/src/openssl/crypto/ec/curve25519.c
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1 | | /* |
2 | | * Copyright 2016-2019 The OpenSSL Project Authors. All Rights Reserved. |
3 | | * |
4 | | * Licensed under the Apache License 2.0 (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 |
8 | | */ |
9 | | |
10 | | /* |
11 | | * ECDSA low level APIs are deprecated for public use, but still ok for |
12 | | * internal use. |
13 | | */ |
14 | | #include "internal/deprecated.h" |
15 | | |
16 | | #include <string.h> |
17 | | #include "ec_local.h" |
18 | | #include <openssl/evp.h> |
19 | | #include <openssl/sha.h> |
20 | | |
21 | | #if defined(X25519_ASM) && (defined(__x86_64) || defined(__x86_64__) || \ |
22 | | defined(_M_AMD64) || defined(_M_X64)) |
23 | | |
24 | | # define BASE_2_64_IMPLEMENTED |
25 | | |
26 | | typedef uint64_t fe64[4]; |
27 | | |
28 | | int x25519_fe64_eligible(void); |
29 | | |
30 | | /* |
31 | | * Following subroutines perform corresponding operations modulo |
32 | | * 2^256-38, i.e. double the curve modulus. However, inputs and |
33 | | * outputs are permitted to be partially reduced, i.e. to remain |
34 | | * in [0..2^256) range. It's all tied up in final fe64_tobytes |
35 | | * that performs full reduction modulo 2^255-19. |
36 | | * |
37 | | * There are no reference C implementations for these. |
38 | | */ |
39 | | void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g); |
40 | | void x25519_fe64_sqr(fe64 h, const fe64 f); |
41 | | void x25519_fe64_mul121666(fe64 h, fe64 f); |
42 | | void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g); |
43 | | void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g); |
44 | | void x25519_fe64_tobytes(uint8_t *s, const fe64 f); |
45 | 0 | # define fe64_mul x25519_fe64_mul |
46 | 0 | # define fe64_sqr x25519_fe64_sqr |
47 | 0 | # define fe64_mul121666 x25519_fe64_mul121666 |
48 | 0 | # define fe64_add x25519_fe64_add |
49 | 0 | # define fe64_sub x25519_fe64_sub |
50 | 0 | # define fe64_tobytes x25519_fe64_tobytes |
51 | | |
52 | | static uint64_t load_8(const uint8_t *in) |
53 | 0 | { |
54 | 0 | uint64_t result; |
55 | |
|
56 | 0 | result = in[0]; |
57 | 0 | result |= ((uint64_t)in[1]) << 8; |
58 | 0 | result |= ((uint64_t)in[2]) << 16; |
59 | 0 | result |= ((uint64_t)in[3]) << 24; |
60 | 0 | result |= ((uint64_t)in[4]) << 32; |
61 | 0 | result |= ((uint64_t)in[5]) << 40; |
62 | 0 | result |= ((uint64_t)in[6]) << 48; |
63 | 0 | result |= ((uint64_t)in[7]) << 56; |
64 | |
|
65 | 0 | return result; |
66 | 0 | } |
67 | | |
68 | | static void fe64_frombytes(fe64 h, const uint8_t *s) |
69 | 0 | { |
70 | 0 | h[0] = load_8(s); |
71 | 0 | h[1] = load_8(s + 8); |
72 | 0 | h[2] = load_8(s + 16); |
73 | 0 | h[3] = load_8(s + 24) & 0x7fffffffffffffff; |
74 | 0 | } |
75 | | |
76 | | static void fe64_0(fe64 h) |
77 | 0 | { |
78 | 0 | h[0] = 0; |
79 | 0 | h[1] = 0; |
80 | 0 | h[2] = 0; |
81 | 0 | h[3] = 0; |
82 | 0 | } |
83 | | |
84 | | static void fe64_1(fe64 h) |
85 | 0 | { |
86 | 0 | h[0] = 1; |
87 | 0 | h[1] = 0; |
88 | 0 | h[2] = 0; |
89 | 0 | h[3] = 0; |
90 | 0 | } |
91 | | |
92 | | static void fe64_copy(fe64 h, const fe64 f) |
93 | 0 | { |
94 | 0 | h[0] = f[0]; |
95 | 0 | h[1] = f[1]; |
96 | 0 | h[2] = f[2]; |
97 | 0 | h[3] = f[3]; |
98 | 0 | } |
99 | | |
100 | | static void fe64_cswap(fe64 f, fe64 g, unsigned int b) |
101 | 0 | { |
102 | 0 | int i; |
103 | 0 | uint64_t mask = 0 - (uint64_t)b; |
104 | |
|
105 | 0 | for (i = 0; i < 4; i++) { |
106 | 0 | uint64_t x = f[i] ^ g[i]; |
107 | 0 | x &= mask; |
108 | 0 | f[i] ^= x; |
109 | 0 | g[i] ^= x; |
110 | 0 | } |
111 | 0 | } |
112 | | |
113 | | static void fe64_invert(fe64 out, const fe64 z) |
114 | 0 | { |
115 | 0 | fe64 t0; |
116 | 0 | fe64 t1; |
117 | 0 | fe64 t2; |
118 | 0 | fe64 t3; |
119 | 0 | int i; |
120 | | |
121 | | /* |
122 | | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as |
123 | | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. |
124 | | */ |
125 | | |
126 | | /* t0 = z ** 2 */ |
127 | 0 | fe64_sqr(t0, z); |
128 | | |
129 | | /* t1 = t0 ** (2 ** 2) = z ** 8 */ |
130 | 0 | fe64_sqr(t1, t0); |
131 | 0 | fe64_sqr(t1, t1); |
132 | | |
133 | | /* t1 = z * t1 = z ** 9 */ |
134 | 0 | fe64_mul(t1, z, t1); |
135 | | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ |
136 | 0 | fe64_mul(t0, t0, t1); |
137 | | |
138 | | /* t2 = t0 ** 2 = z ** 22 */ |
139 | 0 | fe64_sqr(t2, t0); |
140 | | |
141 | | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ |
142 | 0 | fe64_mul(t1, t1, t2); |
143 | | |
144 | | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ |
145 | 0 | fe64_sqr(t2, t1); |
146 | 0 | for (i = 1; i < 5; ++i) |
147 | 0 | fe64_sqr(t2, t2); |
148 | | |
149 | | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ |
150 | 0 | fe64_mul(t1, t2, t1); |
151 | | |
152 | | /* Continuing similarly... */ |
153 | | |
154 | | /* t2 = z ** (2 ** 20 - 1) */ |
155 | 0 | fe64_sqr(t2, t1); |
156 | 0 | for (i = 1; i < 10; ++i) |
157 | 0 | fe64_sqr(t2, t2); |
158 | |
|
159 | 0 | fe64_mul(t2, t2, t1); |
160 | | |
161 | | /* t2 = z ** (2 ** 40 - 1) */ |
162 | 0 | fe64_sqr(t3, t2); |
163 | 0 | for (i = 1; i < 20; ++i) |
164 | 0 | fe64_sqr(t3, t3); |
165 | |
|
166 | 0 | fe64_mul(t2, t3, t2); |
167 | | |
168 | | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ |
169 | 0 | for (i = 0; i < 10; ++i) |
170 | 0 | fe64_sqr(t2, t2); |
171 | | |
172 | | /* t1 = z ** (2 ** 50 - 1) */ |
173 | 0 | fe64_mul(t1, t2, t1); |
174 | | |
175 | | /* t2 = z ** (2 ** 100 - 1) */ |
176 | 0 | fe64_sqr(t2, t1); |
177 | 0 | for (i = 1; i < 50; ++i) |
178 | 0 | fe64_sqr(t2, t2); |
179 | |
|
180 | 0 | fe64_mul(t2, t2, t1); |
181 | | |
182 | | /* t2 = z ** (2 ** 200 - 1) */ |
183 | 0 | fe64_sqr(t3, t2); |
184 | 0 | for (i = 1; i < 100; ++i) |
185 | 0 | fe64_sqr(t3, t3); |
186 | |
|
187 | 0 | fe64_mul(t2, t3, t2); |
188 | | |
189 | | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ |
190 | 0 | for (i = 0; i < 50; ++i) |
191 | 0 | fe64_sqr(t2, t2); |
192 | | |
193 | | /* t1 = z ** (2 ** 250 - 1) */ |
194 | 0 | fe64_mul(t1, t2, t1); |
195 | | |
196 | | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ |
197 | 0 | for (i = 0; i < 5; ++i) |
198 | 0 | fe64_sqr(t1, t1); |
199 | | |
200 | | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ |
201 | 0 | fe64_mul(out, t1, t0); |
202 | 0 | } |
203 | | |
204 | | /* |
205 | | * Duplicate of original x25519_scalar_mult_generic, but using |
206 | | * fe64_* subroutines. |
207 | | */ |
208 | | static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32], |
209 | | const uint8_t point[32]) |
210 | 0 | { |
211 | 0 | fe64 x1, x2, z2, x3, z3, tmp0, tmp1; |
212 | 0 | uint8_t e[32]; |
213 | 0 | unsigned swap = 0; |
214 | 0 | int pos; |
215 | |
|
216 | 0 | memcpy(e, scalar, 32); |
217 | 0 | e[0] &= 0xf8; |
218 | 0 | e[31] &= 0x7f; |
219 | 0 | e[31] |= 0x40; |
220 | 0 | fe64_frombytes(x1, point); |
221 | 0 | fe64_1(x2); |
222 | 0 | fe64_0(z2); |
223 | 0 | fe64_copy(x3, x1); |
224 | 0 | fe64_1(z3); |
225 | |
|
226 | 0 | for (pos = 254; pos >= 0; --pos) { |
227 | 0 | unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); |
228 | |
|
229 | 0 | swap ^= b; |
230 | 0 | fe64_cswap(x2, x3, swap); |
231 | 0 | fe64_cswap(z2, z3, swap); |
232 | 0 | swap = b; |
233 | 0 | fe64_sub(tmp0, x3, z3); |
234 | 0 | fe64_sub(tmp1, x2, z2); |
235 | 0 | fe64_add(x2, x2, z2); |
236 | 0 | fe64_add(z2, x3, z3); |
237 | 0 | fe64_mul(z3, x2, tmp0); |
238 | 0 | fe64_mul(z2, z2, tmp1); |
239 | 0 | fe64_sqr(tmp0, tmp1); |
240 | 0 | fe64_sqr(tmp1, x2); |
241 | 0 | fe64_add(x3, z3, z2); |
242 | 0 | fe64_sub(z2, z3, z2); |
243 | 0 | fe64_mul(x2, tmp1, tmp0); |
244 | 0 | fe64_sub(tmp1, tmp1, tmp0); |
245 | 0 | fe64_sqr(z2, z2); |
246 | 0 | fe64_mul121666(z3, tmp1); |
247 | 0 | fe64_sqr(x3, x3); |
248 | 0 | fe64_add(tmp0, tmp0, z3); |
249 | 0 | fe64_mul(z3, x1, z2); |
250 | 0 | fe64_mul(z2, tmp1, tmp0); |
251 | 0 | } |
252 | |
|
253 | 0 | fe64_invert(z2, z2); |
254 | 0 | fe64_mul(x2, x2, z2); |
255 | 0 | fe64_tobytes(out, x2); |
256 | |
|
257 | 0 | OPENSSL_cleanse(e, sizeof(e)); |
258 | 0 | } |
259 | | #endif |
260 | | |
261 | | #if defined(X25519_ASM) \ |
262 | | || ( (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16) \ |
263 | | && !defined(__sparc__) \ |
264 | | && (!defined(__SIZEOF_LONG__) || (__SIZEOF_LONG__ == 8)) \ |
265 | | && !(defined(__ANDROID__) && !defined(__clang__)) ) |
266 | | /* |
267 | | * Base 2^51 implementation. It's virtually no different from reference |
268 | | * base 2^25.5 implementation in respect to lax boundary conditions for |
269 | | * intermediate values and even individual limbs. So that whatever you |
270 | | * know about the reference, applies even here... |
271 | | */ |
272 | | # define BASE_2_51_IMPLEMENTED |
273 | | |
274 | | typedef uint64_t fe51[5]; |
275 | | |
276 | | static const uint64_t MASK51 = 0x7ffffffffffff; |
277 | | |
278 | | static uint64_t load_7(const uint8_t *in) |
279 | 0 | { |
280 | 0 | uint64_t result; |
281 | |
|
282 | 0 | result = in[0]; |
283 | 0 | result |= ((uint64_t)in[1]) << 8; |
284 | 0 | result |= ((uint64_t)in[2]) << 16; |
285 | 0 | result |= ((uint64_t)in[3]) << 24; |
286 | 0 | result |= ((uint64_t)in[4]) << 32; |
287 | 0 | result |= ((uint64_t)in[5]) << 40; |
288 | 0 | result |= ((uint64_t)in[6]) << 48; |
289 | |
|
290 | 0 | return result; |
291 | 0 | } |
292 | | |
293 | | static uint64_t load_6(const uint8_t *in) |
294 | 0 | { |
295 | 0 | uint64_t result; |
296 | |
|
297 | 0 | result = in[0]; |
298 | 0 | result |= ((uint64_t)in[1]) << 8; |
299 | 0 | result |= ((uint64_t)in[2]) << 16; |
300 | 0 | result |= ((uint64_t)in[3]) << 24; |
301 | 0 | result |= ((uint64_t)in[4]) << 32; |
302 | 0 | result |= ((uint64_t)in[5]) << 40; |
303 | |
|
304 | 0 | return result; |
305 | 0 | } |
306 | | |
307 | | static void fe51_frombytes(fe51 h, const uint8_t *s) |
308 | 0 | { |
309 | 0 | uint64_t h0 = load_7(s); /* 56 bits */ |
310 | 0 | uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */ |
311 | 0 | uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */ |
312 | 0 | uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */ |
313 | 0 | uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */ |
314 | |
|
315 | 0 | h1 |= h0 >> 51; h0 &= MASK51; |
316 | 0 | h2 |= h1 >> 51; h1 &= MASK51; |
317 | 0 | h3 |= h2 >> 51; h2 &= MASK51; |
318 | 0 | h4 |= h3 >> 51; h3 &= MASK51; |
319 | |
|
320 | 0 | h[0] = h0; |
321 | 0 | h[1] = h1; |
322 | 0 | h[2] = h2; |
323 | 0 | h[3] = h3; |
324 | 0 | h[4] = h4; |
325 | 0 | } |
326 | | |
327 | | static void fe51_tobytes(uint8_t *s, const fe51 h) |
328 | 0 | { |
329 | 0 | uint64_t h0 = h[0]; |
330 | 0 | uint64_t h1 = h[1]; |
331 | 0 | uint64_t h2 = h[2]; |
332 | 0 | uint64_t h3 = h[3]; |
333 | 0 | uint64_t h4 = h[4]; |
334 | 0 | uint64_t q; |
335 | | |
336 | | /* compare to modulus */ |
337 | 0 | q = (h0 + 19) >> 51; |
338 | 0 | q = (h1 + q) >> 51; |
339 | 0 | q = (h2 + q) >> 51; |
340 | 0 | q = (h3 + q) >> 51; |
341 | 0 | q = (h4 + q) >> 51; |
342 | | |
343 | | /* full reduce */ |
344 | 0 | h0 += 19 * q; |
345 | 0 | h1 += h0 >> 51; h0 &= MASK51; |
346 | 0 | h2 += h1 >> 51; h1 &= MASK51; |
347 | 0 | h3 += h2 >> 51; h2 &= MASK51; |
348 | 0 | h4 += h3 >> 51; h3 &= MASK51; |
349 | 0 | h4 &= MASK51; |
350 | | |
351 | | /* smash */ |
352 | 0 | s[0] = (uint8_t)(h0 >> 0); |
353 | 0 | s[1] = (uint8_t)(h0 >> 8); |
354 | 0 | s[2] = (uint8_t)(h0 >> 16); |
355 | 0 | s[3] = (uint8_t)(h0 >> 24); |
356 | 0 | s[4] = (uint8_t)(h0 >> 32); |
357 | 0 | s[5] = (uint8_t)(h0 >> 40); |
358 | 0 | s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3)); |
359 | 0 | s[7] = (uint8_t)(h1 >> 5); |
360 | 0 | s[8] = (uint8_t)(h1 >> 13); |
361 | 0 | s[9] = (uint8_t)(h1 >> 21); |
362 | 0 | s[10] = (uint8_t)(h1 >> 29); |
363 | 0 | s[11] = (uint8_t)(h1 >> 37); |
364 | 0 | s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6)); |
365 | 0 | s[13] = (uint8_t)(h2 >> 2); |
366 | 0 | s[14] = (uint8_t)(h2 >> 10); |
367 | 0 | s[15] = (uint8_t)(h2 >> 18); |
368 | 0 | s[16] = (uint8_t)(h2 >> 26); |
369 | 0 | s[17] = (uint8_t)(h2 >> 34); |
370 | 0 | s[18] = (uint8_t)(h2 >> 42); |
371 | 0 | s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1)); |
372 | 0 | s[20] = (uint8_t)(h3 >> 7); |
373 | 0 | s[21] = (uint8_t)(h3 >> 15); |
374 | 0 | s[22] = (uint8_t)(h3 >> 23); |
375 | 0 | s[23] = (uint8_t)(h3 >> 31); |
376 | 0 | s[24] = (uint8_t)(h3 >> 39); |
377 | 0 | s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4)); |
378 | 0 | s[26] = (uint8_t)(h4 >> 4); |
379 | 0 | s[27] = (uint8_t)(h4 >> 12); |
380 | 0 | s[28] = (uint8_t)(h4 >> 20); |
381 | 0 | s[29] = (uint8_t)(h4 >> 28); |
382 | 0 | s[30] = (uint8_t)(h4 >> 36); |
383 | 0 | s[31] = (uint8_t)(h4 >> 44); |
384 | 0 | } |
385 | | |
386 | | # if defined(X25519_ASM) |
387 | | void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g); |
388 | | void x25519_fe51_sqr(fe51 h, const fe51 f); |
389 | | void x25519_fe51_mul121666(fe51 h, fe51 f); |
390 | 0 | # define fe51_mul x25519_fe51_mul |
391 | 0 | # define fe51_sq x25519_fe51_sqr |
392 | 0 | # define fe51_mul121666 x25519_fe51_mul121666 |
393 | | # else |
394 | | |
395 | | typedef __uint128_t u128; |
396 | | |
397 | | static void fe51_mul(fe51 h, const fe51 f, const fe51 g) |
398 | | { |
399 | | u128 h0, h1, h2, h3, h4; |
400 | | uint64_t f_i, g0, g1, g2, g3, g4; |
401 | | |
402 | | f_i = f[0]; |
403 | | h0 = (u128)f_i * (g0 = g[0]); |
404 | | h1 = (u128)f_i * (g1 = g[1]); |
405 | | h2 = (u128)f_i * (g2 = g[2]); |
406 | | h3 = (u128)f_i * (g3 = g[3]); |
407 | | h4 = (u128)f_i * (g4 = g[4]); |
408 | | |
409 | | f_i = f[1]; |
410 | | h0 += (u128)f_i * (g4 *= 19); |
411 | | h1 += (u128)f_i * g0; |
412 | | h2 += (u128)f_i * g1; |
413 | | h3 += (u128)f_i * g2; |
414 | | h4 += (u128)f_i * g3; |
415 | | |
416 | | f_i = f[2]; |
417 | | h0 += (u128)f_i * (g3 *= 19); |
418 | | h1 += (u128)f_i * g4; |
419 | | h2 += (u128)f_i * g0; |
420 | | h3 += (u128)f_i * g1; |
421 | | h4 += (u128)f_i * g2; |
422 | | |
423 | | f_i = f[3]; |
424 | | h0 += (u128)f_i * (g2 *= 19); |
425 | | h1 += (u128)f_i * g3; |
426 | | h2 += (u128)f_i * g4; |
427 | | h3 += (u128)f_i * g0; |
428 | | h4 += (u128)f_i * g1; |
429 | | |
430 | | f_i = f[4]; |
431 | | h0 += (u128)f_i * (g1 *= 19); |
432 | | h1 += (u128)f_i * g2; |
433 | | h2 += (u128)f_i * g3; |
434 | | h3 += (u128)f_i * g4; |
435 | | h4 += (u128)f_i * g0; |
436 | | |
437 | | /* partial [lazy] reduction */ |
438 | | h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; |
439 | | h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; |
440 | | |
441 | | h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; |
442 | | g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; |
443 | | |
444 | | g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; |
445 | | g3 += g2 >> 51; g2 &= MASK51; |
446 | | g1 += g0 >> 51; g0 &= MASK51; |
447 | | |
448 | | h[0] = g0; |
449 | | h[1] = g1; |
450 | | h[2] = g2; |
451 | | h[3] = g3; |
452 | | h[4] = g4; |
453 | | } |
454 | | |
455 | | static void fe51_sq(fe51 h, const fe51 f) |
456 | | { |
457 | | # if defined(OPENSSL_SMALL_FOOTPRINT) |
458 | | fe51_mul(h, f, f); |
459 | | # else |
460 | | /* dedicated squaring gives 16-25% overall improvement */ |
461 | | uint64_t g0 = f[0]; |
462 | | uint64_t g1 = f[1]; |
463 | | uint64_t g2 = f[2]; |
464 | | uint64_t g3 = f[3]; |
465 | | uint64_t g4 = f[4]; |
466 | | u128 h0, h1, h2, h3, h4; |
467 | | |
468 | | h0 = (u128)g0 * g0; g0 *= 2; |
469 | | h1 = (u128)g0 * g1; |
470 | | h2 = (u128)g0 * g2; |
471 | | h3 = (u128)g0 * g3; |
472 | | h4 = (u128)g0 * g4; |
473 | | |
474 | | g0 = g4; /* borrow g0 */ |
475 | | h3 += (u128)g0 * (g4 *= 19); |
476 | | |
477 | | h2 += (u128)g1 * g1; g1 *= 2; |
478 | | h3 += (u128)g1 * g2; |
479 | | h4 += (u128)g1 * g3; |
480 | | h0 += (u128)g1 * g4; |
481 | | |
482 | | g0 = g3; /* borrow g0 */ |
483 | | h1 += (u128)g0 * (g3 *= 19); |
484 | | h2 += (u128)(g0 * 2) * g4; |
485 | | |
486 | | h4 += (u128)g2 * g2; g2 *= 2; |
487 | | h0 += (u128)g2 * g3; |
488 | | h1 += (u128)g2 * g4; |
489 | | |
490 | | /* partial [lazy] reduction */ |
491 | | h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; |
492 | | h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; |
493 | | |
494 | | h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; |
495 | | g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; |
496 | | |
497 | | g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; |
498 | | g3 += g2 >> 51; g2 &= MASK51; |
499 | | g1 += g0 >> 51; g0 &= MASK51; |
500 | | |
501 | | h[0] = g0; |
502 | | h[1] = g1; |
503 | | h[2] = g2; |
504 | | h[3] = g3; |
505 | | h[4] = g4; |
506 | | # endif |
507 | | } |
508 | | |
509 | | static void fe51_mul121666(fe51 h, fe51 f) |
510 | | { |
511 | | u128 h0 = f[0] * (u128)121666; |
512 | | u128 h1 = f[1] * (u128)121666; |
513 | | u128 h2 = f[2] * (u128)121666; |
514 | | u128 h3 = f[3] * (u128)121666; |
515 | | u128 h4 = f[4] * (u128)121666; |
516 | | uint64_t g0, g1, g2, g3, g4; |
517 | | |
518 | | h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; |
519 | | h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; |
520 | | |
521 | | h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; |
522 | | g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; |
523 | | |
524 | | g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; |
525 | | g3 += g2 >> 51; g2 &= MASK51; |
526 | | g1 += g0 >> 51; g0 &= MASK51; |
527 | | |
528 | | h[0] = g0; |
529 | | h[1] = g1; |
530 | | h[2] = g2; |
531 | | h[3] = g3; |
532 | | h[4] = g4; |
533 | | } |
534 | | # endif |
535 | | |
536 | | static void fe51_add(fe51 h, const fe51 f, const fe51 g) |
537 | 0 | { |
538 | 0 | h[0] = f[0] + g[0]; |
539 | 0 | h[1] = f[1] + g[1]; |
540 | 0 | h[2] = f[2] + g[2]; |
541 | 0 | h[3] = f[3] + g[3]; |
542 | 0 | h[4] = f[4] + g[4]; |
543 | 0 | } |
544 | | |
545 | | static void fe51_sub(fe51 h, const fe51 f, const fe51 g) |
546 | 0 | { |
547 | | /* |
548 | | * Add 2*modulus to ensure that result remains positive |
549 | | * even if subtrahend is partially reduced. |
550 | | */ |
551 | 0 | h[0] = (f[0] + 0xfffffffffffda) - g[0]; |
552 | 0 | h[1] = (f[1] + 0xffffffffffffe) - g[1]; |
553 | 0 | h[2] = (f[2] + 0xffffffffffffe) - g[2]; |
554 | 0 | h[3] = (f[3] + 0xffffffffffffe) - g[3]; |
555 | 0 | h[4] = (f[4] + 0xffffffffffffe) - g[4]; |
556 | 0 | } |
557 | | |
558 | | static void fe51_0(fe51 h) |
559 | 0 | { |
560 | 0 | h[0] = 0; |
561 | 0 | h[1] = 0; |
562 | 0 | h[2] = 0; |
563 | 0 | h[3] = 0; |
564 | 0 | h[4] = 0; |
565 | 0 | } |
566 | | |
567 | | static void fe51_1(fe51 h) |
568 | 0 | { |
569 | 0 | h[0] = 1; |
570 | 0 | h[1] = 0; |
571 | 0 | h[2] = 0; |
572 | 0 | h[3] = 0; |
573 | 0 | h[4] = 0; |
574 | 0 | } |
575 | | |
576 | | static void fe51_copy(fe51 h, const fe51 f) |
577 | 0 | { |
578 | 0 | h[0] = f[0]; |
579 | 0 | h[1] = f[1]; |
580 | 0 | h[2] = f[2]; |
581 | 0 | h[3] = f[3]; |
582 | 0 | h[4] = f[4]; |
583 | 0 | } |
584 | | |
585 | | static void fe51_cswap(fe51 f, fe51 g, unsigned int b) |
586 | 0 | { |
587 | 0 | int i; |
588 | 0 | uint64_t mask = 0 - (uint64_t)b; |
589 | |
|
590 | 0 | for (i = 0; i < 5; i++) { |
591 | 0 | int64_t x = f[i] ^ g[i]; |
592 | 0 | x &= mask; |
593 | 0 | f[i] ^= x; |
594 | 0 | g[i] ^= x; |
595 | 0 | } |
596 | 0 | } |
597 | | |
598 | | static void fe51_invert(fe51 out, const fe51 z) |
599 | 0 | { |
600 | 0 | fe51 t0; |
601 | 0 | fe51 t1; |
602 | 0 | fe51 t2; |
603 | 0 | fe51 t3; |
604 | 0 | int i; |
605 | | |
606 | | /* |
607 | | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as |
608 | | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. |
609 | | */ |
610 | | |
611 | | /* t0 = z ** 2 */ |
612 | 0 | fe51_sq(t0, z); |
613 | | |
614 | | /* t1 = t0 ** (2 ** 2) = z ** 8 */ |
615 | 0 | fe51_sq(t1, t0); |
616 | 0 | fe51_sq(t1, t1); |
617 | | |
618 | | /* t1 = z * t1 = z ** 9 */ |
619 | 0 | fe51_mul(t1, z, t1); |
620 | | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ |
621 | 0 | fe51_mul(t0, t0, t1); |
622 | | |
623 | | /* t2 = t0 ** 2 = z ** 22 */ |
624 | 0 | fe51_sq(t2, t0); |
625 | | |
626 | | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ |
627 | 0 | fe51_mul(t1, t1, t2); |
628 | | |
629 | | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ |
630 | 0 | fe51_sq(t2, t1); |
631 | 0 | for (i = 1; i < 5; ++i) |
632 | 0 | fe51_sq(t2, t2); |
633 | | |
634 | | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ |
635 | 0 | fe51_mul(t1, t2, t1); |
636 | | |
637 | | /* Continuing similarly... */ |
638 | | |
639 | | /* t2 = z ** (2 ** 20 - 1) */ |
640 | 0 | fe51_sq(t2, t1); |
641 | 0 | for (i = 1; i < 10; ++i) |
642 | 0 | fe51_sq(t2, t2); |
643 | |
|
644 | 0 | fe51_mul(t2, t2, t1); |
645 | | |
646 | | /* t2 = z ** (2 ** 40 - 1) */ |
647 | 0 | fe51_sq(t3, t2); |
648 | 0 | for (i = 1; i < 20; ++i) |
649 | 0 | fe51_sq(t3, t3); |
650 | |
|
651 | 0 | fe51_mul(t2, t3, t2); |
652 | | |
653 | | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ |
654 | 0 | for (i = 0; i < 10; ++i) |
655 | 0 | fe51_sq(t2, t2); |
656 | | |
657 | | /* t1 = z ** (2 ** 50 - 1) */ |
658 | 0 | fe51_mul(t1, t2, t1); |
659 | | |
660 | | /* t2 = z ** (2 ** 100 - 1) */ |
661 | 0 | fe51_sq(t2, t1); |
662 | 0 | for (i = 1; i < 50; ++i) |
663 | 0 | fe51_sq(t2, t2); |
664 | |
|
665 | 0 | fe51_mul(t2, t2, t1); |
666 | | |
667 | | /* t2 = z ** (2 ** 200 - 1) */ |
668 | 0 | fe51_sq(t3, t2); |
669 | 0 | for (i = 1; i < 100; ++i) |
670 | 0 | fe51_sq(t3, t3); |
671 | |
|
672 | 0 | fe51_mul(t2, t3, t2); |
673 | | |
674 | | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ |
675 | 0 | for (i = 0; i < 50; ++i) |
676 | 0 | fe51_sq(t2, t2); |
677 | | |
678 | | /* t1 = z ** (2 ** 250 - 1) */ |
679 | 0 | fe51_mul(t1, t2, t1); |
680 | | |
681 | | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ |
682 | 0 | for (i = 0; i < 5; ++i) |
683 | 0 | fe51_sq(t1, t1); |
684 | | |
685 | | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ |
686 | 0 | fe51_mul(out, t1, t0); |
687 | 0 | } |
688 | | |
689 | | /* |
690 | | * Duplicate of original x25519_scalar_mult_generic, but using |
691 | | * fe51_* subroutines. |
692 | | */ |
693 | | static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], |
694 | | const uint8_t point[32]) |
695 | 0 | { |
696 | 0 | fe51 x1, x2, z2, x3, z3, tmp0, tmp1; |
697 | 0 | uint8_t e[32]; |
698 | 0 | unsigned swap = 0; |
699 | 0 | int pos; |
700 | |
|
701 | 0 | # ifdef BASE_2_64_IMPLEMENTED |
702 | 0 | if (x25519_fe64_eligible()) { |
703 | 0 | x25519_scalar_mulx(out, scalar, point); |
704 | 0 | return; |
705 | 0 | } |
706 | 0 | # endif |
707 | | |
708 | 0 | memcpy(e, scalar, 32); |
709 | 0 | e[0] &= 0xf8; |
710 | 0 | e[31] &= 0x7f; |
711 | 0 | e[31] |= 0x40; |
712 | 0 | fe51_frombytes(x1, point); |
713 | 0 | fe51_1(x2); |
714 | 0 | fe51_0(z2); |
715 | 0 | fe51_copy(x3, x1); |
716 | 0 | fe51_1(z3); |
717 | |
|
718 | 0 | for (pos = 254; pos >= 0; --pos) { |
719 | 0 | unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); |
720 | |
|
721 | 0 | swap ^= b; |
722 | 0 | fe51_cswap(x2, x3, swap); |
723 | 0 | fe51_cswap(z2, z3, swap); |
724 | 0 | swap = b; |
725 | 0 | fe51_sub(tmp0, x3, z3); |
726 | 0 | fe51_sub(tmp1, x2, z2); |
727 | 0 | fe51_add(x2, x2, z2); |
728 | 0 | fe51_add(z2, x3, z3); |
729 | 0 | fe51_mul(z3, tmp0, x2); |
730 | 0 | fe51_mul(z2, z2, tmp1); |
731 | 0 | fe51_sq(tmp0, tmp1); |
732 | 0 | fe51_sq(tmp1, x2); |
733 | 0 | fe51_add(x3, z3, z2); |
734 | 0 | fe51_sub(z2, z3, z2); |
735 | 0 | fe51_mul(x2, tmp1, tmp0); |
736 | 0 | fe51_sub(tmp1, tmp1, tmp0); |
737 | 0 | fe51_sq(z2, z2); |
738 | 0 | fe51_mul121666(z3, tmp1); |
739 | 0 | fe51_sq(x3, x3); |
740 | 0 | fe51_add(tmp0, tmp0, z3); |
741 | 0 | fe51_mul(z3, x1, z2); |
742 | 0 | fe51_mul(z2, tmp1, tmp0); |
743 | 0 | } |
744 | |
|
745 | 0 | fe51_invert(z2, z2); |
746 | 0 | fe51_mul(x2, x2, z2); |
747 | 0 | fe51_tobytes(out, x2); |
748 | |
|
749 | 0 | OPENSSL_cleanse(e, sizeof(e)); |
750 | 0 | } |
751 | | #endif |
752 | | |
753 | | /* |
754 | | * Reference base 2^25.5 implementation. |
755 | | * |
756 | | * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP |
757 | | * 20141124 (http://bench.cr.yp.to/supercop.html). |
758 | | * |
759 | | * The field functions are shared by Ed25519 and X25519 where possible. |
760 | | */ |
761 | | |
762 | | /* |
763 | | * fe means field element. Here the field is \Z/(2^255-19). An element t, |
764 | | * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 |
765 | | * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on |
766 | | * context. |
767 | | */ |
768 | | typedef int32_t fe[10]; |
769 | | |
770 | | static const int64_t kBottom21Bits = 0x1fffffLL; |
771 | | static const int64_t kBottom25Bits = 0x1ffffffLL; |
772 | | static const int64_t kBottom26Bits = 0x3ffffffLL; |
773 | | static const int64_t kTop39Bits = 0xfffffffffe000000LL; |
774 | | static const int64_t kTop38Bits = 0xfffffffffc000000LL; |
775 | | |
776 | | static uint64_t load_3(const uint8_t *in) |
777 | 0 | { |
778 | 0 | uint64_t result; |
779 | |
|
780 | 0 | result = ((uint64_t)in[0]); |
781 | 0 | result |= ((uint64_t)in[1]) << 8; |
782 | 0 | result |= ((uint64_t)in[2]) << 16; |
783 | 0 | return result; |
784 | 0 | } |
785 | | |
786 | | static uint64_t load_4(const uint8_t *in) |
787 | 0 | { |
788 | 0 | uint64_t result; |
789 | |
|
790 | 0 | result = ((uint64_t)in[0]); |
791 | 0 | result |= ((uint64_t)in[1]) << 8; |
792 | 0 | result |= ((uint64_t)in[2]) << 16; |
793 | 0 | result |= ((uint64_t)in[3]) << 24; |
794 | 0 | return result; |
795 | 0 | } |
796 | | |
797 | | static void fe_frombytes(fe h, const uint8_t *s) |
798 | 0 | { |
799 | | /* Ignores top bit of h. */ |
800 | 0 | int64_t h0 = load_4(s); |
801 | 0 | int64_t h1 = load_3(s + 4) << 6; |
802 | 0 | int64_t h2 = load_3(s + 7) << 5; |
803 | 0 | int64_t h3 = load_3(s + 10) << 3; |
804 | 0 | int64_t h4 = load_3(s + 13) << 2; |
805 | 0 | int64_t h5 = load_4(s + 16); |
806 | 0 | int64_t h6 = load_3(s + 20) << 7; |
807 | 0 | int64_t h7 = load_3(s + 23) << 5; |
808 | 0 | int64_t h8 = load_3(s + 26) << 4; |
809 | 0 | int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2; |
810 | 0 | int64_t carry0; |
811 | 0 | int64_t carry1; |
812 | 0 | int64_t carry2; |
813 | 0 | int64_t carry3; |
814 | 0 | int64_t carry4; |
815 | 0 | int64_t carry5; |
816 | 0 | int64_t carry6; |
817 | 0 | int64_t carry7; |
818 | 0 | int64_t carry8; |
819 | 0 | int64_t carry9; |
820 | |
|
821 | 0 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
822 | 0 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
823 | 0 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
824 | 0 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
825 | 0 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
826 | |
|
827 | 0 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
828 | 0 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
829 | 0 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
830 | 0 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
831 | 0 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
832 | |
|
833 | 0 | h[0] = (int32_t)h0; |
834 | 0 | h[1] = (int32_t)h1; |
835 | 0 | h[2] = (int32_t)h2; |
836 | 0 | h[3] = (int32_t)h3; |
837 | 0 | h[4] = (int32_t)h4; |
838 | 0 | h[5] = (int32_t)h5; |
839 | 0 | h[6] = (int32_t)h6; |
840 | 0 | h[7] = (int32_t)h7; |
841 | 0 | h[8] = (int32_t)h8; |
842 | 0 | h[9] = (int32_t)h9; |
843 | 0 | } |
844 | | |
845 | | /* |
846 | | * Preconditions: |
847 | | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
848 | | * |
849 | | * Write p=2^255-19; q=floor(h/p). |
850 | | * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). |
851 | | * |
852 | | * Proof: |
853 | | * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. |
854 | | * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. |
855 | | * |
856 | | * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). |
857 | | * Then 0<y<1. |
858 | | * |
859 | | * Write r=h-pq. |
860 | | * Have 0<=r<=p-1=2^255-20. |
861 | | * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. |
862 | | * |
863 | | * Write x=r+19(2^-255)r+y. |
864 | | * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. |
865 | | * |
866 | | * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) |
867 | | * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. |
868 | | */ |
869 | | static void fe_tobytes(uint8_t *s, const fe h) |
870 | 0 | { |
871 | 0 | int32_t h0 = h[0]; |
872 | 0 | int32_t h1 = h[1]; |
873 | 0 | int32_t h2 = h[2]; |
874 | 0 | int32_t h3 = h[3]; |
875 | 0 | int32_t h4 = h[4]; |
876 | 0 | int32_t h5 = h[5]; |
877 | 0 | int32_t h6 = h[6]; |
878 | 0 | int32_t h7 = h[7]; |
879 | 0 | int32_t h8 = h[8]; |
880 | 0 | int32_t h9 = h[9]; |
881 | 0 | int32_t q; |
882 | |
|
883 | 0 | q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; |
884 | 0 | q = (h0 + q) >> 26; |
885 | 0 | q = (h1 + q) >> 25; |
886 | 0 | q = (h2 + q) >> 26; |
887 | 0 | q = (h3 + q) >> 25; |
888 | 0 | q = (h4 + q) >> 26; |
889 | 0 | q = (h5 + q) >> 25; |
890 | 0 | q = (h6 + q) >> 26; |
891 | 0 | q = (h7 + q) >> 25; |
892 | 0 | q = (h8 + q) >> 26; |
893 | 0 | q = (h9 + q) >> 25; |
894 | | |
895 | | /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ |
896 | 0 | h0 += 19 * q; |
897 | | /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ |
898 | |
|
899 | 0 | h1 += h0 >> 26; h0 &= kBottom26Bits; |
900 | 0 | h2 += h1 >> 25; h1 &= kBottom25Bits; |
901 | 0 | h3 += h2 >> 26; h2 &= kBottom26Bits; |
902 | 0 | h4 += h3 >> 25; h3 &= kBottom25Bits; |
903 | 0 | h5 += h4 >> 26; h4 &= kBottom26Bits; |
904 | 0 | h6 += h5 >> 25; h5 &= kBottom25Bits; |
905 | 0 | h7 += h6 >> 26; h6 &= kBottom26Bits; |
906 | 0 | h8 += h7 >> 25; h7 &= kBottom25Bits; |
907 | 0 | h9 += h8 >> 26; h8 &= kBottom26Bits; |
908 | 0 | h9 &= kBottom25Bits; |
909 | | /* h10 = carry9 */ |
910 | | |
911 | | /* |
912 | | * Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. |
913 | | * Have h0+...+2^230 h9 between 0 and 2^255-1; |
914 | | * evidently 2^255 h10-2^255 q = 0. |
915 | | * Goal: Output h0+...+2^230 h9. |
916 | | */ |
917 | 0 | s[ 0] = (uint8_t) (h0 >> 0); |
918 | 0 | s[ 1] = (uint8_t) (h0 >> 8); |
919 | 0 | s[ 2] = (uint8_t) (h0 >> 16); |
920 | 0 | s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2)); |
921 | 0 | s[ 4] = (uint8_t) (h1 >> 6); |
922 | 0 | s[ 5] = (uint8_t) (h1 >> 14); |
923 | 0 | s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3)); |
924 | 0 | s[ 7] = (uint8_t) (h2 >> 5); |
925 | 0 | s[ 8] = (uint8_t) (h2 >> 13); |
926 | 0 | s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5)); |
927 | 0 | s[10] = (uint8_t) (h3 >> 3); |
928 | 0 | s[11] = (uint8_t) (h3 >> 11); |
929 | 0 | s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6)); |
930 | 0 | s[13] = (uint8_t) (h4 >> 2); |
931 | 0 | s[14] = (uint8_t) (h4 >> 10); |
932 | 0 | s[15] = (uint8_t) (h4 >> 18); |
933 | 0 | s[16] = (uint8_t) (h5 >> 0); |
934 | 0 | s[17] = (uint8_t) (h5 >> 8); |
935 | 0 | s[18] = (uint8_t) (h5 >> 16); |
936 | 0 | s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1)); |
937 | 0 | s[20] = (uint8_t) (h6 >> 7); |
938 | 0 | s[21] = (uint8_t) (h6 >> 15); |
939 | 0 | s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3)); |
940 | 0 | s[23] = (uint8_t) (h7 >> 5); |
941 | 0 | s[24] = (uint8_t) (h7 >> 13); |
942 | 0 | s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4)); |
943 | 0 | s[26] = (uint8_t) (h8 >> 4); |
944 | 0 | s[27] = (uint8_t) (h8 >> 12); |
945 | 0 | s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6)); |
946 | 0 | s[29] = (uint8_t) (h9 >> 2); |
947 | 0 | s[30] = (uint8_t) (h9 >> 10); |
948 | 0 | s[31] = (uint8_t) (h9 >> 18); |
949 | 0 | } |
950 | | |
951 | | /* h = f */ |
952 | | static void fe_copy(fe h, const fe f) |
953 | 0 | { |
954 | 0 | memmove(h, f, sizeof(int32_t) * 10); |
955 | 0 | } |
956 | | |
957 | | /* h = 0 */ |
958 | | static void fe_0(fe h) |
959 | 0 | { |
960 | 0 | memset(h, 0, sizeof(int32_t) * 10); |
961 | 0 | } |
962 | | |
963 | | /* h = 1 */ |
964 | | static void fe_1(fe h) |
965 | 0 | { |
966 | 0 | memset(h, 0, sizeof(int32_t) * 10); |
967 | 0 | h[0] = 1; |
968 | 0 | } |
969 | | |
970 | | /* |
971 | | * h = f + g |
972 | | * |
973 | | * Can overlap h with f or g. |
974 | | * |
975 | | * Preconditions: |
976 | | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
977 | | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
978 | | * |
979 | | * Postconditions: |
980 | | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
981 | | */ |
982 | | static void fe_add(fe h, const fe f, const fe g) |
983 | 0 | { |
984 | 0 | unsigned i; |
985 | |
|
986 | 0 | for (i = 0; i < 10; i++) { |
987 | 0 | h[i] = f[i] + g[i]; |
988 | 0 | } |
989 | 0 | } |
990 | | |
991 | | /* |
992 | | * h = f - g |
993 | | * |
994 | | * Can overlap h with f or g. |
995 | | * |
996 | | * Preconditions: |
997 | | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
998 | | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
999 | | * |
1000 | | * Postconditions: |
1001 | | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
1002 | | */ |
1003 | | static void fe_sub(fe h, const fe f, const fe g) |
1004 | 0 | { |
1005 | 0 | unsigned i; |
1006 | |
|
1007 | 0 | for (i = 0; i < 10; i++) { |
1008 | 0 | h[i] = f[i] - g[i]; |
1009 | 0 | } |
1010 | 0 | } |
1011 | | |
1012 | | /* |
1013 | | * h = f * g |
1014 | | * |
1015 | | * Can overlap h with f or g. |
1016 | | * |
1017 | | * Preconditions: |
1018 | | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
1019 | | * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
1020 | | * |
1021 | | * Postconditions: |
1022 | | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
1023 | | * |
1024 | | * Notes on implementation strategy: |
1025 | | * |
1026 | | * Using schoolbook multiplication. |
1027 | | * Karatsuba would save a little in some cost models. |
1028 | | * |
1029 | | * Most multiplications by 2 and 19 are 32-bit precomputations; |
1030 | | * cheaper than 64-bit postcomputations. |
1031 | | * |
1032 | | * There is one remaining multiplication by 19 in the carry chain; |
1033 | | * one *19 precomputation can be merged into this, |
1034 | | * but the resulting data flow is considerably less clean. |
1035 | | * |
1036 | | * There are 12 carries below. |
1037 | | * 10 of them are 2-way parallelizable and vectorizable. |
1038 | | * Can get away with 11 carries, but then data flow is much deeper. |
1039 | | * |
1040 | | * With tighter constraints on inputs can squeeze carries into int32. |
1041 | | */ |
1042 | | static void fe_mul(fe h, const fe f, const fe g) |
1043 | 0 | { |
1044 | 0 | int32_t f0 = f[0]; |
1045 | 0 | int32_t f1 = f[1]; |
1046 | 0 | int32_t f2 = f[2]; |
1047 | 0 | int32_t f3 = f[3]; |
1048 | 0 | int32_t f4 = f[4]; |
1049 | 0 | int32_t f5 = f[5]; |
1050 | 0 | int32_t f6 = f[6]; |
1051 | 0 | int32_t f7 = f[7]; |
1052 | 0 | int32_t f8 = f[8]; |
1053 | 0 | int32_t f9 = f[9]; |
1054 | 0 | int32_t g0 = g[0]; |
1055 | 0 | int32_t g1 = g[1]; |
1056 | 0 | int32_t g2 = g[2]; |
1057 | 0 | int32_t g3 = g[3]; |
1058 | 0 | int32_t g4 = g[4]; |
1059 | 0 | int32_t g5 = g[5]; |
1060 | 0 | int32_t g6 = g[6]; |
1061 | 0 | int32_t g7 = g[7]; |
1062 | 0 | int32_t g8 = g[8]; |
1063 | 0 | int32_t g9 = g[9]; |
1064 | 0 | int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ |
1065 | 0 | int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ |
1066 | 0 | int32_t g3_19 = 19 * g3; |
1067 | 0 | int32_t g4_19 = 19 * g4; |
1068 | 0 | int32_t g5_19 = 19 * g5; |
1069 | 0 | int32_t g6_19 = 19 * g6; |
1070 | 0 | int32_t g7_19 = 19 * g7; |
1071 | 0 | int32_t g8_19 = 19 * g8; |
1072 | 0 | int32_t g9_19 = 19 * g9; |
1073 | 0 | int32_t f1_2 = 2 * f1; |
1074 | 0 | int32_t f3_2 = 2 * f3; |
1075 | 0 | int32_t f5_2 = 2 * f5; |
1076 | 0 | int32_t f7_2 = 2 * f7; |
1077 | 0 | int32_t f9_2 = 2 * f9; |
1078 | 0 | int64_t f0g0 = f0 * (int64_t) g0; |
1079 | 0 | int64_t f0g1 = f0 * (int64_t) g1; |
1080 | 0 | int64_t f0g2 = f0 * (int64_t) g2; |
1081 | 0 | int64_t f0g3 = f0 * (int64_t) g3; |
1082 | 0 | int64_t f0g4 = f0 * (int64_t) g4; |
1083 | 0 | int64_t f0g5 = f0 * (int64_t) g5; |
1084 | 0 | int64_t f0g6 = f0 * (int64_t) g6; |
1085 | 0 | int64_t f0g7 = f0 * (int64_t) g7; |
1086 | 0 | int64_t f0g8 = f0 * (int64_t) g8; |
1087 | 0 | int64_t f0g9 = f0 * (int64_t) g9; |
1088 | 0 | int64_t f1g0 = f1 * (int64_t) g0; |
1089 | 0 | int64_t f1g1_2 = f1_2 * (int64_t) g1; |
1090 | 0 | int64_t f1g2 = f1 * (int64_t) g2; |
1091 | 0 | int64_t f1g3_2 = f1_2 * (int64_t) g3; |
1092 | 0 | int64_t f1g4 = f1 * (int64_t) g4; |
1093 | 0 | int64_t f1g5_2 = f1_2 * (int64_t) g5; |
1094 | 0 | int64_t f1g6 = f1 * (int64_t) g6; |
1095 | 0 | int64_t f1g7_2 = f1_2 * (int64_t) g7; |
1096 | 0 | int64_t f1g8 = f1 * (int64_t) g8; |
1097 | 0 | int64_t f1g9_38 = f1_2 * (int64_t) g9_19; |
1098 | 0 | int64_t f2g0 = f2 * (int64_t) g0; |
1099 | 0 | int64_t f2g1 = f2 * (int64_t) g1; |
1100 | 0 | int64_t f2g2 = f2 * (int64_t) g2; |
1101 | 0 | int64_t f2g3 = f2 * (int64_t) g3; |
1102 | 0 | int64_t f2g4 = f2 * (int64_t) g4; |
1103 | 0 | int64_t f2g5 = f2 * (int64_t) g5; |
1104 | 0 | int64_t f2g6 = f2 * (int64_t) g6; |
1105 | 0 | int64_t f2g7 = f2 * (int64_t) g7; |
1106 | 0 | int64_t f2g8_19 = f2 * (int64_t) g8_19; |
1107 | 0 | int64_t f2g9_19 = f2 * (int64_t) g9_19; |
1108 | 0 | int64_t f3g0 = f3 * (int64_t) g0; |
1109 | 0 | int64_t f3g1_2 = f3_2 * (int64_t) g1; |
1110 | 0 | int64_t f3g2 = f3 * (int64_t) g2; |
1111 | 0 | int64_t f3g3_2 = f3_2 * (int64_t) g3; |
1112 | 0 | int64_t f3g4 = f3 * (int64_t) g4; |
1113 | 0 | int64_t f3g5_2 = f3_2 * (int64_t) g5; |
1114 | 0 | int64_t f3g6 = f3 * (int64_t) g6; |
1115 | 0 | int64_t f3g7_38 = f3_2 * (int64_t) g7_19; |
1116 | 0 | int64_t f3g8_19 = f3 * (int64_t) g8_19; |
1117 | 0 | int64_t f3g9_38 = f3_2 * (int64_t) g9_19; |
1118 | 0 | int64_t f4g0 = f4 * (int64_t) g0; |
1119 | 0 | int64_t f4g1 = f4 * (int64_t) g1; |
1120 | 0 | int64_t f4g2 = f4 * (int64_t) g2; |
1121 | 0 | int64_t f4g3 = f4 * (int64_t) g3; |
1122 | 0 | int64_t f4g4 = f4 * (int64_t) g4; |
1123 | 0 | int64_t f4g5 = f4 * (int64_t) g5; |
1124 | 0 | int64_t f4g6_19 = f4 * (int64_t) g6_19; |
1125 | 0 | int64_t f4g7_19 = f4 * (int64_t) g7_19; |
1126 | 0 | int64_t f4g8_19 = f4 * (int64_t) g8_19; |
1127 | 0 | int64_t f4g9_19 = f4 * (int64_t) g9_19; |
1128 | 0 | int64_t f5g0 = f5 * (int64_t) g0; |
1129 | 0 | int64_t f5g1_2 = f5_2 * (int64_t) g1; |
1130 | 0 | int64_t f5g2 = f5 * (int64_t) g2; |
1131 | 0 | int64_t f5g3_2 = f5_2 * (int64_t) g3; |
1132 | 0 | int64_t f5g4 = f5 * (int64_t) g4; |
1133 | 0 | int64_t f5g5_38 = f5_2 * (int64_t) g5_19; |
1134 | 0 | int64_t f5g6_19 = f5 * (int64_t) g6_19; |
1135 | 0 | int64_t f5g7_38 = f5_2 * (int64_t) g7_19; |
1136 | 0 | int64_t f5g8_19 = f5 * (int64_t) g8_19; |
1137 | 0 | int64_t f5g9_38 = f5_2 * (int64_t) g9_19; |
1138 | 0 | int64_t f6g0 = f6 * (int64_t) g0; |
1139 | 0 | int64_t f6g1 = f6 * (int64_t) g1; |
1140 | 0 | int64_t f6g2 = f6 * (int64_t) g2; |
1141 | 0 | int64_t f6g3 = f6 * (int64_t) g3; |
1142 | 0 | int64_t f6g4_19 = f6 * (int64_t) g4_19; |
1143 | 0 | int64_t f6g5_19 = f6 * (int64_t) g5_19; |
1144 | 0 | int64_t f6g6_19 = f6 * (int64_t) g6_19; |
1145 | 0 | int64_t f6g7_19 = f6 * (int64_t) g7_19; |
1146 | 0 | int64_t f6g8_19 = f6 * (int64_t) g8_19; |
1147 | 0 | int64_t f6g9_19 = f6 * (int64_t) g9_19; |
1148 | 0 | int64_t f7g0 = f7 * (int64_t) g0; |
1149 | 0 | int64_t f7g1_2 = f7_2 * (int64_t) g1; |
1150 | 0 | int64_t f7g2 = f7 * (int64_t) g2; |
1151 | 0 | int64_t f7g3_38 = f7_2 * (int64_t) g3_19; |
1152 | 0 | int64_t f7g4_19 = f7 * (int64_t) g4_19; |
1153 | 0 | int64_t f7g5_38 = f7_2 * (int64_t) g5_19; |
1154 | 0 | int64_t f7g6_19 = f7 * (int64_t) g6_19; |
1155 | 0 | int64_t f7g7_38 = f7_2 * (int64_t) g7_19; |
1156 | 0 | int64_t f7g8_19 = f7 * (int64_t) g8_19; |
1157 | 0 | int64_t f7g9_38 = f7_2 * (int64_t) g9_19; |
1158 | 0 | int64_t f8g0 = f8 * (int64_t) g0; |
1159 | 0 | int64_t f8g1 = f8 * (int64_t) g1; |
1160 | 0 | int64_t f8g2_19 = f8 * (int64_t) g2_19; |
1161 | 0 | int64_t f8g3_19 = f8 * (int64_t) g3_19; |
1162 | 0 | int64_t f8g4_19 = f8 * (int64_t) g4_19; |
1163 | 0 | int64_t f8g5_19 = f8 * (int64_t) g5_19; |
1164 | 0 | int64_t f8g6_19 = f8 * (int64_t) g6_19; |
1165 | 0 | int64_t f8g7_19 = f8 * (int64_t) g7_19; |
1166 | 0 | int64_t f8g8_19 = f8 * (int64_t) g8_19; |
1167 | 0 | int64_t f8g9_19 = f8 * (int64_t) g9_19; |
1168 | 0 | int64_t f9g0 = f9 * (int64_t) g0; |
1169 | 0 | int64_t f9g1_38 = f9_2 * (int64_t) g1_19; |
1170 | 0 | int64_t f9g2_19 = f9 * (int64_t) g2_19; |
1171 | 0 | int64_t f9g3_38 = f9_2 * (int64_t) g3_19; |
1172 | 0 | int64_t f9g4_19 = f9 * (int64_t) g4_19; |
1173 | 0 | int64_t f9g5_38 = f9_2 * (int64_t) g5_19; |
1174 | 0 | int64_t f9g6_19 = f9 * (int64_t) g6_19; |
1175 | 0 | int64_t f9g7_38 = f9_2 * (int64_t) g7_19; |
1176 | 0 | int64_t f9g8_19 = f9 * (int64_t) g8_19; |
1177 | 0 | int64_t f9g9_38 = f9_2 * (int64_t) g9_19; |
1178 | 0 | int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; |
1179 | 0 | int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19; |
1180 | 0 | int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38; |
1181 | 0 | int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19; |
1182 | 0 | int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38; |
1183 | 0 | int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19; |
1184 | 0 | int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38; |
1185 | 0 | int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19; |
1186 | 0 | int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38; |
1187 | 0 | int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ; |
1188 | 0 | int64_t carry0; |
1189 | 0 | int64_t carry1; |
1190 | 0 | int64_t carry2; |
1191 | 0 | int64_t carry3; |
1192 | 0 | int64_t carry4; |
1193 | 0 | int64_t carry5; |
1194 | 0 | int64_t carry6; |
1195 | 0 | int64_t carry7; |
1196 | 0 | int64_t carry8; |
1197 | 0 | int64_t carry9; |
1198 | | |
1199 | | /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) |
1200 | | * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 |
1201 | | * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) |
1202 | | * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ |
1203 | |
|
1204 | 0 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
1205 | 0 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
1206 | | /* |h0| <= 2^25 */ |
1207 | | /* |h4| <= 2^25 */ |
1208 | | /* |h1| <= 1.71*2^59 */ |
1209 | | /* |h5| <= 1.71*2^59 */ |
1210 | |
|
1211 | 0 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
1212 | 0 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
1213 | | /* |h1| <= 2^24; from now on fits into int32 */ |
1214 | | /* |h5| <= 2^24; from now on fits into int32 */ |
1215 | | /* |h2| <= 1.41*2^60 */ |
1216 | | /* |h6| <= 1.41*2^60 */ |
1217 | |
|
1218 | 0 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
1219 | 0 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
1220 | | /* |h2| <= 2^25; from now on fits into int32 unchanged */ |
1221 | | /* |h6| <= 2^25; from now on fits into int32 unchanged */ |
1222 | | /* |h3| <= 1.71*2^59 */ |
1223 | | /* |h7| <= 1.71*2^59 */ |
1224 | |
|
1225 | 0 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
1226 | 0 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
1227 | | /* |h3| <= 2^24; from now on fits into int32 unchanged */ |
1228 | | /* |h7| <= 2^24; from now on fits into int32 unchanged */ |
1229 | | /* |h4| <= 1.72*2^34 */ |
1230 | | /* |h8| <= 1.41*2^60 */ |
1231 | |
|
1232 | 0 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
1233 | 0 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
1234 | | /* |h4| <= 2^25; from now on fits into int32 unchanged */ |
1235 | | /* |h8| <= 2^25; from now on fits into int32 unchanged */ |
1236 | | /* |h5| <= 1.01*2^24 */ |
1237 | | /* |h9| <= 1.71*2^59 */ |
1238 | |
|
1239 | 0 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
1240 | | /* |h9| <= 2^24; from now on fits into int32 unchanged */ |
1241 | | /* |h0| <= 1.1*2^39 */ |
1242 | |
|
1243 | 0 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
1244 | | /* |h0| <= 2^25; from now on fits into int32 unchanged */ |
1245 | | /* |h1| <= 1.01*2^24 */ |
1246 | |
|
1247 | 0 | h[0] = (int32_t)h0; |
1248 | 0 | h[1] = (int32_t)h1; |
1249 | 0 | h[2] = (int32_t)h2; |
1250 | 0 | h[3] = (int32_t)h3; |
1251 | 0 | h[4] = (int32_t)h4; |
1252 | 0 | h[5] = (int32_t)h5; |
1253 | 0 | h[6] = (int32_t)h6; |
1254 | 0 | h[7] = (int32_t)h7; |
1255 | 0 | h[8] = (int32_t)h8; |
1256 | 0 | h[9] = (int32_t)h9; |
1257 | 0 | } |
1258 | | |
1259 | | /* |
1260 | | * h = f * f |
1261 | | * |
1262 | | * Can overlap h with f. |
1263 | | * |
1264 | | * Preconditions: |
1265 | | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
1266 | | * |
1267 | | * Postconditions: |
1268 | | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
1269 | | * |
1270 | | * See fe_mul.c for discussion of implementation strategy. |
1271 | | */ |
1272 | | static void fe_sq(fe h, const fe f) |
1273 | 0 | { |
1274 | 0 | int32_t f0 = f[0]; |
1275 | 0 | int32_t f1 = f[1]; |
1276 | 0 | int32_t f2 = f[2]; |
1277 | 0 | int32_t f3 = f[3]; |
1278 | 0 | int32_t f4 = f[4]; |
1279 | 0 | int32_t f5 = f[5]; |
1280 | 0 | int32_t f6 = f[6]; |
1281 | 0 | int32_t f7 = f[7]; |
1282 | 0 | int32_t f8 = f[8]; |
1283 | 0 | int32_t f9 = f[9]; |
1284 | 0 | int32_t f0_2 = 2 * f0; |
1285 | 0 | int32_t f1_2 = 2 * f1; |
1286 | 0 | int32_t f2_2 = 2 * f2; |
1287 | 0 | int32_t f3_2 = 2 * f3; |
1288 | 0 | int32_t f4_2 = 2 * f4; |
1289 | 0 | int32_t f5_2 = 2 * f5; |
1290 | 0 | int32_t f6_2 = 2 * f6; |
1291 | 0 | int32_t f7_2 = 2 * f7; |
1292 | 0 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ |
1293 | 0 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ |
1294 | 0 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ |
1295 | 0 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ |
1296 | 0 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ |
1297 | 0 | int64_t f0f0 = f0 * (int64_t) f0; |
1298 | 0 | int64_t f0f1_2 = f0_2 * (int64_t) f1; |
1299 | 0 | int64_t f0f2_2 = f0_2 * (int64_t) f2; |
1300 | 0 | int64_t f0f3_2 = f0_2 * (int64_t) f3; |
1301 | 0 | int64_t f0f4_2 = f0_2 * (int64_t) f4; |
1302 | 0 | int64_t f0f5_2 = f0_2 * (int64_t) f5; |
1303 | 0 | int64_t f0f6_2 = f0_2 * (int64_t) f6; |
1304 | 0 | int64_t f0f7_2 = f0_2 * (int64_t) f7; |
1305 | 0 | int64_t f0f8_2 = f0_2 * (int64_t) f8; |
1306 | 0 | int64_t f0f9_2 = f0_2 * (int64_t) f9; |
1307 | 0 | int64_t f1f1_2 = f1_2 * (int64_t) f1; |
1308 | 0 | int64_t f1f2_2 = f1_2 * (int64_t) f2; |
1309 | 0 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; |
1310 | 0 | int64_t f1f4_2 = f1_2 * (int64_t) f4; |
1311 | 0 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; |
1312 | 0 | int64_t f1f6_2 = f1_2 * (int64_t) f6; |
1313 | 0 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; |
1314 | 0 | int64_t f1f8_2 = f1_2 * (int64_t) f8; |
1315 | 0 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; |
1316 | 0 | int64_t f2f2 = f2 * (int64_t) f2; |
1317 | 0 | int64_t f2f3_2 = f2_2 * (int64_t) f3; |
1318 | 0 | int64_t f2f4_2 = f2_2 * (int64_t) f4; |
1319 | 0 | int64_t f2f5_2 = f2_2 * (int64_t) f5; |
1320 | 0 | int64_t f2f6_2 = f2_2 * (int64_t) f6; |
1321 | 0 | int64_t f2f7_2 = f2_2 * (int64_t) f7; |
1322 | 0 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; |
1323 | 0 | int64_t f2f9_38 = f2 * (int64_t) f9_38; |
1324 | 0 | int64_t f3f3_2 = f3_2 * (int64_t) f3; |
1325 | 0 | int64_t f3f4_2 = f3_2 * (int64_t) f4; |
1326 | 0 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; |
1327 | 0 | int64_t f3f6_2 = f3_2 * (int64_t) f6; |
1328 | 0 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; |
1329 | 0 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; |
1330 | 0 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; |
1331 | 0 | int64_t f4f4 = f4 * (int64_t) f4; |
1332 | 0 | int64_t f4f5_2 = f4_2 * (int64_t) f5; |
1333 | 0 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; |
1334 | 0 | int64_t f4f7_38 = f4 * (int64_t) f7_38; |
1335 | 0 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; |
1336 | 0 | int64_t f4f9_38 = f4 * (int64_t) f9_38; |
1337 | 0 | int64_t f5f5_38 = f5 * (int64_t) f5_38; |
1338 | 0 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; |
1339 | 0 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; |
1340 | 0 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; |
1341 | 0 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; |
1342 | 0 | int64_t f6f6_19 = f6 * (int64_t) f6_19; |
1343 | 0 | int64_t f6f7_38 = f6 * (int64_t) f7_38; |
1344 | 0 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; |
1345 | 0 | int64_t f6f9_38 = f6 * (int64_t) f9_38; |
1346 | 0 | int64_t f7f7_38 = f7 * (int64_t) f7_38; |
1347 | 0 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; |
1348 | 0 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; |
1349 | 0 | int64_t f8f8_19 = f8 * (int64_t) f8_19; |
1350 | 0 | int64_t f8f9_38 = f8 * (int64_t) f9_38; |
1351 | 0 | int64_t f9f9_38 = f9 * (int64_t) f9_38; |
1352 | 0 | int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; |
1353 | 0 | int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; |
1354 | 0 | int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; |
1355 | 0 | int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; |
1356 | 0 | int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; |
1357 | 0 | int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; |
1358 | 0 | int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; |
1359 | 0 | int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; |
1360 | 0 | int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; |
1361 | 0 | int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; |
1362 | 0 | int64_t carry0; |
1363 | 0 | int64_t carry1; |
1364 | 0 | int64_t carry2; |
1365 | 0 | int64_t carry3; |
1366 | 0 | int64_t carry4; |
1367 | 0 | int64_t carry5; |
1368 | 0 | int64_t carry6; |
1369 | 0 | int64_t carry7; |
1370 | 0 | int64_t carry8; |
1371 | 0 | int64_t carry9; |
1372 | |
|
1373 | 0 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
1374 | 0 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
1375 | |
|
1376 | 0 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
1377 | 0 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
1378 | |
|
1379 | 0 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
1380 | 0 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
1381 | |
|
1382 | 0 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
1383 | 0 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
1384 | |
|
1385 | 0 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
1386 | 0 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
1387 | |
|
1388 | 0 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
1389 | |
|
1390 | 0 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
1391 | |
|
1392 | 0 | h[0] = (int32_t)h0; |
1393 | 0 | h[1] = (int32_t)h1; |
1394 | 0 | h[2] = (int32_t)h2; |
1395 | 0 | h[3] = (int32_t)h3; |
1396 | 0 | h[4] = (int32_t)h4; |
1397 | 0 | h[5] = (int32_t)h5; |
1398 | 0 | h[6] = (int32_t)h6; |
1399 | 0 | h[7] = (int32_t)h7; |
1400 | 0 | h[8] = (int32_t)h8; |
1401 | 0 | h[9] = (int32_t)h9; |
1402 | 0 | } |
1403 | | |
1404 | | static void fe_invert(fe out, const fe z) |
1405 | 0 | { |
1406 | 0 | fe t0; |
1407 | 0 | fe t1; |
1408 | 0 | fe t2; |
1409 | 0 | fe t3; |
1410 | 0 | int i; |
1411 | | |
1412 | | /* |
1413 | | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as |
1414 | | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. |
1415 | | */ |
1416 | | |
1417 | | /* t0 = z ** 2 */ |
1418 | 0 | fe_sq(t0, z); |
1419 | | |
1420 | | /* t1 = t0 ** (2 ** 2) = z ** 8 */ |
1421 | 0 | fe_sq(t1, t0); |
1422 | 0 | fe_sq(t1, t1); |
1423 | | |
1424 | | /* t1 = z * t1 = z ** 9 */ |
1425 | 0 | fe_mul(t1, z, t1); |
1426 | | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ |
1427 | 0 | fe_mul(t0, t0, t1); |
1428 | | |
1429 | | /* t2 = t0 ** 2 = z ** 22 */ |
1430 | 0 | fe_sq(t2, t0); |
1431 | | |
1432 | | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ |
1433 | 0 | fe_mul(t1, t1, t2); |
1434 | | |
1435 | | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ |
1436 | 0 | fe_sq(t2, t1); |
1437 | 0 | for (i = 1; i < 5; ++i) { |
1438 | 0 | fe_sq(t2, t2); |
1439 | 0 | } |
1440 | | |
1441 | | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ |
1442 | 0 | fe_mul(t1, t2, t1); |
1443 | | |
1444 | | /* Continuing similarly... */ |
1445 | | |
1446 | | /* t2 = z ** (2 ** 20 - 1) */ |
1447 | 0 | fe_sq(t2, t1); |
1448 | 0 | for (i = 1; i < 10; ++i) { |
1449 | 0 | fe_sq(t2, t2); |
1450 | 0 | } |
1451 | 0 | fe_mul(t2, t2, t1); |
1452 | | |
1453 | | /* t2 = z ** (2 ** 40 - 1) */ |
1454 | 0 | fe_sq(t3, t2); |
1455 | 0 | for (i = 1; i < 20; ++i) { |
1456 | 0 | fe_sq(t3, t3); |
1457 | 0 | } |
1458 | 0 | fe_mul(t2, t3, t2); |
1459 | | |
1460 | | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ |
1461 | 0 | for (i = 0; i < 10; ++i) { |
1462 | 0 | fe_sq(t2, t2); |
1463 | 0 | } |
1464 | | /* t1 = z ** (2 ** 50 - 1) */ |
1465 | 0 | fe_mul(t1, t2, t1); |
1466 | | |
1467 | | /* t2 = z ** (2 ** 100 - 1) */ |
1468 | 0 | fe_sq(t2, t1); |
1469 | 0 | for (i = 1; i < 50; ++i) { |
1470 | 0 | fe_sq(t2, t2); |
1471 | 0 | } |
1472 | 0 | fe_mul(t2, t2, t1); |
1473 | | |
1474 | | /* t2 = z ** (2 ** 200 - 1) */ |
1475 | 0 | fe_sq(t3, t2); |
1476 | 0 | for (i = 1; i < 100; ++i) { |
1477 | 0 | fe_sq(t3, t3); |
1478 | 0 | } |
1479 | 0 | fe_mul(t2, t3, t2); |
1480 | | |
1481 | | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ |
1482 | 0 | fe_sq(t2, t2); |
1483 | 0 | for (i = 1; i < 50; ++i) { |
1484 | 0 | fe_sq(t2, t2); |
1485 | 0 | } |
1486 | | |
1487 | | /* t1 = z ** (2 ** 250 - 1) */ |
1488 | 0 | fe_mul(t1, t2, t1); |
1489 | | |
1490 | | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ |
1491 | 0 | fe_sq(t1, t1); |
1492 | 0 | for (i = 1; i < 5; ++i) { |
1493 | 0 | fe_sq(t1, t1); |
1494 | 0 | } |
1495 | | |
1496 | | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ |
1497 | 0 | fe_mul(out, t1, t0); |
1498 | 0 | } |
1499 | | |
1500 | | /* |
1501 | | * h = -f |
1502 | | * |
1503 | | * Preconditions: |
1504 | | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
1505 | | * |
1506 | | * Postconditions: |
1507 | | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
1508 | | */ |
1509 | | static void fe_neg(fe h, const fe f) |
1510 | 0 | { |
1511 | 0 | unsigned i; |
1512 | |
|
1513 | 0 | for (i = 0; i < 10; i++) { |
1514 | 0 | h[i] = -f[i]; |
1515 | 0 | } |
1516 | 0 | } |
1517 | | |
1518 | | /* |
1519 | | * Replace (f,g) with (g,g) if b == 1; |
1520 | | * replace (f,g) with (f,g) if b == 0. |
1521 | | * |
1522 | | * Preconditions: b in {0,1}. |
1523 | | */ |
1524 | | static void fe_cmov(fe f, const fe g, unsigned b) |
1525 | 0 | { |
1526 | 0 | size_t i; |
1527 | |
|
1528 | 0 | b = 0-b; |
1529 | 0 | for (i = 0; i < 10; i++) { |
1530 | 0 | int32_t x = f[i] ^ g[i]; |
1531 | 0 | x &= b; |
1532 | 0 | f[i] ^= x; |
1533 | 0 | } |
1534 | 0 | } |
1535 | | |
1536 | | /* |
1537 | | * return 0 if f == 0 |
1538 | | * return 1 if f != 0 |
1539 | | * |
1540 | | * Preconditions: |
1541 | | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
1542 | | */ |
1543 | | static int fe_isnonzero(const fe f) |
1544 | 0 | { |
1545 | 0 | uint8_t s[32]; |
1546 | 0 | static const uint8_t zero[32] = {0}; |
1547 | |
|
1548 | 0 | fe_tobytes(s, f); |
1549 | |
|
1550 | 0 | return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; |
1551 | 0 | } |
1552 | | |
1553 | | /* |
1554 | | * return 1 if f is in {1,3,5,...,q-2} |
1555 | | * return 0 if f is in {0,2,4,...,q-1} |
1556 | | * |
1557 | | * Preconditions: |
1558 | | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
1559 | | */ |
1560 | | static int fe_isnegative(const fe f) |
1561 | 0 | { |
1562 | 0 | uint8_t s[32]; |
1563 | |
|
1564 | 0 | fe_tobytes(s, f); |
1565 | 0 | return s[0] & 1; |
1566 | 0 | } |
1567 | | |
1568 | | /* |
1569 | | * h = 2 * f * f |
1570 | | * |
1571 | | * Can overlap h with f. |
1572 | | * |
1573 | | * Preconditions: |
1574 | | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |
1575 | | * |
1576 | | * Postconditions: |
1577 | | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. |
1578 | | * |
1579 | | * See fe_mul.c for discussion of implementation strategy. |
1580 | | */ |
1581 | | static void fe_sq2(fe h, const fe f) |
1582 | 0 | { |
1583 | 0 | int32_t f0 = f[0]; |
1584 | 0 | int32_t f1 = f[1]; |
1585 | 0 | int32_t f2 = f[2]; |
1586 | 0 | int32_t f3 = f[3]; |
1587 | 0 | int32_t f4 = f[4]; |
1588 | 0 | int32_t f5 = f[5]; |
1589 | 0 | int32_t f6 = f[6]; |
1590 | 0 | int32_t f7 = f[7]; |
1591 | 0 | int32_t f8 = f[8]; |
1592 | 0 | int32_t f9 = f[9]; |
1593 | 0 | int32_t f0_2 = 2 * f0; |
1594 | 0 | int32_t f1_2 = 2 * f1; |
1595 | 0 | int32_t f2_2 = 2 * f2; |
1596 | 0 | int32_t f3_2 = 2 * f3; |
1597 | 0 | int32_t f4_2 = 2 * f4; |
1598 | 0 | int32_t f5_2 = 2 * f5; |
1599 | 0 | int32_t f6_2 = 2 * f6; |
1600 | 0 | int32_t f7_2 = 2 * f7; |
1601 | 0 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ |
1602 | 0 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ |
1603 | 0 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ |
1604 | 0 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ |
1605 | 0 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ |
1606 | 0 | int64_t f0f0 = f0 * (int64_t) f0; |
1607 | 0 | int64_t f0f1_2 = f0_2 * (int64_t) f1; |
1608 | 0 | int64_t f0f2_2 = f0_2 * (int64_t) f2; |
1609 | 0 | int64_t f0f3_2 = f0_2 * (int64_t) f3; |
1610 | 0 | int64_t f0f4_2 = f0_2 * (int64_t) f4; |
1611 | 0 | int64_t f0f5_2 = f0_2 * (int64_t) f5; |
1612 | 0 | int64_t f0f6_2 = f0_2 * (int64_t) f6; |
1613 | 0 | int64_t f0f7_2 = f0_2 * (int64_t) f7; |
1614 | 0 | int64_t f0f8_2 = f0_2 * (int64_t) f8; |
1615 | 0 | int64_t f0f9_2 = f0_2 * (int64_t) f9; |
1616 | 0 | int64_t f1f1_2 = f1_2 * (int64_t) f1; |
1617 | 0 | int64_t f1f2_2 = f1_2 * (int64_t) f2; |
1618 | 0 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; |
1619 | 0 | int64_t f1f4_2 = f1_2 * (int64_t) f4; |
1620 | 0 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; |
1621 | 0 | int64_t f1f6_2 = f1_2 * (int64_t) f6; |
1622 | 0 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; |
1623 | 0 | int64_t f1f8_2 = f1_2 * (int64_t) f8; |
1624 | 0 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; |
1625 | 0 | int64_t f2f2 = f2 * (int64_t) f2; |
1626 | 0 | int64_t f2f3_2 = f2_2 * (int64_t) f3; |
1627 | 0 | int64_t f2f4_2 = f2_2 * (int64_t) f4; |
1628 | 0 | int64_t f2f5_2 = f2_2 * (int64_t) f5; |
1629 | 0 | int64_t f2f6_2 = f2_2 * (int64_t) f6; |
1630 | 0 | int64_t f2f7_2 = f2_2 * (int64_t) f7; |
1631 | 0 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; |
1632 | 0 | int64_t f2f9_38 = f2 * (int64_t) f9_38; |
1633 | 0 | int64_t f3f3_2 = f3_2 * (int64_t) f3; |
1634 | 0 | int64_t f3f4_2 = f3_2 * (int64_t) f4; |
1635 | 0 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; |
1636 | 0 | int64_t f3f6_2 = f3_2 * (int64_t) f6; |
1637 | 0 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; |
1638 | 0 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; |
1639 | 0 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; |
1640 | 0 | int64_t f4f4 = f4 * (int64_t) f4; |
1641 | 0 | int64_t f4f5_2 = f4_2 * (int64_t) f5; |
1642 | 0 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; |
1643 | 0 | int64_t f4f7_38 = f4 * (int64_t) f7_38; |
1644 | 0 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; |
1645 | 0 | int64_t f4f9_38 = f4 * (int64_t) f9_38; |
1646 | 0 | int64_t f5f5_38 = f5 * (int64_t) f5_38; |
1647 | 0 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; |
1648 | 0 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; |
1649 | 0 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; |
1650 | 0 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; |
1651 | 0 | int64_t f6f6_19 = f6 * (int64_t) f6_19; |
1652 | 0 | int64_t f6f7_38 = f6 * (int64_t) f7_38; |
1653 | 0 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; |
1654 | 0 | int64_t f6f9_38 = f6 * (int64_t) f9_38; |
1655 | 0 | int64_t f7f7_38 = f7 * (int64_t) f7_38; |
1656 | 0 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; |
1657 | 0 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; |
1658 | 0 | int64_t f8f8_19 = f8 * (int64_t) f8_19; |
1659 | 0 | int64_t f8f9_38 = f8 * (int64_t) f9_38; |
1660 | 0 | int64_t f9f9_38 = f9 * (int64_t) f9_38; |
1661 | 0 | int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; |
1662 | 0 | int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; |
1663 | 0 | int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; |
1664 | 0 | int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; |
1665 | 0 | int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; |
1666 | 0 | int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; |
1667 | 0 | int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; |
1668 | 0 | int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; |
1669 | 0 | int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; |
1670 | 0 | int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; |
1671 | 0 | int64_t carry0; |
1672 | 0 | int64_t carry1; |
1673 | 0 | int64_t carry2; |
1674 | 0 | int64_t carry3; |
1675 | 0 | int64_t carry4; |
1676 | 0 | int64_t carry5; |
1677 | 0 | int64_t carry6; |
1678 | 0 | int64_t carry7; |
1679 | 0 | int64_t carry8; |
1680 | 0 | int64_t carry9; |
1681 | |
|
1682 | 0 | h0 += h0; |
1683 | 0 | h1 += h1; |
1684 | 0 | h2 += h2; |
1685 | 0 | h3 += h3; |
1686 | 0 | h4 += h4; |
1687 | 0 | h5 += h5; |
1688 | 0 | h6 += h6; |
1689 | 0 | h7 += h7; |
1690 | 0 | h8 += h8; |
1691 | 0 | h9 += h9; |
1692 | |
|
1693 | 0 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
1694 | 0 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
1695 | |
|
1696 | 0 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
1697 | 0 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
1698 | |
|
1699 | 0 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
1700 | 0 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
1701 | |
|
1702 | 0 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
1703 | 0 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
1704 | |
|
1705 | 0 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
1706 | 0 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
1707 | |
|
1708 | 0 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
1709 | |
|
1710 | 0 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
1711 | |
|
1712 | 0 | h[0] = (int32_t)h0; |
1713 | 0 | h[1] = (int32_t)h1; |
1714 | 0 | h[2] = (int32_t)h2; |
1715 | 0 | h[3] = (int32_t)h3; |
1716 | 0 | h[4] = (int32_t)h4; |
1717 | 0 | h[5] = (int32_t)h5; |
1718 | 0 | h[6] = (int32_t)h6; |
1719 | 0 | h[7] = (int32_t)h7; |
1720 | 0 | h[8] = (int32_t)h8; |
1721 | 0 | h[9] = (int32_t)h9; |
1722 | 0 | } |
1723 | | |
1724 | | static void fe_pow22523(fe out, const fe z) |
1725 | 0 | { |
1726 | 0 | fe t0; |
1727 | 0 | fe t1; |
1728 | 0 | fe t2; |
1729 | 0 | int i; |
1730 | |
|
1731 | 0 | fe_sq(t0, z); |
1732 | 0 | fe_sq(t1, t0); |
1733 | 0 | for (i = 1; i < 2; ++i) { |
1734 | 0 | fe_sq(t1, t1); |
1735 | 0 | } |
1736 | 0 | fe_mul(t1, z, t1); |
1737 | 0 | fe_mul(t0, t0, t1); |
1738 | 0 | fe_sq(t0, t0); |
1739 | 0 | fe_mul(t0, t1, t0); |
1740 | 0 | fe_sq(t1, t0); |
1741 | 0 | for (i = 1; i < 5; ++i) { |
1742 | 0 | fe_sq(t1, t1); |
1743 | 0 | } |
1744 | 0 | fe_mul(t0, t1, t0); |
1745 | 0 | fe_sq(t1, t0); |
1746 | 0 | for (i = 1; i < 10; ++i) { |
1747 | 0 | fe_sq(t1, t1); |
1748 | 0 | } |
1749 | 0 | fe_mul(t1, t1, t0); |
1750 | 0 | fe_sq(t2, t1); |
1751 | 0 | for (i = 1; i < 20; ++i) { |
1752 | 0 | fe_sq(t2, t2); |
1753 | 0 | } |
1754 | 0 | fe_mul(t1, t2, t1); |
1755 | 0 | fe_sq(t1, t1); |
1756 | 0 | for (i = 1; i < 10; ++i) { |
1757 | 0 | fe_sq(t1, t1); |
1758 | 0 | } |
1759 | 0 | fe_mul(t0, t1, t0); |
1760 | 0 | fe_sq(t1, t0); |
1761 | 0 | for (i = 1; i < 50; ++i) { |
1762 | 0 | fe_sq(t1, t1); |
1763 | 0 | } |
1764 | 0 | fe_mul(t1, t1, t0); |
1765 | 0 | fe_sq(t2, t1); |
1766 | 0 | for (i = 1; i < 100; ++i) { |
1767 | 0 | fe_sq(t2, t2); |
1768 | 0 | } |
1769 | 0 | fe_mul(t1, t2, t1); |
1770 | 0 | fe_sq(t1, t1); |
1771 | 0 | for (i = 1; i < 50; ++i) { |
1772 | 0 | fe_sq(t1, t1); |
1773 | 0 | } |
1774 | 0 | fe_mul(t0, t1, t0); |
1775 | 0 | fe_sq(t0, t0); |
1776 | 0 | for (i = 1; i < 2; ++i) { |
1777 | 0 | fe_sq(t0, t0); |
1778 | 0 | } |
1779 | 0 | fe_mul(out, t0, z); |
1780 | 0 | } |
1781 | | |
1782 | | /* |
1783 | | * ge means group element. |
1784 | | * |
1785 | | * Here the group is the set of pairs (x,y) of field elements (see fe.h) |
1786 | | * satisfying -x^2 + y^2 = 1 + d x^2y^2 |
1787 | | * where d = -121665/121666. |
1788 | | * |
1789 | | * Representations: |
1790 | | * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z |
1791 | | * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT |
1792 | | * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T |
1793 | | * ge_precomp (Duif): (y+x,y-x,2dxy) |
1794 | | */ |
1795 | | typedef struct { |
1796 | | fe X; |
1797 | | fe Y; |
1798 | | fe Z; |
1799 | | } ge_p2; |
1800 | | |
1801 | | typedef struct { |
1802 | | fe X; |
1803 | | fe Y; |
1804 | | fe Z; |
1805 | | fe T; |
1806 | | } ge_p3; |
1807 | | |
1808 | | typedef struct { |
1809 | | fe X; |
1810 | | fe Y; |
1811 | | fe Z; |
1812 | | fe T; |
1813 | | } ge_p1p1; |
1814 | | |
1815 | | typedef struct { |
1816 | | fe yplusx; |
1817 | | fe yminusx; |
1818 | | fe xy2d; |
1819 | | } ge_precomp; |
1820 | | |
1821 | | typedef struct { |
1822 | | fe YplusX; |
1823 | | fe YminusX; |
1824 | | fe Z; |
1825 | | fe T2d; |
1826 | | } ge_cached; |
1827 | | |
1828 | | static void ge_tobytes(uint8_t *s, const ge_p2 *h) |
1829 | 0 | { |
1830 | 0 | fe recip; |
1831 | 0 | fe x; |
1832 | 0 | fe y; |
1833 | |
|
1834 | 0 | fe_invert(recip, h->Z); |
1835 | 0 | fe_mul(x, h->X, recip); |
1836 | 0 | fe_mul(y, h->Y, recip); |
1837 | 0 | fe_tobytes(s, y); |
1838 | 0 | s[31] ^= fe_isnegative(x) << 7; |
1839 | 0 | } |
1840 | | |
1841 | | static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) |
1842 | 0 | { |
1843 | 0 | fe recip; |
1844 | 0 | fe x; |
1845 | 0 | fe y; |
1846 | |
|
1847 | 0 | fe_invert(recip, h->Z); |
1848 | 0 | fe_mul(x, h->X, recip); |
1849 | 0 | fe_mul(y, h->Y, recip); |
1850 | 0 | fe_tobytes(s, y); |
1851 | 0 | s[31] ^= fe_isnegative(x) << 7; |
1852 | 0 | } |
1853 | | |
1854 | | static const fe d = { |
1855 | | -10913610, 13857413, -15372611, 6949391, 114729, |
1856 | | -8787816, -6275908, -3247719, -18696448, -12055116 |
1857 | | }; |
1858 | | |
1859 | | static const fe sqrtm1 = { |
1860 | | -32595792, -7943725, 9377950, 3500415, 12389472, |
1861 | | -272473, -25146209, -2005654, 326686, 11406482 |
1862 | | }; |
1863 | | |
1864 | | static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) |
1865 | 0 | { |
1866 | 0 | fe u; |
1867 | 0 | fe v; |
1868 | 0 | fe v3; |
1869 | 0 | fe vxx; |
1870 | 0 | fe check; |
1871 | |
|
1872 | 0 | fe_frombytes(h->Y, s); |
1873 | 0 | fe_1(h->Z); |
1874 | 0 | fe_sq(u, h->Y); |
1875 | 0 | fe_mul(v, u, d); |
1876 | 0 | fe_sub(u, u, h->Z); /* u = y^2-1 */ |
1877 | 0 | fe_add(v, v, h->Z); /* v = dy^2+1 */ |
1878 | |
|
1879 | 0 | fe_sq(v3, v); |
1880 | 0 | fe_mul(v3, v3, v); /* v3 = v^3 */ |
1881 | 0 | fe_sq(h->X, v3); |
1882 | 0 | fe_mul(h->X, h->X, v); |
1883 | 0 | fe_mul(h->X, h->X, u); /* x = uv^7 */ |
1884 | |
|
1885 | 0 | fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ |
1886 | 0 | fe_mul(h->X, h->X, v3); |
1887 | 0 | fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ |
1888 | |
|
1889 | 0 | fe_sq(vxx, h->X); |
1890 | 0 | fe_mul(vxx, vxx, v); |
1891 | 0 | fe_sub(check, vxx, u); /* vx^2-u */ |
1892 | 0 | if (fe_isnonzero(check)) { |
1893 | 0 | fe_add(check, vxx, u); /* vx^2+u */ |
1894 | 0 | if (fe_isnonzero(check)) { |
1895 | 0 | return -1; |
1896 | 0 | } |
1897 | 0 | fe_mul(h->X, h->X, sqrtm1); |
1898 | 0 | } |
1899 | | |
1900 | 0 | if (fe_isnegative(h->X) != (s[31] >> 7)) { |
1901 | 0 | fe_neg(h->X, h->X); |
1902 | 0 | } |
1903 | |
|
1904 | 0 | fe_mul(h->T, h->X, h->Y); |
1905 | 0 | return 0; |
1906 | 0 | } |
1907 | | |
1908 | | static void ge_p2_0(ge_p2 *h) |
1909 | 0 | { |
1910 | 0 | fe_0(h->X); |
1911 | 0 | fe_1(h->Y); |
1912 | 0 | fe_1(h->Z); |
1913 | 0 | } |
1914 | | |
1915 | | static void ge_p3_0(ge_p3 *h) |
1916 | 0 | { |
1917 | 0 | fe_0(h->X); |
1918 | 0 | fe_1(h->Y); |
1919 | 0 | fe_1(h->Z); |
1920 | 0 | fe_0(h->T); |
1921 | 0 | } |
1922 | | |
1923 | | static void ge_precomp_0(ge_precomp *h) |
1924 | 0 | { |
1925 | 0 | fe_1(h->yplusx); |
1926 | 0 | fe_1(h->yminusx); |
1927 | 0 | fe_0(h->xy2d); |
1928 | 0 | } |
1929 | | |
1930 | | /* r = p */ |
1931 | | static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) |
1932 | 0 | { |
1933 | 0 | fe_copy(r->X, p->X); |
1934 | 0 | fe_copy(r->Y, p->Y); |
1935 | 0 | fe_copy(r->Z, p->Z); |
1936 | 0 | } |
1937 | | |
1938 | | static const fe d2 = { |
1939 | | -21827239, -5839606, -30745221, 13898782, 229458, |
1940 | | 15978800, -12551817, -6495438, 29715968, 9444199 |
1941 | | }; |
1942 | | |
1943 | | /* r = p */ |
1944 | | static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) |
1945 | 0 | { |
1946 | 0 | fe_add(r->YplusX, p->Y, p->X); |
1947 | 0 | fe_sub(r->YminusX, p->Y, p->X); |
1948 | 0 | fe_copy(r->Z, p->Z); |
1949 | 0 | fe_mul(r->T2d, p->T, d2); |
1950 | 0 | } |
1951 | | |
1952 | | /* r = p */ |
1953 | | static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) |
1954 | 0 | { |
1955 | 0 | fe_mul(r->X, p->X, p->T); |
1956 | 0 | fe_mul(r->Y, p->Y, p->Z); |
1957 | 0 | fe_mul(r->Z, p->Z, p->T); |
1958 | 0 | } |
1959 | | |
1960 | | /* r = p */ |
1961 | | static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) |
1962 | 0 | { |
1963 | 0 | fe_mul(r->X, p->X, p->T); |
1964 | 0 | fe_mul(r->Y, p->Y, p->Z); |
1965 | 0 | fe_mul(r->Z, p->Z, p->T); |
1966 | 0 | fe_mul(r->T, p->X, p->Y); |
1967 | 0 | } |
1968 | | |
1969 | | /* r = 2 * p */ |
1970 | | static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) |
1971 | 0 | { |
1972 | 0 | fe t0; |
1973 | |
|
1974 | 0 | fe_sq(r->X, p->X); |
1975 | 0 | fe_sq(r->Z, p->Y); |
1976 | 0 | fe_sq2(r->T, p->Z); |
1977 | 0 | fe_add(r->Y, p->X, p->Y); |
1978 | 0 | fe_sq(t0, r->Y); |
1979 | 0 | fe_add(r->Y, r->Z, r->X); |
1980 | 0 | fe_sub(r->Z, r->Z, r->X); |
1981 | 0 | fe_sub(r->X, t0, r->Y); |
1982 | 0 | fe_sub(r->T, r->T, r->Z); |
1983 | 0 | } |
1984 | | |
1985 | | /* r = 2 * p */ |
1986 | | static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) |
1987 | 0 | { |
1988 | 0 | ge_p2 q; |
1989 | 0 | ge_p3_to_p2(&q, p); |
1990 | 0 | ge_p2_dbl(r, &q); |
1991 | 0 | } |
1992 | | |
1993 | | /* r = p + q */ |
1994 | | static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) |
1995 | 0 | { |
1996 | 0 | fe t0; |
1997 | |
|
1998 | 0 | fe_add(r->X, p->Y, p->X); |
1999 | 0 | fe_sub(r->Y, p->Y, p->X); |
2000 | 0 | fe_mul(r->Z, r->X, q->yplusx); |
2001 | 0 | fe_mul(r->Y, r->Y, q->yminusx); |
2002 | 0 | fe_mul(r->T, q->xy2d, p->T); |
2003 | 0 | fe_add(t0, p->Z, p->Z); |
2004 | 0 | fe_sub(r->X, r->Z, r->Y); |
2005 | 0 | fe_add(r->Y, r->Z, r->Y); |
2006 | 0 | fe_add(r->Z, t0, r->T); |
2007 | 0 | fe_sub(r->T, t0, r->T); |
2008 | 0 | } |
2009 | | |
2010 | | /* r = p - q */ |
2011 | | static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) |
2012 | 0 | { |
2013 | 0 | fe t0; |
2014 | |
|
2015 | 0 | fe_add(r->X, p->Y, p->X); |
2016 | 0 | fe_sub(r->Y, p->Y, p->X); |
2017 | 0 | fe_mul(r->Z, r->X, q->yminusx); |
2018 | 0 | fe_mul(r->Y, r->Y, q->yplusx); |
2019 | 0 | fe_mul(r->T, q->xy2d, p->T); |
2020 | 0 | fe_add(t0, p->Z, p->Z); |
2021 | 0 | fe_sub(r->X, r->Z, r->Y); |
2022 | 0 | fe_add(r->Y, r->Z, r->Y); |
2023 | 0 | fe_sub(r->Z, t0, r->T); |
2024 | 0 | fe_add(r->T, t0, r->T); |
2025 | 0 | } |
2026 | | |
2027 | | /* r = p + q */ |
2028 | | static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) |
2029 | 0 | { |
2030 | 0 | fe t0; |
2031 | |
|
2032 | 0 | fe_add(r->X, p->Y, p->X); |
2033 | 0 | fe_sub(r->Y, p->Y, p->X); |
2034 | 0 | fe_mul(r->Z, r->X, q->YplusX); |
2035 | 0 | fe_mul(r->Y, r->Y, q->YminusX); |
2036 | 0 | fe_mul(r->T, q->T2d, p->T); |
2037 | 0 | fe_mul(r->X, p->Z, q->Z); |
2038 | 0 | fe_add(t0, r->X, r->X); |
2039 | 0 | fe_sub(r->X, r->Z, r->Y); |
2040 | 0 | fe_add(r->Y, r->Z, r->Y); |
2041 | 0 | fe_add(r->Z, t0, r->T); |
2042 | 0 | fe_sub(r->T, t0, r->T); |
2043 | 0 | } |
2044 | | |
2045 | | /* r = p - q */ |
2046 | | static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) |
2047 | 0 | { |
2048 | 0 | fe t0; |
2049 | |
|
2050 | 0 | fe_add(r->X, p->Y, p->X); |
2051 | 0 | fe_sub(r->Y, p->Y, p->X); |
2052 | 0 | fe_mul(r->Z, r->X, q->YminusX); |
2053 | 0 | fe_mul(r->Y, r->Y, q->YplusX); |
2054 | 0 | fe_mul(r->T, q->T2d, p->T); |
2055 | 0 | fe_mul(r->X, p->Z, q->Z); |
2056 | 0 | fe_add(t0, r->X, r->X); |
2057 | 0 | fe_sub(r->X, r->Z, r->Y); |
2058 | 0 | fe_add(r->Y, r->Z, r->Y); |
2059 | 0 | fe_sub(r->Z, t0, r->T); |
2060 | 0 | fe_add(r->T, t0, r->T); |
2061 | 0 | } |
2062 | | |
2063 | | static uint8_t equal(signed char b, signed char c) |
2064 | 0 | { |
2065 | 0 | uint8_t ub = b; |
2066 | 0 | uint8_t uc = c; |
2067 | 0 | uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ |
2068 | 0 | uint32_t y = x; /* 0: yes; 1..255: no */ |
2069 | 0 | y -= 1; /* 4294967295: yes; 0..254: no */ |
2070 | 0 | y >>= 31; /* 1: yes; 0: no */ |
2071 | 0 | return y; |
2072 | 0 | } |
2073 | | |
2074 | | static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) |
2075 | 0 | { |
2076 | 0 | fe_cmov(t->yplusx, u->yplusx, b); |
2077 | 0 | fe_cmov(t->yminusx, u->yminusx, b); |
2078 | 0 | fe_cmov(t->xy2d, u->xy2d, b); |
2079 | 0 | } |
2080 | | |
2081 | | /* k25519Precomp[i][j] = (j+1)*256^i*B */ |
2082 | | static const ge_precomp k25519Precomp[32][8] = { |
2083 | | { |
2084 | | { |
2085 | | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, |
2086 | | 27544626, -11754271, -6079156, 2047605}, |
2087 | | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, |
2088 | | 5043384, 19500929, -15469378}, |
2089 | | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, |
2090 | | 29287919, 11864899, -24514362, -4438546}, |
2091 | | }, |
2092 | | { |
2093 | | {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, |
2094 | | -11717903, -3814571, -358445, -10211303}, |
2095 | | {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, |
2096 | | -15616551, 11189268, -26829678, -5319081}, |
2097 | | {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, |
2098 | | -3128826, -9541118, -15472047, -4166697}, |
2099 | | }, |
2100 | | { |
2101 | | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, |
2102 | | 27787600, -14772189, 28944400, -1550024}, |
2103 | | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, |
2104 | | 16354577, -11775962, 7689662, 11199574}, |
2105 | | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, |
2106 | | 7512774, 10017326, -17749093, -9920357}, |
2107 | | }, |
2108 | | { |
2109 | | {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, |
2110 | | -28926210, 15006023, 3284568, -6276540}, |
2111 | | {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, |
2112 | | 7464579, 9656445, 13059162, 10374397}, |
2113 | | {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, |
2114 | | -3839045, -641708, -101325}, |
2115 | | }, |
2116 | | { |
2117 | | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, |
2118 | | 32867885, 14515107, -15438304, 10819380}, |
2119 | | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, |
2120 | | 12483688, -12668491, 5581306}, |
2121 | | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, |
2122 | | 28542350, 13850243, -23678021, -15815942}, |
2123 | | }, |
2124 | | { |
2125 | | {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, |
2126 | | -19188627, -15224819, -9818940, -12085777}, |
2127 | | {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, |
2128 | | -15689887, 1762328, 14866737}, |
2129 | | {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, |
2130 | | -28236412, 3959421, 27914454, 4383652}, |
2131 | | }, |
2132 | | { |
2133 | | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, |
2134 | | 5230134, -23952439, -15175766}, |
2135 | | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, |
2136 | | 20654025, 16520125, 30598449, 7715701}, |
2137 | | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, |
2138 | | -31400660, 1370708, 29794553, -1409300}, |
2139 | | }, |
2140 | | { |
2141 | | {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, |
2142 | | 30290735, 10876454, -33154098, 2381726}, |
2143 | | {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, |
2144 | | -6236617, 3696005, -32300832, 15351955}, |
2145 | | {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, |
2146 | | -32961401, -2970515, 29551813, 10109425}, |
2147 | | }, |
2148 | | }, |
2149 | | { |
2150 | | { |
2151 | | {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, |
2152 | | -2378284, -1627556, 10092783, -4764171}, |
2153 | | {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, |
2154 | | -32508754, 12005538, -17810127, 12803510}, |
2155 | | {17228999, -15661624, -1233527, 300140, -1224870, -11714777, |
2156 | | 30364213, -9038194, 18016357, 4397660}, |
2157 | | }, |
2158 | | { |
2159 | | {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, |
2160 | | -26619106, 14544525, -17477504, 982639}, |
2161 | | {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, |
2162 | | -4120128, -21047696, 9934963}, |
2163 | | {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, |
2164 | | -14747930, 4559895, -30123922, -10897950}, |
2165 | | }, |
2166 | | { |
2167 | | {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, |
2168 | | 24191034, 4541697, -13338309, 5500568}, |
2169 | | {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, |
2170 | | -17430592, 12264343, 10874051, 13524335}, |
2171 | | {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, |
2172 | | 5080568, -22528059, 5376628}, |
2173 | | }, |
2174 | | { |
2175 | | {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, |
2176 | | -22321305, -9447443, 4535768, 1569007}, |
2177 | | {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, |
2178 | | -30494562, 3044290, 31848280, 12543772}, |
2179 | | {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, |
2180 | | -27377195, -2062731, 7718482, 14474653}, |
2181 | | }, |
2182 | | { |
2183 | | {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, |
2184 | | -7236665, 24316168, -5253567}, |
2185 | | {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, |
2186 | | 33040651, -13424532, -20729456, 8321686}, |
2187 | | {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, |
2188 | | 23845965, -11874838, -9984458, 608372}, |
2189 | | }, |
2190 | | { |
2191 | | {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, |
2192 | | 1123968, -6780577, 27229399, 23887}, |
2193 | | {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, |
2194 | | 12797024, -6440308, -1633405, 16678954}, |
2195 | | {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, |
2196 | | -1508144, -4795045, -17169265, 4904953}, |
2197 | | }, |
2198 | | { |
2199 | | {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, |
2200 | | 5169211, 16191880, 2128236, -4326833}, |
2201 | | {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, |
2202 | | -29806336, 916033, -6882542, -2986532}, |
2203 | | {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, |
2204 | | 285431, 2763829, 15736322, 4143876}, |
2205 | | }, |
2206 | | { |
2207 | | {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, |
2208 | | -14594663, 23527084, -16458268}, |
2209 | | {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, |
2210 | | -32625340, 4087881, -15188911, -14416214}, |
2211 | | {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, |
2212 | | 4357868, -4774191, -16323038}, |
2213 | | }, |
2214 | | }, |
2215 | | { |
2216 | | { |
2217 | | {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, |
2218 | | 23365147, -3949732, 7390890, 2759800}, |
2219 | | {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, |
2220 | | -4264057, 1244380, -12919645}, |
2221 | | {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, |
2222 | | 9208236, 15886429, 16489664}, |
2223 | | }, |
2224 | | { |
2225 | | {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, |
2226 | | -13693198, 398369, -30606455, -712933}, |
2227 | | {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, |
2228 | | 13348553, 12076947, -30836462, 5113182}, |
2229 | | {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, |
2230 | | -30341101, -7336386, 13847711, 5387222}, |
2231 | | }, |
2232 | | { |
2233 | | {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, |
2234 | | 8763061, 3617786, -19600662, 10370991}, |
2235 | | {20246567, -14369378, 22358229, -543712, 18507283, -10413996, |
2236 | | 14554437, -8746092, 32232924, 16763880}, |
2237 | | {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, |
2238 | | 11094161, 15689506, 3140038, -16510092}, |
2239 | | }, |
2240 | | { |
2241 | | {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, |
2242 | | -27224800, 9448613, -28774454, 366295}, |
2243 | | {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, |
2244 | | 28344573, 8041113, 719605, 11671788}, |
2245 | | {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, |
2246 | | -15266516, 27000813, -10195553}, |
2247 | | }, |
2248 | | { |
2249 | | {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, |
2250 | | 5336097, 6750977, -14521026}, |
2251 | | {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, |
2252 | | 1695823, -8819122, 8169720, 16220347}, |
2253 | | {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, |
2254 | | -11144307, -2627664, -5990708, -14166033}, |
2255 | | }, |
2256 | | { |
2257 | | {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, |
2258 | | 27884329, 2847284, 2655861, 1738395}, |
2259 | | {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, |
2260 | | 21651608, -3239336, -19087449, -11005278}, |
2261 | | {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, |
2262 | | 5821408, 10478196, 8544890}, |
2263 | | }, |
2264 | | { |
2265 | | {32173121, -16129311, 24896207, 3921497, 22579056, -3410854, |
2266 | | 19270449, 12217473, 17789017, -3395995}, |
2267 | | {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, |
2268 | | 15479401, -3853233, 30460520, 1052596}, |
2269 | | {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, |
2270 | | 27491595, -4612359, 3179268, -9478891}, |
2271 | | }, |
2272 | | { |
2273 | | {31947069, -14366651, -4640583, -15339921, -15125977, -6039709, |
2274 | | -14756777, -16411740, 19072640, -9511060}, |
2275 | | {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, |
2276 | | 5977896, -5215017, 473099, 5040608}, |
2277 | | {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, |
2278 | | 28326862, 1721092, -19558642, -3131606}, |
2279 | | }, |
2280 | | }, |
2281 | | { |
2282 | | { |
2283 | | {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, |
2284 | | 8076149, -27868496, 11538389}, |
2285 | | {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, |
2286 | | 8754525, 7446702, -5676054, 5797016}, |
2287 | | {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, |
2288 | | 2014099, -9050574, -2369172, -5877341}, |
2289 | | }, |
2290 | | { |
2291 | | {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, |
2292 | | 1192730, -3714199, 15123619, 10811505}, |
2293 | | {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, |
2294 | | 15776356, -28886779, -11974553}, |
2295 | | {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, |
2296 | | -20654173, -16484855, 4714547, -9600655}, |
2297 | | }, |
2298 | | { |
2299 | | {15200332, 8368572, 19679101, 15970074, -31872674, 1959451, |
2300 | | 24611599, -4543832, -11745876, 12340220}, |
2301 | | {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, |
2302 | | 9613953, 8241152, 15370987, 9608631}, |
2303 | | {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, |
2304 | | 15866074, -28210621, -8814099}, |
2305 | | }, |
2306 | | { |
2307 | | {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, |
2308 | | 858697, 20571223, 8420556}, |
2309 | | {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, |
2310 | | 33531827, 12516406, -21574435, -12476749}, |
2311 | | {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, |
2312 | | 7256740, 8791136, 15069930}, |
2313 | | }, |
2314 | | { |
2315 | | {1276410, -9371918, 22949635, -16322807, -23493039, -5702186, |
2316 | | 14711875, 4874229, -30663140, -2331391}, |
2317 | | {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, |
2318 | | -7912378, -33069337, 9234253}, |
2319 | | {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, |
2320 | | 31559055, -11609587, 18979186, 13396066}, |
2321 | | }, |
2322 | | { |
2323 | | {24474287, 4968103, 22267082, 4407354, 24063882, -8325180, |
2324 | | -18816887, 13594782, 33514650, 7021958}, |
2325 | | {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, |
2326 | | -25948728, -3916677, -21480480, 12868082}, |
2327 | | {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, |
2328 | | -21446107, 2244500, -12455797, -8089383}, |
2329 | | }, |
2330 | | { |
2331 | | {-30595528, 13793479, -5852820, 319136, -25723172, -6263899, |
2332 | | 33086546, 8957937, -15233648, 5540521}, |
2333 | | {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, |
2334 | | -23710744, -1568984, -16128528, -14962807}, |
2335 | | {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, |
2336 | | 892185, -11513277, -15205948}, |
2337 | | }, |
2338 | | { |
2339 | | {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, |
2340 | | 4763127, -19179614, 5867134}, |
2341 | | {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, |
2342 | | 27846559, 5931263, -29749703, -16108455}, |
2343 | | {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, |
2344 | | 7283490, -15148073, -19526700, 7734629}, |
2345 | | }, |
2346 | | }, |
2347 | | { |
2348 | | { |
2349 | | {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, |
2350 | | 7585295, -3176626, 18549497, 15302069}, |
2351 | | {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, |
2352 | | 10458790, -6418461, -8872242, 8424746}, |
2353 | | {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, |
2354 | | 19206234, 7134917, -11284482, -828919}, |
2355 | | }, |
2356 | | { |
2357 | | {11334899, -9218022, 8025293, 12707519, 17523892, -10476071, |
2358 | | 10243738, -14685461, -5066034, 16498837}, |
2359 | | {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, |
2360 | | -14124238, 6536641, 10543906}, |
2361 | | {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, |
2362 | | -2669190, -16625574, -27235709, 8876771}, |
2363 | | }, |
2364 | | { |
2365 | | {-25742899, -12566864, -15649966, -846607, -33026686, -796288, |
2366 | | -33481822, 15824474, -604426, -9039817}, |
2367 | | {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, |
2368 | | -4890037, 1657394, 3084098}, |
2369 | | {10477963, -7470260, 12119566, -13250805, 29016247, -5365589, |
2370 | | 31280319, 14396151, -30233575, 15272409}, |
2371 | | }, |
2372 | | { |
2373 | | {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, |
2374 | | -25173957, -12636138, -25014757, 1950504}, |
2375 | | {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, |
2376 | | -8384306, -8767532, 15341279, 8373727}, |
2377 | | {28685821, 7759505, -14378516, -12002860, -31971820, 4079242, |
2378 | | 298136, -10232602, -2878207, 15190420}, |
2379 | | }, |
2380 | | { |
2381 | | {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, |
2382 | | 8669718, 2742393, -26033313, -6875003}, |
2383 | | {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, |
2384 | | 9291594, -16247779, -12154742, 6048605}, |
2385 | | {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, |
2386 | | 13934231, 5128323, 11213262, 9168384}, |
2387 | | }, |
2388 | | { |
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4038 | | { |
4039 | | {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, |
4040 | | 9328700, 29955601, -11678310}, |
4041 | | {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, |
4042 | | -25892142, -12635595, -9917575, 6216608}, |
4043 | | {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, |
4044 | | 24822830, -6146567, -26767480, 7525079}, |
4045 | | }, |
4046 | | { |
4047 | | {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, |
4048 | | -910336, -2782495, -19386633, 11994101}, |
4049 | | {21691500, -13624626, -641331, -14367021, 3285881, -3483596, |
4050 | | -25064666, 9718258, -7477437, 13381418}, |
4051 | | {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, |
4052 | | 23111648, -6375247, 28535282, 15779576}, |
4053 | | }, |
4054 | | { |
4055 | | {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, |
4056 | | -14068454, 12021730, 9955285, -16303356}, |
4057 | | {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, |
4058 | | -18426029, 9924399, 20194861, 13380996}, |
4059 | | {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, |
4060 | | -1984914, 15707771, 26342023, 10146099}, |
4061 | | }, |
4062 | | }, |
4063 | | { |
4064 | | { |
4065 | | {-26016874, -219943, 21339191, -41388, 19745256, -2878700, |
4066 | | -29637280, 2227040, 21612326, -545728}, |
4067 | | {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, |
4068 | | 25764461, 12243797, -20856566, 11649658}, |
4069 | | {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, |
4070 | | 6114064, 33514190, 2333242}, |
4071 | | }, |
4072 | | { |
4073 | | {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, |
4074 | | -6679750, -12670638, 24350578, -13450001}, |
4075 | | {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, |
4076 | | -31536088, -10406836, 8317860, 12352766}, |
4077 | | {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, |
4078 | | -23552096, -2287550, 20712163, 6719373}, |
4079 | | }, |
4080 | | { |
4081 | | {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, |
4082 | | -3763210, 26224235, -3297458}, |
4083 | | {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, |
4084 | | 21728352, 9493610, 18620611, -16428628}, |
4085 | | {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, |
4086 | | -5269471, -9725556, -30701573, -16479657}, |
4087 | | }, |
4088 | | { |
4089 | | {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, |
4090 | | 12248509, -5240639, 13735342, 1934062}, |
4091 | | {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, |
4092 | | -15136294, -3765346, -21277997, 5473616}, |
4093 | | {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, |
4094 | | -7125085, 12469656, 29111212, -5451014}, |
4095 | | }, |
4096 | | { |
4097 | | {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, |
4098 | | 24367466, 6388839, -10295587, 452383}, |
4099 | | {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, |
4100 | | -24236251, -5915248, 15766062, 8407814}, |
4101 | | {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, |
4102 | | -8917023, -4388953, -8067909, 2276718}, |
4103 | | }, |
4104 | | { |
4105 | | {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, |
4106 | | -23827587, 5096219, 22740376, -7303417}, |
4107 | | {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, |
4108 | | 24051124, 13742383, -15637599, 13295222}, |
4109 | | {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, |
4110 | | -17720195, -4612972, -4451357, -14669444}, |
4111 | | }, |
4112 | | { |
4113 | | {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, |
4114 | | -2469266, -4141880, 7770569, 9620597}, |
4115 | | {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, |
4116 | | -1694323, -33502340, -14767970}, |
4117 | | {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, |
4118 | | 1220118, 30494170, -11440799}, |
4119 | | }, |
4120 | | { |
4121 | | {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, |
4122 | | -26739026, 926050, -1684339, -13333647}, |
4123 | | {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, |
4124 | | 9021034, 9078865, 3353509, 4033511}, |
4125 | | {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, |
4126 | | 23161163, 8839127, 27485041, 7356032}, |
4127 | | }, |
4128 | | }, |
4129 | | { |
4130 | | { |
4131 | | {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, |
4132 | | 2625015, 28431036, -16771834}, |
4133 | | {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, |
4134 | | -22545972, 14150565, 15970762, 4099461}, |
4135 | | {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, |
4136 | | 13617293, -9937143, 11465739, 8317062}, |
4137 | | }, |
4138 | | { |
4139 | | {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, |
4140 | | 14898637, 3848455, 20969334, -5157516}, |
4141 | | {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, |
4142 | | -21610826, -3649888, 11177095, 14989547}, |
4143 | | {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, |
4144 | | 13515641, 2581286, -28487508, 9930240}, |
4145 | | }, |
4146 | | { |
4147 | | {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, |
4148 | | 18345767, -13403753, 16291481, -5314038}, |
4149 | | {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, |
4150 | | 6957617, 4368891, 9788741}, |
4151 | | {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, |
4152 | | -21722536, -8613148, 16250552, -11111103}, |
4153 | | }, |
4154 | | { |
4155 | | {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, |
4156 | | 10604807, -30190403, 4782747}, |
4157 | | {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, |
4158 | | -9981571, 4383045, 22546403, 437323}, |
4159 | | {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, |
4160 | | 27343084, 2786261, -30633590, -14097016}, |
4161 | | }, |
4162 | | { |
4163 | | {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, |
4164 | | -19690631, 2355319, -19284671, -6114373}, |
4165 | | {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, |
4166 | | 18952177, 15496498, -29380133, 11754228}, |
4167 | | {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, |
4168 | | 7141596, 11724556, 22761615, -10134141}, |
4169 | | }, |
4170 | | { |
4171 | | {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, |
4172 | | -28741185, -12227393, 32851222, 11717399}, |
4173 | | {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, |
4174 | | 31474879, 3483633, -1193175, -4030831}, |
4175 | | {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, |
4176 | | 33142652, 6546660, -19985279, -3948376}, |
4177 | | }, |
4178 | | { |
4179 | | {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, |
4180 | | -8537131, -12833048, -30772034, -15486313}, |
4181 | | {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, |
4182 | | -31135347, -16049879, 10928917, 3011958}, |
4183 | | {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, |
4184 | | -30831056, -12805180, 18008031, 10258577}, |
4185 | | }, |
4186 | | { |
4187 | | {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, |
4188 | | -1853465, 1367120, 25127874, 6671743}, |
4189 | | {29701166, -14373934, -10878120, 9279288, -17568, 13127210, |
4190 | | 21382910, 11042292, 25838796, 4642684}, |
4191 | | {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, |
4192 | | 30468147, -13900640, 18423289, 4177476}, |
4193 | | }, |
4194 | | }, |
4195 | | }; |
4196 | | |
4197 | | static uint8_t negative(signed char b) |
4198 | 0 | { |
4199 | 0 | uint32_t x = b; |
4200 | |
|
4201 | 0 | x >>= 31; /* 1: yes; 0: no */ |
4202 | 0 | return x; |
4203 | 0 | } |
4204 | | |
4205 | | static void table_select(ge_precomp *t, int pos, signed char b) |
4206 | 0 | { |
4207 | 0 | ge_precomp minust; |
4208 | 0 | uint8_t bnegative = negative(b); |
4209 | 0 | uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); |
4210 | |
|
4211 | 0 | ge_precomp_0(t); |
4212 | 0 | cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); |
4213 | 0 | cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); |
4214 | 0 | cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); |
4215 | 0 | cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); |
4216 | 0 | cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); |
4217 | 0 | cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); |
4218 | 0 | cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); |
4219 | 0 | cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); |
4220 | 0 | fe_copy(minust.yplusx, t->yminusx); |
4221 | 0 | fe_copy(minust.yminusx, t->yplusx); |
4222 | 0 | fe_neg(minust.xy2d, t->xy2d); |
4223 | 0 | cmov(t, &minust, bnegative); |
4224 | 0 | } |
4225 | | |
4226 | | /* |
4227 | | * h = a * B |
4228 | | * |
4229 | | * where a = a[0]+256*a[1]+...+256^31 a[31] |
4230 | | * B is the Ed25519 base point (x,4/5) with x positive. |
4231 | | * |
4232 | | * Preconditions: |
4233 | | * a[31] <= 127 |
4234 | | */ |
4235 | | static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) |
4236 | 0 | { |
4237 | 0 | signed char e[64]; |
4238 | 0 | signed char carry; |
4239 | 0 | ge_p1p1 r; |
4240 | 0 | ge_p2 s; |
4241 | 0 | ge_precomp t; |
4242 | 0 | int i; |
4243 | |
|
4244 | 0 | for (i = 0; i < 32; ++i) { |
4245 | 0 | e[2 * i + 0] = (a[i] >> 0) & 15; |
4246 | 0 | e[2 * i + 1] = (a[i] >> 4) & 15; |
4247 | 0 | } |
4248 | | /* each e[i] is between 0 and 15 */ |
4249 | | /* e[63] is between 0 and 7 */ |
4250 | |
|
4251 | 0 | carry = 0; |
4252 | 0 | for (i = 0; i < 63; ++i) { |
4253 | 0 | e[i] += carry; |
4254 | 0 | carry = e[i] + 8; |
4255 | 0 | carry >>= 4; |
4256 | 0 | e[i] -= carry << 4; |
4257 | 0 | } |
4258 | 0 | e[63] += carry; |
4259 | | /* each e[i] is between -8 and 8 */ |
4260 | |
|
4261 | 0 | ge_p3_0(h); |
4262 | 0 | for (i = 1; i < 64; i += 2) { |
4263 | 0 | table_select(&t, i / 2, e[i]); |
4264 | 0 | ge_madd(&r, h, &t); |
4265 | 0 | ge_p1p1_to_p3(h, &r); |
4266 | 0 | } |
4267 | |
|
4268 | 0 | ge_p3_dbl(&r, h); |
4269 | 0 | ge_p1p1_to_p2(&s, &r); |
4270 | 0 | ge_p2_dbl(&r, &s); |
4271 | 0 | ge_p1p1_to_p2(&s, &r); |
4272 | 0 | ge_p2_dbl(&r, &s); |
4273 | 0 | ge_p1p1_to_p2(&s, &r); |
4274 | 0 | ge_p2_dbl(&r, &s); |
4275 | 0 | ge_p1p1_to_p3(h, &r); |
4276 | |
|
4277 | 0 | for (i = 0; i < 64; i += 2) { |
4278 | 0 | table_select(&t, i / 2, e[i]); |
4279 | 0 | ge_madd(&r, h, &t); |
4280 | 0 | ge_p1p1_to_p3(h, &r); |
4281 | 0 | } |
4282 | |
|
4283 | 0 | OPENSSL_cleanse(e, sizeof(e)); |
4284 | 0 | } |
4285 | | |
4286 | | #if !defined(BASE_2_51_IMPLEMENTED) |
4287 | | /* |
4288 | | * Replace (f,g) with (g,f) if b == 1; |
4289 | | * replace (f,g) with (f,g) if b == 0. |
4290 | | * |
4291 | | * Preconditions: b in {0,1}. |
4292 | | */ |
4293 | | static void fe_cswap(fe f, fe g, unsigned int b) |
4294 | | { |
4295 | | size_t i; |
4296 | | |
4297 | | b = 0-b; |
4298 | | for (i = 0; i < 10; i++) { |
4299 | | int32_t x = f[i] ^ g[i]; |
4300 | | x &= b; |
4301 | | f[i] ^= x; |
4302 | | g[i] ^= x; |
4303 | | } |
4304 | | } |
4305 | | |
4306 | | /* |
4307 | | * h = f * 121666 |
4308 | | * |
4309 | | * Can overlap h with f. |
4310 | | * |
4311 | | * Preconditions: |
4312 | | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
4313 | | * |
4314 | | * Postconditions: |
4315 | | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
4316 | | */ |
4317 | | static void fe_mul121666(fe h, fe f) |
4318 | | { |
4319 | | int32_t f0 = f[0]; |
4320 | | int32_t f1 = f[1]; |
4321 | | int32_t f2 = f[2]; |
4322 | | int32_t f3 = f[3]; |
4323 | | int32_t f4 = f[4]; |
4324 | | int32_t f5 = f[5]; |
4325 | | int32_t f6 = f[6]; |
4326 | | int32_t f7 = f[7]; |
4327 | | int32_t f8 = f[8]; |
4328 | | int32_t f9 = f[9]; |
4329 | | int64_t h0 = f0 * (int64_t) 121666; |
4330 | | int64_t h1 = f1 * (int64_t) 121666; |
4331 | | int64_t h2 = f2 * (int64_t) 121666; |
4332 | | int64_t h3 = f3 * (int64_t) 121666; |
4333 | | int64_t h4 = f4 * (int64_t) 121666; |
4334 | | int64_t h5 = f5 * (int64_t) 121666; |
4335 | | int64_t h6 = f6 * (int64_t) 121666; |
4336 | | int64_t h7 = f7 * (int64_t) 121666; |
4337 | | int64_t h8 = f8 * (int64_t) 121666; |
4338 | | int64_t h9 = f9 * (int64_t) 121666; |
4339 | | int64_t carry0; |
4340 | | int64_t carry1; |
4341 | | int64_t carry2; |
4342 | | int64_t carry3; |
4343 | | int64_t carry4; |
4344 | | int64_t carry5; |
4345 | | int64_t carry6; |
4346 | | int64_t carry7; |
4347 | | int64_t carry8; |
4348 | | int64_t carry9; |
4349 | | |
4350 | | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; |
4351 | | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; |
4352 | | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; |
4353 | | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; |
4354 | | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; |
4355 | | |
4356 | | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; |
4357 | | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; |
4358 | | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; |
4359 | | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; |
4360 | | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; |
4361 | | |
4362 | | h[0] = (int32_t)h0; |
4363 | | h[1] = (int32_t)h1; |
4364 | | h[2] = (int32_t)h2; |
4365 | | h[3] = (int32_t)h3; |
4366 | | h[4] = (int32_t)h4; |
4367 | | h[5] = (int32_t)h5; |
4368 | | h[6] = (int32_t)h6; |
4369 | | h[7] = (int32_t)h7; |
4370 | | h[8] = (int32_t)h8; |
4371 | | h[9] = (int32_t)h9; |
4372 | | } |
4373 | | |
4374 | | static void x25519_scalar_mult_generic(uint8_t out[32], |
4375 | | const uint8_t scalar[32], |
4376 | | const uint8_t point[32]) { |
4377 | | fe x1, x2, z2, x3, z3, tmp0, tmp1; |
4378 | | uint8_t e[32]; |
4379 | | unsigned swap = 0; |
4380 | | int pos; |
4381 | | |
4382 | | memcpy(e, scalar, 32); |
4383 | | e[0] &= 248; |
4384 | | e[31] &= 127; |
4385 | | e[31] |= 64; |
4386 | | fe_frombytes(x1, point); |
4387 | | fe_1(x2); |
4388 | | fe_0(z2); |
4389 | | fe_copy(x3, x1); |
4390 | | fe_1(z3); |
4391 | | |
4392 | | for (pos = 254; pos >= 0; --pos) { |
4393 | | unsigned b = 1 & (e[pos / 8] >> (pos & 7)); |
4394 | | swap ^= b; |
4395 | | fe_cswap(x2, x3, swap); |
4396 | | fe_cswap(z2, z3, swap); |
4397 | | swap = b; |
4398 | | fe_sub(tmp0, x3, z3); |
4399 | | fe_sub(tmp1, x2, z2); |
4400 | | fe_add(x2, x2, z2); |
4401 | | fe_add(z2, x3, z3); |
4402 | | fe_mul(z3, tmp0, x2); |
4403 | | fe_mul(z2, z2, tmp1); |
4404 | | fe_sq(tmp0, tmp1); |
4405 | | fe_sq(tmp1, x2); |
4406 | | fe_add(x3, z3, z2); |
4407 | | fe_sub(z2, z3, z2); |
4408 | | fe_mul(x2, tmp1, tmp0); |
4409 | | fe_sub(tmp1, tmp1, tmp0); |
4410 | | fe_sq(z2, z2); |
4411 | | fe_mul121666(z3, tmp1); |
4412 | | fe_sq(x3, x3); |
4413 | | fe_add(tmp0, tmp0, z3); |
4414 | | fe_mul(z3, x1, z2); |
4415 | | fe_mul(z2, tmp1, tmp0); |
4416 | | } |
4417 | | |
4418 | | fe_invert(z2, z2); |
4419 | | fe_mul(x2, x2, z2); |
4420 | | fe_tobytes(out, x2); |
4421 | | |
4422 | | OPENSSL_cleanse(e, sizeof(e)); |
4423 | | } |
4424 | | |
4425 | | static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], |
4426 | | const uint8_t point[32]) { |
4427 | | x25519_scalar_mult_generic(out, scalar, point); |
4428 | | } |
4429 | | #endif |
4430 | | |
4431 | | static void slide(signed char *r, const uint8_t *a) |
4432 | 0 | { |
4433 | 0 | int i; |
4434 | 0 | int b; |
4435 | 0 | int k; |
4436 | |
|
4437 | 0 | for (i = 0; i < 256; ++i) { |
4438 | 0 | r[i] = 1 & (a[i >> 3] >> (i & 7)); |
4439 | 0 | } |
4440 | |
|
4441 | 0 | for (i = 0; i < 256; ++i) { |
4442 | 0 | if (r[i]) { |
4443 | 0 | for (b = 1; b <= 6 && i + b < 256; ++b) { |
4444 | 0 | if (r[i + b]) { |
4445 | 0 | if (r[i] + (r[i + b] << b) <= 15) { |
4446 | 0 | r[i] += r[i + b] << b; |
4447 | 0 | r[i + b] = 0; |
4448 | 0 | } else if (r[i] - (r[i + b] << b) >= -15) { |
4449 | 0 | r[i] -= r[i + b] << b; |
4450 | 0 | for (k = i + b; k < 256; ++k) { |
4451 | 0 | if (!r[k]) { |
4452 | 0 | r[k] = 1; |
4453 | 0 | break; |
4454 | 0 | } |
4455 | 0 | r[k] = 0; |
4456 | 0 | } |
4457 | 0 | } else { |
4458 | 0 | break; |
4459 | 0 | } |
4460 | 0 | } |
4461 | 0 | } |
4462 | 0 | } |
4463 | 0 | } |
4464 | 0 | } |
4465 | | |
4466 | | static const ge_precomp Bi[8] = { |
4467 | | { |
4468 | | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, |
4469 | | -11754271, -6079156, 2047605}, |
4470 | | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, |
4471 | | 5043384, 19500929, -15469378}, |
4472 | | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, |
4473 | | 11864899, -24514362, -4438546}, |
4474 | | }, |
4475 | | { |
4476 | | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, |
4477 | | -14772189, 28944400, -1550024}, |
4478 | | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, |
4479 | | -11775962, 7689662, 11199574}, |
4480 | | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, |
4481 | | 10017326, -17749093, -9920357}, |
4482 | | }, |
4483 | | { |
4484 | | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, |
4485 | | 14515107, -15438304, 10819380}, |
4486 | | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, |
4487 | | 12483688, -12668491, 5581306}, |
4488 | | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, |
4489 | | 13850243, -23678021, -15815942}, |
4490 | | }, |
4491 | | { |
4492 | | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, |
4493 | | 5230134, -23952439, -15175766}, |
4494 | | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, |
4495 | | 16520125, 30598449, 7715701}, |
4496 | | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, |
4497 | | 1370708, 29794553, -1409300}, |
4498 | | }, |
4499 | | { |
4500 | | {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, |
4501 | | -1361450, -13062696, 13821877}, |
4502 | | {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, |
4503 | | -7212327, 18853322, -14220951}, |
4504 | | {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, |
4505 | | -10431137, 2207753, -3209784}, |
4506 | | }, |
4507 | | { |
4508 | | {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, |
4509 | | -663000, -31111463, -16132436}, |
4510 | | {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, |
4511 | | 15725684, 171356, 6466918}, |
4512 | | {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, |
4513 | | -14088058, -30714912, 16193877}, |
4514 | | }, |
4515 | | { |
4516 | | {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, |
4517 | | 4729455, -18074513, 9256800}, |
4518 | | {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, |
4519 | | 9761698, -19827198, 630305}, |
4520 | | {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, |
4521 | | -15960994, -2449256, -14291300}, |
4522 | | }, |
4523 | | { |
4524 | | {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, |
4525 | | 15033784, 25105118, -7894876}, |
4526 | | {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, |
4527 | | 1573892, -2625887, 2198790, -15804619}, |
4528 | | {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, |
4529 | | -16236442, -32461234, -12290683}, |
4530 | | }, |
4531 | | }; |
4532 | | |
4533 | | /* |
4534 | | * r = a * A + b * B |
4535 | | * |
4536 | | * where a = a[0]+256*a[1]+...+256^31 a[31]. |
4537 | | * and b = b[0]+256*b[1]+...+256^31 b[31]. |
4538 | | * B is the Ed25519 base point (x,4/5) with x positive. |
4539 | | */ |
4540 | | static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, |
4541 | | const ge_p3 *A, const uint8_t *b) |
4542 | 0 | { |
4543 | 0 | signed char aslide[256]; |
4544 | 0 | signed char bslide[256]; |
4545 | 0 | ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ |
4546 | 0 | ge_p1p1 t; |
4547 | 0 | ge_p3 u; |
4548 | 0 | ge_p3 A2; |
4549 | 0 | int i; |
4550 | |
|
4551 | 0 | slide(aslide, a); |
4552 | 0 | slide(bslide, b); |
4553 | |
|
4554 | 0 | ge_p3_to_cached(&Ai[0], A); |
4555 | 0 | ge_p3_dbl(&t, A); |
4556 | 0 | ge_p1p1_to_p3(&A2, &t); |
4557 | 0 | ge_add(&t, &A2, &Ai[0]); |
4558 | 0 | ge_p1p1_to_p3(&u, &t); |
4559 | 0 | ge_p3_to_cached(&Ai[1], &u); |
4560 | 0 | ge_add(&t, &A2, &Ai[1]); |
4561 | 0 | ge_p1p1_to_p3(&u, &t); |
4562 | 0 | ge_p3_to_cached(&Ai[2], &u); |
4563 | 0 | ge_add(&t, &A2, &Ai[2]); |
4564 | 0 | ge_p1p1_to_p3(&u, &t); |
4565 | 0 | ge_p3_to_cached(&Ai[3], &u); |
4566 | 0 | ge_add(&t, &A2, &Ai[3]); |
4567 | 0 | ge_p1p1_to_p3(&u, &t); |
4568 | 0 | ge_p3_to_cached(&Ai[4], &u); |
4569 | 0 | ge_add(&t, &A2, &Ai[4]); |
4570 | 0 | ge_p1p1_to_p3(&u, &t); |
4571 | 0 | ge_p3_to_cached(&Ai[5], &u); |
4572 | 0 | ge_add(&t, &A2, &Ai[5]); |
4573 | 0 | ge_p1p1_to_p3(&u, &t); |
4574 | 0 | ge_p3_to_cached(&Ai[6], &u); |
4575 | 0 | ge_add(&t, &A2, &Ai[6]); |
4576 | 0 | ge_p1p1_to_p3(&u, &t); |
4577 | 0 | ge_p3_to_cached(&Ai[7], &u); |
4578 | |
|
4579 | 0 | ge_p2_0(r); |
4580 | |
|
4581 | 0 | for (i = 255; i >= 0; --i) { |
4582 | 0 | if (aslide[i] || bslide[i]) { |
4583 | 0 | break; |
4584 | 0 | } |
4585 | 0 | } |
4586 | |
|
4587 | 0 | for (; i >= 0; --i) { |
4588 | 0 | ge_p2_dbl(&t, r); |
4589 | |
|
4590 | 0 | if (aslide[i] > 0) { |
4591 | 0 | ge_p1p1_to_p3(&u, &t); |
4592 | 0 | ge_add(&t, &u, &Ai[aslide[i] / 2]); |
4593 | 0 | } else if (aslide[i] < 0) { |
4594 | 0 | ge_p1p1_to_p3(&u, &t); |
4595 | 0 | ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); |
4596 | 0 | } |
4597 | |
|
4598 | 0 | if (bslide[i] > 0) { |
4599 | 0 | ge_p1p1_to_p3(&u, &t); |
4600 | 0 | ge_madd(&t, &u, &Bi[bslide[i] / 2]); |
4601 | 0 | } else if (bslide[i] < 0) { |
4602 | 0 | ge_p1p1_to_p3(&u, &t); |
4603 | 0 | ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); |
4604 | 0 | } |
4605 | |
|
4606 | 0 | ge_p1p1_to_p2(r, &t); |
4607 | 0 | } |
4608 | 0 | } |
4609 | | |
4610 | | /* |
4611 | | * The set of scalars is \Z/l |
4612 | | * where l = 2^252 + 27742317777372353535851937790883648493. |
4613 | | * |
4614 | | * Input: |
4615 | | * s[0]+256*s[1]+...+256^63*s[63] = s |
4616 | | * |
4617 | | * Output: |
4618 | | * s[0]+256*s[1]+...+256^31*s[31] = s mod l |
4619 | | * where l = 2^252 + 27742317777372353535851937790883648493. |
4620 | | * Overwrites s in place. |
4621 | | */ |
4622 | | static void x25519_sc_reduce(uint8_t *s) |
4623 | 0 | { |
4624 | 0 | int64_t s0 = kBottom21Bits & load_3(s); |
4625 | 0 | int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5); |
4626 | 0 | int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2); |
4627 | 0 | int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7); |
4628 | 0 | int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4); |
4629 | 0 | int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1); |
4630 | 0 | int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6); |
4631 | 0 | int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3); |
4632 | 0 | int64_t s8 = kBottom21Bits & load_3(s + 21); |
4633 | 0 | int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5); |
4634 | 0 | int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2); |
4635 | 0 | int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7); |
4636 | 0 | int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4); |
4637 | 0 | int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1); |
4638 | 0 | int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6); |
4639 | 0 | int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3); |
4640 | 0 | int64_t s16 = kBottom21Bits & load_3(s + 42); |
4641 | 0 | int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5); |
4642 | 0 | int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2); |
4643 | 0 | int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7); |
4644 | 0 | int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4); |
4645 | 0 | int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1); |
4646 | 0 | int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6); |
4647 | 0 | int64_t s23 = (load_4(s + 60) >> 3); |
4648 | 0 | int64_t carry0; |
4649 | 0 | int64_t carry1; |
4650 | 0 | int64_t carry2; |
4651 | 0 | int64_t carry3; |
4652 | 0 | int64_t carry4; |
4653 | 0 | int64_t carry5; |
4654 | 0 | int64_t carry6; |
4655 | 0 | int64_t carry7; |
4656 | 0 | int64_t carry8; |
4657 | 0 | int64_t carry9; |
4658 | 0 | int64_t carry10; |
4659 | 0 | int64_t carry11; |
4660 | 0 | int64_t carry12; |
4661 | 0 | int64_t carry13; |
4662 | 0 | int64_t carry14; |
4663 | 0 | int64_t carry15; |
4664 | 0 | int64_t carry16; |
4665 | |
|
4666 | 0 | s11 += s23 * 666643; |
4667 | 0 | s12 += s23 * 470296; |
4668 | 0 | s13 += s23 * 654183; |
4669 | 0 | s14 -= s23 * 997805; |
4670 | 0 | s15 += s23 * 136657; |
4671 | 0 | s16 -= s23 * 683901; |
4672 | 0 | s23 = 0; |
4673 | |
|
4674 | 0 | s10 += s22 * 666643; |
4675 | 0 | s11 += s22 * 470296; |
4676 | 0 | s12 += s22 * 654183; |
4677 | 0 | s13 -= s22 * 997805; |
4678 | 0 | s14 += s22 * 136657; |
4679 | 0 | s15 -= s22 * 683901; |
4680 | 0 | s22 = 0; |
4681 | |
|
4682 | 0 | s9 += s21 * 666643; |
4683 | 0 | s10 += s21 * 470296; |
4684 | 0 | s11 += s21 * 654183; |
4685 | 0 | s12 -= s21 * 997805; |
4686 | 0 | s13 += s21 * 136657; |
4687 | 0 | s14 -= s21 * 683901; |
4688 | 0 | s21 = 0; |
4689 | |
|
4690 | 0 | s8 += s20 * 666643; |
4691 | 0 | s9 += s20 * 470296; |
4692 | 0 | s10 += s20 * 654183; |
4693 | 0 | s11 -= s20 * 997805; |
4694 | 0 | s12 += s20 * 136657; |
4695 | 0 | s13 -= s20 * 683901; |
4696 | 0 | s20 = 0; |
4697 | |
|
4698 | 0 | s7 += s19 * 666643; |
4699 | 0 | s8 += s19 * 470296; |
4700 | 0 | s9 += s19 * 654183; |
4701 | 0 | s10 -= s19 * 997805; |
4702 | 0 | s11 += s19 * 136657; |
4703 | 0 | s12 -= s19 * 683901; |
4704 | 0 | s19 = 0; |
4705 | |
|
4706 | 0 | s6 += s18 * 666643; |
4707 | 0 | s7 += s18 * 470296; |
4708 | 0 | s8 += s18 * 654183; |
4709 | 0 | s9 -= s18 * 997805; |
4710 | 0 | s10 += s18 * 136657; |
4711 | 0 | s11 -= s18 * 683901; |
4712 | 0 | s18 = 0; |
4713 | |
|
4714 | 0 | carry6 = (s6 + (1 << 20)) >> 21; |
4715 | 0 | s7 += carry6; |
4716 | 0 | s6 -= carry6 * (1 << 21); |
4717 | 0 | carry8 = (s8 + (1 << 20)) >> 21; |
4718 | 0 | s9 += carry8; |
4719 | 0 | s8 -= carry8 * (1 << 21); |
4720 | 0 | carry10 = (s10 + (1 << 20)) >> 21; |
4721 | 0 | s11 += carry10; |
4722 | 0 | s10 -= carry10 * (1 << 21); |
4723 | 0 | carry12 = (s12 + (1 << 20)) >> 21; |
4724 | 0 | s13 += carry12; |
4725 | 0 | s12 -= carry12 * (1 << 21); |
4726 | 0 | carry14 = (s14 + (1 << 20)) >> 21; |
4727 | 0 | s15 += carry14; |
4728 | 0 | s14 -= carry14 * (1 << 21); |
4729 | 0 | carry16 = (s16 + (1 << 20)) >> 21; |
4730 | 0 | s17 += carry16; |
4731 | 0 | s16 -= carry16 * (1 << 21); |
4732 | |
|
4733 | 0 | carry7 = (s7 + (1 << 20)) >> 21; |
4734 | 0 | s8 += carry7; |
4735 | 0 | s7 -= carry7 * (1 << 21); |
4736 | 0 | carry9 = (s9 + (1 << 20)) >> 21; |
4737 | 0 | s10 += carry9; |
4738 | 0 | s9 -= carry9 * (1 << 21); |
4739 | 0 | carry11 = (s11 + (1 << 20)) >> 21; |
4740 | 0 | s12 += carry11; |
4741 | 0 | s11 -= carry11 * (1 << 21); |
4742 | 0 | carry13 = (s13 + (1 << 20)) >> 21; |
4743 | 0 | s14 += carry13; |
4744 | 0 | s13 -= carry13 * (1 << 21); |
4745 | 0 | carry15 = (s15 + (1 << 20)) >> 21; |
4746 | 0 | s16 += carry15; |
4747 | 0 | s15 -= carry15 * (1 << 21); |
4748 | |
|
4749 | 0 | s5 += s17 * 666643; |
4750 | 0 | s6 += s17 * 470296; |
4751 | 0 | s7 += s17 * 654183; |
4752 | 0 | s8 -= s17 * 997805; |
4753 | 0 | s9 += s17 * 136657; |
4754 | 0 | s10 -= s17 * 683901; |
4755 | 0 | s17 = 0; |
4756 | |
|
4757 | 0 | s4 += s16 * 666643; |
4758 | 0 | s5 += s16 * 470296; |
4759 | 0 | s6 += s16 * 654183; |
4760 | 0 | s7 -= s16 * 997805; |
4761 | 0 | s8 += s16 * 136657; |
4762 | 0 | s9 -= s16 * 683901; |
4763 | 0 | s16 = 0; |
4764 | |
|
4765 | 0 | s3 += s15 * 666643; |
4766 | 0 | s4 += s15 * 470296; |
4767 | 0 | s5 += s15 * 654183; |
4768 | 0 | s6 -= s15 * 997805; |
4769 | 0 | s7 += s15 * 136657; |
4770 | 0 | s8 -= s15 * 683901; |
4771 | 0 | s15 = 0; |
4772 | |
|
4773 | 0 | s2 += s14 * 666643; |
4774 | 0 | s3 += s14 * 470296; |
4775 | 0 | s4 += s14 * 654183; |
4776 | 0 | s5 -= s14 * 997805; |
4777 | 0 | s6 += s14 * 136657; |
4778 | 0 | s7 -= s14 * 683901; |
4779 | 0 | s14 = 0; |
4780 | |
|
4781 | 0 | s1 += s13 * 666643; |
4782 | 0 | s2 += s13 * 470296; |
4783 | 0 | s3 += s13 * 654183; |
4784 | 0 | s4 -= s13 * 997805; |
4785 | 0 | s5 += s13 * 136657; |
4786 | 0 | s6 -= s13 * 683901; |
4787 | 0 | s13 = 0; |
4788 | |
|
4789 | 0 | s0 += s12 * 666643; |
4790 | 0 | s1 += s12 * 470296; |
4791 | 0 | s2 += s12 * 654183; |
4792 | 0 | s3 -= s12 * 997805; |
4793 | 0 | s4 += s12 * 136657; |
4794 | 0 | s5 -= s12 * 683901; |
4795 | 0 | s12 = 0; |
4796 | |
|
4797 | 0 | carry0 = (s0 + (1 << 20)) >> 21; |
4798 | 0 | s1 += carry0; |
4799 | 0 | s0 -= carry0 * (1 << 21); |
4800 | 0 | carry2 = (s2 + (1 << 20)) >> 21; |
4801 | 0 | s3 += carry2; |
4802 | 0 | s2 -= carry2 * (1 << 21); |
4803 | 0 | carry4 = (s4 + (1 << 20)) >> 21; |
4804 | 0 | s5 += carry4; |
4805 | 0 | s4 -= carry4 * (1 << 21); |
4806 | 0 | carry6 = (s6 + (1 << 20)) >> 21; |
4807 | 0 | s7 += carry6; |
4808 | 0 | s6 -= carry6 * (1 << 21); |
4809 | 0 | carry8 = (s8 + (1 << 20)) >> 21; |
4810 | 0 | s9 += carry8; |
4811 | 0 | s8 -= carry8 * (1 << 21); |
4812 | 0 | carry10 = (s10 + (1 << 20)) >> 21; |
4813 | 0 | s11 += carry10; |
4814 | 0 | s10 -= carry10 * (1 << 21); |
4815 | |
|
4816 | 0 | carry1 = (s1 + (1 << 20)) >> 21; |
4817 | 0 | s2 += carry1; |
4818 | 0 | s1 -= carry1 * (1 << 21); |
4819 | 0 | carry3 = (s3 + (1 << 20)) >> 21; |
4820 | 0 | s4 += carry3; |
4821 | 0 | s3 -= carry3 * (1 << 21); |
4822 | 0 | carry5 = (s5 + (1 << 20)) >> 21; |
4823 | 0 | s6 += carry5; |
4824 | 0 | s5 -= carry5 * (1 << 21); |
4825 | 0 | carry7 = (s7 + (1 << 20)) >> 21; |
4826 | 0 | s8 += carry7; |
4827 | 0 | s7 -= carry7 * (1 << 21); |
4828 | 0 | carry9 = (s9 + (1 << 20)) >> 21; |
4829 | 0 | s10 += carry9; |
4830 | 0 | s9 -= carry9 * (1 << 21); |
4831 | 0 | carry11 = (s11 + (1 << 20)) >> 21; |
4832 | 0 | s12 += carry11; |
4833 | 0 | s11 -= carry11 * (1 << 21); |
4834 | |
|
4835 | 0 | s0 += s12 * 666643; |
4836 | 0 | s1 += s12 * 470296; |
4837 | 0 | s2 += s12 * 654183; |
4838 | 0 | s3 -= s12 * 997805; |
4839 | 0 | s4 += s12 * 136657; |
4840 | 0 | s5 -= s12 * 683901; |
4841 | 0 | s12 = 0; |
4842 | |
|
4843 | 0 | carry0 = s0 >> 21; |
4844 | 0 | s1 += carry0; |
4845 | 0 | s0 -= carry0 * (1 << 21); |
4846 | 0 | carry1 = s1 >> 21; |
4847 | 0 | s2 += carry1; |
4848 | 0 | s1 -= carry1 * (1 << 21); |
4849 | 0 | carry2 = s2 >> 21; |
4850 | 0 | s3 += carry2; |
4851 | 0 | s2 -= carry2 * (1 << 21); |
4852 | 0 | carry3 = s3 >> 21; |
4853 | 0 | s4 += carry3; |
4854 | 0 | s3 -= carry3 * (1 << 21); |
4855 | 0 | carry4 = s4 >> 21; |
4856 | 0 | s5 += carry4; |
4857 | 0 | s4 -= carry4 * (1 << 21); |
4858 | 0 | carry5 = s5 >> 21; |
4859 | 0 | s6 += carry5; |
4860 | 0 | s5 -= carry5 * (1 << 21); |
4861 | 0 | carry6 = s6 >> 21; |
4862 | 0 | s7 += carry6; |
4863 | 0 | s6 -= carry6 * (1 << 21); |
4864 | 0 | carry7 = s7 >> 21; |
4865 | 0 | s8 += carry7; |
4866 | 0 | s7 -= carry7 * (1 << 21); |
4867 | 0 | carry8 = s8 >> 21; |
4868 | 0 | s9 += carry8; |
4869 | 0 | s8 -= carry8 * (1 << 21); |
4870 | 0 | carry9 = s9 >> 21; |
4871 | 0 | s10 += carry9; |
4872 | 0 | s9 -= carry9 * (1 << 21); |
4873 | 0 | carry10 = s10 >> 21; |
4874 | 0 | s11 += carry10; |
4875 | 0 | s10 -= carry10 * (1 << 21); |
4876 | 0 | carry11 = s11 >> 21; |
4877 | 0 | s12 += carry11; |
4878 | 0 | s11 -= carry11 * (1 << 21); |
4879 | |
|
4880 | 0 | s0 += s12 * 666643; |
4881 | 0 | s1 += s12 * 470296; |
4882 | 0 | s2 += s12 * 654183; |
4883 | 0 | s3 -= s12 * 997805; |
4884 | 0 | s4 += s12 * 136657; |
4885 | 0 | s5 -= s12 * 683901; |
4886 | 0 | s12 = 0; |
4887 | |
|
4888 | 0 | carry0 = s0 >> 21; |
4889 | 0 | s1 += carry0; |
4890 | 0 | s0 -= carry0 * (1 << 21); |
4891 | 0 | carry1 = s1 >> 21; |
4892 | 0 | s2 += carry1; |
4893 | 0 | s1 -= carry1 * (1 << 21); |
4894 | 0 | carry2 = s2 >> 21; |
4895 | 0 | s3 += carry2; |
4896 | 0 | s2 -= carry2 * (1 << 21); |
4897 | 0 | carry3 = s3 >> 21; |
4898 | 0 | s4 += carry3; |
4899 | 0 | s3 -= carry3 * (1 << 21); |
4900 | 0 | carry4 = s4 >> 21; |
4901 | 0 | s5 += carry4; |
4902 | 0 | s4 -= carry4 * (1 << 21); |
4903 | 0 | carry5 = s5 >> 21; |
4904 | 0 | s6 += carry5; |
4905 | 0 | s5 -= carry5 * (1 << 21); |
4906 | 0 | carry6 = s6 >> 21; |
4907 | 0 | s7 += carry6; |
4908 | 0 | s6 -= carry6 * (1 << 21); |
4909 | 0 | carry7 = s7 >> 21; |
4910 | 0 | s8 += carry7; |
4911 | 0 | s7 -= carry7 * (1 << 21); |
4912 | 0 | carry8 = s8 >> 21; |
4913 | 0 | s9 += carry8; |
4914 | 0 | s8 -= carry8 * (1 << 21); |
4915 | 0 | carry9 = s9 >> 21; |
4916 | 0 | s10 += carry9; |
4917 | 0 | s9 -= carry9 * (1 << 21); |
4918 | 0 | carry10 = s10 >> 21; |
4919 | 0 | s11 += carry10; |
4920 | 0 | s10 -= carry10 * (1 << 21); |
4921 | |
|
4922 | 0 | s[ 0] = (uint8_t) (s0 >> 0); |
4923 | 0 | s[ 1] = (uint8_t) (s0 >> 8); |
4924 | 0 | s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5)); |
4925 | 0 | s[ 3] = (uint8_t) (s1 >> 3); |
4926 | 0 | s[ 4] = (uint8_t) (s1 >> 11); |
4927 | 0 | s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2)); |
4928 | 0 | s[ 6] = (uint8_t) (s2 >> 6); |
4929 | 0 | s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7)); |
4930 | 0 | s[ 8] = (uint8_t) (s3 >> 1); |
4931 | 0 | s[ 9] = (uint8_t) (s3 >> 9); |
4932 | 0 | s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); |
4933 | 0 | s[11] = (uint8_t) (s4 >> 4); |
4934 | 0 | s[12] = (uint8_t) (s4 >> 12); |
4935 | 0 | s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); |
4936 | 0 | s[14] = (uint8_t) (s5 >> 7); |
4937 | 0 | s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); |
4938 | 0 | s[16] = (uint8_t) (s6 >> 2); |
4939 | 0 | s[17] = (uint8_t) (s6 >> 10); |
4940 | 0 | s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); |
4941 | 0 | s[19] = (uint8_t) (s7 >> 5); |
4942 | 0 | s[20] = (uint8_t) (s7 >> 13); |
4943 | 0 | s[21] = (uint8_t) (s8 >> 0); |
4944 | 0 | s[22] = (uint8_t) (s8 >> 8); |
4945 | 0 | s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); |
4946 | 0 | s[24] = (uint8_t) (s9 >> 3); |
4947 | 0 | s[25] = (uint8_t) (s9 >> 11); |
4948 | 0 | s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); |
4949 | 0 | s[27] = (uint8_t) (s10 >> 6); |
4950 | 0 | s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); |
4951 | 0 | s[29] = (uint8_t) (s11 >> 1); |
4952 | 0 | s[30] = (uint8_t) (s11 >> 9); |
4953 | 0 | s[31] = (uint8_t) (s11 >> 17); |
4954 | 0 | } |
4955 | | |
4956 | | /* |
4957 | | * Input: |
4958 | | * a[0]+256*a[1]+...+256^31*a[31] = a |
4959 | | * b[0]+256*b[1]+...+256^31*b[31] = b |
4960 | | * c[0]+256*c[1]+...+256^31*c[31] = c |
4961 | | * |
4962 | | * Output: |
4963 | | * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l |
4964 | | * where l = 2^252 + 27742317777372353535851937790883648493. |
4965 | | */ |
4966 | | static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, |
4967 | | const uint8_t *c) |
4968 | 0 | { |
4969 | 0 | int64_t a0 = kBottom21Bits & load_3(a); |
4970 | 0 | int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5); |
4971 | 0 | int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2); |
4972 | 0 | int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7); |
4973 | 0 | int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4); |
4974 | 0 | int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1); |
4975 | 0 | int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6); |
4976 | 0 | int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3); |
4977 | 0 | int64_t a8 = kBottom21Bits & load_3(a + 21); |
4978 | 0 | int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5); |
4979 | 0 | int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2); |
4980 | 0 | int64_t a11 = (load_4(a + 28) >> 7); |
4981 | 0 | int64_t b0 = kBottom21Bits & load_3(b); |
4982 | 0 | int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5); |
4983 | 0 | int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2); |
4984 | 0 | int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7); |
4985 | 0 | int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4); |
4986 | 0 | int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1); |
4987 | 0 | int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6); |
4988 | 0 | int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3); |
4989 | 0 | int64_t b8 = kBottom21Bits & load_3(b + 21); |
4990 | 0 | int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5); |
4991 | 0 | int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2); |
4992 | 0 | int64_t b11 = (load_4(b + 28) >> 7); |
4993 | 0 | int64_t c0 = kBottom21Bits & load_3(c); |
4994 | 0 | int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5); |
4995 | 0 | int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2); |
4996 | 0 | int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7); |
4997 | 0 | int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4); |
4998 | 0 | int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1); |
4999 | 0 | int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6); |
5000 | 0 | int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3); |
5001 | 0 | int64_t c8 = kBottom21Bits & load_3(c + 21); |
5002 | 0 | int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5); |
5003 | 0 | int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2); |
5004 | 0 | int64_t c11 = (load_4(c + 28) >> 7); |
5005 | 0 | int64_t s0; |
5006 | 0 | int64_t s1; |
5007 | 0 | int64_t s2; |
5008 | 0 | int64_t s3; |
5009 | 0 | int64_t s4; |
5010 | 0 | int64_t s5; |
5011 | 0 | int64_t s6; |
5012 | 0 | int64_t s7; |
5013 | 0 | int64_t s8; |
5014 | 0 | int64_t s9; |
5015 | 0 | int64_t s10; |
5016 | 0 | int64_t s11; |
5017 | 0 | int64_t s12; |
5018 | 0 | int64_t s13; |
5019 | 0 | int64_t s14; |
5020 | 0 | int64_t s15; |
5021 | 0 | int64_t s16; |
5022 | 0 | int64_t s17; |
5023 | 0 | int64_t s18; |
5024 | 0 | int64_t s19; |
5025 | 0 | int64_t s20; |
5026 | 0 | int64_t s21; |
5027 | 0 | int64_t s22; |
5028 | 0 | int64_t s23; |
5029 | 0 | int64_t carry0; |
5030 | 0 | int64_t carry1; |
5031 | 0 | int64_t carry2; |
5032 | 0 | int64_t carry3; |
5033 | 0 | int64_t carry4; |
5034 | 0 | int64_t carry5; |
5035 | 0 | int64_t carry6; |
5036 | 0 | int64_t carry7; |
5037 | 0 | int64_t carry8; |
5038 | 0 | int64_t carry9; |
5039 | 0 | int64_t carry10; |
5040 | 0 | int64_t carry11; |
5041 | 0 | int64_t carry12; |
5042 | 0 | int64_t carry13; |
5043 | 0 | int64_t carry14; |
5044 | 0 | int64_t carry15; |
5045 | 0 | int64_t carry16; |
5046 | 0 | int64_t carry17; |
5047 | 0 | int64_t carry18; |
5048 | 0 | int64_t carry19; |
5049 | 0 | int64_t carry20; |
5050 | 0 | int64_t carry21; |
5051 | 0 | int64_t carry22; |
5052 | |
|
5053 | 0 | s0 = c0 + a0 * b0; |
5054 | 0 | s1 = c1 + a0 * b1 + a1 * b0; |
5055 | 0 | s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; |
5056 | 0 | s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; |
5057 | 0 | s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; |
5058 | 0 | s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; |
5059 | 0 | s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; |
5060 | 0 | s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0; |
5061 | 0 | s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0; |
5062 | 0 | s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; |
5063 | 0 | s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; |
5064 | 0 | s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; |
5065 | 0 | s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; |
5066 | 0 | s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; |
5067 | 0 | s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3; |
5068 | 0 | s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4; |
5069 | 0 | s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; |
5070 | 0 | s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; |
5071 | 0 | s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; |
5072 | 0 | s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; |
5073 | 0 | s20 = a9 * b11 + a10 * b10 + a11 * b9; |
5074 | 0 | s21 = a10 * b11 + a11 * b10; |
5075 | 0 | s22 = a11 * b11; |
5076 | 0 | s23 = 0; |
5077 | |
|
5078 | 0 | carry0 = (s0 + (1 << 20)) >> 21; |
5079 | 0 | s1 += carry0; |
5080 | 0 | s0 -= carry0 * (1 << 21); |
5081 | 0 | carry2 = (s2 + (1 << 20)) >> 21; |
5082 | 0 | s3 += carry2; |
5083 | 0 | s2 -= carry2 * (1 << 21); |
5084 | 0 | carry4 = (s4 + (1 << 20)) >> 21; |
5085 | 0 | s5 += carry4; |
5086 | 0 | s4 -= carry4 * (1 << 21); |
5087 | 0 | carry6 = (s6 + (1 << 20)) >> 21; |
5088 | 0 | s7 += carry6; |
5089 | 0 | s6 -= carry6 * (1 << 21); |
5090 | 0 | carry8 = (s8 + (1 << 20)) >> 21; |
5091 | 0 | s9 += carry8; |
5092 | 0 | s8 -= carry8 * (1 << 21); |
5093 | 0 | carry10 = (s10 + (1 << 20)) >> 21; |
5094 | 0 | s11 += carry10; |
5095 | 0 | s10 -= carry10 * (1 << 21); |
5096 | 0 | carry12 = (s12 + (1 << 20)) >> 21; |
5097 | 0 | s13 += carry12; |
5098 | 0 | s12 -= carry12 * (1 << 21); |
5099 | 0 | carry14 = (s14 + (1 << 20)) >> 21; |
5100 | 0 | s15 += carry14; |
5101 | 0 | s14 -= carry14 * (1 << 21); |
5102 | 0 | carry16 = (s16 + (1 << 20)) >> 21; |
5103 | 0 | s17 += carry16; |
5104 | 0 | s16 -= carry16 * (1 << 21); |
5105 | 0 | carry18 = (s18 + (1 << 20)) >> 21; |
5106 | 0 | s19 += carry18; |
5107 | 0 | s18 -= carry18 * (1 << 21); |
5108 | 0 | carry20 = (s20 + (1 << 20)) >> 21; |
5109 | 0 | s21 += carry20; |
5110 | 0 | s20 -= carry20 * (1 << 21); |
5111 | 0 | carry22 = (s22 + (1 << 20)) >> 21; |
5112 | 0 | s23 += carry22; |
5113 | 0 | s22 -= carry22 * (1 << 21); |
5114 | |
|
5115 | 0 | carry1 = (s1 + (1 << 20)) >> 21; |
5116 | 0 | s2 += carry1; |
5117 | 0 | s1 -= carry1 * (1 << 21); |
5118 | 0 | carry3 = (s3 + (1 << 20)) >> 21; |
5119 | 0 | s4 += carry3; |
5120 | 0 | s3 -= carry3 * (1 << 21); |
5121 | 0 | carry5 = (s5 + (1 << 20)) >> 21; |
5122 | 0 | s6 += carry5; |
5123 | 0 | s5 -= carry5 * (1 << 21); |
5124 | 0 | carry7 = (s7 + (1 << 20)) >> 21; |
5125 | 0 | s8 += carry7; |
5126 | 0 | s7 -= carry7 * (1 << 21); |
5127 | 0 | carry9 = (s9 + (1 << 20)) >> 21; |
5128 | 0 | s10 += carry9; |
5129 | 0 | s9 -= carry9 * (1 << 21); |
5130 | 0 | carry11 = (s11 + (1 << 20)) >> 21; |
5131 | 0 | s12 += carry11; |
5132 | 0 | s11 -= carry11 * (1 << 21); |
5133 | 0 | carry13 = (s13 + (1 << 20)) >> 21; |
5134 | 0 | s14 += carry13; |
5135 | 0 | s13 -= carry13 * (1 << 21); |
5136 | 0 | carry15 = (s15 + (1 << 20)) >> 21; |
5137 | 0 | s16 += carry15; |
5138 | 0 | s15 -= carry15 * (1 << 21); |
5139 | 0 | carry17 = (s17 + (1 << 20)) >> 21; |
5140 | 0 | s18 += carry17; |
5141 | 0 | s17 -= carry17 * (1 << 21); |
5142 | 0 | carry19 = (s19 + (1 << 20)) >> 21; |
5143 | 0 | s20 += carry19; |
5144 | 0 | s19 -= carry19 * (1 << 21); |
5145 | 0 | carry21 = (s21 + (1 << 20)) >> 21; |
5146 | 0 | s22 += carry21; |
5147 | 0 | s21 -= carry21 * (1 << 21); |
5148 | |
|
5149 | 0 | s11 += s23 * 666643; |
5150 | 0 | s12 += s23 * 470296; |
5151 | 0 | s13 += s23 * 654183; |
5152 | 0 | s14 -= s23 * 997805; |
5153 | 0 | s15 += s23 * 136657; |
5154 | 0 | s16 -= s23 * 683901; |
5155 | 0 | s23 = 0; |
5156 | |
|
5157 | 0 | s10 += s22 * 666643; |
5158 | 0 | s11 += s22 * 470296; |
5159 | 0 | s12 += s22 * 654183; |
5160 | 0 | s13 -= s22 * 997805; |
5161 | 0 | s14 += s22 * 136657; |
5162 | 0 | s15 -= s22 * 683901; |
5163 | 0 | s22 = 0; |
5164 | |
|
5165 | 0 | s9 += s21 * 666643; |
5166 | 0 | s10 += s21 * 470296; |
5167 | 0 | s11 += s21 * 654183; |
5168 | 0 | s12 -= s21 * 997805; |
5169 | 0 | s13 += s21 * 136657; |
5170 | 0 | s14 -= s21 * 683901; |
5171 | 0 | s21 = 0; |
5172 | |
|
5173 | 0 | s8 += s20 * 666643; |
5174 | 0 | s9 += s20 * 470296; |
5175 | 0 | s10 += s20 * 654183; |
5176 | 0 | s11 -= s20 * 997805; |
5177 | 0 | s12 += s20 * 136657; |
5178 | 0 | s13 -= s20 * 683901; |
5179 | 0 | s20 = 0; |
5180 | |
|
5181 | 0 | s7 += s19 * 666643; |
5182 | 0 | s8 += s19 * 470296; |
5183 | 0 | s9 += s19 * 654183; |
5184 | 0 | s10 -= s19 * 997805; |
5185 | 0 | s11 += s19 * 136657; |
5186 | 0 | s12 -= s19 * 683901; |
5187 | 0 | s19 = 0; |
5188 | |
|
5189 | 0 | s6 += s18 * 666643; |
5190 | 0 | s7 += s18 * 470296; |
5191 | 0 | s8 += s18 * 654183; |
5192 | 0 | s9 -= s18 * 997805; |
5193 | 0 | s10 += s18 * 136657; |
5194 | 0 | s11 -= s18 * 683901; |
5195 | 0 | s18 = 0; |
5196 | |
|
5197 | 0 | carry6 = (s6 + (1 << 20)) >> 21; |
5198 | 0 | s7 += carry6; |
5199 | 0 | s6 -= carry6 * (1 << 21); |
5200 | 0 | carry8 = (s8 + (1 << 20)) >> 21; |
5201 | 0 | s9 += carry8; |
5202 | 0 | s8 -= carry8 * (1 << 21); |
5203 | 0 | carry10 = (s10 + (1 << 20)) >> 21; |
5204 | 0 | s11 += carry10; |
5205 | 0 | s10 -= carry10 * (1 << 21); |
5206 | 0 | carry12 = (s12 + (1 << 20)) >> 21; |
5207 | 0 | s13 += carry12; |
5208 | 0 | s12 -= carry12 * (1 << 21); |
5209 | 0 | carry14 = (s14 + (1 << 20)) >> 21; |
5210 | 0 | s15 += carry14; |
5211 | 0 | s14 -= carry14 * (1 << 21); |
5212 | 0 | carry16 = (s16 + (1 << 20)) >> 21; |
5213 | 0 | s17 += carry16; |
5214 | 0 | s16 -= carry16 * (1 << 21); |
5215 | |
|
5216 | 0 | carry7 = (s7 + (1 << 20)) >> 21; |
5217 | 0 | s8 += carry7; |
5218 | 0 | s7 -= carry7 * (1 << 21); |
5219 | 0 | carry9 = (s9 + (1 << 20)) >> 21; |
5220 | 0 | s10 += carry9; |
5221 | 0 | s9 -= carry9 * (1 << 21); |
5222 | 0 | carry11 = (s11 + (1 << 20)) >> 21; |
5223 | 0 | s12 += carry11; |
5224 | 0 | s11 -= carry11 * (1 << 21); |
5225 | 0 | carry13 = (s13 + (1 << 20)) >> 21; |
5226 | 0 | s14 += carry13; |
5227 | 0 | s13 -= carry13 * (1 << 21); |
5228 | 0 | carry15 = (s15 + (1 << 20)) >> 21; |
5229 | 0 | s16 += carry15; |
5230 | 0 | s15 -= carry15 * (1 << 21); |
5231 | |
|
5232 | 0 | s5 += s17 * 666643; |
5233 | 0 | s6 += s17 * 470296; |
5234 | 0 | s7 += s17 * 654183; |
5235 | 0 | s8 -= s17 * 997805; |
5236 | 0 | s9 += s17 * 136657; |
5237 | 0 | s10 -= s17 * 683901; |
5238 | 0 | s17 = 0; |
5239 | |
|
5240 | 0 | s4 += s16 * 666643; |
5241 | 0 | s5 += s16 * 470296; |
5242 | 0 | s6 += s16 * 654183; |
5243 | 0 | s7 -= s16 * 997805; |
5244 | 0 | s8 += s16 * 136657; |
5245 | 0 | s9 -= s16 * 683901; |
5246 | 0 | s16 = 0; |
5247 | |
|
5248 | 0 | s3 += s15 * 666643; |
5249 | 0 | s4 += s15 * 470296; |
5250 | 0 | s5 += s15 * 654183; |
5251 | 0 | s6 -= s15 * 997805; |
5252 | 0 | s7 += s15 * 136657; |
5253 | 0 | s8 -= s15 * 683901; |
5254 | 0 | s15 = 0; |
5255 | |
|
5256 | 0 | s2 += s14 * 666643; |
5257 | 0 | s3 += s14 * 470296; |
5258 | 0 | s4 += s14 * 654183; |
5259 | 0 | s5 -= s14 * 997805; |
5260 | 0 | s6 += s14 * 136657; |
5261 | 0 | s7 -= s14 * 683901; |
5262 | 0 | s14 = 0; |
5263 | |
|
5264 | 0 | s1 += s13 * 666643; |
5265 | 0 | s2 += s13 * 470296; |
5266 | 0 | s3 += s13 * 654183; |
5267 | 0 | s4 -= s13 * 997805; |
5268 | 0 | s5 += s13 * 136657; |
5269 | 0 | s6 -= s13 * 683901; |
5270 | 0 | s13 = 0; |
5271 | |
|
5272 | 0 | s0 += s12 * 666643; |
5273 | 0 | s1 += s12 * 470296; |
5274 | 0 | s2 += s12 * 654183; |
5275 | 0 | s3 -= s12 * 997805; |
5276 | 0 | s4 += s12 * 136657; |
5277 | 0 | s5 -= s12 * 683901; |
5278 | 0 | s12 = 0; |
5279 | |
|
5280 | 0 | carry0 = (s0 + (1 << 20)) >> 21; |
5281 | 0 | s1 += carry0; |
5282 | 0 | s0 -= carry0 * (1 << 21); |
5283 | 0 | carry2 = (s2 + (1 << 20)) >> 21; |
5284 | 0 | s3 += carry2; |
5285 | 0 | s2 -= carry2 * (1 << 21); |
5286 | 0 | carry4 = (s4 + (1 << 20)) >> 21; |
5287 | 0 | s5 += carry4; |
5288 | 0 | s4 -= carry4 * (1 << 21); |
5289 | 0 | carry6 = (s6 + (1 << 20)) >> 21; |
5290 | 0 | s7 += carry6; |
5291 | 0 | s6 -= carry6 * (1 << 21); |
5292 | 0 | carry8 = (s8 + (1 << 20)) >> 21; |
5293 | 0 | s9 += carry8; |
5294 | 0 | s8 -= carry8 * (1 << 21); |
5295 | 0 | carry10 = (s10 + (1 << 20)) >> 21; |
5296 | 0 | s11 += carry10; |
5297 | 0 | s10 -= carry10 * (1 << 21); |
5298 | |
|
5299 | 0 | carry1 = (s1 + (1 << 20)) >> 21; |
5300 | 0 | s2 += carry1; |
5301 | 0 | s1 -= carry1 * (1 << 21); |
5302 | 0 | carry3 = (s3 + (1 << 20)) >> 21; |
5303 | 0 | s4 += carry3; |
5304 | 0 | s3 -= carry3 * (1 << 21); |
5305 | 0 | carry5 = (s5 + (1 << 20)) >> 21; |
5306 | 0 | s6 += carry5; |
5307 | 0 | s5 -= carry5 * (1 << 21); |
5308 | 0 | carry7 = (s7 + (1 << 20)) >> 21; |
5309 | 0 | s8 += carry7; |
5310 | 0 | s7 -= carry7 * (1 << 21); |
5311 | 0 | carry9 = (s9 + (1 << 20)) >> 21; |
5312 | 0 | s10 += carry9; |
5313 | 0 | s9 -= carry9 * (1 << 21); |
5314 | 0 | carry11 = (s11 + (1 << 20)) >> 21; |
5315 | 0 | s12 += carry11; |
5316 | 0 | s11 -= carry11 * (1 << 21); |
5317 | |
|
5318 | 0 | s0 += s12 * 666643; |
5319 | 0 | s1 += s12 * 470296; |
5320 | 0 | s2 += s12 * 654183; |
5321 | 0 | s3 -= s12 * 997805; |
5322 | 0 | s4 += s12 * 136657; |
5323 | 0 | s5 -= s12 * 683901; |
5324 | 0 | s12 = 0; |
5325 | |
|
5326 | 0 | carry0 = s0 >> 21; |
5327 | 0 | s1 += carry0; |
5328 | 0 | s0 -= carry0 * (1 << 21); |
5329 | 0 | carry1 = s1 >> 21; |
5330 | 0 | s2 += carry1; |
5331 | 0 | s1 -= carry1 * (1 << 21); |
5332 | 0 | carry2 = s2 >> 21; |
5333 | 0 | s3 += carry2; |
5334 | 0 | s2 -= carry2 * (1 << 21); |
5335 | 0 | carry3 = s3 >> 21; |
5336 | 0 | s4 += carry3; |
5337 | 0 | s3 -= carry3 * (1 << 21); |
5338 | 0 | carry4 = s4 >> 21; |
5339 | 0 | s5 += carry4; |
5340 | 0 | s4 -= carry4 * (1 << 21); |
5341 | 0 | carry5 = s5 >> 21; |
5342 | 0 | s6 += carry5; |
5343 | 0 | s5 -= carry5 * (1 << 21); |
5344 | 0 | carry6 = s6 >> 21; |
5345 | 0 | s7 += carry6; |
5346 | 0 | s6 -= carry6 * (1 << 21); |
5347 | 0 | carry7 = s7 >> 21; |
5348 | 0 | s8 += carry7; |
5349 | 0 | s7 -= carry7 * (1 << 21); |
5350 | 0 | carry8 = s8 >> 21; |
5351 | 0 | s9 += carry8; |
5352 | 0 | s8 -= carry8 * (1 << 21); |
5353 | 0 | carry9 = s9 >> 21; |
5354 | 0 | s10 += carry9; |
5355 | 0 | s9 -= carry9 * (1 << 21); |
5356 | 0 | carry10 = s10 >> 21; |
5357 | 0 | s11 += carry10; |
5358 | 0 | s10 -= carry10 * (1 << 21); |
5359 | 0 | carry11 = s11 >> 21; |
5360 | 0 | s12 += carry11; |
5361 | 0 | s11 -= carry11 * (1 << 21); |
5362 | |
|
5363 | 0 | s0 += s12 * 666643; |
5364 | 0 | s1 += s12 * 470296; |
5365 | 0 | s2 += s12 * 654183; |
5366 | 0 | s3 -= s12 * 997805; |
5367 | 0 | s4 += s12 * 136657; |
5368 | 0 | s5 -= s12 * 683901; |
5369 | 0 | s12 = 0; |
5370 | |
|
5371 | 0 | carry0 = s0 >> 21; |
5372 | 0 | s1 += carry0; |
5373 | 0 | s0 -= carry0 * (1 << 21); |
5374 | 0 | carry1 = s1 >> 21; |
5375 | 0 | s2 += carry1; |
5376 | 0 | s1 -= carry1 * (1 << 21); |
5377 | 0 | carry2 = s2 >> 21; |
5378 | 0 | s3 += carry2; |
5379 | 0 | s2 -= carry2 * (1 << 21); |
5380 | 0 | carry3 = s3 >> 21; |
5381 | 0 | s4 += carry3; |
5382 | 0 | s3 -= carry3 * (1 << 21); |
5383 | 0 | carry4 = s4 >> 21; |
5384 | 0 | s5 += carry4; |
5385 | 0 | s4 -= carry4 * (1 << 21); |
5386 | 0 | carry5 = s5 >> 21; |
5387 | 0 | s6 += carry5; |
5388 | 0 | s5 -= carry5 * (1 << 21); |
5389 | 0 | carry6 = s6 >> 21; |
5390 | 0 | s7 += carry6; |
5391 | 0 | s6 -= carry6 * (1 << 21); |
5392 | 0 | carry7 = s7 >> 21; |
5393 | 0 | s8 += carry7; |
5394 | 0 | s7 -= carry7 * (1 << 21); |
5395 | 0 | carry8 = s8 >> 21; |
5396 | 0 | s9 += carry8; |
5397 | 0 | s8 -= carry8 * (1 << 21); |
5398 | 0 | carry9 = s9 >> 21; |
5399 | 0 | s10 += carry9; |
5400 | 0 | s9 -= carry9 * (1 << 21); |
5401 | 0 | carry10 = s10 >> 21; |
5402 | 0 | s11 += carry10; |
5403 | 0 | s10 -= carry10 * (1 << 21); |
5404 | |
|
5405 | 0 | s[ 0] = (uint8_t) (s0 >> 0); |
5406 | 0 | s[ 1] = (uint8_t) (s0 >> 8); |
5407 | 0 | s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5)); |
5408 | 0 | s[ 3] = (uint8_t) (s1 >> 3); |
5409 | 0 | s[ 4] = (uint8_t) (s1 >> 11); |
5410 | 0 | s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2)); |
5411 | 0 | s[ 6] = (uint8_t) (s2 >> 6); |
5412 | 0 | s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7)); |
5413 | 0 | s[ 8] = (uint8_t) (s3 >> 1); |
5414 | 0 | s[ 9] = (uint8_t) (s3 >> 9); |
5415 | 0 | s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); |
5416 | 0 | s[11] = (uint8_t) (s4 >> 4); |
5417 | 0 | s[12] = (uint8_t) (s4 >> 12); |
5418 | 0 | s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); |
5419 | 0 | s[14] = (uint8_t) (s5 >> 7); |
5420 | 0 | s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); |
5421 | 0 | s[16] = (uint8_t) (s6 >> 2); |
5422 | 0 | s[17] = (uint8_t) (s6 >> 10); |
5423 | 0 | s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); |
5424 | 0 | s[19] = (uint8_t) (s7 >> 5); |
5425 | 0 | s[20] = (uint8_t) (s7 >> 13); |
5426 | 0 | s[21] = (uint8_t) (s8 >> 0); |
5427 | 0 | s[22] = (uint8_t) (s8 >> 8); |
5428 | 0 | s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); |
5429 | 0 | s[24] = (uint8_t) (s9 >> 3); |
5430 | 0 | s[25] = (uint8_t) (s9 >> 11); |
5431 | 0 | s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); |
5432 | 0 | s[27] = (uint8_t) (s10 >> 6); |
5433 | 0 | s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); |
5434 | 0 | s[29] = (uint8_t) (s11 >> 1); |
5435 | 0 | s[30] = (uint8_t) (s11 >> 9); |
5436 | 0 | s[31] = (uint8_t) (s11 >> 17); |
5437 | 0 | } |
5438 | | |
5439 | | int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, |
5440 | | const uint8_t public_key[32], const uint8_t private_key[32]) |
5441 | 0 | { |
5442 | 0 | uint8_t az[SHA512_DIGEST_LENGTH]; |
5443 | 0 | uint8_t nonce[SHA512_DIGEST_LENGTH]; |
5444 | 0 | ge_p3 R; |
5445 | 0 | uint8_t hram[SHA512_DIGEST_LENGTH]; |
5446 | 0 | EVP_MD *sha512 = EVP_MD_fetch(NULL, SN_sha512, NULL); |
5447 | 0 | EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new(); |
5448 | 0 | unsigned int sz; |
5449 | 0 | int res = 0; |
5450 | |
|
5451 | 0 | if (sha512 == NULL || hash_ctx == NULL) |
5452 | 0 | goto err; |
5453 | | |
5454 | 0 | if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL) |
5455 | 0 | || !EVP_DigestUpdate(hash_ctx, private_key, 32) |
5456 | 0 | || !EVP_DigestFinal_ex(hash_ctx, az, &sz)) |
5457 | 0 | goto err; |
5458 | | |
5459 | 0 | az[0] &= 248; |
5460 | 0 | az[31] &= 63; |
5461 | 0 | az[31] |= 64; |
5462 | |
|
5463 | 0 | if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL) |
5464 | 0 | || !EVP_DigestUpdate(hash_ctx, az + 32, 32) |
5465 | 0 | || !EVP_DigestUpdate(hash_ctx, message, message_len) |
5466 | 0 | || !EVP_DigestFinal_ex(hash_ctx, nonce, &sz)) |
5467 | 0 | goto err; |
5468 | | |
5469 | 0 | x25519_sc_reduce(nonce); |
5470 | 0 | ge_scalarmult_base(&R, nonce); |
5471 | 0 | ge_p3_tobytes(out_sig, &R); |
5472 | |
|
5473 | 0 | if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL) |
5474 | 0 | || !EVP_DigestUpdate(hash_ctx, out_sig, 32) |
5475 | 0 | || !EVP_DigestUpdate(hash_ctx, public_key, 32) |
5476 | 0 | || !EVP_DigestUpdate(hash_ctx, message, message_len) |
5477 | 0 | || !EVP_DigestFinal_ex(hash_ctx, hram, &sz)) |
5478 | 0 | goto err; |
5479 | | |
5480 | 0 | x25519_sc_reduce(hram); |
5481 | 0 | sc_muladd(out_sig + 32, hram, az, nonce); |
5482 | |
|
5483 | 0 | res = 1; |
5484 | 0 | err: |
5485 | 0 | OPENSSL_cleanse(nonce, sizeof(nonce)); |
5486 | 0 | OPENSSL_cleanse(az, sizeof(az)); |
5487 | 0 | EVP_MD_free(sha512); |
5488 | 0 | EVP_MD_CTX_free(hash_ctx); |
5489 | 0 | return res; |
5490 | 0 | } |
5491 | | |
5492 | | static const char allzeroes[15]; |
5493 | | |
5494 | | int ED25519_verify(const uint8_t *message, size_t message_len, |
5495 | | const uint8_t signature[64], const uint8_t public_key[32]) |
5496 | 0 | { |
5497 | 0 | int i; |
5498 | 0 | ge_p3 A; |
5499 | 0 | const uint8_t *r, *s; |
5500 | 0 | EVP_MD *sha512; |
5501 | 0 | EVP_MD_CTX *hash_ctx = NULL; |
5502 | 0 | unsigned int sz; |
5503 | 0 | int res = 0; |
5504 | 0 | ge_p2 R; |
5505 | 0 | uint8_t rcheck[32]; |
5506 | 0 | uint8_t h[SHA512_DIGEST_LENGTH]; |
5507 | | /* 27742317777372353535851937790883648493 in little endian format */ |
5508 | 0 | const uint8_t l_low[16] = { |
5509 | 0 | 0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, |
5510 | 0 | 0xDE, 0xF9, 0xDE, 0x14 |
5511 | 0 | }; |
5512 | |
|
5513 | 0 | r = signature; |
5514 | 0 | s = signature + 32; |
5515 | | |
5516 | | /* |
5517 | | * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493 |
5518 | | * |
5519 | | * If not the signature is publicly invalid. Since it's public we can do the |
5520 | | * check in variable time. |
5521 | | * |
5522 | | * First check the most significant byte |
5523 | | */ |
5524 | 0 | if (s[31] > 0x10) |
5525 | 0 | return 0; |
5526 | 0 | if (s[31] == 0x10) { |
5527 | | /* |
5528 | | * Most significant byte indicates a value close to 2^252 so check the |
5529 | | * rest |
5530 | | */ |
5531 | 0 | if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0) |
5532 | 0 | return 0; |
5533 | 0 | for (i = 15; i >= 0; i--) { |
5534 | 0 | if (s[i] < l_low[i]) |
5535 | 0 | break; |
5536 | 0 | if (s[i] > l_low[i]) |
5537 | 0 | return 0; |
5538 | 0 | } |
5539 | 0 | if (i < 0) |
5540 | 0 | return 0; |
5541 | 0 | } |
5542 | | |
5543 | 0 | if (ge_frombytes_vartime(&A, public_key) != 0) { |
5544 | 0 | return 0; |
5545 | 0 | } |
5546 | | |
5547 | 0 | fe_neg(A.X, A.X); |
5548 | 0 | fe_neg(A.T, A.T); |
5549 | |
|
5550 | 0 | sha512 = EVP_MD_fetch(NULL, SN_sha512, NULL); |
5551 | 0 | if (sha512 == NULL) |
5552 | 0 | return 0; |
5553 | 0 | hash_ctx = EVP_MD_CTX_new(); |
5554 | 0 | if (hash_ctx == NULL) |
5555 | 0 | goto err; |
5556 | | |
5557 | 0 | if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL) |
5558 | 0 | || !EVP_DigestUpdate(hash_ctx, r, 32) |
5559 | 0 | || !EVP_DigestUpdate(hash_ctx, public_key, 32) |
5560 | 0 | || !EVP_DigestUpdate(hash_ctx, message, message_len) |
5561 | 0 | || !EVP_DigestFinal_ex(hash_ctx, h, &sz)) |
5562 | 0 | goto err; |
5563 | | |
5564 | 0 | x25519_sc_reduce(h); |
5565 | |
|
5566 | 0 | ge_double_scalarmult_vartime(&R, h, &A, s); |
5567 | |
|
5568 | 0 | ge_tobytes(rcheck, &R); |
5569 | |
|
5570 | 0 | res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0; |
5571 | 0 | err: |
5572 | 0 | EVP_MD_free(sha512); |
5573 | 0 | EVP_MD_CTX_free(hash_ctx); |
5574 | 0 | return res; |
5575 | 0 | } |
5576 | | |
5577 | | void ED25519_public_from_private(uint8_t out_public_key[32], |
5578 | | const uint8_t private_key[32]) |
5579 | 0 | { |
5580 | 0 | uint8_t az[SHA512_DIGEST_LENGTH]; |
5581 | 0 | ge_p3 A; |
5582 | |
|
5583 | 0 | SHA512(private_key, 32, az); |
5584 | |
|
5585 | 0 | az[0] &= 248; |
5586 | 0 | az[31] &= 63; |
5587 | 0 | az[31] |= 64; |
5588 | |
|
5589 | 0 | ge_scalarmult_base(&A, az); |
5590 | 0 | ge_p3_tobytes(out_public_key, &A); |
5591 | |
|
5592 | 0 | OPENSSL_cleanse(az, sizeof(az)); |
5593 | 0 | } |
5594 | | |
5595 | | int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], |
5596 | | const uint8_t peer_public_value[32]) |
5597 | 0 | { |
5598 | 0 | static const uint8_t kZeros[32] = {0}; |
5599 | 0 | x25519_scalar_mult(out_shared_key, private_key, peer_public_value); |
5600 | | /* The all-zero output results when the input is a point of small order. */ |
5601 | 0 | return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0; |
5602 | 0 | } |
5603 | | |
5604 | | void X25519_public_from_private(uint8_t out_public_value[32], |
5605 | | const uint8_t private_key[32]) |
5606 | 0 | { |
5607 | 0 | uint8_t e[32]; |
5608 | 0 | ge_p3 A; |
5609 | 0 | fe zplusy, zminusy, zminusy_inv; |
5610 | |
|
5611 | 0 | memcpy(e, private_key, 32); |
5612 | 0 | e[0] &= 248; |
5613 | 0 | e[31] &= 127; |
5614 | 0 | e[31] |= 64; |
5615 | |
|
5616 | 0 | ge_scalarmult_base(&A, e); |
5617 | | |
5618 | | /* |
5619 | | * We only need the u-coordinate of the curve25519 point. |
5620 | | * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives |
5621 | | * u=(Z+Y)/(Z-Y). |
5622 | | */ |
5623 | 0 | fe_add(zplusy, A.Z, A.Y); |
5624 | 0 | fe_sub(zminusy, A.Z, A.Y); |
5625 | 0 | fe_invert(zminusy_inv, zminusy); |
5626 | 0 | fe_mul(zplusy, zplusy, zminusy_inv); |
5627 | 0 | fe_tobytes(out_public_value, zplusy); |
5628 | |
|
5629 | 0 | OPENSSL_cleanse(e, sizeof(e)); |
5630 | 0 | } |