]>
Commit | Line | Data |
---|---|---|
aa6bb135 RS |
1 | /* |
2 | * Copyright 2016 The OpenSSL Project Authors. All Rights Reserved. | |
df3bde67 | 3 | * |
aa6bb135 RS |
4 | * Licensed under the OpenSSL license (the "License"). You may not use |
5 | * this file except in compliance with the License. You can obtain a copy | |
6 | * in the file LICENSE in the source distribution or at | |
7 | * https://www.openssl.org/source/license.html | |
df3bde67 | 8 | */ |
a90def6b DSH |
9 | |
10 | /* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP | |
df3bde67 | 11 | * 20141124 (http://bench.cr.yp.to/supercop.html). |
a90def6b DSH |
12 | * |
13 | * The field functions are shared by Ed25519 and X25519 where possible. */ | |
14 | ||
a90def6b | 15 | #include <string.h> |
244e5f5d | 16 | #include "ec_lcl.h" |
a90def6b DSH |
17 | |
18 | ||
19 | /* fe means field element. Here the field is \Z/(2^255-19). An element t, | |
20 | * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 | |
21 | * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on | |
22 | * context. */ | |
23 | typedef int32_t fe[10]; | |
24 | ||
5b7af0dd EK |
25 | static const int64_t kBottom25Bits = 0x1ffffffLL; |
26 | static const int64_t kBottom26Bits = 0x3ffffffLL; | |
27 | static const int64_t kTop39Bits = 0xfffffffffe000000LL; | |
28 | static const int64_t kTop38Bits = 0xfffffffffc000000LL; | |
b9577984 | 29 | |
a90def6b DSH |
30 | static uint64_t load_3(const uint8_t *in) { |
31 | uint64_t result; | |
32 | result = (uint64_t)in[0]; | |
33 | result |= ((uint64_t)in[1]) << 8; | |
34 | result |= ((uint64_t)in[2]) << 16; | |
35 | return result; | |
36 | } | |
37 | ||
38 | static uint64_t load_4(const uint8_t *in) { | |
39 | uint64_t result; | |
40 | result = (uint64_t)in[0]; | |
41 | result |= ((uint64_t)in[1]) << 8; | |
42 | result |= ((uint64_t)in[2]) << 16; | |
43 | result |= ((uint64_t)in[3]) << 24; | |
44 | return result; | |
45 | } | |
46 | ||
47 | static void fe_frombytes(fe h, const uint8_t *s) { | |
48 | /* Ignores top bit of h. */ | |
49 | int64_t h0 = load_4(s); | |
50 | int64_t h1 = load_3(s + 4) << 6; | |
51 | int64_t h2 = load_3(s + 7) << 5; | |
52 | int64_t h3 = load_3(s + 10) << 3; | |
53 | int64_t h4 = load_3(s + 13) << 2; | |
54 | int64_t h5 = load_4(s + 16); | |
55 | int64_t h6 = load_3(s + 20) << 7; | |
56 | int64_t h7 = load_3(s + 23) << 5; | |
57 | int64_t h8 = load_3(s + 26) << 4; | |
58 | int64_t h9 = (load_3(s + 29) & 8388607) << 2; | |
59 | int64_t carry0; | |
60 | int64_t carry1; | |
61 | int64_t carry2; | |
62 | int64_t carry3; | |
63 | int64_t carry4; | |
64 | int64_t carry5; | |
65 | int64_t carry6; | |
66 | int64_t carry7; | |
67 | int64_t carry8; | |
68 | int64_t carry9; | |
69 | ||
b9577984 EK |
70 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
71 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; | |
72 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; | |
73 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
74 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
a90def6b | 75 | |
b9577984 EK |
76 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
77 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; | |
78 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
79 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
80 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
a90def6b DSH |
81 | |
82 | h[0] = h0; | |
83 | h[1] = h1; | |
84 | h[2] = h2; | |
85 | h[3] = h3; | |
86 | h[4] = h4; | |
87 | h[5] = h5; | |
88 | h[6] = h6; | |
89 | h[7] = h7; | |
90 | h[8] = h8; | |
91 | h[9] = h9; | |
92 | } | |
93 | ||
94 | /* Preconditions: | |
95 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. | |
96 | * | |
97 | * Write p=2^255-19; q=floor(h/p). | |
98 | * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). | |
99 | * | |
100 | * Proof: | |
101 | * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. | |
102 | * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. | |
103 | * | |
104 | * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). | |
105 | * Then 0<y<1. | |
106 | * | |
107 | * Write r=h-pq. | |
108 | * Have 0<=r<=p-1=2^255-20. | |
109 | * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. | |
110 | * | |
111 | * Write x=r+19(2^-255)r+y. | |
112 | * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. | |
113 | * | |
114 | * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) | |
115 | * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */ | |
116 | static void fe_tobytes(uint8_t *s, const fe h) { | |
117 | int32_t h0 = h[0]; | |
118 | int32_t h1 = h[1]; | |
119 | int32_t h2 = h[2]; | |
120 | int32_t h3 = h[3]; | |
121 | int32_t h4 = h[4]; | |
122 | int32_t h5 = h[5]; | |
123 | int32_t h6 = h[6]; | |
124 | int32_t h7 = h[7]; | |
125 | int32_t h8 = h[8]; | |
126 | int32_t h9 = h[9]; | |
127 | int32_t q; | |
a90def6b DSH |
128 | |
129 | q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; | |
130 | q = (h0 + q) >> 26; | |
131 | q = (h1 + q) >> 25; | |
132 | q = (h2 + q) >> 26; | |
133 | q = (h3 + q) >> 25; | |
134 | q = (h4 + q) >> 26; | |
135 | q = (h5 + q) >> 25; | |
136 | q = (h6 + q) >> 26; | |
137 | q = (h7 + q) >> 25; | |
138 | q = (h8 + q) >> 26; | |
139 | q = (h9 + q) >> 25; | |
140 | ||
141 | /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ | |
142 | h0 += 19 * q; | |
143 | /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ | |
144 | ||
b9577984 EK |
145 | h1 += h0 >> 26; h0 &= kBottom26Bits; |
146 | h2 += h1 >> 25; h1 &= kBottom25Bits; | |
147 | h3 += h2 >> 26; h2 &= kBottom26Bits; | |
148 | h4 += h3 >> 25; h3 &= kBottom25Bits; | |
149 | h5 += h4 >> 26; h4 &= kBottom26Bits; | |
150 | h6 += h5 >> 25; h5 &= kBottom25Bits; | |
151 | h7 += h6 >> 26; h6 &= kBottom26Bits; | |
152 | h8 += h7 >> 25; h7 &= kBottom25Bits; | |
153 | h9 += h8 >> 26; h8 &= kBottom26Bits; | |
154 | h9 &= kBottom25Bits; | |
a90def6b DSH |
155 | /* h10 = carry9 */ |
156 | ||
157 | /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. | |
158 | * Have h0+...+2^230 h9 between 0 and 2^255-1; | |
159 | * evidently 2^255 h10-2^255 q = 0. | |
160 | * Goal: Output h0+...+2^230 h9. */ | |
161 | ||
162 | s[0] = h0 >> 0; | |
163 | s[1] = h0 >> 8; | |
164 | s[2] = h0 >> 16; | |
b9577984 | 165 | s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2); |
a90def6b DSH |
166 | s[4] = h1 >> 6; |
167 | s[5] = h1 >> 14; | |
b9577984 | 168 | s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3); |
a90def6b DSH |
169 | s[7] = h2 >> 5; |
170 | s[8] = h2 >> 13; | |
b9577984 | 171 | s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5); |
a90def6b DSH |
172 | s[10] = h3 >> 3; |
173 | s[11] = h3 >> 11; | |
b9577984 | 174 | s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6); |
a90def6b DSH |
175 | s[13] = h4 >> 2; |
176 | s[14] = h4 >> 10; | |
177 | s[15] = h4 >> 18; | |
178 | s[16] = h5 >> 0; | |
179 | s[17] = h5 >> 8; | |
180 | s[18] = h5 >> 16; | |
b9577984 | 181 | s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1); |
a90def6b DSH |
182 | s[20] = h6 >> 7; |
183 | s[21] = h6 >> 15; | |
b9577984 | 184 | s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3); |
a90def6b DSH |
185 | s[23] = h7 >> 5; |
186 | s[24] = h7 >> 13; | |
b9577984 | 187 | s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4); |
a90def6b DSH |
188 | s[26] = h8 >> 4; |
189 | s[27] = h8 >> 12; | |
b9577984 | 190 | s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6); |
a90def6b DSH |
191 | s[29] = h9 >> 2; |
192 | s[30] = h9 >> 10; | |
193 | s[31] = h9 >> 18; | |
194 | } | |
195 | ||
196 | /* h = f */ | |
197 | static void fe_copy(fe h, const fe f) { | |
198 | memmove(h, f, sizeof(int32_t) * 10); | |
199 | } | |
200 | ||
201 | /* h = 0 */ | |
202 | static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } | |
203 | ||
204 | /* h = 1 */ | |
205 | static void fe_1(fe h) { | |
206 | memset(h, 0, sizeof(int32_t) * 10); | |
207 | h[0] = 1; | |
208 | } | |
209 | ||
210 | /* h = f + g | |
211 | * Can overlap h with f or g. | |
212 | * | |
213 | * Preconditions: | |
214 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
215 | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
216 | * | |
217 | * Postconditions: | |
218 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ | |
219 | static void fe_add(fe h, const fe f, const fe g) { | |
220 | unsigned i; | |
221 | for (i = 0; i < 10; i++) { | |
222 | h[i] = f[i] + g[i]; | |
223 | } | |
224 | } | |
225 | ||
226 | /* h = f - g | |
227 | * Can overlap h with f or g. | |
228 | * | |
229 | * Preconditions: | |
230 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
231 | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
232 | * | |
233 | * Postconditions: | |
234 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ | |
235 | static void fe_sub(fe h, const fe f, const fe g) { | |
236 | unsigned i; | |
237 | for (i = 0; i < 10; i++) { | |
238 | h[i] = f[i] - g[i]; | |
239 | } | |
240 | } | |
241 | ||
242 | /* h = f * g | |
243 | * Can overlap h with f or g. | |
244 | * | |
245 | * Preconditions: | |
246 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. | |
247 | * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. | |
248 | * | |
249 | * Postconditions: | |
250 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. | |
251 | * | |
252 | * Notes on implementation strategy: | |
253 | * | |
254 | * Using schoolbook multiplication. | |
255 | * Karatsuba would save a little in some cost models. | |
256 | * | |
257 | * Most multiplications by 2 and 19 are 32-bit precomputations; | |
258 | * cheaper than 64-bit postcomputations. | |
259 | * | |
260 | * There is one remaining multiplication by 19 in the carry chain; | |
261 | * one *19 precomputation can be merged into this, | |
262 | * but the resulting data flow is considerably less clean. | |
263 | * | |
264 | * There are 12 carries below. | |
265 | * 10 of them are 2-way parallelizable and vectorizable. | |
266 | * Can get away with 11 carries, but then data flow is much deeper. | |
267 | * | |
268 | * With tighter constraints on inputs can squeeze carries into int32. */ | |
269 | static void fe_mul(fe h, const fe f, const fe g) { | |
270 | int32_t f0 = f[0]; | |
271 | int32_t f1 = f[1]; | |
272 | int32_t f2 = f[2]; | |
273 | int32_t f3 = f[3]; | |
274 | int32_t f4 = f[4]; | |
275 | int32_t f5 = f[5]; | |
276 | int32_t f6 = f[6]; | |
277 | int32_t f7 = f[7]; | |
278 | int32_t f8 = f[8]; | |
279 | int32_t f9 = f[9]; | |
280 | int32_t g0 = g[0]; | |
281 | int32_t g1 = g[1]; | |
282 | int32_t g2 = g[2]; | |
283 | int32_t g3 = g[3]; | |
284 | int32_t g4 = g[4]; | |
285 | int32_t g5 = g[5]; | |
286 | int32_t g6 = g[6]; | |
287 | int32_t g7 = g[7]; | |
288 | int32_t g8 = g[8]; | |
289 | int32_t g9 = g[9]; | |
290 | int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ | |
291 | int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ | |
292 | int32_t g3_19 = 19 * g3; | |
293 | int32_t g4_19 = 19 * g4; | |
294 | int32_t g5_19 = 19 * g5; | |
295 | int32_t g6_19 = 19 * g6; | |
296 | int32_t g7_19 = 19 * g7; | |
297 | int32_t g8_19 = 19 * g8; | |
298 | int32_t g9_19 = 19 * g9; | |
299 | int32_t f1_2 = 2 * f1; | |
300 | int32_t f3_2 = 2 * f3; | |
301 | int32_t f5_2 = 2 * f5; | |
302 | int32_t f7_2 = 2 * f7; | |
303 | int32_t f9_2 = 2 * f9; | |
304 | int64_t f0g0 = f0 * (int64_t) g0; | |
305 | int64_t f0g1 = f0 * (int64_t) g1; | |
306 | int64_t f0g2 = f0 * (int64_t) g2; | |
307 | int64_t f0g3 = f0 * (int64_t) g3; | |
308 | int64_t f0g4 = f0 * (int64_t) g4; | |
309 | int64_t f0g5 = f0 * (int64_t) g5; | |
310 | int64_t f0g6 = f0 * (int64_t) g6; | |
311 | int64_t f0g7 = f0 * (int64_t) g7; | |
312 | int64_t f0g8 = f0 * (int64_t) g8; | |
313 | int64_t f0g9 = f0 * (int64_t) g9; | |
314 | int64_t f1g0 = f1 * (int64_t) g0; | |
315 | int64_t f1g1_2 = f1_2 * (int64_t) g1; | |
316 | int64_t f1g2 = f1 * (int64_t) g2; | |
317 | int64_t f1g3_2 = f1_2 * (int64_t) g3; | |
318 | int64_t f1g4 = f1 * (int64_t) g4; | |
319 | int64_t f1g5_2 = f1_2 * (int64_t) g5; | |
320 | int64_t f1g6 = f1 * (int64_t) g6; | |
321 | int64_t f1g7_2 = f1_2 * (int64_t) g7; | |
322 | int64_t f1g8 = f1 * (int64_t) g8; | |
323 | int64_t f1g9_38 = f1_2 * (int64_t) g9_19; | |
324 | int64_t f2g0 = f2 * (int64_t) g0; | |
325 | int64_t f2g1 = f2 * (int64_t) g1; | |
326 | int64_t f2g2 = f2 * (int64_t) g2; | |
327 | int64_t f2g3 = f2 * (int64_t) g3; | |
328 | int64_t f2g4 = f2 * (int64_t) g4; | |
329 | int64_t f2g5 = f2 * (int64_t) g5; | |
330 | int64_t f2g6 = f2 * (int64_t) g6; | |
331 | int64_t f2g7 = f2 * (int64_t) g7; | |
332 | int64_t f2g8_19 = f2 * (int64_t) g8_19; | |
333 | int64_t f2g9_19 = f2 * (int64_t) g9_19; | |
334 | int64_t f3g0 = f3 * (int64_t) g0; | |
335 | int64_t f3g1_2 = f3_2 * (int64_t) g1; | |
336 | int64_t f3g2 = f3 * (int64_t) g2; | |
337 | int64_t f3g3_2 = f3_2 * (int64_t) g3; | |
338 | int64_t f3g4 = f3 * (int64_t) g4; | |
339 | int64_t f3g5_2 = f3_2 * (int64_t) g5; | |
340 | int64_t f3g6 = f3 * (int64_t) g6; | |
341 | int64_t f3g7_38 = f3_2 * (int64_t) g7_19; | |
342 | int64_t f3g8_19 = f3 * (int64_t) g8_19; | |
343 | int64_t f3g9_38 = f3_2 * (int64_t) g9_19; | |
344 | int64_t f4g0 = f4 * (int64_t) g0; | |
345 | int64_t f4g1 = f4 * (int64_t) g1; | |
346 | int64_t f4g2 = f4 * (int64_t) g2; | |
347 | int64_t f4g3 = f4 * (int64_t) g3; | |
348 | int64_t f4g4 = f4 * (int64_t) g4; | |
349 | int64_t f4g5 = f4 * (int64_t) g5; | |
350 | int64_t f4g6_19 = f4 * (int64_t) g6_19; | |
351 | int64_t f4g7_19 = f4 * (int64_t) g7_19; | |
352 | int64_t f4g8_19 = f4 * (int64_t) g8_19; | |
353 | int64_t f4g9_19 = f4 * (int64_t) g9_19; | |
354 | int64_t f5g0 = f5 * (int64_t) g0; | |
355 | int64_t f5g1_2 = f5_2 * (int64_t) g1; | |
356 | int64_t f5g2 = f5 * (int64_t) g2; | |
357 | int64_t f5g3_2 = f5_2 * (int64_t) g3; | |
358 | int64_t f5g4 = f5 * (int64_t) g4; | |
359 | int64_t f5g5_38 = f5_2 * (int64_t) g5_19; | |
360 | int64_t f5g6_19 = f5 * (int64_t) g6_19; | |
361 | int64_t f5g7_38 = f5_2 * (int64_t) g7_19; | |
362 | int64_t f5g8_19 = f5 * (int64_t) g8_19; | |
363 | int64_t f5g9_38 = f5_2 * (int64_t) g9_19; | |
364 | int64_t f6g0 = f6 * (int64_t) g0; | |
365 | int64_t f6g1 = f6 * (int64_t) g1; | |
366 | int64_t f6g2 = f6 * (int64_t) g2; | |
367 | int64_t f6g3 = f6 * (int64_t) g3; | |
368 | int64_t f6g4_19 = f6 * (int64_t) g4_19; | |
369 | int64_t f6g5_19 = f6 * (int64_t) g5_19; | |
370 | int64_t f6g6_19 = f6 * (int64_t) g6_19; | |
371 | int64_t f6g7_19 = f6 * (int64_t) g7_19; | |
372 | int64_t f6g8_19 = f6 * (int64_t) g8_19; | |
373 | int64_t f6g9_19 = f6 * (int64_t) g9_19; | |
374 | int64_t f7g0 = f7 * (int64_t) g0; | |
375 | int64_t f7g1_2 = f7_2 * (int64_t) g1; | |
376 | int64_t f7g2 = f7 * (int64_t) g2; | |
377 | int64_t f7g3_38 = f7_2 * (int64_t) g3_19; | |
378 | int64_t f7g4_19 = f7 * (int64_t) g4_19; | |
379 | int64_t f7g5_38 = f7_2 * (int64_t) g5_19; | |
380 | int64_t f7g6_19 = f7 * (int64_t) g6_19; | |
381 | int64_t f7g7_38 = f7_2 * (int64_t) g7_19; | |
382 | int64_t f7g8_19 = f7 * (int64_t) g8_19; | |
383 | int64_t f7g9_38 = f7_2 * (int64_t) g9_19; | |
384 | int64_t f8g0 = f8 * (int64_t) g0; | |
385 | int64_t f8g1 = f8 * (int64_t) g1; | |
386 | int64_t f8g2_19 = f8 * (int64_t) g2_19; | |
387 | int64_t f8g3_19 = f8 * (int64_t) g3_19; | |
388 | int64_t f8g4_19 = f8 * (int64_t) g4_19; | |
389 | int64_t f8g5_19 = f8 * (int64_t) g5_19; | |
390 | int64_t f8g6_19 = f8 * (int64_t) g6_19; | |
391 | int64_t f8g7_19 = f8 * (int64_t) g7_19; | |
392 | int64_t f8g8_19 = f8 * (int64_t) g8_19; | |
393 | int64_t f8g9_19 = f8 * (int64_t) g9_19; | |
394 | int64_t f9g0 = f9 * (int64_t) g0; | |
395 | int64_t f9g1_38 = f9_2 * (int64_t) g1_19; | |
396 | int64_t f9g2_19 = f9 * (int64_t) g2_19; | |
397 | int64_t f9g3_38 = f9_2 * (int64_t) g3_19; | |
398 | int64_t f9g4_19 = f9 * (int64_t) g4_19; | |
399 | int64_t f9g5_38 = f9_2 * (int64_t) g5_19; | |
400 | int64_t f9g6_19 = f9 * (int64_t) g6_19; | |
401 | int64_t f9g7_38 = f9_2 * (int64_t) g7_19; | |
402 | int64_t f9g8_19 = f9 * (int64_t) g8_19; | |
403 | int64_t f9g9_38 = f9_2 * (int64_t) g9_19; | |
404 | int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; | |
405 | int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; | |
406 | int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; | |
407 | int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; | |
408 | int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; | |
409 | int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; | |
410 | int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; | |
411 | int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; | |
412 | int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; | |
413 | int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; | |
414 | int64_t carry0; | |
415 | int64_t carry1; | |
416 | int64_t carry2; | |
417 | int64_t carry3; | |
418 | int64_t carry4; | |
419 | int64_t carry5; | |
420 | int64_t carry6; | |
421 | int64_t carry7; | |
422 | int64_t carry8; | |
423 | int64_t carry9; | |
424 | ||
425 | /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) | |
426 | * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 | |
427 | * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) | |
428 | * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ | |
429 | ||
b9577984 EK |
430 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
431 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
a90def6b DSH |
432 | /* |h0| <= 2^25 */ |
433 | /* |h4| <= 2^25 */ | |
434 | /* |h1| <= 1.71*2^59 */ | |
435 | /* |h5| <= 1.71*2^59 */ | |
436 | ||
b9577984 EK |
437 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
438 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
a90def6b DSH |
439 | /* |h1| <= 2^24; from now on fits into int32 */ |
440 | /* |h5| <= 2^24; from now on fits into int32 */ | |
441 | /* |h2| <= 1.41*2^60 */ | |
442 | /* |h6| <= 1.41*2^60 */ | |
443 | ||
b9577984 EK |
444 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
445 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
a90def6b DSH |
446 | /* |h2| <= 2^25; from now on fits into int32 unchanged */ |
447 | /* |h6| <= 2^25; from now on fits into int32 unchanged */ | |
448 | /* |h3| <= 1.71*2^59 */ | |
449 | /* |h7| <= 1.71*2^59 */ | |
450 | ||
b9577984 EK |
451 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
452 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
a90def6b DSH |
453 | /* |h3| <= 2^24; from now on fits into int32 unchanged */ |
454 | /* |h7| <= 2^24; from now on fits into int32 unchanged */ | |
455 | /* |h4| <= 1.72*2^34 */ | |
456 | /* |h8| <= 1.41*2^60 */ | |
457 | ||
b9577984 EK |
458 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
459 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
a90def6b DSH |
460 | /* |h4| <= 2^25; from now on fits into int32 unchanged */ |
461 | /* |h8| <= 2^25; from now on fits into int32 unchanged */ | |
462 | /* |h5| <= 1.01*2^24 */ | |
463 | /* |h9| <= 1.71*2^59 */ | |
464 | ||
b9577984 | 465 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
a90def6b DSH |
466 | /* |h9| <= 2^24; from now on fits into int32 unchanged */ |
467 | /* |h0| <= 1.1*2^39 */ | |
468 | ||
b9577984 | 469 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
a90def6b DSH |
470 | /* |h0| <= 2^25; from now on fits into int32 unchanged */ |
471 | /* |h1| <= 1.01*2^24 */ | |
472 | ||
473 | h[0] = h0; | |
474 | h[1] = h1; | |
475 | h[2] = h2; | |
476 | h[3] = h3; | |
477 | h[4] = h4; | |
478 | h[5] = h5; | |
479 | h[6] = h6; | |
480 | h[7] = h7; | |
481 | h[8] = h8; | |
482 | h[9] = h9; | |
483 | } | |
484 | ||
485 | /* h = f * f | |
486 | * Can overlap h with f. | |
487 | * | |
488 | * Preconditions: | |
489 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. | |
490 | * | |
491 | * Postconditions: | |
492 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. | |
493 | * | |
494 | * See fe_mul.c for discussion of implementation strategy. */ | |
495 | static void fe_sq(fe h, const fe f) { | |
496 | int32_t f0 = f[0]; | |
497 | int32_t f1 = f[1]; | |
498 | int32_t f2 = f[2]; | |
499 | int32_t f3 = f[3]; | |
500 | int32_t f4 = f[4]; | |
501 | int32_t f5 = f[5]; | |
502 | int32_t f6 = f[6]; | |
503 | int32_t f7 = f[7]; | |
504 | int32_t f8 = f[8]; | |
505 | int32_t f9 = f[9]; | |
506 | int32_t f0_2 = 2 * f0; | |
507 | int32_t f1_2 = 2 * f1; | |
508 | int32_t f2_2 = 2 * f2; | |
509 | int32_t f3_2 = 2 * f3; | |
510 | int32_t f4_2 = 2 * f4; | |
511 | int32_t f5_2 = 2 * f5; | |
512 | int32_t f6_2 = 2 * f6; | |
513 | int32_t f7_2 = 2 * f7; | |
514 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ | |
515 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ | |
516 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ | |
517 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ | |
518 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ | |
519 | int64_t f0f0 = f0 * (int64_t) f0; | |
520 | int64_t f0f1_2 = f0_2 * (int64_t) f1; | |
521 | int64_t f0f2_2 = f0_2 * (int64_t) f2; | |
522 | int64_t f0f3_2 = f0_2 * (int64_t) f3; | |
523 | int64_t f0f4_2 = f0_2 * (int64_t) f4; | |
524 | int64_t f0f5_2 = f0_2 * (int64_t) f5; | |
525 | int64_t f0f6_2 = f0_2 * (int64_t) f6; | |
526 | int64_t f0f7_2 = f0_2 * (int64_t) f7; | |
527 | int64_t f0f8_2 = f0_2 * (int64_t) f8; | |
528 | int64_t f0f9_2 = f0_2 * (int64_t) f9; | |
529 | int64_t f1f1_2 = f1_2 * (int64_t) f1; | |
530 | int64_t f1f2_2 = f1_2 * (int64_t) f2; | |
531 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; | |
532 | int64_t f1f4_2 = f1_2 * (int64_t) f4; | |
533 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; | |
534 | int64_t f1f6_2 = f1_2 * (int64_t) f6; | |
535 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; | |
536 | int64_t f1f8_2 = f1_2 * (int64_t) f8; | |
537 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; | |
538 | int64_t f2f2 = f2 * (int64_t) f2; | |
539 | int64_t f2f3_2 = f2_2 * (int64_t) f3; | |
540 | int64_t f2f4_2 = f2_2 * (int64_t) f4; | |
541 | int64_t f2f5_2 = f2_2 * (int64_t) f5; | |
542 | int64_t f2f6_2 = f2_2 * (int64_t) f6; | |
543 | int64_t f2f7_2 = f2_2 * (int64_t) f7; | |
544 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; | |
545 | int64_t f2f9_38 = f2 * (int64_t) f9_38; | |
546 | int64_t f3f3_2 = f3_2 * (int64_t) f3; | |
547 | int64_t f3f4_2 = f3_2 * (int64_t) f4; | |
548 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; | |
549 | int64_t f3f6_2 = f3_2 * (int64_t) f6; | |
550 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; | |
551 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; | |
552 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; | |
553 | int64_t f4f4 = f4 * (int64_t) f4; | |
554 | int64_t f4f5_2 = f4_2 * (int64_t) f5; | |
555 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; | |
556 | int64_t f4f7_38 = f4 * (int64_t) f7_38; | |
557 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; | |
558 | int64_t f4f9_38 = f4 * (int64_t) f9_38; | |
559 | int64_t f5f5_38 = f5 * (int64_t) f5_38; | |
560 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; | |
561 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; | |
562 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; | |
563 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; | |
564 | int64_t f6f6_19 = f6 * (int64_t) f6_19; | |
565 | int64_t f6f7_38 = f6 * (int64_t) f7_38; | |
566 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; | |
567 | int64_t f6f9_38 = f6 * (int64_t) f9_38; | |
568 | int64_t f7f7_38 = f7 * (int64_t) f7_38; | |
569 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; | |
570 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; | |
571 | int64_t f8f8_19 = f8 * (int64_t) f8_19; | |
572 | int64_t f8f9_38 = f8 * (int64_t) f9_38; | |
573 | int64_t f9f9_38 = f9 * (int64_t) f9_38; | |
574 | int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; | |
575 | int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; | |
576 | int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; | |
577 | int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; | |
578 | int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; | |
579 | int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; | |
580 | int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; | |
581 | int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; | |
582 | int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; | |
583 | int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; | |
584 | int64_t carry0; | |
585 | int64_t carry1; | |
586 | int64_t carry2; | |
587 | int64_t carry3; | |
588 | int64_t carry4; | |
589 | int64_t carry5; | |
590 | int64_t carry6; | |
591 | int64_t carry7; | |
592 | int64_t carry8; | |
593 | int64_t carry9; | |
594 | ||
b9577984 EK |
595 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
596 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
a90def6b | 597 | |
b9577984 EK |
598 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
599 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
a90def6b | 600 | |
b9577984 EK |
601 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
602 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
a90def6b | 603 | |
b9577984 EK |
604 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
605 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
a90def6b | 606 | |
b9577984 EK |
607 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
608 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
a90def6b | 609 | |
b9577984 | 610 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
a90def6b | 611 | |
b9577984 | 612 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
a90def6b DSH |
613 | |
614 | h[0] = h0; | |
615 | h[1] = h1; | |
616 | h[2] = h2; | |
617 | h[3] = h3; | |
618 | h[4] = h4; | |
619 | h[5] = h5; | |
620 | h[6] = h6; | |
621 | h[7] = h7; | |
622 | h[8] = h8; | |
623 | h[9] = h9; | |
624 | } | |
625 | ||
626 | static void fe_invert(fe out, const fe z) { | |
627 | fe t0; | |
628 | fe t1; | |
629 | fe t2; | |
630 | fe t3; | |
631 | int i; | |
632 | ||
0eadff03 EK |
633 | /* |
634 | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as | |
635 | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. | |
636 | */ | |
637 | ||
638 | /* t0 = z ** 2 */ | |
a90def6b | 639 | fe_sq(t0, z); |
0eadff03 EK |
640 | |
641 | /* t1 = t0 ** (2 ** 2) = z ** 8 */ | |
a90def6b | 642 | fe_sq(t1, t0); |
0eadff03 EK |
643 | fe_sq(t1, t1); |
644 | ||
645 | /* t1 = z * t1 = z ** 9 */ | |
a90def6b | 646 | fe_mul(t1, z, t1); |
0eadff03 | 647 | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ |
a90def6b | 648 | fe_mul(t0, t0, t1); |
0eadff03 EK |
649 | |
650 | /* t2 = t0 ** 2 = z ** 22 */ | |
a90def6b | 651 | fe_sq(t2, t0); |
0eadff03 EK |
652 | |
653 | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ | |
a90def6b | 654 | fe_mul(t1, t1, t2); |
0eadff03 EK |
655 | |
656 | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ | |
a90def6b DSH |
657 | fe_sq(t2, t1); |
658 | for (i = 1; i < 5; ++i) { | |
659 | fe_sq(t2, t2); | |
660 | } | |
0eadff03 EK |
661 | |
662 | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ | |
a90def6b | 663 | fe_mul(t1, t2, t1); |
0eadff03 EK |
664 | |
665 | /* Continuing similarly... */ | |
666 | ||
667 | /* t2 = z ** (2 ** 20 - 1) */ | |
a90def6b DSH |
668 | fe_sq(t2, t1); |
669 | for (i = 1; i < 10; ++i) { | |
670 | fe_sq(t2, t2); | |
671 | } | |
672 | fe_mul(t2, t2, t1); | |
0eadff03 EK |
673 | |
674 | /* t2 = z ** (2 ** 40 - 1) */ | |
a90def6b DSH |
675 | fe_sq(t3, t2); |
676 | for (i = 1; i < 20; ++i) { | |
677 | fe_sq(t3, t3); | |
678 | } | |
679 | fe_mul(t2, t3, t2); | |
0eadff03 EK |
680 | |
681 | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ | |
682 | for (i = 0; i < 10; ++i) { | |
a90def6b DSH |
683 | fe_sq(t2, t2); |
684 | } | |
0eadff03 | 685 | /* t1 = z ** (2 ** 50 - 1) */ |
a90def6b | 686 | fe_mul(t1, t2, t1); |
0eadff03 EK |
687 | |
688 | /* t2 = z ** (2 ** 100 - 1) */ | |
a90def6b DSH |
689 | fe_sq(t2, t1); |
690 | for (i = 1; i < 50; ++i) { | |
691 | fe_sq(t2, t2); | |
692 | } | |
693 | fe_mul(t2, t2, t1); | |
0eadff03 EK |
694 | |
695 | /* t2 = z ** (2 ** 200 - 1) */ | |
a90def6b DSH |
696 | fe_sq(t3, t2); |
697 | for (i = 1; i < 100; ++i) { | |
698 | fe_sq(t3, t3); | |
699 | } | |
700 | fe_mul(t2, t3, t2); | |
0eadff03 EK |
701 | |
702 | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ | |
a90def6b DSH |
703 | fe_sq(t2, t2); |
704 | for (i = 1; i < 50; ++i) { | |
705 | fe_sq(t2, t2); | |
706 | } | |
0eadff03 EK |
707 | |
708 | /* t1 = z ** (2 ** 250 - 1) */ | |
a90def6b | 709 | fe_mul(t1, t2, t1); |
0eadff03 EK |
710 | |
711 | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ | |
a90def6b DSH |
712 | fe_sq(t1, t1); |
713 | for (i = 1; i < 5; ++i) { | |
714 | fe_sq(t1, t1); | |
715 | } | |
0eadff03 EK |
716 | |
717 | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ | |
a90def6b DSH |
718 | fe_mul(out, t1, t0); |
719 | } | |
720 | ||
721 | /* h = -f | |
722 | * | |
723 | * Preconditions: | |
724 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
725 | * | |
726 | * Postconditions: | |
727 | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ | |
728 | static void fe_neg(fe h, const fe f) { | |
729 | unsigned i; | |
730 | for (i = 0; i < 10; i++) { | |
731 | h[i] = -f[i]; | |
732 | } | |
733 | } | |
734 | ||
735 | /* Replace (f,g) with (g,g) if b == 1; | |
736 | * replace (f,g) with (f,g) if b == 0. | |
737 | * | |
738 | * Preconditions: b in {0,1}. */ | |
739 | static void fe_cmov(fe f, const fe g, unsigned b) { | |
244e5f5d | 740 | size_t i; |
a90def6b | 741 | b = 0-b; |
a90def6b DSH |
742 | for (i = 0; i < 10; i++) { |
743 | int32_t x = f[i] ^ g[i]; | |
744 | x &= b; | |
745 | f[i] ^= x; | |
746 | } | |
747 | } | |
748 | ||
a90def6b DSH |
749 | /* h = 2 * f * f |
750 | * Can overlap h with f. | |
751 | * | |
752 | * Preconditions: | |
753 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. | |
754 | * | |
755 | * Postconditions: | |
756 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. | |
757 | * | |
758 | * See fe_mul.c for discussion of implementation strategy. */ | |
759 | static void fe_sq2(fe h, const fe f) { | |
760 | int32_t f0 = f[0]; | |
761 | int32_t f1 = f[1]; | |
762 | int32_t f2 = f[2]; | |
763 | int32_t f3 = f[3]; | |
764 | int32_t f4 = f[4]; | |
765 | int32_t f5 = f[5]; | |
766 | int32_t f6 = f[6]; | |
767 | int32_t f7 = f[7]; | |
768 | int32_t f8 = f[8]; | |
769 | int32_t f9 = f[9]; | |
770 | int32_t f0_2 = 2 * f0; | |
771 | int32_t f1_2 = 2 * f1; | |
772 | int32_t f2_2 = 2 * f2; | |
773 | int32_t f3_2 = 2 * f3; | |
774 | int32_t f4_2 = 2 * f4; | |
775 | int32_t f5_2 = 2 * f5; | |
776 | int32_t f6_2 = 2 * f6; | |
777 | int32_t f7_2 = 2 * f7; | |
778 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ | |
779 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ | |
780 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ | |
781 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ | |
782 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ | |
783 | int64_t f0f0 = f0 * (int64_t) f0; | |
784 | int64_t f0f1_2 = f0_2 * (int64_t) f1; | |
785 | int64_t f0f2_2 = f0_2 * (int64_t) f2; | |
786 | int64_t f0f3_2 = f0_2 * (int64_t) f3; | |
787 | int64_t f0f4_2 = f0_2 * (int64_t) f4; | |
788 | int64_t f0f5_2 = f0_2 * (int64_t) f5; | |
789 | int64_t f0f6_2 = f0_2 * (int64_t) f6; | |
790 | int64_t f0f7_2 = f0_2 * (int64_t) f7; | |
791 | int64_t f0f8_2 = f0_2 * (int64_t) f8; | |
792 | int64_t f0f9_2 = f0_2 * (int64_t) f9; | |
793 | int64_t f1f1_2 = f1_2 * (int64_t) f1; | |
794 | int64_t f1f2_2 = f1_2 * (int64_t) f2; | |
795 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; | |
796 | int64_t f1f4_2 = f1_2 * (int64_t) f4; | |
797 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; | |
798 | int64_t f1f6_2 = f1_2 * (int64_t) f6; | |
799 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; | |
800 | int64_t f1f8_2 = f1_2 * (int64_t) f8; | |
801 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; | |
802 | int64_t f2f2 = f2 * (int64_t) f2; | |
803 | int64_t f2f3_2 = f2_2 * (int64_t) f3; | |
804 | int64_t f2f4_2 = f2_2 * (int64_t) f4; | |
805 | int64_t f2f5_2 = f2_2 * (int64_t) f5; | |
806 | int64_t f2f6_2 = f2_2 * (int64_t) f6; | |
807 | int64_t f2f7_2 = f2_2 * (int64_t) f7; | |
808 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; | |
809 | int64_t f2f9_38 = f2 * (int64_t) f9_38; | |
810 | int64_t f3f3_2 = f3_2 * (int64_t) f3; | |
811 | int64_t f3f4_2 = f3_2 * (int64_t) f4; | |
812 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; | |
813 | int64_t f3f6_2 = f3_2 * (int64_t) f6; | |
814 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; | |
815 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; | |
816 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; | |
817 | int64_t f4f4 = f4 * (int64_t) f4; | |
818 | int64_t f4f5_2 = f4_2 * (int64_t) f5; | |
819 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; | |
820 | int64_t f4f7_38 = f4 * (int64_t) f7_38; | |
821 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; | |
822 | int64_t f4f9_38 = f4 * (int64_t) f9_38; | |
823 | int64_t f5f5_38 = f5 * (int64_t) f5_38; | |
824 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; | |
825 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; | |
826 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; | |
827 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; | |
828 | int64_t f6f6_19 = f6 * (int64_t) f6_19; | |
829 | int64_t f6f7_38 = f6 * (int64_t) f7_38; | |
830 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; | |
831 | int64_t f6f9_38 = f6 * (int64_t) f9_38; | |
832 | int64_t f7f7_38 = f7 * (int64_t) f7_38; | |
833 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; | |
834 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; | |
835 | int64_t f8f8_19 = f8 * (int64_t) f8_19; | |
836 | int64_t f8f9_38 = f8 * (int64_t) f9_38; | |
837 | int64_t f9f9_38 = f9 * (int64_t) f9_38; | |
838 | int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; | |
839 | int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; | |
840 | int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; | |
841 | int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; | |
842 | int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; | |
843 | int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; | |
844 | int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; | |
845 | int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; | |
846 | int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; | |
847 | int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; | |
848 | int64_t carry0; | |
849 | int64_t carry1; | |
850 | int64_t carry2; | |
851 | int64_t carry3; | |
852 | int64_t carry4; | |
853 | int64_t carry5; | |
854 | int64_t carry6; | |
855 | int64_t carry7; | |
856 | int64_t carry8; | |
857 | int64_t carry9; | |
858 | ||
859 | h0 += h0; | |
860 | h1 += h1; | |
861 | h2 += h2; | |
862 | h3 += h3; | |
863 | h4 += h4; | |
864 | h5 += h5; | |
865 | h6 += h6; | |
866 | h7 += h7; | |
867 | h8 += h8; | |
868 | h9 += h9; | |
869 | ||
b9577984 EK |
870 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
871 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
a90def6b | 872 | |
b9577984 EK |
873 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
874 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
a90def6b | 875 | |
b9577984 EK |
876 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
877 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
a90def6b | 878 | |
b9577984 EK |
879 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
880 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
a90def6b | 881 | |
b9577984 EK |
882 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
883 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
a90def6b | 884 | |
b9577984 | 885 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
a90def6b | 886 | |
b9577984 | 887 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
a90def6b DSH |
888 | |
889 | h[0] = h0; | |
890 | h[1] = h1; | |
891 | h[2] = h2; | |
892 | h[3] = h3; | |
893 | h[4] = h4; | |
894 | h[5] = h5; | |
895 | h[6] = h6; | |
896 | h[7] = h7; | |
897 | h[8] = h8; | |
898 | h[9] = h9; | |
899 | } | |
900 | ||
a90def6b DSH |
901 | /* ge means group element. |
902 | ||
903 | * Here the group is the set of pairs (x,y) of field elements (see fe.h) | |
904 | * satisfying -x^2 + y^2 = 1 + d x^2y^2 | |
905 | * where d = -121665/121666. | |
906 | * | |
907 | * Representations: | |
908 | * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z | |
909 | * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT | |
910 | * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T | |
911 | * ge_precomp (Duif): (y+x,y-x,2dxy) */ | |
912 | ||
913 | typedef struct { | |
914 | fe X; | |
915 | fe Y; | |
916 | fe Z; | |
917 | } ge_p2; | |
918 | ||
919 | typedef struct { | |
920 | fe X; | |
921 | fe Y; | |
922 | fe Z; | |
923 | fe T; | |
924 | } ge_p3; | |
925 | ||
926 | typedef struct { | |
927 | fe X; | |
928 | fe Y; | |
929 | fe Z; | |
930 | fe T; | |
931 | } ge_p1p1; | |
932 | ||
933 | typedef struct { | |
934 | fe yplusx; | |
935 | fe yminusx; | |
936 | fe xy2d; | |
937 | } ge_precomp; | |
938 | ||
939 | typedef struct { | |
940 | fe YplusX; | |
941 | fe YminusX; | |
942 | fe Z; | |
943 | fe T2d; | |
944 | } ge_cached; | |
945 | ||
a90def6b DSH |
946 | static void ge_p3_0(ge_p3 *h) { |
947 | fe_0(h->X); | |
948 | fe_1(h->Y); | |
949 | fe_1(h->Z); | |
950 | fe_0(h->T); | |
951 | } | |
952 | ||
953 | static void ge_precomp_0(ge_precomp *h) { | |
954 | fe_1(h->yplusx); | |
955 | fe_1(h->yminusx); | |
956 | fe_0(h->xy2d); | |
957 | } | |
958 | ||
959 | /* r = p */ | |
960 | static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { | |
961 | fe_copy(r->X, p->X); | |
962 | fe_copy(r->Y, p->Y); | |
963 | fe_copy(r->Z, p->Z); | |
964 | } | |
965 | ||
a90def6b DSH |
966 | /* r = p */ |
967 | static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { | |
968 | fe_mul(r->X, p->X, p->T); | |
969 | fe_mul(r->Y, p->Y, p->Z); | |
970 | fe_mul(r->Z, p->Z, p->T); | |
971 | } | |
972 | ||
973 | /* r = p */ | |
974 | static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { | |
975 | fe_mul(r->X, p->X, p->T); | |
976 | fe_mul(r->Y, p->Y, p->Z); | |
977 | fe_mul(r->Z, p->Z, p->T); | |
978 | fe_mul(r->T, p->X, p->Y); | |
979 | } | |
980 | ||
981 | /* r = 2 * p */ | |
982 | static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { | |
983 | fe t0; | |
984 | ||
985 | fe_sq(r->X, p->X); | |
986 | fe_sq(r->Z, p->Y); | |
987 | fe_sq2(r->T, p->Z); | |
988 | fe_add(r->Y, p->X, p->Y); | |
989 | fe_sq(t0, r->Y); | |
990 | fe_add(r->Y, r->Z, r->X); | |
991 | fe_sub(r->Z, r->Z, r->X); | |
992 | fe_sub(r->X, t0, r->Y); | |
993 | fe_sub(r->T, r->T, r->Z); | |
994 | } | |
995 | ||
996 | /* r = 2 * p */ | |
997 | static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { | |
998 | ge_p2 q; | |
999 | ge_p3_to_p2(&q, p); | |
1000 | ge_p2_dbl(r, &q); | |
1001 | } | |
1002 | ||
1003 | /* r = p + q */ | |
1004 | static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { | |
1005 | fe t0; | |
1006 | ||
1007 | fe_add(r->X, p->Y, p->X); | |
1008 | fe_sub(r->Y, p->Y, p->X); | |
1009 | fe_mul(r->Z, r->X, q->yplusx); | |
1010 | fe_mul(r->Y, r->Y, q->yminusx); | |
1011 | fe_mul(r->T, q->xy2d, p->T); | |
1012 | fe_add(t0, p->Z, p->Z); | |
1013 | fe_sub(r->X, r->Z, r->Y); | |
1014 | fe_add(r->Y, r->Z, r->Y); | |
1015 | fe_add(r->Z, t0, r->T); | |
1016 | fe_sub(r->T, t0, r->T); | |
1017 | } | |
1018 | ||
a90def6b DSH |
1019 | static uint8_t equal(signed char b, signed char c) { |
1020 | uint8_t ub = b; | |
1021 | uint8_t uc = c; | |
1022 | uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ | |
1023 | uint32_t y = x; /* 0: yes; 1..255: no */ | |
1024 | y -= 1; /* 4294967295: yes; 0..254: no */ | |
1025 | y >>= 31; /* 1: yes; 0: no */ | |
1026 | return y; | |
1027 | } | |
1028 | ||
fdfb8c84 | 1029 | static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { |
a90def6b DSH |
1030 | fe_cmov(t->yplusx, u->yplusx, b); |
1031 | fe_cmov(t->yminusx, u->yminusx, b); | |
1032 | fe_cmov(t->xy2d, u->xy2d, b); | |
1033 | } | |
1034 | ||
a90def6b | 1035 | /* k25519Precomp[i][j] = (j+1)*256^i*B */ |
dc22d6b3 | 1036 | static const ge_precomp k25519Precomp[32][8] = { |
a90def6b DSH |
1037 | { |
1038 | { | |
1039 | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, | |
1040 | 27544626, -11754271, -6079156, 2047605}, | |
1041 | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, | |
1042 | 5043384, 19500929, -15469378}, | |
1043 | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, | |
1044 | 29287919, 11864899, -24514362, -4438546}, | |
1045 | }, | |
1046 | { | |
1047 | {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, | |
1048 | -11717903, -3814571, -358445, -10211303}, | |
1049 | {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, | |
1050 | -15616551, 11189268, -26829678, -5319081}, | |
1051 | {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, | |
1052 | -3128826, -9541118, -15472047, -4166697}, | |
1053 | }, | |
1054 | { | |
1055 | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, | |
1056 | 27787600, -14772189, 28944400, -1550024}, | |
1057 | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, | |
1058 | 16354577, -11775962, 7689662, 11199574}, | |
1059 | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, | |
1060 | 7512774, 10017326, -17749093, -9920357}, | |
1061 | }, | |
1062 | { | |
1063 | {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, | |
1064 | -28926210, 15006023, 3284568, -6276540}, | |
1065 | {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, | |
1066 | 7464579, 9656445, 13059162, 10374397}, | |
1067 | {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, | |
1068 | -3839045, -641708, -101325}, | |
1069 | }, | |
1070 | { | |
1071 | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, | |
1072 | 32867885, 14515107, -15438304, 10819380}, | |
1073 | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, | |
1074 | 12483688, -12668491, 5581306}, | |
1075 | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, | |
1076 | 28542350, 13850243, -23678021, -15815942}, | |
1077 | }, | |
1078 | { | |
1079 | {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, | |
1080 | -19188627, -15224819, -9818940, -12085777}, | |
1081 | {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, | |
1082 | -15689887, 1762328, 14866737}, | |
1083 | {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, | |
1084 | -28236412, 3959421, 27914454, 4383652}, | |
1085 | }, | |
1086 | { | |
1087 | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, | |
1088 | 5230134, -23952439, -15175766}, | |
1089 | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, | |
1090 | 20654025, 16520125, 30598449, 7715701}, | |
1091 | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, | |
1092 | -31400660, 1370708, 29794553, -1409300}, | |
1093 | }, | |
1094 | { | |
1095 | {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, | |
1096 | 30290735, 10876454, -33154098, 2381726}, | |
1097 | {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, | |
1098 | -6236617, 3696005, -32300832, 15351955}, | |
1099 | {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, | |
1100 | -32961401, -2970515, 29551813, 10109425}, | |
1101 | }, | |
1102 | }, | |
1103 | { | |
1104 | { | |
1105 | {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, | |
1106 | -2378284, -1627556, 10092783, -4764171}, | |
1107 | {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, | |
1108 | -32508754, 12005538, -17810127, 12803510}, | |
1109 | {17228999, -15661624, -1233527, 300140, -1224870, -11714777, | |
1110 | 30364213, -9038194, 18016357, 4397660}, | |
1111 | }, | |
1112 | { | |
1113 | {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, | |
1114 | -26619106, 14544525, -17477504, 982639}, | |
1115 | {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, | |
1116 | -4120128, -21047696, 9934963}, | |
1117 | {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, | |
1118 | -14747930, 4559895, -30123922, -10897950}, | |
1119 | }, | |
1120 | { | |
1121 | {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, | |
1122 | 24191034, 4541697, -13338309, 5500568}, | |
1123 | {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, | |
1124 | -17430592, 12264343, 10874051, 13524335}, | |
1125 | {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, | |
1126 | 5080568, -22528059, 5376628}, | |
1127 | }, | |
1128 | { | |
1129 | {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, | |
1130 | -22321305, -9447443, 4535768, 1569007}, | |
1131 | {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, | |
1132 | -30494562, 3044290, 31848280, 12543772}, | |
1133 | {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, | |
1134 | -27377195, -2062731, 7718482, 14474653}, | |
1135 | }, | |
1136 | { | |
1137 | {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, | |
1138 | -7236665, 24316168, -5253567}, | |
1139 | {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, | |
1140 | 33040651, -13424532, -20729456, 8321686}, | |
1141 | {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, | |
1142 | 23845965, -11874838, -9984458, 608372}, | |
1143 | }, | |
1144 | { | |
1145 | {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, | |
1146 | 1123968, -6780577, 27229399, 23887}, | |
1147 | {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, | |
1148 | 12797024, -6440308, -1633405, 16678954}, | |
1149 | {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, | |
1150 | -1508144, -4795045, -17169265, 4904953}, | |
1151 | }, | |
1152 | { | |
1153 | {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, | |
1154 | 5169211, 16191880, 2128236, -4326833}, | |
1155 | {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, | |
1156 | -29806336, 916033, -6882542, -2986532}, | |
1157 | {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, | |
1158 | 285431, 2763829, 15736322, 4143876}, | |
1159 | }, | |
1160 | { | |
1161 | {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, | |
1162 | -14594663, 23527084, -16458268}, | |
1163 | {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, | |
1164 | -32625340, 4087881, -15188911, -14416214}, | |
1165 | {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, | |
1166 | 4357868, -4774191, -16323038}, | |
1167 | }, | |
1168 | }, | |
1169 | { | |
1170 | { | |
1171 | {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, | |
1172 | 23365147, -3949732, 7390890, 2759800}, | |
1173 | {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, | |
1174 | -4264057, 1244380, -12919645}, | |
1175 | {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, | |
1176 | 9208236, 15886429, 16489664}, | |
1177 | }, | |
1178 | { | |
1179 | {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, | |
1180 | -13693198, 398369, -30606455, -712933}, | |
1181 | {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, | |
1182 | 13348553, 12076947, -30836462, 5113182}, | |
1183 | {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, | |
1184 | -30341101, -7336386, 13847711, 5387222}, | |
1185 | }, | |
1186 | { | |
1187 | {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, | |
1188 | 8763061, 3617786, -19600662, 10370991}, | |
1189 | {20246567, -14369378, 22358229, -543712, 18507283, -10413996, | |
1190 | 14554437, -8746092, 32232924, 16763880}, | |
1191 | {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, | |
1192 | 11094161, 15689506, 3140038, -16510092}, | |
1193 | }, | |
1194 | { | |
1195 | {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, | |
1196 | -27224800, 9448613, -28774454, 366295}, | |
1197 | {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, | |
1198 | 28344573, 8041113, 719605, 11671788}, | |
1199 | {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, | |
1200 | -15266516, 27000813, -10195553}, | |
1201 | }, | |
1202 | { | |
1203 | {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, | |
1204 | 5336097, 6750977, -14521026}, | |
1205 | {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, | |
1206 | 1695823, -8819122, 8169720, 16220347}, | |
1207 | {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, | |
1208 | -11144307, -2627664, -5990708, -14166033}, | |
1209 | }, | |
1210 | { | |
1211 | {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, | |
1212 | 27884329, 2847284, 2655861, 1738395}, | |
1213 | {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, | |
1214 | 21651608, -3239336, -19087449, -11005278}, | |
1215 | {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, | |
1216 | 5821408, 10478196, 8544890}, | |
1217 | }, | |
1218 | { | |
1219 | {32173121, -16129311, 24896207, 3921497, 22579056, -3410854, | |
1220 | 19270449, 12217473, 17789017, -3395995}, | |
1221 | {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, | |
1222 | 15479401, -3853233, 30460520, 1052596}, | |
1223 | {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, | |
1224 | 27491595, -4612359, 3179268, -9478891}, | |
1225 | }, | |
1226 | { | |
1227 | {31947069, -14366651, -4640583, -15339921, -15125977, -6039709, | |
1228 | -14756777, -16411740, 19072640, -9511060}, | |
1229 | {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, | |
1230 | 5977896, -5215017, 473099, 5040608}, | |
1231 | {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, | |
1232 | 28326862, 1721092, -19558642, -3131606}, | |
1233 | }, | |
1234 | }, | |
1235 | { | |
1236 | { | |
1237 | {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, | |
1238 | 8076149, -27868496, 11538389}, | |
1239 | {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, | |
1240 | 8754525, 7446702, -5676054, 5797016}, | |
1241 | {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, | |
1242 | 2014099, -9050574, -2369172, -5877341}, | |
1243 | }, | |
1244 | { | |
1245 | {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, | |
1246 | 1192730, -3714199, 15123619, 10811505}, | |
1247 | {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, | |
1248 | 15776356, -28886779, -11974553}, | |
1249 | {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, | |
1250 | -20654173, -16484855, 4714547, -9600655}, | |
1251 | }, | |
1252 | { | |
1253 | {15200332, 8368572, 19679101, 15970074, -31872674, 1959451, | |
1254 | 24611599, -4543832, -11745876, 12340220}, | |
1255 | {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, | |
1256 | 9613953, 8241152, 15370987, 9608631}, | |
1257 | {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, | |
1258 | 15866074, -28210621, -8814099}, | |
1259 | }, | |
1260 | { | |
1261 | {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, | |
1262 | 858697, 20571223, 8420556}, | |
1263 | {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, | |
1264 | 33531827, 12516406, -21574435, -12476749}, | |
1265 | {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, | |
1266 | 7256740, 8791136, 15069930}, | |
1267 | }, | |
1268 | { | |
1269 | {1276410, -9371918, 22949635, -16322807, -23493039, -5702186, | |
1270 | 14711875, 4874229, -30663140, -2331391}, | |
1271 | {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, | |
1272 | -7912378, -33069337, 9234253}, | |
1273 | {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, | |
1274 | 31559055, -11609587, 18979186, 13396066}, | |
1275 | }, | |
1276 | { | |
1277 | {24474287, 4968103, 22267082, 4407354, 24063882, -8325180, | |
1278 | -18816887, 13594782, 33514650, 7021958}, | |
1279 | {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, | |
1280 | -25948728, -3916677, -21480480, 12868082}, | |
1281 | {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, | |
1282 | -21446107, 2244500, -12455797, -8089383}, | |
1283 | }, | |
1284 | { | |
1285 | {-30595528, 13793479, -5852820, 319136, -25723172, -6263899, | |
1286 | 33086546, 8957937, -15233648, 5540521}, | |
1287 | {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, | |
1288 | -23710744, -1568984, -16128528, -14962807}, | |
1289 | {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, | |
1290 | 892185, -11513277, -15205948}, | |
1291 | }, | |
1292 | { | |
1293 | {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, | |
1294 | 4763127, -19179614, 5867134}, | |
1295 | {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, | |
1296 | 27846559, 5931263, -29749703, -16108455}, | |
1297 | {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, | |
1298 | 7283490, -15148073, -19526700, 7734629}, | |
1299 | }, | |
1300 | }, | |
1301 | { | |
1302 | { | |
1303 | {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, | |
1304 | 7585295, -3176626, 18549497, 15302069}, | |
1305 | {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, | |
1306 | 10458790, -6418461, -8872242, 8424746}, | |
1307 | {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, | |
1308 | 19206234, 7134917, -11284482, -828919}, | |
1309 | }, | |
1310 | { | |
1311 | {11334899, -9218022, 8025293, 12707519, 17523892, -10476071, | |
1312 | 10243738, -14685461, -5066034, 16498837}, | |
1313 | {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, | |
1314 | -14124238, 6536641, 10543906}, | |
1315 | {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, | |
1316 | -2669190, -16625574, -27235709, 8876771}, | |
1317 | }, | |
1318 | { | |
1319 | {-25742899, -12566864, -15649966, -846607, -33026686, -796288, | |
1320 | -33481822, 15824474, -604426, -9039817}, | |
1321 | {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, | |
1322 | -4890037, 1657394, 3084098}, | |
1323 | {10477963, -7470260, 12119566, -13250805, 29016247, -5365589, | |
1324 | 31280319, 14396151, -30233575, 15272409}, | |
1325 | }, | |
1326 | { | |
1327 | {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, | |
1328 | -25173957, -12636138, -25014757, 1950504}, | |
1329 | {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, | |
1330 | -8384306, -8767532, 15341279, 8373727}, | |
1331 | {28685821, 7759505, -14378516, -12002860, -31971820, 4079242, | |
1332 | 298136, -10232602, -2878207, 15190420}, | |
1333 | }, | |
1334 | { | |
1335 | {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, | |
1336 | 8669718, 2742393, -26033313, -6875003}, | |
1337 | {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, | |
1338 | 9291594, -16247779, -12154742, 6048605}, | |
1339 | {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, | |
1340 | 13934231, 5128323, 11213262, 9168384}, | |
1341 | }, | |
1342 | { | |
1343 | {-26280513, 11007847, 19408960, -940758, -18592965, -4328580, | |
1344 | -5088060, -11105150, 20470157, -16398701}, | |
1345 | {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, | |
1346 | -22783952, 14461608, 14042978, 5230683}, | |
1347 | {29969567, -2741594, -16711867, -8552442, 9175486, -2468974, | |
1348 | 21556951, 3506042, -5933891, -12449708}, | |
1349 | }, | |
1350 | { | |
1351 | {-3144746, 8744661, 19704003, 4581278, -20430686, 6830683, | |
1352 | -21284170, 8971513, -28539189, 15326563}, | |
1353 | {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669, | |
1354 | -15523050, 15300988, -20514118, 9168260}, | |
1355 | {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939, | |
1356 | -28948358, 9601605, 33087103, -9011387}, | |
1357 | }, | |
1358 | { | |
1359 | {-19443170, -15512900, -20797467, -12445323, -29824447, 10229461, | |
1360 | -27444329, -15000531, -5996870, 15664672}, | |
1361 | {23294591, -16632613, -22650781, -8470978, 27844204, 11461195, | |
1362 | 13099750, -2460356, 18151676, 13417686}, | |
1363 | {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065, | |
1364 | 1661597, -12551441, 15271676, -15452665}, | |
1365 | }, | |
1366 | }, | |
1367 | { | |
1368 | { | |
1369 | {11433042, -13228665, 8239631, -5279517, -1985436, -725718, | |
1370 | -18698764, 2167544, -6921301, -13440182}, | |
1371 | {-31436171, 15575146, 30436815, 12192228, -22463353, 9395379, | |
1372 | -9917708, -8638997, 12215110, 12028277}, | |
1373 | {14098400, 6555944, 23007258, 5757252, -15427832, -12950502, | |
1374 | 30123440, 4617780, -16900089, -655628}, | |
1375 | }, | |
1376 | { | |
1377 | {-4026201, -15240835, 11893168, 13718664, -14809462, 1847385, | |
1378 | -15819999, 10154009, 23973261, -12684474}, | |
1379 | {-26531820, -3695990, -1908898, 2534301, -31870557, -16550355, | |
1380 | 18341390, -11419951, 32013174, -10103539}, | |
1381 | {-25479301, 10876443, -11771086, -14625140, -12369567, 1838104, | |
1382 | 21911214, 6354752, 4425632, -837822}, | |
1383 | }, | |
1384 | { | |
1385 | {-10433389, -14612966, 22229858, -3091047, -13191166, 776729, | |
1386 | -17415375, -12020462, 4725005, 14044970}, | |
1387 | {19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, | |
1388 | -1411784, -19522291, -16109756}, | |
1389 | {-24864089, 12986008, -10898878, -5558584, -11312371, -148526, | |
1390 | 19541418, 8180106, 9282262, 10282508}, | |
1391 | }, | |
1392 | { | |
1393 | {-26205082, 4428547, -8661196, -13194263, 4098402, -14165257, | |
1394 | 15522535, 8372215, 5542595, -10702683}, | |
1395 | {-10562541, 14895633, 26814552, -16673850, -17480754, -2489360, | |
1396 | -2781891, 6993761, -18093885, 10114655}, | |
1397 | {-20107055, -929418, 31422704, 10427861, -7110749, 6150669, | |
1398 | -29091755, -11529146, 25953725, -106158}, | |
1399 | }, | |
1400 | { | |
1401 | {-4234397, -8039292, -9119125, 3046000, 2101609, -12607294, | |
1402 | 19390020, 6094296, -3315279, 12831125}, | |
1403 | {-15998678, 7578152, 5310217, 14408357, -33548620, -224739, | |
1404 | 31575954, 6326196, 7381791, -2421839}, | |
1405 | {-20902779, 3296811, 24736065, -16328389, 18374254, 7318640, | |
1406 | 6295303, 8082724, -15362489, 12339664}, | |
1407 | }, | |
1408 | { | |
1409 | {27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414, | |
1410 | 15768922, 25091167, 14856294}, | |
1411 | {-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, | |
1412 | -12695493, -22182473, -9012899}, | |
1413 | {-11423429, -5421590, 11632845, 3405020, 30536730, -11674039, | |
1414 | -27260765, 13866390, 30146206, 9142070}, | |
1415 | }, | |
1416 | { | |
1417 | {3924129, -15307516, -13817122, -10054960, 12291820, -668366, | |
1418 | -27702774, 9326384, -8237858, 4171294}, | |
1419 | {-15921940, 16037937, 6713787, 16606682, -21612135, 2790944, | |
1420 | 26396185, 3731949, 345228, -5462949}, | |
1421 | {-21327538, 13448259, 25284571, 1143661, 20614966, -8849387, | |
1422 | 2031539, -12391231, -16253183, -13582083}, | |
1423 | }, | |
1424 | { | |
1425 | {31016211, -16722429, 26371392, -14451233, -5027349, 14854137, | |
1426 | 17477601, 3842657, 28012650, -16405420}, | |
1427 | {-5075835, 9368966, -8562079, -4600902, -15249953, 6970560, | |
1428 | -9189873, 16292057, -8867157, 3507940}, | |
1429 | {29439664, 3537914, 23333589, 6997794, -17555561, -11018068, | |
1430 | -15209202, -15051267, -9164929, 6580396}, | |
1431 | }, | |
1432 | }, | |
1433 | { | |
1434 | { | |
1435 | {-12185861, -7679788, 16438269, 10826160, -8696817, -6235611, | |
1436 | 17860444, -9273846, -2095802, 9304567}, | |
1437 | {20714564, -4336911, 29088195, 7406487, 11426967, -5095705, | |
1438 | 14792667, -14608617, 5289421, -477127}, | |
1439 | {-16665533, -10650790, -6160345, -13305760, 9192020, -1802462, | |
1440 | 17271490, 12349094, 26939669, -3752294}, | |
1441 | }, | |
1442 | { | |
1443 | {-12889898, 9373458, 31595848, 16374215, 21471720, 13221525, | |
1444 | -27283495, -12348559, -3698806, 117887}, | |
1445 | {22263325, -6560050, 3984570, -11174646, -15114008, -566785, | |
1446 | 28311253, 5358056, -23319780, 541964}, | |
1447 | {16259219, 3261970, 2309254, -15534474, -16885711, -4581916, | |
1448 | 24134070, -16705829, -13337066, -13552195}, | |
1449 | }, | |
1450 | { | |
1451 | {9378160, -13140186, -22845982, -12745264, 28198281, -7244098, | |
1452 | -2399684, -717351, 690426, 14876244}, | |
1453 | {24977353, -314384, -8223969, -13465086, 28432343, -1176353, | |
1454 | -13068804, -12297348, -22380984, 6618999}, | |
1455 | {-1538174, 11685646, 12944378, 13682314, -24389511, -14413193, | |
1456 | 8044829, -13817328, 32239829, -5652762}, | |
1457 | }, | |
1458 | { | |
1459 | {-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647, | |
1460 | -10350059, 32779359, 5095274}, | |
1461 | {-33008130, -5214506, -32264887, -3685216, 9460461, -9327423, | |
1462 | -24601656, 14506724, 21639561, -2630236}, | |
1463 | {-16400943, -13112215, 25239338, 15531969, 3987758, -4499318, | |
1464 | -1289502, -6863535, 17874574, 558605}, | |
1465 | }, | |
1466 | { | |
1467 | {-13600129, 10240081, 9171883, 16131053, -20869254, 9599700, | |
1468 | 33499487, 5080151, 2085892, 5119761}, | |
1469 | {-22205145, -2519528, -16381601, 414691, -25019550, 2170430, | |
1470 | 30634760, -8363614, -31999993, -5759884}, | |
1471 | {-6845704, 15791202, 8550074, -1312654, 29928809, -12092256, | |
1472 | 27534430, -7192145, -22351378, 12961482}, | |
1473 | }, | |
1474 | { | |
1475 | {-24492060, -9570771, 10368194, 11582341, -23397293, -2245287, | |
1476 | 16533930, 8206996, -30194652, -5159638}, | |
1477 | {-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, | |
1478 | 7031275, 7589640, 8945490}, | |
1479 | {-32152748, 8917967, 6661220, -11677616, -1192060, -15793393, | |
1480 | 7251489, -11182180, 24099109, -14456170}, | |
1481 | }, | |
1482 | { | |
1483 | {5019558, -7907470, 4244127, -14714356, -26933272, 6453165, | |
1484 | -19118182, -13289025, -6231896, -10280736}, | |
1485 | {10853594, 10721687, 26480089, 5861829, -22995819, 1972175, | |
1486 | -1866647, -10557898, -3363451, -6441124}, | |
1487 | {-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, | |
1488 | -2008168, -13866408, 7421392}, | |
1489 | }, | |
1490 | { | |
1491 | {8139927, -6546497, 32257646, -5890546, 30375719, 1886181, | |
1492 | -21175108, 15441252, 28826358, -4123029}, | |
1493 | {6267086, 9695052, 7709135, -16603597, -32869068, -1886135, | |
1494 | 14795160, -7840124, 13746021, -1742048}, | |
1495 | {28584902, 7787108, -6732942, -15050729, 22846041, -7571236, | |
1496 | -3181936, -363524, 4771362, -8419958}, | |
1497 | }, | |
1498 | }, | |
1499 | { | |
1500 | { | |
1501 | {24949256, 6376279, -27466481, -8174608, -18646154, -9930606, | |
1502 | 33543569, -12141695, 3569627, 11342593}, | |
1503 | {26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, | |
1504 | 4608608, 7325975, -14801071}, | |
1505 | {-11618399, -14554430, -24321212, 7655128, -1369274, 5214312, | |
1506 | -27400540, 10258390, -17646694, -8186692}, | |
1507 | }, | |
1508 | { | |
1509 | {11431204, 15823007, 26570245, 14329124, 18029990, 4796082, | |
1510 | -31446179, 15580664, 9280358, -3973687}, | |
1511 | {-160783, -10326257, -22855316, -4304997, -20861367, -13621002, | |
1512 | -32810901, -11181622, -15545091, 4387441}, | |
1513 | {-20799378, 12194512, 3937617, -5805892, -27154820, 9340370, | |
1514 | -24513992, 8548137, 20617071, -7482001}, | |
1515 | }, | |
1516 | { | |
1517 | {-938825, -3930586, -8714311, 16124718, 24603125, -6225393, | |
1518 | -13775352, -11875822, 24345683, 10325460}, | |
1519 | {-19855277, -1568885, -22202708, 8714034, 14007766, 6928528, | |
1520 | 16318175, -1010689, 4766743, 3552007}, | |
1521 | {-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, | |
1522 | 14481909, 10988822, -3994762}, | |
1523 | }, | |
1524 | { | |
1525 | {15564307, -14311570, 3101243, 5684148, 30446780, -8051356, | |
1526 | 12677127, -6505343, -8295852, 13296005}, | |
1527 | {-9442290, 6624296, -30298964, -11913677, -4670981, -2057379, | |
1528 | 31521204, 9614054, -30000824, 12074674}, | |
1529 | {4771191, -135239, 14290749, -13089852, 27992298, 14998318, | |
1530 | -1413936, -1556716, 29832613, -16391035}, | |
1531 | }, | |
1532 | { | |
1533 | {7064884, -7541174, -19161962, -5067537, -18891269, -2912736, | |
1534 | 25825242, 5293297, -27122660, 13101590}, | |
1535 | {-2298563, 2439670, -7466610, 1719965, -27267541, -16328445, | |
1536 | 32512469, -5317593, -30356070, -4190957}, | |
1537 | {-30006540, 10162316, -33180176, 3981723, -16482138, -13070044, | |
1538 | 14413974, 9515896, 19568978, 9628812}, | |
1539 | }, | |
1540 | { | |
1541 | {33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, | |
1542 | -6106839, -6291786, 3437740}, | |
1543 | {-18978877, 3884493, 19469877, 12726490, 15913552, 13614290, | |
1544 | -22961733, 70104, 7463304, 4176122}, | |
1545 | {-27124001, 10659917, 11482427, -16070381, 12771467, -6635117, | |
1546 | -32719404, -5322751, 24216882, 5944158}, | |
1547 | }, | |
1548 | { | |
1549 | {8894125, 7450974, -2664149, -9765752, -28080517, -12389115, | |
1550 | 19345746, 14680796, 11632993, 5847885}, | |
1551 | {26942781, -2315317, 9129564, -4906607, 26024105, 11769399, | |
1552 | -11518837, 6367194, -9727230, 4782140}, | |
1553 | {19916461, -4828410, -22910704, -11414391, 25606324, -5972441, | |
1554 | 33253853, 8220911, 6358847, -1873857}, | |
1555 | }, | |
1556 | { | |
1557 | {801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, | |
1558 | -4480480, -13538503, 1387155}, | |
1559 | {19646058, 5720633, -11416706, 12814209, 11607948, 12749789, | |
1560 | 14147075, 15156355, -21866831, 11835260}, | |
1561 | {19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, | |
1562 | 15467869, -26560550, 5052483}, | |
1563 | }, | |
1564 | }, | |
1565 | { | |
1566 | { | |
1567 | {-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, | |
1568 | -12618185, 12228557, -7003677}, | |
1569 | {32944382, 14922211, -22844894, 5188528, 21913450, -8719943, | |
1570 | 4001465, 13238564, -6114803, 8653815}, | |
1571 | {22865569, -4652735, 27603668, -12545395, 14348958, 8234005, | |
1572 | 24808405, 5719875, 28483275, 2841751}, | |
1573 | }, | |
1574 | { | |
1575 | {-16420968, -1113305, -327719, -12107856, 21886282, -15552774, | |
1576 | -1887966, -315658, 19932058, -12739203}, | |
1577 | {-11656086, 10087521, -8864888, -5536143, -19278573, -3055912, | |
1578 | 3999228, 13239134, -4777469, -13910208}, | |
1579 | {1382174, -11694719, 17266790, 9194690, -13324356, 9720081, | |
1580 | 20403944, 11284705, -14013818, 3093230}, | |
1581 | }, | |
1582 | { | |
1583 | {16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, | |
1584 | 16271225, -24049421, -6691850}, | |
1585 | {-21911077, -5927941, -4611316, -5560156, -31744103, -10785293, | |
1586 | 24123614, 15193618, -21652117, -16739389}, | |
1587 | {-9935934, -4289447, -25279823, 4372842, 2087473, 10399484, | |
1588 | 31870908, 14690798, 17361620, 11864968}, | |
1589 | }, | |
1590 | { | |
1591 | {-11307610, 6210372, 13206574, 5806320, -29017692, -13967200, | |
1592 | -12331205, -7486601, -25578460, -16240689}, | |
1593 | {14668462, -12270235, 26039039, 15305210, 25515617, 4542480, | |
1594 | 10453892, 6577524, 9145645, -6443880}, | |
1595 | {5974874, 3053895, -9433049, -10385191, -31865124, 3225009, | |
1596 | -7972642, 3936128, -5652273, -3050304}, | |
1597 | }, | |
1598 | { | |
1599 | {30625386, -4729400, -25555961, -12792866, -20484575, 7695099, | |
1600 | 17097188, -16303496, -27999779, 1803632}, | |
1601 | {-3553091, 9865099, -5228566, 4272701, -5673832, -16689700, | |
1602 | 14911344, 12196514, -21405489, 7047412}, | |
1603 | {20093277, 9920966, -11138194, -5343857, 13161587, 12044805, | |
1604 | -32856851, 4124601, -32343828, -10257566}, | |
1605 | }, | |
1606 | { | |
1607 | {-20788824, 14084654, -13531713, 7842147, 19119038, -13822605, | |
1608 | 4752377, -8714640, -21679658, 2288038}, | |
1609 | {-26819236, -3283715, 29965059, 3039786, -14473765, 2540457, | |
1610 | 29457502, 14625692, -24819617, 12570232}, | |
1611 | {-1063558, -11551823, 16920318, 12494842, 1278292, -5869109, | |
1612 | -21159943, -3498680, -11974704, 4724943}, | |
1613 | }, | |
1614 | { | |
1615 | {17960970, -11775534, -4140968, -9702530, -8876562, -1410617, | |
1616 | -12907383, -8659932, -29576300, 1903856}, | |
1617 | {23134274, -14279132, -10681997, -1611936, 20684485, 15770816, | |
1618 | -12989750, 3190296, 26955097, 14109738}, | |
1619 | {15308788, 5320727, -30113809, -14318877, 22902008, 7767164, | |
1620 | 29425325, -11277562, 31960942, 11934971}, | |
1621 | }, | |
1622 | { | |
1623 | {-27395711, 8435796, 4109644, 12222639, -24627868, 14818669, | |
1624 | 20638173, 4875028, 10491392, 1379718}, | |
1625 | {-13159415, 9197841, 3875503, -8936108, -1383712, -5879801, | |
1626 | 33518459, 16176658, 21432314, 12180697}, | |
1627 | {-11787308, 11500838, 13787581, -13832590, -22430679, 10140205, | |
1628 | 1465425, 12689540, -10301319, -13872883}, | |
1629 | }, | |
1630 | }, | |
1631 | { | |
1632 | { | |
1633 | {5414091, -15386041, -21007664, 9643570, 12834970, 1186149, | |
1634 | -2622916, -1342231, 26128231, 6032912}, | |
1635 | {-26337395, -13766162, 32496025, -13653919, 17847801, -12669156, | |
1636 | 3604025, 8316894, -25875034, -10437358}, | |
1637 | {3296484, 6223048, 24680646, -12246460, -23052020, 5903205, | |
1638 | -8862297, -4639164, 12376617, 3188849}, | |
1639 | }, | |
1640 | { | |
1641 | {29190488, -14659046, 27549113, -1183516, 3520066, -10697301, | |
1642 | 32049515, -7309113, -16109234, -9852307}, | |
1643 | {-14744486, -9309156, 735818, -598978, -20407687, -5057904, | |
1644 | 25246078, -15795669, 18640741, -960977}, | |
1645 | {-6928835, -16430795, 10361374, 5642961, 4910474, 12345252, | |
1646 | -31638386, -494430, 10530747, 1053335}, | |
1647 | }, | |
1648 | { | |
1649 | {-29265967, -14186805, -13538216, -12117373, -19457059, -10655384, | |
1650 | -31462369, -2948985, 24018831, 15026644}, | |
1651 | {-22592535, -3145277, -2289276, 5953843, -13440189, 9425631, | |
1652 | 25310643, 13003497, -2314791, -15145616}, | |
1653 | {-27419985, -603321, -8043984, -1669117, -26092265, 13987819, | |
1654 | -27297622, 187899, -23166419, -2531735}, | |
1655 | }, | |
1656 | { | |
1657 | {-21744398, -13810475, 1844840, 5021428, -10434399, -15911473, | |
1658 | 9716667, 16266922, -5070217, 726099}, | |
1659 | {29370922, -6053998, 7334071, -15342259, 9385287, 2247707, | |
1660 | -13661962, -4839461, 30007388, -15823341}, | |
1661 | {-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, | |
1662 | 730663, 9835848, 4555336}, | |
1663 | }, | |
1664 | { | |
1665 | {-23376435, 1410446, -22253753, -12899614, 30867635, 15826977, | |
1666 | 17693930, 544696, -11985298, 12422646}, | |
1667 | {31117226, -12215734, -13502838, 6561947, -9876867, -12757670, | |
1668 | -5118685, -4096706, 29120153, 13924425}, | |
1669 | {-17400879, -14233209, 19675799, -2734756, -11006962, -5858820, | |
1670 | -9383939, -11317700, 7240931, -237388}, | |
1671 | }, | |
1672 | { | |
1673 | {-31361739, -11346780, -15007447, -5856218, -22453340, -12152771, | |
1674 | 1222336, 4389483, 3293637, -15551743}, | |
1675 | {-16684801, -14444245, 11038544, 11054958, -13801175, -3338533, | |
1676 | -24319580, 7733547, 12796905, -6335822}, | |
1677 | {-8759414, -10817836, -25418864, 10783769, -30615557, -9746811, | |
1678 | -28253339, 3647836, 3222231, -11160462}, | |
1679 | }, | |
1680 | { | |
1681 | {18606113, 1693100, -25448386, -15170272, 4112353, 10045021, | |
1682 | 23603893, -2048234, -7550776, 2484985}, | |
1683 | {9255317, -3131197, -12156162, -1004256, 13098013, -9214866, | |
1684 | 16377220, -2102812, -19802075, -3034702}, | |
1685 | {-22729289, 7496160, -5742199, 11329249, 19991973, -3347502, | |
1686 | -31718148, 9936966, -30097688, -10618797}, | |
1687 | }, | |
1688 | { | |
1689 | {21878590, -5001297, 4338336, 13643897, -3036865, 13160960, | |
1690 | 19708896, 5415497, -7360503, -4109293}, | |
1691 | {27736861, 10103576, 12500508, 8502413, -3413016, -9633558, | |
1692 | 10436918, -1550276, -23659143, -8132100}, | |
1693 | {19492550, -12104365, -29681976, -852630, -3208171, 12403437, | |
1694 | 30066266, 8367329, 13243957, 8709688}, | |
1695 | }, | |
1696 | }, | |
1697 | { | |
1698 | { | |
1699 | {12015105, 2801261, 28198131, 10151021, 24818120, -4743133, | |
1700 | -11194191, -5645734, 5150968, 7274186}, | |
1701 | {2831366, -12492146, 1478975, 6122054, 23825128, -12733586, | |
1702 | 31097299, 6083058, 31021603, -9793610}, | |
1703 | {-2529932, -2229646, 445613, 10720828, -13849527, -11505937, | |
1704 | -23507731, 16354465, 15067285, -14147707}, | |
1705 | }, | |
1706 | { | |
1707 | {7840942, 14037873, -33364863, 15934016, -728213, -3642706, | |
1708 | 21403988, 1057586, -19379462, -12403220}, | |
1709 | {915865, -16469274, 15608285, -8789130, -24357026, 6060030, | |
1710 | -17371319, 8410997, -7220461, 16527025}, | |
1711 | {32922597, -556987, 20336074, -16184568, 10903705, -5384487, | |
1712 | 16957574, 52992, 23834301, 6588044}, | |
1713 | }, | |
1714 | { | |
1715 | {32752030, 11232950, 3381995, -8714866, 22652988, -10744103, | |
1716 | 17159699, 16689107, -20314580, -1305992}, | |
1717 | {-4689649, 9166776, -25710296, -10847306, 11576752, 12733943, | |
1718 | 7924251, -2752281, 1976123, -7249027}, | |
1719 | {21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, | |
1720 | -3371252, 12331345, -8237197}, | |
1721 | }, | |
1722 | { | |
1723 | {8651614, -4477032, -16085636, -4996994, 13002507, 2950805, | |
1724 | 29054427, -5106970, 10008136, -4667901}, | |
1725 | {31486080, 15114593, -14261250, 12951354, 14369431, -7387845, | |
1726 | 16347321, -13662089, 8684155, -10532952}, | |
1727 | {19443825, 11385320, 24468943, -9659068, -23919258, 2187569, | |
1728 | -26263207, -6086921, 31316348, 14219878}, | |
1729 | }, | |
1730 | { | |
1731 | {-28594490, 1193785, 32245219, 11392485, 31092169, 15722801, | |
1732 | 27146014, 6992409, 29126555, 9207390}, | |
1733 | {32382935, 1110093, 18477781, 11028262, -27411763, -7548111, | |
1734 | -4980517, 10843782, -7957600, -14435730}, | |
1735 | {2814918, 7836403, 27519878, -7868156, -20894015, -11553689, | |
1736 | -21494559, 8550130, 28346258, 1994730}, | |
1737 | }, | |
1738 | { | |
1739 | {-19578299, 8085545, -14000519, -3948622, 2785838, -16231307, | |
1740 | -19516951, 7174894, 22628102, 8115180}, | |
1741 | {-30405132, 955511, -11133838, -15078069, -32447087, -13278079, | |
1742 | -25651578, 3317160, -9943017, 930272}, | |
1743 | {-15303681, -6833769, 28856490, 1357446, 23421993, 1057177, | |
1744 | 24091212, -1388970, -22765376, -10650715}, | |
1745 | }, | |
1746 | { | |
1747 | {-22751231, -5303997, -12907607, -12768866, -15811511, -7797053, | |
1748 | -14839018, -16554220, -1867018, 8398970}, | |
1749 | {-31969310, 2106403, -4736360, 1362501, 12813763, 16200670, | |
1750 | 22981545, -6291273, 18009408, -15772772}, | |
1751 | {-17220923, -9545221, -27784654, 14166835, 29815394, 7444469, | |
1752 | 29551787, -3727419, 19288549, 1325865}, | |
1753 | }, | |
1754 | { | |
1755 | {15100157, -15835752, -23923978, -1005098, -26450192, 15509408, | |
1756 | 12376730, -3479146, 33166107, -8042750}, | |
1757 | {20909231, 13023121, -9209752, 16251778, -5778415, -8094914, | |
1758 | 12412151, 10018715, 2213263, -13878373}, | |
1759 | {32529814, -11074689, 30361439, -16689753, -9135940, 1513226, | |
1760 | 22922121, 6382134, -5766928, 8371348}, | |
1761 | }, | |
1762 | }, | |
1763 | { | |
1764 | { | |
1765 | {9923462, 11271500, 12616794, 3544722, -29998368, -1721626, | |
1766 | 12891687, -8193132, -26442943, 10486144}, | |
1767 | {-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, | |
1768 | 2610596, -23921530, -11455195}, | |
1769 | {5408411, -1136691, -4969122, 10561668, 24145918, 14240566, | |
1770 | 31319731, -4235541, 19985175, -3436086}, | |
1771 | }, | |
1772 | { | |
1773 | {-13994457, 16616821, 14549246, 3341099, 32155958, 13648976, | |
1774 | -17577068, 8849297, 65030, 8370684}, | |
1775 | {-8320926, -12049626, 31204563, 5839400, -20627288, -1057277, | |
1776 | -19442942, 6922164, 12743482, -9800518}, | |
1777 | {-2361371, 12678785, 28815050, 4759974, -23893047, 4884717, | |
1778 | 23783145, 11038569, 18800704, 255233}, | |
1779 | }, | |
1780 | { | |
1781 | {-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, | |
1782 | 9066957, 19258688, -14753793}, | |
1783 | {-2936654, -10827535, -10432089, 14516793, -3640786, 4372541, | |
1784 | -31934921, 2209390, -1524053, 2055794}, | |
1785 | {580882, 16705327, 5468415, -2683018, -30926419, -14696000, | |
1786 | -7203346, -8994389, -30021019, 7394435}, | |
1787 | }, | |
1788 | { | |
1789 | {23838809, 1822728, -15738443, 15242727, 8318092, -3733104, | |
1790 | -21672180, -3492205, -4821741, 14799921}, | |
1791 | {13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, | |
1792 | 13496856, -9056018, 7402518}, | |
1793 | {2286874, -4435931, -20042458, -2008336, -13696227, 5038122, | |
1794 | 11006906, -15760352, 8205061, 1607563}, | |
1795 | }, | |
1796 | { | |
1797 | {14414086, -8002132, 3331830, -3208217, 22249151, -5594188, | |
1798 | 18364661, -2906958, 30019587, -9029278}, | |
1799 | {-27688051, 1585953, -10775053, 931069, -29120221, -11002319, | |
1800 | -14410829, 12029093, 9944378, 8024}, | |
1801 | {4368715, -3709630, 29874200, -15022983, -20230386, -11410704, | |
1802 | -16114594, -999085, -8142388, 5640030}, | |
1803 | }, | |
1804 | { | |
1805 | {10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, | |
1806 | -16694564, 15219798, -14327783}, | |
1807 | {27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, | |
1808 | -1173195, -18342183, 9742717}, | |
1809 | {6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, | |
1810 | 7406442, 12420155, 1994844}, | |
1811 | }, | |
1812 | { | |
1813 | {14012521, -5024720, -18384453, -9578469, -26485342, -3936439, | |
1814 | -13033478, -10909803, 24319929, -6446333}, | |
1815 | {16412690, -4507367, 10772641, 15929391, -17068788, -4658621, | |
1816 | 10555945, -10484049, -30102368, -4739048}, | |
1817 | {22397382, -7767684, -9293161, -12792868, 17166287, -9755136, | |
1818 | -27333065, 6199366, 21880021, -12250760}, | |
1819 | }, | |
1820 | { | |
1821 | {-4283307, 5368523, -31117018, 8163389, -30323063, 3209128, | |
1822 | 16557151, 8890729, 8840445, 4957760}, | |
1823 | {-15447727, 709327, -6919446, -10870178, -29777922, 6522332, | |
1824 | -21720181, 12130072, -14796503, 5005757}, | |
1825 | {-2114751, -14308128, 23019042, 15765735, -25269683, 6002752, | |
1826 | 10183197, -13239326, -16395286, -2176112}, | |
1827 | }, | |
1828 | }, | |
1829 | { | |
1830 | { | |
1831 | {-19025756, 1632005, 13466291, -7995100, -23640451, 16573537, | |
1832 | -32013908, -3057104, 22208662, 2000468}, | |
1833 | {3065073, -1412761, -25598674, -361432, -17683065, -5703415, | |
1834 | -8164212, 11248527, -3691214, -7414184}, | |
1835 | {10379208, -6045554, 8877319, 1473647, -29291284, -12507580, | |
1836 | 16690915, 2553332, -3132688, 16400289}, | |
1837 | }, | |
1838 | { | |
1839 | {15716668, 1254266, -18472690, 7446274, -8448918, 6344164, | |
1840 | -22097271, -7285580, 26894937, 9132066}, | |
1841 | {24158887, 12938817, 11085297, -8177598, -28063478, -4457083, | |
1842 | -30576463, 64452, -6817084, -2692882}, | |
1843 | {13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, | |
1844 | -3418511, -4688006, 2364226}, | |
1845 | }, | |
1846 | { | |
1847 | {16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024, | |
1848 | -11697457, 15445875, -7798101}, | |
1849 | {29004207, -7867081, 28661402, -640412, -12794003, -7943086, | |
1850 | 31863255, -4135540, -278050, -15759279}, | |
1851 | {-6122061, -14866665, -28614905, 14569919, -10857999, -3591829, | |
1852 | 10343412, -6976290, -29828287, -10815811}, | |
1853 | }, | |
1854 | { | |
1855 | {27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636, | |
1856 | 15372179, 17293797, 960709}, | |
1857 | {20263915, 11434237, -5765435, 11236810, 13505955, -10857102, | |
1858 | -16111345, 6493122, -19384511, 7639714}, | |
1859 | {-2830798, -14839232, 25403038, -8215196, -8317012, -16173699, | |
1860 | 18006287, -16043750, 29994677, -15808121}, | |
1861 | }, | |
1862 | { | |
1863 | {9769828, 5202651, -24157398, -13631392, -28051003, -11561624, | |
1864 | -24613141, -13860782, -31184575, 709464}, | |
1865 | {12286395, 13076066, -21775189, -1176622, -25003198, 4057652, | |
1866 | -32018128, -8890874, 16102007, 13205847}, | |
1867 | {13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, | |
1868 | 8525972, 10151379, 10394400}, | |
1869 | }, | |
1870 | { | |
1871 | {4024660, -16137551, 22436262, 12276534, -9099015, -2686099, | |
1872 | 19698229, 11743039, -33302334, 8934414}, | |
1873 | {-15879800, -4525240, -8580747, -2934061, 14634845, -698278, | |
1874 | -9449077, 3137094, -11536886, 11721158}, | |
1875 | {17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, | |
1876 | 8835153, -9205489, -1280045}, | |
1877 | }, | |
1878 | { | |
1879 | {-461409, -7830014, 20614118, 16688288, -7514766, -4807119, | |
1880 | 22300304, 505429, 6108462, -6183415}, | |
1881 | {-5070281, 12367917, -30663534, 3234473, 32617080, -8422642, | |
1882 | 29880583, -13483331, -26898490, -7867459}, | |
1883 | {-31975283, 5726539, 26934134, 10237677, -3173717, -605053, | |
1884 | 24199304, 3795095, 7592688, -14992079}, | |
1885 | }, | |
1886 | { | |
1887 | {21594432, -14964228, 17466408, -4077222, 32537084, 2739898, | |
1888 | 6407723, 12018833, -28256052, 4298412}, | |
1889 | {-20650503, -11961496, -27236275, 570498, 3767144, -1717540, | |
1890 | 13891942, -1569194, 13717174, 10805743}, | |
1891 | {-14676630, -15644296, 15287174, 11927123, 24177847, -8175568, | |
1892 | -796431, 14860609, -26938930, -5863836}, | |
1893 | }, | |
1894 | }, | |
1895 | { | |
1896 | { | |
1897 | {12962541, 5311799, -10060768, 11658280, 18855286, -7954201, | |
1898 | 13286263, -12808704, -4381056, 9882022}, | |
1899 | {18512079, 11319350, -20123124, 15090309, 18818594, 5271736, | |
1900 | -22727904, 3666879, -23967430, -3299429}, | |
1901 | {-6789020, -3146043, 16192429, 13241070, 15898607, -14206114, | |
1902 | -10084880, -6661110, -2403099, 5276065}, | |
1903 | }, | |
1904 | { | |
1905 | {30169808, -5317648, 26306206, -11750859, 27814964, 7069267, | |
1906 | 7152851, 3684982, 1449224, 13082861}, | |
1907 | {10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, | |
1908 | 15056736, -21016438, -8202000}, | |
1909 | {-33150110, 3261608, 22745853, 7948688, 19370557, -15177665, | |
1910 | -26171976, 6482814, -10300080, -11060101}, | |
1911 | }, | |
1912 | { | |
1913 | {32869458, -5408545, 25609743, 15678670, -10687769, -15471071, | |
1914 | 26112421, 2521008, -22664288, 6904815}, | |
1915 | {29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737, | |
1916 | 3841096, -29003639, -6657642}, | |
1917 | {10340844, -6630377, -18656632, -2278430, 12621151, -13339055, | |
1918 | 30878497, -11824370, -25584551, 5181966}, | |
1919 | }, | |
1920 | { | |
1921 | {25940115, -12658025, 17324188, -10307374, -8671468, 15029094, | |
1922 | 24396252, -16450922, -2322852, -12388574}, | |
1923 | {-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390, | |
1924 | 12641087, 20603771, -6561742}, | |
1925 | {-18882287, -11673380, 24849422, 11501709, 13161720, -4768874, | |
1926 | 1925523, 11914390, 4662781, 7820689}, | |
1927 | }, | |
1928 | { | |
1929 | {12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456, | |
1930 | 12172924, 16136752, 15264020}, | |
1931 | {-10349955, -14680563, -8211979, 2330220, -17662549, -14545780, | |
1932 | 10658213, 6671822, 19012087, 3772772}, | |
1933 | {3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732, | |
1934 | -15762884, 20527771, 12988982}, | |
1935 | }, | |
1936 | { | |
1937 | {-14822485, -5797269, -3707987, 12689773, -898983, -10914866, | |
1938 | -24183046, -10564943, 3299665, -12424953}, | |
1939 | {-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197, | |
1940 | 6461331, -25583147, 8991218}, | |
1941 | {-17226263, 1816362, -1673288, -6086439, 31783888, -8175991, | |
1942 | -32948145, 7417950, -30242287, 1507265}, | |
1943 | }, | |
1944 | { | |
1945 | {29692663, 6829891, -10498800, 4334896, 20945975, -11906496, | |
1946 | -28887608, 8209391, 14606362, -10647073}, | |
1947 | {-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695, | |
1948 | 9761487, 4170404, -2085325}, | |
1949 | {-11587470, 14855945, -4127778, -1531857, -26649089, 15084046, | |
1950 | 22186522, 16002000, -14276837, -8400798}, | |
1951 | }, | |
1952 | { | |
1953 | {-4811456, 13761029, -31703877, -2483919, -3312471, 7869047, | |
1954 | -7113572, -9620092, 13240845, 10965870}, | |
1955 | {-7742563, -8256762, -14768334, -13656260, -23232383, 12387166, | |
1956 | 4498947, 14147411, 29514390, 4302863}, | |
1957 | {-13413405, -12407859, 20757302, -13801832, 14785143, 8976368, | |
1958 | -5061276, -2144373, 17846988, -13971927}, | |
1959 | }, | |
1960 | }, | |
1961 | { | |
1962 | { | |
1963 | {-2244452, -754728, -4597030, -1066309, -6247172, 1455299, | |
1964 | -21647728, -9214789, -5222701, 12650267}, | |
1965 | {-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813, | |
1966 | 13770293, -19134326, 10958663}, | |
1967 | {22470984, 12369526, 23446014, -5441109, -21520802, -9698723, | |
1968 | -11772496, -11574455, -25083830, 4271862}, | |
1969 | }, | |
1970 | { | |
1971 | {-25169565, -10053642, -19909332, 15361595, -5984358, 2159192, | |
1972 | 75375, -4278529, -32526221, 8469673}, | |
1973 | {15854970, 4148314, -8893890, 7259002, 11666551, 13824734, | |
1974 | -30531198, 2697372, 24154791, -9460943}, | |
1975 | {15446137, -15806644, 29759747, 14019369, 30811221, -9610191, | |
1976 | -31582008, 12840104, 24913809, 9815020}, | |
1977 | }, | |
1978 | { | |
1979 | {-4709286, -5614269, -31841498, -12288893, -14443537, 10799414, | |
1980 | -9103676, 13438769, 18735128, 9466238}, | |
1981 | {11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821, | |
1982 | -10896103, -22728655, 16199064}, | |
1983 | {14576810, 379472, -26786533, -8317236, -29426508, -10812974, | |
1984 | -102766, 1876699, 30801119, 2164795}, | |
1985 | }, | |
1986 | { | |
1987 | {15995086, 3199873, 13672555, 13712240, -19378835, -4647646, | |
1988 | -13081610, -15496269, -13492807, 1268052}, | |
1989 | {-10290614, -3659039, -3286592, 10948818, 23037027, 3794475, | |
1990 | -3470338, -12600221, -17055369, 3565904}, | |
1991 | {29210088, -9419337, -5919792, -4952785, 10834811, -13327726, | |
1992 | -16512102, -10820713, -27162222, -14030531}, | |
1993 | }, | |
1994 | { | |
1995 | {-13161890, 15508588, 16663704, -8156150, -28349942, 9019123, | |
1996 | -29183421, -3769423, 2244111, -14001979}, | |
1997 | {-5152875, -3800936, -9306475, -6071583, 16243069, 14684434, | |
1998 | -25673088, -16180800, 13491506, 4641841}, | |
1999 | {10813417, 643330, -19188515, -728916, 30292062, -16600078, | |
2000 | 27548447, -7721242, 14476989, -12767431}, | |
2001 | }, | |
2002 | { | |
2003 | {10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937, | |
2004 | -1644259, -27912810, 12651324}, | |
2005 | {-31185513, -813383, 22271204, 11835308, 10201545, 15351028, | |
2006 | 17099662, 3988035, 21721536, -3148940}, | |
2007 | {10202177, -6545839, -31373232, -9574638, -32150642, -8119683, | |
2008 | -12906320, 3852694, 13216206, 14842320}, | |
2009 | }, | |
2010 | { | |
2011 | {-15815640, -10601066, -6538952, -7258995, -6984659, -6581778, | |
2012 | -31500847, 13765824, -27434397, 9900184}, | |
2013 | {14465505, -13833331, -32133984, -14738873, -27443187, 12990492, | |
2014 | 33046193, 15796406, -7051866, -8040114}, | |
2015 | {30924417, -8279620, 6359016, -12816335, 16508377, 9071735, | |
2016 | -25488601, 15413635, 9524356, -7018878}, | |
2017 | }, | |
2018 | { | |
2019 | {12274201, -13175547, 32627641, -1785326, 6736625, 13267305, | |
2020 | 5237659, -5109483, 15663516, 4035784}, | |
2021 | {-2951309, 8903985, 17349946, 601635, -16432815, -4612556, | |
2022 | -13732739, -15889334, -22258478, 4659091}, | |
2023 | {-16916263, -4952973, -30393711, -15158821, 20774812, 15897498, | |
2024 | 5736189, 15026997, -2178256, -13455585}, | |
2025 | }, | |
2026 | }, | |
2027 | { | |
2028 | { | |
2029 | {-8858980, -2219056, 28571666, -10155518, -474467, -10105698, | |
2030 | -3801496, 278095, 23440562, -290208}, | |
2031 | {10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275, | |
2032 | 11551483, -16571960, -7442864}, | |
2033 | {17932739, -12437276, -24039557, 10749060, 11316803, 7535897, | |
2034 | 22503767, 5561594, -3646624, 3898661}, | |
2035 | }, | |
2036 | { | |
2037 | {7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531, | |
2038 | 7152530, 21831162, 1245233}, | |
2039 | {26958459, -14658026, 4314586, 8346991, -5677764, 11960072, | |
2040 | -32589295, -620035, -30402091, -16716212}, | |
2041 | {-12165896, 9166947, 33491384, 13673479, 29787085, 13096535, | |
2042 | 6280834, 14587357, -22338025, 13987525}, | |
2043 | }, | |
2044 | { | |
2045 | {-24349909, 7778775, 21116000, 15572597, -4833266, -5357778, | |
2046 | -4300898, -5124639, -7469781, -2858068}, | |
2047 | {9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781, | |
2048 | 6439245, -14581012, 4091397}, | |
2049 | {-8426427, 1470727, -28109679, -1596990, 3978627, -5123623, | |
2050 | -19622683, 12092163, 29077877, -14741988}, | |
2051 | }, | |
2052 | { | |
2053 | {5269168, -6859726, -13230211, -8020715, 25932563, 1763552, | |
2054 | -5606110, -5505881, -20017847, 2357889}, | |
2055 | {32264008, -15407652, -5387735, -1160093, -2091322, -3946900, | |
2056 | 23104804, -12869908, 5727338, 189038}, | |
2057 | {14609123, -8954470, -6000566, -16622781, -14577387, -7743898, | |
2058 | -26745169, 10942115, -25888931, -14884697}, | |
2059 | }, | |
2060 | { | |
2061 | {20513500, 5557931, -15604613, 7829531, 26413943, -2019404, | |
2062 | -21378968, 7471781, 13913677, -5137875}, | |
2063 | {-25574376, 11967826, 29233242, 12948236, -6754465, 4713227, | |
2064 | -8940970, 14059180, 12878652, 8511905}, | |
2065 | {-25656801, 3393631, -2955415, -7075526, -2250709, 9366908, | |
2066 | -30223418, 6812974, 5568676, -3127656}, | |
2067 | }, | |
2068 | { | |
2069 | {11630004, 12144454, 2116339, 13606037, 27378885, 15676917, | |
2070 | -17408753, -13504373, -14395196, 8070818}, | |
2071 | {27117696, -10007378, -31282771, -5570088, 1127282, 12772488, | |
2072 | -29845906, 10483306, -11552749, -1028714}, | |
2073 | {10637467, -5688064, 5674781, 1072708, -26343588, -6982302, | |
2074 | -1683975, 9177853, -27493162, 15431203}, | |
2075 | }, | |
2076 | { | |
2077 | {20525145, 10892566, -12742472, 12779443, -29493034, 16150075, | |
2078 | -28240519, 14943142, -15056790, -7935931}, | |
2079 | {-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767, | |
2080 | -3239766, -3356550, 9594024}, | |
2081 | {-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683, | |
2082 | -6492290, 13352335, -10977084}, | |
2083 | }, | |
2084 | { | |
2085 | {-1931799, -5407458, 3304649, -12884869, 17015806, -4877091, | |
2086 | -29783850, -7752482, -13215537, -319204}, | |
2087 | {20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742, | |
2088 | 15077870, -22750759, 14523817}, | |
2089 | {27406042, -6041657, 27423596, -4497394, 4996214, 10002360, | |
2090 | -28842031, -4545494, -30172742, -4805667}, | |
2091 | }, | |
2092 | }, | |
2093 | { | |
2094 | { | |
2095 | {11374242, 12660715, 17861383, -12540833, 10935568, 1099227, | |
2096 | -13886076, -9091740, -27727044, 11358504}, | |
2097 | {-12730809, 10311867, 1510375, 10778093, -2119455, -9145702, | |
2098 | 32676003, 11149336, -26123651, 4985768}, | |
2099 | {-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043, | |
2100 | 13794114, -19414307, -15621255}, | |
2101 | }, | |
2102 | { | |
2103 | {6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603, | |
2104 | 6970005, -1691065, -9004790}, | |
2105 | {1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622, | |
2106 | -5475723, -16796596, -5031438}, | |
2107 | {-22273315, -13524424, -64685, -4334223, -18605636, -10921968, | |
2108 | -20571065, -7007978, -99853, -10237333}, | |
2109 | }, | |
2110 | { | |
2111 | {17747465, 10039260, 19368299, -4050591, -20630635, -16041286, | |
2112 | 31992683, -15857976, -29260363, -5511971}, | |
2113 | {31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999, | |
2114 | -3744247, 4882242, -10626905}, | |
2115 | {29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198, | |
2116 | 3272828, -5190932, -4162409}, | |
2117 | }, | |
2118 | { | |
2119 | {12501286, 4044383, -8612957, -13392385, -32430052, 5136599, | |
2120 | -19230378, -3529697, 330070, -3659409}, | |
2121 | {6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522, | |
2122 | -8573892, -271295, 12071499}, | |
2123 | {-8365515, -4042521, 25133448, -4517355, -6211027, 2265927, | |
2124 | -32769618, 1936675, -5159697, 3829363}, | |
2125 | }, | |
2126 | { | |
2127 | {28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550, | |
2128 | -6567787, 26333140, 14267664}, | |
2129 | {-11067219, 11871231, 27385719, -10559544, -4585914, -11189312, | |
2130 | 10004786, -8709488, -21761224, 8930324}, | |
2131 | {-21197785, -16396035, 25654216, -1725397, 12282012, 11008919, | |
2132 | 1541940, 4757911, -26491501, -16408940}, | |
2133 | }, | |
2134 | { | |
2135 | {13537262, -7759490, -20604840, 10961927, -5922820, -13218065, | |
2136 | -13156584, 6217254, -15943699, 13814990}, | |
2137 | {-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681, | |
2138 | 9257833, -1956526, -1776914}, | |
2139 | {-25045300, -10191966, 15366585, 15166509, -13105086, 8423556, | |
2140 | -29171540, 12361135, -18685978, 4578290}, | |
2141 | }, | |
2142 | { | |
2143 | {24579768, 3711570, 1342322, -11180126, -27005135, 14124956, | |
2144 | -22544529, 14074919, 21964432, 8235257}, | |
2145 | {-6528613, -2411497, 9442966, -5925588, 12025640, -1487420, | |
2146 | -2981514, -1669206, 13006806, 2355433}, | |
2147 | {-16304899, -13605259, -6632427, -5142349, 16974359, -10911083, | |
2148 | 27202044, 1719366, 1141648, -12796236}, | |
2149 | }, | |
2150 | { | |
2151 | {-12863944, -13219986, -8318266, -11018091, -6810145, -4843894, | |
2152 | 13475066, -3133972, 32674895, 13715045}, | |
2153 | {11423335, -5468059, 32344216, 8962751, 24989809, 9241752, | |
2154 | -13265253, 16086212, -28740881, -15642093}, | |
2155 | {-1409668, 12530728, -6368726, 10847387, 19531186, -14132160, | |
2156 | -11709148, 7791794, -27245943, 4383347}, | |
2157 | }, | |
2158 | }, | |
2159 | { | |
2160 | { | |
2161 | {-28970898, 5271447, -1266009, -9736989, -12455236, 16732599, | |
2162 | -4862407, -4906449, 27193557, 6245191}, | |
2163 | {-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898, | |
2164 | 3260492, 22510453, 8577507}, | |
2165 | {-12632451, 11257346, -32692994, 13548177, -721004, 10879011, | |
2166 | 31168030, 13952092, -29571492, -3635906}, | |
2167 | }, | |
2168 | { | |
2169 | {3877321, -9572739, 32416692, 5405324, -11004407, -13656635, | |
2170 | 3759769, 11935320, 5611860, 8164018}, | |
2171 | {-16275802, 14667797, 15906460, 12155291, -22111149, -9039718, | |
2172 | 32003002, -8832289, 5773085, -8422109}, | |
2173 | {-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725, | |
2174 | 12376320, 31632953, 190926}, | |
2175 | }, | |
2176 | { | |
2177 | {-24593607, -16138885, -8423991, 13378746, 14162407, 6901328, | |
2178 | -8288749, 4508564, -25341555, -3627528}, | |
2179 | {8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941, | |
2180 | -14786005, -1672488, 827625}, | |
2181 | {-32720583, -16289296, -32503547, 7101210, 13354605, 2659080, | |
2182 | -1800575, -14108036, -24878478, 1541286}, | |
2183 | }, | |
2184 | { | |
2185 | {2901347, -1117687, 3880376, -10059388, -17620940, -3612781, | |
2186 | -21802117, -3567481, 20456845, -1885033}, | |
2187 | {27019610, 12299467, -13658288, -1603234, -12861660, -4861471, | |
2188 | -19540150, -5016058, 29439641, 15138866}, | |
2189 | {21536104, -6626420, -32447818, -10690208, -22408077, 5175814, | |
2190 | -5420040, -16361163, 7779328, 109896}, | |
2191 | }, | |
2192 | { | |
2193 | {30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390, | |
2194 | 12180118, 23177719, -554075}, | |
2195 | {26572847, 3405927, -31701700, 12890905, -19265668, 5335866, | |
2196 | -6493768, 2378492, 4439158, -13279347}, | |
2197 | {-22716706, 3489070, -9225266, -332753, 18875722, -1140095, | |
2198 | 14819434, -12731527, -17717757, -5461437}, | |
2199 | }, | |
2200 | { | |
2201 | {-5056483, 16566551, 15953661, 3767752, -10436499, 15627060, | |
2202 | -820954, 2177225, 8550082, -15114165}, | |
2203 | {-18473302, 16596775, -381660, 15663611, 22860960, 15585581, | |
2204 | -27844109, -3582739, -23260460, -8428588}, | |
2205 | {-32480551, 15707275, -8205912, -5652081, 29464558, 2713815, | |
2206 | -22725137, 15860482, -21902570, 1494193}, | |
2207 | }, | |
2208 | { | |
2209 | {-19562091, -14087393, -25583872, -9299552, 13127842, 759709, | |
2210 | 21923482, 16529112, 8742704, 12967017}, | |
2211 | {-28464899, 1553205, 32536856, -10473729, -24691605, -406174, | |
2212 | -8914625, -2933896, -29903758, 15553883}, | |
2213 | {21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572, | |
2214 | 14513274, 19375923, -12647961}, | |
2215 | }, | |
2216 | { | |
2217 | {8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818, | |
2218 | -6222716, 2862653, 9455043}, | |
2219 | {29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124, | |
2220 | -2990080, 15511449, 4789663}, | |
2221 | {-20679756, 7004547, 8824831, -9434977, -4045704, -3750736, | |
2222 | -5754762, 108893, 23513200, 16652362}, | |
2223 | }, | |
2224 | }, | |
2225 | { | |
2226 | { | |
2227 | {-33256173, 4144782, -4476029, -6579123, 10770039, -7155542, | |
2228 | -6650416, -12936300, -18319198, 10212860}, | |
2229 | {2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801, | |
2230 | 2600940, -9988298, -12506466}, | |
2231 | {-24645692, 13317462, -30449259, -15653928, 21365574, -10869657, | |
2232 | 11344424, 864440, -2499677, -16710063}, | |
2233 | }, | |
2234 | { | |
2235 | {-26432803, 6148329, -17184412, -14474154, 18782929, -275997, | |
2236 | -22561534, 211300, 2719757, 4940997}, | |
2237 | {-1323882, 3911313, -6948744, 14759765, -30027150, 7851207, | |
2238 | 21690126, 8518463, 26699843, 5276295}, | |
2239 | {-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586, | |
2240 | 149635, -15452774, 7159369}, | |
2241 | }, | |
2242 | { | |
2243 | {9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009, | |
2244 | 8312176, 22477218, -8403385}, | |
2245 | {18155857, -16504990, 19744716, 9006923, 15154154, -10538976, | |
2246 | 24256460, -4864995, -22548173, 9334109}, | |
2247 | {2986088, -4911893, 10776628, -3473844, 10620590, -7083203, | |
2248 | -21413845, 14253545, -22587149, 536906}, | |
2249 | }, | |
2250 | { | |
2251 | {4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551, | |
2252 | 10589625, 10838060, -15420424}, | |
2253 | {-19342404, 867880, 9277171, -3218459, -14431572, -1986443, | |
2254 | 19295826, -15796950, 6378260, 699185}, | |
2255 | {7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039, | |
2256 | 15693155, -5045064, -13373962}, | |
2257 | }, | |
2258 | { | |
2259 | {-7737563, -5869402, -14566319, -7406919, 11385654, 13201616, | |
2260 | 31730678, -10962840, -3918636, -9669325}, | |
2261 | {10188286, -15770834, -7336361, 13427543, 22223443, 14896287, | |
2262 | 30743455, 7116568, -21786507, 5427593}, | |
2263 | {696102, 13206899, 27047647, -10632082, 15285305, -9853179, | |
2264 | 10798490, -4578720, 19236243, 12477404}, | |
2265 | }, | |
2266 | { | |
2267 | {-11229439, 11243796, -17054270, -8040865, -788228, -8167967, | |
2268 | -3897669, 11180504, -23169516, 7733644}, | |
2269 | {17800790, -14036179, -27000429, -11766671, 23887827, 3149671, | |
2270 | 23466177, -10538171, 10322027, 15313801}, | |
2271 | {26246234, 11968874, 32263343, -5468728, 6830755, -13323031, | |
2272 | -15794704, -101982, -24449242, 10890804}, | |
2273 | }, | |
2274 | { | |
2275 | {-31365647, 10271363, -12660625, -6267268, 16690207, -13062544, | |
2276 | -14982212, 16484931, 25180797, -5334884}, | |
2277 | {-586574, 10376444, -32586414, -11286356, 19801893, 10997610, | |
2278 | 2276632, 9482883, 316878, 13820577}, | |
2279 | {-9882808, -4510367, -2115506, 16457136, -11100081, 11674996, | |
2280 | 30756178, -7515054, 30696930, -3712849}, | |
2281 | }, | |
2282 | { | |
2283 | {32988917, -9603412, 12499366, 7910787, -10617257, -11931514, | |
2284 | -7342816, -9985397, -32349517, 7392473}, | |
2285 | {-8855661, 15927861, 9866406, -3649411, -2396914, -16655781, | |
2286 | -30409476, -9134995, 25112947, -2926644}, | |
2287 | {-2504044, -436966, 25621774, -5678772, 15085042, -5479877, | |
2288 | -24884878, -13526194, 5537438, -13914319}, | |
2289 | }, | |
2290 | }, | |
2291 | { | |
2292 | { | |
2293 | {-11225584, 2320285, -9584280, 10149187, -33444663, 5808648, | |
2294 | -14876251, -1729667, 31234590, 6090599}, | |
2295 | {-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721, | |
2296 | 15878753, -6970405, -9034768}, | |
2297 | {-27757857, 247744, -15194774, -9002551, 23288161, -10011936, | |
2298 | -23869595, 6503646, 20650474, 1804084}, | |
2299 | }, | |
2300 | { | |
2301 | {-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995, | |
2302 | -10329713, 27842616, -202328}, | |
2303 | {-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656, | |
2304 | 5031932, -11375082, 12714369}, | |
2305 | {20807691, -7270825, 29286141, 11421711, -27876523, -13868230, | |
2306 | -21227475, 1035546, -19733229, 12796920}, | |
2307 | }, | |
2308 | { | |
2309 | {12076899, -14301286, -8785001, -11848922, -25012791, 16400684, | |
2310 | -17591495, -12899438, 3480665, -15182815}, | |
2311 | {-32361549, 5457597, 28548107, 7833186, 7303070, -11953545, | |
2312 | -24363064, -15921875, -33374054, 2771025}, | |
2313 | {-21389266, 421932, 26597266, 6860826, 22486084, -6737172, | |
2314 | -17137485, -4210226, -24552282, 15673397}, | |
2315 | }, | |
2316 | { | |
2317 | {-20184622, 2338216, 19788685, -9620956, -4001265, -8740893, | |
2318 | -20271184, 4733254, 3727144, -12934448}, | |
2319 | {6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594, | |
2320 | 7975683, 31123697, -10958981}, | |
2321 | {30069250, -11435332, 30434654, 2958439, 18399564, -976289, | |
2322 | 12296869, 9204260, -16432438, 9648165}, | |
2323 | }, | |
2324 | { | |
2325 | {32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266, | |
2326 | 5248604, -26008332, -11377501}, | |
2327 | {17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711, | |
2328 | 15298639, 2662509, -16297073}, | |
2329 | {-1172927, -7558695, -4366770, -4287744, -21346413, -8434326, | |
2330 | 32087529, -1222777, 32247248, -14389861}, | |
2331 | }, | |
2332 | { | |
2333 | {14312628, 1221556, 17395390, -8700143, -4945741, -8684635, | |
2334 | -28197744, -9637817, -16027623, -13378845}, | |
2335 | {-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502, | |
2336 | 9803137, 17597934, 2346211}, | |
2337 | {18510800, 15337574, 26171504, 981392, -22241552, 7827556, | |
2338 | -23491134, -11323352, 3059833, -11782870}, | |
2339 | }, | |
2340 | { | |
2341 | {10141598, 6082907, 17829293, -1947643, 9830092, 13613136, | |
2342 | -25556636, -5544586, -33502212, 3592096}, | |
2343 | {33114168, -15889352, -26525686, -13343397, 33076705, 8716171, | |
2344 | 1151462, 1521897, -982665, -6837803}, | |
2345 | {-32939165, -4255815, 23947181, -324178, -33072974, -12305637, | |
2346 | -16637686, 3891704, 26353178, 693168}, | |
2347 | }, | |
2348 | { | |
2349 | {30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294, | |
2350 | -400668, 31375464, 14369965}, | |
2351 | {-14370654, -7772529, 1510301, 6434173, -18784789, -6262728, | |
2352 | 32732230, -13108839, 17901441, 16011505}, | |
2353 | {18171223, -11934626, -12500402, 15197122, -11038147, -15230035, | |
2354 | -19172240, -16046376, 8764035, 12309598}, | |
2355 | }, | |
2356 | }, | |
2357 | { | |
2358 | { | |
2359 | {5975908, -5243188, -19459362, -9681747, -11541277, 14015782, | |
2360 | -23665757, 1228319, 17544096, -10593782}, | |
2361 | {5811932, -1715293, 3442887, -2269310, -18367348, -8359541, | |
2362 | -18044043, -15410127, -5565381, 12348900}, | |
2363 | {-31399660, 11407555, 25755363, 6891399, -3256938, 14872274, | |
2364 | -24849353, 8141295, -10632534, -585479}, | |
2365 | }, | |
2366 | { | |
2367 | {-12675304, 694026, -5076145, 13300344, 14015258, -14451394, | |
2368 | -9698672, -11329050, 30944593, 1130208}, | |
2369 | {8247766, -6710942, -26562381, -7709309, -14401939, -14648910, | |
2370 | 4652152, 2488540, 23550156, -271232}, | |
2371 | {17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737, | |
2372 | -5908146, -408818, -137719}, | |
2373 | }, | |
2374 | { | |
2375 | {16091085, -16253926, 18599252, 7340678, 2137637, -1221657, | |
2376 | -3364161, 14550936, 3260525, -7166271}, | |
2377 | {-4910104, -13332887, 18550887, 10864893, -16459325, -7291596, | |
2378 | -23028869, -13204905, -12748722, 2701326}, | |
2379 | {-8574695, 16099415, 4629974, -16340524, -20786213, -6005432, | |
2380 | -10018363, 9276971, 11329923, 1862132}, | |
2381 | }, | |
2382 | { | |
2383 | {14763076, -15903608, -30918270, 3689867, 3511892, 10313526, | |
2384 | -21951088, 12219231, -9037963, -940300}, | |
2385 | {8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216, | |
2386 | -2909717, -15438168, 11595570}, | |
2387 | {15214962, 3537601, -26238722, -14058872, 4418657, -15230761, | |
2388 | 13947276, 10730794, -13489462, -4363670}, | |
2389 | }, | |
2390 | { | |
2391 | {-2538306, 7682793, 32759013, 263109, -29984731, -7955452, | |
2392 | -22332124, -10188635, 977108, 699994}, | |
2393 | {-12466472, 4195084, -9211532, 550904, -15565337, 12917920, | |
2394 | 19118110, -439841, -30534533, -14337913}, | |
2395 | {31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237, | |
2396 | -10051775, 12493932, -5409317}, | |
2397 | }, | |
2398 | { | |
2399 | {-25680606, 5260744, -19235809, -6284470, -3695942, 16566087, | |
2400 | 27218280, 2607121, 29375955, 6024730}, | |
2401 | {842132, -2794693, -4763381, -8722815, 26332018, -12405641, | |
2402 | 11831880, 6985184, -9940361, 2854096}, | |
2403 | {-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645, | |
2404 | 960770, 12121869, 16648078}, | |
2405 | }, | |
2406 | { | |
2407 | {-15218652, 14667096, -13336229, 2013717, 30598287, -464137, | |
2408 | -31504922, -7882064, 20237806, 2838411}, | |
2409 | {-19288047, 4453152, 15298546, -16178388, 22115043, -15972604, | |
2410 | 12544294, -13470457, 1068881, -12499905}, | |
2411 | {-9558883, -16518835, 33238498, 13506958, 30505848, -1114596, | |
2412 | -8486907, -2630053, 12521378, 4845654}, | |
2413 | }, | |
2414 | { | |
2415 | {-28198521, 10744108, -2958380, 10199664, 7759311, -13088600, | |
2416 | 3409348, -873400, -6482306, -12885870}, | |
2417 | {-23561822, 6230156, -20382013, 10655314, -24040585, -11621172, | |
2418 | 10477734, -1240216, -3113227, 13974498}, | |
2419 | {12966261, 15550616, -32038948, -1615346, 21025980, -629444, | |
2420 | 5642325, 7188737, 18895762, 12629579}, | |
2421 | }, | |
2422 | }, | |
2423 | { | |
2424 | { | |
2425 | {14741879, -14946887, 22177208, -11721237, 1279741, 8058600, | |
2426 | 11758140, 789443, 32195181, 3895677}, | |
2427 | {10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575, | |
2428 | -3566119, -8982069, 4429647}, | |
2429 | {-2453894, 15725973, -20436342, -10410672, -5803908, -11040220, | |
2430 | -7135870, -11642895, 18047436, -15281743}, | |
2431 | }, | |
2432 | { | |
2433 | {-25173001, -11307165, 29759956, 11776784, -22262383, -15820455, | |
2434 | 10993114, -12850837, -17620701, -9408468}, | |
2435 | {21987233, 700364, -24505048, 14972008, -7774265, -5718395, | |
2436 | 32155026, 2581431, -29958985, 8773375}, | |
2437 | {-25568350, 454463, -13211935, 16126715, 25240068, 8594567, | |
2438 | 20656846, 12017935, -7874389, -13920155}, | |
2439 | }, | |
2440 | { | |
2441 | {6028182, 6263078, -31011806, -11301710, -818919, 2461772, | |
2442 | -31841174, -5468042, -1721788, -2776725}, | |
2443 | {-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845, | |
2444 | -4166698, 28408820, 6816612}, | |
2445 | {-10358094, -8237829, 19549651, -12169222, 22082623, 16147817, | |
2446 | 20613181, 13982702, -10339570, 5067943}, | |
2447 | }, | |
2448 | { | |
2449 | {-30505967, -3821767, 12074681, 13582412, -19877972, 2443951, | |
2450 | -19719286, 12746132, 5331210, -10105944}, | |
2451 | {30528811, 3601899, -1957090, 4619785, -27361822, -15436388, | |
2452 | 24180793, -12570394, 27679908, -1648928}, | |
2453 | {9402404, -13957065, 32834043, 10838634, -26580150, -13237195, | |
2454 | 26653274, -8685565, 22611444, -12715406}, | |
2455 | }, | |
2456 | { | |
2457 | {22190590, 1118029, 22736441, 15130463, -30460692, -5991321, | |
2458 | 19189625, -4648942, 4854859, 6622139}, | |
2459 | {-8310738, -2953450, -8262579, -3388049, -10401731, -271929, | |
2460 | 13424426, -3567227, 26404409, 13001963}, | |
2461 | {-31241838, -15415700, -2994250, 8939346, 11562230, -12840670, | |
2462 | -26064365, -11621720, -15405155, 11020693}, | |
2463 | }, | |
2464 | { | |
2465 | {1866042, -7949489, -7898649, -10301010, 12483315, 13477547, | |
2466 | 3175636, -12424163, 28761762, 1406734}, | |
2467 | {-448555, -1777666, 13018551, 3194501, -9580420, -11161737, | |
2468 | 24760585, -4347088, 25577411, -13378680}, | |
2469 | {-24290378, 4759345, -690653, -1852816, 2066747, 10693769, | |
2470 | -29595790, 9884936, -9368926, 4745410}, | |
2471 | }, | |
2472 | { | |
2473 | {-9141284, 6049714, -19531061, -4341411, -31260798, 9944276, | |
2474 | -15462008, -11311852, 10931924, -11931931}, | |
2475 | {-16561513, 14112680, -8012645, 4817318, -8040464, -11414606, | |
2476 | -22853429, 10856641, -20470770, 13434654}, | |
2477 | {22759489, -10073434, -16766264, -1871422, 13637442, -10168091, | |
2478 | 1765144, -12654326, 28445307, -5364710}, | |
2479 | }, | |
2480 | { | |
2481 | {29875063, 12493613, 2795536, -3786330, 1710620, 15181182, | |
2482 | -10195717, -8788675, 9074234, 1167180}, | |
2483 | {-26205683, 11014233, -9842651, -2635485, -26908120, 7532294, | |
2484 | -18716888, -9535498, 3843903, 9367684}, | |
2485 | {-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123, | |
2486 | 8601684, -139197, 4242895}, | |
2487 | }, | |
2488 | }, | |
2489 | { | |
2490 | { | |
2491 | {22092954, -13191123, -2042793, -11968512, 32186753, -11517388, | |
2492 | -6574341, 2470660, -27417366, 16625501}, | |
2493 | {-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857, | |
2494 | 2602725, -27351616, 14247413}, | |
2495 | {6314175, -10264892, -32772502, 15957557, -10157730, 168750, | |
2496 | -8618807, 14290061, 27108877, -1180880}, | |
2497 | }, | |
2498 | { | |
2499 | {-8586597, -7170966, 13241782, 10960156, -32991015, -13794596, | |
2500 | 33547976, -11058889, -27148451, 981874}, | |
2501 | {22833440, 9293594, -32649448, -13618667, -9136966, 14756819, | |
2502 | -22928859, -13970780, -10479804, -16197962}, | |
2503 | {-7768587, 3326786, -28111797, 10783824, 19178761, 14905060, | |
2504 | 22680049, 13906969, -15933690, 3797899}, | |
2505 | }, | |
2506 | { | |
2507 | {21721356, -4212746, -12206123, 9310182, -3882239, -13653110, | |
2508 | 23740224, -2709232, 20491983, -8042152}, | |
2509 | {9209270, -15135055, -13256557, -6167798, -731016, 15289673, | |
2510 | 25947805, 15286587, 30997318, -6703063}, | |
2511 | {7392032, 16618386, 23946583, -8039892, -13265164, -1533858, | |
2512 | -14197445, -2321576, 17649998, -250080}, | |
2513 | }, | |
2514 | { | |
2515 | {-9301088, -14193827, 30609526, -3049543, -25175069, -1283752, | |
2516 | -15241566, -9525724, -2233253, 7662146}, | |
2517 | {-17558673, 1763594, -33114336, 15908610, -30040870, -12174295, | |
2518 | 7335080, -8472199, -3174674, 3440183}, | |
2519 | {-19889700, -5977008, -24111293, -9688870, 10799743, -16571957, | |
2520 | 40450, -4431835, 4862400, 1133}, | |
2521 | }, | |
2522 | { | |
2523 | {-32856209, -7873957, -5422389, 14860950, -16319031, 7956142, | |
2524 | 7258061, 311861, -30594991, -7379421}, | |
2525 | {-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763, | |
2526 | 16527196, 18278453, 15405622}, | |
2527 | {-4381906, 8508652, -19898366, -3674424, -5984453, 15149970, | |
2528 | -13313598, 843523, -21875062, 13626197}, | |
2529 | }, | |
2530 | { | |
2531 | {2281448, -13487055, -10915418, -2609910, 1879358, 16164207, | |
2532 | -10783882, 3953792, 13340839, 15928663}, | |
2533 | {31727126, -7179855, -18437503, -8283652, 2875793, -16390330, | |
2534 | -25269894, -7014826, -23452306, 5964753}, | |
2535 | {4100420, -5959452, -17179337, 6017714, -18705837, 12227141, | |
2536 | -26684835, 11344144, 2538215, -7570755}, | |
2537 | }, | |
2538 | { | |
2539 | {-9433605, 6123113, 11159803, -2156608, 30016280, 14966241, | |
2540 | -20474983, 1485421, -629256, -15958862}, | |
2541 | {-26804558, 4260919, 11851389, 9658551, -32017107, 16367492, | |
2542 | -20205425, -13191288, 11659922, -11115118}, | |
2543 | {26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568, | |
2544 | -10170080, 33100372, -1306171}, | |
2545 | }, | |
2546 | { | |
2547 | {15121113, -5201871, -10389905, 15427821, -27509937, -15992507, | |
2548 | 21670947, 4486675, -5931810, -14466380}, | |
2549 | {16166486, -9483733, -11104130, 6023908, -31926798, -1364923, | |
2550 | 2340060, -16254968, -10735770, -10039824}, | |
2551 | {28042865, -3557089, -12126526, 12259706, -3717498, -6945899, | |
2552 | 6766453, -8689599, 18036436, 5803270}, | |
2553 | }, | |
2554 | }, | |
2555 | { | |
2556 | { | |
2557 | {-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391, | |
2558 | 4598332, -6159431, -14117438}, | |
2559 | {-31031306, -14256194, 17332029, -2383520, 31312682, -5967183, | |
2560 | 696309, 50292, -20095739, 11763584}, | |
2561 | {-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117, | |
2562 | -12613632, -19773211, -10713562}, | |
2563 | }, | |
2564 | { | |
2565 | {30464590, -11262872, -4127476, -12734478, 19835327, -7105613, | |
2566 | -24396175, 2075773, -17020157, 992471}, | |
2567 | {18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841, | |
2568 | 8080033, -11574335, -10601610}, | |
2569 | {19598397, 10334610, 12555054, 2555664, 18821899, -10339780, | |
2570 | 21873263, 16014234, 26224780, 16452269}, | |
2571 | }, | |
2572 | { | |
2573 | {-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804, | |
2574 | -7618186, -20533829, 3698650}, | |
2575 | {14187449, 3448569, -10636236, -10810935, -22663880, -3433596, | |
2576 | 7268410, -10890444, 27394301, 12015369}, | |
2577 | {19695761, 16087646, 28032085, 12999827, 6817792, 11427614, | |
2578 | 20244189, -1312777, -13259127, -3402461}, | |
2579 | }, | |
2580 | { | |
2581 | {30860103, 12735208, -1888245, -4699734, -16974906, 2256940, | |
2582 | -8166013, 12298312, -8550524, -10393462}, | |
2583 | {-5719826, -11245325, -1910649, 15569035, 26642876, -7587760, | |
2584 | -5789354, -15118654, -4976164, 12651793}, | |
2585 | {-2848395, 9953421, 11531313, -5282879, 26895123, -12697089, | |
2586 | -13118820, -16517902, 9768698, -2533218}, | |
2587 | }, | |
2588 | { | |
2589 | {-24719459, 1894651, -287698, -4704085, 15348719, -8156530, | |
2590 | 32767513, 12765450, 4940095, 10678226}, | |
2591 | {18860224, 15980149, -18987240, -1562570, -26233012, -11071856, | |
2592 | -7843882, 13944024, -24372348, 16582019}, | |
2593 | {-15504260, 4970268, -29893044, 4175593, -20993212, -2199756, | |
2594 | -11704054, 15444560, -11003761, 7989037}, | |
2595 | }, | |
2596 | { | |
2597 | {31490452, 5568061, -2412803, 2182383, -32336847, 4531686, | |
2598 | -32078269, 6200206, -19686113, -14800171}, | |
2599 | {-17308668, -15879940, -31522777, -2831, -32887382, 16375549, | |
2600 | 8680158, -16371713, 28550068, -6857132}, | |
2601 | {-28126887, -5688091, 16837845, -1820458, -6850681, 12700016, | |
2602 | -30039981, 4364038, 1155602, 5988841}, | |
2603 | }, | |
2604 | { | |
2605 | {21890435, -13272907, -12624011, 12154349, -7831873, 15300496, | |
2606 | 23148983, -4470481, 24618407, 8283181}, | |
2607 | {-33136107, -10512751, 9975416, 6841041, -31559793, 16356536, | |
2608 | 3070187, -7025928, 1466169, 10740210}, | |
2609 | {-1509399, -15488185, -13503385, -10655916, 32799044, 909394, | |
2610 | -13938903, -5779719, -32164649, -15327040}, | |
2611 | }, | |
2612 | { | |
2613 | {3960823, -14267803, -28026090, -15918051, -19404858, 13146868, | |
2614 | 15567327, 951507, -3260321, -573935}, | |
2615 | {24740841, 5052253, -30094131, 8961361, 25877428, 6165135, | |
2616 | -24368180, 14397372, -7380369, -6144105}, | |
2617 | {-28888365, 3510803, -28103278, -1158478, -11238128, -10631454, | |
2618 | -15441463, -14453128, -1625486, -6494814}, | |
2619 | }, | |
2620 | }, | |
2621 | { | |
2622 | { | |
2623 | {793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843, | |
2624 | -4885251, -9906200, -621852}, | |
2625 | {5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374, | |
2626 | 1468826, -6171428, -15186581}, | |
2627 | {-4859255, -3779343, -2917758, -6748019, 7778750, 11688288, | |
2628 | -30404353, -9871238, -1558923, -9863646}, | |
2629 | }, | |
2630 | { | |
2631 | {10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958, | |
2632 | 14783338, -30581476, -15757844}, | |
2633 | {10566929, 12612572, -31944212, 11118703, -12633376, 12362879, | |
2634 | 21752402, 8822496, 24003793, 14264025}, | |
2635 | {27713862, -7355973, -11008240, 9227530, 27050101, 2504721, | |
2636 | 23886875, -13117525, 13958495, -5732453}, | |
2637 | }, | |
2638 | { | |
2639 | {-23481610, 4867226, -27247128, 3900521, 29838369, -8212291, | |
2640 | -31889399, -10041781, 7340521, -15410068}, | |
2641 | {4646514, -8011124, -22766023, -11532654, 23184553, 8566613, | |
2642 | 31366726, -1381061, -15066784, -10375192}, | |
2643 | {-17270517, 12723032, -16993061, 14878794, 21619651, -6197576, | |
2644 | 27584817, 3093888, -8843694, 3849921}, | |
2645 | }, | |
2646 | { | |
2647 | {-9064912, 2103172, 25561640, -15125738, -5239824, 9582958, | |
2648 | 32477045, -9017955, 5002294, -15550259}, | |
2649 | {-12057553, -11177906, 21115585, -13365155, 8808712, -12030708, | |
2650 | 16489530, 13378448, -25845716, 12741426}, | |
2651 | {-5946367, 10645103, -30911586, 15390284, -3286982, -7118677, | |
2652 | 24306472, 15852464, 28834118, -7646072}, | |
2653 | }, | |
2654 | { | |
2655 | {-17335748, -9107057, -24531279, 9434953, -8472084, -583362, | |
2656 | -13090771, 455841, 20461858, 5491305}, | |
2657 | {13669248, -16095482, -12481974, -10203039, -14569770, -11893198, | |
2658 | -24995986, 11293807, -28588204, -9421832}, | |
2659 | {28497928, 6272777, -33022994, 14470570, 8906179, -1225630, | |
2660 | 18504674, -14165166, 29867745, -8795943}, | |
2661 | }, | |
2662 | { | |
2663 | {-16207023, 13517196, -27799630, -13697798, 24009064, -6373891, | |
2664 | -6367600, -13175392, 22853429, -4012011}, | |
2665 | {24191378, 16712145, -13931797, 15217831, 14542237, 1646131, | |
2666 | 18603514, -11037887, 12876623, -2112447}, | |
2667 | {17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753, | |
2668 | 608397, 16031844, 3723494}, | |
2669 | }, | |
2670 | { | |
2671 | {-28632773, 12763728, -20446446, 7577504, 33001348, -13017745, | |
2672 | 17558842, -7872890, 23896954, -4314245}, | |
2673 | {-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064, | |
2674 | 7229064, -9919646, -8826859}, | |
2675 | {28816045, 298879, -28165016, -15920938, 19000928, -1665890, | |
2676 | -12680833, -2949325, -18051778, -2082915}, | |
2677 | }, | |
2678 | { | |
2679 | {16000882, -344896, 3493092, -11447198, -29504595, -13159789, | |
2680 | 12577740, 16041268, -19715240, 7847707}, | |
2681 | {10151868, 10572098, 27312476, 7922682, 14825339, 4723128, | |
2682 | -32855931, -6519018, -10020567, 3852848}, | |
2683 | {-11430470, 15697596, -21121557, -4420647, 5386314, 15063598, | |
2684 | 16514493, -15932110, 29330899, -15076224}, | |
2685 | }, | |
2686 | }, | |
2687 | { | |
2688 | { | |
2689 | {-25499735, -4378794, -15222908, -6901211, 16615731, 2051784, | |
2690 | 3303702, 15490, -27548796, 12314391}, | |
2691 | {15683520, -6003043, 18109120, -9980648, 15337968, -5997823, | |
2692 | -16717435, 15921866, 16103996, -3731215}, | |
2693 | {-23169824, -10781249, 13588192, -1628807, -3798557, -1074929, | |
2694 | -19273607, 5402699, -29815713, -9841101}, | |
2695 | }, | |
2696 | { | |
2697 | {23190676, 2384583, -32714340, 3462154, -29903655, -1529132, | |
2698 | -11266856, 8911517, -25205859, 2739713}, | |
2699 | {21374101, -3554250, -33524649, 9874411, 15377179, 11831242, | |
2700 | -33529904, 6134907, 4931255, 11987849}, | |
2701 | {-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539, | |
2702 | 13861388, -30076310, 10117930}, | |
2703 | }, | |
2704 | { | |
2705 | {-29501170, -10744872, -26163768, 13051539, -25625564, 5089643, | |
2706 | -6325503, 6704079, 12890019, 15728940}, | |
2707 | {-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376, | |
2708 | -10428139, 12885167, 8311031}, | |
2709 | {-17516482, 5352194, 10384213, -13811658, 7506451, 13453191, | |
2710 | 26423267, 4384730, 1888765, -5435404}, | |
2711 | }, | |
2712 | { | |
2713 | {-25817338, -3107312, -13494599, -3182506, 30896459, -13921729, | |
2714 | -32251644, -12707869, -19464434, -3340243}, | |
2715 | {-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245, | |
2716 | 14845197, 17151279, -9854116}, | |
2717 | {-24830458, -12733720, -15165978, 10367250, -29530908, -265356, | |
2718 | 22825805, -7087279, -16866484, 16176525}, | |
2719 | }, | |
2720 | { | |
2721 | {-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182, | |
2722 | -10363426, -28746253, -10197509}, | |
2723 | {-10626600, -4486402, -13320562, -5125317, 3432136, -6393229, | |
2724 | 23632037, -1940610, 32808310, 1099883}, | |
2725 | {15030977, 5768825, -27451236, -2887299, -6427378, -15361371, | |
2726 | -15277896, -6809350, 2051441, -15225865}, | |
2727 | }, | |
2728 | { | |
2729 | {-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398, | |
2730 | -14154188, -22686354, 16633660}, | |
2731 | {4577086, -16752288, 13249841, -15304328, 19958763, -14537274, | |
2732 | 18559670, -10759549, 8402478, -9864273}, | |
2733 | {-28406330, -1051581, -26790155, -907698, -17212414, -11030789, | |
2734 | 9453451, -14980072, 17983010, 9967138}, | |
2735 | }, | |
2736 | { | |
2737 | {-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990, | |
2738 | 7806337, 17507396, 3651560}, | |
2739 | {-10420457, -4118111, 14584639, 15971087, -15768321, 8861010, | |
2740 | 26556809, -5574557, -18553322, -11357135}, | |
2741 | {2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121, | |
2742 | 8459447, -5605463, -7621941}, | |
2743 | }, | |
2744 | { | |
2745 | {-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813, | |
2746 | -849066, 17258084, -7977739}, | |
2747 | {18164541, -10595176, -17154882, -1542417, 19237078, -9745295, | |
2748 | 23357533, -15217008, 26908270, 12150756}, | |
2749 | {-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168, | |
2750 | -5537701, -32302074, 16215819}, | |
2751 | }, | |
2752 | }, | |
2753 | { | |
2754 | { | |
2755 | {-6898905, 9824394, -12304779, -4401089, -31397141, -6276835, | |
2756 | 32574489, 12532905, -7503072, -8675347}, | |
2757 | {-27343522, -16515468, -27151524, -10722951, 946346, 16291093, | |
2758 | 254968, 7168080, 21676107, -1943028}, | |
2759 | {21260961, -8424752, -16831886, -11920822, -23677961, 3968121, | |
2760 | -3651949, -6215466, -3556191, -7913075}, | |
2761 | }, | |
2762 | { | |
2763 | {16544754, 13250366, -16804428, 15546242, -4583003, 12757258, | |
2764 | -2462308, -8680336, -18907032, -9662799}, | |
2765 | {-2415239, -15577728, 18312303, 4964443, -15272530, -12653564, | |
2766 | 26820651, 16690659, 25459437, -4564609}, | |
2767 | {-25144690, 11425020, 28423002, -11020557, -6144921, -15826224, | |
2768 | 9142795, -2391602, -6432418, -1644817}, | |
2769 | }, | |
2770 | { | |
2771 | {-23104652, 6253476, 16964147, -3768872, -25113972, -12296437, | |
2772 | -27457225, -16344658, 6335692, 7249989}, | |
2773 | {-30333227, 13979675, 7503222, -12368314, -11956721, -4621693, | |
2774 | -30272269, 2682242, 25993170, -12478523}, | |
2775 | {4364628, 5930691, 32304656, -10044554, -8054781, 15091131, | |
2776 | 22857016, -10598955, 31820368, 15075278}, | |
2777 | }, | |
2778 | { | |
2779 | {31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, | |
2780 | -9650886, -17970238, 12833045}, | |
2781 | {19073683, 14851414, -24403169, -11860168, 7625278, 11091125, | |
2782 | -19619190, 2074449, -9413939, 14905377}, | |
2783 | {24483667, -11935567, -2518866, -11547418, -1553130, 15355506, | |
2784 | -25282080, 9253129, 27628530, -7555480}, | |
2785 | }, | |
2786 | { | |
2787 | {17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, | |
2788 | -9157582, -14110875, 15297016}, | |
2789 | {510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, | |
2790 | -11864220, 8683221, 2921426}, | |
2791 | {18606791, 11874196, 27155355, -5281482, -24031742, 6265446, | |
2792 | -25178240, -1278924, 4674690, 13890525}, | |
2793 | }, | |
2794 | { | |
2795 | {13609624, 13069022, -27372361, -13055908, 24360586, 9592974, | |
2796 | 14977157, 9835105, 4389687, 288396}, | |
2797 | {9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, | |
2798 | 8317628, 23388070, 16052080}, | |
2799 | {12720016, 11937594, -31970060, -5028689, 26900120, 8561328, | |
2800 | -20155687, -11632979, -14754271, -10812892}, | |
2801 | }, | |
2802 | { | |
2803 | {15961858, 14150409, 26716931, -665832, -22794328, 13603569, | |
2804 | 11829573, 7467844, -28822128, 929275}, | |
2805 | {11038231, -11582396, -27310482, -7316562, -10498527, -16307831, | |
2806 | -23479533, -9371869, -21393143, 2465074}, | |
2807 | {20017163, -4323226, 27915242, 1529148, 12396362, 15675764, | |
2808 | 13817261, -9658066, 2463391, -4622140}, | |
2809 | }, | |
2810 | { | |
2811 | {-16358878, -12663911, -12065183, 4996454, -1256422, 1073572, | |
2812 | 9583558, 12851107, 4003896, 12673717}, | |
2813 | {-1731589, -15155870, -3262930, 16143082, 19294135, 13385325, | |
2814 | 14741514, -9103726, 7903886, 2348101}, | |
2815 | {24536016, -16515207, 12715592, -3862155, 1511293, 10047386, | |
2816 | -3842346, -7129159, -28377538, 10048127}, | |
2817 | }, | |
2818 | }, | |
2819 | { | |
2820 | { | |
2821 | {-12622226, -6204820, 30718825, 2591312, -10617028, 12192840, | |
2822 | 18873298, -7297090, -32297756, 15221632}, | |
2823 | {-26478122, -11103864, 11546244, -1852483, 9180880, 7656409, | |
2824 | -21343950, 2095755, 29769758, 6593415}, | |
2825 | {-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, | |
2826 | -6118678, 30958054, 8292160}, | |
2827 | }, | |
2828 | { | |
2829 | {31429822, -13959116, 29173532, 15632448, 12174511, -2760094, | |
2830 | 32808831, 3977186, 26143136, -3148876}, | |
2831 | {22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, | |
2832 | -1674433, -3758243, -2304625}, | |
2833 | {-15491917, 8012313, -2514730, -12702462, -23965846, -10254029, | |
2834 | -1612713, -1535569, -16664475, 8194478}, | |
2835 | }, | |
2836 | { | |
2837 | {27338066, -7507420, -7414224, 10140405, -19026427, -6589889, | |
2838 | 27277191, 8855376, 28572286, 3005164}, | |
2839 | {26287124, 4821776, 25476601, -4145903, -3764513, -15788984, | |
2840 | -18008582, 1182479, -26094821, -13079595}, | |
2841 | {-7171154, 3178080, 23970071, 6201893, -17195577, -4489192, | |
2842 | -21876275, -13982627, 32208683, -1198248}, | |
2843 | }, | |
2844 | { | |
2845 | {-16657702, 2817643, -10286362, 14811298, 6024667, 13349505, | |
2846 | -27315504, -10497842, -27672585, -11539858}, | |
2847 | {15941029, -9405932, -21367050, 8062055, 31876073, -238629, | |
2848 | -15278393, -1444429, 15397331, -4130193}, | |
2849 | {8934485, -13485467, -23286397, -13423241, -32446090, 14047986, | |
2850 | 31170398, -1441021, -27505566, 15087184}, | |
2851 | }, | |
2852 | { | |
2853 | {-18357243, -2156491, 24524913, -16677868, 15520427, -6360776, | |
2854 | -15502406, 11461896, 16788528, -5868942}, | |
2855 | {-1947386, 16013773, 21750665, 3714552, -17401782, -16055433, | |
2856 | -3770287, -10323320, 31322514, -11615635}, | |
2857 | {21426655, -5650218, -13648287, -5347537, -28812189, -4920970, | |
2858 | -18275391, -14621414, 13040862, -12112948}, | |
2859 | }, | |
2860 | { | |
2861 | {11293895, 12478086, -27136401, 15083750, -29307421, 14748872, | |
2862 | 14555558, -13417103, 1613711, 4896935}, | |
2863 | {-25894883, 15323294, -8489791, -8057900, 25967126, -13425460, | |
2864 | 2825960, -4897045, -23971776, -11267415}, | |
2865 | {-15924766, -5229880, -17443532, 6410664, 3622847, 10243618, | |
2866 | 20615400, 12405433, -23753030, -8436416}, | |
2867 | }, | |
2868 | { | |
2869 | {-7091295, 12556208, -20191352, 9025187, -17072479, 4333801, | |
2870 | 4378436, 2432030, 23097949, -566018}, | |
2871 | {4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, | |
2872 | 10103221, -18512313, 2424778}, | |
2873 | {366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, | |
2874 | 1344109, -3642553, 12412659}, | |
2875 | }, | |
2876 | { | |
2877 | {-24001791, 7690286, 14929416, -168257, -32210835, -13412986, | |
2878 | 24162697, -15326504, -3141501, 11179385}, | |
2879 | {18289522, -14724954, 8056945, 16430056, -21729724, 7842514, | |
2880 | -6001441, -1486897, -18684645, -11443503}, | |
2881 | {476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, | |
2882 | 13403813, 11052904, 5219329}, | |
2883 | }, | |
2884 | }, | |
2885 | { | |
2886 | { | |
2887 | {20678546, -8375738, -32671898, 8849123, -5009758, 14574752, | |
2888 | 31186971, -3973730, 9014762, -8579056}, | |
2889 | {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, | |
2890 | -33102500, 9160280, 8473550, -3256838}, | |
2891 | {24900749, 14435722, 17209120, -15292541, -22592275, 9878983, | |
2892 | -7689309, -16335821, -24568481, 11788948}, | |
2893 | }, | |
2894 | { | |
2895 | {-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, | |
2896 | -20037437, 10410733, -24568470, -1458691}, | |
2897 | {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, | |
2898 | 11871841, -12505194, -18513325, 8464118}, | |
2899 | {-23400612, 8348507, -14585951, -861714, -3950205, -6373419, | |
2900 | 14325289, 8628612, 33313881, -8370517}, | |
2901 | }, | |
2902 | { | |
2903 | {-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, | |
2904 | -24805667, -10236854, -8940735, -5818269}, | |
2905 | {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, | |
2906 | 15989197, -12838188, 28358192, -4253904}, | |
2907 | {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, | |
2908 | -16637684, 4072016, -5351664, 5596589}, | |
2909 | }, | |
2910 | { | |
2911 | {-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, | |
2912 | 29266239, 2557221, 1768301, 15373193}, | |
2913 | {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, | |
2914 | -4504991, -24660491, 3442910}, | |
2915 | {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, | |
2916 | 22597931, 7176455, -18585478, 13365930}, | |
2917 | }, | |
2918 | { | |
2919 | {-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, | |
2920 | -8570186, -9689599, -3031667}, | |
2921 | {25008904, -10771599, -4305031, -9638010, 16265036, 15721635, | |
2922 | 683793, -11823784, 15723479, -15163481}, | |
2923 | {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, | |
2924 | 11879682, 5400171, 519526, -1235876}, | |
2925 | }, | |
2926 | { | |
2927 | {22258397, -16332233, -7869817, 14613016, -22520255, -2950923, | |
2928 | -20353881, 7315967, 16648397, 7605640}, | |
2929 | {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, | |
2930 | 23994942, -5281555, -9468848, 4763278}, | |
2931 | {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, | |
2932 | 31088447, -7764523, -11356529, 728112}, | |
2933 | }, | |
2934 | { | |
2935 | {26047220, -11751471, -6900323, -16521798, 24092068, 9158119, | |
2936 | -4273545, -12555558, -29365436, -5498272}, | |
2937 | {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, | |
2938 | 12327945, 10750447, 10014012}, | |
2939 | {-10312768, 3936952, 9156313, -8897683, 16498692, -994647, | |
2940 | -27481051, -666732, 3424691, 7540221}, | |
2941 | }, | |
2942 | { | |
2943 | {30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, | |
2944 | -16317219, -9244265, 15258046}, | |
2945 | {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, | |
2946 | 2711395, 1062915, -5136345}, | |
2947 | {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, | |
2948 | -6066489, 12194497, 32960380, 1459310}, | |
2949 | }, | |
2950 | }, | |
2951 | { | |
2952 | { | |
2953 | {19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, | |
2954 | -6101885, 18638003, -11174937}, | |
2955 | {31395534, 15098109, 26581030, 8030562, -16527914, -5007134, | |
2956 | 9012486, -7584354, -6643087, -5442636}, | |
2957 | {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, | |
2958 | 9677543, -32294889, -6456008}, | |
2959 | }, | |
2960 | { | |
2961 | {-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, | |
2962 | -7839692, -7852844, -8138429}, | |
2963 | {-15236356, -15433509, 7766470, 746860, 26346930, -10221762, | |
2964 | -27333451, 10754588, -9431476, 5203576}, | |
2965 | {31834314, 14135496, -770007, 5159118, 20917671, -16768096, | |
2966 | -7467973, -7337524, 31809243, 7347066}, | |
2967 | }, | |
2968 | { | |
2969 | {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, | |
2970 | 19797970, -12211255, 15192876, -2087490}, | |
2971 | {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, | |
2972 | 10609330, 12694420, 33473243, -13382104}, | |
2973 | {33184999, 11180355, 15832085, -11385430, -1633671, 225884, | |
2974 | 15089336, -11023903, -6135662, 14480053}, | |
2975 | }, | |
2976 | { | |
2977 | {31308717, -5619998, 31030840, -1897099, 15674547, -6582883, | |
2978 | 5496208, 13685227, 27595050, 8737275}, | |
2979 | {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, | |
2980 | -31008351, -12610604, 26498114, 66511}, | |
2981 | {22644454, -8761729, -16671776, 4884562, -3105614, -13559366, | |
2982 | 30540766, -4286747, -13327787, -7515095}, | |
2983 | }, | |
2984 | { | |
2985 | {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, | |
2986 | 8205540, 13585437, -17127465, 15115439}, | |
2987 | {23711543, -672915, 31206561, -8362711, 6164647, -9709987, | |
2988 | -33535882, -1426096, 8236921, 16492939}, | |
2989 | {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, | |
2990 | 19574902, 10071562, 6708380, -6222424}, | |
2991 | }, | |
2992 | { | |
2993 | {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, | |
2994 | 9328700, 29955601, -11678310}, | |
2995 | {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, | |
2996 | -25892142, -12635595, -9917575, 6216608}, | |
2997 | {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, | |
2998 | 24822830, -6146567, -26767480, 7525079}, | |
2999 | }, | |
3000 | { | |
3001 | {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, | |
3002 | -910336, -2782495, -19386633, 11994101}, | |
3003 | {21691500, -13624626, -641331, -14367021, 3285881, -3483596, | |
3004 | -25064666, 9718258, -7477437, 13381418}, | |
3005 | {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, | |
3006 | 23111648, -6375247, 28535282, 15779576}, | |
3007 | }, | |
3008 | { | |
3009 | {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, | |
3010 | -14068454, 12021730, 9955285, -16303356}, | |
3011 | {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, | |
3012 | -18426029, 9924399, 20194861, 13380996}, | |
3013 | {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, | |
3014 | -1984914, 15707771, 26342023, 10146099}, | |
3015 | }, | |
3016 | }, | |
3017 | { | |
3018 | { | |
3019 | {-26016874, -219943, 21339191, -41388, 19745256, -2878700, | |
3020 | -29637280, 2227040, 21612326, -545728}, | |
3021 | {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, | |
3022 | 25764461, 12243797, -20856566, 11649658}, | |
3023 | {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, | |
3024 | 6114064, 33514190, 2333242}, | |
3025 | }, | |
3026 | { | |
3027 | {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, | |
3028 | -6679750, -12670638, 24350578, -13450001}, | |
3029 | {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, | |
3030 | -31536088, -10406836, 8317860, 12352766}, | |
3031 | {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, | |
3032 | -23552096, -2287550, 20712163, 6719373}, | |
3033 | }, | |
3034 | { | |
3035 | {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, | |
3036 | -3763210, 26224235, -3297458}, | |
3037 | {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, | |
3038 | 21728352, 9493610, 18620611, -16428628}, | |
3039 | {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, | |
3040 | -5269471, -9725556, -30701573, -16479657}, | |
3041 | }, | |
3042 | { | |
3043 | {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, | |
3044 | 12248509, -5240639, 13735342, 1934062}, | |
3045 | {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, | |
3046 | -15136294, -3765346, -21277997, 5473616}, | |
3047 | {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, | |
3048 | -7125085, 12469656, 29111212, -5451014}, | |
3049 | }, | |
3050 | { | |
3051 | {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, | |
3052 | 24367466, 6388839, -10295587, 452383}, | |
3053 | {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, | |
3054 | -24236251, -5915248, 15766062, 8407814}, | |
3055 | {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, | |
3056 | -8917023, -4388953, -8067909, 2276718}, | |
3057 | }, | |
3058 | { | |
3059 | {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, | |
3060 | -23827587, 5096219, 22740376, -7303417}, | |
3061 | {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, | |
3062 | 24051124, 13742383, -15637599, 13295222}, | |
3063 | {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, | |
3064 | -17720195, -4612972, -4451357, -14669444}, | |
3065 | }, | |
3066 | { | |
3067 | {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, | |
3068 | -2469266, -4141880, 7770569, 9620597}, | |
3069 | {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, | |
3070 | -1694323, -33502340, -14767970}, | |
3071 | {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, | |
3072 | 1220118, 30494170, -11440799}, | |
3073 | }, | |
3074 | { | |
3075 | {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, | |
3076 | -26739026, 926050, -1684339, -13333647}, | |
3077 | {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, | |
3078 | 9021034, 9078865, 3353509, 4033511}, | |
3079 | {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, | |
3080 | 23161163, 8839127, 27485041, 7356032}, | |
3081 | }, | |
3082 | }, | |
3083 | { | |
3084 | { | |
3085 | {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, | |
3086 | 2625015, 28431036, -16771834}, | |
3087 | {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, | |
3088 | -22545972, 14150565, 15970762, 4099461}, | |
3089 | {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, | |
3090 | 13617293, -9937143, 11465739, 8317062}, | |
3091 | }, | |
3092 | { | |
3093 | {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, | |
3094 | 14898637, 3848455, 20969334, -5157516}, | |
3095 | {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, | |
3096 | -21610826, -3649888, 11177095, 14989547}, | |
3097 | {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, | |
3098 | 13515641, 2581286, -28487508, 9930240}, | |
3099 | }, | |
3100 | { | |
3101 | {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, | |
3102 | 18345767, -13403753, 16291481, -5314038}, | |
3103 | {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, | |
3104 | 6957617, 4368891, 9788741}, | |
3105 | {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, | |
3106 | -21722536, -8613148, 16250552, -11111103}, | |
3107 | }, | |
3108 | { | |
3109 | {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, | |
3110 | 10604807, -30190403, 4782747}, | |
3111 | {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, | |
3112 | -9981571, 4383045, 22546403, 437323}, | |
3113 | {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, | |
3114 | 27343084, 2786261, -30633590, -14097016}, | |
3115 | }, | |
3116 | { | |
3117 | {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, | |
3118 | -19690631, 2355319, -19284671, -6114373}, | |
3119 | {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, | |
3120 | 18952177, 15496498, -29380133, 11754228}, | |
3121 | {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, | |
3122 | 7141596, 11724556, 22761615, -10134141}, | |
3123 | }, | |
3124 | { | |
3125 | {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, | |
3126 | -28741185, -12227393, 32851222, 11717399}, | |
3127 | {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, | |
3128 | 31474879, 3483633, -1193175, -4030831}, | |
3129 | {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, | |
3130 | 33142652, 6546660, -19985279, -3948376}, | |
3131 | }, | |
3132 | { | |
3133 | {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, | |
3134 | -8537131, -12833048, -30772034, -15486313}, | |
3135 | {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, | |
3136 | -31135347, -16049879, 10928917, 3011958}, | |
3137 | {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, | |
3138 | -30831056, -12805180, 18008031, 10258577}, | |
3139 | }, | |
3140 | { | |
3141 | {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, | |
3142 | -1853465, 1367120, 25127874, 6671743}, | |
3143 | {29701166, -14373934, -10878120, 9279288, -17568, 13127210, | |
3144 | 21382910, 11042292, 25838796, 4642684}, | |
3145 | {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, | |
3146 | 30468147, -13900640, 18423289, 4177476}, | |
3147 | }, | |
3148 | }, | |
3149 | }; | |
3150 | ||
3151 | static uint8_t negative(signed char b) { | |
3152 | uint32_t x = b; | |
3153 | x >>= 31; /* 1: yes; 0: no */ | |
3154 | return x; | |
3155 | } | |
3156 | ||
3157 | static void table_select(ge_precomp *t, int pos, signed char b) { | |
3158 | ge_precomp minust; | |
3159 | uint8_t bnegative = negative(b); | |
b9577984 | 3160 | uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); |
a90def6b DSH |
3161 | |
3162 | ge_precomp_0(t); | |
3163 | cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); | |
3164 | cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); | |
3165 | cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); | |
3166 | cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); | |
3167 | cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); | |
3168 | cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); | |
3169 | cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); | |
3170 | cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); | |
3171 | fe_copy(minust.yplusx, t->yminusx); | |
3172 | fe_copy(minust.yminusx, t->yplusx); | |
3173 | fe_neg(minust.xy2d, t->xy2d); | |
3174 | cmov(t, &minust, bnegative); | |
3175 | } | |
3176 | ||
3177 | /* h = a * B | |
3178 | * where a = a[0]+256*a[1]+...+256^31 a[31] | |
3179 | * B is the Ed25519 base point (x,4/5) with x positive. | |
3180 | * | |
3181 | * Preconditions: | |
3182 | * a[31] <= 127 */ | |
3183 | static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { | |
3184 | signed char e[64]; | |
3185 | signed char carry; | |
3186 | ge_p1p1 r; | |
3187 | ge_p2 s; | |
3188 | ge_precomp t; | |
3189 | int i; | |
3190 | ||
3191 | for (i = 0; i < 32; ++i) { | |
3192 | e[2 * i + 0] = (a[i] >> 0) & 15; | |
3193 | e[2 * i + 1] = (a[i] >> 4) & 15; | |
3194 | } | |
3195 | /* each e[i] is between 0 and 15 */ | |
3196 | /* e[63] is between 0 and 7 */ | |
3197 | ||
3198 | carry = 0; | |
3199 | for (i = 0; i < 63; ++i) { | |
3200 | e[i] += carry; | |
3201 | carry = e[i] + 8; | |
3202 | carry >>= 4; | |
3203 | e[i] -= carry << 4; | |
3204 | } | |
3205 | e[63] += carry; | |
3206 | /* each e[i] is between -8 and 8 */ | |
3207 | ||
3208 | ge_p3_0(h); | |
3209 | for (i = 1; i < 64; i += 2) { | |
3210 | table_select(&t, i / 2, e[i]); | |
3211 | ge_madd(&r, h, &t); | |
3212 | ge_p1p1_to_p3(h, &r); | |
3213 | } | |
3214 | ||
3215 | ge_p3_dbl(&r, h); | |
3216 | ge_p1p1_to_p2(&s, &r); | |
3217 | ge_p2_dbl(&r, &s); | |
3218 | ge_p1p1_to_p2(&s, &r); | |
3219 | ge_p2_dbl(&r, &s); | |
3220 | ge_p1p1_to_p2(&s, &r); | |
3221 | ge_p2_dbl(&r, &s); | |
3222 | ge_p1p1_to_p3(h, &r); | |
3223 | ||
3224 | for (i = 0; i < 64; i += 2) { | |
3225 | table_select(&t, i / 2, e[i]); | |
3226 | ge_madd(&r, h, &t); | |
3227 | ge_p1p1_to_p3(h, &r); | |
3228 | } | |
3229 | } | |
3230 | ||
a90def6b DSH |
3231 | /* Replace (f,g) with (g,f) if b == 1; |
3232 | * replace (f,g) with (f,g) if b == 0. | |
3233 | * | |
3234 | * Preconditions: b in {0,1}. */ | |
3235 | static void fe_cswap(fe f, fe g, unsigned int b) { | |
244e5f5d | 3236 | size_t i; |
a90def6b | 3237 | b = 0-b; |
a90def6b DSH |
3238 | for (i = 0; i < 10; i++) { |
3239 | int32_t x = f[i] ^ g[i]; | |
3240 | x &= b; | |
3241 | f[i] ^= x; | |
3242 | g[i] ^= x; | |
3243 | } | |
3244 | } | |
3245 | ||
3246 | /* h = f * 121666 | |
3247 | * Can overlap h with f. | |
3248 | * | |
3249 | * Preconditions: | |
3250 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. | |
3251 | * | |
3252 | * Postconditions: | |
3253 | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ | |
3254 | static void fe_mul121666(fe h, fe f) { | |
3255 | int32_t f0 = f[0]; | |
3256 | int32_t f1 = f[1]; | |
3257 | int32_t f2 = f[2]; | |
3258 | int32_t f3 = f[3]; | |
3259 | int32_t f4 = f[4]; | |
3260 | int32_t f5 = f[5]; | |
3261 | int32_t f6 = f[6]; | |
3262 | int32_t f7 = f[7]; | |
3263 | int32_t f8 = f[8]; | |
3264 | int32_t f9 = f[9]; | |
3265 | int64_t h0 = f0 * (int64_t) 121666; | |
3266 | int64_t h1 = f1 * (int64_t) 121666; | |
3267 | int64_t h2 = f2 * (int64_t) 121666; | |
3268 | int64_t h3 = f3 * (int64_t) 121666; | |
3269 | int64_t h4 = f4 * (int64_t) 121666; | |
3270 | int64_t h5 = f5 * (int64_t) 121666; | |
3271 | int64_t h6 = f6 * (int64_t) 121666; | |
3272 | int64_t h7 = f7 * (int64_t) 121666; | |
3273 | int64_t h8 = f8 * (int64_t) 121666; | |
3274 | int64_t h9 = f9 * (int64_t) 121666; | |
3275 | int64_t carry0; | |
3276 | int64_t carry1; | |
3277 | int64_t carry2; | |
3278 | int64_t carry3; | |
3279 | int64_t carry4; | |
3280 | int64_t carry5; | |
3281 | int64_t carry6; | |
3282 | int64_t carry7; | |
3283 | int64_t carry8; | |
3284 | int64_t carry9; | |
3285 | ||
b9577984 EK |
3286 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
3287 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; | |
3288 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; | |
3289 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
3290 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
3291 | ||
3292 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; | |
3293 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; | |
3294 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
3295 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
3296 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
a90def6b DSH |
3297 | |
3298 | h[0] = h0; | |
3299 | h[1] = h1; | |
3300 | h[2] = h2; | |
3301 | h[3] = h3; | |
3302 | h[4] = h4; | |
3303 | h[5] = h5; | |
3304 | h[6] = h6; | |
3305 | h[7] = h7; | |
3306 | h[8] = h8; | |
3307 | h[9] = h9; | |
3308 | } | |
3309 | ||
3310 | static void x25519_scalar_mult_generic(uint8_t out[32], | |
3311 | const uint8_t scalar[32], | |
3312 | const uint8_t point[32]) { | |
3313 | fe x1, x2, z2, x3, z3, tmp0, tmp1; | |
a90def6b | 3314 | uint8_t e[32]; |
244e5f5d DSH |
3315 | unsigned swap = 0; |
3316 | int pos; | |
3317 | ||
a90def6b DSH |
3318 | memcpy(e, scalar, 32); |
3319 | e[0] &= 248; | |
3320 | e[31] &= 127; | |
3321 | e[31] |= 64; | |
3322 | fe_frombytes(x1, point); | |
3323 | fe_1(x2); | |
3324 | fe_0(z2); | |
3325 | fe_copy(x3, x1); | |
3326 | fe_1(z3); | |
3327 | ||
a90def6b DSH |
3328 | for (pos = 254; pos >= 0; --pos) { |
3329 | unsigned b = 1 & (e[pos / 8] >> (pos & 7)); | |
3330 | swap ^= b; | |
3331 | fe_cswap(x2, x3, swap); | |
3332 | fe_cswap(z2, z3, swap); | |
3333 | swap = b; | |
3334 | fe_sub(tmp0, x3, z3); | |
3335 | fe_sub(tmp1, x2, z2); | |
3336 | fe_add(x2, x2, z2); | |
3337 | fe_add(z2, x3, z3); | |
3338 | fe_mul(z3, tmp0, x2); | |
3339 | fe_mul(z2, z2, tmp1); | |
3340 | fe_sq(tmp0, tmp1); | |
3341 | fe_sq(tmp1, x2); | |
3342 | fe_add(x3, z3, z2); | |
3343 | fe_sub(z2, z3, z2); | |
3344 | fe_mul(x2, tmp1, tmp0); | |
3345 | fe_sub(tmp1, tmp1, tmp0); | |
3346 | fe_sq(z2, z2); | |
3347 | fe_mul121666(z3, tmp1); | |
3348 | fe_sq(x3, x3); | |
3349 | fe_add(tmp0, tmp0, z3); | |
3350 | fe_mul(z3, x1, z2); | |
3351 | fe_mul(z2, tmp1, tmp0); | |
3352 | } | |
3353 | fe_cswap(x2, x3, swap); | |
3354 | fe_cswap(z2, z3, swap); | |
3355 | ||
3356 | fe_invert(z2, z2); | |
3357 | fe_mul(x2, x2, z2); | |
3358 | fe_tobytes(out, x2); | |
3359 | } | |
3360 | ||
3361 | static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], | |
3362 | const uint8_t point[32]) { | |
a90def6b DSH |
3363 | x25519_scalar_mult_generic(out, scalar, point); |
3364 | } | |
3365 | ||
a90def6b DSH |
3366 | int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], |
3367 | const uint8_t peer_public_value[32]) { | |
3368 | static const uint8_t kZeros[32] = {0}; | |
3369 | x25519_scalar_mult(out_shared_key, private_key, peer_public_value); | |
3370 | /* The all-zero output results when the input is a point of small order. */ | |
3371 | return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0; | |
3372 | } | |
3373 | ||
a90def6b DSH |
3374 | void X25519_public_from_private(uint8_t out_public_value[32], |
3375 | const uint8_t private_key[32]) { | |
244e5f5d DSH |
3376 | uint8_t e[32]; |
3377 | ge_p3 A; | |
3378 | fe zplusy, zminusy, zminusy_inv; | |
3379 | ||
a90def6b DSH |
3380 | memcpy(e, private_key, 32); |
3381 | e[0] &= 248; | |
3382 | e[31] &= 127; | |
3383 | e[31] |= 64; | |
3384 | ||
a90def6b DSH |
3385 | ge_scalarmult_base(&A, e); |
3386 | ||
3387 | /* We only need the u-coordinate of the curve25519 point. The map is | |
3388 | * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ | |
a90def6b DSH |
3389 | fe_add(zplusy, A.Z, A.Y); |
3390 | fe_sub(zminusy, A.Z, A.Y); | |
3391 | fe_invert(zminusy_inv, zminusy); | |
3392 | fe_mul(zplusy, zplusy, zminusy_inv); | |
3393 | fe_tobytes(out_public_value, zplusy); | |
3394 | } |