] < out[i] + 2^63 | |
345 | */ | |
346 | static void felem_diff_128_64(largefelem out, const felem in) | |
0f113f3e MC |
347 | { |
348 | /* | |
13fbce17 MC |
349 | * In order to prevent underflow, we add 64p mod p (which is equivalent |
350 | * to 0 mod p) before subtracting. p is 2^521 - 1, i.e. in binary a 521 | |
351 | * digit number with all bits set to 1. See "The representation of field | |
352 | * elements" comment above for a description of how limbs are used to | |
353 | * represent a number. 64p is represented with 8 limbs containing a number | |
354 | * with 58 bits set and one limb with a number with 57 bits set. | |
0f113f3e | 355 | */ |
13fbce17 MC |
356 | static const limb two63m6 = (((limb) 1) << 63) - (((limb) 1) << 6); |
357 | static const limb two63m5 = (((limb) 1) << 63) - (((limb) 1) << 5); | |
0f113f3e MC |
358 | |
359 | out[0] += two63m6 - in[0]; | |
360 | out[1] += two63m5 - in[1]; | |
361 | out[2] += two63m5 - in[2]; | |
362 | out[3] += two63m5 - in[3]; | |
363 | out[4] += two63m5 - in[4]; | |
364 | out[5] += two63m5 - in[5]; | |
365 | out[6] += two63m5 - in[6]; | |
366 | out[7] += two63m5 - in[7]; | |
367 | out[8] += two63m5 - in[8]; | |
368 | } | |
3e00b4c9 | 369 | |
1d97c843 TH |
370 | /*- |
371 | * felem_diff_128_64 subtracts |in| from |out| | |
3e00b4c9 BM |
372 | * On entry: |
373 | * in[i] < 2^126 | |
374 | * On exit: | |
375 | * out[i] < out[i] + 2^127 - 2^69 | |
376 | */ | |
377 | static void felem_diff128(largefelem out, const largefelem in) | |
0f113f3e MC |
378 | { |
379 | /* | |
380 | * In order to prevent underflow, we add 0 mod p before subtracting. | |
381 | */ | |
382 | static const uint128_t two127m70 = | |
383 | (((uint128_t) 1) << 127) - (((uint128_t) 1) << 70); | |
384 | static const uint128_t two127m69 = | |
385 | (((uint128_t) 1) << 127) - (((uint128_t) 1) << 69); | |
386 | ||
387 | out[0] += (two127m70 - in[0]); | |
388 | out[1] += (two127m69 - in[1]); | |
389 | out[2] += (two127m69 - in[2]); | |
390 | out[3] += (two127m69 - in[3]); | |
391 | out[4] += (two127m69 - in[4]); | |
392 | out[5] += (two127m69 - in[5]); | |
393 | out[6] += (two127m69 - in[6]); | |
394 | out[7] += (two127m69 - in[7]); | |
395 | out[8] += (two127m69 - in[8]); | |
396 | } | |
3e00b4c9 | 397 | |
1d97c843 TH |
398 | /*- |
399 | * felem_square sets |out| = |in|^2 | |
3e00b4c9 BM |
400 | * On entry: |
401 | * in[i] < 2^62 | |
402 | * On exit: | |
403 | * out[i] < 17 * max(in[i]) * max(in[i]) | |
404 | */ | |
405 | static void felem_square(largefelem out, const felem in) | |
0f113f3e MC |
406 | { |
407 | felem inx2, inx4; | |
408 | felem_scalar(inx2, in, 2); | |
409 | felem_scalar(inx4, in, 4); | |
410 | ||
35a1cc90 MC |
411 | /*- |
412 | * We have many cases were we want to do | |
413 | * in[x] * in[y] + | |
414 | * in[y] * in[x] | |
415 | * This is obviously just | |
416 | * 2 * in[x] * in[y] | |
417 | * However, rather than do the doubling on the 128 bit result, we | |
418 | * double one of the inputs to the multiplication by reading from | |
419 | * |inx2| | |
420 | */ | |
0f113f3e MC |
421 | |
422 | out[0] = ((uint128_t) in[0]) * in[0]; | |
423 | out[1] = ((uint128_t) in[0]) * inx2[1]; | |
424 | out[2] = ((uint128_t) in[0]) * inx2[2] + ((uint128_t) in[1]) * in[1]; | |
425 | out[3] = ((uint128_t) in[0]) * inx2[3] + ((uint128_t) in[1]) * inx2[2]; | |
426 | out[4] = ((uint128_t) in[0]) * inx2[4] + | |
4eb504ae | 427 | ((uint128_t) in[1]) * inx2[3] + ((uint128_t) in[2]) * in[2]; |
0f113f3e | 428 | out[5] = ((uint128_t) in[0]) * inx2[5] + |
4eb504ae | 429 | ((uint128_t) in[1]) * inx2[4] + ((uint128_t) in[2]) * inx2[3]; |
0f113f3e | 430 | out[6] = ((uint128_t) in[0]) * inx2[6] + |
4eb504ae AP |
431 | ((uint128_t) in[1]) * inx2[5] + |
432 | ((uint128_t) in[2]) * inx2[4] + ((uint128_t) in[3]) * in[3]; | |
0f113f3e | 433 | out[7] = ((uint128_t) in[0]) * inx2[7] + |
4eb504ae AP |
434 | ((uint128_t) in[1]) * inx2[6] + |
435 | ((uint128_t) in[2]) * inx2[5] + ((uint128_t) in[3]) * inx2[4]; | |
0f113f3e | 436 | out[8] = ((uint128_t) in[0]) * inx2[8] + |
4eb504ae AP |
437 | ((uint128_t) in[1]) * inx2[7] + |
438 | ((uint128_t) in[2]) * inx2[6] + | |
439 | ((uint128_t) in[3]) * inx2[5] + ((uint128_t) in[4]) * in[4]; | |
0f113f3e MC |
440 | |
441 | /* | |
442 | * The remaining limbs fall above 2^521, with the first falling at 2^522. | |
443 | * They correspond to locations one bit up from the limbs produced above | |
444 | * so we would have to multiply by two to align them. Again, rather than | |
445 | * operate on the 128-bit result, we double one of the inputs to the | |
446 | * multiplication. If we want to double for both this reason, and the | |
447 | * reason above, then we end up multiplying by four. | |
448 | */ | |
449 | ||
450 | /* 9 */ | |
451 | out[0] += ((uint128_t) in[1]) * inx4[8] + | |
4eb504ae AP |
452 | ((uint128_t) in[2]) * inx4[7] + |
453 | ((uint128_t) in[3]) * inx4[6] + ((uint128_t) in[4]) * inx4[5]; | |
0f113f3e MC |
454 | |
455 | /* 10 */ | |
456 | out[1] += ((uint128_t) in[2]) * inx4[8] + | |
4eb504ae AP |
457 | ((uint128_t) in[3]) * inx4[7] + |
458 | ((uint128_t) in[4]) * inx4[6] + ((uint128_t) in[5]) * inx2[5]; | |
0f113f3e MC |
459 | |
460 | /* 11 */ | |
461 | out[2] += ((uint128_t) in[3]) * inx4[8] + | |
4eb504ae | 462 | ((uint128_t) in[4]) * inx4[7] + ((uint128_t) in[5]) * inx4[6]; |
0f113f3e MC |
463 | |
464 | /* 12 */ | |
465 | out[3] += ((uint128_t) in[4]) * inx4[8] + | |
4eb504ae | 466 | ((uint128_t) in[5]) * inx4[7] + ((uint128_t) in[6]) * inx2[6]; |
0f113f3e MC |
467 | |
468 | /* 13 */ | |
469 | out[4] += ((uint128_t) in[5]) * inx4[8] + ((uint128_t) in[6]) * inx4[7]; | |
470 | ||
471 | /* 14 */ | |
472 | out[5] += ((uint128_t) in[6]) * inx4[8] + ((uint128_t) in[7]) * inx2[7]; | |
473 | ||
474 | /* 15 */ | |
475 | out[6] += ((uint128_t) in[7]) * inx4[8]; | |
476 | ||
477 | /* 16 */ | |
478 | out[7] += ((uint128_t) in[8]) * inx2[8]; | |
479 | } | |
3e00b4c9 | 480 | |
1d97c843 TH |
481 | /*- |
482 | * felem_mul sets |out| = |in1| * |in2| | |
3e00b4c9 BM |
483 | * On entry: |
484 | * in1[i] < 2^64 | |
485 | * in2[i] < 2^63 | |
486 | * On exit: | |
487 | * out[i] < 17 * max(in1[i]) * max(in2[i]) | |
488 | */ | |
489 | static void felem_mul(largefelem out, const felem in1, const felem in2) | |
0f113f3e MC |
490 | { |
491 | felem in2x2; | |
492 | felem_scalar(in2x2, in2, 2); | |
493 | ||
494 | out[0] = ((uint128_t) in1[0]) * in2[0]; | |
495 | ||
4eb504ae AP |
496 | out[1] = ((uint128_t) in1[0]) * in2[1] + |
497 | ((uint128_t) in1[1]) * in2[0]; | |
0f113f3e MC |
498 | |
499 | out[2] = ((uint128_t) in1[0]) * in2[2] + | |
4eb504ae AP |
500 | ((uint128_t) in1[1]) * in2[1] + |
501 | ((uint128_t) in1[2]) * in2[0]; | |
0f113f3e MC |
502 | |
503 | out[3] = ((uint128_t) in1[0]) * in2[3] + | |
4eb504ae AP |
504 | ((uint128_t) in1[1]) * in2[2] + |
505 | ((uint128_t) in1[2]) * in2[1] + | |
506 | ((uint128_t) in1[3]) * in2[0]; | |
0f113f3e MC |
507 | |
508 | out[4] = ((uint128_t) in1[0]) * in2[4] + | |
4eb504ae AP |
509 | ((uint128_t) in1[1]) * in2[3] + |
510 | ((uint128_t) in1[2]) * in2[2] + | |
511 | ((uint128_t) in1[3]) * in2[1] + | |
512 | ((uint128_t) in1[4]) * in2[0]; | |
0f113f3e MC |
513 | |
514 | out[5] = ((uint128_t) in1[0]) * in2[5] + | |
4eb504ae AP |
515 | ((uint128_t) in1[1]) * in2[4] + |
516 | ((uint128_t) in1[2]) * in2[3] + | |
517 | ((uint128_t) in1[3]) * in2[2] + | |
518 | ((uint128_t) in1[4]) * in2[1] + | |
519 | ((uint128_t) in1[5]) * in2[0]; | |
0f113f3e MC |
520 | |
521 | out[6] = ((uint128_t) in1[0]) * in2[6] + | |
4eb504ae AP |
522 | ((uint128_t) in1[1]) * in2[5] + |
523 | ((uint128_t) in1[2]) * in2[4] + | |
524 | ((uint128_t) in1[3]) * in2[3] + | |
525 | ((uint128_t) in1[4]) * in2[2] + | |
526 | ((uint128_t) in1[5]) * in2[1] + | |
527 | ((uint128_t) in1[6]) * in2[0]; | |
0f113f3e MC |
528 | |
529 | out[7] = ((uint128_t) in1[0]) * in2[7] + | |
4eb504ae AP |
530 | ((uint128_t) in1[1]) * in2[6] + |
531 | ((uint128_t) in1[2]) * in2[5] + | |
532 | ((uint128_t) in1[3]) * in2[4] + | |
533 | ((uint128_t) in1[4]) * in2[3] + | |
534 | ((uint128_t) in1[5]) * in2[2] + | |
535 | ((uint128_t) in1[6]) * in2[1] + | |
536 | ((uint128_t) in1[7]) * in2[0]; | |
0f113f3e MC |
537 | |
538 | out[8] = ((uint128_t) in1[0]) * in2[8] + | |
4eb504ae AP |
539 | ((uint128_t) in1[1]) * in2[7] + |
540 | ((uint128_t) in1[2]) * in2[6] + | |
541 | ((uint128_t) in1[3]) * in2[5] + | |
542 | ((uint128_t) in1[4]) * in2[4] + | |
543 | ((uint128_t) in1[5]) * in2[3] + | |
544 | ((uint128_t) in1[6]) * in2[2] + | |
545 | ((uint128_t) in1[7]) * in2[1] + | |
546 | ((uint128_t) in1[8]) * in2[0]; | |
0f113f3e MC |
547 | |
548 | /* See comment in felem_square about the use of in2x2 here */ | |
549 | ||
550 | out[0] += ((uint128_t) in1[1]) * in2x2[8] + | |
4eb504ae AP |
551 | ((uint128_t) in1[2]) * in2x2[7] + |
552 | ((uint128_t) in1[3]) * in2x2[6] + | |
553 | ((uint128_t) in1[4]) * in2x2[5] + | |
554 | ((uint128_t) in1[5]) * in2x2[4] + | |
555 | ((uint128_t) in1[6]) * in2x2[3] + | |
556 | ((uint128_t) in1[7]) * in2x2[2] + | |
557 | ((uint128_t) in1[8]) * in2x2[1]; | |
0f113f3e MC |
558 | |
559 | out[1] += ((uint128_t) in1[2]) * in2x2[8] + | |
4eb504ae AP |
560 | ((uint128_t) in1[3]) * in2x2[7] + |
561 | ((uint128_t) in1[4]) * in2x2[6] + | |
562 | ((uint128_t) in1[5]) * in2x2[5] + | |
563 | ((uint128_t) in1[6]) * in2x2[4] + | |
564 | ((uint128_t) in1[7]) * in2x2[3] + | |
565 | ((uint128_t) in1[8]) * in2x2[2]; | |
0f113f3e MC |
566 | |
567 | out[2] += ((uint128_t) in1[3]) * in2x2[8] + | |
4eb504ae AP |
568 | ((uint128_t) in1[4]) * in2x2[7] + |
569 | ((uint128_t) in1[5]) * in2x2[6] + | |
570 | ((uint128_t) in1[6]) * in2x2[5] + | |
571 | ((uint128_t) in1[7]) * in2x2[4] + | |
572 | ((uint128_t) in1[8]) * in2x2[3]; | |
0f113f3e MC |
573 | |
574 | out[3] += ((uint128_t) in1[4]) * in2x2[8] + | |
4eb504ae AP |
575 | ((uint128_t) in1[5]) * in2x2[7] + |
576 | ((uint128_t) in1[6]) * in2x2[6] + | |
577 | ((uint128_t) in1[7]) * in2x2[5] + | |
578 | ((uint128_t) in1[8]) * in2x2[4]; | |
0f113f3e MC |
579 | |
580 | out[4] += ((uint128_t) in1[5]) * in2x2[8] + | |
4eb504ae AP |
581 | ((uint128_t) in1[6]) * in2x2[7] + |
582 | ((uint128_t) in1[7]) * in2x2[6] + | |
583 | ((uint128_t) in1[8]) * in2x2[5]; | |
0f113f3e MC |
584 | |
585 | out[5] += ((uint128_t) in1[6]) * in2x2[8] + | |
4eb504ae AP |
586 | ((uint128_t) in1[7]) * in2x2[7] + |
587 | ((uint128_t) in1[8]) * in2x2[6]; | |
0f113f3e MC |
588 | |
589 | out[6] += ((uint128_t) in1[7]) * in2x2[8] + | |
4eb504ae | 590 | ((uint128_t) in1[8]) * in2x2[7]; |
0f113f3e MC |
591 | |
592 | out[7] += ((uint128_t) in1[8]) * in2x2[8]; | |
593 | } | |
3e00b4c9 BM |
594 | |
595 | static const limb bottom52bits = 0xfffffffffffff; | |
596 | ||
1d97c843 TH |
597 | /*- |
598 | * felem_reduce converts a largefelem to an felem. | |
3e00b4c9 BM |
599 | * On entry: |
600 | * in[i] < 2^128 | |
601 | * On exit: | |
602 | * out[i] < 2^59 + 2^14 | |
603 | */ | |
604 | static void felem_reduce(felem out, const largefelem in) | |
0f113f3e MC |
605 | { |
606 | u64 overflow1, overflow2; | |
607 | ||
608 | out[0] = ((limb) in[0]) & bottom58bits; | |
609 | out[1] = ((limb) in[1]) & bottom58bits; | |
610 | out[2] = ((limb) in[2]) & bottom58bits; | |
611 | out[3] = ((limb) in[3]) & bottom58bits; | |
612 | out[4] = ((limb) in[4]) & bottom58bits; | |
613 | out[5] = ((limb) in[5]) & bottom58bits; | |
614 | out[6] = ((limb) in[6]) & bottom58bits; | |
615 | out[7] = ((limb) in[7]) & bottom58bits; | |
616 | out[8] = ((limb) in[8]) & bottom58bits; | |
617 | ||
618 | /* out[i] < 2^58 */ | |
619 | ||
620 | out[1] += ((limb) in[0]) >> 58; | |
621 | out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6; | |
35a1cc90 MC |
622 | /*- |
623 | * out[1] < 2^58 + 2^6 + 2^58 | |
624 | * = 2^59 + 2^6 | |
625 | */ | |
0f113f3e MC |
626 | out[2] += ((limb) (in[0] >> 64)) >> 52; |
627 | ||
628 | out[2] += ((limb) in[1]) >> 58; | |
629 | out[2] += (((limb) (in[1] >> 64)) & bottom52bits) << 6; | |
630 | out[3] += ((limb) (in[1] >> 64)) >> 52; | |
631 | ||
632 | out[3] += ((limb) in[2]) >> 58; | |
633 | out[3] += (((limb) (in[2] >> 64)) & bottom52bits) << 6; | |
634 | out[4] += ((limb) (in[2] >> 64)) >> 52; | |
635 | ||
636 | out[4] += ((limb) in[3]) >> 58; | |
637 | out[4] += (((limb) (in[3] >> 64)) & bottom52bits) << 6; | |
638 | out[5] += ((limb) (in[3] >> 64)) >> 52; | |
639 | ||
640 | out[5] += ((limb) in[4]) >> 58; | |
641 | out[5] += (((limb) (in[4] >> 64)) & bottom52bits) << 6; | |
642 | out[6] += ((limb) (in[4] >> 64)) >> 52; | |
643 | ||
644 | out[6] += ((limb) in[5]) >> 58; | |
645 | out[6] += (((limb) (in[5] >> 64)) & bottom52bits) << 6; | |
646 | out[7] += ((limb) (in[5] >> 64)) >> 52; | |
647 | ||
648 | out[7] += ((limb) in[6]) >> 58; | |
649 | out[7] += (((limb) (in[6] >> 64)) & bottom52bits) << 6; | |
650 | out[8] += ((limb) (in[6] >> 64)) >> 52; | |
651 | ||
652 | out[8] += ((limb) in[7]) >> 58; | |
653 | out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6; | |
35a1cc90 MC |
654 | /*- |
655 | * out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 | |
656 | * < 2^59 + 2^13 | |
657 | */ | |
0f113f3e MC |
658 | overflow1 = ((limb) (in[7] >> 64)) >> 52; |
659 | ||
660 | overflow1 += ((limb) in[8]) >> 58; | |
661 | overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6; | |
662 | overflow2 = ((limb) (in[8] >> 64)) >> 52; | |
663 | ||
664 | overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ | |
665 | overflow2 <<= 1; /* overflow2 < 2^13 */ | |
666 | ||
667 | out[0] += overflow1; /* out[0] < 2^60 */ | |
668 | out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ | |
669 | ||
670 | out[1] += out[0] >> 58; | |
671 | out[0] &= bottom58bits; | |
35a1cc90 MC |
672 | /*- |
673 | * out[0] < 2^58 | |
674 | * out[1] < 2^59 + 2^6 + 2^13 + 2^2 | |
675 | * < 2^59 + 2^14 | |
676 | */ | |
0f113f3e | 677 | } |
3e00b4c9 BM |
678 | |
679 | static void felem_square_reduce(felem out, const felem in) | |
0f113f3e MC |
680 | { |
681 | largefelem tmp; | |
682 | felem_square(tmp, in); | |
683 | felem_reduce(out, tmp); | |
684 | } | |
3e00b4c9 BM |
685 | |
686 | static void felem_mul_reduce(felem out, const felem in1, const felem in2) | |
0f113f3e MC |
687 | { |
688 | largefelem tmp; | |
689 | felem_mul(tmp, in1, in2); | |
690 | felem_reduce(out, tmp); | |
691 | } | |
3e00b4c9 | 692 | |
1d97c843 TH |
693 | /*- |
694 | * felem_inv calculates |out| = |in|^{-1} | |
3e00b4c9 BM |
695 | * |
696 | * Based on Fermat's Little Theorem: | |
697 | * a^p = a (mod p) | |
698 | * a^{p-1} = 1 (mod p) | |
699 | * a^{p-2} = a^{-1} (mod p) | |
700 | */ | |
701 | static void felem_inv(felem out, const felem in) | |
0f113f3e MC |
702 | { |
703 | felem ftmp, ftmp2, ftmp3, ftmp4; | |
704 | largefelem tmp; | |
705 | unsigned i; | |
706 | ||
707 | felem_square(tmp, in); | |
708 | felem_reduce(ftmp, tmp); /* 2^1 */ | |
709 | felem_mul(tmp, in, ftmp); | |
710 | felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ | |
711 | felem_assign(ftmp2, ftmp); | |
712 | felem_square(tmp, ftmp); | |
713 | felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ | |
714 | felem_mul(tmp, in, ftmp); | |
715 | felem_reduce(ftmp, tmp); /* 2^3 - 2^0 */ | |
716 | felem_square(tmp, ftmp); | |
717 | felem_reduce(ftmp, tmp); /* 2^4 - 2^1 */ | |
718 | ||
719 | felem_square(tmp, ftmp2); | |
720 | felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ | |
721 | felem_square(tmp, ftmp3); | |
722 | felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ | |
723 | felem_mul(tmp, ftmp3, ftmp2); | |
724 | felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ | |
725 | ||
726 | felem_assign(ftmp2, ftmp3); | |
727 | felem_square(tmp, ftmp3); | |
728 | felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ | |
729 | felem_square(tmp, ftmp3); | |
730 | felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ | |
731 | felem_square(tmp, ftmp3); | |
732 | felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ | |
733 | felem_square(tmp, ftmp3); | |
734 | felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ | |
735 | felem_assign(ftmp4, ftmp3); | |
736 | felem_mul(tmp, ftmp3, ftmp); | |
737 | felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ | |
738 | felem_square(tmp, ftmp4); | |
739 | felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ | |
740 | felem_mul(tmp, ftmp3, ftmp2); | |
741 | felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ | |
742 | felem_assign(ftmp2, ftmp3); | |
743 | ||
744 | for (i = 0; i < 8; i++) { | |
745 | felem_square(tmp, ftmp3); | |
746 | felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ | |
747 | } | |
748 | felem_mul(tmp, ftmp3, ftmp2); | |
749 | felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ | |
750 | felem_assign(ftmp2, ftmp3); | |
751 | ||
752 | for (i = 0; i < 16; i++) { | |
753 | felem_square(tmp, ftmp3); | |
754 | felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ | |
755 | } | |
756 | felem_mul(tmp, ftmp3, ftmp2); | |
757 | felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ | |
758 | felem_assign(ftmp2, ftmp3); | |
759 | ||
760 | for (i = 0; i < 32; i++) { | |
761 | felem_square(tmp, ftmp3); | |
762 | felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ | |
763 | } | |
764 | felem_mul(tmp, ftmp3, ftmp2); | |
765 | felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ | |
766 | felem_assign(ftmp2, ftmp3); | |
767 | ||
768 | for (i = 0; i < 64; i++) { | |
769 | felem_square(tmp, ftmp3); | |
770 | felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ | |
771 | } | |
772 | felem_mul(tmp, ftmp3, ftmp2); | |
773 | felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ | |
774 | felem_assign(ftmp2, ftmp3); | |
775 | ||
776 | for (i = 0; i < 128; i++) { | |
777 | felem_square(tmp, ftmp3); | |
778 | felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ | |
779 | } | |
780 | felem_mul(tmp, ftmp3, ftmp2); | |
781 | felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ | |
782 | felem_assign(ftmp2, ftmp3); | |
783 | ||
784 | for (i = 0; i < 256; i++) { | |
785 | felem_square(tmp, ftmp3); | |
786 | felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ | |
787 | } | |
788 | felem_mul(tmp, ftmp3, ftmp2); | |
789 | felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ | |
790 | ||
791 | for (i = 0; i < 9; i++) { | |
792 | felem_square(tmp, ftmp3); | |
793 | felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ | |
794 | } | |
795 | felem_mul(tmp, ftmp3, ftmp4); | |
796 | felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ | |
797 | felem_mul(tmp, ftmp3, in); | |
798 | felem_reduce(out, tmp); /* 2^512 - 3 */ | |
3e00b4c9 BM |
799 | } |
800 | ||
801 | /* This is 2^521-1, expressed as an felem */ | |
0f113f3e MC |
802 | static const felem kPrime = { |
803 | 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, | |
804 | 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, | |
805 | 0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff | |
806 | }; | |
3e00b4c9 | 807 | |
1d97c843 TH |
808 | /*- |
809 | * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 | |
3e00b4c9 BM |
810 | * otherwise. |
811 | * On entry: | |
812 | * in[i] < 2^59 + 2^14 | |
813 | */ | |
814 | static limb felem_is_zero(const felem in) | |
0f113f3e MC |
815 | { |
816 | felem ftmp; | |
817 | limb is_zero, is_p; | |
818 | felem_assign(ftmp, in); | |
819 | ||
820 | ftmp[0] += ftmp[8] >> 57; | |
821 | ftmp[8] &= bottom57bits; | |
822 | /* ftmp[8] < 2^57 */ | |
823 | ftmp[1] += ftmp[0] >> 58; | |
824 | ftmp[0] &= bottom58bits; | |
825 | ftmp[2] += ftmp[1] >> 58; | |
826 | ftmp[1] &= bottom58bits; | |
827 | ftmp[3] += ftmp[2] >> 58; | |
828 | ftmp[2] &= bottom58bits; | |
829 | ftmp[4] += ftmp[3] >> 58; | |
830 | ftmp[3] &= bottom58bits; | |
831 | ftmp[5] += ftmp[4] >> 58; | |
832 | ftmp[4] &= bottom58bits; | |
833 | ftmp[6] += ftmp[5] >> 58; | |
834 | ftmp[5] &= bottom58bits; | |
835 | ftmp[7] += ftmp[6] >> 58; | |
836 | ftmp[6] &= bottom58bits; | |
837 | ftmp[8] += ftmp[7] >> 58; | |
838 | ftmp[7] &= bottom58bits; | |
839 | /* ftmp[8] < 2^57 + 4 */ | |
840 | ||
841 | /* | |
842 | * The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is greater | |
843 | * than our bound for ftmp[8]. Therefore we only have to check if the | |
844 | * zero is zero or 2^521-1. | |
845 | */ | |
846 | ||
847 | is_zero = 0; | |
848 | is_zero |= ftmp[0]; | |
849 | is_zero |= ftmp[1]; | |
850 | is_zero |= ftmp[2]; | |
851 | is_zero |= ftmp[3]; | |
852 | is_zero |= ftmp[4]; | |
853 | is_zero |= ftmp[5]; | |
854 | is_zero |= ftmp[6]; | |
855 | is_zero |= ftmp[7]; | |
856 | is_zero |= ftmp[8]; | |
857 | ||
858 | is_zero--; | |
859 | /* | |
860 | * We know that ftmp[i] < 2^63, therefore the only way that the top bit | |
861 | * can be set is if is_zero was 0 before the decrement. | |
862 | */ | |
8af7e94d | 863 | is_zero = 0 - (is_zero >> 63); |
0f113f3e MC |
864 | |
865 | is_p = ftmp[0] ^ kPrime[0]; | |
866 | is_p |= ftmp[1] ^ kPrime[1]; | |
867 | is_p |= ftmp[2] ^ kPrime[2]; | |
868 | is_p |= ftmp[3] ^ kPrime[3]; | |
869 | is_p |= ftmp[4] ^ kPrime[4]; | |
870 | is_p |= ftmp[5] ^ kPrime[5]; | |
871 | is_p |= ftmp[6] ^ kPrime[6]; | |
872 | is_p |= ftmp[7] ^ kPrime[7]; | |
873 | is_p |= ftmp[8] ^ kPrime[8]; | |
874 | ||
875 | is_p--; | |
8af7e94d | 876 | is_p = 0 - (is_p >> 63); |
0f113f3e MC |
877 | |
878 | is_zero |= is_p; | |
879 | return is_zero; | |
880 | } | |
3e00b4c9 | 881 | |
c55b786a | 882 | static int felem_is_zero_int(const void *in) |
0f113f3e MC |
883 | { |
884 | return (int)(felem_is_zero(in) & ((limb) 1)); | |
885 | } | |
3e00b4c9 | 886 | |
1d97c843 TH |
887 | /*- |
888 | * felem_contract converts |in| to its unique, minimal representation. | |
3e00b4c9 BM |
889 | * On entry: |
890 | * in[i] < 2^59 + 2^14 | |
891 | */ | |
892 | static void felem_contract(felem out, const felem in) | |
0f113f3e MC |
893 | { |
894 | limb is_p, is_greater, sign; | |
895 | static const limb two58 = ((limb) 1) << 58; | |
896 | ||
897 | felem_assign(out, in); | |
898 | ||
899 | out[0] += out[8] >> 57; | |
900 | out[8] &= bottom57bits; | |
901 | /* out[8] < 2^57 */ | |
902 | out[1] += out[0] >> 58; | |
903 | out[0] &= bottom58bits; | |
904 | out[2] += out[1] >> 58; | |
905 | out[1] &= bottom58bits; | |
906 | out[3] += out[2] >> 58; | |
907 | out[2] &= bottom58bits; | |
908 | out[4] += out[3] >> 58; | |
909 | out[3] &= bottom58bits; | |
910 | out[5] += out[4] >> 58; | |
911 | out[4] &= bottom58bits; | |
912 | out[6] += out[5] >> 58; | |
913 | out[5] &= bottom58bits; | |
914 | out[7] += out[6] >> 58; | |
915 | out[6] &= bottom58bits; | |
916 | out[8] += out[7] >> 58; | |
917 | out[7] &= bottom58bits; | |
918 | /* out[8] < 2^57 + 4 */ | |
919 | ||
920 | /* | |
921 | * If the value is greater than 2^521-1 then we have to subtract 2^521-1 | |
922 | * out. See the comments in felem_is_zero regarding why we don't test for | |
923 | * other multiples of the prime. | |
924 | */ | |
925 | ||
926 | /* | |
927 | * First, if |out| is equal to 2^521-1, we subtract it out to get zero. | |
928 | */ | |
929 | ||
930 | is_p = out[0] ^ kPrime[0]; | |
931 | is_p |= out[1] ^ kPrime[1]; | |
932 | is_p |= out[2] ^ kPrime[2]; | |
933 | is_p |= out[3] ^ kPrime[3]; | |
934 | is_p |= out[4] ^ kPrime[4]; | |
935 | is_p |= out[5] ^ kPrime[5]; | |
936 | is_p |= out[6] ^ kPrime[6]; | |
937 | is_p |= out[7] ^ kPrime[7]; | |
938 | is_p |= out[8] ^ kPrime[8]; | |
939 | ||
940 | is_p--; | |
941 | is_p &= is_p << 32; | |
942 | is_p &= is_p << 16; | |
943 | is_p &= is_p << 8; | |
944 | is_p &= is_p << 4; | |
945 | is_p &= is_p << 2; | |
946 | is_p &= is_p << 1; | |
8af7e94d | 947 | is_p = 0 - (is_p >> 63); |
0f113f3e MC |
948 | is_p = ~is_p; |
949 | ||
950 | /* is_p is 0 iff |out| == 2^521-1 and all ones otherwise */ | |
951 | ||
952 | out[0] &= is_p; | |
953 | out[1] &= is_p; | |
954 | out[2] &= is_p; | |
955 | out[3] &= is_p; | |
956 | out[4] &= is_p; | |
957 | out[5] &= is_p; | |
958 | out[6] &= is_p; | |
959 | out[7] &= is_p; | |
960 | out[8] &= is_p; | |
961 | ||
962 | /* | |
963 | * In order to test that |out| >= 2^521-1 we need only test if out[8] >> | |
964 | * 57 is greater than zero as (2^521-1) + x >= 2^522 | |
965 | */ | |
966 | is_greater = out[8] >> 57; | |
967 | is_greater |= is_greater << 32; | |
968 | is_greater |= is_greater << 16; | |
969 | is_greater |= is_greater << 8; | |
970 | is_greater |= is_greater << 4; | |
971 | is_greater |= is_greater << 2; | |
972 | is_greater |= is_greater << 1; | |
8af7e94d | 973 | is_greater = 0 - (is_greater >> 63); |
0f113f3e MC |
974 | |
975 | out[0] -= kPrime[0] & is_greater; | |
976 | out[1] -= kPrime[1] & is_greater; | |
977 | out[2] -= kPrime[2] & is_greater; | |
978 | out[3] -= kPrime[3] & is_greater; | |
979 | out[4] -= kPrime[4] & is_greater; | |
980 | out[5] -= kPrime[5] & is_greater; | |
981 | out[6] -= kPrime[6] & is_greater; | |
982 | out[7] -= kPrime[7] & is_greater; | |
983 | out[8] -= kPrime[8] & is_greater; | |
984 | ||
985 | /* Eliminate negative coefficients */ | |
986 | sign = -(out[0] >> 63); | |
987 | out[0] += (two58 & sign); | |
988 | out[1] -= (1 & sign); | |
989 | sign = -(out[1] >> 63); | |
990 | out[1] += (two58 & sign); | |
991 | out[2] -= (1 & sign); | |
992 | sign = -(out[2] >> 63); | |
993 | out[2] += (two58 & sign); | |
994 | out[3] -= (1 & sign); | |
995 | sign = -(out[3] >> 63); | |
996 | out[3] += (two58 & sign); | |
997 | out[4] -= (1 & sign); | |
998 | sign = -(out[4] >> 63); | |
999 | out[4] += (two58 & sign); | |
1000 | out[5] -= (1 & sign); | |
1001 | sign = -(out[0] >> 63); | |
1002 | out[5] += (two58 & sign); | |
1003 | out[6] -= (1 & sign); | |
1004 | sign = -(out[6] >> 63); | |
1005 | out[6] += (two58 & sign); | |
1006 | out[7] -= (1 & sign); | |
1007 | sign = -(out[7] >> 63); | |
1008 | out[7] += (two58 & sign); | |
1009 | out[8] -= (1 & sign); | |
1010 | sign = -(out[5] >> 63); | |
1011 | out[5] += (two58 & sign); | |
1012 | out[6] -= (1 & sign); | |
1013 | sign = -(out[6] >> 63); | |
1014 | out[6] += (two58 & sign); | |
1015 | out[7] -= (1 & sign); | |
1016 | sign = -(out[7] >> 63); | |
1017 | out[7] += (two58 & sign); | |
1018 | out[8] -= (1 & sign); | |
1019 | } | |
3e00b4c9 | 1020 | |
1d97c843 TH |
1021 | /*- |
1022 | * Group operations | |
3e00b4c9 BM |
1023 | * ---------------- |
1024 | * | |
1025 | * Building on top of the field operations we have the operations on the | |
1026 | * elliptic curve group itself. Points on the curve are represented in Jacobian | |
1027 | * coordinates */ | |
1028 | ||
1d97c843 | 1029 | /*- |
0d4fb843 | 1030 | * point_double calculates 2*(x_in, y_in, z_in) |
3e00b4c9 BM |
1031 | * |
1032 | * The method is taken from: | |
1033 | * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b | |
1034 | * | |
1035 | * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. | |
1036 | * while x_out == y_in is not (maybe this works, but it's not tested). */ | |
1037 | static void | |
1038 | point_double(felem x_out, felem y_out, felem z_out, | |
0f113f3e MC |
1039 | const felem x_in, const felem y_in, const felem z_in) |
1040 | { | |
1041 | largefelem tmp, tmp2; | |
1042 | felem delta, gamma, beta, alpha, ftmp, ftmp2; | |
1043 | ||
1044 | felem_assign(ftmp, x_in); | |
1045 | felem_assign(ftmp2, x_in); | |
1046 | ||
1047 | /* delta = z^2 */ | |
1048 | felem_square(tmp, z_in); | |
1049 | felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ | |
1050 | ||
1051 | /* gamma = y^2 */ | |
1052 | felem_square(tmp, y_in); | |
1053 | felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ | |
1054 | ||
1055 | /* beta = x*gamma */ | |
1056 | felem_mul(tmp, x_in, gamma); | |
1057 | felem_reduce(beta, tmp); /* beta[i] < 2^59 + 2^14 */ | |
1058 | ||
1059 | /* alpha = 3*(x-delta)*(x+delta) */ | |
1060 | felem_diff64(ftmp, delta); | |
1061 | /* ftmp[i] < 2^61 */ | |
1062 | felem_sum64(ftmp2, delta); | |
1063 | /* ftmp2[i] < 2^60 + 2^15 */ | |
1064 | felem_scalar64(ftmp2, 3); | |
1065 | /* ftmp2[i] < 3*2^60 + 3*2^15 */ | |
1066 | felem_mul(tmp, ftmp, ftmp2); | |
50e735f9 MC |
1067 | /*- |
1068 | * tmp[i] < 17(3*2^121 + 3*2^76) | |
1069 | * = 61*2^121 + 61*2^76 | |
1070 | * < 64*2^121 + 64*2^76 | |
1071 | * = 2^127 + 2^82 | |
1072 | * < 2^128 | |
1073 | */ | |
0f113f3e MC |
1074 | felem_reduce(alpha, tmp); |
1075 | ||
1076 | /* x' = alpha^2 - 8*beta */ | |
1077 | felem_square(tmp, alpha); | |
1078 | /* | |
1079 | * tmp[i] < 17*2^120 < 2^125 | |
1080 | */ | |
1081 | felem_assign(ftmp, beta); | |
1082 | felem_scalar64(ftmp, 8); | |
1083 | /* ftmp[i] < 2^62 + 2^17 */ | |
1084 | felem_diff_128_64(tmp, ftmp); | |
1085 | /* tmp[i] < 2^125 + 2^63 + 2^62 + 2^17 */ | |
1086 | felem_reduce(x_out, tmp); | |
1087 | ||
1088 | /* z' = (y + z)^2 - gamma - delta */ | |
1089 | felem_sum64(delta, gamma); | |
1090 | /* delta[i] < 2^60 + 2^15 */ | |
1091 | felem_assign(ftmp, y_in); | |
1092 | felem_sum64(ftmp, z_in); | |
1093 | /* ftmp[i] < 2^60 + 2^15 */ | |
1094 | felem_square(tmp, ftmp); | |
1095 | /* | |
1096 | * tmp[i] < 17(2^122) < 2^127 | |
1097 | */ | |
1098 | felem_diff_128_64(tmp, delta); | |
1099 | /* tmp[i] < 2^127 + 2^63 */ | |
1100 | felem_reduce(z_out, tmp); | |
1101 | ||
1102 | /* y' = alpha*(4*beta - x') - 8*gamma^2 */ | |
1103 | felem_scalar64(beta, 4); | |
1104 | /* beta[i] < 2^61 + 2^16 */ | |
1105 | felem_diff64(beta, x_out); | |
1106 | /* beta[i] < 2^61 + 2^60 + 2^16 */ | |
1107 | felem_mul(tmp, alpha, beta); | |
50e735f9 MC |
1108 | /*- |
1109 | * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) | |
1110 | * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30) | |
1111 | * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30) | |
1112 | * < 2^128 | |
1113 | */ | |
0f113f3e | 1114 | felem_square(tmp2, gamma); |
50e735f9 MC |
1115 | /*- |
1116 | * tmp2[i] < 17*(2^59 + 2^14)^2 | |
1117 | * = 17*(2^118 + 2^74 + 2^28) | |
1118 | */ | |
0f113f3e | 1119 | felem_scalar128(tmp2, 8); |
50e735f9 MC |
1120 | /*- |
1121 | * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) | |
1122 | * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31 | |
1123 | * < 2^126 | |
1124 | */ | |
0f113f3e | 1125 | felem_diff128(tmp, tmp2); |
50e735f9 MC |
1126 | /*- |
1127 | * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) | |
1128 | * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + | |
1129 | * 2^74 + 2^69 + 2^34 + 2^30 | |
1130 | * < 2^128 | |
1131 | */ | |
0f113f3e MC |
1132 | felem_reduce(y_out, tmp); |
1133 | } | |
3e00b4c9 BM |
1134 | |
1135 | /* copy_conditional copies in to out iff mask is all ones. */ | |
0f113f3e MC |
1136 | static void copy_conditional(felem out, const felem in, limb mask) |
1137 | { | |
1138 | unsigned i; | |
1139 | for (i = 0; i < NLIMBS; ++i) { | |
1140 | const limb tmp = mask & (in[i] ^ out[i]); | |
1141 | out[i] ^= tmp; | |
1142 | } | |
1143 | } | |
3e00b4c9 | 1144 | |
1d97c843 | 1145 | /*- |
0d4fb843 | 1146 | * point_add calculates (x1, y1, z1) + (x2, y2, z2) |
3e00b4c9 BM |
1147 | * |
1148 | * The method is taken from | |
1149 | * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, | |
1150 | * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). | |
1151 | * | |
1152 | * This function includes a branch for checking whether the two input points | |
2dbfa844 AL |
1153 | * are equal (while not equal to the point at infinity). See comment below |
1154 | * on constant-time. | |
1155 | */ | |
3e00b4c9 | 1156 | static void point_add(felem x3, felem y3, felem z3, |
0f113f3e MC |
1157 | const felem x1, const felem y1, const felem z1, |
1158 | const int mixed, const felem x2, const felem y2, | |
1159 | const felem z2) | |
1160 | { | |
1161 | felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; | |
1162 | largefelem tmp, tmp2; | |
1163 | limb x_equal, y_equal, z1_is_zero, z2_is_zero; | |
0164bf81 | 1164 | limb points_equal; |
0f113f3e MC |
1165 | |
1166 | z1_is_zero = felem_is_zero(z1); | |
1167 | z2_is_zero = felem_is_zero(z2); | |
1168 | ||
1169 | /* ftmp = z1z1 = z1**2 */ | |
1170 | felem_square(tmp, z1); | |
1171 | felem_reduce(ftmp, tmp); | |
1172 | ||
1173 | if (!mixed) { | |
1174 | /* ftmp2 = z2z2 = z2**2 */ | |
1175 | felem_square(tmp, z2); | |
1176 | felem_reduce(ftmp2, tmp); | |
1177 | ||
1178 | /* u1 = ftmp3 = x1*z2z2 */ | |
1179 | felem_mul(tmp, x1, ftmp2); | |
1180 | felem_reduce(ftmp3, tmp); | |
1181 | ||
1182 | /* ftmp5 = z1 + z2 */ | |
1183 | felem_assign(ftmp5, z1); | |
1184 | felem_sum64(ftmp5, z2); | |
1185 | /* ftmp5[i] < 2^61 */ | |
1186 | ||
1187 | /* ftmp5 = (z1 + z2)**2 - z1z1 - z2z2 = 2*z1z2 */ | |
1188 | felem_square(tmp, ftmp5); | |
1189 | /* tmp[i] < 17*2^122 */ | |
1190 | felem_diff_128_64(tmp, ftmp); | |
1191 | /* tmp[i] < 17*2^122 + 2^63 */ | |
1192 | felem_diff_128_64(tmp, ftmp2); | |
1193 | /* tmp[i] < 17*2^122 + 2^64 */ | |
1194 | felem_reduce(ftmp5, tmp); | |
1195 | ||
1196 | /* ftmp2 = z2 * z2z2 */ | |
1197 | felem_mul(tmp, ftmp2, z2); | |
1198 | felem_reduce(ftmp2, tmp); | |
1199 | ||
1200 | /* s1 = ftmp6 = y1 * z2**3 */ | |
1201 | felem_mul(tmp, y1, ftmp2); | |
1202 | felem_reduce(ftmp6, tmp); | |
1203 | } else { | |
1204 | /* | |
1205 | * We'll assume z2 = 1 (special case z2 = 0 is handled later) | |
1206 | */ | |
1207 | ||
1208 | /* u1 = ftmp3 = x1*z2z2 */ | |
1209 | felem_assign(ftmp3, x1); | |
1210 | ||
1211 | /* ftmp5 = 2*z1z2 */ | |
1212 | felem_scalar(ftmp5, z1, 2); | |
1213 | ||
1214 | /* s1 = ftmp6 = y1 * z2**3 */ | |
1215 | felem_assign(ftmp6, y1); | |
1216 | } | |
1217 | ||
1218 | /* u2 = x2*z1z1 */ | |
1219 | felem_mul(tmp, x2, ftmp); | |
1220 | /* tmp[i] < 17*2^120 */ | |
1221 | ||
1222 | /* h = ftmp4 = u2 - u1 */ | |
1223 | felem_diff_128_64(tmp, ftmp3); | |
1224 | /* tmp[i] < 17*2^120 + 2^63 */ | |
1225 | felem_reduce(ftmp4, tmp); | |
1226 | ||
1227 | x_equal = felem_is_zero(ftmp4); | |
1228 | ||
1229 | /* z_out = ftmp5 * h */ | |
1230 | felem_mul(tmp, ftmp5, ftmp4); | |
1231 | felem_reduce(z_out, tmp); | |
1232 | ||
1233 | /* ftmp = z1 * z1z1 */ | |
1234 | felem_mul(tmp, ftmp, z1); | |
1235 | felem_reduce(ftmp, tmp); | |
1236 | ||
1237 | /* s2 = tmp = y2 * z1**3 */ | |
1238 | felem_mul(tmp, y2, ftmp); | |
1239 | /* tmp[i] < 17*2^120 */ | |
1240 | ||
1241 | /* r = ftmp5 = (s2 - s1)*2 */ | |
1242 | felem_diff_128_64(tmp, ftmp6); | |
1243 | /* tmp[i] < 17*2^120 + 2^63 */ | |
1244 | felem_reduce(ftmp5, tmp); | |
1245 | y_equal = felem_is_zero(ftmp5); | |
1246 | felem_scalar64(ftmp5, 2); | |
1247 | /* ftmp5[i] < 2^61 */ | |
1248 | ||
0164bf81 NT |
1249 | /* |
1250 | * The formulae are incorrect if the points are equal, in affine coordinates | |
1251 | * (X_1, Y_1) == (X_2, Y_2), so we check for this and do doubling if this | |
1252 | * happens. | |
1253 | * | |
1254 | * We use bitwise operations to avoid potential side-channels introduced by | |
1255 | * the short-circuiting behaviour of boolean operators. | |
1256 | * | |
1257 | * The special case of either point being the point at infinity (z1 and/or | |
1258 | * z2 are zero), is handled separately later on in this function, so we | |
1259 | * avoid jumping to point_double here in those special cases. | |
1260 | * | |
1261 | * Notice the comment below on the implications of this branching for timing | |
1262 | * leaks and why it is considered practically irrelevant. | |
1263 | */ | |
1264 | points_equal = (x_equal & y_equal & (~z1_is_zero) & (~z2_is_zero)); | |
1265 | ||
1266 | if (points_equal) { | |
2dbfa844 AL |
1267 | /* |
1268 | * This is obviously not constant-time but it will almost-never happen | |
1269 | * for ECDH / ECDSA. The case where it can happen is during scalar-mult | |
1270 | * where the intermediate value gets very close to the group order. | |
1271 | * Since |ec_GFp_nistp_recode_scalar_bits| produces signed digits for | |
1272 | * the scalar, it's possible for the intermediate value to be a small | |
1273 | * negative multiple of the base point, and for the final signed digit | |
1274 | * to be the same value. We believe that this only occurs for the scalar | |
1275 | * 1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff | |
1276 | * ffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb | |
1277 | * 71e913863f7, in that case the penultimate intermediate is -9G and | |
1278 | * the final digit is also -9G. Since this only happens for a single | |
c2969ff6 | 1279 | * scalar, the timing leak is irrelevant. (Any attacker who wanted to |
2dbfa844 AL |
1280 | * check whether a secret scalar was that exact value, can already do |
1281 | * so.) | |
1282 | */ | |
0f113f3e MC |
1283 | point_double(x3, y3, z3, x1, y1, z1); |
1284 | return; | |
1285 | } | |
1286 | ||
1287 | /* I = ftmp = (2h)**2 */ | |
1288 | felem_assign(ftmp, ftmp4); | |
1289 | felem_scalar64(ftmp, 2); | |
1290 | /* ftmp[i] < 2^61 */ | |
1291 | felem_square(tmp, ftmp); | |
1292 | /* tmp[i] < 17*2^122 */ | |
1293 | felem_reduce(ftmp, tmp); | |
1294 | ||
1295 | /* J = ftmp2 = h * I */ | |
1296 | felem_mul(tmp, ftmp4, ftmp); | |
1297 | felem_reduce(ftmp2, tmp); | |
1298 | ||
1299 | /* V = ftmp4 = U1 * I */ | |
1300 | felem_mul(tmp, ftmp3, ftmp); | |
1301 | felem_reduce(ftmp4, tmp); | |
1302 | ||
1303 | /* x_out = r**2 - J - 2V */ | |
1304 | felem_square(tmp, ftmp5); | |
1305 | /* tmp[i] < 17*2^122 */ | |
1306 | felem_diff_128_64(tmp, ftmp2); | |
1307 | /* tmp[i] < 17*2^122 + 2^63 */ | |
1308 | felem_assign(ftmp3, ftmp4); | |
1309 | felem_scalar64(ftmp4, 2); | |
1310 | /* ftmp4[i] < 2^61 */ | |
1311 | felem_diff_128_64(tmp, ftmp4); | |
1312 | /* tmp[i] < 17*2^122 + 2^64 */ | |
1313 | felem_reduce(x_out, tmp); | |
1314 | ||
1315 | /* y_out = r(V-x_out) - 2 * s1 * J */ | |
1316 | felem_diff64(ftmp3, x_out); | |
1317 | /* | |
1318 | * ftmp3[i] < 2^60 + 2^60 = 2^61 | |
1319 | */ | |
1320 | felem_mul(tmp, ftmp5, ftmp3); | |
1321 | /* tmp[i] < 17*2^122 */ | |
1322 | felem_mul(tmp2, ftmp6, ftmp2); | |
1323 | /* tmp2[i] < 17*2^120 */ | |
1324 | felem_scalar128(tmp2, 2); | |
1325 | /* tmp2[i] < 17*2^121 */ | |
1326 | felem_diff128(tmp, tmp2); | |
1327 | /*- | |
1328 | * tmp[i] < 2^127 - 2^69 + 17*2^122 | |
1329 | * = 2^126 - 2^122 - 2^6 - 2^2 - 1 | |
1330 | * < 2^127 | |
1331 | */ | |
1332 | felem_reduce(y_out, tmp); | |
1333 | ||
1334 | copy_conditional(x_out, x2, z1_is_zero); | |
1335 | copy_conditional(x_out, x1, z2_is_zero); | |
1336 | copy_conditional(y_out, y2, z1_is_zero); | |
1337 | copy_conditional(y_out, y1, z2_is_zero); | |
1338 | copy_conditional(z_out, z2, z1_is_zero); | |
1339 | copy_conditional(z_out, z1, z2_is_zero); | |
1340 | felem_assign(x3, x_out); | |
1341 | felem_assign(y3, y_out); | |
1342 | felem_assign(z3, z_out); | |
1343 | } | |
3e00b4c9 | 1344 | |
1d97c843 TH |
1345 | /*- |
1346 | * Base point pre computation | |
3e00b4c9 BM |
1347 | * -------------------------- |
1348 | * | |
1349 | * Two different sorts of precomputed tables are used in the following code. | |
1350 | * Each contain various points on the curve, where each point is three field | |
1351 | * elements (x, y, z). | |
1352 | * | |
1353 | * For the base point table, z is usually 1 (0 for the point at infinity). | |
1354 | * This table has 16 elements: | |
1355 | * index | bits | point | |
1356 | * ------+---------+------------------------------ | |
1357 | * 0 | 0 0 0 0 | 0G | |
1358 | * 1 | 0 0 0 1 | 1G | |
1359 | * 2 | 0 0 1 0 | 2^130G | |
1360 | * 3 | 0 0 1 1 | (2^130 + 1)G | |
1361 | * 4 | 0 1 0 0 | 2^260G | |
1362 | * 5 | 0 1 0 1 | (2^260 + 1)G | |
1363 | * 6 | 0 1 1 0 | (2^260 + 2^130)G | |
1364 | * 7 | 0 1 1 1 | (2^260 + 2^130 + 1)G | |
1365 | * 8 | 1 0 0 0 | 2^390G | |
1366 | * 9 | 1 0 0 1 | (2^390 + 1)G | |
1367 | * 10 | 1 0 1 0 | (2^390 + 2^130)G | |
1368 | * 11 | 1 0 1 1 | (2^390 + 2^130 + 1)G | |
1369 | * 12 | 1 1 0 0 | (2^390 + 2^260)G | |
1370 | * 13 | 1 1 0 1 | (2^390 + 2^260 + 1)G | |
1371 | * 14 | 1 1 1 0 | (2^390 + 2^260 + 2^130)G | |
1372 | * 15 | 1 1 1 1 | (2^390 + 2^260 + 2^130 + 1)G | |
1373 | * | |
1374 | * The reason for this is so that we can clock bits into four different | |
1375 | * locations when doing simple scalar multiplies against the base point. | |
1376 | * | |
1377 | * Tables for other points have table[i] = iG for i in 0 .. 16. */ | |
1378 | ||
1379 | /* gmul is the table of precomputed base points */ | |
4eb504ae AP |
1380 | static const felem gmul[16][3] = { |
1381 | {{0, 0, 0, 0, 0, 0, 0, 0, 0}, | |
1382 | {0, 0, 0, 0, 0, 0, 0, 0, 0}, | |
1383 | {0, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
0f113f3e MC |
1384 | {{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, |
1385 | 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, | |
1386 | 0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, | |
1387 | {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, | |
1388 | 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, | |
1389 | 0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, | |
1390 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1391 | {{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, | |
1392 | 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, | |
1393 | 0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, | |
1394 | {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, | |
1395 | 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, | |
1396 | 0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, | |
1397 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1398 | {{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, | |
1399 | 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, | |
1400 | 0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, | |
1401 | {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, | |
1402 | 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, | |
1403 | 0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, | |
1404 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1405 | {{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, | |
1406 | 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, | |
1407 | 0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, | |
1408 | {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, | |
1409 | 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, | |
1410 | 0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, | |
1411 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1412 | {{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, | |
1413 | 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, | |
1414 | 0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, | |
1415 | {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, | |
1416 | 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, | |
1417 | 0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, | |
1418 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1419 | {{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, | |
1420 | 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, | |
1421 | 0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, | |
1422 | {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, | |
1423 | 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, | |
1424 | 0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, | |
1425 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1426 | {{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, | |
1427 | 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, | |
1428 | 0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, | |
1429 | {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, | |
1430 | 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, | |
1431 | 0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, | |
1432 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1433 | {{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, | |
1434 | 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, | |
1435 | 0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, | |
1436 | {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, | |
1437 | 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, | |
1438 | 0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, | |
1439 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1440 | {{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, | |
1441 | 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, | |
1442 | 0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, | |
1443 | {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, | |
1444 | 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, | |
1445 | 0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, | |
1446 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1447 | {{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, | |
1448 | 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, | |
1449 | 0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, | |
1450 | {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, | |
1451 | 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, | |
1452 | 0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, | |
1453 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1454 | {{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, | |
1455 | 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, | |
1456 | 0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, | |
1457 | {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, | |
1458 | 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, | |
1459 | 0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, | |
1460 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1461 | {{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, | |
1462 | 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, | |
1463 | 0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, | |
1464 | {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, | |
1465 | 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, | |
1466 | 0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, | |
1467 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1468 | {{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, | |
1469 | 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, | |
1470 | 0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, | |
1471 | {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, | |
1472 | 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, | |
1473 | 0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, | |
1474 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1475 | {{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, | |
1476 | 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, | |
1477 | 0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, | |
1478 | {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, | |
1479 | 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, | |
1480 | 0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, | |
1481 | {1, 0, 0, 0, 0, 0, 0, 0, 0}}, | |
1482 | {{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, | |
1483 | 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, | |
1484 | 0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, | |
1485 | {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, | |
1486 | 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, | |
1487 | 0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, | |
1488 | {1, 0, 0, 0, 0, 0, 0, 0, 0}} | |
1489 | }; | |
1490 | ||
1491 | /* | |
1492 | * select_point selects the |idx|th point from a precomputation table and | |
1493 | * copies it to out. | |
1494 | */ | |
b853717f | 1495 | /* pre_comp below is of the size provided in |size| */ |
0f113f3e MC |
1496 | static void select_point(const limb idx, unsigned int size, |
1497 | const felem pre_comp[][3], felem out[3]) | |
1498 | { | |
1499 | unsigned i, j; | |
1500 | limb *outlimbs = &out[0][0]; | |
16f8d4eb | 1501 | |
88f4c6f3 | 1502 | memset(out, 0, sizeof(*out) * 3); |
0f113f3e MC |
1503 | |
1504 | for (i = 0; i < size; i++) { | |
1505 | const limb *inlimbs = &pre_comp[i][0][0]; | |
1506 | limb mask = i ^ idx; | |
1507 | mask |= mask >> 4; | |
1508 | mask |= mask >> 2; | |
1509 | mask |= mask >> 1; | |
1510 | mask &= 1; | |
1511 | mask--; | |
1512 | for (j = 0; j < NLIMBS * 3; j++) | |
1513 | outlimbs[j] |= inlimbs[j] & mask; | |
1514 | } | |
1515 | } | |
3e00b4c9 BM |
1516 | |
1517 | /* get_bit returns the |i|th bit in |in| */ | |
1518 | static char get_bit(const felem_bytearray in, int i) | |
0f113f3e MC |
1519 | { |
1520 | if (i < 0) | |
1521 | return 0; | |
1522 | return (in[i >> 3] >> (i & 7)) & 1; | |
1523 | } | |
3e00b4c9 | 1524 | |
0f113f3e MC |
1525 | /* |
1526 | * Interleaved point multiplication using precomputed point multiples: The | |
1527 | * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars | |
1528 | * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the | |
1529 | * generator, using certain (large) precomputed multiples in g_pre_comp. | |
1530 | * Output point (X, Y, Z) is stored in x_out, y_out, z_out | |
1531 | */ | |
1532 | static void batch_mul(felem x_out, felem y_out, felem z_out, | |
1533 | const felem_bytearray scalars[], | |
1534 | const unsigned num_points, const u8 *g_scalar, | |
1535 | const int mixed, const felem pre_comp[][17][3], | |
1536 | const felem g_pre_comp[16][3]) | |
1537 | { | |
1538 | int i, skip; | |
1539 | unsigned num, gen_mul = (g_scalar != NULL); | |
1540 | felem nq[3], tmp[4]; | |
1541 | limb bits; | |
1542 | u8 sign, digit; | |
1543 | ||
1544 | /* set nq to the point at infinity */ | |
16f8d4eb | 1545 | memset(nq, 0, sizeof(nq)); |
0f113f3e MC |
1546 | |
1547 | /* | |
1548 | * Loop over all scalars msb-to-lsb, interleaving additions of multiples | |
1549 | * of the generator (last quarter of rounds) and additions of other | |
1550 | * points multiples (every 5th round). | |
1551 | */ | |
1552 | skip = 1; /* save two point operations in the first | |
1553 | * round */ | |
1554 | for (i = (num_points ? 520 : 130); i >= 0; --i) { | |
1555 | /* double */ | |
1556 | if (!skip) | |
1557 | point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); | |
1558 | ||
1559 | /* add multiples of the generator */ | |
1560 | if (gen_mul && (i <= 130)) { | |
1561 | bits = get_bit(g_scalar, i + 390) << 3; | |
1562 | if (i < 130) { | |
1563 | bits |= get_bit(g_scalar, i + 260) << 2; | |
1564 | bits |= get_bit(g_scalar, i + 130) << 1; | |
1565 | bits |= get_bit(g_scalar, i); | |
1566 | } | |
1567 | /* select the point to add, in constant time */ | |
1568 | select_point(bits, 16, g_pre_comp, tmp); | |
1569 | if (!skip) { | |
1570 | /* The 1 argument below is for "mixed" */ | |
1571 | point_add(nq[0], nq[1], nq[2], | |
1572 | nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); | |
1573 | } else { | |
1574 | memcpy(nq, tmp, 3 * sizeof(felem)); | |
1575 | skip = 0; | |
1576 | } | |
1577 | } | |
1578 | ||
1579 | /* do other additions every 5 doublings */ | |
1580 | if (num_points && (i % 5 == 0)) { | |
1581 | /* loop over all scalars */ | |
1582 | for (num = 0; num < num_points; ++num) { | |
1583 | bits = get_bit(scalars[num], i + 4) << 5; | |
1584 | bits |= get_bit(scalars[num], i + 3) << 4; | |
1585 | bits |= get_bit(scalars[num], i + 2) << 3; | |
1586 | bits |= get_bit(scalars[num], i + 1) << 2; | |
1587 | bits |= get_bit(scalars[num], i) << 1; | |
1588 | bits |= get_bit(scalars[num], i - 1); | |
1589 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); | |
1590 | ||
1591 | /* | |
1592 | * select the point to add or subtract, in constant time | |
1593 | */ | |
1594 | select_point(digit, 17, pre_comp[num], tmp); | |
1595 | felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative | |
1596 | * point */ | |
1597 | copy_conditional(tmp[1], tmp[3], (-(limb) sign)); | |
1598 | ||
1599 | if (!skip) { | |
1600 | point_add(nq[0], nq[1], nq[2], | |
1601 | nq[0], nq[1], nq[2], | |
1602 | mixed, tmp[0], tmp[1], tmp[2]); | |
1603 | } else { | |
1604 | memcpy(nq, tmp, 3 * sizeof(felem)); | |
1605 | skip = 0; | |
1606 | } | |
1607 | } | |
1608 | } | |
1609 | } | |
1610 | felem_assign(x_out, nq[0]); | |
1611 | felem_assign(y_out, nq[1]); | |
1612 | felem_assign(z_out, nq[2]); | |
1613 | } | |
3e00b4c9 BM |
1614 | |
1615 | /* Precomputation for the group generator. */ | |
126d6864 | 1616 | struct nistp521_pre_comp_st { |
0f113f3e | 1617 | felem g_pre_comp[16][3]; |
2f545ae4 | 1618 | CRYPTO_REF_COUNT references; |
9b398ef2 | 1619 | CRYPTO_RWLOCK *lock; |
3aef36ff | 1620 | }; |
3e00b4c9 BM |
1621 | |
1622 | const EC_METHOD *EC_GFp_nistp521_method(void) | |
0f113f3e MC |
1623 | { |
1624 | static const EC_METHOD ret = { | |
1625 | EC_FLAGS_DEFAULT_OCT, | |
1626 | NID_X9_62_prime_field, | |
1627 | ec_GFp_nistp521_group_init, | |
1628 | ec_GFp_simple_group_finish, | |
1629 | ec_GFp_simple_group_clear_finish, | |
1630 | ec_GFp_nist_group_copy, | |
1631 | ec_GFp_nistp521_group_set_curve, | |
1632 | ec_GFp_simple_group_get_curve, | |
1633 | ec_GFp_simple_group_get_degree, | |
9ff9bccc | 1634 | ec_group_simple_order_bits, |
0f113f3e MC |
1635 | ec_GFp_simple_group_check_discriminant, |
1636 | ec_GFp_simple_point_init, | |
1637 | ec_GFp_simple_point_finish, | |
1638 | ec_GFp_simple_point_clear_finish, | |
1639 | ec_GFp_simple_point_copy, | |
1640 | ec_GFp_simple_point_set_to_infinity, | |
0f113f3e MC |
1641 | ec_GFp_simple_point_set_affine_coordinates, |
1642 | ec_GFp_nistp521_point_get_affine_coordinates, | |
1643 | 0 /* point_set_compressed_coordinates */ , | |
1644 | 0 /* point2oct */ , | |
1645 | 0 /* oct2point */ , | |
1646 | ec_GFp_simple_add, | |
1647 | ec_GFp_simple_dbl, | |
1648 | ec_GFp_simple_invert, | |
1649 | ec_GFp_simple_is_at_infinity, | |
1650 | ec_GFp_simple_is_on_curve, | |
1651 | ec_GFp_simple_cmp, | |
1652 | ec_GFp_simple_make_affine, | |
1653 | ec_GFp_simple_points_make_affine, | |
1654 | ec_GFp_nistp521_points_mul, | |
1655 | ec_GFp_nistp521_precompute_mult, | |
1656 | ec_GFp_nistp521_have_precompute_mult, | |
1657 | ec_GFp_nist_field_mul, | |
1658 | ec_GFp_nist_field_sqr, | |
1659 | 0 /* field_div */ , | |
e0033efc | 1660 | ec_GFp_simple_field_inv, |
0f113f3e MC |
1661 | 0 /* field_encode */ , |
1662 | 0 /* field_decode */ , | |
9ff9bccc DSH |
1663 | 0, /* field_set_to_one */ |
1664 | ec_key_simple_priv2oct, | |
1665 | ec_key_simple_oct2priv, | |
1666 | 0, /* set private */ | |
1667 | ec_key_simple_generate_key, | |
1668 | ec_key_simple_check_key, | |
1669 | ec_key_simple_generate_public_key, | |
1670 | 0, /* keycopy */ | |
1671 | 0, /* keyfinish */ | |
f667820c | 1672 | ecdh_simple_compute_key, |
9bf682f6 PS |
1673 | ecdsa_simple_sign_setup, |
1674 | ecdsa_simple_sign_sig, | |
1675 | ecdsa_simple_verify_sig, | |
f667820c | 1676 | 0, /* field_inverse_mod_ord */ |
37124360 NT |
1677 | 0, /* blind_coordinates */ |
1678 | 0, /* ladder_pre */ | |
1679 | 0, /* ladder_step */ | |
1680 | 0 /* ladder_post */ | |
0f113f3e MC |
1681 | }; |
1682 | ||
1683 | return &ret; | |
1684 | } | |
3e00b4c9 BM |
1685 | |
1686 | /******************************************************************************/ | |
0f113f3e MC |
1687 | /* |
1688 | * FUNCTIONS TO MANAGE PRECOMPUTATION | |
3e00b4c9 BM |
1689 | */ |
1690 | ||
3f5abab9 | 1691 | static NISTP521_PRE_COMP *nistp521_pre_comp_new(void) |
0f113f3e | 1692 | { |
b51bce94 | 1693 | NISTP521_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); |
b4faea50 | 1694 | |
90945fa3 | 1695 | if (ret == NULL) { |
0f113f3e MC |
1696 | ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
1697 | return ret; | |
1698 | } | |
9b398ef2 | 1699 | |
0f113f3e | 1700 | ret->references = 1; |
9b398ef2 AG |
1701 | |
1702 | ret->lock = CRYPTO_THREAD_lock_new(); | |
1703 | if (ret->lock == NULL) { | |
1704 | ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
1705 | OPENSSL_free(ret); | |
1706 | return NULL; | |
1707 | } | |
0f113f3e MC |
1708 | return ret; |
1709 | } | |
3e00b4c9 | 1710 | |
3aef36ff | 1711 | NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *p) |
0f113f3e | 1712 | { |
9b398ef2 | 1713 | int i; |
3aef36ff | 1714 | if (p != NULL) |
2f545ae4 | 1715 | CRYPTO_UP_REF(&p->references, &i, p->lock); |
3aef36ff | 1716 | return p; |
0f113f3e | 1717 | } |
3e00b4c9 | 1718 | |
3aef36ff | 1719 | void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *p) |
0f113f3e | 1720 | { |
9b398ef2 AG |
1721 | int i; |
1722 | ||
1723 | if (p == NULL) | |
1724 | return; | |
1725 | ||
2f545ae4 | 1726 | CRYPTO_DOWN_REF(&p->references, &i, p->lock); |
9b398ef2 AG |
1727 | REF_PRINT_COUNT("EC_nistp521", x); |
1728 | if (i > 0) | |
0f113f3e | 1729 | return; |
9b398ef2 AG |
1730 | REF_ASSERT_ISNT(i < 0); |
1731 | ||
1732 | CRYPTO_THREAD_lock_free(p->lock); | |
3aef36ff | 1733 | OPENSSL_free(p); |
0f113f3e | 1734 | } |
3e00b4c9 BM |
1735 | |
1736 | /******************************************************************************/ | |
0f113f3e MC |
1737 | /* |
1738 | * OPENSSL EC_METHOD FUNCTIONS | |
3e00b4c9 BM |
1739 | */ |
1740 | ||
1741 | int ec_GFp_nistp521_group_init(EC_GROUP *group) | |
0f113f3e MC |
1742 | { |
1743 | int ret; | |
1744 | ret = ec_GFp_simple_group_init(group); | |
1745 | group->a_is_minus3 = 1; | |
1746 | return ret; | |
1747 | } | |
3e00b4c9 BM |
1748 | |
1749 | int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, | |
0f113f3e MC |
1750 | const BIGNUM *a, const BIGNUM *b, |
1751 | BN_CTX *ctx) | |
1752 | { | |
1753 | int ret = 0; | |
0f113f3e | 1754 | BIGNUM *curve_p, *curve_a, *curve_b; |
a9612d6c MC |
1755 | #ifndef FIPS_MODE |
1756 | BN_CTX *new_ctx = NULL; | |
0f113f3e MC |
1757 | |
1758 | if (ctx == NULL) | |
a6482df0 | 1759 | ctx = new_ctx = BN_CTX_new(); |
a9612d6c MC |
1760 | #endif |
1761 | if (ctx == NULL) | |
1762 | return 0; | |
1763 | ||
0f113f3e | 1764 | BN_CTX_start(ctx); |
edea42c6 PY |
1765 | curve_p = BN_CTX_get(ctx); |
1766 | curve_a = BN_CTX_get(ctx); | |
1767 | curve_b = BN_CTX_get(ctx); | |
1768 | if (curve_b == NULL) | |
0f113f3e MC |
1769 | goto err; |
1770 | BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p); | |
1771 | BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a); | |
1772 | BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b); | |
1773 | if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { | |
1774 | ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE, | |
1775 | EC_R_WRONG_CURVE_PARAMETERS); | |
1776 | goto err; | |
1777 | } | |
1778 | group->field_mod_func = BN_nist_mod_521; | |
1779 | ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); | |
1780 | err: | |
1781 | BN_CTX_end(ctx); | |
a9612d6c | 1782 | #ifndef FIPS_MODE |
23a1d5e9 | 1783 | BN_CTX_free(new_ctx); |
a9612d6c | 1784 | #endif |
0f113f3e MC |
1785 | return ret; |
1786 | } | |
1787 | ||
1788 | /* | |
1789 | * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = | |
1790 | * (X/Z^2, Y/Z^3) | |
1791 | */ | |
3e00b4c9 | 1792 | int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, |
0f113f3e MC |
1793 | const EC_POINT *point, |
1794 | BIGNUM *x, BIGNUM *y, | |
1795 | BN_CTX *ctx) | |
1796 | { | |
1797 | felem z1, z2, x_in, y_in, x_out, y_out; | |
1798 | largefelem tmp; | |
1799 | ||
1800 | if (EC_POINT_is_at_infinity(group, point)) { | |
1801 | ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, | |
1802 | EC_R_POINT_AT_INFINITY); | |
1803 | return 0; | |
1804 | } | |
ace8f546 AP |
1805 | if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || |
1806 | (!BN_to_felem(z1, point->Z))) | |
0f113f3e MC |
1807 | return 0; |
1808 | felem_inv(z2, z1); | |
1809 | felem_square(tmp, z2); | |
1810 | felem_reduce(z1, tmp); | |
1811 | felem_mul(tmp, x_in, z1); | |
1812 | felem_reduce(x_in, tmp); | |
1813 | felem_contract(x_out, x_in); | |
1814 | if (x != NULL) { | |
1815 | if (!felem_to_BN(x, x_out)) { | |
1816 | ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, | |
1817 | ERR_R_BN_LIB); | |
1818 | return 0; | |
1819 | } | |
1820 | } | |
1821 | felem_mul(tmp, z1, z2); | |
1822 | felem_reduce(z1, tmp); | |
1823 | felem_mul(tmp, y_in, z1); | |
1824 | felem_reduce(y_in, tmp); | |
1825 | felem_contract(y_out, y_in); | |
1826 | if (y != NULL) { | |
1827 | if (!felem_to_BN(y, y_out)) { | |
1828 | ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, | |
1829 | ERR_R_BN_LIB); | |
1830 | return 0; | |
1831 | } | |
1832 | } | |
1833 | return 1; | |
1834 | } | |
3e00b4c9 | 1835 | |
b853717f | 1836 | /* points below is of size |num|, and tmp_felems is of size |num+1/ */ |
0f113f3e MC |
1837 | static void make_points_affine(size_t num, felem points[][3], |
1838 | felem tmp_felems[]) | |
1839 | { | |
1840 | /* | |
1841 | * Runs in constant time, unless an input is the point at infinity (which | |
1842 | * normally shouldn't happen). | |
1843 | */ | |
1844 | ec_GFp_nistp_points_make_affine_internal(num, | |
1845 | points, | |
1846 | sizeof(felem), | |
1847 | tmp_felems, | |
1848 | (void (*)(void *))felem_one, | |
0f113f3e MC |
1849 | felem_is_zero_int, |
1850 | (void (*)(void *, const void *)) | |
1851 | felem_assign, | |
1852 | (void (*)(void *, const void *)) | |
1853 | felem_square_reduce, (void (*) | |
1854 | (void *, | |
1855 | const void | |
1856 | *, | |
1857 | const void | |
1858 | *)) | |
1859 | felem_mul_reduce, | |
1860 | (void (*)(void *, const void *)) | |
1861 | felem_inv, | |
1862 | (void (*)(void *, const void *)) | |
1863 | felem_contract); | |
1864 | } | |
1865 | ||
1866 | /* | |
1867 | * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL | |
1868 | * values Result is stored in r (r can equal one of the inputs). | |
1869 | */ | |
3e00b4c9 | 1870 | int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, |
0f113f3e MC |
1871 | const BIGNUM *scalar, size_t num, |
1872 | const EC_POINT *points[], | |
1873 | const BIGNUM *scalars[], BN_CTX *ctx) | |
1874 | { | |
1875 | int ret = 0; | |
1876 | int j; | |
1877 | int mixed = 0; | |
0f113f3e MC |
1878 | BIGNUM *x, *y, *z, *tmp_scalar; |
1879 | felem_bytearray g_secret; | |
1880 | felem_bytearray *secrets = NULL; | |
16f8d4eb | 1881 | felem (*pre_comp)[17][3] = NULL; |
0f113f3e | 1882 | felem *tmp_felems = NULL; |
e0b660c2 NT |
1883 | unsigned i; |
1884 | int num_bytes; | |
0f113f3e MC |
1885 | int have_pre_comp = 0; |
1886 | size_t num_points = num; | |
1887 | felem x_in, y_in, z_in, x_out, y_out, z_out; | |
1888 | NISTP521_PRE_COMP *pre = NULL; | |
1889 | felem(*g_pre_comp)[3] = NULL; | |
1890 | EC_POINT *generator = NULL; | |
1891 | const EC_POINT *p = NULL; | |
1892 | const BIGNUM *p_scalar = NULL; | |
1893 | ||
0f113f3e | 1894 | BN_CTX_start(ctx); |
edea42c6 PY |
1895 | x = BN_CTX_get(ctx); |
1896 | y = BN_CTX_get(ctx); | |
1897 | z = BN_CTX_get(ctx); | |
1898 | tmp_scalar = BN_CTX_get(ctx); | |
1899 | if (tmp_scalar == NULL) | |
0f113f3e MC |
1900 | goto err; |
1901 | ||
1902 | if (scalar != NULL) { | |
3aef36ff | 1903 | pre = group->pre_comp.nistp521; |
0f113f3e MC |
1904 | if (pre) |
1905 | /* we have precomputation, try to use it */ | |
1906 | g_pre_comp = &pre->g_pre_comp[0]; | |
1907 | else | |
1908 | /* try to use the standard precomputation */ | |
1909 | g_pre_comp = (felem(*)[3]) gmul; | |
1910 | generator = EC_POINT_new(group); | |
1911 | if (generator == NULL) | |
1912 | goto err; | |
1913 | /* get the generator from precomputation */ | |
1914 | if (!felem_to_BN(x, g_pre_comp[1][0]) || | |
1915 | !felem_to_BN(y, g_pre_comp[1][1]) || | |
1916 | !felem_to_BN(z, g_pre_comp[1][2])) { | |
1917 | ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); | |
1918 | goto err; | |
1919 | } | |
07caec83 BB |
1920 | if (!ec_GFp_simple_set_Jprojective_coordinates_GFp(group, generator, x, |
1921 | y, z, ctx)) | |
0f113f3e MC |
1922 | goto err; |
1923 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) | |
1924 | /* precomputation matches generator */ | |
1925 | have_pre_comp = 1; | |
1926 | else | |
1927 | /* | |
1928 | * we don't have valid precomputation: treat the generator as a | |
1929 | * random point | |
1930 | */ | |
1931 | num_points++; | |
1932 | } | |
1933 | ||
1934 | if (num_points > 0) { | |
1935 | if (num_points >= 2) { | |
1936 | /* | |
1937 | * unless we precompute multiples for just one point, converting | |
1938 | * those into affine form is time well spent | |
1939 | */ | |
1940 | mixed = 1; | |
1941 | } | |
b51bce94 RS |
1942 | secrets = OPENSSL_zalloc(sizeof(*secrets) * num_points); |
1943 | pre_comp = OPENSSL_zalloc(sizeof(*pre_comp) * num_points); | |
0f113f3e MC |
1944 | if (mixed) |
1945 | tmp_felems = | |
88f4c6f3 | 1946 | OPENSSL_malloc(sizeof(*tmp_felems) * (num_points * 17 + 1)); |
0f113f3e MC |
1947 | if ((secrets == NULL) || (pre_comp == NULL) |
1948 | || (mixed && (tmp_felems == NULL))) { | |
1949 | ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE); | |
1950 | goto err; | |
1951 | } | |
1952 | ||
1953 | /* | |
1954 | * we treat NULL scalars as 0, and NULL points as points at infinity, | |
1955 | * i.e., they contribute nothing to the linear combination | |
1956 | */ | |
0f113f3e | 1957 | for (i = 0; i < num_points; ++i) { |
4fe2ee3a | 1958 | if (i == num) { |
0f113f3e MC |
1959 | /* |
1960 | * we didn't have a valid precomputation, so we pick the | |
1961 | * generator | |
1962 | */ | |
0f113f3e MC |
1963 | p = EC_GROUP_get0_generator(group); |
1964 | p_scalar = scalar; | |
4fe2ee3a | 1965 | } else { |
0f113f3e | 1966 | /* the i^th point */ |
0f113f3e MC |
1967 | p = points[i]; |
1968 | p_scalar = scalars[i]; | |
1969 | } | |
1970 | if ((p_scalar != NULL) && (p != NULL)) { | |
1971 | /* reduce scalar to 0 <= scalar < 2^521 */ | |
1972 | if ((BN_num_bits(p_scalar) > 521) | |
1973 | || (BN_is_negative(p_scalar))) { | |
1974 | /* | |
1975 | * this is an unusual input, and we don't guarantee | |
1976 | * constant-timeness | |
1977 | */ | |
ace8f546 | 1978 | if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { |
0f113f3e MC |
1979 | ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); |
1980 | goto err; | |
1981 | } | |
e0b660c2 NT |
1982 | num_bytes = BN_bn2lebinpad(tmp_scalar, |
1983 | secrets[i], sizeof(secrets[i])); | |
1984 | } else { | |
1985 | num_bytes = BN_bn2lebinpad(p_scalar, | |
1986 | secrets[i], sizeof(secrets[i])); | |
1987 | } | |
1988 | if (num_bytes < 0) { | |
1989 | ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); | |
1990 | goto err; | |
1991 | } | |
0f113f3e | 1992 | /* precompute multiples */ |
ace8f546 AP |
1993 | if ((!BN_to_felem(x_out, p->X)) || |
1994 | (!BN_to_felem(y_out, p->Y)) || | |
1995 | (!BN_to_felem(z_out, p->Z))) | |
0f113f3e MC |
1996 | goto err; |
1997 | memcpy(pre_comp[i][1][0], x_out, sizeof(felem)); | |
1998 | memcpy(pre_comp[i][1][1], y_out, sizeof(felem)); | |
1999 | memcpy(pre_comp[i][1][2], z_out, sizeof(felem)); | |
2000 | for (j = 2; j <= 16; ++j) { | |
2001 | if (j & 1) { | |
2002 | point_add(pre_comp[i][j][0], pre_comp[i][j][1], | |
2003 | pre_comp[i][j][2], pre_comp[i][1][0], | |
2004 | pre_comp[i][1][1], pre_comp[i][1][2], 0, | |
2005 | pre_comp[i][j - 1][0], | |
2006 | pre_comp[i][j - 1][1], | |
2007 | pre_comp[i][j - 1][2]); | |
2008 | } else { | |
2009 | point_double(pre_comp[i][j][0], pre_comp[i][j][1], | |
2010 | pre_comp[i][j][2], pre_comp[i][j / 2][0], | |
2011 | pre_comp[i][j / 2][1], | |
2012 | pre_comp[i][j / 2][2]); | |
2013 | } | |
2014 | } | |
2015 | } | |
2016 | } | |
2017 | if (mixed) | |
2018 | make_points_affine(num_points * 17, pre_comp[0], tmp_felems); | |
2019 | } | |
2020 | ||
2021 | /* the scalar for the generator */ | |
2022 | if ((scalar != NULL) && (have_pre_comp)) { | |
2023 | memset(g_secret, 0, sizeof(g_secret)); | |
2024 | /* reduce scalar to 0 <= scalar < 2^521 */ | |
2025 | if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) { | |
2026 | /* | |
2027 | * this is an unusual input, and we don't guarantee | |
2028 | * constant-timeness | |
2029 | */ | |
ace8f546 | 2030 | if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { |
0f113f3e MC |
2031 | ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); |
2032 | goto err; | |
2033 | } | |
e0b660c2 | 2034 | num_bytes = BN_bn2lebinpad(tmp_scalar, g_secret, sizeof(g_secret)); |
4fe2ee3a | 2035 | } else { |
e0b660c2 | 2036 | num_bytes = BN_bn2lebinpad(scalar, g_secret, sizeof(g_secret)); |
4fe2ee3a | 2037 | } |
0f113f3e MC |
2038 | /* do the multiplication with generator precomputation */ |
2039 | batch_mul(x_out, y_out, z_out, | |
2040 | (const felem_bytearray(*))secrets, num_points, | |
2041 | g_secret, | |
2042 | mixed, (const felem(*)[17][3])pre_comp, | |
2043 | (const felem(*)[3])g_pre_comp); | |
4fe2ee3a | 2044 | } else { |
0f113f3e MC |
2045 | /* do the multiplication without generator precomputation */ |
2046 | batch_mul(x_out, y_out, z_out, | |
2047 | (const felem_bytearray(*))secrets, num_points, | |
2048 | NULL, mixed, (const felem(*)[17][3])pre_comp, NULL); | |
4fe2ee3a | 2049 | } |
0f113f3e MC |
2050 | /* reduce the output to its unique minimal representation */ |
2051 | felem_contract(x_in, x_out); | |
2052 | felem_contract(y_in, y_out); | |
2053 | felem_contract(z_in, z_out); | |
2054 | if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || | |
2055 | (!felem_to_BN(z, z_in))) { | |
2056 | ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); | |
2057 | goto err; | |
2058 | } | |
07caec83 | 2059 | ret = ec_GFp_simple_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); |
0f113f3e MC |
2060 | |
2061 | err: | |
2062 | BN_CTX_end(ctx); | |
8fdc3734 | 2063 | EC_POINT_free(generator); |
b548a1f1 RS |
2064 | OPENSSL_free(secrets); |
2065 | OPENSSL_free(pre_comp); | |
2066 | OPENSSL_free(tmp_felems); | |
0f113f3e MC |
2067 | return ret; |
2068 | } | |
3e00b4c9 BM |
2069 | |
2070 | int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) | |
0f113f3e MC |
2071 | { |
2072 | int ret = 0; | |
2073 | NISTP521_PRE_COMP *pre = NULL; | |
2074 | int i, j; | |
0f113f3e MC |
2075 | BIGNUM *x, *y; |
2076 | EC_POINT *generator = NULL; | |
2077 | felem tmp_felems[16]; | |
a9612d6c MC |
2078 | #ifndef FIPS_MODE |
2079 | BN_CTX *new_ctx = NULL; | |
2080 | #endif | |
0f113f3e MC |
2081 | |
2082 | /* throw away old precomputation */ | |
2c52ac9b | 2083 | EC_pre_comp_free(group); |
a9612d6c MC |
2084 | |
2085 | #ifndef FIPS_MODE | |
0f113f3e | 2086 | if (ctx == NULL) |
a6482df0 | 2087 | ctx = new_ctx = BN_CTX_new(); |
a9612d6c MC |
2088 | #endif |
2089 | if (ctx == NULL) | |
2090 | return 0; | |
2091 | ||
0f113f3e | 2092 | BN_CTX_start(ctx); |
edea42c6 PY |
2093 | x = BN_CTX_get(ctx); |
2094 | y = BN_CTX_get(ctx); | |
2095 | if (y == NULL) | |
0f113f3e MC |
2096 | goto err; |
2097 | /* get the generator */ | |
2098 | if (group->generator == NULL) | |
2099 | goto err; | |
2100 | generator = EC_POINT_new(group); | |
2101 | if (generator == NULL) | |
2102 | goto err; | |
2103 | BN_bin2bn(nistp521_curve_params[3], sizeof(felem_bytearray), x); | |
2104 | BN_bin2bn(nistp521_curve_params[4], sizeof(felem_bytearray), y); | |
9cc570d4 | 2105 | if (!EC_POINT_set_affine_coordinates(group, generator, x, y, ctx)) |
0f113f3e MC |
2106 | goto err; |
2107 | if ((pre = nistp521_pre_comp_new()) == NULL) | |
2108 | goto err; | |
2109 | /* | |
2110 | * if the generator is the standard one, use built-in precomputation | |
2111 | */ | |
2112 | if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { | |
2113 | memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); | |
615614c8 | 2114 | goto done; |
0f113f3e | 2115 | } |
ace8f546 AP |
2116 | if ((!BN_to_felem(pre->g_pre_comp[1][0], group->generator->X)) || |
2117 | (!BN_to_felem(pre->g_pre_comp[1][1], group->generator->Y)) || | |
2118 | (!BN_to_felem(pre->g_pre_comp[1][2], group->generator->Z))) | |
0f113f3e MC |
2119 | goto err; |
2120 | /* compute 2^130*G, 2^260*G, 2^390*G */ | |
2121 | for (i = 1; i <= 4; i <<= 1) { | |
2122 | point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], | |
2123 | pre->g_pre_comp[2 * i][2], pre->g_pre_comp[i][0], | |
2124 | pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); | |
2125 | for (j = 0; j < 129; ++j) { | |
2126 | point_double(pre->g_pre_comp[2 * i][0], | |
2127 | pre->g_pre_comp[2 * i][1], | |
2128 | pre->g_pre_comp[2 * i][2], | |
2129 | pre->g_pre_comp[2 * i][0], | |
2130 | pre->g_pre_comp[2 * i][1], | |
2131 | pre->g_pre_comp[2 * i][2]); | |
2132 | } | |
2133 | } | |
2134 | /* g_pre_comp[0] is the point at infinity */ | |
2135 | memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); | |
2136 | /* the remaining multiples */ | |
2137 | /* 2^130*G + 2^260*G */ | |
2138 | point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], | |
2139 | pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], | |
2140 | pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], | |
2141 | 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], | |
2142 | pre->g_pre_comp[2][2]); | |
2143 | /* 2^130*G + 2^390*G */ | |
2144 | point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], | |
2145 | pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], | |
2146 | pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], | |
2147 | 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], | |
2148 | pre->g_pre_comp[2][2]); | |
2149 | /* 2^260*G + 2^390*G */ | |
2150 | point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], | |
2151 | pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], | |
2152 | pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], | |
2153 | 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], | |
2154 | pre->g_pre_comp[4][2]); | |
2155 | /* 2^130*G + 2^260*G + 2^390*G */ | |
2156 | point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], | |
2157 | pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], | |
2158 | pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], | |
2159 | 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], | |
2160 | pre->g_pre_comp[2][2]); | |
2161 | for (i = 1; i < 8; ++i) { | |
2162 | /* odd multiples: add G */ | |
2163 | point_add(pre->g_pre_comp[2 * i + 1][0], | |
2164 | pre->g_pre_comp[2 * i + 1][1], | |
2165 | pre->g_pre_comp[2 * i + 1][2], pre->g_pre_comp[2 * i][0], | |
2166 | pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], 0, | |
2167 | pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], | |
2168 | pre->g_pre_comp[1][2]); | |
2169 | } | |
2170 | make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems); | |
2171 | ||
615614c8 | 2172 | done: |
3aef36ff | 2173 | SETPRECOMP(group, nistp521, pre); |
0f113f3e MC |
2174 | ret = 1; |
2175 | pre = NULL; | |
3e00b4c9 | 2176 | err: |
0f113f3e | 2177 | BN_CTX_end(ctx); |
8fdc3734 | 2178 | EC_POINT_free(generator); |
a9612d6c | 2179 | #ifndef FIPS_MODE |
23a1d5e9 | 2180 | BN_CTX_free(new_ctx); |
a9612d6c | 2181 | #endif |
3aef36ff | 2182 | EC_nistp521_pre_comp_free(pre); |
0f113f3e MC |
2183 | return ret; |
2184 | } | |
3e00b4c9 BM |
2185 | |
2186 | int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group) | |
0f113f3e | 2187 | { |
126d6864 | 2188 | return HAVEPRECOMP(group, nistp521); |
0f113f3e | 2189 | } |