/src/libressl/crypto/curve25519/curve25519.c
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1 | | /* $OpenBSD: curve25519.c,v 1.6 2022/02/08 16:44:23 tb Exp $ */ |
2 | | /* |
3 | | * Copyright (c) 2015, Google Inc. |
4 | | * |
5 | | * Permission to use, copy, modify, and/or distribute this software for any |
6 | | * purpose with or without fee is hereby granted, provided that the above |
7 | | * copyright notice and this permission notice appear in all copies. |
8 | | * |
9 | | * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
10 | | * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
11 | | * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY |
12 | | * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
13 | | * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION |
14 | | * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN |
15 | | * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. |
16 | | */ |
17 | | |
18 | | /* |
19 | | * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP |
20 | | * 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as |
21 | | * public domain but this file has the ISC license just to keep licencing |
22 | | * simple. |
23 | | * |
24 | | * The field functions are shared by Ed25519 and X25519 where possible. |
25 | | */ |
26 | | |
27 | | #include <stdlib.h> |
28 | | #include <string.h> |
29 | | |
30 | | #include <openssl/curve25519.h> |
31 | | |
32 | | #ifdef ED25519 |
33 | | #include <openssl/sha.h> |
34 | | #endif |
35 | | |
36 | | #include "curve25519_internal.h" |
37 | | |
38 | | static const int64_t kBottom25Bits = 0x1ffffffLL; |
39 | | static const int64_t kBottom26Bits = 0x3ffffffLL; |
40 | | static const int64_t kTop39Bits = 0xfffffffffe000000LL; |
41 | | static const int64_t kTop38Bits = 0xfffffffffc000000LL; |
42 | | |
43 | 2.60k | static uint64_t load_3(const uint8_t *in) { |
44 | 2.60k | uint64_t result; |
45 | 2.60k | result = (uint64_t)in[0]; |
46 | 2.60k | result |= ((uint64_t)in[1]) << 8; |
47 | 2.60k | result |= ((uint64_t)in[2]) << 16; |
48 | 2.60k | return result; |
49 | 2.60k | } |
50 | | |
51 | 650 | static uint64_t load_4(const uint8_t *in) { |
52 | 650 | uint64_t result; |
53 | 650 | result = (uint64_t)in[0]; |
54 | 650 | result |= ((uint64_t)in[1]) << 8; |
55 | 650 | result |= ((uint64_t)in[2]) << 16; |
56 | 650 | result |= ((uint64_t)in[3]) << 24; |
57 | 650 | return result; |
58 | 650 | } |
59 | | |
60 | 325 | static void fe_frombytes(fe h, const uint8_t *s) { |
61 | | /* Ignores top bit of h. */ |
62 | 325 | int64_t h0 = load_4(s); |
63 | 325 | int64_t h1 = load_3(s + 4) << 6; |
64 | 325 | int64_t h2 = load_3(s + 7) << 5; |
65 | 325 | int64_t h3 = load_3(s + 10) << 3; |
66 | 325 | int64_t h4 = load_3(s + 13) << 2; |
67 | 325 | int64_t h5 = load_4(s + 16); |
68 | 325 | int64_t h6 = load_3(s + 20) << 7; |
69 | 325 | int64_t h7 = load_3(s + 23) << 5; |
70 | 325 | int64_t h8 = load_3(s + 26) << 4; |
71 | 325 | int64_t h9 = (load_3(s + 29) & 8388607) << 2; |
72 | 325 | int64_t carry0; |
73 | 325 | int64_t carry1; |
74 | 325 | int64_t carry2; |
75 | 325 | int64_t carry3; |
76 | 325 | int64_t carry4; |
77 | 325 | int64_t carry5; |
78 | 325 | int64_t carry6; |
79 | 325 | int64_t carry7; |
80 | 325 | int64_t carry8; |
81 | 325 | int64_t carry9; |
82 | | |
83 | 325 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
84 | 325 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
85 | 325 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
86 | 325 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
87 | 325 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
88 | | |
89 | 325 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
90 | 325 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
91 | 325 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
92 | 325 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
93 | 325 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
94 | | |
95 | 325 | h[0] = h0; |
96 | 325 | h[1] = h1; |
97 | 325 | h[2] = h2; |
98 | 325 | h[3] = h3; |
99 | 325 | h[4] = h4; |
100 | 325 | h[5] = h5; |
101 | 325 | h[6] = h6; |
102 | 325 | h[7] = h7; |
103 | 325 | h[8] = h8; |
104 | 325 | h[9] = h9; |
105 | 325 | } |
106 | | |
107 | | /* Preconditions: |
108 | | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
109 | | * |
110 | | * Write p=2^255-19; q=floor(h/p). |
111 | | * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). |
112 | | * |
113 | | * Proof: |
114 | | * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. |
115 | | * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. |
116 | | * |
117 | | * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). |
118 | | * Then 0<y<1. |
119 | | * |
120 | | * Write r=h-pq. |
121 | | * Have 0<=r<=p-1=2^255-20. |
122 | | * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. |
123 | | * |
124 | | * Write x=r+19(2^-255)r+y. |
125 | | * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. |
126 | | * |
127 | | * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) |
128 | | * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */ |
129 | 325 | static void fe_tobytes(uint8_t *s, const fe h) { |
130 | 325 | int32_t h0 = h[0]; |
131 | 325 | int32_t h1 = h[1]; |
132 | 325 | int32_t h2 = h[2]; |
133 | 325 | int32_t h3 = h[3]; |
134 | 325 | int32_t h4 = h[4]; |
135 | 325 | int32_t h5 = h[5]; |
136 | 325 | int32_t h6 = h[6]; |
137 | 325 | int32_t h7 = h[7]; |
138 | 325 | int32_t h8 = h[8]; |
139 | 325 | int32_t h9 = h[9]; |
140 | 325 | int32_t q; |
141 | | |
142 | 325 | q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; |
143 | 325 | q = (h0 + q) >> 26; |
144 | 325 | q = (h1 + q) >> 25; |
145 | 325 | q = (h2 + q) >> 26; |
146 | 325 | q = (h3 + q) >> 25; |
147 | 325 | q = (h4 + q) >> 26; |
148 | 325 | q = (h5 + q) >> 25; |
149 | 325 | q = (h6 + q) >> 26; |
150 | 325 | q = (h7 + q) >> 25; |
151 | 325 | q = (h8 + q) >> 26; |
152 | 325 | q = (h9 + q) >> 25; |
153 | | |
154 | | /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ |
155 | 325 | h0 += 19 * q; |
156 | | /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ |
157 | | |
158 | 325 | h1 += h0 >> 26; h0 &= kBottom26Bits; |
159 | 325 | h2 += h1 >> 25; h1 &= kBottom25Bits; |
160 | 325 | h3 += h2 >> 26; h2 &= kBottom26Bits; |
161 | 325 | h4 += h3 >> 25; h3 &= kBottom25Bits; |
162 | 325 | h5 += h4 >> 26; h4 &= kBottom26Bits; |
163 | 325 | h6 += h5 >> 25; h5 &= kBottom25Bits; |
164 | 325 | h7 += h6 >> 26; h6 &= kBottom26Bits; |
165 | 325 | h8 += h7 >> 25; h7 &= kBottom25Bits; |
166 | 325 | h9 += h8 >> 26; h8 &= kBottom26Bits; |
167 | 325 | h9 &= kBottom25Bits; |
168 | | /* h10 = carry9 */ |
169 | | |
170 | | /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. |
171 | | * Have h0+...+2^230 h9 between 0 and 2^255-1; |
172 | | * evidently 2^255 h10-2^255 q = 0. |
173 | | * Goal: Output h0+...+2^230 h9. */ |
174 | | |
175 | 325 | s[0] = h0 >> 0; |
176 | 325 | s[1] = h0 >> 8; |
177 | 325 | s[2] = h0 >> 16; |
178 | 325 | s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2); |
179 | 325 | s[4] = h1 >> 6; |
180 | 325 | s[5] = h1 >> 14; |
181 | 325 | s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3); |
182 | 325 | s[7] = h2 >> 5; |
183 | 325 | s[8] = h2 >> 13; |
184 | 325 | s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5); |
185 | 325 | s[10] = h3 >> 3; |
186 | 325 | s[11] = h3 >> 11; |
187 | 325 | s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6); |
188 | 325 | s[13] = h4 >> 2; |
189 | 325 | s[14] = h4 >> 10; |
190 | 325 | s[15] = h4 >> 18; |
191 | 325 | s[16] = h5 >> 0; |
192 | 325 | s[17] = h5 >> 8; |
193 | 325 | s[18] = h5 >> 16; |
194 | 325 | s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1); |
195 | 325 | s[20] = h6 >> 7; |
196 | 325 | s[21] = h6 >> 15; |
197 | 325 | s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3); |
198 | 325 | s[23] = h7 >> 5; |
199 | 325 | s[24] = h7 >> 13; |
200 | 325 | s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4); |
201 | 325 | s[26] = h8 >> 4; |
202 | 325 | s[27] = h8 >> 12; |
203 | 325 | s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6); |
204 | 325 | s[29] = h9 >> 2; |
205 | 325 | s[30] = h9 >> 10; |
206 | 325 | s[31] = h9 >> 18; |
207 | 325 | } |
208 | | |
209 | | /* h = f */ |
210 | 325 | static void fe_copy(fe h, const fe f) { |
211 | 325 | memmove(h, f, sizeof(int32_t) * 10); |
212 | 325 | } |
213 | | |
214 | | /* h = 0 */ |
215 | 325 | static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } |
216 | | |
217 | | /* h = 1 */ |
218 | 650 | static void fe_1(fe h) { |
219 | 650 | memset(h, 0, sizeof(int32_t) * 10); |
220 | 650 | h[0] = 1; |
221 | 650 | } |
222 | | |
223 | | /* h = f + g |
224 | | * Can overlap h with f or g. |
225 | | * |
226 | | * Preconditions: |
227 | | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
228 | | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
229 | | * |
230 | | * Postconditions: |
231 | | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ |
232 | 331k | static void fe_add(fe h, const fe f, const fe g) { |
233 | 331k | unsigned i; |
234 | 3.64M | for (i = 0; i < 10; i++) { |
235 | 3.31M | h[i] = f[i] + g[i]; |
236 | 3.31M | } |
237 | 331k | } |
238 | | |
239 | | /* h = f - g |
240 | | * Can overlap h with f or g. |
241 | | * |
242 | | * Preconditions: |
243 | | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
244 | | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
245 | | * |
246 | | * Postconditions: |
247 | | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ |
248 | 331k | static void fe_sub(fe h, const fe f, const fe g) { |
249 | 331k | unsigned i; |
250 | 3.64M | for (i = 0; i < 10; i++) { |
251 | 3.31M | h[i] = f[i] - g[i]; |
252 | 3.31M | } |
253 | 331k | } |
254 | | |
255 | | /* h = f * g |
256 | | * Can overlap h with f or g. |
257 | | * |
258 | | * Preconditions: |
259 | | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
260 | | * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
261 | | * |
262 | | * Postconditions: |
263 | | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
264 | | * |
265 | | * Notes on implementation strategy: |
266 | | * |
267 | | * Using schoolbook multiplication. |
268 | | * Karatsuba would save a little in some cost models. |
269 | | * |
270 | | * Most multiplications by 2 and 19 are 32-bit precomputations; |
271 | | * cheaper than 64-bit postcomputations. |
272 | | * |
273 | | * There is one remaining multiplication by 19 in the carry chain; |
274 | | * one *19 precomputation can be merged into this, |
275 | | * but the resulting data flow is considerably less clean. |
276 | | * |
277 | | * There are 12 carries below. |
278 | | * 10 of them are 2-way parallelizable and vectorizable. |
279 | | * Can get away with 11 carries, but then data flow is much deeper. |
280 | | * |
281 | | * With tighter constraints on inputs can squeeze carries into int32. */ |
282 | 418k | static void fe_mul(fe h, const fe f, const fe g) { |
283 | 418k | int32_t f0 = f[0]; |
284 | 418k | int32_t f1 = f[1]; |
285 | 418k | int32_t f2 = f[2]; |
286 | 418k | int32_t f3 = f[3]; |
287 | 418k | int32_t f4 = f[4]; |
288 | 418k | int32_t f5 = f[5]; |
289 | 418k | int32_t f6 = f[6]; |
290 | 418k | int32_t f7 = f[7]; |
291 | 418k | int32_t f8 = f[8]; |
292 | 418k | int32_t f9 = f[9]; |
293 | 418k | int32_t g0 = g[0]; |
294 | 418k | int32_t g1 = g[1]; |
295 | 418k | int32_t g2 = g[2]; |
296 | 418k | int32_t g3 = g[3]; |
297 | 418k | int32_t g4 = g[4]; |
298 | 418k | int32_t g5 = g[5]; |
299 | 418k | int32_t g6 = g[6]; |
300 | 418k | int32_t g7 = g[7]; |
301 | 418k | int32_t g8 = g[8]; |
302 | 418k | int32_t g9 = g[9]; |
303 | 418k | int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ |
304 | 418k | int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ |
305 | 418k | int32_t g3_19 = 19 * g3; |
306 | 418k | int32_t g4_19 = 19 * g4; |
307 | 418k | int32_t g5_19 = 19 * g5; |
308 | 418k | int32_t g6_19 = 19 * g6; |
309 | 418k | int32_t g7_19 = 19 * g7; |
310 | 418k | int32_t g8_19 = 19 * g8; |
311 | 418k | int32_t g9_19 = 19 * g9; |
312 | 418k | int32_t f1_2 = 2 * f1; |
313 | 418k | int32_t f3_2 = 2 * f3; |
314 | 418k | int32_t f5_2 = 2 * f5; |
315 | 418k | int32_t f7_2 = 2 * f7; |
316 | 418k | int32_t f9_2 = 2 * f9; |
317 | 418k | int64_t f0g0 = f0 * (int64_t) g0; |
318 | 418k | int64_t f0g1 = f0 * (int64_t) g1; |
319 | 418k | int64_t f0g2 = f0 * (int64_t) g2; |
320 | 418k | int64_t f0g3 = f0 * (int64_t) g3; |
321 | 418k | int64_t f0g4 = f0 * (int64_t) g4; |
322 | 418k | int64_t f0g5 = f0 * (int64_t) g5; |
323 | 418k | int64_t f0g6 = f0 * (int64_t) g6; |
324 | 418k | int64_t f0g7 = f0 * (int64_t) g7; |
325 | 418k | int64_t f0g8 = f0 * (int64_t) g8; |
326 | 418k | int64_t f0g9 = f0 * (int64_t) g9; |
327 | 418k | int64_t f1g0 = f1 * (int64_t) g0; |
328 | 418k | int64_t f1g1_2 = f1_2 * (int64_t) g1; |
329 | 418k | int64_t f1g2 = f1 * (int64_t) g2; |
330 | 418k | int64_t f1g3_2 = f1_2 * (int64_t) g3; |
331 | 418k | int64_t f1g4 = f1 * (int64_t) g4; |
332 | 418k | int64_t f1g5_2 = f1_2 * (int64_t) g5; |
333 | 418k | int64_t f1g6 = f1 * (int64_t) g6; |
334 | 418k | int64_t f1g7_2 = f1_2 * (int64_t) g7; |
335 | 418k | int64_t f1g8 = f1 * (int64_t) g8; |
336 | 418k | int64_t f1g9_38 = f1_2 * (int64_t) g9_19; |
337 | 418k | int64_t f2g0 = f2 * (int64_t) g0; |
338 | 418k | int64_t f2g1 = f2 * (int64_t) g1; |
339 | 418k | int64_t f2g2 = f2 * (int64_t) g2; |
340 | 418k | int64_t f2g3 = f2 * (int64_t) g3; |
341 | 418k | int64_t f2g4 = f2 * (int64_t) g4; |
342 | 418k | int64_t f2g5 = f2 * (int64_t) g5; |
343 | 418k | int64_t f2g6 = f2 * (int64_t) g6; |
344 | 418k | int64_t f2g7 = f2 * (int64_t) g7; |
345 | 418k | int64_t f2g8_19 = f2 * (int64_t) g8_19; |
346 | 418k | int64_t f2g9_19 = f2 * (int64_t) g9_19; |
347 | 418k | int64_t f3g0 = f3 * (int64_t) g0; |
348 | 418k | int64_t f3g1_2 = f3_2 * (int64_t) g1; |
349 | 418k | int64_t f3g2 = f3 * (int64_t) g2; |
350 | 418k | int64_t f3g3_2 = f3_2 * (int64_t) g3; |
351 | 418k | int64_t f3g4 = f3 * (int64_t) g4; |
352 | 418k | int64_t f3g5_2 = f3_2 * (int64_t) g5; |
353 | 418k | int64_t f3g6 = f3 * (int64_t) g6; |
354 | 418k | int64_t f3g7_38 = f3_2 * (int64_t) g7_19; |
355 | 418k | int64_t f3g8_19 = f3 * (int64_t) g8_19; |
356 | 418k | int64_t f3g9_38 = f3_2 * (int64_t) g9_19; |
357 | 418k | int64_t f4g0 = f4 * (int64_t) g0; |
358 | 418k | int64_t f4g1 = f4 * (int64_t) g1; |
359 | 418k | int64_t f4g2 = f4 * (int64_t) g2; |
360 | 418k | int64_t f4g3 = f4 * (int64_t) g3; |
361 | 418k | int64_t f4g4 = f4 * (int64_t) g4; |
362 | 418k | int64_t f4g5 = f4 * (int64_t) g5; |
363 | 418k | int64_t f4g6_19 = f4 * (int64_t) g6_19; |
364 | 418k | int64_t f4g7_19 = f4 * (int64_t) g7_19; |
365 | 418k | int64_t f4g8_19 = f4 * (int64_t) g8_19; |
366 | 418k | int64_t f4g9_19 = f4 * (int64_t) g9_19; |
367 | 418k | int64_t f5g0 = f5 * (int64_t) g0; |
368 | 418k | int64_t f5g1_2 = f5_2 * (int64_t) g1; |
369 | 418k | int64_t f5g2 = f5 * (int64_t) g2; |
370 | 418k | int64_t f5g3_2 = f5_2 * (int64_t) g3; |
371 | 418k | int64_t f5g4 = f5 * (int64_t) g4; |
372 | 418k | int64_t f5g5_38 = f5_2 * (int64_t) g5_19; |
373 | 418k | int64_t f5g6_19 = f5 * (int64_t) g6_19; |
374 | 418k | int64_t f5g7_38 = f5_2 * (int64_t) g7_19; |
375 | 418k | int64_t f5g8_19 = f5 * (int64_t) g8_19; |
376 | 418k | int64_t f5g9_38 = f5_2 * (int64_t) g9_19; |
377 | 418k | int64_t f6g0 = f6 * (int64_t) g0; |
378 | 418k | int64_t f6g1 = f6 * (int64_t) g1; |
379 | 418k | int64_t f6g2 = f6 * (int64_t) g2; |
380 | 418k | int64_t f6g3 = f6 * (int64_t) g3; |
381 | 418k | int64_t f6g4_19 = f6 * (int64_t) g4_19; |
382 | 418k | int64_t f6g5_19 = f6 * (int64_t) g5_19; |
383 | 418k | int64_t f6g6_19 = f6 * (int64_t) g6_19; |
384 | 418k | int64_t f6g7_19 = f6 * (int64_t) g7_19; |
385 | 418k | int64_t f6g8_19 = f6 * (int64_t) g8_19; |
386 | 418k | int64_t f6g9_19 = f6 * (int64_t) g9_19; |
387 | 418k | int64_t f7g0 = f7 * (int64_t) g0; |
388 | 418k | int64_t f7g1_2 = f7_2 * (int64_t) g1; |
389 | 418k | int64_t f7g2 = f7 * (int64_t) g2; |
390 | 418k | int64_t f7g3_38 = f7_2 * (int64_t) g3_19; |
391 | 418k | int64_t f7g4_19 = f7 * (int64_t) g4_19; |
392 | 418k | int64_t f7g5_38 = f7_2 * (int64_t) g5_19; |
393 | 418k | int64_t f7g6_19 = f7 * (int64_t) g6_19; |
394 | 418k | int64_t f7g7_38 = f7_2 * (int64_t) g7_19; |
395 | 418k | int64_t f7g8_19 = f7 * (int64_t) g8_19; |
396 | 418k | int64_t f7g9_38 = f7_2 * (int64_t) g9_19; |
397 | 418k | int64_t f8g0 = f8 * (int64_t) g0; |
398 | 418k | int64_t f8g1 = f8 * (int64_t) g1; |
399 | 418k | int64_t f8g2_19 = f8 * (int64_t) g2_19; |
400 | 418k | int64_t f8g3_19 = f8 * (int64_t) g3_19; |
401 | 418k | int64_t f8g4_19 = f8 * (int64_t) g4_19; |
402 | 418k | int64_t f8g5_19 = f8 * (int64_t) g5_19; |
403 | 418k | int64_t f8g6_19 = f8 * (int64_t) g6_19; |
404 | 418k | int64_t f8g7_19 = f8 * (int64_t) g7_19; |
405 | 418k | int64_t f8g8_19 = f8 * (int64_t) g8_19; |
406 | 418k | int64_t f8g9_19 = f8 * (int64_t) g9_19; |
407 | 418k | int64_t f9g0 = f9 * (int64_t) g0; |
408 | 418k | int64_t f9g1_38 = f9_2 * (int64_t) g1_19; |
409 | 418k | int64_t f9g2_19 = f9 * (int64_t) g2_19; |
410 | 418k | int64_t f9g3_38 = f9_2 * (int64_t) g3_19; |
411 | 418k | int64_t f9g4_19 = f9 * (int64_t) g4_19; |
412 | 418k | int64_t f9g5_38 = f9_2 * (int64_t) g5_19; |
413 | 418k | int64_t f9g6_19 = f9 * (int64_t) g6_19; |
414 | 418k | int64_t f9g7_38 = f9_2 * (int64_t) g7_19; |
415 | 418k | int64_t f9g8_19 = f9 * (int64_t) g8_19; |
416 | 418k | int64_t f9g9_38 = f9_2 * (int64_t) g9_19; |
417 | 418k | int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; |
418 | 418k | int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; |
419 | 418k | int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; |
420 | 418k | int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; |
421 | 418k | int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; |
422 | 418k | int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; |
423 | 418k | int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; |
424 | 418k | int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; |
425 | 418k | int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; |
426 | 418k | int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; |
427 | 418k | int64_t carry0; |
428 | 418k | int64_t carry1; |
429 | 418k | int64_t carry2; |
430 | 418k | int64_t carry3; |
431 | 418k | int64_t carry4; |
432 | 418k | int64_t carry5; |
433 | 418k | int64_t carry6; |
434 | 418k | int64_t carry7; |
435 | 418k | int64_t carry8; |
436 | 418k | int64_t carry9; |
437 | | |
438 | | /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) |
439 | | * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 |
440 | | * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) |
441 | | * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ |
442 | | |
443 | 418k | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
444 | 418k | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
445 | | /* |h0| <= 2^25 */ |
446 | | /* |h4| <= 2^25 */ |
447 | | /* |h1| <= 1.71*2^59 */ |
448 | | /* |h5| <= 1.71*2^59 */ |
449 | | |
450 | 418k | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
451 | 418k | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
452 | | /* |h1| <= 2^24; from now on fits into int32 */ |
453 | | /* |h5| <= 2^24; from now on fits into int32 */ |
454 | | /* |h2| <= 1.41*2^60 */ |
455 | | /* |h6| <= 1.41*2^60 */ |
456 | | |
457 | 418k | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
458 | 418k | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
459 | | /* |h2| <= 2^25; from now on fits into int32 unchanged */ |
460 | | /* |h6| <= 2^25; from now on fits into int32 unchanged */ |
461 | | /* |h3| <= 1.71*2^59 */ |
462 | | /* |h7| <= 1.71*2^59 */ |
463 | | |
464 | 418k | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
465 | 418k | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
466 | | /* |h3| <= 2^24; from now on fits into int32 unchanged */ |
467 | | /* |h7| <= 2^24; from now on fits into int32 unchanged */ |
468 | | /* |h4| <= 1.72*2^34 */ |
469 | | /* |h8| <= 1.41*2^60 */ |
470 | | |
471 | 418k | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
472 | 418k | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
473 | | /* |h4| <= 2^25; from now on fits into int32 unchanged */ |
474 | | /* |h8| <= 2^25; from now on fits into int32 unchanged */ |
475 | | /* |h5| <= 1.01*2^24 */ |
476 | | /* |h9| <= 1.71*2^59 */ |
477 | | |
478 | 418k | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
479 | | /* |h9| <= 2^24; from now on fits into int32 unchanged */ |
480 | | /* |h0| <= 1.1*2^39 */ |
481 | | |
482 | 418k | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
483 | | /* |h0| <= 2^25; from now on fits into int32 unchanged */ |
484 | | /* |h1| <= 1.01*2^24 */ |
485 | | |
486 | 418k | h[0] = h0; |
487 | 418k | h[1] = h1; |
488 | 418k | h[2] = h2; |
489 | 418k | h[3] = h3; |
490 | 418k | h[4] = h4; |
491 | 418k | h[5] = h5; |
492 | 418k | h[6] = h6; |
493 | 418k | h[7] = h7; |
494 | 418k | h[8] = h8; |
495 | 418k | h[9] = h9; |
496 | 418k | } |
497 | | |
498 | | /* h = f * f |
499 | | * Can overlap h with f. |
500 | | * |
501 | | * Preconditions: |
502 | | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
503 | | * |
504 | | * Postconditions: |
505 | | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
506 | | * |
507 | | * See fe_mul.c for discussion of implementation strategy. */ |
508 | 414k | static void fe_sq(fe h, const fe f) { |
509 | 414k | int32_t f0 = f[0]; |
510 | 414k | int32_t f1 = f[1]; |
511 | 414k | int32_t f2 = f[2]; |
512 | 414k | int32_t f3 = f[3]; |
513 | 414k | int32_t f4 = f[4]; |
514 | 414k | int32_t f5 = f[5]; |
515 | 414k | int32_t f6 = f[6]; |
516 | 414k | int32_t f7 = f[7]; |
517 | 414k | int32_t f8 = f[8]; |
518 | 414k | int32_t f9 = f[9]; |
519 | 414k | int32_t f0_2 = 2 * f0; |
520 | 414k | int32_t f1_2 = 2 * f1; |
521 | 414k | int32_t f2_2 = 2 * f2; |
522 | 414k | int32_t f3_2 = 2 * f3; |
523 | 414k | int32_t f4_2 = 2 * f4; |
524 | 414k | int32_t f5_2 = 2 * f5; |
525 | 414k | int32_t f6_2 = 2 * f6; |
526 | 414k | int32_t f7_2 = 2 * f7; |
527 | 414k | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ |
528 | 414k | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ |
529 | 414k | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ |
530 | 414k | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ |
531 | 414k | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ |
532 | 414k | int64_t f0f0 = f0 * (int64_t) f0; |
533 | 414k | int64_t f0f1_2 = f0_2 * (int64_t) f1; |
534 | 414k | int64_t f0f2_2 = f0_2 * (int64_t) f2; |
535 | 414k | int64_t f0f3_2 = f0_2 * (int64_t) f3; |
536 | 414k | int64_t f0f4_2 = f0_2 * (int64_t) f4; |
537 | 414k | int64_t f0f5_2 = f0_2 * (int64_t) f5; |
538 | 414k | int64_t f0f6_2 = f0_2 * (int64_t) f6; |
539 | 414k | int64_t f0f7_2 = f0_2 * (int64_t) f7; |
540 | 414k | int64_t f0f8_2 = f0_2 * (int64_t) f8; |
541 | 414k | int64_t f0f9_2 = f0_2 * (int64_t) f9; |
542 | 414k | int64_t f1f1_2 = f1_2 * (int64_t) f1; |
543 | 414k | int64_t f1f2_2 = f1_2 * (int64_t) f2; |
544 | 414k | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; |
545 | 414k | int64_t f1f4_2 = f1_2 * (int64_t) f4; |
546 | 414k | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; |
547 | 414k | int64_t f1f6_2 = f1_2 * (int64_t) f6; |
548 | 414k | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; |
549 | 414k | int64_t f1f8_2 = f1_2 * (int64_t) f8; |
550 | 414k | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; |
551 | 414k | int64_t f2f2 = f2 * (int64_t) f2; |
552 | 414k | int64_t f2f3_2 = f2_2 * (int64_t) f3; |
553 | 414k | int64_t f2f4_2 = f2_2 * (int64_t) f4; |
554 | 414k | int64_t f2f5_2 = f2_2 * (int64_t) f5; |
555 | 414k | int64_t f2f6_2 = f2_2 * (int64_t) f6; |
556 | 414k | int64_t f2f7_2 = f2_2 * (int64_t) f7; |
557 | 414k | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; |
558 | 414k | int64_t f2f9_38 = f2 * (int64_t) f9_38; |
559 | 414k | int64_t f3f3_2 = f3_2 * (int64_t) f3; |
560 | 414k | int64_t f3f4_2 = f3_2 * (int64_t) f4; |
561 | 414k | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; |
562 | 414k | int64_t f3f6_2 = f3_2 * (int64_t) f6; |
563 | 414k | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; |
564 | 414k | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; |
565 | 414k | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; |
566 | 414k | int64_t f4f4 = f4 * (int64_t) f4; |
567 | 414k | int64_t f4f5_2 = f4_2 * (int64_t) f5; |
568 | 414k | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; |
569 | 414k | int64_t f4f7_38 = f4 * (int64_t) f7_38; |
570 | 414k | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; |
571 | 414k | int64_t f4f9_38 = f4 * (int64_t) f9_38; |
572 | 414k | int64_t f5f5_38 = f5 * (int64_t) f5_38; |
573 | 414k | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; |
574 | 414k | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; |
575 | 414k | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; |
576 | 414k | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; |
577 | 414k | int64_t f6f6_19 = f6 * (int64_t) f6_19; |
578 | 414k | int64_t f6f7_38 = f6 * (int64_t) f7_38; |
579 | 414k | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; |
580 | 414k | int64_t f6f9_38 = f6 * (int64_t) f9_38; |
581 | 414k | int64_t f7f7_38 = f7 * (int64_t) f7_38; |
582 | 414k | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; |
583 | 414k | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; |
584 | 414k | int64_t f8f8_19 = f8 * (int64_t) f8_19; |
585 | 414k | int64_t f8f9_38 = f8 * (int64_t) f9_38; |
586 | 414k | int64_t f9f9_38 = f9 * (int64_t) f9_38; |
587 | 414k | int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; |
588 | 414k | int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; |
589 | 414k | int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; |
590 | 414k | int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; |
591 | 414k | int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; |
592 | 414k | int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; |
593 | 414k | int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; |
594 | 414k | int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; |
595 | 414k | int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; |
596 | 414k | int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; |
597 | 414k | int64_t carry0; |
598 | 414k | int64_t carry1; |
599 | 414k | int64_t carry2; |
600 | 414k | int64_t carry3; |
601 | 414k | int64_t carry4; |
602 | 414k | int64_t carry5; |
603 | 414k | int64_t carry6; |
604 | 414k | int64_t carry7; |
605 | 414k | int64_t carry8; |
606 | 414k | int64_t carry9; |
607 | | |
608 | 414k | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
609 | 414k | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
610 | | |
611 | 414k | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
612 | 414k | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
613 | | |
614 | 414k | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
615 | 414k | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
616 | | |
617 | 414k | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
618 | 414k | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
619 | | |
620 | 414k | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
621 | 414k | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
622 | | |
623 | 414k | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
624 | | |
625 | 414k | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
626 | | |
627 | 414k | h[0] = h0; |
628 | 414k | h[1] = h1; |
629 | 414k | h[2] = h2; |
630 | 414k | h[3] = h3; |
631 | 414k | h[4] = h4; |
632 | 414k | h[5] = h5; |
633 | 414k | h[6] = h6; |
634 | 414k | h[7] = h7; |
635 | 414k | h[8] = h8; |
636 | 414k | h[9] = h9; |
637 | 414k | } |
638 | | |
639 | 325 | static void fe_invert(fe out, const fe z) { |
640 | 325 | fe t0; |
641 | 325 | fe t1; |
642 | 325 | fe t2; |
643 | 325 | fe t3; |
644 | 325 | int i; |
645 | | |
646 | 325 | fe_sq(t0, z); |
647 | 325 | for (i = 1; i < 1; ++i) { |
648 | 0 | fe_sq(t0, t0); |
649 | 0 | } |
650 | 325 | fe_sq(t1, t0); |
651 | 650 | for (i = 1; i < 2; ++i) { |
652 | 325 | fe_sq(t1, t1); |
653 | 325 | } |
654 | 325 | fe_mul(t1, z, t1); |
655 | 325 | fe_mul(t0, t0, t1); |
656 | 325 | fe_sq(t2, t0); |
657 | 325 | for (i = 1; i < 1; ++i) { |
658 | 0 | fe_sq(t2, t2); |
659 | 0 | } |
660 | 325 | fe_mul(t1, t1, t2); |
661 | 325 | fe_sq(t2, t1); |
662 | 1.62k | for (i = 1; i < 5; ++i) { |
663 | 1.30k | fe_sq(t2, t2); |
664 | 1.30k | } |
665 | 325 | fe_mul(t1, t2, t1); |
666 | 325 | fe_sq(t2, t1); |
667 | 3.25k | for (i = 1; i < 10; ++i) { |
668 | 2.92k | fe_sq(t2, t2); |
669 | 2.92k | } |
670 | 325 | fe_mul(t2, t2, t1); |
671 | 325 | fe_sq(t3, t2); |
672 | 6.50k | for (i = 1; i < 20; ++i) { |
673 | 6.17k | fe_sq(t3, t3); |
674 | 6.17k | } |
675 | 325 | fe_mul(t2, t3, t2); |
676 | 325 | fe_sq(t2, t2); |
677 | 3.25k | for (i = 1; i < 10; ++i) { |
678 | 2.92k | fe_sq(t2, t2); |
679 | 2.92k | } |
680 | 325 | fe_mul(t1, t2, t1); |
681 | 325 | fe_sq(t2, t1); |
682 | 16.2k | for (i = 1; i < 50; ++i) { |
683 | 15.9k | fe_sq(t2, t2); |
684 | 15.9k | } |
685 | 325 | fe_mul(t2, t2, t1); |
686 | 325 | fe_sq(t3, t2); |
687 | 32.5k | for (i = 1; i < 100; ++i) { |
688 | 32.1k | fe_sq(t3, t3); |
689 | 32.1k | } |
690 | 325 | fe_mul(t2, t3, t2); |
691 | 325 | fe_sq(t2, t2); |
692 | 16.2k | for (i = 1; i < 50; ++i) { |
693 | 15.9k | fe_sq(t2, t2); |
694 | 15.9k | } |
695 | 325 | fe_mul(t1, t2, t1); |
696 | 325 | fe_sq(t1, t1); |
697 | 1.62k | for (i = 1; i < 5; ++i) { |
698 | 1.30k | fe_sq(t1, t1); |
699 | 1.30k | } |
700 | 325 | fe_mul(out, t1, t0); |
701 | 325 | } |
702 | | |
703 | | /* h = -f |
704 | | * |
705 | | * Preconditions: |
706 | | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
707 | | * |
708 | | * Postconditions: |
709 | | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ |
710 | 0 | static void fe_neg(fe h, const fe f) { |
711 | 0 | unsigned i; |
712 | 0 | for (i = 0; i < 10; i++) { |
713 | 0 | h[i] = -f[i]; |
714 | 0 | } |
715 | 0 | } |
716 | | |
717 | | /* Replace (f,g) with (g,g) if b == 1; |
718 | | * replace (f,g) with (f,g) if b == 0. |
719 | | * |
720 | | * Preconditions: b in {0,1}. */ |
721 | 0 | static void fe_cmov(fe f, const fe g, unsigned b) { |
722 | 0 | b = 0-b; |
723 | 0 | unsigned i; |
724 | 0 | for (i = 0; i < 10; i++) { |
725 | 0 | int32_t x = f[i] ^ g[i]; |
726 | 0 | x &= b; |
727 | 0 | f[i] ^= x; |
728 | 0 | } |
729 | 0 | } |
730 | | |
731 | | /* return 0 if f == 0 |
732 | | * return 1 if f != 0 |
733 | | * |
734 | | * Preconditions: |
735 | | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ |
736 | 0 | static int fe_isnonzero(const fe f) { |
737 | 0 | uint8_t s[32]; |
738 | 0 | fe_tobytes(s, f); |
739 | |
|
740 | 0 | static const uint8_t zero[32] = {0}; |
741 | 0 | return timingsafe_memcmp(s, zero, sizeof(zero)) != 0; |
742 | 0 | } |
743 | | |
744 | | /* return 1 if f is in {1,3,5,...,q-2} |
745 | | * return 0 if f is in {0,2,4,...,q-1} |
746 | | * |
747 | | * Preconditions: |
748 | | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ |
749 | 0 | static int fe_isnegative(const fe f) { |
750 | 0 | uint8_t s[32]; |
751 | 0 | fe_tobytes(s, f); |
752 | 0 | return s[0] & 1; |
753 | 0 | } |
754 | | |
755 | | /* h = 2 * f * f |
756 | | * Can overlap h with f. |
757 | | * |
758 | | * Preconditions: |
759 | | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
760 | | * |
761 | | * Postconditions: |
762 | | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
763 | | * |
764 | | * See fe_mul.c for discussion of implementation strategy. */ |
765 | 0 | static void fe_sq2(fe h, const fe f) { |
766 | 0 | int32_t f0 = f[0]; |
767 | 0 | int32_t f1 = f[1]; |
768 | 0 | int32_t f2 = f[2]; |
769 | 0 | int32_t f3 = f[3]; |
770 | 0 | int32_t f4 = f[4]; |
771 | 0 | int32_t f5 = f[5]; |
772 | 0 | int32_t f6 = f[6]; |
773 | 0 | int32_t f7 = f[7]; |
774 | 0 | int32_t f8 = f[8]; |
775 | 0 | int32_t f9 = f[9]; |
776 | 0 | int32_t f0_2 = 2 * f0; |
777 | 0 | int32_t f1_2 = 2 * f1; |
778 | 0 | int32_t f2_2 = 2 * f2; |
779 | 0 | int32_t f3_2 = 2 * f3; |
780 | 0 | int32_t f4_2 = 2 * f4; |
781 | 0 | int32_t f5_2 = 2 * f5; |
782 | 0 | int32_t f6_2 = 2 * f6; |
783 | 0 | int32_t f7_2 = 2 * f7; |
784 | 0 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ |
785 | 0 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ |
786 | 0 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ |
787 | 0 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ |
788 | 0 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ |
789 | 0 | int64_t f0f0 = f0 * (int64_t) f0; |
790 | 0 | int64_t f0f1_2 = f0_2 * (int64_t) f1; |
791 | 0 | int64_t f0f2_2 = f0_2 * (int64_t) f2; |
792 | 0 | int64_t f0f3_2 = f0_2 * (int64_t) f3; |
793 | 0 | int64_t f0f4_2 = f0_2 * (int64_t) f4; |
794 | 0 | int64_t f0f5_2 = f0_2 * (int64_t) f5; |
795 | 0 | int64_t f0f6_2 = f0_2 * (int64_t) f6; |
796 | 0 | int64_t f0f7_2 = f0_2 * (int64_t) f7; |
797 | 0 | int64_t f0f8_2 = f0_2 * (int64_t) f8; |
798 | 0 | int64_t f0f9_2 = f0_2 * (int64_t) f9; |
799 | 0 | int64_t f1f1_2 = f1_2 * (int64_t) f1; |
800 | 0 | int64_t f1f2_2 = f1_2 * (int64_t) f2; |
801 | 0 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; |
802 | 0 | int64_t f1f4_2 = f1_2 * (int64_t) f4; |
803 | 0 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; |
804 | 0 | int64_t f1f6_2 = f1_2 * (int64_t) f6; |
805 | 0 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; |
806 | 0 | int64_t f1f8_2 = f1_2 * (int64_t) f8; |
807 | 0 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; |
808 | 0 | int64_t f2f2 = f2 * (int64_t) f2; |
809 | 0 | int64_t f2f3_2 = f2_2 * (int64_t) f3; |
810 | 0 | int64_t f2f4_2 = f2_2 * (int64_t) f4; |
811 | 0 | int64_t f2f5_2 = f2_2 * (int64_t) f5; |
812 | 0 | int64_t f2f6_2 = f2_2 * (int64_t) f6; |
813 | 0 | int64_t f2f7_2 = f2_2 * (int64_t) f7; |
814 | 0 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; |
815 | 0 | int64_t f2f9_38 = f2 * (int64_t) f9_38; |
816 | 0 | int64_t f3f3_2 = f3_2 * (int64_t) f3; |
817 | 0 | int64_t f3f4_2 = f3_2 * (int64_t) f4; |
818 | 0 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; |
819 | 0 | int64_t f3f6_2 = f3_2 * (int64_t) f6; |
820 | 0 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; |
821 | 0 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; |
822 | 0 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; |
823 | 0 | int64_t f4f4 = f4 * (int64_t) f4; |
824 | 0 | int64_t f4f5_2 = f4_2 * (int64_t) f5; |
825 | 0 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; |
826 | 0 | int64_t f4f7_38 = f4 * (int64_t) f7_38; |
827 | 0 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; |
828 | 0 | int64_t f4f9_38 = f4 * (int64_t) f9_38; |
829 | 0 | int64_t f5f5_38 = f5 * (int64_t) f5_38; |
830 | 0 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; |
831 | 0 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; |
832 | 0 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; |
833 | 0 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; |
834 | 0 | int64_t f6f6_19 = f6 * (int64_t) f6_19; |
835 | 0 | int64_t f6f7_38 = f6 * (int64_t) f7_38; |
836 | 0 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; |
837 | 0 | int64_t f6f9_38 = f6 * (int64_t) f9_38; |
838 | 0 | int64_t f7f7_38 = f7 * (int64_t) f7_38; |
839 | 0 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; |
840 | 0 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; |
841 | 0 | int64_t f8f8_19 = f8 * (int64_t) f8_19; |
842 | 0 | int64_t f8f9_38 = f8 * (int64_t) f9_38; |
843 | 0 | int64_t f9f9_38 = f9 * (int64_t) f9_38; |
844 | 0 | int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; |
845 | 0 | int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; |
846 | 0 | int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; |
847 | 0 | int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; |
848 | 0 | int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; |
849 | 0 | int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; |
850 | 0 | int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; |
851 | 0 | int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; |
852 | 0 | int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; |
853 | 0 | int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; |
854 | 0 | int64_t carry0; |
855 | 0 | int64_t carry1; |
856 | 0 | int64_t carry2; |
857 | 0 | int64_t carry3; |
858 | 0 | int64_t carry4; |
859 | 0 | int64_t carry5; |
860 | 0 | int64_t carry6; |
861 | 0 | int64_t carry7; |
862 | 0 | int64_t carry8; |
863 | 0 | int64_t carry9; |
864 | |
|
865 | 0 | h0 += h0; |
866 | 0 | h1 += h1; |
867 | 0 | h2 += h2; |
868 | 0 | h3 += h3; |
869 | 0 | h4 += h4; |
870 | 0 | h5 += h5; |
871 | 0 | h6 += h6; |
872 | 0 | h7 += h7; |
873 | 0 | h8 += h8; |
874 | 0 | h9 += h9; |
875 | |
|
876 | 0 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
877 | 0 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
878 | |
|
879 | 0 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
880 | 0 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
881 | |
|
882 | 0 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
883 | 0 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
884 | |
|
885 | 0 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
886 | 0 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
887 | |
|
888 | 0 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
889 | 0 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
890 | |
|
891 | 0 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
892 | |
|
893 | 0 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
894 | |
|
895 | 0 | h[0] = h0; |
896 | 0 | h[1] = h1; |
897 | 0 | h[2] = h2; |
898 | 0 | h[3] = h3; |
899 | 0 | h[4] = h4; |
900 | 0 | h[5] = h5; |
901 | 0 | h[6] = h6; |
902 | 0 | h[7] = h7; |
903 | 0 | h[8] = h8; |
904 | 0 | h[9] = h9; |
905 | 0 | } |
906 | | |
907 | 0 | static void fe_pow22523(fe out, const fe z) { |
908 | 0 | fe t0; |
909 | 0 | fe t1; |
910 | 0 | fe t2; |
911 | 0 | int i; |
912 | |
|
913 | 0 | fe_sq(t0, z); |
914 | 0 | for (i = 1; i < 1; ++i) { |
915 | 0 | fe_sq(t0, t0); |
916 | 0 | } |
917 | 0 | fe_sq(t1, t0); |
918 | 0 | for (i = 1; i < 2; ++i) { |
919 | 0 | fe_sq(t1, t1); |
920 | 0 | } |
921 | 0 | fe_mul(t1, z, t1); |
922 | 0 | fe_mul(t0, t0, t1); |
923 | 0 | fe_sq(t0, t0); |
924 | 0 | for (i = 1; i < 1; ++i) { |
925 | 0 | fe_sq(t0, t0); |
926 | 0 | } |
927 | 0 | fe_mul(t0, t1, t0); |
928 | 0 | fe_sq(t1, t0); |
929 | 0 | for (i = 1; i < 5; ++i) { |
930 | 0 | fe_sq(t1, t1); |
931 | 0 | } |
932 | 0 | fe_mul(t0, t1, t0); |
933 | 0 | fe_sq(t1, t0); |
934 | 0 | for (i = 1; i < 10; ++i) { |
935 | 0 | fe_sq(t1, t1); |
936 | 0 | } |
937 | 0 | fe_mul(t1, t1, t0); |
938 | 0 | fe_sq(t2, t1); |
939 | 0 | for (i = 1; i < 20; ++i) { |
940 | 0 | fe_sq(t2, t2); |
941 | 0 | } |
942 | 0 | fe_mul(t1, t2, t1); |
943 | 0 | fe_sq(t1, t1); |
944 | 0 | for (i = 1; i < 10; ++i) { |
945 | 0 | fe_sq(t1, t1); |
946 | 0 | } |
947 | 0 | fe_mul(t0, t1, t0); |
948 | 0 | fe_sq(t1, t0); |
949 | 0 | for (i = 1; i < 50; ++i) { |
950 | 0 | fe_sq(t1, t1); |
951 | 0 | } |
952 | 0 | fe_mul(t1, t1, t0); |
953 | 0 | fe_sq(t2, t1); |
954 | 0 | for (i = 1; i < 100; ++i) { |
955 | 0 | fe_sq(t2, t2); |
956 | 0 | } |
957 | 0 | fe_mul(t1, t2, t1); |
958 | 0 | fe_sq(t1, t1); |
959 | 0 | for (i = 1; i < 50; ++i) { |
960 | 0 | fe_sq(t1, t1); |
961 | 0 | } |
962 | 0 | fe_mul(t0, t1, t0); |
963 | 0 | fe_sq(t0, t0); |
964 | 0 | for (i = 1; i < 2; ++i) { |
965 | 0 | fe_sq(t0, t0); |
966 | 0 | } |
967 | 0 | fe_mul(out, t0, z); |
968 | 0 | } |
969 | | |
970 | 0 | void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h) { |
971 | 0 | fe recip; |
972 | 0 | fe x; |
973 | 0 | fe y; |
974 | |
|
975 | 0 | fe_invert(recip, h->Z); |
976 | 0 | fe_mul(x, h->X, recip); |
977 | 0 | fe_mul(y, h->Y, recip); |
978 | 0 | fe_tobytes(s, y); |
979 | 0 | s[31] ^= fe_isnegative(x) << 7; |
980 | 0 | } |
981 | | |
982 | | #ifdef ED25519 |
983 | | static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) { |
984 | | fe recip; |
985 | | fe x; |
986 | | fe y; |
987 | | |
988 | | fe_invert(recip, h->Z); |
989 | | fe_mul(x, h->X, recip); |
990 | | fe_mul(y, h->Y, recip); |
991 | | fe_tobytes(s, y); |
992 | | s[31] ^= fe_isnegative(x) << 7; |
993 | | } |
994 | | #endif |
995 | | |
996 | | static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729, |
997 | | -8787816, -6275908, -3247719, -18696448, -12055116}; |
998 | | |
999 | | static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, |
1000 | | -272473, -25146209, -2005654, 326686, 11406482}; |
1001 | | |
1002 | 0 | int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { |
1003 | 0 | fe u; |
1004 | 0 | fe v; |
1005 | 0 | fe v3; |
1006 | 0 | fe vxx; |
1007 | 0 | fe check; |
1008 | |
|
1009 | 0 | fe_frombytes(h->Y, s); |
1010 | 0 | fe_1(h->Z); |
1011 | 0 | fe_sq(u, h->Y); |
1012 | 0 | fe_mul(v, u, d); |
1013 | 0 | fe_sub(u, u, h->Z); /* u = y^2-1 */ |
1014 | 0 | fe_add(v, v, h->Z); /* v = dy^2+1 */ |
1015 | |
|
1016 | 0 | fe_sq(v3, v); |
1017 | 0 | fe_mul(v3, v3, v); /* v3 = v^3 */ |
1018 | 0 | fe_sq(h->X, v3); |
1019 | 0 | fe_mul(h->X, h->X, v); |
1020 | 0 | fe_mul(h->X, h->X, u); /* x = uv^7 */ |
1021 | |
|
1022 | 0 | fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ |
1023 | 0 | fe_mul(h->X, h->X, v3); |
1024 | 0 | fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ |
1025 | |
|
1026 | 0 | fe_sq(vxx, h->X); |
1027 | 0 | fe_mul(vxx, vxx, v); |
1028 | 0 | fe_sub(check, vxx, u); /* vx^2-u */ |
1029 | 0 | if (fe_isnonzero(check)) { |
1030 | 0 | fe_add(check, vxx, u); /* vx^2+u */ |
1031 | 0 | if (fe_isnonzero(check)) { |
1032 | 0 | return -1; |
1033 | 0 | } |
1034 | 0 | fe_mul(h->X, h->X, sqrtm1); |
1035 | 0 | } |
1036 | | |
1037 | 0 | if (fe_isnegative(h->X) != (s[31] >> 7)) { |
1038 | 0 | fe_neg(h->X, h->X); |
1039 | 0 | } |
1040 | |
|
1041 | 0 | fe_mul(h->T, h->X, h->Y); |
1042 | 0 | return 0; |
1043 | 0 | } |
1044 | | |
1045 | 0 | static void ge_p2_0(ge_p2 *h) { |
1046 | 0 | fe_0(h->X); |
1047 | 0 | fe_1(h->Y); |
1048 | 0 | fe_1(h->Z); |
1049 | 0 | } |
1050 | | |
1051 | 0 | static void ge_p3_0(ge_p3 *h) { |
1052 | 0 | fe_0(h->X); |
1053 | 0 | fe_1(h->Y); |
1054 | 0 | fe_1(h->Z); |
1055 | 0 | fe_0(h->T); |
1056 | 0 | } |
1057 | | |
1058 | 0 | static void ge_cached_0(ge_cached *h) { |
1059 | 0 | fe_1(h->YplusX); |
1060 | 0 | fe_1(h->YminusX); |
1061 | 0 | fe_1(h->Z); |
1062 | 0 | fe_0(h->T2d); |
1063 | 0 | } |
1064 | | |
1065 | 0 | static void ge_precomp_0(ge_precomp *h) { |
1066 | 0 | fe_1(h->yplusx); |
1067 | 0 | fe_1(h->yminusx); |
1068 | 0 | fe_0(h->xy2d); |
1069 | 0 | } |
1070 | | |
1071 | | /* r = p */ |
1072 | 0 | static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { |
1073 | 0 | fe_copy(r->X, p->X); |
1074 | 0 | fe_copy(r->Y, p->Y); |
1075 | 0 | fe_copy(r->Z, p->Z); |
1076 | 0 | } |
1077 | | |
1078 | | static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458, |
1079 | | 15978800, -12551817, -6495438, 29715968, 9444199}; |
1080 | | |
1081 | | /* r = p */ |
1082 | 0 | void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { |
1083 | 0 | fe_add(r->YplusX, p->Y, p->X); |
1084 | 0 | fe_sub(r->YminusX, p->Y, p->X); |
1085 | 0 | fe_copy(r->Z, p->Z); |
1086 | 0 | fe_mul(r->T2d, p->T, d2); |
1087 | 0 | } |
1088 | | |
1089 | | /* r = p */ |
1090 | 0 | void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { |
1091 | 0 | fe_mul(r->X, p->X, p->T); |
1092 | 0 | fe_mul(r->Y, p->Y, p->Z); |
1093 | 0 | fe_mul(r->Z, p->Z, p->T); |
1094 | 0 | } |
1095 | | |
1096 | | /* r = p */ |
1097 | 0 | void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { |
1098 | 0 | fe_mul(r->X, p->X, p->T); |
1099 | 0 | fe_mul(r->Y, p->Y, p->Z); |
1100 | 0 | fe_mul(r->Z, p->Z, p->T); |
1101 | 0 | fe_mul(r->T, p->X, p->Y); |
1102 | 0 | } |
1103 | | |
1104 | | /* r = p */ |
1105 | 0 | static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) { |
1106 | 0 | ge_p3 t; |
1107 | 0 | x25519_ge_p1p1_to_p3(&t, p); |
1108 | 0 | x25519_ge_p3_to_cached(r, &t); |
1109 | 0 | } |
1110 | | |
1111 | | /* r = 2 * p */ |
1112 | 0 | static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { |
1113 | 0 | fe t0; |
1114 | |
|
1115 | 0 | fe_sq(r->X, p->X); |
1116 | 0 | fe_sq(r->Z, p->Y); |
1117 | 0 | fe_sq2(r->T, p->Z); |
1118 | 0 | fe_add(r->Y, p->X, p->Y); |
1119 | 0 | fe_sq(t0, r->Y); |
1120 | 0 | fe_add(r->Y, r->Z, r->X); |
1121 | 0 | fe_sub(r->Z, r->Z, r->X); |
1122 | 0 | fe_sub(r->X, t0, r->Y); |
1123 | 0 | fe_sub(r->T, r->T, r->Z); |
1124 | 0 | } |
1125 | | |
1126 | | /* r = 2 * p */ |
1127 | 0 | static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { |
1128 | 0 | ge_p2 q; |
1129 | 0 | ge_p3_to_p2(&q, p); |
1130 | 0 | ge_p2_dbl(r, &q); |
1131 | 0 | } |
1132 | | |
1133 | | /* r = p + q */ |
1134 | 0 | static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
1135 | 0 | fe t0; |
1136 | |
|
1137 | 0 | fe_add(r->X, p->Y, p->X); |
1138 | 0 | fe_sub(r->Y, p->Y, p->X); |
1139 | 0 | fe_mul(r->Z, r->X, q->yplusx); |
1140 | 0 | fe_mul(r->Y, r->Y, q->yminusx); |
1141 | 0 | fe_mul(r->T, q->xy2d, p->T); |
1142 | 0 | fe_add(t0, p->Z, p->Z); |
1143 | 0 | fe_sub(r->X, r->Z, r->Y); |
1144 | 0 | fe_add(r->Y, r->Z, r->Y); |
1145 | 0 | fe_add(r->Z, t0, r->T); |
1146 | 0 | fe_sub(r->T, t0, r->T); |
1147 | 0 | } |
1148 | | |
1149 | | #ifdef ED25519 |
1150 | | /* r = p - q */ |
1151 | | static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
1152 | | fe t0; |
1153 | | |
1154 | | fe_add(r->X, p->Y, p->X); |
1155 | | fe_sub(r->Y, p->Y, p->X); |
1156 | | fe_mul(r->Z, r->X, q->yminusx); |
1157 | | fe_mul(r->Y, r->Y, q->yplusx); |
1158 | | fe_mul(r->T, q->xy2d, p->T); |
1159 | | fe_add(t0, p->Z, p->Z); |
1160 | | fe_sub(r->X, r->Z, r->Y); |
1161 | | fe_add(r->Y, r->Z, r->Y); |
1162 | | fe_sub(r->Z, t0, r->T); |
1163 | | fe_add(r->T, t0, r->T); |
1164 | | } |
1165 | | #endif |
1166 | | |
1167 | | /* r = p + q */ |
1168 | 0 | void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
1169 | 0 | fe t0; |
1170 | |
|
1171 | 0 | fe_add(r->X, p->Y, p->X); |
1172 | 0 | fe_sub(r->Y, p->Y, p->X); |
1173 | 0 | fe_mul(r->Z, r->X, q->YplusX); |
1174 | 0 | fe_mul(r->Y, r->Y, q->YminusX); |
1175 | 0 | fe_mul(r->T, q->T2d, p->T); |
1176 | 0 | fe_mul(r->X, p->Z, q->Z); |
1177 | 0 | fe_add(t0, r->X, r->X); |
1178 | 0 | fe_sub(r->X, r->Z, r->Y); |
1179 | 0 | fe_add(r->Y, r->Z, r->Y); |
1180 | 0 | fe_add(r->Z, t0, r->T); |
1181 | 0 | fe_sub(r->T, t0, r->T); |
1182 | 0 | } |
1183 | | |
1184 | | /* r = p - q */ |
1185 | 0 | void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
1186 | 0 | fe t0; |
1187 | |
|
1188 | 0 | fe_add(r->X, p->Y, p->X); |
1189 | 0 | fe_sub(r->Y, p->Y, p->X); |
1190 | 0 | fe_mul(r->Z, r->X, q->YminusX); |
1191 | 0 | fe_mul(r->Y, r->Y, q->YplusX); |
1192 | 0 | fe_mul(r->T, q->T2d, p->T); |
1193 | 0 | fe_mul(r->X, p->Z, q->Z); |
1194 | 0 | fe_add(t0, r->X, r->X); |
1195 | 0 | fe_sub(r->X, r->Z, r->Y); |
1196 | 0 | fe_add(r->Y, r->Z, r->Y); |
1197 | 0 | fe_sub(r->Z, t0, r->T); |
1198 | 0 | fe_add(r->T, t0, r->T); |
1199 | 0 | } |
1200 | | |
1201 | 0 | static uint8_t equal(signed char b, signed char c) { |
1202 | 0 | uint8_t ub = b; |
1203 | 0 | uint8_t uc = c; |
1204 | 0 | uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ |
1205 | 0 | uint32_t y = x; /* 0: yes; 1..255: no */ |
1206 | 0 | y -= 1; /* 4294967295: yes; 0..254: no */ |
1207 | 0 | y >>= 31; /* 1: yes; 0: no */ |
1208 | 0 | return y; |
1209 | 0 | } |
1210 | | |
1211 | 0 | static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { |
1212 | 0 | fe_cmov(t->yplusx, u->yplusx, b); |
1213 | 0 | fe_cmov(t->yminusx, u->yminusx, b); |
1214 | 0 | fe_cmov(t->xy2d, u->xy2d, b); |
1215 | 0 | } |
1216 | | |
1217 | | void x25519_ge_scalarmult_small_precomp( |
1218 | 0 | ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) { |
1219 | | /* precomp_table is first expanded into matching |ge_precomp| |
1220 | | * elements. */ |
1221 | 0 | ge_precomp multiples[15]; |
1222 | |
|
1223 | 0 | unsigned i; |
1224 | 0 | for (i = 0; i < 15; i++) { |
1225 | 0 | const uint8_t *bytes = &precomp_table[i*(2 * 32)]; |
1226 | 0 | fe x, y; |
1227 | 0 | fe_frombytes(x, bytes); |
1228 | 0 | fe_frombytes(y, bytes + 32); |
1229 | |
|
1230 | 0 | ge_precomp *out = &multiples[i]; |
1231 | 0 | fe_add(out->yplusx, y, x); |
1232 | 0 | fe_sub(out->yminusx, y, x); |
1233 | 0 | fe_mul(out->xy2d, x, y); |
1234 | 0 | fe_mul(out->xy2d, out->xy2d, d2); |
1235 | 0 | } |
1236 | | |
1237 | | /* See the comment above |k25519SmallPrecomp| about the structure of the |
1238 | | * precomputed elements. This loop does 64 additions and 64 doublings to |
1239 | | * calculate the result. */ |
1240 | 0 | ge_p3_0(h); |
1241 | |
|
1242 | 0 | for (i = 63; i < 64; i--) { |
1243 | 0 | unsigned j; |
1244 | 0 | signed char index = 0; |
1245 | |
|
1246 | 0 | for (j = 0; j < 4; j++) { |
1247 | 0 | const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7)); |
1248 | 0 | index |= (bit << j); |
1249 | 0 | } |
1250 | |
|
1251 | 0 | ge_precomp e; |
1252 | 0 | ge_precomp_0(&e); |
1253 | |
|
1254 | 0 | for (j = 1; j < 16; j++) { |
1255 | 0 | cmov(&e, &multiples[j-1], equal(index, j)); |
1256 | 0 | } |
1257 | |
|
1258 | 0 | ge_cached cached; |
1259 | 0 | ge_p1p1 r; |
1260 | 0 | x25519_ge_p3_to_cached(&cached, h); |
1261 | 0 | x25519_ge_add(&r, h, &cached); |
1262 | 0 | x25519_ge_p1p1_to_p3(h, &r); |
1263 | |
|
1264 | 0 | ge_madd(&r, h, &e); |
1265 | 0 | x25519_ge_p1p1_to_p3(h, &r); |
1266 | 0 | } |
1267 | 0 | } |
1268 | | |
1269 | | #if defined(OPENSSL_SMALL) |
1270 | | |
1271 | | /* This block of code replaces the standard base-point table with a much smaller |
1272 | | * one. The standard table is 30,720 bytes while this one is just 960. |
1273 | | * |
1274 | | * This table contains 15 pairs of group elements, (x, y), where each field |
1275 | | * element is serialised with |fe_tobytes|. If |i| is the index of the group |
1276 | | * element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀ |
1277 | | * is the most significant bit). The value of the group element is then: |
1278 | | * (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. */ |
1279 | | static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = { |
1280 | | 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, |
1281 | | 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, |
1282 | | 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66, |
1283 | | 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, |
1284 | | 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, |
1285 | | 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e, |
1286 | | 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4, |
1287 | | 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62, |
1288 | | 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba, |
1289 | | 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd, |
1290 | | 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61, |
1291 | | 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c, |
1292 | | 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c, |
1293 | | 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5, |
1294 | | 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3, |
1295 | | 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18, |
1296 | | 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2, |
1297 | | 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95, |
1298 | | 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b, |
1299 | | 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90, |
1300 | | 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52, |
1301 | | 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb, |
1302 | | 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c, |
1303 | | 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e, |
1304 | | 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e, |
1305 | | 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a, |
1306 | | 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43, |
1307 | | 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53, |
1308 | | 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8, |
1309 | | 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89, |
1310 | | 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef, |
1311 | | 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60, |
1312 | | 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a, |
1313 | | 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8, |
1314 | | 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54, |
1315 | | 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b, |
1316 | | 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd, |
1317 | | 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb, |
1318 | | 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c, |
1319 | | 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b, |
1320 | | 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63, |
1321 | | 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a, |
1322 | | 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07, |
1323 | | 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa, |
1324 | | 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a, |
1325 | | 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84, |
1326 | | 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc, |
1327 | | 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42, |
1328 | | 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0, |
1329 | | 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0, |
1330 | | 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a, |
1331 | | 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5, |
1332 | | 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c, |
1333 | | 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27, |
1334 | | 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31, |
1335 | | 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c, |
1336 | | 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87, |
1337 | | 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0, |
1338 | | 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23, |
1339 | | 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2, |
1340 | | 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87, |
1341 | | 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d, |
1342 | | 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b, |
1343 | | 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d, |
1344 | | 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6, |
1345 | | 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84, |
1346 | | 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04, |
1347 | | 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19, |
1348 | | 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b, |
1349 | | 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a, |
1350 | | 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea, |
1351 | | 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30, |
1352 | | 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7, |
1353 | | 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa, |
1354 | | 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5, |
1355 | | 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71, |
1356 | | 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab, |
1357 | | 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb, |
1358 | | 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c, |
1359 | | 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25, |
1360 | | }; |
1361 | | |
1362 | | void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) { |
1363 | | x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp); |
1364 | | } |
1365 | | |
1366 | | #else |
1367 | | |
1368 | | /* k25519Precomp[i][j] = (j+1)*256^i*B */ |
1369 | | static const ge_precomp k25519Precomp[32][8] = { |
1370 | | { |
1371 | | { |
1372 | | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, |
1373 | | 27544626, -11754271, -6079156, 2047605}, |
1374 | | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, |
1375 | | 5043384, 19500929, -15469378}, |
1376 | | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, |
1377 | | 29287919, 11864899, -24514362, -4438546}, |
1378 | | }, |
1379 | | { |
1380 | | {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, |
1381 | | -11717903, -3814571, -358445, -10211303}, |
1382 | | {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, |
1383 | | -15616551, 11189268, -26829678, -5319081}, |
1384 | | {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, |
1385 | | -3128826, -9541118, -15472047, -4166697}, |
1386 | | }, |
1387 | | { |
1388 | | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, |
1389 | | 27787600, -14772189, 28944400, -1550024}, |
1390 | | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, |
1391 | | 16354577, -11775962, 7689662, 11199574}, |
1392 | | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, |
1393 | | 7512774, 10017326, -17749093, -9920357}, |
1394 | | }, |
1395 | | { |
1396 | | {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, |
1397 | | -28926210, 15006023, 3284568, -6276540}, |
1398 | | {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, |
1399 | | 7464579, 9656445, 13059162, 10374397}, |
1400 | | {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, |
1401 | | -3839045, -641708, -101325}, |
1402 | | }, |
1403 | | { |
1404 | | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, |
1405 | | 32867885, 14515107, -15438304, 10819380}, |
1406 | | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, |
1407 | | 12483688, -12668491, 5581306}, |
1408 | | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, |
1409 | | 28542350, 13850243, -23678021, -15815942}, |
1410 | | }, |
1411 | | { |
1412 | | {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, |
1413 | | -19188627, -15224819, -9818940, -12085777}, |
1414 | | {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, |
1415 | | -15689887, 1762328, 14866737}, |
1416 | | {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, |
1417 | | -28236412, 3959421, 27914454, 4383652}, |
1418 | | }, |
1419 | | { |
1420 | | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, |
1421 | | 5230134, -23952439, -15175766}, |
1422 | | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, |
1423 | | 20654025, 16520125, 30598449, 7715701}, |
1424 | | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, |
1425 | | -31400660, 1370708, 29794553, -1409300}, |
1426 | | }, |
1427 | | { |
1428 | | {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, |
1429 | | 30290735, 10876454, -33154098, 2381726}, |
1430 | | {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, |
1431 | | -6236617, 3696005, -32300832, 15351955}, |
1432 | | {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, |
1433 | | -32961401, -2970515, 29551813, 10109425}, |
1434 | | }, |
1435 | | }, |
1436 | | { |
1437 | | { |
1438 | | {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, |
1439 | | -2378284, -1627556, 10092783, -4764171}, |
1440 | | {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, |
1441 | | -32508754, 12005538, -17810127, 12803510}, |
1442 | | {17228999, -15661624, -1233527, 300140, -1224870, -11714777, |
1443 | | 30364213, -9038194, 18016357, 4397660}, |
1444 | | }, |
1445 | | { |
1446 | | {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, |
1447 | | -26619106, 14544525, -17477504, 982639}, |
1448 | | {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, |
1449 | | -4120128, -21047696, 9934963}, |
1450 | | {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, |
1451 | | -14747930, 4559895, -30123922, -10897950}, |
1452 | | }, |
1453 | | { |
1454 | | {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, |
1455 | | 24191034, 4541697, -13338309, 5500568}, |
1456 | | {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, |
1457 | | -17430592, 12264343, 10874051, 13524335}, |
1458 | | {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, |
1459 | | 5080568, -22528059, 5376628}, |
1460 | | }, |
1461 | | { |
1462 | | {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, |
1463 | | -22321305, -9447443, 4535768, 1569007}, |
1464 | | {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, |
1465 | | -30494562, 3044290, 31848280, 12543772}, |
1466 | | {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, |
1467 | | -27377195, -2062731, 7718482, 14474653}, |
1468 | | }, |
1469 | | { |
1470 | | {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, |
1471 | | -7236665, 24316168, -5253567}, |
1472 | | {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, |
1473 | | 33040651, -13424532, -20729456, 8321686}, |
1474 | | {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, |
1475 | | 23845965, -11874838, -9984458, 608372}, |
1476 | | }, |
1477 | | { |
1478 | | {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, |
1479 | | 1123968, -6780577, 27229399, 23887}, |
1480 | | {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, |
1481 | | 12797024, -6440308, -1633405, 16678954}, |
1482 | | {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, |
1483 | | -1508144, -4795045, -17169265, 4904953}, |
1484 | | }, |
1485 | | { |
1486 | | {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, |
1487 | | 5169211, 16191880, 2128236, -4326833}, |
1488 | | {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, |
1489 | | -29806336, 916033, -6882542, -2986532}, |
1490 | | {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, |
1491 | | 285431, 2763829, 15736322, 4143876}, |
1492 | | }, |
1493 | | { |
1494 | | {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, |
1495 | | -14594663, 23527084, -16458268}, |
1496 | | {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, |
1497 | | -32625340, 4087881, -15188911, -14416214}, |
1498 | | {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, |
1499 | | 4357868, -4774191, -16323038}, |
1500 | | }, |
1501 | | }, |
1502 | | { |
1503 | | { |
1504 | | {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, |
1505 | | 23365147, -3949732, 7390890, 2759800}, |
1506 | | {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, |
1507 | | -4264057, 1244380, -12919645}, |
1508 | | {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, |
1509 | | 9208236, 15886429, 16489664}, |
1510 | | }, |
1511 | | { |
1512 | | {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, |
1513 | | -13693198, 398369, -30606455, -712933}, |
1514 | | {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, |
1515 | | 13348553, 12076947, -30836462, 5113182}, |
1516 | | {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, |
1517 | | -30341101, -7336386, 13847711, 5387222}, |
1518 | | }, |
1519 | | { |
1520 | | {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, |
1521 | | 8763061, 3617786, -19600662, 10370991}, |
1522 | | {20246567, -14369378, 22358229, -543712, 18507283, -10413996, |
1523 | | 14554437, -8746092, 32232924, 16763880}, |
1524 | | {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, |
1525 | | 11094161, 15689506, 3140038, -16510092}, |
1526 | | }, |
1527 | | { |
1528 | | {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, |
1529 | | -27224800, 9448613, -28774454, 366295}, |
1530 | | {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, |
1531 | | 28344573, 8041113, 719605, 11671788}, |
1532 | | {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, |
1533 | | -15266516, 27000813, -10195553}, |
1534 | | }, |
1535 | | { |
1536 | | {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, |
1537 | | 5336097, 6750977, -14521026}, |
1538 | | {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, |
1539 | | 1695823, -8819122, 8169720, 16220347}, |
1540 | | {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, |
1541 | | -11144307, -2627664, -5990708, -14166033}, |
1542 | | }, |
1543 | | { |
1544 | | {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, |
1545 | | 27884329, 2847284, 2655861, 1738395}, |
1546 | | {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, |
1547 | | 21651608, -3239336, -19087449, -11005278}, |
1548 | | {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, |
1549 | | 5821408, 10478196, 8544890}, |
1550 | | }, |
1551 | | { |
1552 | | {32173121, -16129311, 24896207, 3921497, 22579056, -3410854, |
1553 | | 19270449, 12217473, 17789017, -3395995}, |
1554 | | {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, |
1555 | | 15479401, -3853233, 30460520, 1052596}, |
1556 | | {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, |
1557 | | 27491595, -4612359, 3179268, -9478891}, |
1558 | | }, |
1559 | | { |
1560 | | {31947069, -14366651, -4640583, -15339921, -15125977, -6039709, |
1561 | | -14756777, -16411740, 19072640, -9511060}, |
1562 | | {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, |
1563 | | 5977896, -5215017, 473099, 5040608}, |
1564 | | {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, |
1565 | | 28326862, 1721092, -19558642, -3131606}, |
1566 | | }, |
1567 | | }, |
1568 | | { |
1569 | | { |
1570 | | {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, |
1571 | | 8076149, -27868496, 11538389}, |
1572 | | {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, |
1573 | | 8754525, 7446702, -5676054, 5797016}, |
1574 | | {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, |
1575 | | 2014099, -9050574, -2369172, -5877341}, |
1576 | | }, |
1577 | | { |
1578 | | {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, |
1579 | | 1192730, -3714199, 15123619, 10811505}, |
1580 | | {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, |
1581 | | 15776356, -28886779, -11974553}, |
1582 | | {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, |
1583 | | -20654173, -16484855, 4714547, -9600655}, |
1584 | | }, |
1585 | | { |
1586 | | {15200332, 8368572, 19679101, 15970074, -31872674, 1959451, |
1587 | | 24611599, -4543832, -11745876, 12340220}, |
1588 | | {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, |
1589 | | 9613953, 8241152, 15370987, 9608631}, |
1590 | | {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, |
1591 | | 15866074, -28210621, -8814099}, |
1592 | | }, |
1593 | | { |
1594 | | {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, |
1595 | | 858697, 20571223, 8420556}, |
1596 | | {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, |
1597 | | 33531827, 12516406, -21574435, -12476749}, |
1598 | | {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, |
1599 | | 7256740, 8791136, 15069930}, |
1600 | | }, |
1601 | | { |
1602 | | {1276410, -9371918, 22949635, -16322807, -23493039, -5702186, |
1603 | | 14711875, 4874229, -30663140, -2331391}, |
1604 | | {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, |
1605 | | -7912378, -33069337, 9234253}, |
1606 | | {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, |
1607 | | 31559055, -11609587, 18979186, 13396066}, |
1608 | | }, |
1609 | | { |
1610 | | {24474287, 4968103, 22267082, 4407354, 24063882, -8325180, |
1611 | | -18816887, 13594782, 33514650, 7021958}, |
1612 | | {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, |
1613 | | -25948728, -3916677, -21480480, 12868082}, |
1614 | | {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, |
1615 | | -21446107, 2244500, -12455797, -8089383}, |
1616 | | }, |
1617 | | { |
1618 | | {-30595528, 13793479, -5852820, 319136, -25723172, -6263899, |
1619 | | 33086546, 8957937, -15233648, 5540521}, |
1620 | | {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, |
1621 | | -23710744, -1568984, -16128528, -14962807}, |
1622 | | {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, |
1623 | | 892185, -11513277, -15205948}, |
1624 | | }, |
1625 | | { |
1626 | | {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, |
1627 | | 4763127, -19179614, 5867134}, |
1628 | | {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, |
1629 | | 27846559, 5931263, -29749703, -16108455}, |
1630 | | {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, |
1631 | | 7283490, -15148073, -19526700, 7734629}, |
1632 | | }, |
1633 | | }, |
1634 | | { |
1635 | | { |
1636 | | {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, |
1637 | | 7585295, -3176626, 18549497, 15302069}, |
1638 | | {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, |
1639 | | 10458790, -6418461, -8872242, 8424746}, |
1640 | | {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, |
1641 | | 19206234, 7134917, -11284482, -828919}, |
1642 | | }, |
1643 | | { |
1644 | | {11334899, -9218022, 8025293, 12707519, 17523892, -10476071, |
1645 | | 10243738, -14685461, -5066034, 16498837}, |
1646 | | {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, |
1647 | | -14124238, 6536641, 10543906}, |
1648 | | {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, |
1649 | | -2669190, -16625574, -27235709, 8876771}, |
1650 | | }, |
1651 | | { |
1652 | | {-25742899, -12566864, -15649966, -846607, -33026686, -796288, |
1653 | | -33481822, 15824474, -604426, -9039817}, |
1654 | | {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, |
1655 | | -4890037, 1657394, 3084098}, |
1656 | | {10477963, -7470260, 12119566, -13250805, 29016247, -5365589, |
1657 | | 31280319, 14396151, -30233575, 15272409}, |
1658 | | }, |
1659 | | { |
1660 | | {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, |
1661 | | -25173957, -12636138, -25014757, 1950504}, |
1662 | | {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, |
1663 | | -8384306, -8767532, 15341279, 8373727}, |
1664 | | {28685821, 7759505, -14378516, -12002860, -31971820, 4079242, |
1665 | | 298136, -10232602, -2878207, 15190420}, |
1666 | | }, |
1667 | | { |
1668 | | {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, |
1669 | | 8669718, 2742393, -26033313, -6875003}, |
1670 | | {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, |
1671 | | 9291594, -16247779, -12154742, 6048605}, |
1672 | | {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, |
1673 | | 13934231, 5128323, 11213262, 9168384}, |
1674 | | }, |
1675 | | { |
1676 | | {-26280513, 11007847, 19408960, -940758, -18592965, -4328580, |
1677 | | -5088060, -11105150, 20470157, -16398701}, |
1678 | | {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, |
1679 | | -22783952, 14461608, 14042978, 5230683}, |
1680 | | {29969567, -2741594, -16711867, -8552442, 9175486, -2468974, |
1681 | | 21556951, 3506042, -5933891, -12449708}, |
1682 | | }, |
1683 | | { |
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1685 | | -21284170, 8971513, -28539189, 15326563}, |
1686 | | {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669, |
1687 | | -15523050, 15300988, -20514118, 9168260}, |
1688 | | {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939, |
1689 | | -28948358, 9601605, 33087103, -9011387}, |
1690 | | }, |
1691 | | { |
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1693 | | -27444329, -15000531, -5996870, 15664672}, |
1694 | | {23294591, -16632613, -22650781, -8470978, 27844204, 11461195, |
1695 | | 13099750, -2460356, 18151676, 13417686}, |
1696 | | {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065, |
1697 | | 1661597, -12551441, 15271676, -15452665}, |
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1700 | | { |
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1703 | | -18698764, 2167544, -6921301, -13440182}, |
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1705 | | -9917708, -8638997, 12215110, 12028277}, |
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1707 | | 30123440, 4617780, -16900089, -655628}, |
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1719 | | -17415375, -12020462, 4725005, 14044970}, |
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1721 | | -1411784, -19522291, -16109756}, |
1722 | | {-24864089, 12986008, -10898878, -5558584, -11312371, -148526, |
1723 | | 19541418, 8180106, 9282262, 10282508}, |
1724 | | }, |
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1728 | | {-10562541, 14895633, 26814552, -16673850, -17480754, -2489360, |
1729 | | -2781891, 6993761, -18093885, 10114655}, |
1730 | | {-20107055, -929418, 31422704, 10427861, -7110749, 6150669, |
1731 | | -29091755, -11529146, 25953725, -106158}, |
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1733 | | { |
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1736 | | {-15998678, 7578152, 5310217, 14408357, -33548620, -224739, |
1737 | | 31575954, 6326196, 7381791, -2421839}, |
1738 | | {-20902779, 3296811, 24736065, -16328389, 18374254, 7318640, |
1739 | | 6295303, 8082724, -15362489, 12339664}, |
1740 | | }, |
1741 | | { |
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1743 | | 15768922, 25091167, 14856294}, |
1744 | | {-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, |
1745 | | -12695493, -22182473, -9012899}, |
1746 | | {-11423429, -5421590, 11632845, 3405020, 30536730, -11674039, |
1747 | | -27260765, 13866390, 30146206, 9142070}, |
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1749 | | { |
1750 | | {3924129, -15307516, -13817122, -10054960, 12291820, -668366, |
1751 | | -27702774, 9326384, -8237858, 4171294}, |
1752 | | {-15921940, 16037937, 6713787, 16606682, -21612135, 2790944, |
1753 | | 26396185, 3731949, 345228, -5462949}, |
1754 | | {-21327538, 13448259, 25284571, 1143661, 20614966, -8849387, |
1755 | | 2031539, -12391231, -16253183, -13582083}, |
1756 | | }, |
1757 | | { |
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1759 | | 17477601, 3842657, 28012650, -16405420}, |
1760 | | {-5075835, 9368966, -8562079, -4600902, -15249953, 6970560, |
1761 | | -9189873, 16292057, -8867157, 3507940}, |
1762 | | {29439664, 3537914, 23333589, 6997794, -17555561, -11018068, |
1763 | | -15209202, -15051267, -9164929, 6580396}, |
1764 | | }, |
1765 | | }, |
1766 | | { |
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1769 | | 17860444, -9273846, -2095802, 9304567}, |
1770 | | {20714564, -4336911, 29088195, 7406487, 11426967, -5095705, |
1771 | | 14792667, -14608617, 5289421, -477127}, |
1772 | | {-16665533, -10650790, -6160345, -13305760, 9192020, -1802462, |
1773 | | 17271490, 12349094, 26939669, -3752294}, |
1774 | | }, |
1775 | | { |
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1777 | | -27283495, -12348559, -3698806, 117887}, |
1778 | | {22263325, -6560050, 3984570, -11174646, -15114008, -566785, |
1779 | | 28311253, 5358056, -23319780, 541964}, |
1780 | | {16259219, 3261970, 2309254, -15534474, -16885711, -4581916, |
1781 | | 24134070, -16705829, -13337066, -13552195}, |
1782 | | }, |
1783 | | { |
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1785 | | -2399684, -717351, 690426, 14876244}, |
1786 | | {24977353, -314384, -8223969, -13465086, 28432343, -1176353, |
1787 | | -13068804, -12297348, -22380984, 6618999}, |
1788 | | {-1538174, 11685646, 12944378, 13682314, -24389511, -14413193, |
1789 | | 8044829, -13817328, 32239829, -5652762}, |
1790 | | }, |
1791 | | { |
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1793 | | -10350059, 32779359, 5095274}, |
1794 | | {-33008130, -5214506, -32264887, -3685216, 9460461, -9327423, |
1795 | | -24601656, 14506724, 21639561, -2630236}, |
1796 | | {-16400943, -13112215, 25239338, 15531969, 3987758, -4499318, |
1797 | | -1289502, -6863535, 17874574, 558605}, |
1798 | | }, |
1799 | | { |
1800 | | {-13600129, 10240081, 9171883, 16131053, -20869254, 9599700, |
1801 | | 33499487, 5080151, 2085892, 5119761}, |
1802 | | {-22205145, -2519528, -16381601, 414691, -25019550, 2170430, |
1803 | | 30634760, -8363614, -31999993, -5759884}, |
1804 | | {-6845704, 15791202, 8550074, -1312654, 29928809, -12092256, |
1805 | | 27534430, -7192145, -22351378, 12961482}, |
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1807 | | { |
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1809 | | 16533930, 8206996, -30194652, -5159638}, |
1810 | | {-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, |
1811 | | 7031275, 7589640, 8945490}, |
1812 | | {-32152748, 8917967, 6661220, -11677616, -1192060, -15793393, |
1813 | | 7251489, -11182180, 24099109, -14456170}, |
1814 | | }, |
1815 | | { |
1816 | | {5019558, -7907470, 4244127, -14714356, -26933272, 6453165, |
1817 | | -19118182, -13289025, -6231896, -10280736}, |
1818 | | {10853594, 10721687, 26480089, 5861829, -22995819, 1972175, |
1819 | | -1866647, -10557898, -3363451, -6441124}, |
1820 | | {-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, |
1821 | | -2008168, -13866408, 7421392}, |
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1823 | | { |
1824 | | {8139927, -6546497, 32257646, -5890546, 30375719, 1886181, |
1825 | | -21175108, 15441252, 28826358, -4123029}, |
1826 | | {6267086, 9695052, 7709135, -16603597, -32869068, -1886135, |
1827 | | 14795160, -7840124, 13746021, -1742048}, |
1828 | | {28584902, 7787108, -6732942, -15050729, 22846041, -7571236, |
1829 | | -3181936, -363524, 4771362, -8419958}, |
1830 | | }, |
1831 | | }, |
1832 | | { |
1833 | | { |
1834 | | {24949256, 6376279, -27466481, -8174608, -18646154, -9930606, |
1835 | | 33543569, -12141695, 3569627, 11342593}, |
1836 | | {26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, |
1837 | | 4608608, 7325975, -14801071}, |
1838 | | {-11618399, -14554430, -24321212, 7655128, -1369274, 5214312, |
1839 | | -27400540, 10258390, -17646694, -8186692}, |
1840 | | }, |
1841 | | { |
1842 | | {11431204, 15823007, 26570245, 14329124, 18029990, 4796082, |
1843 | | -31446179, 15580664, 9280358, -3973687}, |
1844 | | {-160783, -10326257, -22855316, -4304997, -20861367, -13621002, |
1845 | | -32810901, -11181622, -15545091, 4387441}, |
1846 | | {-20799378, 12194512, 3937617, -5805892, -27154820, 9340370, |
1847 | | -24513992, 8548137, 20617071, -7482001}, |
1848 | | }, |
1849 | | { |
1850 | | {-938825, -3930586, -8714311, 16124718, 24603125, -6225393, |
1851 | | -13775352, -11875822, 24345683, 10325460}, |
1852 | | {-19855277, -1568885, -22202708, 8714034, 14007766, 6928528, |
1853 | | 16318175, -1010689, 4766743, 3552007}, |
1854 | | {-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, |
1855 | | 14481909, 10988822, -3994762}, |
1856 | | }, |
1857 | | { |
1858 | | {15564307, -14311570, 3101243, 5684148, 30446780, -8051356, |
1859 | | 12677127, -6505343, -8295852, 13296005}, |
1860 | | {-9442290, 6624296, -30298964, -11913677, -4670981, -2057379, |
1861 | | 31521204, 9614054, -30000824, 12074674}, |
1862 | | {4771191, -135239, 14290749, -13089852, 27992298, 14998318, |
1863 | | -1413936, -1556716, 29832613, -16391035}, |
1864 | | }, |
1865 | | { |
1866 | | {7064884, -7541174, -19161962, -5067537, -18891269, -2912736, |
1867 | | 25825242, 5293297, -27122660, 13101590}, |
1868 | | {-2298563, 2439670, -7466610, 1719965, -27267541, -16328445, |
1869 | | 32512469, -5317593, -30356070, -4190957}, |
1870 | | {-30006540, 10162316, -33180176, 3981723, -16482138, -13070044, |
1871 | | 14413974, 9515896, 19568978, 9628812}, |
1872 | | }, |
1873 | | { |
1874 | | {33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, |
1875 | | -6106839, -6291786, 3437740}, |
1876 | | {-18978877, 3884493, 19469877, 12726490, 15913552, 13614290, |
1877 | | -22961733, 70104, 7463304, 4176122}, |
1878 | | {-27124001, 10659917, 11482427, -16070381, 12771467, -6635117, |
1879 | | -32719404, -5322751, 24216882, 5944158}, |
1880 | | }, |
1881 | | { |
1882 | | {8894125, 7450974, -2664149, -9765752, -28080517, -12389115, |
1883 | | 19345746, 14680796, 11632993, 5847885}, |
1884 | | {26942781, -2315317, 9129564, -4906607, 26024105, 11769399, |
1885 | | -11518837, 6367194, -9727230, 4782140}, |
1886 | | {19916461, -4828410, -22910704, -11414391, 25606324, -5972441, |
1887 | | 33253853, 8220911, 6358847, -1873857}, |
1888 | | }, |
1889 | | { |
1890 | | {801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, |
1891 | | -4480480, -13538503, 1387155}, |
1892 | | {19646058, 5720633, -11416706, 12814209, 11607948, 12749789, |
1893 | | 14147075, 15156355, -21866831, 11835260}, |
1894 | | {19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, |
1895 | | 15467869, -26560550, 5052483}, |
1896 | | }, |
1897 | | }, |
1898 | | { |
1899 | | { |
1900 | | {-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, |
1901 | | -12618185, 12228557, -7003677}, |
1902 | | {32944382, 14922211, -22844894, 5188528, 21913450, -8719943, |
1903 | | 4001465, 13238564, -6114803, 8653815}, |
1904 | | {22865569, -4652735, 27603668, -12545395, 14348958, 8234005, |
1905 | | 24808405, 5719875, 28483275, 2841751}, |
1906 | | }, |
1907 | | { |
1908 | | {-16420968, -1113305, -327719, -12107856, 21886282, -15552774, |
1909 | | -1887966, -315658, 19932058, -12739203}, |
1910 | | {-11656086, 10087521, -8864888, -5536143, -19278573, -3055912, |
1911 | | 3999228, 13239134, -4777469, -13910208}, |
1912 | | {1382174, -11694719, 17266790, 9194690, -13324356, 9720081, |
1913 | | 20403944, 11284705, -14013818, 3093230}, |
1914 | | }, |
1915 | | { |
1916 | | {16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, |
1917 | | 16271225, -24049421, -6691850}, |
1918 | | {-21911077, -5927941, -4611316, -5560156, -31744103, -10785293, |
1919 | | 24123614, 15193618, -21652117, -16739389}, |
1920 | | {-9935934, -4289447, -25279823, 4372842, 2087473, 10399484, |
1921 | | 31870908, 14690798, 17361620, 11864968}, |
1922 | | }, |
1923 | | { |
1924 | | {-11307610, 6210372, 13206574, 5806320, -29017692, -13967200, |
1925 | | -12331205, -7486601, -25578460, -16240689}, |
1926 | | {14668462, -12270235, 26039039, 15305210, 25515617, 4542480, |
1927 | | 10453892, 6577524, 9145645, -6443880}, |
1928 | | {5974874, 3053895, -9433049, -10385191, -31865124, 3225009, |
1929 | | -7972642, 3936128, -5652273, -3050304}, |
1930 | | }, |
1931 | | { |
1932 | | {30625386, -4729400, -25555961, -12792866, -20484575, 7695099, |
1933 | | 17097188, -16303496, -27999779, 1803632}, |
1934 | | {-3553091, 9865099, -5228566, 4272701, -5673832, -16689700, |
1935 | | 14911344, 12196514, -21405489, 7047412}, |
1936 | | {20093277, 9920966, -11138194, -5343857, 13161587, 12044805, |
1937 | | -32856851, 4124601, -32343828, -10257566}, |
1938 | | }, |
1939 | | { |
1940 | | {-20788824, 14084654, -13531713, 7842147, 19119038, -13822605, |
1941 | | 4752377, -8714640, -21679658, 2288038}, |
1942 | | {-26819236, -3283715, 29965059, 3039786, -14473765, 2540457, |
1943 | | 29457502, 14625692, -24819617, 12570232}, |
1944 | | {-1063558, -11551823, 16920318, 12494842, 1278292, -5869109, |
1945 | | -21159943, -3498680, -11974704, 4724943}, |
1946 | | }, |
1947 | | { |
1948 | | {17960970, -11775534, -4140968, -9702530, -8876562, -1410617, |
1949 | | -12907383, -8659932, -29576300, 1903856}, |
1950 | | {23134274, -14279132, -10681997, -1611936, 20684485, 15770816, |
1951 | | -12989750, 3190296, 26955097, 14109738}, |
1952 | | {15308788, 5320727, -30113809, -14318877, 22902008, 7767164, |
1953 | | 29425325, -11277562, 31960942, 11934971}, |
1954 | | }, |
1955 | | { |
1956 | | {-27395711, 8435796, 4109644, 12222639, -24627868, 14818669, |
1957 | | 20638173, 4875028, 10491392, 1379718}, |
1958 | | {-13159415, 9197841, 3875503, -8936108, -1383712, -5879801, |
1959 | | 33518459, 16176658, 21432314, 12180697}, |
1960 | | {-11787308, 11500838, 13787581, -13832590, -22430679, 10140205, |
1961 | | 1465425, 12689540, -10301319, -13872883}, |
1962 | | }, |
1963 | | }, |
1964 | | { |
1965 | | { |
1966 | | {5414091, -15386041, -21007664, 9643570, 12834970, 1186149, |
1967 | | -2622916, -1342231, 26128231, 6032912}, |
1968 | | {-26337395, -13766162, 32496025, -13653919, 17847801, -12669156, |
1969 | | 3604025, 8316894, -25875034, -10437358}, |
1970 | | {3296484, 6223048, 24680646, -12246460, -23052020, 5903205, |
1971 | | -8862297, -4639164, 12376617, 3188849}, |
1972 | | }, |
1973 | | { |
1974 | | {29190488, -14659046, 27549113, -1183516, 3520066, -10697301, |
1975 | | 32049515, -7309113, -16109234, -9852307}, |
1976 | | {-14744486, -9309156, 735818, -598978, -20407687, -5057904, |
1977 | | 25246078, -15795669, 18640741, -960977}, |
1978 | | {-6928835, -16430795, 10361374, 5642961, 4910474, 12345252, |
1979 | | -31638386, -494430, 10530747, 1053335}, |
1980 | | }, |
1981 | | { |
1982 | | {-29265967, -14186805, -13538216, -12117373, -19457059, -10655384, |
1983 | | -31462369, -2948985, 24018831, 15026644}, |
1984 | | {-22592535, -3145277, -2289276, 5953843, -13440189, 9425631, |
1985 | | 25310643, 13003497, -2314791, -15145616}, |
1986 | | {-27419985, -603321, -8043984, -1669117, -26092265, 13987819, |
1987 | | -27297622, 187899, -23166419, -2531735}, |
1988 | | }, |
1989 | | { |
1990 | | {-21744398, -13810475, 1844840, 5021428, -10434399, -15911473, |
1991 | | 9716667, 16266922, -5070217, 726099}, |
1992 | | {29370922, -6053998, 7334071, -15342259, 9385287, 2247707, |
1993 | | -13661962, -4839461, 30007388, -15823341}, |
1994 | | {-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, |
1995 | | 730663, 9835848, 4555336}, |
1996 | | }, |
1997 | | { |
1998 | | {-23376435, 1410446, -22253753, -12899614, 30867635, 15826977, |
1999 | | 17693930, 544696, -11985298, 12422646}, |
2000 | | {31117226, -12215734, -13502838, 6561947, -9876867, -12757670, |
2001 | | -5118685, -4096706, 29120153, 13924425}, |
2002 | | {-17400879, -14233209, 19675799, -2734756, -11006962, -5858820, |
2003 | | -9383939, -11317700, 7240931, -237388}, |
2004 | | }, |
2005 | | { |
2006 | | {-31361739, -11346780, -15007447, -5856218, -22453340, -12152771, |
2007 | | 1222336, 4389483, 3293637, -15551743}, |
2008 | | {-16684801, -14444245, 11038544, 11054958, -13801175, -3338533, |
2009 | | -24319580, 7733547, 12796905, -6335822}, |
2010 | | {-8759414, -10817836, -25418864, 10783769, -30615557, -9746811, |
2011 | | -28253339, 3647836, 3222231, -11160462}, |
2012 | | }, |
2013 | | { |
2014 | | {18606113, 1693100, -25448386, -15170272, 4112353, 10045021, |
2015 | | 23603893, -2048234, -7550776, 2484985}, |
2016 | | {9255317, -3131197, -12156162, -1004256, 13098013, -9214866, |
2017 | | 16377220, -2102812, -19802075, -3034702}, |
2018 | | {-22729289, 7496160, -5742199, 11329249, 19991973, -3347502, |
2019 | | -31718148, 9936966, -30097688, -10618797}, |
2020 | | }, |
2021 | | { |
2022 | | {21878590, -5001297, 4338336, 13643897, -3036865, 13160960, |
2023 | | 19708896, 5415497, -7360503, -4109293}, |
2024 | | {27736861, 10103576, 12500508, 8502413, -3413016, -9633558, |
2025 | | 10436918, -1550276, -23659143, -8132100}, |
2026 | | {19492550, -12104365, -29681976, -852630, -3208171, 12403437, |
2027 | | 30066266, 8367329, 13243957, 8709688}, |
2028 | | }, |
2029 | | }, |
2030 | | { |
2031 | | { |
2032 | | {12015105, 2801261, 28198131, 10151021, 24818120, -4743133, |
2033 | | -11194191, -5645734, 5150968, 7274186}, |
2034 | | {2831366, -12492146, 1478975, 6122054, 23825128, -12733586, |
2035 | | 31097299, 6083058, 31021603, -9793610}, |
2036 | | {-2529932, -2229646, 445613, 10720828, -13849527, -11505937, |
2037 | | -23507731, 16354465, 15067285, -14147707}, |
2038 | | }, |
2039 | | { |
2040 | | {7840942, 14037873, -33364863, 15934016, -728213, -3642706, |
2041 | | 21403988, 1057586, -19379462, -12403220}, |
2042 | | {915865, -16469274, 15608285, -8789130, -24357026, 6060030, |
2043 | | -17371319, 8410997, -7220461, 16527025}, |
2044 | | {32922597, -556987, 20336074, -16184568, 10903705, -5384487, |
2045 | | 16957574, 52992, 23834301, 6588044}, |
2046 | | }, |
2047 | | { |
2048 | | {32752030, 11232950, 3381995, -8714866, 22652988, -10744103, |
2049 | | 17159699, 16689107, -20314580, -1305992}, |
2050 | | {-4689649, 9166776, -25710296, -10847306, 11576752, 12733943, |
2051 | | 7924251, -2752281, 1976123, -7249027}, |
2052 | | {21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, |
2053 | | -3371252, 12331345, -8237197}, |
2054 | | }, |
2055 | | { |
2056 | | {8651614, -4477032, -16085636, -4996994, 13002507, 2950805, |
2057 | | 29054427, -5106970, 10008136, -4667901}, |
2058 | | {31486080, 15114593, -14261250, 12951354, 14369431, -7387845, |
2059 | | 16347321, -13662089, 8684155, -10532952}, |
2060 | | {19443825, 11385320, 24468943, -9659068, -23919258, 2187569, |
2061 | | -26263207, -6086921, 31316348, 14219878}, |
2062 | | }, |
2063 | | { |
2064 | | {-28594490, 1193785, 32245219, 11392485, 31092169, 15722801, |
2065 | | 27146014, 6992409, 29126555, 9207390}, |
2066 | | {32382935, 1110093, 18477781, 11028262, -27411763, -7548111, |
2067 | | -4980517, 10843782, -7957600, -14435730}, |
2068 | | {2814918, 7836403, 27519878, -7868156, -20894015, -11553689, |
2069 | | -21494559, 8550130, 28346258, 1994730}, |
2070 | | }, |
2071 | | { |
2072 | | {-19578299, 8085545, -14000519, -3948622, 2785838, -16231307, |
2073 | | -19516951, 7174894, 22628102, 8115180}, |
2074 | | {-30405132, 955511, -11133838, -15078069, -32447087, -13278079, |
2075 | | -25651578, 3317160, -9943017, 930272}, |
2076 | | {-15303681, -6833769, 28856490, 1357446, 23421993, 1057177, |
2077 | | 24091212, -1388970, -22765376, -10650715}, |
2078 | | }, |
2079 | | { |
2080 | | {-22751231, -5303997, -12907607, -12768866, -15811511, -7797053, |
2081 | | -14839018, -16554220, -1867018, 8398970}, |
2082 | | {-31969310, 2106403, -4736360, 1362501, 12813763, 16200670, |
2083 | | 22981545, -6291273, 18009408, -15772772}, |
2084 | | {-17220923, -9545221, -27784654, 14166835, 29815394, 7444469, |
2085 | | 29551787, -3727419, 19288549, 1325865}, |
2086 | | }, |
2087 | | { |
2088 | | {15100157, -15835752, -23923978, -1005098, -26450192, 15509408, |
2089 | | 12376730, -3479146, 33166107, -8042750}, |
2090 | | {20909231, 13023121, -9209752, 16251778, -5778415, -8094914, |
2091 | | 12412151, 10018715, 2213263, -13878373}, |
2092 | | {32529814, -11074689, 30361439, -16689753, -9135940, 1513226, |
2093 | | 22922121, 6382134, -5766928, 8371348}, |
2094 | | }, |
2095 | | }, |
2096 | | { |
2097 | | { |
2098 | | {9923462, 11271500, 12616794, 3544722, -29998368, -1721626, |
2099 | | 12891687, -8193132, -26442943, 10486144}, |
2100 | | {-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, |
2101 | | 2610596, -23921530, -11455195}, |
2102 | | {5408411, -1136691, -4969122, 10561668, 24145918, 14240566, |
2103 | | 31319731, -4235541, 19985175, -3436086}, |
2104 | | }, |
2105 | | { |
2106 | | {-13994457, 16616821, 14549246, 3341099, 32155958, 13648976, |
2107 | | -17577068, 8849297, 65030, 8370684}, |
2108 | | {-8320926, -12049626, 31204563, 5839400, -20627288, -1057277, |
2109 | | -19442942, 6922164, 12743482, -9800518}, |
2110 | | {-2361371, 12678785, 28815050, 4759974, -23893047, 4884717, |
2111 | | 23783145, 11038569, 18800704, 255233}, |
2112 | | }, |
2113 | | { |
2114 | | {-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, |
2115 | | 9066957, 19258688, -14753793}, |
2116 | | {-2936654, -10827535, -10432089, 14516793, -3640786, 4372541, |
2117 | | -31934921, 2209390, -1524053, 2055794}, |
2118 | | {580882, 16705327, 5468415, -2683018, -30926419, -14696000, |
2119 | | -7203346, -8994389, -30021019, 7394435}, |
2120 | | }, |
2121 | | { |
2122 | | {23838809, 1822728, -15738443, 15242727, 8318092, -3733104, |
2123 | | -21672180, -3492205, -4821741, 14799921}, |
2124 | | {13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, |
2125 | | 13496856, -9056018, 7402518}, |
2126 | | {2286874, -4435931, -20042458, -2008336, -13696227, 5038122, |
2127 | | 11006906, -15760352, 8205061, 1607563}, |
2128 | | }, |
2129 | | { |
2130 | | {14414086, -8002132, 3331830, -3208217, 22249151, -5594188, |
2131 | | 18364661, -2906958, 30019587, -9029278}, |
2132 | | {-27688051, 1585953, -10775053, 931069, -29120221, -11002319, |
2133 | | -14410829, 12029093, 9944378, 8024}, |
2134 | | {4368715, -3709630, 29874200, -15022983, -20230386, -11410704, |
2135 | | -16114594, -999085, -8142388, 5640030}, |
2136 | | }, |
2137 | | { |
2138 | | {10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, |
2139 | | -16694564, 15219798, -14327783}, |
2140 | | {27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, |
2141 | | -1173195, -18342183, 9742717}, |
2142 | | {6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, |
2143 | | 7406442, 12420155, 1994844}, |
2144 | | }, |
2145 | | { |
2146 | | {14012521, -5024720, -18384453, -9578469, -26485342, -3936439, |
2147 | | -13033478, -10909803, 24319929, -6446333}, |
2148 | | {16412690, -4507367, 10772641, 15929391, -17068788, -4658621, |
2149 | | 10555945, -10484049, -30102368, -4739048}, |
2150 | | {22397382, -7767684, -9293161, -12792868, 17166287, -9755136, |
2151 | | -27333065, 6199366, 21880021, -12250760}, |
2152 | | }, |
2153 | | { |
2154 | | {-4283307, 5368523, -31117018, 8163389, -30323063, 3209128, |
2155 | | 16557151, 8890729, 8840445, 4957760}, |
2156 | | {-15447727, 709327, -6919446, -10870178, -29777922, 6522332, |
2157 | | -21720181, 12130072, -14796503, 5005757}, |
2158 | | {-2114751, -14308128, 23019042, 15765735, -25269683, 6002752, |
2159 | | 10183197, -13239326, -16395286, -2176112}, |
2160 | | }, |
2161 | | }, |
2162 | | { |
2163 | | { |
2164 | | {-19025756, 1632005, 13466291, -7995100, -23640451, 16573537, |
2165 | | -32013908, -3057104, 22208662, 2000468}, |
2166 | | {3065073, -1412761, -25598674, -361432, -17683065, -5703415, |
2167 | | -8164212, 11248527, -3691214, -7414184}, |
2168 | | {10379208, -6045554, 8877319, 1473647, -29291284, -12507580, |
2169 | | 16690915, 2553332, -3132688, 16400289}, |
2170 | | }, |
2171 | | { |
2172 | | {15716668, 1254266, -18472690, 7446274, -8448918, 6344164, |
2173 | | -22097271, -7285580, 26894937, 9132066}, |
2174 | | {24158887, 12938817, 11085297, -8177598, -28063478, -4457083, |
2175 | | -30576463, 64452, -6817084, -2692882}, |
2176 | | {13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, |
2177 | | -3418511, -4688006, 2364226}, |
2178 | | }, |
2179 | | { |
2180 | | {16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024, |
2181 | | -11697457, 15445875, -7798101}, |
2182 | | {29004207, -7867081, 28661402, -640412, -12794003, -7943086, |
2183 | | 31863255, -4135540, -278050, -15759279}, |
2184 | | {-6122061, -14866665, -28614905, 14569919, -10857999, -3591829, |
2185 | | 10343412, -6976290, -29828287, -10815811}, |
2186 | | }, |
2187 | | { |
2188 | | {27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636, |
2189 | | 15372179, 17293797, 960709}, |
2190 | | {20263915, 11434237, -5765435, 11236810, 13505955, -10857102, |
2191 | | -16111345, 6493122, -19384511, 7639714}, |
2192 | | {-2830798, -14839232, 25403038, -8215196, -8317012, -16173699, |
2193 | | 18006287, -16043750, 29994677, -15808121}, |
2194 | | }, |
2195 | | { |
2196 | | {9769828, 5202651, -24157398, -13631392, -28051003, -11561624, |
2197 | | -24613141, -13860782, -31184575, 709464}, |
2198 | | {12286395, 13076066, -21775189, -1176622, -25003198, 4057652, |
2199 | | -32018128, -8890874, 16102007, 13205847}, |
2200 | | {13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, |
2201 | | 8525972, 10151379, 10394400}, |
2202 | | }, |
2203 | | { |
2204 | | {4024660, -16137551, 22436262, 12276534, -9099015, -2686099, |
2205 | | 19698229, 11743039, -33302334, 8934414}, |
2206 | | {-15879800, -4525240, -8580747, -2934061, 14634845, -698278, |
2207 | | -9449077, 3137094, -11536886, 11721158}, |
2208 | | {17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, |
2209 | | 8835153, -9205489, -1280045}, |
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2211 | | { |
2212 | | {-461409, -7830014, 20614118, 16688288, -7514766, -4807119, |
2213 | | 22300304, 505429, 6108462, -6183415}, |
2214 | | {-5070281, 12367917, -30663534, 3234473, 32617080, -8422642, |
2215 | | 29880583, -13483331, -26898490, -7867459}, |
2216 | | {-31975283, 5726539, 26934134, 10237677, -3173717, -605053, |
2217 | | 24199304, 3795095, 7592688, -14992079}, |
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2219 | | { |
2220 | | {21594432, -14964228, 17466408, -4077222, 32537084, 2739898, |
2221 | | 6407723, 12018833, -28256052, 4298412}, |
2222 | | {-20650503, -11961496, -27236275, 570498, 3767144, -1717540, |
2223 | | 13891942, -1569194, 13717174, 10805743}, |
2224 | | {-14676630, -15644296, 15287174, 11927123, 24177847, -8175568, |
2225 | | -796431, 14860609, -26938930, -5863836}, |
2226 | | }, |
2227 | | }, |
2228 | | { |
2229 | | { |
2230 | | {12962541, 5311799, -10060768, 11658280, 18855286, -7954201, |
2231 | | 13286263, -12808704, -4381056, 9882022}, |
2232 | | {18512079, 11319350, -20123124, 15090309, 18818594, 5271736, |
2233 | | -22727904, 3666879, -23967430, -3299429}, |
2234 | | {-6789020, -3146043, 16192429, 13241070, 15898607, -14206114, |
2235 | | -10084880, -6661110, -2403099, 5276065}, |
2236 | | }, |
2237 | | { |
2238 | | {30169808, -5317648, 26306206, -11750859, 27814964, 7069267, |
2239 | | 7152851, 3684982, 1449224, 13082861}, |
2240 | | {10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, |
2241 | | 15056736, -21016438, -8202000}, |
2242 | | {-33150110, 3261608, 22745853, 7948688, 19370557, -15177665, |
2243 | | -26171976, 6482814, -10300080, -11060101}, |
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2245 | | { |
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2247 | | 26112421, 2521008, -22664288, 6904815}, |
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2249 | | 3841096, -29003639, -6657642}, |
2250 | | {10340844, -6630377, -18656632, -2278430, 12621151, -13339055, |
2251 | | 30878497, -11824370, -25584551, 5181966}, |
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2253 | | { |
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2258 | | {-18882287, -11673380, 24849422, 11501709, 13161720, -4768874, |
2259 | | 1925523, 11914390, 4662781, 7820689}, |
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2275 | | -32948145, 7417950, -30242287, 1507265}, |
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2309 | | -31582008, 12840104, 24913809, 9815020}, |
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2324 | | {29210088, -9419337, -5919792, -4952785, 10834811, -13327726, |
2325 | | -16512102, -10820713, -27162222, -14030531}, |
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2327 | | { |
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2333 | | 27548447, -7721242, 14476989, -12767431}, |
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2335 | | { |
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2341 | | -12906320, 3852694, 13216206, 14842320}, |
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3333 | | { |
3334 | | {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, |
3335 | | -910336, -2782495, -19386633, 11994101}, |
3336 | | {21691500, -13624626, -641331, -14367021, 3285881, -3483596, |
3337 | | -25064666, 9718258, -7477437, 13381418}, |
3338 | | {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, |
3339 | | 23111648, -6375247, 28535282, 15779576}, |
3340 | | }, |
3341 | | { |
3342 | | {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, |
3343 | | -14068454, 12021730, 9955285, -16303356}, |
3344 | | {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, |
3345 | | -18426029, 9924399, 20194861, 13380996}, |
3346 | | {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, |
3347 | | -1984914, 15707771, 26342023, 10146099}, |
3348 | | }, |
3349 | | }, |
3350 | | { |
3351 | | { |
3352 | | {-26016874, -219943, 21339191, -41388, 19745256, -2878700, |
3353 | | -29637280, 2227040, 21612326, -545728}, |
3354 | | {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, |
3355 | | 25764461, 12243797, -20856566, 11649658}, |
3356 | | {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, |
3357 | | 6114064, 33514190, 2333242}, |
3358 | | }, |
3359 | | { |
3360 | | {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, |
3361 | | -6679750, -12670638, 24350578, -13450001}, |
3362 | | {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, |
3363 | | -31536088, -10406836, 8317860, 12352766}, |
3364 | | {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, |
3365 | | -23552096, -2287550, 20712163, 6719373}, |
3366 | | }, |
3367 | | { |
3368 | | {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, |
3369 | | -3763210, 26224235, -3297458}, |
3370 | | {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, |
3371 | | 21728352, 9493610, 18620611, -16428628}, |
3372 | | {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, |
3373 | | -5269471, -9725556, -30701573, -16479657}, |
3374 | | }, |
3375 | | { |
3376 | | {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, |
3377 | | 12248509, -5240639, 13735342, 1934062}, |
3378 | | {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, |
3379 | | -15136294, -3765346, -21277997, 5473616}, |
3380 | | {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, |
3381 | | -7125085, 12469656, 29111212, -5451014}, |
3382 | | }, |
3383 | | { |
3384 | | {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, |
3385 | | 24367466, 6388839, -10295587, 452383}, |
3386 | | {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, |
3387 | | -24236251, -5915248, 15766062, 8407814}, |
3388 | | {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, |
3389 | | -8917023, -4388953, -8067909, 2276718}, |
3390 | | }, |
3391 | | { |
3392 | | {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, |
3393 | | -23827587, 5096219, 22740376, -7303417}, |
3394 | | {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, |
3395 | | 24051124, 13742383, -15637599, 13295222}, |
3396 | | {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, |
3397 | | -17720195, -4612972, -4451357, -14669444}, |
3398 | | }, |
3399 | | { |
3400 | | {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, |
3401 | | -2469266, -4141880, 7770569, 9620597}, |
3402 | | {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, |
3403 | | -1694323, -33502340, -14767970}, |
3404 | | {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, |
3405 | | 1220118, 30494170, -11440799}, |
3406 | | }, |
3407 | | { |
3408 | | {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, |
3409 | | -26739026, 926050, -1684339, -13333647}, |
3410 | | {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, |
3411 | | 9021034, 9078865, 3353509, 4033511}, |
3412 | | {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, |
3413 | | 23161163, 8839127, 27485041, 7356032}, |
3414 | | }, |
3415 | | }, |
3416 | | { |
3417 | | { |
3418 | | {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, |
3419 | | 2625015, 28431036, -16771834}, |
3420 | | {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, |
3421 | | -22545972, 14150565, 15970762, 4099461}, |
3422 | | {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, |
3423 | | 13617293, -9937143, 11465739, 8317062}, |
3424 | | }, |
3425 | | { |
3426 | | {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, |
3427 | | 14898637, 3848455, 20969334, -5157516}, |
3428 | | {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, |
3429 | | -21610826, -3649888, 11177095, 14989547}, |
3430 | | {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, |
3431 | | 13515641, 2581286, -28487508, 9930240}, |
3432 | | }, |
3433 | | { |
3434 | | {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, |
3435 | | 18345767, -13403753, 16291481, -5314038}, |
3436 | | {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, |
3437 | | 6957617, 4368891, 9788741}, |
3438 | | {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, |
3439 | | -21722536, -8613148, 16250552, -11111103}, |
3440 | | }, |
3441 | | { |
3442 | | {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, |
3443 | | 10604807, -30190403, 4782747}, |
3444 | | {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, |
3445 | | -9981571, 4383045, 22546403, 437323}, |
3446 | | {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, |
3447 | | 27343084, 2786261, -30633590, -14097016}, |
3448 | | }, |
3449 | | { |
3450 | | {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, |
3451 | | -19690631, 2355319, -19284671, -6114373}, |
3452 | | {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, |
3453 | | 18952177, 15496498, -29380133, 11754228}, |
3454 | | {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, |
3455 | | 7141596, 11724556, 22761615, -10134141}, |
3456 | | }, |
3457 | | { |
3458 | | {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, |
3459 | | -28741185, -12227393, 32851222, 11717399}, |
3460 | | {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, |
3461 | | 31474879, 3483633, -1193175, -4030831}, |
3462 | | {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, |
3463 | | 33142652, 6546660, -19985279, -3948376}, |
3464 | | }, |
3465 | | { |
3466 | | {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, |
3467 | | -8537131, -12833048, -30772034, -15486313}, |
3468 | | {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, |
3469 | | -31135347, -16049879, 10928917, 3011958}, |
3470 | | {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, |
3471 | | -30831056, -12805180, 18008031, 10258577}, |
3472 | | }, |
3473 | | { |
3474 | | {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, |
3475 | | -1853465, 1367120, 25127874, 6671743}, |
3476 | | {29701166, -14373934, -10878120, 9279288, -17568, 13127210, |
3477 | | 21382910, 11042292, 25838796, 4642684}, |
3478 | | {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, |
3479 | | 30468147, -13900640, 18423289, 4177476}, |
3480 | | }, |
3481 | | }, |
3482 | | }; |
3483 | | |
3484 | 0 | static uint8_t negative(signed char b) { |
3485 | 0 | uint32_t x = b; |
3486 | 0 | x >>= 31; /* 1: yes; 0: no */ |
3487 | 0 | return x; |
3488 | 0 | } |
3489 | | |
3490 | 0 | static void table_select(ge_precomp *t, int pos, signed char b) { |
3491 | 0 | ge_precomp minust; |
3492 | 0 | uint8_t bnegative = negative(b); |
3493 | 0 | uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); |
3494 | |
|
3495 | 0 | ge_precomp_0(t); |
3496 | 0 | cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); |
3497 | 0 | cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); |
3498 | 0 | cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); |
3499 | 0 | cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); |
3500 | 0 | cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); |
3501 | 0 | cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); |
3502 | 0 | cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); |
3503 | 0 | cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); |
3504 | 0 | fe_copy(minust.yplusx, t->yminusx); |
3505 | 0 | fe_copy(minust.yminusx, t->yplusx); |
3506 | 0 | fe_neg(minust.xy2d, t->xy2d); |
3507 | 0 | cmov(t, &minust, bnegative); |
3508 | 0 | } |
3509 | | |
3510 | | /* h = a * B |
3511 | | * where a = a[0]+256*a[1]+...+256^31 a[31] |
3512 | | * B is the Ed25519 base point (x,4/5) with x positive. |
3513 | | * |
3514 | | * Preconditions: |
3515 | | * a[31] <= 127 */ |
3516 | 0 | void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) { |
3517 | 0 | signed char e[64]; |
3518 | 0 | signed char carry; |
3519 | 0 | ge_p1p1 r; |
3520 | 0 | ge_p2 s; |
3521 | 0 | ge_precomp t; |
3522 | 0 | int i; |
3523 | |
|
3524 | 0 | for (i = 0; i < 32; ++i) { |
3525 | 0 | e[2 * i + 0] = (a[i] >> 0) & 15; |
3526 | 0 | e[2 * i + 1] = (a[i] >> 4) & 15; |
3527 | 0 | } |
3528 | | /* each e[i] is between 0 and 15 */ |
3529 | | /* e[63] is between 0 and 7 */ |
3530 | |
|
3531 | 0 | carry = 0; |
3532 | 0 | for (i = 0; i < 63; ++i) { |
3533 | 0 | e[i] += carry; |
3534 | 0 | carry = e[i] + 8; |
3535 | 0 | carry >>= 4; |
3536 | 0 | e[i] -= carry << 4; |
3537 | 0 | } |
3538 | 0 | e[63] += carry; |
3539 | | /* each e[i] is between -8 and 8 */ |
3540 | |
|
3541 | 0 | ge_p3_0(h); |
3542 | 0 | for (i = 1; i < 64; i += 2) { |
3543 | 0 | table_select(&t, i / 2, e[i]); |
3544 | 0 | ge_madd(&r, h, &t); |
3545 | 0 | x25519_ge_p1p1_to_p3(h, &r); |
3546 | 0 | } |
3547 | |
|
3548 | 0 | ge_p3_dbl(&r, h); |
3549 | 0 | x25519_ge_p1p1_to_p2(&s, &r); |
3550 | 0 | ge_p2_dbl(&r, &s); |
3551 | 0 | x25519_ge_p1p1_to_p2(&s, &r); |
3552 | 0 | ge_p2_dbl(&r, &s); |
3553 | 0 | x25519_ge_p1p1_to_p2(&s, &r); |
3554 | 0 | ge_p2_dbl(&r, &s); |
3555 | 0 | x25519_ge_p1p1_to_p3(h, &r); |
3556 | |
|
3557 | 0 | for (i = 0; i < 64; i += 2) { |
3558 | 0 | table_select(&t, i / 2, e[i]); |
3559 | 0 | ge_madd(&r, h, &t); |
3560 | 0 | x25519_ge_p1p1_to_p3(h, &r); |
3561 | 0 | } |
3562 | 0 | } |
3563 | | |
3564 | | #endif |
3565 | | |
3566 | 0 | static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) { |
3567 | 0 | fe_cmov(t->YplusX, u->YplusX, b); |
3568 | 0 | fe_cmov(t->YminusX, u->YminusX, b); |
3569 | 0 | fe_cmov(t->Z, u->Z, b); |
3570 | 0 | fe_cmov(t->T2d, u->T2d, b); |
3571 | 0 | } |
3572 | | |
3573 | | /* r = scalar * A. |
3574 | | * where a = a[0]+256*a[1]+...+256^31 a[31]. */ |
3575 | 0 | void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) { |
3576 | 0 | ge_p2 Ai_p2[8]; |
3577 | 0 | ge_cached Ai[16]; |
3578 | 0 | ge_p1p1 t; |
3579 | |
|
3580 | 0 | ge_cached_0(&Ai[0]); |
3581 | 0 | x25519_ge_p3_to_cached(&Ai[1], A); |
3582 | 0 | ge_p3_to_p2(&Ai_p2[1], A); |
3583 | |
|
3584 | 0 | unsigned i; |
3585 | 0 | for (i = 2; i < 16; i += 2) { |
3586 | 0 | ge_p2_dbl(&t, &Ai_p2[i / 2]); |
3587 | 0 | ge_p1p1_to_cached(&Ai[i], &t); |
3588 | 0 | if (i < 8) { |
3589 | 0 | x25519_ge_p1p1_to_p2(&Ai_p2[i], &t); |
3590 | 0 | } |
3591 | 0 | x25519_ge_add(&t, A, &Ai[i]); |
3592 | 0 | ge_p1p1_to_cached(&Ai[i + 1], &t); |
3593 | 0 | if (i < 7) { |
3594 | 0 | x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t); |
3595 | 0 | } |
3596 | 0 | } |
3597 | |
|
3598 | 0 | ge_p2_0(r); |
3599 | 0 | ge_p3 u; |
3600 | |
|
3601 | 0 | for (i = 0; i < 256; i += 4) { |
3602 | 0 | ge_p2_dbl(&t, r); |
3603 | 0 | x25519_ge_p1p1_to_p2(r, &t); |
3604 | 0 | ge_p2_dbl(&t, r); |
3605 | 0 | x25519_ge_p1p1_to_p2(r, &t); |
3606 | 0 | ge_p2_dbl(&t, r); |
3607 | 0 | x25519_ge_p1p1_to_p2(r, &t); |
3608 | 0 | ge_p2_dbl(&t, r); |
3609 | 0 | x25519_ge_p1p1_to_p3(&u, &t); |
3610 | |
|
3611 | 0 | uint8_t index = scalar[31 - i/8]; |
3612 | 0 | index >>= 4 - (i & 4); |
3613 | 0 | index &= 0xf; |
3614 | |
|
3615 | 0 | unsigned j; |
3616 | 0 | ge_cached selected; |
3617 | 0 | ge_cached_0(&selected); |
3618 | 0 | for (j = 0; j < 16; j++) { |
3619 | 0 | cmov_cached(&selected, &Ai[j], equal(j, index)); |
3620 | 0 | } |
3621 | |
|
3622 | 0 | x25519_ge_add(&t, &u, &selected); |
3623 | 0 | x25519_ge_p1p1_to_p2(r, &t); |
3624 | 0 | } |
3625 | 0 | } |
3626 | | |
3627 | | #ifdef ED25519 |
3628 | | static void slide(signed char *r, const uint8_t *a) { |
3629 | | int i; |
3630 | | int b; |
3631 | | int k; |
3632 | | |
3633 | | for (i = 0; i < 256; ++i) { |
3634 | | r[i] = 1 & (a[i >> 3] >> (i & 7)); |
3635 | | } |
3636 | | |
3637 | | for (i = 0; i < 256; ++i) { |
3638 | | if (r[i]) { |
3639 | | for (b = 1; b <= 6 && i + b < 256; ++b) { |
3640 | | if (r[i + b]) { |
3641 | | if (r[i] + (r[i + b] << b) <= 15) { |
3642 | | r[i] += r[i + b] << b; |
3643 | | r[i + b] = 0; |
3644 | | } else if (r[i] - (r[i + b] << b) >= -15) { |
3645 | | r[i] -= r[i + b] << b; |
3646 | | for (k = i + b; k < 256; ++k) { |
3647 | | if (!r[k]) { |
3648 | | r[k] = 1; |
3649 | | break; |
3650 | | } |
3651 | | r[k] = 0; |
3652 | | } |
3653 | | } else { |
3654 | | break; |
3655 | | } |
3656 | | } |
3657 | | } |
3658 | | } |
3659 | | } |
3660 | | } |
3661 | | |
3662 | | static const ge_precomp Bi[8] = { |
3663 | | { |
3664 | | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, |
3665 | | -11754271, -6079156, 2047605}, |
3666 | | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, |
3667 | | 5043384, 19500929, -15469378}, |
3668 | | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, |
3669 | | 11864899, -24514362, -4438546}, |
3670 | | }, |
3671 | | { |
3672 | | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, |
3673 | | -14772189, 28944400, -1550024}, |
3674 | | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, |
3675 | | -11775962, 7689662, 11199574}, |
3676 | | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, |
3677 | | 10017326, -17749093, -9920357}, |
3678 | | }, |
3679 | | { |
3680 | | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, |
3681 | | 14515107, -15438304, 10819380}, |
3682 | | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, |
3683 | | 12483688, -12668491, 5581306}, |
3684 | | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, |
3685 | | 13850243, -23678021, -15815942}, |
3686 | | }, |
3687 | | { |
3688 | | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, |
3689 | | 5230134, -23952439, -15175766}, |
3690 | | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, |
3691 | | 16520125, 30598449, 7715701}, |
3692 | | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, |
3693 | | 1370708, 29794553, -1409300}, |
3694 | | }, |
3695 | | { |
3696 | | {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, |
3697 | | -1361450, -13062696, 13821877}, |
3698 | | {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, |
3699 | | -7212327, 18853322, -14220951}, |
3700 | | {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, |
3701 | | -10431137, 2207753, -3209784}, |
3702 | | }, |
3703 | | { |
3704 | | {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, |
3705 | | -663000, -31111463, -16132436}, |
3706 | | {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, |
3707 | | 15725684, 171356, 6466918}, |
3708 | | {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, |
3709 | | -14088058, -30714912, 16193877}, |
3710 | | }, |
3711 | | { |
3712 | | {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, |
3713 | | 4729455, -18074513, 9256800}, |
3714 | | {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, |
3715 | | 9761698, -19827198, 630305}, |
3716 | | {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, |
3717 | | -15960994, -2449256, -14291300}, |
3718 | | }, |
3719 | | { |
3720 | | {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, |
3721 | | 15033784, 25105118, -7894876}, |
3722 | | {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, |
3723 | | 1573892, -2625887, 2198790, -15804619}, |
3724 | | {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, |
3725 | | -16236442, -32461234, -12290683}, |
3726 | | }, |
3727 | | }; |
3728 | | |
3729 | | /* r = a * A + b * B |
3730 | | * where a = a[0]+256*a[1]+...+256^31 a[31]. |
3731 | | * and b = b[0]+256*b[1]+...+256^31 b[31]. |
3732 | | * B is the Ed25519 base point (x,4/5) with x positive. */ |
3733 | | static void |
3734 | | ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, |
3735 | | const ge_p3 *A, const uint8_t *b) { |
3736 | | signed char aslide[256]; |
3737 | | signed char bslide[256]; |
3738 | | ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ |
3739 | | ge_p1p1 t; |
3740 | | ge_p3 u; |
3741 | | ge_p3 A2; |
3742 | | int i; |
3743 | | |
3744 | | slide(aslide, a); |
3745 | | slide(bslide, b); |
3746 | | |
3747 | | x25519_ge_p3_to_cached(&Ai[0], A); |
3748 | | ge_p3_dbl(&t, A); |
3749 | | x25519_ge_p1p1_to_p3(&A2, &t); |
3750 | | x25519_ge_add(&t, &A2, &Ai[0]); |
3751 | | x25519_ge_p1p1_to_p3(&u, &t); |
3752 | | x25519_ge_p3_to_cached(&Ai[1], &u); |
3753 | | x25519_ge_add(&t, &A2, &Ai[1]); |
3754 | | x25519_ge_p1p1_to_p3(&u, &t); |
3755 | | x25519_ge_p3_to_cached(&Ai[2], &u); |
3756 | | x25519_ge_add(&t, &A2, &Ai[2]); |
3757 | | x25519_ge_p1p1_to_p3(&u, &t); |
3758 | | x25519_ge_p3_to_cached(&Ai[3], &u); |
3759 | | x25519_ge_add(&t, &A2, &Ai[3]); |
3760 | | x25519_ge_p1p1_to_p3(&u, &t); |
3761 | | x25519_ge_p3_to_cached(&Ai[4], &u); |
3762 | | x25519_ge_add(&t, &A2, &Ai[4]); |
3763 | | x25519_ge_p1p1_to_p3(&u, &t); |
3764 | | x25519_ge_p3_to_cached(&Ai[5], &u); |
3765 | | x25519_ge_add(&t, &A2, &Ai[5]); |
3766 | | x25519_ge_p1p1_to_p3(&u, &t); |
3767 | | x25519_ge_p3_to_cached(&Ai[6], &u); |
3768 | | x25519_ge_add(&t, &A2, &Ai[6]); |
3769 | | x25519_ge_p1p1_to_p3(&u, &t); |
3770 | | x25519_ge_p3_to_cached(&Ai[7], &u); |
3771 | | |
3772 | | ge_p2_0(r); |
3773 | | |
3774 | | for (i = 255; i >= 0; --i) { |
3775 | | if (aslide[i] || bslide[i]) { |
3776 | | break; |
3777 | | } |
3778 | | } |
3779 | | |
3780 | | for (; i >= 0; --i) { |
3781 | | ge_p2_dbl(&t, r); |
3782 | | |
3783 | | if (aslide[i] > 0) { |
3784 | | x25519_ge_p1p1_to_p3(&u, &t); |
3785 | | x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]); |
3786 | | } else if (aslide[i] < 0) { |
3787 | | x25519_ge_p1p1_to_p3(&u, &t); |
3788 | | x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); |
3789 | | } |
3790 | | |
3791 | | if (bslide[i] > 0) { |
3792 | | x25519_ge_p1p1_to_p3(&u, &t); |
3793 | | ge_madd(&t, &u, &Bi[bslide[i] / 2]); |
3794 | | } else if (bslide[i] < 0) { |
3795 | | x25519_ge_p1p1_to_p3(&u, &t); |
3796 | | ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); |
3797 | | } |
3798 | | |
3799 | | x25519_ge_p1p1_to_p2(r, &t); |
3800 | | } |
3801 | | } |
3802 | | #endif |
3803 | | |
3804 | | /* The set of scalars is \Z/l |
3805 | | * where l = 2^252 + 27742317777372353535851937790883648493. */ |
3806 | | |
3807 | | /* Input: |
3808 | | * s[0]+256*s[1]+...+256^63*s[63] = s |
3809 | | * |
3810 | | * Output: |
3811 | | * s[0]+256*s[1]+...+256^31*s[31] = s mod l |
3812 | | * where l = 2^252 + 27742317777372353535851937790883648493. |
3813 | | * Overwrites s in place. */ |
3814 | | void |
3815 | 0 | x25519_sc_reduce(uint8_t *s) { |
3816 | 0 | int64_t s0 = 2097151 & load_3(s); |
3817 | 0 | int64_t s1 = 2097151 & (load_4(s + 2) >> 5); |
3818 | 0 | int64_t s2 = 2097151 & (load_3(s + 5) >> 2); |
3819 | 0 | int64_t s3 = 2097151 & (load_4(s + 7) >> 7); |
3820 | 0 | int64_t s4 = 2097151 & (load_4(s + 10) >> 4); |
3821 | 0 | int64_t s5 = 2097151 & (load_3(s + 13) >> 1); |
3822 | 0 | int64_t s6 = 2097151 & (load_4(s + 15) >> 6); |
3823 | 0 | int64_t s7 = 2097151 & (load_3(s + 18) >> 3); |
3824 | 0 | int64_t s8 = 2097151 & load_3(s + 21); |
3825 | 0 | int64_t s9 = 2097151 & (load_4(s + 23) >> 5); |
3826 | 0 | int64_t s10 = 2097151 & (load_3(s + 26) >> 2); |
3827 | 0 | int64_t s11 = 2097151 & (load_4(s + 28) >> 7); |
3828 | 0 | int64_t s12 = 2097151 & (load_4(s + 31) >> 4); |
3829 | 0 | int64_t s13 = 2097151 & (load_3(s + 34) >> 1); |
3830 | 0 | int64_t s14 = 2097151 & (load_4(s + 36) >> 6); |
3831 | 0 | int64_t s15 = 2097151 & (load_3(s + 39) >> 3); |
3832 | 0 | int64_t s16 = 2097151 & load_3(s + 42); |
3833 | 0 | int64_t s17 = 2097151 & (load_4(s + 44) >> 5); |
3834 | 0 | int64_t s18 = 2097151 & (load_3(s + 47) >> 2); |
3835 | 0 | int64_t s19 = 2097151 & (load_4(s + 49) >> 7); |
3836 | 0 | int64_t s20 = 2097151 & (load_4(s + 52) >> 4); |
3837 | 0 | int64_t s21 = 2097151 & (load_3(s + 55) >> 1); |
3838 | 0 | int64_t s22 = 2097151 & (load_4(s + 57) >> 6); |
3839 | 0 | int64_t s23 = (load_4(s + 60) >> 3); |
3840 | 0 | int64_t carry0; |
3841 | 0 | int64_t carry1; |
3842 | 0 | int64_t carry2; |
3843 | 0 | int64_t carry3; |
3844 | 0 | int64_t carry4; |
3845 | 0 | int64_t carry5; |
3846 | 0 | int64_t carry6; |
3847 | 0 | int64_t carry7; |
3848 | 0 | int64_t carry8; |
3849 | 0 | int64_t carry9; |
3850 | 0 | int64_t carry10; |
3851 | 0 | int64_t carry11; |
3852 | 0 | int64_t carry12; |
3853 | 0 | int64_t carry13; |
3854 | 0 | int64_t carry14; |
3855 | 0 | int64_t carry15; |
3856 | 0 | int64_t carry16; |
3857 | |
|
3858 | 0 | s11 += s23 * 666643; |
3859 | 0 | s12 += s23 * 470296; |
3860 | 0 | s13 += s23 * 654183; |
3861 | 0 | s14 -= s23 * 997805; |
3862 | 0 | s15 += s23 * 136657; |
3863 | 0 | s16 -= s23 * 683901; |
3864 | 0 | s23 = 0; |
3865 | |
|
3866 | 0 | s10 += s22 * 666643; |
3867 | 0 | s11 += s22 * 470296; |
3868 | 0 | s12 += s22 * 654183; |
3869 | 0 | s13 -= s22 * 997805; |
3870 | 0 | s14 += s22 * 136657; |
3871 | 0 | s15 -= s22 * 683901; |
3872 | 0 | s22 = 0; |
3873 | |
|
3874 | 0 | s9 += s21 * 666643; |
3875 | 0 | s10 += s21 * 470296; |
3876 | 0 | s11 += s21 * 654183; |
3877 | 0 | s12 -= s21 * 997805; |
3878 | 0 | s13 += s21 * 136657; |
3879 | 0 | s14 -= s21 * 683901; |
3880 | 0 | s21 = 0; |
3881 | |
|
3882 | 0 | s8 += s20 * 666643; |
3883 | 0 | s9 += s20 * 470296; |
3884 | 0 | s10 += s20 * 654183; |
3885 | 0 | s11 -= s20 * 997805; |
3886 | 0 | s12 += s20 * 136657; |
3887 | 0 | s13 -= s20 * 683901; |
3888 | 0 | s20 = 0; |
3889 | |
|
3890 | 0 | s7 += s19 * 666643; |
3891 | 0 | s8 += s19 * 470296; |
3892 | 0 | s9 += s19 * 654183; |
3893 | 0 | s10 -= s19 * 997805; |
3894 | 0 | s11 += s19 * 136657; |
3895 | 0 | s12 -= s19 * 683901; |
3896 | 0 | s19 = 0; |
3897 | |
|
3898 | 0 | s6 += s18 * 666643; |
3899 | 0 | s7 += s18 * 470296; |
3900 | 0 | s8 += s18 * 654183; |
3901 | 0 | s9 -= s18 * 997805; |
3902 | 0 | s10 += s18 * 136657; |
3903 | 0 | s11 -= s18 * 683901; |
3904 | 0 | s18 = 0; |
3905 | |
|
3906 | 0 | carry6 = (s6 + (1 << 20)) >> 21; |
3907 | 0 | s7 += carry6; |
3908 | 0 | s6 -= carry6 << 21; |
3909 | 0 | carry8 = (s8 + (1 << 20)) >> 21; |
3910 | 0 | s9 += carry8; |
3911 | 0 | s8 -= carry8 << 21; |
3912 | 0 | carry10 = (s10 + (1 << 20)) >> 21; |
3913 | 0 | s11 += carry10; |
3914 | 0 | s10 -= carry10 << 21; |
3915 | 0 | carry12 = (s12 + (1 << 20)) >> 21; |
3916 | 0 | s13 += carry12; |
3917 | 0 | s12 -= carry12 << 21; |
3918 | 0 | carry14 = (s14 + (1 << 20)) >> 21; |
3919 | 0 | s15 += carry14; |
3920 | 0 | s14 -= carry14 << 21; |
3921 | 0 | carry16 = (s16 + (1 << 20)) >> 21; |
3922 | 0 | s17 += carry16; |
3923 | 0 | s16 -= carry16 << 21; |
3924 | |
|
3925 | 0 | carry7 = (s7 + (1 << 20)) >> 21; |
3926 | 0 | s8 += carry7; |
3927 | 0 | s7 -= carry7 << 21; |
3928 | 0 | carry9 = (s9 + (1 << 20)) >> 21; |
3929 | 0 | s10 += carry9; |
3930 | 0 | s9 -= carry9 << 21; |
3931 | 0 | carry11 = (s11 + (1 << 20)) >> 21; |
3932 | 0 | s12 += carry11; |
3933 | 0 | s11 -= carry11 << 21; |
3934 | 0 | carry13 = (s13 + (1 << 20)) >> 21; |
3935 | 0 | s14 += carry13; |
3936 | 0 | s13 -= carry13 << 21; |
3937 | 0 | carry15 = (s15 + (1 << 20)) >> 21; |
3938 | 0 | s16 += carry15; |
3939 | 0 | s15 -= carry15 << 21; |
3940 | |
|
3941 | 0 | s5 += s17 * 666643; |
3942 | 0 | s6 += s17 * 470296; |
3943 | 0 | s7 += s17 * 654183; |
3944 | 0 | s8 -= s17 * 997805; |
3945 | 0 | s9 += s17 * 136657; |
3946 | 0 | s10 -= s17 * 683901; |
3947 | 0 | s17 = 0; |
3948 | |
|
3949 | 0 | s4 += s16 * 666643; |
3950 | 0 | s5 += s16 * 470296; |
3951 | 0 | s6 += s16 * 654183; |
3952 | 0 | s7 -= s16 * 997805; |
3953 | 0 | s8 += s16 * 136657; |
3954 | 0 | s9 -= s16 * 683901; |
3955 | 0 | s16 = 0; |
3956 | |
|
3957 | 0 | s3 += s15 * 666643; |
3958 | 0 | s4 += s15 * 470296; |
3959 | 0 | s5 += s15 * 654183; |
3960 | 0 | s6 -= s15 * 997805; |
3961 | 0 | s7 += s15 * 136657; |
3962 | 0 | s8 -= s15 * 683901; |
3963 | 0 | s15 = 0; |
3964 | |
|
3965 | 0 | s2 += s14 * 666643; |
3966 | 0 | s3 += s14 * 470296; |
3967 | 0 | s4 += s14 * 654183; |
3968 | 0 | s5 -= s14 * 997805; |
3969 | 0 | s6 += s14 * 136657; |
3970 | 0 | s7 -= s14 * 683901; |
3971 | 0 | s14 = 0; |
3972 | |
|
3973 | 0 | s1 += s13 * 666643; |
3974 | 0 | s2 += s13 * 470296; |
3975 | 0 | s3 += s13 * 654183; |
3976 | 0 | s4 -= s13 * 997805; |
3977 | 0 | s5 += s13 * 136657; |
3978 | 0 | s6 -= s13 * 683901; |
3979 | 0 | s13 = 0; |
3980 | |
|
3981 | 0 | s0 += s12 * 666643; |
3982 | 0 | s1 += s12 * 470296; |
3983 | 0 | s2 += s12 * 654183; |
3984 | 0 | s3 -= s12 * 997805; |
3985 | 0 | s4 += s12 * 136657; |
3986 | 0 | s5 -= s12 * 683901; |
3987 | 0 | s12 = 0; |
3988 | |
|
3989 | 0 | carry0 = (s0 + (1 << 20)) >> 21; |
3990 | 0 | s1 += carry0; |
3991 | 0 | s0 -= carry0 << 21; |
3992 | 0 | carry2 = (s2 + (1 << 20)) >> 21; |
3993 | 0 | s3 += carry2; |
3994 | 0 | s2 -= carry2 << 21; |
3995 | 0 | carry4 = (s4 + (1 << 20)) >> 21; |
3996 | 0 | s5 += carry4; |
3997 | 0 | s4 -= carry4 << 21; |
3998 | 0 | carry6 = (s6 + (1 << 20)) >> 21; |
3999 | 0 | s7 += carry6; |
4000 | 0 | s6 -= carry6 << 21; |
4001 | 0 | carry8 = (s8 + (1 << 20)) >> 21; |
4002 | 0 | s9 += carry8; |
4003 | 0 | s8 -= carry8 << 21; |
4004 | 0 | carry10 = (s10 + (1 << 20)) >> 21; |
4005 | 0 | s11 += carry10; |
4006 | 0 | s10 -= carry10 << 21; |
4007 | |
|
4008 | 0 | carry1 = (s1 + (1 << 20)) >> 21; |
4009 | 0 | s2 += carry1; |
4010 | 0 | s1 -= carry1 << 21; |
4011 | 0 | carry3 = (s3 + (1 << 20)) >> 21; |
4012 | 0 | s4 += carry3; |
4013 | 0 | s3 -= carry3 << 21; |
4014 | 0 | carry5 = (s5 + (1 << 20)) >> 21; |
4015 | 0 | s6 += carry5; |
4016 | 0 | s5 -= carry5 << 21; |
4017 | 0 | carry7 = (s7 + (1 << 20)) >> 21; |
4018 | 0 | s8 += carry7; |
4019 | 0 | s7 -= carry7 << 21; |
4020 | 0 | carry9 = (s9 + (1 << 20)) >> 21; |
4021 | 0 | s10 += carry9; |
4022 | 0 | s9 -= carry9 << 21; |
4023 | 0 | carry11 = (s11 + (1 << 20)) >> 21; |
4024 | 0 | s12 += carry11; |
4025 | 0 | s11 -= carry11 << 21; |
4026 | |
|
4027 | 0 | s0 += s12 * 666643; |
4028 | 0 | s1 += s12 * 470296; |
4029 | 0 | s2 += s12 * 654183; |
4030 | 0 | s3 -= s12 * 997805; |
4031 | 0 | s4 += s12 * 136657; |
4032 | 0 | s5 -= s12 * 683901; |
4033 | 0 | s12 = 0; |
4034 | |
|
4035 | 0 | carry0 = s0 >> 21; |
4036 | 0 | s1 += carry0; |
4037 | 0 | s0 -= carry0 << 21; |
4038 | 0 | carry1 = s1 >> 21; |
4039 | 0 | s2 += carry1; |
4040 | 0 | s1 -= carry1 << 21; |
4041 | 0 | carry2 = s2 >> 21; |
4042 | 0 | s3 += carry2; |
4043 | 0 | s2 -= carry2 << 21; |
4044 | 0 | carry3 = s3 >> 21; |
4045 | 0 | s4 += carry3; |
4046 | 0 | s3 -= carry3 << 21; |
4047 | 0 | carry4 = s4 >> 21; |
4048 | 0 | s5 += carry4; |
4049 | 0 | s4 -= carry4 << 21; |
4050 | 0 | carry5 = s5 >> 21; |
4051 | 0 | s6 += carry5; |
4052 | 0 | s5 -= carry5 << 21; |
4053 | 0 | carry6 = s6 >> 21; |
4054 | 0 | s7 += carry6; |
4055 | 0 | s6 -= carry6 << 21; |
4056 | 0 | carry7 = s7 >> 21; |
4057 | 0 | s8 += carry7; |
4058 | 0 | s7 -= carry7 << 21; |
4059 | 0 | carry8 = s8 >> 21; |
4060 | 0 | s9 += carry8; |
4061 | 0 | s8 -= carry8 << 21; |
4062 | 0 | carry9 = s9 >> 21; |
4063 | 0 | s10 += carry9; |
4064 | 0 | s9 -= carry9 << 21; |
4065 | 0 | carry10 = s10 >> 21; |
4066 | 0 | s11 += carry10; |
4067 | 0 | s10 -= carry10 << 21; |
4068 | 0 | carry11 = s11 >> 21; |
4069 | 0 | s12 += carry11; |
4070 | 0 | s11 -= carry11 << 21; |
4071 | |
|
4072 | 0 | s0 += s12 * 666643; |
4073 | 0 | s1 += s12 * 470296; |
4074 | 0 | s2 += s12 * 654183; |
4075 | 0 | s3 -= s12 * 997805; |
4076 | 0 | s4 += s12 * 136657; |
4077 | 0 | s5 -= s12 * 683901; |
4078 | 0 | s12 = 0; |
4079 | |
|
4080 | 0 | carry0 = s0 >> 21; |
4081 | 0 | s1 += carry0; |
4082 | 0 | s0 -= carry0 << 21; |
4083 | 0 | carry1 = s1 >> 21; |
4084 | 0 | s2 += carry1; |
4085 | 0 | s1 -= carry1 << 21; |
4086 | 0 | carry2 = s2 >> 21; |
4087 | 0 | s3 += carry2; |
4088 | 0 | s2 -= carry2 << 21; |
4089 | 0 | carry3 = s3 >> 21; |
4090 | 0 | s4 += carry3; |
4091 | 0 | s3 -= carry3 << 21; |
4092 | 0 | carry4 = s4 >> 21; |
4093 | 0 | s5 += carry4; |
4094 | 0 | s4 -= carry4 << 21; |
4095 | 0 | carry5 = s5 >> 21; |
4096 | 0 | s6 += carry5; |
4097 | 0 | s5 -= carry5 << 21; |
4098 | 0 | carry6 = s6 >> 21; |
4099 | 0 | s7 += carry6; |
4100 | 0 | s6 -= carry6 << 21; |
4101 | 0 | carry7 = s7 >> 21; |
4102 | 0 | s8 += carry7; |
4103 | 0 | s7 -= carry7 << 21; |
4104 | 0 | carry8 = s8 >> 21; |
4105 | 0 | s9 += carry8; |
4106 | 0 | s8 -= carry8 << 21; |
4107 | 0 | carry9 = s9 >> 21; |
4108 | 0 | s10 += carry9; |
4109 | 0 | s9 -= carry9 << 21; |
4110 | 0 | carry10 = s10 >> 21; |
4111 | 0 | s11 += carry10; |
4112 | 0 | s10 -= carry10 << 21; |
4113 | |
|
4114 | 0 | s[0] = s0 >> 0; |
4115 | 0 | s[1] = s0 >> 8; |
4116 | 0 | s[2] = (s0 >> 16) | (s1 << 5); |
4117 | 0 | s[3] = s1 >> 3; |
4118 | 0 | s[4] = s1 >> 11; |
4119 | 0 | s[5] = (s1 >> 19) | (s2 << 2); |
4120 | 0 | s[6] = s2 >> 6; |
4121 | 0 | s[7] = (s2 >> 14) | (s3 << 7); |
4122 | 0 | s[8] = s3 >> 1; |
4123 | 0 | s[9] = s3 >> 9; |
4124 | 0 | s[10] = (s3 >> 17) | (s4 << 4); |
4125 | 0 | s[11] = s4 >> 4; |
4126 | 0 | s[12] = s4 >> 12; |
4127 | 0 | s[13] = (s4 >> 20) | (s5 << 1); |
4128 | 0 | s[14] = s5 >> 7; |
4129 | 0 | s[15] = (s5 >> 15) | (s6 << 6); |
4130 | 0 | s[16] = s6 >> 2; |
4131 | 0 | s[17] = s6 >> 10; |
4132 | 0 | s[18] = (s6 >> 18) | (s7 << 3); |
4133 | 0 | s[19] = s7 >> 5; |
4134 | 0 | s[20] = s7 >> 13; |
4135 | 0 | s[21] = s8 >> 0; |
4136 | 0 | s[22] = s8 >> 8; |
4137 | 0 | s[23] = (s8 >> 16) | (s9 << 5); |
4138 | 0 | s[24] = s9 >> 3; |
4139 | 0 | s[25] = s9 >> 11; |
4140 | 0 | s[26] = (s9 >> 19) | (s10 << 2); |
4141 | 0 | s[27] = s10 >> 6; |
4142 | 0 | s[28] = (s10 >> 14) | (s11 << 7); |
4143 | 0 | s[29] = s11 >> 1; |
4144 | 0 | s[30] = s11 >> 9; |
4145 | 0 | s[31] = s11 >> 17; |
4146 | 0 | } |
4147 | | |
4148 | | #ifdef ED25519 |
4149 | | /* Input: |
4150 | | * a[0]+256*a[1]+...+256^31*a[31] = a |
4151 | | * b[0]+256*b[1]+...+256^31*b[31] = b |
4152 | | * c[0]+256*c[1]+...+256^31*c[31] = c |
4153 | | * |
4154 | | * Output: |
4155 | | * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l |
4156 | | * where l = 2^252 + 27742317777372353535851937790883648493. */ |
4157 | | static void |
4158 | | sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, |
4159 | | const uint8_t *c) |
4160 | | { |
4161 | | int64_t a0 = 2097151 & load_3(a); |
4162 | | int64_t a1 = 2097151 & (load_4(a + 2) >> 5); |
4163 | | int64_t a2 = 2097151 & (load_3(a + 5) >> 2); |
4164 | | int64_t a3 = 2097151 & (load_4(a + 7) >> 7); |
4165 | | int64_t a4 = 2097151 & (load_4(a + 10) >> 4); |
4166 | | int64_t a5 = 2097151 & (load_3(a + 13) >> 1); |
4167 | | int64_t a6 = 2097151 & (load_4(a + 15) >> 6); |
4168 | | int64_t a7 = 2097151 & (load_3(a + 18) >> 3); |
4169 | | int64_t a8 = 2097151 & load_3(a + 21); |
4170 | | int64_t a9 = 2097151 & (load_4(a + 23) >> 5); |
4171 | | int64_t a10 = 2097151 & (load_3(a + 26) >> 2); |
4172 | | int64_t a11 = (load_4(a + 28) >> 7); |
4173 | | int64_t b0 = 2097151 & load_3(b); |
4174 | | int64_t b1 = 2097151 & (load_4(b + 2) >> 5); |
4175 | | int64_t b2 = 2097151 & (load_3(b + 5) >> 2); |
4176 | | int64_t b3 = 2097151 & (load_4(b + 7) >> 7); |
4177 | | int64_t b4 = 2097151 & (load_4(b + 10) >> 4); |
4178 | | int64_t b5 = 2097151 & (load_3(b + 13) >> 1); |
4179 | | int64_t b6 = 2097151 & (load_4(b + 15) >> 6); |
4180 | | int64_t b7 = 2097151 & (load_3(b + 18) >> 3); |
4181 | | int64_t b8 = 2097151 & load_3(b + 21); |
4182 | | int64_t b9 = 2097151 & (load_4(b + 23) >> 5); |
4183 | | int64_t b10 = 2097151 & (load_3(b + 26) >> 2); |
4184 | | int64_t b11 = (load_4(b + 28) >> 7); |
4185 | | int64_t c0 = 2097151 & load_3(c); |
4186 | | int64_t c1 = 2097151 & (load_4(c + 2) >> 5); |
4187 | | int64_t c2 = 2097151 & (load_3(c + 5) >> 2); |
4188 | | int64_t c3 = 2097151 & (load_4(c + 7) >> 7); |
4189 | | int64_t c4 = 2097151 & (load_4(c + 10) >> 4); |
4190 | | int64_t c5 = 2097151 & (load_3(c + 13) >> 1); |
4191 | | int64_t c6 = 2097151 & (load_4(c + 15) >> 6); |
4192 | | int64_t c7 = 2097151 & (load_3(c + 18) >> 3); |
4193 | | int64_t c8 = 2097151 & load_3(c + 21); |
4194 | | int64_t c9 = 2097151 & (load_4(c + 23) >> 5); |
4195 | | int64_t c10 = 2097151 & (load_3(c + 26) >> 2); |
4196 | | int64_t c11 = (load_4(c + 28) >> 7); |
4197 | | int64_t s0; |
4198 | | int64_t s1; |
4199 | | int64_t s2; |
4200 | | int64_t s3; |
4201 | | int64_t s4; |
4202 | | int64_t s5; |
4203 | | int64_t s6; |
4204 | | int64_t s7; |
4205 | | int64_t s8; |
4206 | | int64_t s9; |
4207 | | int64_t s10; |
4208 | | int64_t s11; |
4209 | | int64_t s12; |
4210 | | int64_t s13; |
4211 | | int64_t s14; |
4212 | | int64_t s15; |
4213 | | int64_t s16; |
4214 | | int64_t s17; |
4215 | | int64_t s18; |
4216 | | int64_t s19; |
4217 | | int64_t s20; |
4218 | | int64_t s21; |
4219 | | int64_t s22; |
4220 | | int64_t s23; |
4221 | | int64_t carry0; |
4222 | | int64_t carry1; |
4223 | | int64_t carry2; |
4224 | | int64_t carry3; |
4225 | | int64_t carry4; |
4226 | | int64_t carry5; |
4227 | | int64_t carry6; |
4228 | | int64_t carry7; |
4229 | | int64_t carry8; |
4230 | | int64_t carry9; |
4231 | | int64_t carry10; |
4232 | | int64_t carry11; |
4233 | | int64_t carry12; |
4234 | | int64_t carry13; |
4235 | | int64_t carry14; |
4236 | | int64_t carry15; |
4237 | | int64_t carry16; |
4238 | | int64_t carry17; |
4239 | | int64_t carry18; |
4240 | | int64_t carry19; |
4241 | | int64_t carry20; |
4242 | | int64_t carry21; |
4243 | | int64_t carry22; |
4244 | | |
4245 | | s0 = c0 + a0 * b0; |
4246 | | s1 = c1 + a0 * b1 + a1 * b0; |
4247 | | s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; |
4248 | | s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; |
4249 | | s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; |
4250 | | s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; |
4251 | | s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; |
4252 | | s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + |
4253 | | a6 * b1 + a7 * b0; |
4254 | | s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + |
4255 | | a6 * b2 + a7 * b1 + a8 * b0; |
4256 | | s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + |
4257 | | a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; |
4258 | | s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + |
4259 | | a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; |
4260 | | s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + |
4261 | | a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; |
4262 | | s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + |
4263 | | a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; |
4264 | | s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + |
4265 | | a9 * b4 + a10 * b3 + a11 * b2; |
4266 | | s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + |
4267 | | a10 * b4 + a11 * b3; |
4268 | | s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + |
4269 | | a11 * b4; |
4270 | | s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; |
4271 | | s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; |
4272 | | s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; |
4273 | | s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; |
4274 | | s20 = a9 * b11 + a10 * b10 + a11 * b9; |
4275 | | s21 = a10 * b11 + a11 * b10; |
4276 | | s22 = a11 * b11; |
4277 | | s23 = 0; |
4278 | | |
4279 | | carry0 = (s0 + (1 << 20)) >> 21; |
4280 | | s1 += carry0; |
4281 | | s0 -= carry0 << 21; |
4282 | | carry2 = (s2 + (1 << 20)) >> 21; |
4283 | | s3 += carry2; |
4284 | | s2 -= carry2 << 21; |
4285 | | carry4 = (s4 + (1 << 20)) >> 21; |
4286 | | s5 += carry4; |
4287 | | s4 -= carry4 << 21; |
4288 | | carry6 = (s6 + (1 << 20)) >> 21; |
4289 | | s7 += carry6; |
4290 | | s6 -= carry6 << 21; |
4291 | | carry8 = (s8 + (1 << 20)) >> 21; |
4292 | | s9 += carry8; |
4293 | | s8 -= carry8 << 21; |
4294 | | carry10 = (s10 + (1 << 20)) >> 21; |
4295 | | s11 += carry10; |
4296 | | s10 -= carry10 << 21; |
4297 | | carry12 = (s12 + (1 << 20)) >> 21; |
4298 | | s13 += carry12; |
4299 | | s12 -= carry12 << 21; |
4300 | | carry14 = (s14 + (1 << 20)) >> 21; |
4301 | | s15 += carry14; |
4302 | | s14 -= carry14 << 21; |
4303 | | carry16 = (s16 + (1 << 20)) >> 21; |
4304 | | s17 += carry16; |
4305 | | s16 -= carry16 << 21; |
4306 | | carry18 = (s18 + (1 << 20)) >> 21; |
4307 | | s19 += carry18; |
4308 | | s18 -= carry18 << 21; |
4309 | | carry20 = (s20 + (1 << 20)) >> 21; |
4310 | | s21 += carry20; |
4311 | | s20 -= carry20 << 21; |
4312 | | carry22 = (s22 + (1 << 20)) >> 21; |
4313 | | s23 += carry22; |
4314 | | s22 -= carry22 << 21; |
4315 | | |
4316 | | carry1 = (s1 + (1 << 20)) >> 21; |
4317 | | s2 += carry1; |
4318 | | s1 -= carry1 << 21; |
4319 | | carry3 = (s3 + (1 << 20)) >> 21; |
4320 | | s4 += carry3; |
4321 | | s3 -= carry3 << 21; |
4322 | | carry5 = (s5 + (1 << 20)) >> 21; |
4323 | | s6 += carry5; |
4324 | | s5 -= carry5 << 21; |
4325 | | carry7 = (s7 + (1 << 20)) >> 21; |
4326 | | s8 += carry7; |
4327 | | s7 -= carry7 << 21; |
4328 | | carry9 = (s9 + (1 << 20)) >> 21; |
4329 | | s10 += carry9; |
4330 | | s9 -= carry9 << 21; |
4331 | | carry11 = (s11 + (1 << 20)) >> 21; |
4332 | | s12 += carry11; |
4333 | | s11 -= carry11 << 21; |
4334 | | carry13 = (s13 + (1 << 20)) >> 21; |
4335 | | s14 += carry13; |
4336 | | s13 -= carry13 << 21; |
4337 | | carry15 = (s15 + (1 << 20)) >> 21; |
4338 | | s16 += carry15; |
4339 | | s15 -= carry15 << 21; |
4340 | | carry17 = (s17 + (1 << 20)) >> 21; |
4341 | | s18 += carry17; |
4342 | | s17 -= carry17 << 21; |
4343 | | carry19 = (s19 + (1 << 20)) >> 21; |
4344 | | s20 += carry19; |
4345 | | s19 -= carry19 << 21; |
4346 | | carry21 = (s21 + (1 << 20)) >> 21; |
4347 | | s22 += carry21; |
4348 | | s21 -= carry21 << 21; |
4349 | | |
4350 | | s11 += s23 * 666643; |
4351 | | s12 += s23 * 470296; |
4352 | | s13 += s23 * 654183; |
4353 | | s14 -= s23 * 997805; |
4354 | | s15 += s23 * 136657; |
4355 | | s16 -= s23 * 683901; |
4356 | | s23 = 0; |
4357 | | |
4358 | | s10 += s22 * 666643; |
4359 | | s11 += s22 * 470296; |
4360 | | s12 += s22 * 654183; |
4361 | | s13 -= s22 * 997805; |
4362 | | s14 += s22 * 136657; |
4363 | | s15 -= s22 * 683901; |
4364 | | s22 = 0; |
4365 | | |
4366 | | s9 += s21 * 666643; |
4367 | | s10 += s21 * 470296; |
4368 | | s11 += s21 * 654183; |
4369 | | s12 -= s21 * 997805; |
4370 | | s13 += s21 * 136657; |
4371 | | s14 -= s21 * 683901; |
4372 | | s21 = 0; |
4373 | | |
4374 | | s8 += s20 * 666643; |
4375 | | s9 += s20 * 470296; |
4376 | | s10 += s20 * 654183; |
4377 | | s11 -= s20 * 997805; |
4378 | | s12 += s20 * 136657; |
4379 | | s13 -= s20 * 683901; |
4380 | | s20 = 0; |
4381 | | |
4382 | | s7 += s19 * 666643; |
4383 | | s8 += s19 * 470296; |
4384 | | s9 += s19 * 654183; |
4385 | | s10 -= s19 * 997805; |
4386 | | s11 += s19 * 136657; |
4387 | | s12 -= s19 * 683901; |
4388 | | s19 = 0; |
4389 | | |
4390 | | s6 += s18 * 666643; |
4391 | | s7 += s18 * 470296; |
4392 | | s8 += s18 * 654183; |
4393 | | s9 -= s18 * 997805; |
4394 | | s10 += s18 * 136657; |
4395 | | s11 -= s18 * 683901; |
4396 | | s18 = 0; |
4397 | | |
4398 | | carry6 = (s6 + (1 << 20)) >> 21; |
4399 | | s7 += carry6; |
4400 | | s6 -= carry6 << 21; |
4401 | | carry8 = (s8 + (1 << 20)) >> 21; |
4402 | | s9 += carry8; |
4403 | | s8 -= carry8 << 21; |
4404 | | carry10 = (s10 + (1 << 20)) >> 21; |
4405 | | s11 += carry10; |
4406 | | s10 -= carry10 << 21; |
4407 | | carry12 = (s12 + (1 << 20)) >> 21; |
4408 | | s13 += carry12; |
4409 | | s12 -= carry12 << 21; |
4410 | | carry14 = (s14 + (1 << 20)) >> 21; |
4411 | | s15 += carry14; |
4412 | | s14 -= carry14 << 21; |
4413 | | carry16 = (s16 + (1 << 20)) >> 21; |
4414 | | s17 += carry16; |
4415 | | s16 -= carry16 << 21; |
4416 | | |
4417 | | carry7 = (s7 + (1 << 20)) >> 21; |
4418 | | s8 += carry7; |
4419 | | s7 -= carry7 << 21; |
4420 | | carry9 = (s9 + (1 << 20)) >> 21; |
4421 | | s10 += carry9; |
4422 | | s9 -= carry9 << 21; |
4423 | | carry11 = (s11 + (1 << 20)) >> 21; |
4424 | | s12 += carry11; |
4425 | | s11 -= carry11 << 21; |
4426 | | carry13 = (s13 + (1 << 20)) >> 21; |
4427 | | s14 += carry13; |
4428 | | s13 -= carry13 << 21; |
4429 | | carry15 = (s15 + (1 << 20)) >> 21; |
4430 | | s16 += carry15; |
4431 | | s15 -= carry15 << 21; |
4432 | | |
4433 | | s5 += s17 * 666643; |
4434 | | s6 += s17 * 470296; |
4435 | | s7 += s17 * 654183; |
4436 | | s8 -= s17 * 997805; |
4437 | | s9 += s17 * 136657; |
4438 | | s10 -= s17 * 683901; |
4439 | | s17 = 0; |
4440 | | |
4441 | | s4 += s16 * 666643; |
4442 | | s5 += s16 * 470296; |
4443 | | s6 += s16 * 654183; |
4444 | | s7 -= s16 * 997805; |
4445 | | s8 += s16 * 136657; |
4446 | | s9 -= s16 * 683901; |
4447 | | s16 = 0; |
4448 | | |
4449 | | s3 += s15 * 666643; |
4450 | | s4 += s15 * 470296; |
4451 | | s5 += s15 * 654183; |
4452 | | s6 -= s15 * 997805; |
4453 | | s7 += s15 * 136657; |
4454 | | s8 -= s15 * 683901; |
4455 | | s15 = 0; |
4456 | | |
4457 | | s2 += s14 * 666643; |
4458 | | s3 += s14 * 470296; |
4459 | | s4 += s14 * 654183; |
4460 | | s5 -= s14 * 997805; |
4461 | | s6 += s14 * 136657; |
4462 | | s7 -= s14 * 683901; |
4463 | | s14 = 0; |
4464 | | |
4465 | | s1 += s13 * 666643; |
4466 | | s2 += s13 * 470296; |
4467 | | s3 += s13 * 654183; |
4468 | | s4 -= s13 * 997805; |
4469 | | s5 += s13 * 136657; |
4470 | | s6 -= s13 * 683901; |
4471 | | s13 = 0; |
4472 | | |
4473 | | s0 += s12 * 666643; |
4474 | | s1 += s12 * 470296; |
4475 | | s2 += s12 * 654183; |
4476 | | s3 -= s12 * 997805; |
4477 | | s4 += s12 * 136657; |
4478 | | s5 -= s12 * 683901; |
4479 | | s12 = 0; |
4480 | | |
4481 | | carry0 = (s0 + (1 << 20)) >> 21; |
4482 | | s1 += carry0; |
4483 | | s0 -= carry0 << 21; |
4484 | | carry2 = (s2 + (1 << 20)) >> 21; |
4485 | | s3 += carry2; |
4486 | | s2 -= carry2 << 21; |
4487 | | carry4 = (s4 + (1 << 20)) >> 21; |
4488 | | s5 += carry4; |
4489 | | s4 -= carry4 << 21; |
4490 | | carry6 = (s6 + (1 << 20)) >> 21; |
4491 | | s7 += carry6; |
4492 | | s6 -= carry6 << 21; |
4493 | | carry8 = (s8 + (1 << 20)) >> 21; |
4494 | | s9 += carry8; |
4495 | | s8 -= carry8 << 21; |
4496 | | carry10 = (s10 + (1 << 20)) >> 21; |
4497 | | s11 += carry10; |
4498 | | s10 -= carry10 << 21; |
4499 | | |
4500 | | carry1 = (s1 + (1 << 20)) >> 21; |
4501 | | s2 += carry1; |
4502 | | s1 -= carry1 << 21; |
4503 | | carry3 = (s3 + (1 << 20)) >> 21; |
4504 | | s4 += carry3; |
4505 | | s3 -= carry3 << 21; |
4506 | | carry5 = (s5 + (1 << 20)) >> 21; |
4507 | | s6 += carry5; |
4508 | | s5 -= carry5 << 21; |
4509 | | carry7 = (s7 + (1 << 20)) >> 21; |
4510 | | s8 += carry7; |
4511 | | s7 -= carry7 << 21; |
4512 | | carry9 = (s9 + (1 << 20)) >> 21; |
4513 | | s10 += carry9; |
4514 | | s9 -= carry9 << 21; |
4515 | | carry11 = (s11 + (1 << 20)) >> 21; |
4516 | | s12 += carry11; |
4517 | | s11 -= carry11 << 21; |
4518 | | |
4519 | | s0 += s12 * 666643; |
4520 | | s1 += s12 * 470296; |
4521 | | s2 += s12 * 654183; |
4522 | | s3 -= s12 * 997805; |
4523 | | s4 += s12 * 136657; |
4524 | | s5 -= s12 * 683901; |
4525 | | s12 = 0; |
4526 | | |
4527 | | carry0 = s0 >> 21; |
4528 | | s1 += carry0; |
4529 | | s0 -= carry0 << 21; |
4530 | | carry1 = s1 >> 21; |
4531 | | s2 += carry1; |
4532 | | s1 -= carry1 << 21; |
4533 | | carry2 = s2 >> 21; |
4534 | | s3 += carry2; |
4535 | | s2 -= carry2 << 21; |
4536 | | carry3 = s3 >> 21; |
4537 | | s4 += carry3; |
4538 | | s3 -= carry3 << 21; |
4539 | | carry4 = s4 >> 21; |
4540 | | s5 += carry4; |
4541 | | s4 -= carry4 << 21; |
4542 | | carry5 = s5 >> 21; |
4543 | | s6 += carry5; |
4544 | | s5 -= carry5 << 21; |
4545 | | carry6 = s6 >> 21; |
4546 | | s7 += carry6; |
4547 | | s6 -= carry6 << 21; |
4548 | | carry7 = s7 >> 21; |
4549 | | s8 += carry7; |
4550 | | s7 -= carry7 << 21; |
4551 | | carry8 = s8 >> 21; |
4552 | | s9 += carry8; |
4553 | | s8 -= carry8 << 21; |
4554 | | carry9 = s9 >> 21; |
4555 | | s10 += carry9; |
4556 | | s9 -= carry9 << 21; |
4557 | | carry10 = s10 >> 21; |
4558 | | s11 += carry10; |
4559 | | s10 -= carry10 << 21; |
4560 | | carry11 = s11 >> 21; |
4561 | | s12 += carry11; |
4562 | | s11 -= carry11 << 21; |
4563 | | |
4564 | | s0 += s12 * 666643; |
4565 | | s1 += s12 * 470296; |
4566 | | s2 += s12 * 654183; |
4567 | | s3 -= s12 * 997805; |
4568 | | s4 += s12 * 136657; |
4569 | | s5 -= s12 * 683901; |
4570 | | s12 = 0; |
4571 | | |
4572 | | carry0 = s0 >> 21; |
4573 | | s1 += carry0; |
4574 | | s0 -= carry0 << 21; |
4575 | | carry1 = s1 >> 21; |
4576 | | s2 += carry1; |
4577 | | s1 -= carry1 << 21; |
4578 | | carry2 = s2 >> 21; |
4579 | | s3 += carry2; |
4580 | | s2 -= carry2 << 21; |
4581 | | carry3 = s3 >> 21; |
4582 | | s4 += carry3; |
4583 | | s3 -= carry3 << 21; |
4584 | | carry4 = s4 >> 21; |
4585 | | s5 += carry4; |
4586 | | s4 -= carry4 << 21; |
4587 | | carry5 = s5 >> 21; |
4588 | | s6 += carry5; |
4589 | | s5 -= carry5 << 21; |
4590 | | carry6 = s6 >> 21; |
4591 | | s7 += carry6; |
4592 | | s6 -= carry6 << 21; |
4593 | | carry7 = s7 >> 21; |
4594 | | s8 += carry7; |
4595 | | s7 -= carry7 << 21; |
4596 | | carry8 = s8 >> 21; |
4597 | | s9 += carry8; |
4598 | | s8 -= carry8 << 21; |
4599 | | carry9 = s9 >> 21; |
4600 | | s10 += carry9; |
4601 | | s9 -= carry9 << 21; |
4602 | | carry10 = s10 >> 21; |
4603 | | s11 += carry10; |
4604 | | s10 -= carry10 << 21; |
4605 | | |
4606 | | s[0] = s0 >> 0; |
4607 | | s[1] = s0 >> 8; |
4608 | | s[2] = (s0 >> 16) | (s1 << 5); |
4609 | | s[3] = s1 >> 3; |
4610 | | s[4] = s1 >> 11; |
4611 | | s[5] = (s1 >> 19) | (s2 << 2); |
4612 | | s[6] = s2 >> 6; |
4613 | | s[7] = (s2 >> 14) | (s3 << 7); |
4614 | | s[8] = s3 >> 1; |
4615 | | s[9] = s3 >> 9; |
4616 | | s[10] = (s3 >> 17) | (s4 << 4); |
4617 | | s[11] = s4 >> 4; |
4618 | | s[12] = s4 >> 12; |
4619 | | s[13] = (s4 >> 20) | (s5 << 1); |
4620 | | s[14] = s5 >> 7; |
4621 | | s[15] = (s5 >> 15) | (s6 << 6); |
4622 | | s[16] = s6 >> 2; |
4623 | | s[17] = s6 >> 10; |
4624 | | s[18] = (s6 >> 18) | (s7 << 3); |
4625 | | s[19] = s7 >> 5; |
4626 | | s[20] = s7 >> 13; |
4627 | | s[21] = s8 >> 0; |
4628 | | s[22] = s8 >> 8; |
4629 | | s[23] = (s8 >> 16) | (s9 << 5); |
4630 | | s[24] = s9 >> 3; |
4631 | | s[25] = s9 >> 11; |
4632 | | s[26] = (s9 >> 19) | (s10 << 2); |
4633 | | s[27] = s10 >> 6; |
4634 | | s[28] = (s10 >> 14) | (s11 << 7); |
4635 | | s[29] = s11 >> 1; |
4636 | | s[30] = s11 >> 9; |
4637 | | s[31] = s11 >> 17; |
4638 | | } |
4639 | | #endif |
4640 | | |
4641 | | #ifdef ED25519 |
4642 | | void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) { |
4643 | | uint8_t seed[32]; |
4644 | | arc4random_buf(seed, 32); |
4645 | | |
4646 | | uint8_t az[SHA512_DIGEST_LENGTH]; |
4647 | | SHA512(seed, 32, az); |
4648 | | |
4649 | | az[0] &= 248; |
4650 | | az[31] &= 63; |
4651 | | az[31] |= 64; |
4652 | | |
4653 | | ge_p3 A; |
4654 | | x25519_ge_scalarmult_base(&A, az); |
4655 | | ge_p3_tobytes(out_public_key, &A); |
4656 | | |
4657 | | memcpy(out_private_key, seed, 32); |
4658 | | memmove(out_private_key + 32, out_public_key, 32); |
4659 | | } |
4660 | | |
4661 | | int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, |
4662 | | const uint8_t private_key[64]) { |
4663 | | uint8_t az[SHA512_DIGEST_LENGTH]; |
4664 | | SHA512(private_key, 32, az); |
4665 | | |
4666 | | az[0] &= 248; |
4667 | | az[31] &= 63; |
4668 | | az[31] |= 64; |
4669 | | |
4670 | | SHA512_CTX hash_ctx; |
4671 | | SHA512_Init(&hash_ctx); |
4672 | | SHA512_Update(&hash_ctx, az + 32, 32); |
4673 | | SHA512_Update(&hash_ctx, message, message_len); |
4674 | | uint8_t nonce[SHA512_DIGEST_LENGTH]; |
4675 | | SHA512_Final(nonce, &hash_ctx); |
4676 | | |
4677 | | x25519_sc_reduce(nonce); |
4678 | | ge_p3 R; |
4679 | | x25519_ge_scalarmult_base(&R, nonce); |
4680 | | ge_p3_tobytes(out_sig, &R); |
4681 | | |
4682 | | SHA512_Init(&hash_ctx); |
4683 | | SHA512_Update(&hash_ctx, out_sig, 32); |
4684 | | SHA512_Update(&hash_ctx, private_key + 32, 32); |
4685 | | SHA512_Update(&hash_ctx, message, message_len); |
4686 | | uint8_t hram[SHA512_DIGEST_LENGTH]; |
4687 | | SHA512_Final(hram, &hash_ctx); |
4688 | | |
4689 | | x25519_sc_reduce(hram); |
4690 | | sc_muladd(out_sig + 32, hram, az, nonce); |
4691 | | |
4692 | | return 1; |
4693 | | } |
4694 | | |
4695 | | int ED25519_verify(const uint8_t *message, size_t message_len, |
4696 | | const uint8_t signature[64], const uint8_t public_key[32]) { |
4697 | | ge_p3 A; |
4698 | | if ((signature[63] & 224) != 0 || |
4699 | | x25519_ge_frombytes_vartime(&A, public_key) != 0) { |
4700 | | return 0; |
4701 | | } |
4702 | | |
4703 | | fe_neg(A.X, A.X); |
4704 | | fe_neg(A.T, A.T); |
4705 | | |
4706 | | uint8_t pkcopy[32]; |
4707 | | memcpy(pkcopy, public_key, 32); |
4708 | | uint8_t rcopy[32]; |
4709 | | memcpy(rcopy, signature, 32); |
4710 | | uint8_t scopy[32]; |
4711 | | memcpy(scopy, signature + 32, 32); |
4712 | | |
4713 | | SHA512_CTX hash_ctx; |
4714 | | SHA512_Init(&hash_ctx); |
4715 | | SHA512_Update(&hash_ctx, signature, 32); |
4716 | | SHA512_Update(&hash_ctx, public_key, 32); |
4717 | | SHA512_Update(&hash_ctx, message, message_len); |
4718 | | uint8_t h[SHA512_DIGEST_LENGTH]; |
4719 | | SHA512_Final(h, &hash_ctx); |
4720 | | |
4721 | | x25519_sc_reduce(h); |
4722 | | |
4723 | | ge_p2 R; |
4724 | | ge_double_scalarmult_vartime(&R, h, &A, scopy); |
4725 | | |
4726 | | uint8_t rcheck[32]; |
4727 | | x25519_ge_tobytes(rcheck, &R); |
4728 | | |
4729 | | return timingsafe_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0; |
4730 | | } |
4731 | | #endif |
4732 | | |
4733 | | /* Replace (f,g) with (g,f) if b == 1; |
4734 | | * replace (f,g) with (f,g) if b == 0. |
4735 | | * |
4736 | | * Preconditions: b in {0,1}. */ |
4737 | 166k | static void fe_cswap(fe f, fe g, unsigned int b) { |
4738 | 166k | b = 0-b; |
4739 | 166k | unsigned i; |
4740 | 1.83M | for (i = 0; i < 10; i++) { |
4741 | 1.66M | int32_t x = f[i] ^ g[i]; |
4742 | 1.66M | x &= b; |
4743 | 1.66M | f[i] ^= x; |
4744 | 1.66M | g[i] ^= x; |
4745 | 1.66M | } |
4746 | 166k | } |
4747 | | |
4748 | | /* h = f * 121666 |
4749 | | * Can overlap h with f. |
4750 | | * |
4751 | | * Preconditions: |
4752 | | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
4753 | | * |
4754 | | * Postconditions: |
4755 | | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ |
4756 | 82.8k | static void fe_mul121666(fe h, fe f) { |
4757 | 82.8k | int32_t f0 = f[0]; |
4758 | 82.8k | int32_t f1 = f[1]; |
4759 | 82.8k | int32_t f2 = f[2]; |
4760 | 82.8k | int32_t f3 = f[3]; |
4761 | 82.8k | int32_t f4 = f[4]; |
4762 | 82.8k | int32_t f5 = f[5]; |
4763 | 82.8k | int32_t f6 = f[6]; |
4764 | 82.8k | int32_t f7 = f[7]; |
4765 | 82.8k | int32_t f8 = f[8]; |
4766 | 82.8k | int32_t f9 = f[9]; |
4767 | 82.8k | int64_t h0 = f0 * (int64_t) 121666; |
4768 | 82.8k | int64_t h1 = f1 * (int64_t) 121666; |
4769 | 82.8k | int64_t h2 = f2 * (int64_t) 121666; |
4770 | 82.8k | int64_t h3 = f3 * (int64_t) 121666; |
4771 | 82.8k | int64_t h4 = f4 * (int64_t) 121666; |
4772 | 82.8k | int64_t h5 = f5 * (int64_t) 121666; |
4773 | 82.8k | int64_t h6 = f6 * (int64_t) 121666; |
4774 | 82.8k | int64_t h7 = f7 * (int64_t) 121666; |
4775 | 82.8k | int64_t h8 = f8 * (int64_t) 121666; |
4776 | 82.8k | int64_t h9 = f9 * (int64_t) 121666; |
4777 | 82.8k | int64_t carry0; |
4778 | 82.8k | int64_t carry1; |
4779 | 82.8k | int64_t carry2; |
4780 | 82.8k | int64_t carry3; |
4781 | 82.8k | int64_t carry4; |
4782 | 82.8k | int64_t carry5; |
4783 | 82.8k | int64_t carry6; |
4784 | 82.8k | int64_t carry7; |
4785 | 82.8k | int64_t carry8; |
4786 | 82.8k | int64_t carry9; |
4787 | | |
4788 | 82.8k | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
4789 | 82.8k | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
4790 | 82.8k | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
4791 | 82.8k | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
4792 | 82.8k | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
4793 | | |
4794 | 82.8k | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
4795 | 82.8k | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
4796 | 82.8k | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
4797 | 82.8k | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
4798 | 82.8k | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
4799 | | |
4800 | 82.8k | h[0] = h0; |
4801 | 82.8k | h[1] = h1; |
4802 | 82.8k | h[2] = h2; |
4803 | 82.8k | h[3] = h3; |
4804 | 82.8k | h[4] = h4; |
4805 | 82.8k | h[5] = h5; |
4806 | 82.8k | h[6] = h6; |
4807 | 82.8k | h[7] = h7; |
4808 | 82.8k | h[8] = h8; |
4809 | 82.8k | h[9] = h9; |
4810 | 82.8k | } |
4811 | | |
4812 | | void |
4813 | | x25519_scalar_mult_generic(uint8_t out[32], const uint8_t scalar[32], |
4814 | 325 | const uint8_t point[32]) { |
4815 | 325 | fe x1, x2, z2, x3, z3, tmp0, tmp1; |
4816 | | |
4817 | 325 | uint8_t e[32]; |
4818 | 325 | memcpy(e, scalar, 32); |
4819 | 325 | e[0] &= 248; |
4820 | 325 | e[31] &= 127; |
4821 | 325 | e[31] |= 64; |
4822 | 325 | fe_frombytes(x1, point); |
4823 | 325 | fe_1(x2); |
4824 | 325 | fe_0(z2); |
4825 | 325 | fe_copy(x3, x1); |
4826 | 325 | fe_1(z3); |
4827 | | |
4828 | 325 | unsigned swap = 0; |
4829 | 325 | int pos; |
4830 | 83.2k | for (pos = 254; pos >= 0; --pos) { |
4831 | 82.8k | unsigned b = 1 & (e[pos / 8] >> (pos & 7)); |
4832 | 82.8k | swap ^= b; |
4833 | 82.8k | fe_cswap(x2, x3, swap); |
4834 | 82.8k | fe_cswap(z2, z3, swap); |
4835 | 82.8k | swap = b; |
4836 | 82.8k | fe_sub(tmp0, x3, z3); |
4837 | 82.8k | fe_sub(tmp1, x2, z2); |
4838 | 82.8k | fe_add(x2, x2, z2); |
4839 | 82.8k | fe_add(z2, x3, z3); |
4840 | 82.8k | fe_mul(z3, tmp0, x2); |
4841 | 82.8k | fe_mul(z2, z2, tmp1); |
4842 | 82.8k | fe_sq(tmp0, tmp1); |
4843 | 82.8k | fe_sq(tmp1, x2); |
4844 | 82.8k | fe_add(x3, z3, z2); |
4845 | 82.8k | fe_sub(z2, z3, z2); |
4846 | 82.8k | fe_mul(x2, tmp1, tmp0); |
4847 | 82.8k | fe_sub(tmp1, tmp1, tmp0); |
4848 | 82.8k | fe_sq(z2, z2); |
4849 | 82.8k | fe_mul121666(z3, tmp1); |
4850 | 82.8k | fe_sq(x3, x3); |
4851 | 82.8k | fe_add(tmp0, tmp0, z3); |
4852 | 82.8k | fe_mul(z3, x1, z2); |
4853 | 82.8k | fe_mul(z2, tmp1, tmp0); |
4854 | 82.8k | } |
4855 | 325 | fe_cswap(x2, x3, swap); |
4856 | 325 | fe_cswap(z2, z3, swap); |
4857 | | |
4858 | 325 | fe_invert(z2, z2); |
4859 | 325 | fe_mul(x2, x2, z2); |
4860 | 325 | fe_tobytes(out, x2); |
4861 | 325 | } |
4862 | | |
4863 | | #ifdef unused |
4864 | | void |
4865 | | x25519_public_from_private_generic(uint8_t out_public_value[32], |
4866 | | const uint8_t private_key[32]) |
4867 | | { |
4868 | | uint8_t e[32]; |
4869 | | |
4870 | | memcpy(e, private_key, 32); |
4871 | | e[0] &= 248; |
4872 | | e[31] &= 127; |
4873 | | e[31] |= 64; |
4874 | | |
4875 | | ge_p3 A; |
4876 | | x25519_ge_scalarmult_base(&A, e); |
4877 | | |
4878 | | /* We only need the u-coordinate of the curve25519 point. The map is |
4879 | | * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ |
4880 | | fe zplusy, zminusy, zminusy_inv; |
4881 | | fe_add(zplusy, A.Z, A.Y); |
4882 | | fe_sub(zminusy, A.Z, A.Y); |
4883 | | fe_invert(zminusy_inv, zminusy); |
4884 | | fe_mul(zplusy, zplusy, zminusy_inv); |
4885 | | fe_tobytes(out_public_value, zplusy); |
4886 | | } |
4887 | | #endif |
4888 | | |
4889 | | void |
4890 | | x25519_public_from_private(uint8_t out_public_value[32], |
4891 | | const uint8_t private_key[32]) |
4892 | 197 | { |
4893 | 197 | static const uint8_t kMongomeryBasePoint[32] = {9}; |
4894 | | |
4895 | 197 | x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint); |
4896 | 197 | } |
4897 | | |
4898 | | void |
4899 | | X25519_keypair(uint8_t out_public_value[X25519_KEY_LENGTH], |
4900 | | uint8_t out_private_key[X25519_KEY_LENGTH]) |
4901 | 197 | { |
4902 | | /* All X25519 implementations should decode scalars correctly (see |
4903 | | * https://tools.ietf.org/html/rfc7748#section-5). However, if an |
4904 | | * implementation doesn't then it might interoperate with random keys a |
4905 | | * fraction of the time because they'll, randomly, happen to be correctly |
4906 | | * formed. |
4907 | | * |
4908 | | * Thus we do the opposite of the masking here to make sure that our private |
4909 | | * keys are never correctly masked and so, hopefully, any incorrect |
4910 | | * implementations are deterministically broken. |
4911 | | * |
4912 | | * This does not affect security because, although we're throwing away |
4913 | | * entropy, a valid implementation of scalarmult should throw away the exact |
4914 | | * same bits anyway. */ |
4915 | 197 | arc4random_buf(out_private_key, 32); |
4916 | | |
4917 | 197 | out_private_key[0] |= 7; |
4918 | 197 | out_private_key[31] &= 63; |
4919 | 197 | out_private_key[31] |= 128; |
4920 | | |
4921 | 197 | x25519_public_from_private(out_public_value, out_private_key); |
4922 | 197 | } |
4923 | | |
4924 | | int |
4925 | | X25519(uint8_t out_shared_key[X25519_KEY_LENGTH], |
4926 | | const uint8_t private_key[X25519_KEY_LENGTH], |
4927 | | const uint8_t peer_public_value[X25519_KEY_LENGTH]) |
4928 | 128 | { |
4929 | 128 | static const uint8_t kZeros[32] = {0}; |
4930 | | |
4931 | 128 | x25519_scalar_mult(out_shared_key, private_key, peer_public_value); |
4932 | | |
4933 | | /* The all-zero output results when the input is a point of small order. */ |
4934 | 128 | return timingsafe_memcmp(kZeros, out_shared_key, 32) != 0; |
4935 | 128 | } |