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aa6bb135 1/*
33388b44 2 * Copyright 2016-2020 The OpenSSL Project Authors. All Rights Reserved.
df3bde67 3 *
a7f182b7 4 * Licensed under the Apache License 2.0 (the "License"). You may not use
aa6bb135
RS		 5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
df3bde67 8 */
a90def6b 9
579422c8
P		 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
a90def6b 16#include <string.h>
4de88fe6 17#include "crypto/ecx.h"
706457b7 18#include "ec_local.h"
85d843c8 19#include <openssl/evp.h>
06c6d05f 20#include <openssl/sha.h>
a90def6b 21
3c849bc9
AP		 22#if defined(X25519_ASM) && (defined(__x86_64) || defined(__x86_64__) || \
23 defined(_M_AMD64) || defined(_M_X64))
cfc32a1e 24
3c849bc9 25# define BASE_2_64_IMPLEMENTED
c521e439
AP		 26
27typedef uint64_t fe64[4];
28
91860165 29int x25519_fe64_eligible(void);
c521e439
AP		 30
31/*
3c849bc9
AP		 32 * Following subroutines perform corresponding operations modulo
33 * 2^256-38, i.e. double the curve modulus. However, inputs and
34 * outputs are permitted to be partially reduced, i.e. to remain
35 * in [0..2^256) range. It's all tied up in final fe64_tobytes
36 * that performs full reduction modulo 2^255-19.
37 *
38 * There are no reference C implementations for these.
c521e439
AP		 39 */
40void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
41void x25519_fe64_sqr(fe64 h, const fe64 f);
42void x25519_fe64_mul121666(fe64 h, fe64 f);
43void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
44void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
45void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
3c849bc9
AP		 46# define fe64_mul x25519_fe64_mul
47# define fe64_sqr x25519_fe64_sqr
48# define fe64_mul121666 x25519_fe64_mul121666
49# define fe64_add x25519_fe64_add
50# define fe64_sub x25519_fe64_sub
51# define fe64_tobytes x25519_fe64_tobytes
c521e439
AP		 52
53static uint64_t load_8(const uint8_t *in)
54{
55 uint64_t result;
56
57 result = in[0];
58 result |= ((uint64_t)in[1]) << 8;
59 result |= ((uint64_t)in[2]) << 16;
60 result |= ((uint64_t)in[3]) << 24;
61 result |= ((uint64_t)in[4]) << 32;
62 result |= ((uint64_t)in[5]) << 40;
63 result |= ((uint64_t)in[6]) << 48;
64 result |= ((uint64_t)in[7]) << 56;
65
66 return result;
67}
68
69static void fe64_frombytes(fe64 h, const uint8_t *s)
70{
71 h[0] = load_8(s);
72 h[1] = load_8(s + 8);
73 h[2] = load_8(s + 16);
74 h[3] = load_8(s + 24) & 0x7fffffffffffffff;
75}
76
77static void fe64_0(fe64 h)
78{
79 h[0] = 0;
80 h[1] = 0;
81 h[2] = 0;
82 h[3] = 0;
83}
84
85static void fe64_1(fe64 h)
86{
87 h[0] = 1;
88 h[1] = 0;
89 h[2] = 0;
90 h[3] = 0;
91}
92
93static void fe64_copy(fe64 h, const fe64 f)
94{
95 h[0] = f[0];
96 h[1] = f[1];
97 h[2] = f[2];
98 h[3] = f[3];
99}
100
101static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
102{
103 int i;
104 uint64_t mask = 0 - (uint64_t)b;
105
106 for (i = 0; i < 4; i++) {
107 uint64_t x = f[i] ^ g[i];
108 x &= mask;
109 f[i] ^= x;
110 g[i] ^= x;
111 }
112}
113
114static void fe64_invert(fe64 out, const fe64 z)
115{
116 fe64 t0;
117 fe64 t1;
118 fe64 t2;
119 fe64 t3;
120 int i;
121
122 /*
123 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
124 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
125 */
126
127 /* t0 = z ** 2 */
128 fe64_sqr(t0, z);
129
130 /* t1 = t0 ** (2 ** 2) = z ** 8 */
131 fe64_sqr(t1, t0);
132 fe64_sqr(t1, t1);
133
134 /* t1 = z * t1 = z ** 9 */
135 fe64_mul(t1, z, t1);
136 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
137 fe64_mul(t0, t0, t1);
138
139 /* t2 = t0 ** 2 = z ** 22 */
140 fe64_sqr(t2, t0);
141
142 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
143 fe64_mul(t1, t1, t2);
144
145 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
146 fe64_sqr(t2, t1);
147 for (i = 1; i < 5; ++i)
148 fe64_sqr(t2, t2);
149
150 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
151 fe64_mul(t1, t2, t1);
152
153 /* Continuing similarly... */
154
155 /* t2 = z ** (2 ** 20 - 1) */
156 fe64_sqr(t2, t1);
157 for (i = 1; i < 10; ++i)
158 fe64_sqr(t2, t2);
159
160 fe64_mul(t2, t2, t1);
161
162 /* t2 = z ** (2 ** 40 - 1) */
163 fe64_sqr(t3, t2);
164 for (i = 1; i < 20; ++i)
165 fe64_sqr(t3, t3);
166
167 fe64_mul(t2, t3, t2);
168
169 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
170 for (i = 0; i < 10; ++i)
171 fe64_sqr(t2, t2);
172
173 /* t1 = z ** (2 ** 50 - 1) */
174 fe64_mul(t1, t2, t1);
175
176 /* t2 = z ** (2 ** 100 - 1) */
177 fe64_sqr(t2, t1);
178 for (i = 1; i < 50; ++i)
179 fe64_sqr(t2, t2);
180
181 fe64_mul(t2, t2, t1);
182
183 /* t2 = z ** (2 ** 200 - 1) */
184 fe64_sqr(t3, t2);
185 for (i = 1; i < 100; ++i)
186 fe64_sqr(t3, t3);
187
188 fe64_mul(t2, t3, t2);
189
190 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
191 for (i = 0; i < 50; ++i)
192 fe64_sqr(t2, t2);
193
194 /* t1 = z ** (2 ** 250 - 1) */
195 fe64_mul(t1, t2, t1);
196
197 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
198 for (i = 0; i < 5; ++i)
199 fe64_sqr(t1, t1);
200
201 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
202 fe64_mul(out, t1, t0);
203}
204
205/*
206 * Duplicate of original x25519_scalar_mult_generic, but using
207 * fe64_* subroutines.
208 */
209static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
210 const uint8_t point[32])
211{
212 fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
213 uint8_t e[32];
214 unsigned swap = 0;
215 int pos;
216
217 memcpy(e, scalar, 32);
218 e[0] &= 0xf8;
219 e[31] &= 0x7f;
220 e[31] |= 0x40;
221 fe64_frombytes(x1, point);
222 fe64_1(x2);
223 fe64_0(z2);
224 fe64_copy(x3, x1);
225 fe64_1(z3);
226
227 for (pos = 254; pos >= 0; --pos) {
228 unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
229
230 swap ^= b;
231 fe64_cswap(x2, x3, swap);
232 fe64_cswap(z2, z3, swap);
233 swap = b;
234 fe64_sub(tmp0, x3, z3);
235 fe64_sub(tmp1, x2, z2);
236 fe64_add(x2, x2, z2);
237 fe64_add(z2, x3, z3);
238 fe64_mul(z3, x2, tmp0);
239 fe64_mul(z2, z2, tmp1);
240 fe64_sqr(tmp0, tmp1);
241 fe64_sqr(tmp1, x2);
242 fe64_add(x3, z3, z2);
243 fe64_sub(z2, z3, z2);
244 fe64_mul(x2, tmp1, tmp0);
245 fe64_sub(tmp1, tmp1, tmp0);
246 fe64_sqr(z2, z2);
247 fe64_mul121666(z3, tmp1);
248 fe64_sqr(x3, x3);
249 fe64_add(tmp0, tmp0, z3);
250 fe64_mul(z3, x1, z2);
251 fe64_mul(z2, tmp1, tmp0);
252 }
253
254 fe64_invert(z2, z2);
255 fe64_mul(x2, x2, z2);
256 fe64_tobytes(out, x2);
257
258 OPENSSL_cleanse(e, sizeof(e));
259}
3c849bc9 260#endif
c521e439 261
3c849bc9
AP		 262#if defined(X25519_ASM) \
263 || ( (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16) \
264 && !defined(__sparc__) \
3a86f1db 265 && (!defined(__SIZEOF_LONG__) || (__SIZEOF_LONG__ == 8)) \
3c849bc9
AP		 266 && !(defined(__ANDROID__) && !defined(__clang__)) )
267/*
268 * Base 2^51 implementation. It's virtually no different from reference
269 * base 2^25.5 implementation in respect to lax boundary conditions for
270 * intermediate values and even individual limbs. So that whatever you
271 * know about the reference, applies even here...
272 */
273# define BASE_2_51_IMPLEMENTED
274
275typedef uint64_t fe51[5];
276
277static const uint64_t MASK51 = 0x7ffffffffffff;
278
279static uint64_t load_7(const uint8_t *in)
280{
281 uint64_t result;
282
283 result = in[0];
284 result |= ((uint64_t)in[1]) << 8;
285 result |= ((uint64_t)in[2]) << 16;
286 result |= ((uint64_t)in[3]) << 24;
287 result |= ((uint64_t)in[4]) << 32;
288 result |= ((uint64_t)in[5]) << 40;
289 result |= ((uint64_t)in[6]) << 48;
290
291 return result;
292}
293
294static uint64_t load_6(const uint8_t *in)
295{
296 uint64_t result;
297
298 result = in[0];
299 result |= ((uint64_t)in[1]) << 8;
300 result |= ((uint64_t)in[2]) << 16;
301 result |= ((uint64_t)in[3]) << 24;
302 result |= ((uint64_t)in[4]) << 32;
303 result |= ((uint64_t)in[5]) << 40;
304
305 return result;
306}
307
308static void fe51_frombytes(fe51 h, const uint8_t *s)
309{
310 uint64_t h0 = load_7(s); /* 56 bits */
311 uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
312 uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
313 uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
314 uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
315
316 h1 |= h0 >> 51; h0 &= MASK51;
317 h2 |= h1 >> 51; h1 &= MASK51;
318 h3 |= h2 >> 51; h2 &= MASK51;
319 h4 |= h3 >> 51; h3 &= MASK51;
320
321 h[0] = h0;
322 h[1] = h1;
323 h[2] = h2;
324 h[3] = h3;
325 h[4] = h4;
326}
327
328static void fe51_tobytes(uint8_t *s, const fe51 h)
329{
330 uint64_t h0 = h[0];
331 uint64_t h1 = h[1];
332 uint64_t h2 = h[2];
333 uint64_t h3 = h[3];
334 uint64_t h4 = h[4];
335 uint64_t q;
336
337 /* compare to modulus */
338 q = (h0 + 19) >> 51;
339 q = (h1 + q) >> 51;
340 q = (h2 + q) >> 51;
341 q = (h3 + q) >> 51;
342 q = (h4 + q) >> 51;
343
344 /* full reduce */
345 h0 += 19 * q;
346 h1 += h0 >> 51; h0 &= MASK51;
347 h2 += h1 >> 51; h1 &= MASK51;
348 h3 += h2 >> 51; h2 &= MASK51;
349 h4 += h3 >> 51; h3 &= MASK51;
350 h4 &= MASK51;
351
352 /* smash */
353 s[0] = (uint8_t)(h0 >> 0);
354 s[1] = (uint8_t)(h0 >> 8);
355 s[2] = (uint8_t)(h0 >> 16);
356 s[3] = (uint8_t)(h0 >> 24);
357 s[4] = (uint8_t)(h0 >> 32);
358 s[5] = (uint8_t)(h0 >> 40);
359 s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3));
360 s[7] = (uint8_t)(h1 >> 5);
361 s[8] = (uint8_t)(h1 >> 13);
362 s[9] = (uint8_t)(h1 >> 21);
363 s[10] = (uint8_t)(h1 >> 29);
364 s[11] = (uint8_t)(h1 >> 37);
365 s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6));
366 s[13] = (uint8_t)(h2 >> 2);
367 s[14] = (uint8_t)(h2 >> 10);
368 s[15] = (uint8_t)(h2 >> 18);
369 s[16] = (uint8_t)(h2 >> 26);
370 s[17] = (uint8_t)(h2 >> 34);
371 s[18] = (uint8_t)(h2 >> 42);
372 s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1));
373 s[20] = (uint8_t)(h3 >> 7);
374 s[21] = (uint8_t)(h3 >> 15);
375 s[22] = (uint8_t)(h3 >> 23);
376 s[23] = (uint8_t)(h3 >> 31);
377 s[24] = (uint8_t)(h3 >> 39);
378 s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4));
379 s[26] = (uint8_t)(h4 >> 4);
380 s[27] = (uint8_t)(h4 >> 12);
381 s[28] = (uint8_t)(h4 >> 20);
382 s[29] = (uint8_t)(h4 >> 28);
383 s[30] = (uint8_t)(h4 >> 36);
384 s[31] = (uint8_t)(h4 >> 44);
385}
386
387# if defined(X25519_ASM)
388void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
389void x25519_fe51_sqr(fe51 h, const fe51 f);
390void x25519_fe51_mul121666(fe51 h, fe51 f);
391# define fe51_mul x25519_fe51_mul
392# define fe51_sq x25519_fe51_sqr
393# define fe51_mul121666 x25519_fe51_mul121666
c521e439
AP		 394# else
395
3c849bc9
AP		 396typedef __uint128_t u128;
397
cfc32a1e
AP		 398static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
399{
400 u128 h0, h1, h2, h3, h4;
401 uint64_t f_i, g0, g1, g2, g3, g4;
402
403 f_i = f[0];
404 h0 = (u128)f_i * (g0 = g[0]);
405 h1 = (u128)f_i * (g1 = g[1]);
406 h2 = (u128)f_i * (g2 = g[2]);
407 h3 = (u128)f_i * (g3 = g[3]);
408 h4 = (u128)f_i * (g4 = g[4]);
409
410 f_i = f[1];
411 h0 += (u128)f_i * (g4 *= 19);
412 h1 += (u128)f_i * g0;
413 h2 += (u128)f_i * g1;
414 h3 += (u128)f_i * g2;
415 h4 += (u128)f_i * g3;
416
417 f_i = f[2];
418 h0 += (u128)f_i * (g3 *= 19);
419 h1 += (u128)f_i * g4;
420 h2 += (u128)f_i * g0;
421 h3 += (u128)f_i * g1;
422 h4 += (u128)f_i * g2;
423
424 f_i = f[3];
425 h0 += (u128)f_i * (g2 *= 19);
426 h1 += (u128)f_i * g3;
427 h2 += (u128)f_i * g4;
428 h3 += (u128)f_i * g0;
429 h4 += (u128)f_i * g1;
430
431 f_i = f[4];
432 h0 += (u128)f_i * (g1 *= 19);
433 h1 += (u128)f_i * g2;
434 h2 += (u128)f_i * g3;
435 h3 += (u128)f_i * g4;
436 h4 += (u128)f_i * g0;
437
438 /* partial [lazy] reduction */
439 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
440 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
441
442 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
443 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
444
445 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
446 g3 += g2 >> 51; g2 &= MASK51;
447 g1 += g0 >> 51; g0 &= MASK51;
448
449 h[0] = g0;
450 h[1] = g1;
451 h[2] = g2;
452 h[3] = g3;
453 h[4] = g4;
454}
455
456static void fe51_sq(fe51 h, const fe51 f)
457{
c521e439 458# if defined(OPENSSL_SMALL_FOOTPRINT)
cfc32a1e 459 fe51_mul(h, f, f);
c521e439 460# else
cfc32a1e
AP		 461 /* dedicated squaring gives 16-25% overall improvement */
462 uint64_t g0 = f[0];
463 uint64_t g1 = f[1];
464 uint64_t g2 = f[2];
465 uint64_t g3 = f[3];
466 uint64_t g4 = f[4];
467 u128 h0, h1, h2, h3, h4;
468
469 h0 = (u128)g0 * g0; g0 *= 2;
470 h1 = (u128)g0 * g1;
471 h2 = (u128)g0 * g2;
472 h3 = (u128)g0 * g3;
473 h4 = (u128)g0 * g4;
474
475 g0 = g4; /* borrow g0 */
476 h3 += (u128)g0 * (g4 *= 19);
477
478 h2 += (u128)g1 * g1; g1 *= 2;
479 h3 += (u128)g1 * g2;
480 h4 += (u128)g1 * g3;
481 h0 += (u128)g1 * g4;
482
483 g0 = g3; /* borrow g0 */
484 h1 += (u128)g0 * (g3 *= 19);
485 h2 += (u128)(g0 * 2) * g4;
486
487 h4 += (u128)g2 * g2; g2 *= 2;
488 h0 += (u128)g2 * g3;
489 h1 += (u128)g2 * g4;
490
491 /* partial [lazy] reduction */
492 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
493 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
494
495 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
496 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
497
498 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
499 g3 += g2 >> 51; g2 &= MASK51;
500 g1 += g0 >> 51; g0 &= MASK51;
501
502 h[0] = g0;
503 h[1] = g1;
504 h[2] = g2;
505 h[3] = g3;
506 h[4] = g4;
c521e439 507# endif
cfc32a1e
AP		 508}
509
c521e439
AP		 510static void fe51_mul121666(fe51 h, fe51 f)
511{
512 u128 h0 = f[0] * (u128)121666;
513 u128 h1 = f[1] * (u128)121666;
514 u128 h2 = f[2] * (u128)121666;
515 u128 h3 = f[3] * (u128)121666;
516 u128 h4 = f[4] * (u128)121666;
517 uint64_t g0, g1, g2, g3, g4;
518
519 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
520 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
521
522 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
523 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
524
525 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
526 g3 += g2 >> 51; g2 &= MASK51;
527 g1 += g0 >> 51; g0 &= MASK51;
528
529 h[0] = g0;
530 h[1] = g1;
531 h[2] = g2;
532 h[3] = g3;
533 h[4] = g4;
534}
535# endif
536
cfc32a1e
AP		 537static void fe51_add(fe51 h, const fe51 f, const fe51 g)
538{
539 h[0] = f[0] + g[0];
540 h[1] = f[1] + g[1];
541 h[2] = f[2] + g[2];
542 h[3] = f[3] + g[3];
543 h[4] = f[4] + g[4];
544}
545
546static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
547{
548 /*
549 * Add 2*modulus to ensure that result remains positive
550 * even if subtrahend is partially reduced.
551 */
552 h[0] = (f[0] + 0xfffffffffffda) - g[0];
553 h[1] = (f[1] + 0xffffffffffffe) - g[1];
554 h[2] = (f[2] + 0xffffffffffffe) - g[2];
555 h[3] = (f[3] + 0xffffffffffffe) - g[3];
556 h[4] = (f[4] + 0xffffffffffffe) - g[4];
557}
558
559static void fe51_0(fe51 h)
560{
561 h[0] = 0;
562 h[1] = 0;
563 h[2] = 0;
564 h[3] = 0;
565 h[4] = 0;
566}
567
568static void fe51_1(fe51 h)
569{
570 h[0] = 1;
571 h[1] = 0;
572 h[2] = 0;
573 h[3] = 0;
574 h[4] = 0;
575}
576
577static void fe51_copy(fe51 h, const fe51 f)
578{
579 h[0] = f[0];
580 h[1] = f[1];
581 h[2] = f[2];
582 h[3] = f[3];
583 h[4] = f[4];
584}
585
586static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
587{
588 int i;
589 uint64_t mask = 0 - (uint64_t)b;
590
591 for (i = 0; i < 5; i++) {
592 int64_t x = f[i] ^ g[i];
593 x &= mask;
594 f[i] ^= x;
595 g[i] ^= x;
596 }
597}
598
599static void fe51_invert(fe51 out, const fe51 z)
600{
601 fe51 t0;
602 fe51 t1;
603 fe51 t2;
604 fe51 t3;
605 int i;
606
607 /*
608 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
609 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
610 */
611
612 /* t0 = z ** 2 */
613 fe51_sq(t0, z);
614
615 /* t1 = t0 ** (2 ** 2) = z ** 8 */
616 fe51_sq(t1, t0);
617 fe51_sq(t1, t1);
618
619 /* t1 = z * t1 = z ** 9 */
620 fe51_mul(t1, z, t1);
621 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
622 fe51_mul(t0, t0, t1);
623
624 /* t2 = t0 ** 2 = z ** 22 */
625 fe51_sq(t2, t0);
626
627 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
628 fe51_mul(t1, t1, t2);
629
630 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
631 fe51_sq(t2, t1);
632 for (i = 1; i < 5; ++i)
633 fe51_sq(t2, t2);
634
635 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
636 fe51_mul(t1, t2, t1);
637
638 /* Continuing similarly... */
639
640 /* t2 = z ** (2 ** 20 - 1) */
641 fe51_sq(t2, t1);
642 for (i = 1; i < 10; ++i)
643 fe51_sq(t2, t2);
644
645 fe51_mul(t2, t2, t1);
646
647 /* t2 = z ** (2 ** 40 - 1) */
648 fe51_sq(t3, t2);
649 for (i = 1; i < 20; ++i)
650 fe51_sq(t3, t3);
651
652 fe51_mul(t2, t3, t2);
653
654 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
655 for (i = 0; i < 10; ++i)
656 fe51_sq(t2, t2);
657
658 /* t1 = z ** (2 ** 50 - 1) */
659 fe51_mul(t1, t2, t1);
660
661 /* t2 = z ** (2 ** 100 - 1) */
662 fe51_sq(t2, t1);
663 for (i = 1; i < 50; ++i)
664 fe51_sq(t2, t2);
665
666 fe51_mul(t2, t2, t1);
667
668 /* t2 = z ** (2 ** 200 - 1) */
669 fe51_sq(t3, t2);
670 for (i = 1; i < 100; ++i)
671 fe51_sq(t3, t3);
672
673 fe51_mul(t2, t3, t2);
674
675 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
676 for (i = 0; i < 50; ++i)
677 fe51_sq(t2, t2);
678
679 /* t1 = z ** (2 ** 250 - 1) */
680 fe51_mul(t1, t2, t1);
681
682 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
683 for (i = 0; i < 5; ++i)
684 fe51_sq(t1, t1);
685
686 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
687 fe51_mul(out, t1, t0);
688}
689
cfc32a1e
AP		 690/*
691 * Duplicate of original x25519_scalar_mult_generic, but using
692 * fe51_* subroutines.
693 */
694static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
695 const uint8_t point[32])
696{
697 fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
698 uint8_t e[32];
699 unsigned swap = 0;
700 int pos;
701
c521e439
AP		 702# ifdef BASE_2_64_IMPLEMENTED
703 if (x25519_fe64_eligible()) {
704 x25519_scalar_mulx(out, scalar, point);
705 return;
706 }
707# endif
708
cfc32a1e
AP		 709 memcpy(e, scalar, 32);
710 e[0] &= 0xf8;
711 e[31] &= 0x7f;
712 e[31] |= 0x40;
713 fe51_frombytes(x1, point);
714 fe51_1(x2);
715 fe51_0(z2);
716 fe51_copy(x3, x1);
717 fe51_1(z3);
718
719 for (pos = 254; pos >= 0; --pos) {
720 unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
721
722 swap ^= b;
723 fe51_cswap(x2, x3, swap);
724 fe51_cswap(z2, z3, swap);
725 swap = b;
726 fe51_sub(tmp0, x3, z3);
727 fe51_sub(tmp1, x2, z2);
728 fe51_add(x2, x2, z2);
729 fe51_add(z2, x3, z3);
730 fe51_mul(z3, tmp0, x2);
731 fe51_mul(z2, z2, tmp1);
732 fe51_sq(tmp0, tmp1);
733 fe51_sq(tmp1, x2);
734 fe51_add(x3, z3, z2);
735 fe51_sub(z2, z3, z2);
736 fe51_mul(x2, tmp1, tmp0);
737 fe51_sub(tmp1, tmp1, tmp0);
738 fe51_sq(z2, z2);
739 fe51_mul121666(z3, tmp1);
740 fe51_sq(x3, x3);
741 fe51_add(tmp0, tmp0, z3);
742 fe51_mul(z3, x1, z2);
743 fe51_mul(z2, tmp1, tmp0);
744 }
cfc32a1e
AP		 745
746 fe51_invert(z2, z2);
747 fe51_mul(x2, x2, z2);
748 fe51_tobytes(out, x2);
749
750 OPENSSL_cleanse(e, sizeof(e));
751}
752#endif
753
754/*
755 * Reference base 2^25.5 implementation.
3a17b9a4 756 *
cfc32a1e
AP		 757 * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
758 * 20141124 (http://bench.cr.yp.to/supercop.html).
759 *
760 * The field functions are shared by Ed25519 and X25519 where possible.
761 */
a90def6b 762
3a17b9a4
DMSP		 763/*
764 * fe means field element. Here the field is \Z/(2^255-19). An element t,
a90def6b
DSH		 765 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
766 * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
3a17b9a4
DMSP		 767 * context.
768 */
a90def6b
DSH		 769typedef int32_t fe[10];
770
425dde5d 771static const int64_t kBottom21Bits = 0x1fffffLL;
5b7af0dd
EK		 772static const int64_t kBottom25Bits = 0x1ffffffLL;
773static const int64_t kBottom26Bits = 0x3ffffffLL;
774static const int64_t kTop39Bits = 0xfffffffffe000000LL;
775static const int64_t kTop38Bits = 0xfffffffffc000000LL;
b9577984 776
3a17b9a4
DMSP		 777static uint64_t load_3(const uint8_t *in)
778{
779 uint64_t result;
780
425dde5d 781 result = ((uint64_t)in[0]);
3a17b9a4
DMSP		 782 result |= ((uint64_t)in[1]) << 8;
783 result |= ((uint64_t)in[2]) << 16;
784 return result;
a90def6b
DSH		 785}
786
3a17b9a4
DMSP		 787static uint64_t load_4(const uint8_t *in)
788{
789 uint64_t result;
790
425dde5d 791 result = ((uint64_t)in[0]);
3a17b9a4
DMSP		 792 result |= ((uint64_t)in[1]) << 8;
793 result |= ((uint64_t)in[2]) << 16;
794 result |= ((uint64_t)in[3]) << 24;
795 return result;
a90def6b
DSH		 796}
797
3a17b9a4
DMSP		 798static void fe_frombytes(fe h, const uint8_t *s)
799{
800 /* Ignores top bit of h. */
425dde5d
DMSP		 801 int64_t h0 = load_4(s);
802 int64_t h1 = load_3(s + 4) << 6;
803 int64_t h2 = load_3(s + 7) << 5;
804 int64_t h3 = load_3(s + 10) << 3;
805 int64_t h4 = load_3(s + 13) << 2;
806 int64_t h5 = load_4(s + 16);
807 int64_t h6 = load_3(s + 20) << 7;
808 int64_t h7 = load_3(s + 23) << 5;
809 int64_t h8 = load_3(s + 26) << 4;
810 int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
3a17b9a4
DMSP		 811 int64_t carry0;
812 int64_t carry1;
813 int64_t carry2;
814 int64_t carry3;
815 int64_t carry4;
816 int64_t carry5;
817 int64_t carry6;
818 int64_t carry7;
819 int64_t carry8;
820 int64_t carry9;
821
822 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
823 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
824 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
825 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
826 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
827
828 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
829 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
830 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
831 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
832 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
833
834 h[0] = (int32_t)h0;
835 h[1] = (int32_t)h1;
836 h[2] = (int32_t)h2;
837 h[3] = (int32_t)h3;
838 h[4] = (int32_t)h4;
839 h[5] = (int32_t)h5;
840 h[6] = (int32_t)h6;
841 h[7] = (int32_t)h7;
842 h[8] = (int32_t)h8;
843 h[9] = (int32_t)h9;
a90def6b
DSH		 844}
845
3a17b9a4
DMSP		 846/*
847 * Preconditions:
848 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
a90def6b
DSH		 849 *
850 * Write p=2^255-19; q=floor(h/p).
851 * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
852 *
853 * Proof:
854 * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
855 * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
856 *
857 * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
858 * Then 0<y<1.
859 *
860 * Write r=h-pq.
861 * Have 0<=r<=p-1=2^255-20.
862 * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
863 *
864 * Write x=r+19(2^-255)r+y.
865 * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
866 *
867 * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
3a17b9a4
DMSP		 868 * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
869 */
870static void fe_tobytes(uint8_t *s, const fe h)
871{
872 int32_t h0 = h[0];
873 int32_t h1 = h[1];
874 int32_t h2 = h[2];
875 int32_t h3 = h[3];
876 int32_t h4 = h[4];
877 int32_t h5 = h[5];
878 int32_t h6 = h[6];
879 int32_t h7 = h[7];
880 int32_t h8 = h[8];
881 int32_t h9 = h[9];
882 int32_t q;
883
884 q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
885 q = (h0 + q) >> 26;
886 q = (h1 + q) >> 25;
887 q = (h2 + q) >> 26;
888 q = (h3 + q) >> 25;
889 q = (h4 + q) >> 26;
890 q = (h5 + q) >> 25;
891 q = (h6 + q) >> 26;
892 q = (h7 + q) >> 25;
893 q = (h8 + q) >> 26;
894 q = (h9 + q) >> 25;
895
896 /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
897 h0 += 19 * q;
898 /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
899
900 h1 += h0 >> 26; h0 &= kBottom26Bits;
901 h2 += h1 >> 25; h1 &= kBottom25Bits;
902 h3 += h2 >> 26; h2 &= kBottom26Bits;
903 h4 += h3 >> 25; h3 &= kBottom25Bits;
904 h5 += h4 >> 26; h4 &= kBottom26Bits;
905 h6 += h5 >> 25; h5 &= kBottom25Bits;
906 h7 += h6 >> 26; h6 &= kBottom26Bits;
907 h8 += h7 >> 25; h7 &= kBottom25Bits;
908 h9 += h8 >> 26; h8 &= kBottom26Bits;
909 h9 &= kBottom25Bits;
910 /* h10 = carry9 */
911
912 /*
913 * Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
914 * Have h0+...+2^230 h9 between 0 and 2^255-1;
915 * evidently 2^255 h10-2^255 q = 0.
916 * Goal: Output h0+...+2^230 h9.
917 */
425dde5d
DMSP		 918 s[ 0] = (uint8_t) (h0 >> 0);
919 s[ 1] = (uint8_t) (h0 >> 8);
920 s[ 2] = (uint8_t) (h0 >> 16);
921 s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2));
922 s[ 4] = (uint8_t) (h1 >> 6);
923 s[ 5] = (uint8_t) (h1 >> 14);
924 s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3));
925 s[ 7] = (uint8_t) (h2 >> 5);
926 s[ 8] = (uint8_t) (h2 >> 13);
927 s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5));
928 s[10] = (uint8_t) (h3 >> 3);
929 s[11] = (uint8_t) (h3 >> 11);
3a17b9a4 930 s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6));
425dde5d
DMSP		 931 s[13] = (uint8_t) (h4 >> 2);
932 s[14] = (uint8_t) (h4 >> 10);
933 s[15] = (uint8_t) (h4 >> 18);
934 s[16] = (uint8_t) (h5 >> 0);
935 s[17] = (uint8_t) (h5 >> 8);
936 s[18] = (uint8_t) (h5 >> 16);
3a17b9a4 937 s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1));
425dde5d
DMSP		 938 s[20] = (uint8_t) (h6 >> 7);
939 s[21] = (uint8_t) (h6 >> 15);
3a17b9a4 940 s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3));
425dde5d
DMSP		 941 s[23] = (uint8_t) (h7 >> 5);
942 s[24] = (uint8_t) (h7 >> 13);
3a17b9a4 943 s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4));
425dde5d
DMSP		 944 s[26] = (uint8_t) (h8 >> 4);
945 s[27] = (uint8_t) (h8 >> 12);
3a17b9a4 946 s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6));
425dde5d
DMSP		 947 s[29] = (uint8_t) (h9 >> 2);
948 s[30] = (uint8_t) (h9 >> 10);
949 s[31] = (uint8_t) (h9 >> 18);
a90def6b
DSH		 950}
951
952/* h = f */
3a17b9a4
DMSP		 953static void fe_copy(fe h, const fe f)
954{
955 memmove(h, f, sizeof(int32_t) * 10);
a90def6b
DSH		 956}
957
958/* h = 0 */
3a17b9a4
DMSP		 959static void fe_0(fe h)
960{
961 memset(h, 0, sizeof(int32_t) * 10);
962}
a90def6b
DSH		 963
964/* h = 1 */
3a17b9a4
DMSP		 965static void fe_1(fe h)
966{
967 memset(h, 0, sizeof(int32_t) * 10);
968 h[0] = 1;
a90def6b
DSH		 969}
970
3a17b9a4
DMSP		 971/*
972 * h = f + g
973 *
a90def6b
DSH		 974 * Can overlap h with f or g.
975 *
976 * Preconditions:
977 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
978 * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
979 *
980 * Postconditions:
3a17b9a4
DMSP		 981 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
982 */
983static void fe_add(fe h, const fe f, const fe g)
984{
985 unsigned i;
986
987 for (i = 0; i < 10; i++) {
988 h[i] = f[i] + g[i];
989 }
a90def6b
DSH		 990}
991
3a17b9a4
DMSP		 992/*
993 * h = f - g
994 *
a90def6b
DSH		 995 * Can overlap h with f or g.
996 *
997 * Preconditions:
998 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
999 * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1000 *
1001 * Postconditions:
3a17b9a4
DMSP		 1002 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1003 */
1004static void fe_sub(fe h, const fe f, const fe g)
1005{
1006 unsigned i;
1007
1008 for (i = 0; i < 10; i++) {
1009 h[i] = f[i] - g[i];
1010 }
a90def6b
DSH		 1011}
1012
3a17b9a4
DMSP		 1013/*
1014 * h = f * g
1015 *
a90def6b
DSH		 1016 * Can overlap h with f or g.
1017 *
1018 * Preconditions:
1019 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1020 * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1021 *
1022 * Postconditions:
1023 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1024 *
1025 * Notes on implementation strategy:
1026 *
1027 * Using schoolbook multiplication.
1028 * Karatsuba would save a little in some cost models.
1029 *
1030 * Most multiplications by 2 and 19 are 32-bit precomputations;
1031 * cheaper than 64-bit postcomputations.
1032 *
1033 * There is one remaining multiplication by 19 in the carry chain;
1034 * one *19 precomputation can be merged into this,
1035 * but the resulting data flow is considerably less clean.
1036 *
1037 * There are 12 carries below.
1038 * 10 of them are 2-way parallelizable and vectorizable.
1039 * Can get away with 11 carries, but then data flow is much deeper.
1040 *
3a17b9a4
DMSP		 1041 * With tighter constraints on inputs can squeeze carries into int32.
1042 */
1043static void fe_mul(fe h, const fe f, const fe g)
1044{
1045 int32_t f0 = f[0];
1046 int32_t f1 = f[1];
1047 int32_t f2 = f[2];
1048 int32_t f3 = f[3];
1049 int32_t f4 = f[4];
1050 int32_t f5 = f[5];
1051 int32_t f6 = f[6];
1052 int32_t f7 = f[7];
1053 int32_t f8 = f[8];
1054 int32_t f9 = f[9];
1055 int32_t g0 = g[0];
1056 int32_t g1 = g[1];
1057 int32_t g2 = g[2];
1058 int32_t g3 = g[3];
1059 int32_t g4 = g[4];
1060 int32_t g5 = g[5];
1061 int32_t g6 = g[6];
1062 int32_t g7 = g[7];
1063 int32_t g8 = g[8];
1064 int32_t g9 = g[9];
1065 int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
1066 int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
1067 int32_t g3_19 = 19 * g3;
1068 int32_t g4_19 = 19 * g4;
1069 int32_t g5_19 = 19 * g5;
1070 int32_t g6_19 = 19 * g6;
1071 int32_t g7_19 = 19 * g7;
1072 int32_t g8_19 = 19 * g8;
1073 int32_t g9_19 = 19 * g9;
1074 int32_t f1_2 = 2 * f1;
1075 int32_t f3_2 = 2 * f3;
1076 int32_t f5_2 = 2 * f5;
1077 int32_t f7_2 = 2 * f7;
1078 int32_t f9_2 = 2 * f9;
1079 int64_t f0g0 = f0 * (int64_t) g0;
1080 int64_t f0g1 = f0 * (int64_t) g1;
1081 int64_t f0g2 = f0 * (int64_t) g2;
1082 int64_t f0g3 = f0 * (int64_t) g3;
1083 int64_t f0g4 = f0 * (int64_t) g4;
1084 int64_t f0g5 = f0 * (int64_t) g5;
1085 int64_t f0g6 = f0 * (int64_t) g6;
1086 int64_t f0g7 = f0 * (int64_t) g7;
1087 int64_t f0g8 = f0 * (int64_t) g8;
1088 int64_t f0g9 = f0 * (int64_t) g9;
1089 int64_t f1g0 = f1 * (int64_t) g0;
1090 int64_t f1g1_2 = f1_2 * (int64_t) g1;
1091 int64_t f1g2 = f1 * (int64_t) g2;
1092 int64_t f1g3_2 = f1_2 * (int64_t) g3;
1093 int64_t f1g4 = f1 * (int64_t) g4;
1094 int64_t f1g5_2 = f1_2 * (int64_t) g5;
1095 int64_t f1g6 = f1 * (int64_t) g6;
1096 int64_t f1g7_2 = f1_2 * (int64_t) g7;
1097 int64_t f1g8 = f1 * (int64_t) g8;
1098 int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
1099 int64_t f2g0 = f2 * (int64_t) g0;
1100 int64_t f2g1 = f2 * (int64_t) g1;
1101 int64_t f2g2 = f2 * (int64_t) g2;
1102 int64_t f2g3 = f2 * (int64_t) g3;
1103 int64_t f2g4 = f2 * (int64_t) g4;
1104 int64_t f2g5 = f2 * (int64_t) g5;
1105 int64_t f2g6 = f2 * (int64_t) g6;
1106 int64_t f2g7 = f2 * (int64_t) g7;
1107 int64_t f2g8_19 = f2 * (int64_t) g8_19;
1108 int64_t f2g9_19 = f2 * (int64_t) g9_19;
1109 int64_t f3g0 = f3 * (int64_t) g0;
1110 int64_t f3g1_2 = f3_2 * (int64_t) g1;
1111 int64_t f3g2 = f3 * (int64_t) g2;
1112 int64_t f3g3_2 = f3_2 * (int64_t) g3;
1113 int64_t f3g4 = f3 * (int64_t) g4;
1114 int64_t f3g5_2 = f3_2 * (int64_t) g5;
1115 int64_t f3g6 = f3 * (int64_t) g6;
1116 int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
1117 int64_t f3g8_19 = f3 * (int64_t) g8_19;
1118 int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
1119 int64_t f4g0 = f4 * (int64_t) g0;
1120 int64_t f4g1 = f4 * (int64_t) g1;
1121 int64_t f4g2 = f4 * (int64_t) g2;
1122 int64_t f4g3 = f4 * (int64_t) g3;
1123 int64_t f4g4 = f4 * (int64_t) g4;
1124 int64_t f4g5 = f4 * (int64_t) g5;
1125 int64_t f4g6_19 = f4 * (int64_t) g6_19;
1126 int64_t f4g7_19 = f4 * (int64_t) g7_19;
1127 int64_t f4g8_19 = f4 * (int64_t) g8_19;
1128 int64_t f4g9_19 = f4 * (int64_t) g9_19;
1129 int64_t f5g0 = f5 * (int64_t) g0;
1130 int64_t f5g1_2 = f5_2 * (int64_t) g1;
1131 int64_t f5g2 = f5 * (int64_t) g2;
1132 int64_t f5g3_2 = f5_2 * (int64_t) g3;
1133 int64_t f5g4 = f5 * (int64_t) g4;
1134 int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
1135 int64_t f5g6_19 = f5 * (int64_t) g6_19;
1136 int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
1137 int64_t f5g8_19 = f5 * (int64_t) g8_19;
1138 int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
1139 int64_t f6g0 = f6 * (int64_t) g0;
1140 int64_t f6g1 = f6 * (int64_t) g1;
1141 int64_t f6g2 = f6 * (int64_t) g2;
1142 int64_t f6g3 = f6 * (int64_t) g3;
1143 int64_t f6g4_19 = f6 * (int64_t) g4_19;
1144 int64_t f6g5_19 = f6 * (int64_t) g5_19;
1145 int64_t f6g6_19 = f6 * (int64_t) g6_19;
1146 int64_t f6g7_19 = f6 * (int64_t) g7_19;
1147 int64_t f6g8_19 = f6 * (int64_t) g8_19;
1148 int64_t f6g9_19 = f6 * (int64_t) g9_19;
1149 int64_t f7g0 = f7 * (int64_t) g0;
1150 int64_t f7g1_2 = f7_2 * (int64_t) g1;
1151 int64_t f7g2 = f7 * (int64_t) g2;
1152 int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
1153 int64_t f7g4_19 = f7 * (int64_t) g4_19;
1154 int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
1155 int64_t f7g6_19 = f7 * (int64_t) g6_19;
1156 int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
1157 int64_t f7g8_19 = f7 * (int64_t) g8_19;
1158 int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
1159 int64_t f8g0 = f8 * (int64_t) g0;
1160 int64_t f8g1 = f8 * (int64_t) g1;
1161 int64_t f8g2_19 = f8 * (int64_t) g2_19;
1162 int64_t f8g3_19 = f8 * (int64_t) g3_19;
1163 int64_t f8g4_19 = f8 * (int64_t) g4_19;
1164 int64_t f8g5_19 = f8 * (int64_t) g5_19;
1165 int64_t f8g6_19 = f8 * (int64_t) g6_19;
1166 int64_t f8g7_19 = f8 * (int64_t) g7_19;
1167 int64_t f8g8_19 = f8 * (int64_t) g8_19;
1168 int64_t f8g9_19 = f8 * (int64_t) g9_19;
1169 int64_t f9g0 = f9 * (int64_t) g0;
1170 int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
1171 int64_t f9g2_19 = f9 * (int64_t) g2_19;
1172 int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
1173 int64_t f9g4_19 = f9 * (int64_t) g4_19;
1174 int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
1175 int64_t f9g6_19 = f9 * (int64_t) g6_19;
1176 int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
1177 int64_t f9g8_19 = f9 * (int64_t) g8_19;
1178 int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
425dde5d
DMSP		 1179 int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1180 int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1181 int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1182 int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1183 int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1184 int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1185 int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
1186 int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
1187 int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
1188 int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ;
3a17b9a4
DMSP		 1189 int64_t carry0;
1190 int64_t carry1;
1191 int64_t carry2;
1192 int64_t carry3;
1193 int64_t carry4;
1194 int64_t carry5;
1195 int64_t carry6;
1196 int64_t carry7;
1197 int64_t carry8;
1198 int64_t carry9;
1199
1200 /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
1201 * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1202 * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
1203 * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
1204
1205 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1206 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1207 /* |h0| <= 2^25 */
1208 /* |h4| <= 2^25 */
1209 /* |h1| <= 1.71*2^59 */
1210 /* |h5| <= 1.71*2^59 */
1211
1212 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1213 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1214 /* |h1| <= 2^24; from now on fits into int32 */
1215 /* |h5| <= 2^24; from now on fits into int32 */
1216 /* |h2| <= 1.41*2^60 */
1217 /* |h6| <= 1.41*2^60 */
1218
1219 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1220 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1221 /* |h2| <= 2^25; from now on fits into int32 unchanged */
1222 /* |h6| <= 2^25; from now on fits into int32 unchanged */
1223 /* |h3| <= 1.71*2^59 */
1224 /* |h7| <= 1.71*2^59 */
1225
1226 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1227 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1228 /* |h3| <= 2^24; from now on fits into int32 unchanged */
1229 /* |h7| <= 2^24; from now on fits into int32 unchanged */
1230 /* |h4| <= 1.72*2^34 */
1231 /* |h8| <= 1.41*2^60 */
1232
1233 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1234 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1235 /* |h4| <= 2^25; from now on fits into int32 unchanged */
1236 /* |h8| <= 2^25; from now on fits into int32 unchanged */
1237 /* |h5| <= 1.01*2^24 */
1238 /* |h9| <= 1.71*2^59 */
1239
1240 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1241 /* |h9| <= 2^24; from now on fits into int32 unchanged */
1242 /* |h0| <= 1.1*2^39 */
1243
1244 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1245 /* |h0| <= 2^25; from now on fits into int32 unchanged */
1246 /* |h1| <= 1.01*2^24 */
1247
1248 h[0] = (int32_t)h0;
1249 h[1] = (int32_t)h1;
1250 h[2] = (int32_t)h2;
1251 h[3] = (int32_t)h3;
1252 h[4] = (int32_t)h4;
1253 h[5] = (int32_t)h5;
1254 h[6] = (int32_t)h6;
1255 h[7] = (int32_t)h7;
1256 h[8] = (int32_t)h8;
1257 h[9] = (int32_t)h9;
a90def6b
DSH		 1258}
1259
3a17b9a4
DMSP		 1260/*
1261 * h = f * f
1262 *
a90def6b
DSH		 1263 * Can overlap h with f.
1264 *
1265 * Preconditions:
1266 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1267 *
1268 * Postconditions:
1269 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1270 *
3a17b9a4
DMSP		 1271 * See fe_mul.c for discussion of implementation strategy.
1272 */
1273static void fe_sq(fe h, const fe f)
1274{
1275 int32_t f0 = f[0];
1276 int32_t f1 = f[1];
1277 int32_t f2 = f[2];
1278 int32_t f3 = f[3];
1279 int32_t f4 = f[4];
1280 int32_t f5 = f[5];
1281 int32_t f6 = f[6];
1282 int32_t f7 = f[7];
1283 int32_t f8 = f[8];
1284 int32_t f9 = f[9];
1285 int32_t f0_2 = 2 * f0;
1286 int32_t f1_2 = 2 * f1;
1287 int32_t f2_2 = 2 * f2;
1288 int32_t f3_2 = 2 * f3;
1289 int32_t f4_2 = 2 * f4;
1290 int32_t f5_2 = 2 * f5;
1291 int32_t f6_2 = 2 * f6;
1292 int32_t f7_2 = 2 * f7;
1293 int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
1294 int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
1295 int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
1296 int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
1297 int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
1298 int64_t f0f0 = f0 * (int64_t) f0;
1299 int64_t f0f1_2 = f0_2 * (int64_t) f1;
1300 int64_t f0f2_2 = f0_2 * (int64_t) f2;
1301 int64_t f0f3_2 = f0_2 * (int64_t) f3;
1302 int64_t f0f4_2 = f0_2 * (int64_t) f4;
1303 int64_t f0f5_2 = f0_2 * (int64_t) f5;
1304 int64_t f0f6_2 = f0_2 * (int64_t) f6;
1305 int64_t f0f7_2 = f0_2 * (int64_t) f7;
1306 int64_t f0f8_2 = f0_2 * (int64_t) f8;
1307 int64_t f0f9_2 = f0_2 * (int64_t) f9;
1308 int64_t f1f1_2 = f1_2 * (int64_t) f1;
1309 int64_t f1f2_2 = f1_2 * (int64_t) f2;
1310 int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1311 int64_t f1f4_2 = f1_2 * (int64_t) f4;
1312 int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1313 int64_t f1f6_2 = f1_2 * (int64_t) f6;
1314 int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1315 int64_t f1f8_2 = f1_2 * (int64_t) f8;
1316 int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1317 int64_t f2f2 = f2 * (int64_t) f2;
1318 int64_t f2f3_2 = f2_2 * (int64_t) f3;
1319 int64_t f2f4_2 = f2_2 * (int64_t) f4;
1320 int64_t f2f5_2 = f2_2 * (int64_t) f5;
1321 int64_t f2f6_2 = f2_2 * (int64_t) f6;
1322 int64_t f2f7_2 = f2_2 * (int64_t) f7;
1323 int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1324 int64_t f2f9_38 = f2 * (int64_t) f9_38;
1325 int64_t f3f3_2 = f3_2 * (int64_t) f3;
1326 int64_t f3f4_2 = f3_2 * (int64_t) f4;
1327 int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1328 int64_t f3f6_2 = f3_2 * (int64_t) f6;
1329 int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1330 int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1331 int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1332 int64_t f4f4 = f4 * (int64_t) f4;
1333 int64_t f4f5_2 = f4_2 * (int64_t) f5;
1334 int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1335 int64_t f4f7_38 = f4 * (int64_t) f7_38;
1336 int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1337 int64_t f4f9_38 = f4 * (int64_t) f9_38;
1338 int64_t f5f5_38 = f5 * (int64_t) f5_38;
1339 int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1340 int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1341 int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1342 int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1343 int64_t f6f6_19 = f6 * (int64_t) f6_19;
1344 int64_t f6f7_38 = f6 * (int64_t) f7_38;
1345 int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1346 int64_t f6f9_38 = f6 * (int64_t) f9_38;
1347 int64_t f7f7_38 = f7 * (int64_t) f7_38;
1348 int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1349 int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1350 int64_t f8f8_19 = f8 * (int64_t) f8_19;
1351 int64_t f8f9_38 = f8 * (int64_t) f9_38;
1352 int64_t f9f9_38 = f9 * (int64_t) f9_38;
425dde5d
DMSP		 1353 int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1354 int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1355 int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1356 int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1357 int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1358 int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1359 int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1360 int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1361 int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1362 int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
3a17b9a4
DMSP		 1363 int64_t carry0;
1364 int64_t carry1;
1365 int64_t carry2;
1366 int64_t carry3;
1367 int64_t carry4;
1368 int64_t carry5;
1369 int64_t carry6;
1370 int64_t carry7;
1371 int64_t carry8;
1372 int64_t carry9;
1373
1374 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1375 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1376
1377 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1378 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1379
1380 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1381 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1382
1383 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1384 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1385
1386 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1387 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1388
1389 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1390
1391 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1392
1393 h[0] = (int32_t)h0;
1394 h[1] = (int32_t)h1;
1395 h[2] = (int32_t)h2;
1396 h[3] = (int32_t)h3;
1397 h[4] = (int32_t)h4;
1398 h[5] = (int32_t)h5;
1399 h[6] = (int32_t)h6;
1400 h[7] = (int32_t)h7;
1401 h[8] = (int32_t)h8;
1402 h[9] = (int32_t)h9;
a90def6b
DSH		 1403}
1404
3a17b9a4
DMSP		 1405static void fe_invert(fe out, const fe z)
1406{
1407 fe t0;
1408 fe t1;
1409 fe t2;
1410 fe t3;
1411 int i;
1412
1413 /*
1414 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
1415 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
1416 */
1417
1418 /* t0 = z ** 2 */
1419 fe_sq(t0, z);
1420
1421 /* t1 = t0 ** (2 ** 2) = z ** 8 */
1422 fe_sq(t1, t0);
1423 fe_sq(t1, t1);
1424
1425 /* t1 = z * t1 = z ** 9 */
1426 fe_mul(t1, z, t1);
1427 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1428 fe_mul(t0, t0, t1);
a90def6b 1429
3a17b9a4
DMSP		 1430 /* t2 = t0 ** 2 = z ** 22 */
1431 fe_sq(t2, t0);
0eadff03 1432
3a17b9a4
DMSP		 1433 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
1434 fe_mul(t1, t1, t2);
0eadff03 1435
3a17b9a4
DMSP		 1436 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
1437 fe_sq(t2, t1);
1438 for (i = 1; i < 5; ++i) {
1439 fe_sq(t2, t2);
1440 }
0eadff03 1441
3a17b9a4
DMSP		 1442 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
1443 fe_mul(t1, t2, t1);
0eadff03 1444
3a17b9a4 1445 /* Continuing similarly... */
0eadff03 1446
3a17b9a4
DMSP		 1447 /* t2 = z ** (2 ** 20 - 1) */
1448 fe_sq(t2, t1);
1449 for (i = 1; i < 10; ++i) {
1450 fe_sq(t2, t2);
1451 }
1452 fe_mul(t2, t2, t1);
0eadff03 1453
3a17b9a4
DMSP		 1454 /* t2 = z ** (2 ** 40 - 1) */
1455 fe_sq(t3, t2);
1456 for (i = 1; i < 20; ++i) {
1457 fe_sq(t3, t3);
1458 }
1459 fe_mul(t2, t3, t2);
0eadff03 1460
3a17b9a4
DMSP		 1461 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
1462 for (i = 0; i < 10; ++i) {
1463 fe_sq(t2, t2);
1464 }
1465 /* t1 = z ** (2 ** 50 - 1) */
1466 fe_mul(t1, t2, t1);
0eadff03 1467
3a17b9a4
DMSP		 1468 /* t2 = z ** (2 ** 100 - 1) */
1469 fe_sq(t2, t1);
1470 for (i = 1; i < 50; ++i) {
1471 fe_sq(t2, t2);
1472 }
1473 fe_mul(t2, t2, t1);
0eadff03 1474
3a17b9a4
DMSP		 1475 /* t2 = z ** (2 ** 200 - 1) */
1476 fe_sq(t3, t2);
1477 for (i = 1; i < 100; ++i) {
1478 fe_sq(t3, t3);
1479 }
1480 fe_mul(t2, t3, t2);
0eadff03 1481
3a17b9a4 1482 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
a90def6b 1483 fe_sq(t2, t2);
3a17b9a4
DMSP		 1484 for (i = 1; i < 50; ++i) {
1485 fe_sq(t2, t2);
1486 }
0eadff03 1487
3a17b9a4
DMSP		 1488 /* t1 = z ** (2 ** 250 - 1) */
1489 fe_mul(t1, t2, t1);
0eadff03 1490
3a17b9a4 1491 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
a90def6b 1492 fe_sq(t1, t1);
3a17b9a4
DMSP		 1493 for (i = 1; i < 5; ++i) {
1494 fe_sq(t1, t1);
1495 }
0eadff03 1496
3a17b9a4
DMSP		 1497 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
1498 fe_mul(out, t1, t0);
a90def6b
DSH		 1499}
1500
3a17b9a4
DMSP		 1501/*
1502 * h = -f
a90def6b
DSH		 1503 *
1504 * Preconditions:
1505 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1506 *
1507 * Postconditions:
3a17b9a4
DMSP		 1508 * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1509 */
1510static void fe_neg(fe h, const fe f)
1511{
1512 unsigned i;
1513
1514 for (i = 0; i < 10; i++) {
1515 h[i] = -f[i];
1516 }
a90def6b
DSH		 1517}
1518
3a17b9a4
DMSP		 1519/*
1520 * Replace (f,g) with (g,g) if b == 1;
a90def6b
DSH		 1521 * replace (f,g) with (f,g) if b == 0.
1522 *
3a17b9a4
DMSP		 1523 * Preconditions: b in {0,1}.
1524 */
1525static void fe_cmov(fe f, const fe g, unsigned b)
1526{
1527 size_t i;
1528
1529 b = 0-b;
1530 for (i = 0; i < 10; i++) {
1531 int32_t x = f[i] ^ g[i];
1532 x &= b;
1533 f[i] ^= x;
1534 }
a90def6b
DSH		 1535}
1536
3a17b9a4
DMSP		 1537/*
1538 * return 0 if f == 0
06c6d05f
DSH		 1539 * return 1 if f != 0
1540 *
1541 * Preconditions:
3a17b9a4
DMSP		 1542 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1543 */
1544static int fe_isnonzero(const fe f)
1545{
1546 uint8_t s[32];
1547 static const uint8_t zero[32] = {0};
06c6d05f 1548
3a17b9a4
DMSP		 1549 fe_tobytes(s, f);
1550
1551 return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
06c6d05f
DSH		 1552}
1553
3a17b9a4
DMSP		 1554/*
1555 * return 1 if f is in {1,3,5,...,q-2}
06c6d05f
DSH		 1556 * return 0 if f is in {0,2,4,...,q-1}
1557 *
1558 * Preconditions:
3a17b9a4
DMSP		 1559 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1560 */
1561static int fe_isnegative(const fe f)
1562{
1563 uint8_t s[32];
1564
1565 fe_tobytes(s, f);
1566 return s[0] & 1;
06c6d05f
DSH		 1567}
1568
3a17b9a4
DMSP		 1569/*
1570 * h = 2 * f * f
1571 *
a90def6b
DSH		 1572 * Can overlap h with f.
1573 *
1574 * Preconditions:
1575 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1576 *
1577 * Postconditions:
1578 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1579 *
3a17b9a4
DMSP		 1580 * See fe_mul.c for discussion of implementation strategy.
1581 */
1582static void fe_sq2(fe h, const fe f)
1583{
1584 int32_t f0 = f[0];
1585 int32_t f1 = f[1];
1586 int32_t f2 = f[2];
1587 int32_t f3 = f[3];
1588 int32_t f4 = f[4];
1589 int32_t f5 = f[5];
1590 int32_t f6 = f[6];
1591 int32_t f7 = f[7];
1592 int32_t f8 = f[8];
1593 int32_t f9 = f[9];
1594 int32_t f0_2 = 2 * f0;
1595 int32_t f1_2 = 2 * f1;
1596 int32_t f2_2 = 2 * f2;
1597 int32_t f3_2 = 2 * f3;
1598 int32_t f4_2 = 2 * f4;
1599 int32_t f5_2 = 2 * f5;
1600 int32_t f6_2 = 2 * f6;
1601 int32_t f7_2 = 2 * f7;
1602 int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
1603 int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
1604 int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
1605 int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
1606 int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
1607 int64_t f0f0 = f0 * (int64_t) f0;
1608 int64_t f0f1_2 = f0_2 * (int64_t) f1;
1609 int64_t f0f2_2 = f0_2 * (int64_t) f2;
1610 int64_t f0f3_2 = f0_2 * (int64_t) f3;
1611 int64_t f0f4_2 = f0_2 * (int64_t) f4;
1612 int64_t f0f5_2 = f0_2 * (int64_t) f5;
1613 int64_t f0f6_2 = f0_2 * (int64_t) f6;
1614 int64_t f0f7_2 = f0_2 * (int64_t) f7;
1615 int64_t f0f8_2 = f0_2 * (int64_t) f8;
1616 int64_t f0f9_2 = f0_2 * (int64_t) f9;
1617 int64_t f1f1_2 = f1_2 * (int64_t) f1;
1618 int64_t f1f2_2 = f1_2 * (int64_t) f2;
1619 int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1620 int64_t f1f4_2 = f1_2 * (int64_t) f4;
1621 int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1622 int64_t f1f6_2 = f1_2 * (int64_t) f6;
1623 int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1624 int64_t f1f8_2 = f1_2 * (int64_t) f8;
1625 int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1626 int64_t f2f2 = f2 * (int64_t) f2;
1627 int64_t f2f3_2 = f2_2 * (int64_t) f3;
1628 int64_t f2f4_2 = f2_2 * (int64_t) f4;
1629 int64_t f2f5_2 = f2_2 * (int64_t) f5;
1630 int64_t f2f6_2 = f2_2 * (int64_t) f6;
1631 int64_t f2f7_2 = f2_2 * (int64_t) f7;
1632 int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1633 int64_t f2f9_38 = f2 * (int64_t) f9_38;
1634 int64_t f3f3_2 = f3_2 * (int64_t) f3;
1635 int64_t f3f4_2 = f3_2 * (int64_t) f4;
1636 int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1637 int64_t f3f6_2 = f3_2 * (int64_t) f6;
1638 int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1639 int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1640 int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1641 int64_t f4f4 = f4 * (int64_t) f4;
1642 int64_t f4f5_2 = f4_2 * (int64_t) f5;
1643 int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1644 int64_t f4f7_38 = f4 * (int64_t) f7_38;
1645 int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1646 int64_t f4f9_38 = f4 * (int64_t) f9_38;
1647 int64_t f5f5_38 = f5 * (int64_t) f5_38;
1648 int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1649 int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1650 int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1651 int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1652 int64_t f6f6_19 = f6 * (int64_t) f6_19;
1653 int64_t f6f7_38 = f6 * (int64_t) f7_38;
1654 int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1655 int64_t f6f9_38 = f6 * (int64_t) f9_38;
1656 int64_t f7f7_38 = f7 * (int64_t) f7_38;
1657 int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1658 int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1659 int64_t f8f8_19 = f8 * (int64_t) f8_19;
1660 int64_t f8f9_38 = f8 * (int64_t) f9_38;
1661 int64_t f9f9_38 = f9 * (int64_t) f9_38;
425dde5d
DMSP		 1662 int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1663 int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1664 int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1665 int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1666 int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1667 int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1668 int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1669 int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1670 int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1671 int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
3a17b9a4
DMSP		 1672 int64_t carry0;
1673 int64_t carry1;
1674 int64_t carry2;
1675 int64_t carry3;
1676 int64_t carry4;
1677 int64_t carry5;
1678 int64_t carry6;
1679 int64_t carry7;
1680 int64_t carry8;
1681 int64_t carry9;
1682
1683 h0 += h0;
1684 h1 += h1;
1685 h2 += h2;
1686 h3 += h3;
1687 h4 += h4;
1688 h5 += h5;
1689 h6 += h6;
1690 h7 += h7;
1691 h8 += h8;
1692 h9 += h9;
1693
1694 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1695 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1696
1697 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1698 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1699
1700 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1701 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1702
1703 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1704 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1705
1706 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1707 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1708
1709 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1710
1711 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1712
1713 h[0] = (int32_t)h0;
1714 h[1] = (int32_t)h1;
1715 h[2] = (int32_t)h2;
1716 h[3] = (int32_t)h3;
1717 h[4] = (int32_t)h4;
1718 h[5] = (int32_t)h5;
1719 h[6] = (int32_t)h6;
1720 h[7] = (int32_t)h7;
1721 h[8] = (int32_t)h8;
1722 h[9] = (int32_t)h9;
a90def6b
DSH		 1723}
1724
3a17b9a4
DMSP		 1725static void fe_pow22523(fe out, const fe z)
1726{
1727 fe t0;
1728 fe t1;
1729 fe t2;
1730 int i;
06c6d05f 1731
3a17b9a4
DMSP		 1732 fe_sq(t0, z);
1733 fe_sq(t1, t0);
1734 for (i = 1; i < 2; ++i) {
1735 fe_sq(t1, t1);
1736 }
1737 fe_mul(t1, z, t1);
1738 fe_mul(t0, t0, t1);
1739 fe_sq(t0, t0);
1740 fe_mul(t0, t1, t0);
1741 fe_sq(t1, t0);
1742 for (i = 1; i < 5; ++i) {
1743 fe_sq(t1, t1);
1744 }
1745 fe_mul(t0, t1, t0);
1746 fe_sq(t1, t0);
1747 for (i = 1; i < 10; ++i) {
1748 fe_sq(t1, t1);
1749 }
1750 fe_mul(t1, t1, t0);
1751 fe_sq(t2, t1);
1752 for (i = 1; i < 20; ++i) {
1753 fe_sq(t2, t2);
1754 }
1755 fe_mul(t1, t2, t1);
06c6d05f 1756 fe_sq(t1, t1);
3a17b9a4
DMSP		 1757 for (i = 1; i < 10; ++i) {
1758 fe_sq(t1, t1);
1759 }
1760 fe_mul(t0, t1, t0);
1761 fe_sq(t1, t0);
1762 for (i = 1; i < 50; ++i) {
1763 fe_sq(t1, t1);
1764 }
1765 fe_mul(t1, t1, t0);
1766 fe_sq(t2, t1);
1767 for (i = 1; i < 100; ++i) {
1768 fe_sq(t2, t2);
1769 }
1770 fe_mul(t1, t2, t1);
06c6d05f 1771 fe_sq(t1, t1);
3a17b9a4
DMSP		 1772 for (i = 1; i < 50; ++i) {
1773 fe_sq(t1, t1);
1774 }
1775 fe_mul(t0, t1, t0);
06c6d05f 1776 fe_sq(t0, t0);
3a17b9a4
DMSP		 1777 for (i = 1; i < 2; ++i) {
1778 fe_sq(t0, t0);
1779 }
1780 fe_mul(out, t0, z);
06c6d05f
DSH		 1781}
1782
3a17b9a4
DMSP		 1783/*
1784 * ge means group element.
1785 *
a90def6b
DSH		 1786 * Here the group is the set of pairs (x,y) of field elements (see fe.h)
1787 * satisfying -x^2 + y^2 = 1 + d x^2y^2
1788 * where d = -121665/121666.
1789 *
1790 * Representations:
1791 * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1792 * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1793 * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
3a17b9a4
DMSP		 1794 * ge_precomp (Duif): (y+x,y-x,2dxy)
1795 */
a90def6b 1796typedef struct {
3a17b9a4
DMSP		 1797 fe X;
1798 fe Y;
1799 fe Z;
a90def6b
DSH		 1800} ge_p2;
1801
1802typedef struct {
3a17b9a4
DMSP		 1803 fe X;
1804 fe Y;
1805 fe Z;
1806 fe T;
a90def6b
DSH		 1807} ge_p3;
1808
1809typedef struct {
3a17b9a4
DMSP		 1810 fe X;
1811 fe Y;
1812 fe Z;
1813 fe T;
a90def6b
DSH		 1814} ge_p1p1;
1815
1816typedef struct {
3a17b9a4
DMSP		 1817 fe yplusx;
1818 fe yminusx;
1819 fe xy2d;
a90def6b
DSH		 1820} ge_precomp;
1821
1822typedef struct {
3a17b9a4
DMSP		 1823 fe YplusX;
1824 fe YminusX;
1825 fe Z;
1826 fe T2d;
a90def6b
DSH		 1827} ge_cached;
1828
3a17b9a4
DMSP		 1829static void ge_tobytes(uint8_t *s, const ge_p2 *h)
1830{
1831 fe recip;
1832 fe x;
1833 fe y;
1834
1835 fe_invert(recip, h->Z);
1836 fe_mul(x, h->X, recip);
1837 fe_mul(y, h->Y, recip);
1838 fe_tobytes(s, y);
1839 s[31] ^= fe_isnegative(x) << 7;
1840}
06c6d05f 1841
3a17b9a4
DMSP		 1842static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h)
1843{
1844 fe recip;
1845 fe x;
1846 fe y;
1847
1848 fe_invert(recip, h->Z);
1849 fe_mul(x, h->X, recip);
1850 fe_mul(y, h->Y, recip);
1851 fe_tobytes(s, y);
1852 s[31] ^= fe_isnegative(x) << 7;
06c6d05f
DSH		 1853}
1854
3a17b9a4
DMSP		 1855static const fe d = {
1856 -10913610, 13857413, -15372611, 6949391, 114729,
1857 -8787816, -6275908, -3247719, -18696448, -12055116
1858};
06c6d05f 1859
3a17b9a4
DMSP		 1860static const fe sqrtm1 = {
1861 -32595792, -7943725, 9377950, 3500415, 12389472,
1862 -272473, -25146209, -2005654, 326686, 11406482
1863};
06c6d05f 1864
3a17b9a4
DMSP		 1865static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s)
1866{
1867 fe u;
1868 fe v;
1869 fe v3;
1870 fe vxx;
1871 fe check;
1872
1873 fe_frombytes(h->Y, s);
1874 fe_1(h->Z);
1875 fe_sq(u, h->Y);
1876 fe_mul(v, u, d);
1877 fe_sub(u, u, h->Z); /* u = y^2-1 */
1878 fe_add(v, v, h->Z); /* v = dy^2+1 */
1879
1880 fe_sq(v3, v);
1881 fe_mul(v3, v3, v); /* v3 = v^3 */
1882 fe_sq(h->X, v3);
1883 fe_mul(h->X, h->X, v);
1884 fe_mul(h->X, h->X, u); /* x = uv^7 */
1885
1886 fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
1887 fe_mul(h->X, h->X, v3);
1888 fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
1889
1890 fe_sq(vxx, h->X);
1891 fe_mul(vxx, vxx, v);
1892 fe_sub(check, vxx, u); /* vx^2-u */
06c6d05f 1893 if (fe_isnonzero(check)) {
3a17b9a4
DMSP		 1894 fe_add(check, vxx, u); /* vx^2+u */
1895 if (fe_isnonzero(check)) {
1896 return -1;
1897 }
1898 fe_mul(h->X, h->X, sqrtm1);
06c6d05f 1899 }
06c6d05f 1900
3a17b9a4
DMSP		 1901 if (fe_isnegative(h->X) != (s[31] >> 7)) {
1902 fe_neg(h->X, h->X);
1903 }
06c6d05f 1904
3a17b9a4
DMSP		 1905 fe_mul(h->T, h->X, h->Y);
1906 return 0;
06c6d05f
DSH		 1907}
1908
3a17b9a4
DMSP		 1909static void ge_p2_0(ge_p2 *h)
1910{
1911 fe_0(h->X);
1912 fe_1(h->Y);
1913 fe_1(h->Z);
06c6d05f
DSH		 1914}
1915
3a17b9a4
DMSP		 1916static void ge_p3_0(ge_p3 *h)
1917{
1918 fe_0(h->X);
1919 fe_1(h->Y);
1920 fe_1(h->Z);
1921 fe_0(h->T);
a90def6b
DSH		 1922}
1923
3a17b9a4
DMSP		 1924static void ge_precomp_0(ge_precomp *h)
1925{
1926 fe_1(h->yplusx);
1927 fe_1(h->yminusx);
1928 fe_0(h->xy2d);
a90def6b
DSH		 1929}
1930
1931/* r = p */
3a17b9a4
DMSP		 1932static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p)
1933{
1934 fe_copy(r->X, p->X);
1935 fe_copy(r->Y, p->Y);
1936 fe_copy(r->Z, p->Z);
a90def6b
DSH		 1937}
1938
3a17b9a4
DMSP		 1939static const fe d2 = {
1940 -21827239, -5839606, -30745221, 13898782, 229458,
1941 15978800, -12551817, -6495438, 29715968, 9444199
1942};
06c6d05f
DSH		 1943
1944/* r = p */
3a17b9a4
DMSP		 1945static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p)
1946{
1947 fe_add(r->YplusX, p->Y, p->X);
1948 fe_sub(r->YminusX, p->Y, p->X);
1949 fe_copy(r->Z, p->Z);
1950 fe_mul(r->T2d, p->T, d2);
06c6d05f
DSH		 1951}
1952
a90def6b 1953/* r = p */
3a17b9a4
DMSP		 1954static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p)
1955{
1956 fe_mul(r->X, p->X, p->T);
1957 fe_mul(r->Y, p->Y, p->Z);
1958 fe_mul(r->Z, p->Z, p->T);
a90def6b
DSH		 1959}
1960
1961/* r = p */
3a17b9a4
DMSP		 1962static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p)
1963{
1964 fe_mul(r->X, p->X, p->T);
1965 fe_mul(r->Y, p->Y, p->Z);
1966 fe_mul(r->Z, p->Z, p->T);
1967 fe_mul(r->T, p->X, p->Y);
a90def6b
DSH		 1968}
1969
1970/* r = 2 * p */
3a17b9a4
DMSP		 1971static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p)
1972{
1973 fe t0;
1974
1975 fe_sq(r->X, p->X);
1976 fe_sq(r->Z, p->Y);
1977 fe_sq2(r->T, p->Z);
1978 fe_add(r->Y, p->X, p->Y);
1979 fe_sq(t0, r->Y);
1980 fe_add(r->Y, r->Z, r->X);
1981 fe_sub(r->Z, r->Z, r->X);
1982 fe_sub(r->X, t0, r->Y);
1983 fe_sub(r->T, r->T, r->Z);
a90def6b
DSH		 1984}
1985
1986/* r = 2 * p */
3a17b9a4
DMSP		 1987static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p)
1988{
1989 ge_p2 q;
1990 ge_p3_to_p2(&q, p);
1991 ge_p2_dbl(r, &q);
a90def6b
DSH		 1992}
1993
1994/* r = p + q */
3a17b9a4
DMSP		 1995static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
1996{
1997 fe t0;
1998
1999 fe_add(r->X, p->Y, p->X);
2000 fe_sub(r->Y, p->Y, p->X);
2001 fe_mul(r->Z, r->X, q->yplusx);
2002 fe_mul(r->Y, r->Y, q->yminusx);
2003 fe_mul(r->T, q->xy2d, p->T);
2004 fe_add(t0, p->Z, p->Z);
2005 fe_sub(r->X, r->Z, r->Y);
2006 fe_add(r->Y, r->Z, r->Y);
2007 fe_add(r->Z, t0, r->T);
2008 fe_sub(r->T, t0, r->T);
a90def6b
DSH		 2009}
2010
06c6d05f 2011/* r = p - q */
3a17b9a4
DMSP		 2012static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
2013{
2014 fe t0;
2015
2016 fe_add(r->X, p->Y, p->X);
2017 fe_sub(r->Y, p->Y, p->X);
2018 fe_mul(r->Z, r->X, q->yminusx);
2019 fe_mul(r->Y, r->Y, q->yplusx);
2020 fe_mul(r->T, q->xy2d, p->T);
2021 fe_add(t0, p->Z, p->Z);
2022 fe_sub(r->X, r->Z, r->Y);
2023 fe_add(r->Y, r->Z, r->Y);
2024 fe_sub(r->Z, t0, r->T);
2025 fe_add(r->T, t0, r->T);
06c6d05f
DSH		 2026}
2027
2028/* r = p + q */
3a17b9a4
DMSP		 2029static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
2030{
2031 fe t0;
2032
2033 fe_add(r->X, p->Y, p->X);
2034 fe_sub(r->Y, p->Y, p->X);
2035 fe_mul(r->Z, r->X, q->YplusX);
2036 fe_mul(r->Y, r->Y, q->YminusX);
2037 fe_mul(r->T, q->T2d, p->T);
2038 fe_mul(r->X, p->Z, q->Z);
2039 fe_add(t0, r->X, r->X);
2040 fe_sub(r->X, r->Z, r->Y);
2041 fe_add(r->Y, r->Z, r->Y);
2042 fe_add(r->Z, t0, r->T);
2043 fe_sub(r->T, t0, r->T);
06c6d05f
DSH		 2044}
2045
2046/* r = p - q */
3a17b9a4
DMSP		 2047static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
2048{
2049 fe t0;
2050
2051 fe_add(r->X, p->Y, p->X);
2052 fe_sub(r->Y, p->Y, p->X);
2053 fe_mul(r->Z, r->X, q->YminusX);
2054 fe_mul(r->Y, r->Y, q->YplusX);
2055 fe_mul(r->T, q->T2d, p->T);
2056 fe_mul(r->X, p->Z, q->Z);
2057 fe_add(t0, r->X, r->X);
2058 fe_sub(r->X, r->Z, r->Y);
2059 fe_add(r->Y, r->Z, r->Y);
2060 fe_sub(r->Z, t0, r->T);
2061 fe_add(r->T, t0, r->T);
06c6d05f
DSH		 2062}
2063
3a17b9a4
DMSP		 2064static uint8_t equal(signed char b, signed char c)
2065{
2066 uint8_t ub = b;
2067 uint8_t uc = c;
2068 uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2069 uint32_t y = x; /* 0: yes; 1..255: no */
2070 y -= 1; /* 4294967295: yes; 0..254: no */
2071 y >>= 31; /* 1: yes; 0: no */
2072 return y;
a90def6b
DSH		 2073}
2074
3a17b9a4
DMSP		 2075static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b)
2076{
2077 fe_cmov(t->yplusx, u->yplusx, b);
2078 fe_cmov(t->yminusx, u->yminusx, b);
2079 fe_cmov(t->xy2d, u->xy2d, b);
a90def6b
DSH		 2080}
2081
a90def6b 2082/* k25519Precomp[i][j] = (j+1)*256^i*B */
dc22d6b3 2083static const ge_precomp k25519Precomp[32][8] = {
a90def6b
DSH		 2084 {
2085 {
2086 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2087 27544626, -11754271, -6079156, 2047605},
2088 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2089 5043384, 19500929, -15469378},
2090 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2091 29287919, 11864899, -24514362, -4438546},
2092 },
2093 {
2094 {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2095 -11717903, -3814571, -358445, -10211303},
2096 {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2097 -15616551, 11189268, -26829678, -5319081},
2098 {26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2099 -3128826, -9541118, -15472047, -4166697},
2100 },
2101 {
2102 {15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2103 27787600, -14772189, 28944400, -1550024},
2104 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2105 16354577, -11775962, 7689662, 11199574},
2106 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2107 7512774, 10017326, -17749093, -9920357},
2108 },
2109 {
2110 {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2111 -28926210, 15006023, 3284568, -6276540},
2112 {23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2113 7464579, 9656445, 13059162, 10374397},
2114 {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2115 -3839045, -641708, -101325},
2116 },
2117 {
2118 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2119 32867885, 14515107, -15438304, 10819380},
2120 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2121 12483688, -12668491, 5581306},
2122 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2123 28542350, 13850243, -23678021, -15815942},
2124 },
2125 {
2126 {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2127 -19188627, -15224819, -9818940, -12085777},
2128 {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2129 -15689887, 1762328, 14866737},
2130 {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2131 -28236412, 3959421, 27914454, 4383652},
2132 },
2133 {
2134 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2135 5230134, -23952439, -15175766},
2136 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2137 20654025, 16520125, 30598449, 7715701},
2138 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2139 -31400660, 1370708, 29794553, -1409300},
2140 },
2141 {
2142 {14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2143 30290735, 10876454, -33154098, 2381726},
2144 {-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2145 -6236617, 3696005, -32300832, 15351955},
2146 {27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2147 -32961401, -2970515, 29551813, 10109425},
2148 },
2149 },
2150 {
2151 {
2152 {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2153 -2378284, -1627556, 10092783, -4764171},
2154 {27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2155 -32508754, 12005538, -17810127, 12803510},
2156 {17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2157 30364213, -9038194, 18016357, 4397660},
2158 },
2159 {
2160 {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2161 -26619106, 14544525, -17477504, 982639},
2162 {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2163 -4120128, -21047696, 9934963},
2164 {5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2165 -14747930, 4559895, -30123922, -10897950},
2166 },
2167 {
2168 {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2169 24191034, 4541697, -13338309, 5500568},
2170 {12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2171 -17430592, 12264343, 10874051, 13524335},
2172 {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2173 5080568, -22528059, 5376628},
2174 },
2175 {
2176 {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2177 -22321305, -9447443, 4535768, 1569007},
2178 {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2179 -30494562, 3044290, 31848280, 12543772},
2180 {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2181 -27377195, -2062731, 7718482, 14474653},
2182 },
2183 {
2184 {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2185 -7236665, 24316168, -5253567},
2186 {13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2187 33040651, -13424532, -20729456, 8321686},
2188 {21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
2189 23845965, -11874838, -9984458, 608372},
2190 },
2191 {
2192 {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
2193 1123968, -6780577, 27229399, 23887},
2194 {-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
2195 12797024, -6440308, -1633405, 16678954},
2196 {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
2197 -1508144, -4795045, -17169265, 4904953},
2198 },
2199 {
2200 {24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
2201 5169211, 16191880, 2128236, -4326833},
2202 {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
2203 -29806336, 916033, -6882542, -2986532},
2204 {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
2205 285431, 2763829, 15736322, 4143876},
2206 },
2207 {
2208 {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
2209 -14594663, 23527084, -16458268},
2210 {33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
2211 -32625340, 4087881, -15188911, -14416214},
2212 {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
2213 4357868, -4774191, -16323038},
2214 },
2215 },
2216 {
2217 {
2218 {6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
2219 23365147, -3949732, 7390890, 2759800},
2220 {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
2221 -4264057, 1244380, -12919645},
2222 {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
2223 9208236, 15886429, 16489664},
2224 },
2225 {
2226 {1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
2227 -13693198, 398369, -30606455, -712933},
2228 {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
2229 13348553, 12076947, -30836462, 5113182},
2230 {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
2231 -30341101, -7336386, 13847711, 5387222},
2232 },
2233 {
2234 {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
2235 8763061, 3617786, -19600662, 10370991},
2236 {20246567, -14369378, 22358229, -543712, 18507283, -10413996,
2237 14554437, -8746092, 32232924, 16763880},
2238 {9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
2239 11094161, 15689506, 3140038, -16510092},
2240 },
2241 {
2242 {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
2243 -27224800, 9448613, -28774454, 366295},
2244 {19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
2245 28344573, 8041113, 719605, 11671788},
2246 {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
2247 -15266516, 27000813, -10195553},
2248 },
2249 {
2250 {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
2251 5336097, 6750977, -14521026},
2252 {11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
2253 1695823, -8819122, 8169720, 16220347},
2254 {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
2255 -11144307, -2627664, -5990708, -14166033},
2256 },
2257 {
2258 {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
2259 27884329, 2847284, 2655861, 1738395},
2260 {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
2261 21651608, -3239336, -19087449, -11005278},
2262 {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
2263 5821408, 10478196, 8544890},
2264 },
2265 {
2266 {32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
2267 19270449, 12217473, 17789017, -3395995},
2268 {-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
2269 15479401, -3853233, 30460520, 1052596},
2270 {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
2271 27491595, -4612359, 3179268, -9478891},
2272 },
2273 {
2274 {31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
2275 -14756777, -16411740, 19072640, -9511060},
2276 {11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
2277 5977896, -5215017, 473099, 5040608},
2278 {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
2279 28326862, 1721092, -19558642, -3131606},
2280 },
2281 },
2282 {
2283 {
2284 {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
2285 8076149, -27868496, 11538389},
2286 {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
2287 8754525, 7446702, -5676054, 5797016},
2288 {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
2289 2014099, -9050574, -2369172, -5877341},
2290 },
2291 {
2292 {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
2293 1192730, -3714199, 15123619, 10811505},
2294 {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
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4175 31474879, 3483633, -1193175, -4030831},
4176 {-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4177 33142652, 6546660, -19985279, -3948376},
4178 },
4179 {
4180 {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4181 -8537131, -12833048, -30772034, -15486313},
4182 {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4183 -31135347, -16049879, 10928917, 3011958},
4184 {-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4185 -30831056, -12805180, 18008031, 10258577},
4186 },
4187 {
4188 {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4189 -1853465, 1367120, 25127874, 6671743},
4190 {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4191 21382910, 11042292, 25838796, 4642684},
4192 {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4193 30468147, -13900640, 18423289, 4177476},
4194 },
4195 },
4196};
4197
3a17b9a4
DMSP		 4198static uint8_t negative(signed char b)
4199{
4200 uint32_t x = b;
4201
4202 x >>= 31; /* 1: yes; 0: no */
4203 return x;
a90def6b
DSH		 4204}
4205
3a17b9a4
DMSP		 4206static void table_select(ge_precomp *t, int pos, signed char b)
4207{
4208 ge_precomp minust;
4209 uint8_t bnegative = negative(b);
4210 uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4211
4212 ge_precomp_0(t);
4213 cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4214 cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4215 cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4216 cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4217 cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4218 cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4219 cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4220 cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4221 fe_copy(minust.yplusx, t->yminusx);
4222 fe_copy(minust.yminusx, t->yplusx);
4223 fe_neg(minust.xy2d, t->xy2d);
4224 cmov(t, &minust, bnegative);
a90def6b
DSH		 4225}
4226
3a17b9a4
DMSP		 4227/*
4228 * h = a * B
4229 *
a90def6b
DSH		 4230 * where a = a[0]+256*a[1]+...+256^31 a[31]
4231 * B is the Ed25519 base point (x,4/5) with x positive.
4232 *
4233 * Preconditions:
3a17b9a4
DMSP		 4234 * a[31] <= 127
4235 */
4236static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a)
4237{
4238 signed char e[64];
4239 signed char carry;
4240 ge_p1p1 r;
4241 ge_p2 s;
4242 ge_precomp t;
4243 int i;
4244
4245 for (i = 0; i < 32; ++i) {
4246 e[2 * i + 0] = (a[i] >> 0) & 15;
4247 e[2 * i + 1] = (a[i] >> 4) & 15;
4248 }
4249 /* each e[i] is between 0 and 15 */
4250 /* e[63] is between 0 and 7 */
4251
4252 carry = 0;
4253 for (i = 0; i < 63; ++i) {
4254 e[i] += carry;
4255 carry = e[i] + 8;
4256 carry >>= 4;
4257 e[i] -= carry << 4;
4258 }
4259 e[63] += carry;
4260 /* each e[i] is between -8 and 8 */
4261
4262 ge_p3_0(h);
4263 for (i = 1; i < 64; i += 2) {
4264 table_select(&t, i / 2, e[i]);
4265 ge_madd(&r, h, &t);
4266 ge_p1p1_to_p3(h, &r);
4267 }
4268
4269 ge_p3_dbl(&r, h);
4270 ge_p1p1_to_p2(&s, &r);
4271 ge_p2_dbl(&r, &s);
4272 ge_p1p1_to_p2(&s, &r);
4273 ge_p2_dbl(&r, &s);
4274 ge_p1p1_to_p2(&s, &r);
4275 ge_p2_dbl(&r, &s);
a90def6b 4276 ge_p1p1_to_p3(h, &r);
78f1e4d0 4277
3a17b9a4
DMSP		 4278 for (i = 0; i < 64; i += 2) {
4279 table_select(&t, i / 2, e[i]);
4280 ge_madd(&r, h, &t);
4281 ge_p1p1_to_p3(h, &r);
4282 }
4283
4284 OPENSSL_cleanse(e, sizeof(e));
a90def6b
DSH		 4285}
4286
cfc32a1e 4287#if !defined(BASE_2_51_IMPLEMENTED)
3a17b9a4
DMSP		 4288/*
4289 * Replace (f,g) with (g,f) if b == 1;
a90def6b
DSH		 4290 * replace (f,g) with (f,g) if b == 0.
4291 *
3a17b9a4
DMSP		 4292 * Preconditions: b in {0,1}.
4293 */
4294static void fe_cswap(fe f, fe g, unsigned int b)
4295{
4296 size_t i;
4297
4298 b = 0-b;
4299 for (i = 0; i < 10; i++) {
4300 int32_t x = f[i] ^ g[i];
4301 x &= b;
4302 f[i] ^= x;
4303 g[i] ^= x;
4304 }
a90def6b
DSH		 4305}
4306
3a17b9a4
DMSP		 4307/*
4308 * h = f * 121666
4309 *
a90def6b
DSH		 4310 * Can overlap h with f.
4311 *
4312 * Preconditions:
4313 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
4314 *
4315 * Postconditions:
3a17b9a4
DMSP		 4316 * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
4317 */
4318static void fe_mul121666(fe h, fe f)
4319{
4320 int32_t f0 = f[0];
4321 int32_t f1 = f[1];
4322 int32_t f2 = f[2];
4323 int32_t f3 = f[3];
4324 int32_t f4 = f[4];
4325 int32_t f5 = f[5];
4326 int32_t f6 = f[6];
4327 int32_t f7 = f[7];
4328 int32_t f8 = f[8];
4329 int32_t f9 = f[9];
4330 int64_t h0 = f0 * (int64_t) 121666;
4331 int64_t h1 = f1 * (int64_t) 121666;
4332 int64_t h2 = f2 * (int64_t) 121666;
4333 int64_t h3 = f3 * (int64_t) 121666;
4334 int64_t h4 = f4 * (int64_t) 121666;
4335 int64_t h5 = f5 * (int64_t) 121666;
4336 int64_t h6 = f6 * (int64_t) 121666;
4337 int64_t h7 = f7 * (int64_t) 121666;
4338 int64_t h8 = f8 * (int64_t) 121666;
4339 int64_t h9 = f9 * (int64_t) 121666;
4340 int64_t carry0;
4341 int64_t carry1;
4342 int64_t carry2;
4343 int64_t carry3;
4344 int64_t carry4;
4345 int64_t carry5;
4346 int64_t carry6;
4347 int64_t carry7;
4348 int64_t carry8;
4349 int64_t carry9;
4350
4351 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
4352 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
4353 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
4354 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
4355 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
4356
4357 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
4358 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
4359 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
4360 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
4361 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
4362
4363 h[0] = (int32_t)h0;
4364 h[1] = (int32_t)h1;
4365 h[2] = (int32_t)h2;
4366 h[3] = (int32_t)h3;
4367 h[4] = (int32_t)h4;
4368 h[5] = (int32_t)h5;
4369 h[6] = (int32_t)h6;
4370 h[7] = (int32_t)h7;
4371 h[8] = (int32_t)h8;
4372 h[9] = (int32_t)h9;
a90def6b
DSH		 4373}
4374
4375static void x25519_scalar_mult_generic(uint8_t out[32],
4376 const uint8_t scalar[32],
4377 const uint8_t point[32]) {
3a17b9a4
DMSP		 4378 fe x1, x2, z2, x3, z3, tmp0, tmp1;
4379 uint8_t e[32];
4380 unsigned swap = 0;
4381 int pos;
4382
4383 memcpy(e, scalar, 32);
4384 e[0] &= 248;
4385 e[31] &= 127;
4386 e[31] |= 64;
4387 fe_frombytes(x1, point);
4388 fe_1(x2);
4389 fe_0(z2);
4390 fe_copy(x3, x1);
4391 fe_1(z3);
4392
4393 for (pos = 254; pos >= 0; --pos) {
4394 unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4395 swap ^= b;
4396 fe_cswap(x2, x3, swap);
4397 fe_cswap(z2, z3, swap);
4398 swap = b;
4399 fe_sub(tmp0, x3, z3);
4400 fe_sub(tmp1, x2, z2);
4401 fe_add(x2, x2, z2);
4402 fe_add(z2, x3, z3);
4403 fe_mul(z3, tmp0, x2);
4404 fe_mul(z2, z2, tmp1);
4405 fe_sq(tmp0, tmp1);
4406 fe_sq(tmp1, x2);
4407 fe_add(x3, z3, z2);
4408 fe_sub(z2, z3, z2);
4409 fe_mul(x2, tmp1, tmp0);
4410 fe_sub(tmp1, tmp1, tmp0);
4411 fe_sq(z2, z2);
4412 fe_mul121666(z3, tmp1);
4413 fe_sq(x3, x3);
4414 fe_add(tmp0, tmp0, z3);
4415 fe_mul(z3, x1, z2);
4416 fe_mul(z2, tmp1, tmp0);
4417 }
4418
4419 fe_invert(z2, z2);
4420 fe_mul(x2, x2, z2);
4421 fe_tobytes(out, x2);
4422
4423 OPENSSL_cleanse(e, sizeof(e));
a90def6b
DSH		 4424}
4425
4426static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4427 const uint8_t point[32]) {
3a17b9a4 4428 x25519_scalar_mult_generic(out, scalar, point);
a90def6b 4429}
cfc32a1e 4430#endif
a90def6b 4431
3a17b9a4
DMSP		 4432static void slide(signed char *r, const uint8_t *a)
4433{
4434 int i;
4435 int b;
4436 int k;
4437
4438 for (i = 0; i < 256; ++i) {
4439 r[i] = 1 & (a[i >> 3] >> (i & 7));
4440 }
4441
4442 for (i = 0; i < 256; ++i) {
4443 if (r[i]) {
4444 for (b = 1; b <= 6 && i + b < 256; ++b) {
4445 if (r[i + b]) {
4446 if (r[i] + (r[i + b] << b) <= 15) {
4447 r[i] += r[i + b] << b;
4448 r[i + b] = 0;
4449 } else if (r[i] - (r[i + b] << b) >= -15) {
4450 r[i] -= r[i + b] << b;
4451 for (k = i + b; k < 256; ++k) {
4452 if (!r[k]) {
4453 r[k] = 1;
4454 break;
4455 }
4456 r[k] = 0;
4457 }
4458 } else {
4459 break;
4460 }
4461 }
06c6d05f 4462 }
06c6d05f 4463 }
06c6d05f 4464 }
06c6d05f
DSH		 4465}
4466
4467static const ge_precomp Bi[8] = {
4468 {
4469 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4470 -11754271, -6079156, 2047605},
4471 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4472 5043384, 19500929, -15469378},
4473 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4474 11864899, -24514362, -4438546},
4475 },
4476 {
4477 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4478 -14772189, 28944400, -1550024},
4479 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4480 -11775962, 7689662, 11199574},
4481 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4482 10017326, -17749093, -9920357},
4483 },
4484 {
4485 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4486 14515107, -15438304, 10819380},
4487 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4488 12483688, -12668491, 5581306},
4489 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4490 13850243, -23678021, -15815942},
4491 },
4492 {
4493 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4494 5230134, -23952439, -15175766},
4495 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4496 16520125, 30598449, 7715701},
4497 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4498 1370708, 29794553, -1409300},
4499 },
4500 {
4501 {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4502 -1361450, -13062696, 13821877},
4503 {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4504 -7212327, 18853322, -14220951},
4505 {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4506 -10431137, 2207753, -3209784},
4507 },
4508 {
4509 {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4510 -663000, -31111463, -16132436},
4511 {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4512 15725684, 171356, 6466918},
4513 {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4514 -14088058, -30714912, 16193877},
4515 },
4516 {
4517 {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4518 4729455, -18074513, 9256800},
4519 {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4520 9761698, -19827198, 630305},
4521 {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4522 -15960994, -2449256, -14291300},
4523 },
4524 {
4525 {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4526 15033784, 25105118, -7894876},
4527 {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4528 1573892, -2625887, 2198790, -15804619},
4529 {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4530 -16236442, -32461234, -12290683},
4531 },
4532};
4533
3a17b9a4
DMSP		 4534/*
4535 * r = a * A + b * B
4536 *
06c6d05f
DSH		 4537 * where a = a[0]+256*a[1]+...+256^31 a[31].
4538 * and b = b[0]+256*b[1]+...+256^31 b[31].
3a17b9a4
DMSP		 4539 * B is the Ed25519 base point (x,4/5) with x positive.
4540 */
06c6d05f 4541static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
3a17b9a4
DMSP		 4542 const ge_p3 *A, const uint8_t *b)
4543{
4544 signed char aslide[256];
4545 signed char bslide[256];
4546 ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4547 ge_p1p1 t;
4548 ge_p3 u;
4549 ge_p3 A2;
4550 int i;
4551
4552 slide(aslide, a);
4553 slide(bslide, b);
4554
4555 ge_p3_to_cached(&Ai[0], A);
4556 ge_p3_dbl(&t, A);
4557 ge_p1p1_to_p3(&A2, &t);
4558 ge_add(&t, &A2, &Ai[0]);
4559 ge_p1p1_to_p3(&u, &t);
4560 ge_p3_to_cached(&Ai[1], &u);
4561 ge_add(&t, &A2, &Ai[1]);
4562 ge_p1p1_to_p3(&u, &t);
4563 ge_p3_to_cached(&Ai[2], &u);
4564 ge_add(&t, &A2, &Ai[2]);
4565 ge_p1p1_to_p3(&u, &t);
4566 ge_p3_to_cached(&Ai[3], &u);
4567 ge_add(&t, &A2, &Ai[3]);
4568 ge_p1p1_to_p3(&u, &t);
4569 ge_p3_to_cached(&Ai[4], &u);
4570 ge_add(&t, &A2, &Ai[4]);
4571 ge_p1p1_to_p3(&u, &t);
4572 ge_p3_to_cached(&Ai[5], &u);
4573 ge_add(&t, &A2, &Ai[5]);
4574 ge_p1p1_to_p3(&u, &t);
4575 ge_p3_to_cached(&Ai[6], &u);
4576 ge_add(&t, &A2, &Ai[6]);
4577 ge_p1p1_to_p3(&u, &t);
4578 ge_p3_to_cached(&Ai[7], &u);
4579
4580 ge_p2_0(r);
4581
4582 for (i = 255; i >= 0; --i) {
4583 if (aslide[i] || bslide[i]) {
4584 break;
4585 }
06c6d05f 4586 }
06c6d05f 4587
3a17b9a4
DMSP		 4588 for (; i >= 0; --i) {
4589 ge_p2_dbl(&t, r);
06c6d05f 4590
3a17b9a4
DMSP		 4591 if (aslide[i] > 0) {
4592 ge_p1p1_to_p3(&u, &t);
4593 ge_add(&t, &u, &Ai[aslide[i] / 2]);
4594 } else if (aslide[i] < 0) {
4595 ge_p1p1_to_p3(&u, &t);
4596 ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4597 }
06c6d05f 4598
3a17b9a4
DMSP		 4599 if (bslide[i] > 0) {
4600 ge_p1p1_to_p3(&u, &t);
4601 ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4602 } else if (bslide[i] < 0) {
4603 ge_p1p1_to_p3(&u, &t);
4604 ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4605 }
06c6d05f 4606
3a17b9a4
DMSP		 4607 ge_p1p1_to_p2(r, &t);
4608 }
06c6d05f
DSH		 4609}
4610
3a17b9a4
DMSP		 4611/*
4612 * The set of scalars is \Z/l
4613 * where l = 2^252 + 27742317777372353535851937790883648493.
4614 *
4615 * Input:
06c6d05f
DSH		 4616 * s[0]+256*s[1]+...+256^63*s[63] = s
4617 *
4618 * Output:
4619 * s[0]+256*s[1]+...+256^31*s[31] = s mod l
4620 * where l = 2^252 + 27742317777372353535851937790883648493.
3a17b9a4
DMSP		 4621 * Overwrites s in place.
4622*/
4623static void x25519_sc_reduce(uint8_t *s)
4624{
425dde5d
DMSP		 4625 int64_t s0 = kBottom21Bits & load_3(s);
4626 int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
4627 int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
4628 int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
4629 int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
4630 int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
4631 int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
4632 int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
4633 int64_t s8 = kBottom21Bits & load_3(s + 21);
4634 int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
4635 int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4636 int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4637 int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4638 int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4639 int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4640 int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4641 int64_t s16 = kBottom21Bits & load_3(s + 42);
4642 int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4643 int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4644 int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4645 int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4646 int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4647 int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4648 int64_t s23 = (load_4(s + 60) >> 3);
3a17b9a4
DMSP		 4649 int64_t carry0;
4650 int64_t carry1;
4651 int64_t carry2;
4652 int64_t carry3;
4653 int64_t carry4;
4654 int64_t carry5;
4655 int64_t carry6;
4656 int64_t carry7;
4657 int64_t carry8;
4658 int64_t carry9;
4659 int64_t carry10;
4660 int64_t carry11;
4661 int64_t carry12;
4662 int64_t carry13;
4663 int64_t carry14;
4664 int64_t carry15;
4665 int64_t carry16;
4666
4667 s11 += s23 * 666643;
4668 s12 += s23 * 470296;
4669 s13 += s23 * 654183;
4670 s14 -= s23 * 997805;
4671 s15 += s23 * 136657;
4672 s16 -= s23 * 683901;
425dde5d 4673 s23 = 0;
3a17b9a4
DMSP		 4674
4675 s10 += s22 * 666643;
4676 s11 += s22 * 470296;
4677 s12 += s22 * 654183;
4678 s13 -= s22 * 997805;
4679 s14 += s22 * 136657;
4680 s15 -= s22 * 683901;
425dde5d 4681 s22 = 0;
3a17b9a4 4682
425dde5d 4683 s9 += s21 * 666643;
3a17b9a4
DMSP		 4684 s10 += s21 * 470296;
4685 s11 += s21 * 654183;
4686 s12 -= s21 * 997805;
4687 s13 += s21 * 136657;
4688 s14 -= s21 * 683901;
425dde5d 4689 s21 = 0;
3a17b9a4 4690
425dde5d
DMSP		 4691 s8 += s20 * 666643;
4692 s9 += s20 * 470296;
3a17b9a4
DMSP		 4693 s10 += s20 * 654183;
4694 s11 -= s20 * 997805;
4695 s12 += s20 * 136657;
4696 s13 -= s20 * 683901;
425dde5d 4697 s20 = 0;
3a17b9a4 4698
425dde5d
DMSP		 4699 s7 += s19 * 666643;
4700 s8 += s19 * 470296;
4701 s9 += s19 * 654183;
3a17b9a4
DMSP		 4702 s10 -= s19 * 997805;
4703 s11 += s19 * 136657;
4704 s12 -= s19 * 683901;
425dde5d 4705 s19 = 0;
3a17b9a4 4706
425dde5d
DMSP		 4707 s6 += s18 * 666643;
4708 s7 += s18 * 470296;
4709 s8 += s18 * 654183;
4710 s9 -= s18 * 997805;
3a17b9a4
DMSP		 4711 s10 += s18 * 136657;
4712 s11 -= s18 * 683901;
425dde5d 4713 s18 = 0;
3a17b9a4
DMSP		 4714
4715 carry6 = (s6 + (1 << 20)) >> 21;
425dde5d
DMSP		 4716 s7 += carry6;
4717 s6 -= carry6 * (1 << 21);
3a17b9a4 4718 carry8 = (s8 + (1 << 20)) >> 21;
425dde5d
DMSP		 4719 s9 += carry8;
4720 s8 -= carry8 * (1 << 21);
3a17b9a4
DMSP		 4721 carry10 = (s10 + (1 << 20)) >> 21;
4722 s11 += carry10;
4723 s10 -= carry10 * (1 << 21);
4724 carry12 = (s12 + (1 << 20)) >> 21;
4725 s13 += carry12;
4726 s12 -= carry12 * (1 << 21);
4727 carry14 = (s14 + (1 << 20)) >> 21;
4728 s15 += carry14;
4729 s14 -= carry14 * (1 << 21);
4730 carry16 = (s16 + (1 << 20)) >> 21;
4731 s17 += carry16;
4732 s16 -= carry16 * (1 << 21);
4733
4734 carry7 = (s7 + (1 << 20)) >> 21;
425dde5d
DMSP		 4735 s8 += carry7;
4736 s7 -= carry7 * (1 << 21);
3a17b9a4
DMSP		 4737 carry9 = (s9 + (1 << 20)) >> 21;
4738 s10 += carry9;
425dde5d 4739 s9 -= carry9 * (1 << 21);
3a17b9a4
DMSP		 4740 carry11 = (s11 + (1 << 20)) >> 21;
4741 s12 += carry11;
4742 s11 -= carry11 * (1 << 21);
4743 carry13 = (s13 + (1 << 20)) >> 21;
4744 s14 += carry13;
4745 s13 -= carry13 * (1 << 21);
4746 carry15 = (s15 + (1 << 20)) >> 21;
4747 s16 += carry15;
4748 s15 -= carry15 * (1 << 21);
4749
425dde5d
DMSP		 4750 s5 += s17 * 666643;
4751 s6 += s17 * 470296;
4752 s7 += s17 * 654183;
4753 s8 -= s17 * 997805;
4754 s9 += s17 * 136657;
3a17b9a4 4755 s10 -= s17 * 683901;
425dde5d
DMSP		 4756 s17 = 0;
4757
4758 s4 += s16 * 666643;
4759 s5 += s16 * 470296;
4760 s6 += s16 * 654183;
4761 s7 -= s16 * 997805;
4762 s8 += s16 * 136657;
4763 s9 -= s16 * 683901;
4764 s16 = 0;
4765
4766 s3 += s15 * 666643;
4767 s4 += s15 * 470296;
4768 s5 += s15 * 654183;
4769 s6 -= s15 * 997805;
4770 s7 += s15 * 136657;
4771 s8 -= s15 * 683901;
4772 s15 = 0;
4773
4774 s2 += s14 * 666643;
4775 s3 += s14 * 470296;
4776 s4 += s14 * 654183;
4777 s5 -= s14 * 997805;
4778 s6 += s14 * 136657;
4779 s7 -= s14 * 683901;
4780 s14 = 0;
4781
4782 s1 += s13 * 666643;
4783 s2 += s13 * 470296;
4784 s3 += s13 * 654183;
4785 s4 -= s13 * 997805;
4786 s5 += s13 * 136657;
4787 s6 -= s13 * 683901;
4788 s13 = 0;
4789
4790 s0 += s12 * 666643;
4791 s1 += s12 * 470296;
4792 s2 += s12 * 654183;
4793 s3 -= s12 * 997805;
4794 s4 += s12 * 136657;
4795 s5 -= s12 * 683901;
4796 s12 = 0;
3a17b9a4
DMSP		 4797
4798 carry0 = (s0 + (1 << 20)) >> 21;
425dde5d
DMSP		 4799 s1 += carry0;
4800 s0 -= carry0 * (1 << 21);
3a17b9a4 4801 carry2 = (s2 + (1 << 20)) >> 21;
425dde5d
DMSP		 4802 s3 += carry2;
4803 s2 -= carry2 * (1 << 21);
3a17b9a4 4804 carry4 = (s4 + (1 << 20)) >> 21;
425dde5d
DMSP		 4805 s5 += carry4;
4806 s4 -= carry4 * (1 << 21);
3a17b9a4
DMSP		 4807 carry6 = (s6 + (1 << 20)) >> 21;
4808 s7 += carry6;
4809 s6 -= carry6 * (1 << 21);
4810 carry8 = (s8 + (1 << 20)) >> 21;
425dde5d
DMSP		 4811 s9 += carry8;
4812 s8 -= carry8 * (1 << 21);
3a17b9a4
DMSP		 4813 carry10 = (s10 + (1 << 20)) >> 21;
4814 s11 += carry10;
4815 s10 -= carry10 * (1 << 21);
4816
4817 carry1 = (s1 + (1 << 20)) >> 21;
425dde5d
DMSP		 4818 s2 += carry1;
4819 s1 -= carry1 * (1 << 21);
3a17b9a4 4820 carry3 = (s3 + (1 << 20)) >> 21;
425dde5d
DMSP		 4821 s4 += carry3;
4822 s3 -= carry3 * (1 << 21);
3a17b9a4 4823 carry5 = (s5 + (1 << 20)) >> 21;
425dde5d
DMSP		 4824 s6 += carry5;
4825 s5 -= carry5 * (1 << 21);
3a17b9a4 4826 carry7 = (s7 + (1 << 20)) >> 21;
425dde5d
DMSP		 4827 s8 += carry7;
4828 s7 -= carry7 * (1 << 21);
3a17b9a4
DMSP		 4829 carry9 = (s9 + (1 << 20)) >> 21;
4830 s10 += carry9;
425dde5d 4831 s9 -= carry9 * (1 << 21);
3a17b9a4
DMSP		 4832 carry11 = (s11 + (1 << 20)) >> 21;
4833 s12 += carry11;
4834 s11 -= carry11 * (1 << 21);
4835
425dde5d
DMSP		 4836 s0 += s12 * 666643;
4837 s1 += s12 * 470296;
4838 s2 += s12 * 654183;
4839 s3 -= s12 * 997805;
4840 s4 += s12 * 136657;
4841 s5 -= s12 * 683901;
4842 s12 = 0;
3a17b9a4
DMSP		 4843
4844 carry0 = s0 >> 21;
425dde5d
DMSP		 4845 s1 += carry0;
4846 s0 -= carry0 * (1 << 21);
3a17b9a4 4847 carry1 = s1 >> 21;
425dde5d
DMSP		 4848 s2 += carry1;
4849 s1 -= carry1 * (1 << 21);
3a17b9a4 4850 carry2 = s2 >> 21;
425dde5d
DMSP		 4851 s3 += carry2;
4852 s2 -= carry2 * (1 << 21);
3a17b9a4 4853 carry3 = s3 >> 21;
425dde5d
DMSP		 4854 s4 += carry3;
4855 s3 -= carry3 * (1 << 21);
3a17b9a4 4856 carry4 = s4 >> 21;
425dde5d
DMSP		 4857 s5 += carry4;
4858 s4 -= carry4 * (1 << 21);
3a17b9a4 4859 carry5 = s5 >> 21;
425dde5d
DMSP		 4860 s6 += carry5;
4861 s5 -= carry5 * (1 << 21);
3a17b9a4 4862 carry6 = s6 >> 21;
425dde5d
DMSP		 4863 s7 += carry6;
4864 s6 -= carry6 * (1 << 21);
3a17b9a4 4865 carry7 = s7 >> 21;
425dde5d
DMSP		 4866 s8 += carry7;
4867 s7 -= carry7 * (1 << 21);
3a17b9a4 4868 carry8 = s8 >> 21;
425dde5d
DMSP		 4869 s9 += carry8;
4870 s8 -= carry8 * (1 << 21);
3a17b9a4
DMSP		 4871 carry9 = s9 >> 21;
4872 s10 += carry9;
425dde5d 4873 s9 -= carry9 * (1 << 21);
3a17b9a4
DMSP		 4874 carry10 = s10 >> 21;
4875 s11 += carry10;
4876 s10 -= carry10 * (1 << 21);
4877 carry11 = s11 >> 21;
4878 s12 += carry11;
4879 s11 -= carry11 * (1 << 21);
4880
425dde5d
DMSP		 4881 s0 += s12 * 666643;
4882 s1 += s12 * 470296;
4883 s2 += s12 * 654183;
4884 s3 -= s12 * 997805;
4885 s4 += s12 * 136657;
4886 s5 -= s12 * 683901;
4887 s12 = 0;
3a17b9a4
DMSP		 4888
4889 carry0 = s0 >> 21;
425dde5d
DMSP		 4890 s1 += carry0;
4891 s0 -= carry0 * (1 << 21);
3a17b9a4 4892 carry1 = s1 >> 21;
425dde5d
DMSP		 4893 s2 += carry1;
4894 s1 -= carry1 * (1 << 21);
3a17b9a4 4895 carry2 = s2 >> 21;
425dde5d
DMSP		 4896 s3 += carry2;
4897 s2 -= carry2 * (1 << 21);
3a17b9a4 4898 carry3 = s3 >> 21;
425dde5d
DMSP		 4899 s4 += carry3;
4900 s3 -= carry3 * (1 << 21);
3a17b9a4 4901 carry4 = s4 >> 21;
425dde5d
DMSP		 4902 s5 += carry4;
4903 s4 -= carry4 * (1 << 21);
3a17b9a4 4904 carry5 = s5 >> 21;
425dde5d
DMSP		 4905 s6 += carry5;
4906 s5 -= carry5 * (1 << 21);
3a17b9a4 4907 carry6 = s6 >> 21;
425dde5d
DMSP		 4908 s7 += carry6;
4909 s6 -= carry6 * (1 << 21);
3a17b9a4 4910 carry7 = s7 >> 21;
425dde5d
DMSP		 4911 s8 += carry7;
4912 s7 -= carry7 * (1 << 21);
3a17b9a4 4913 carry8 = s8 >> 21;
425dde5d
DMSP		 4914 s9 += carry8;
4915 s8 -= carry8 * (1 << 21);
3a17b9a4
DMSP		 4916 carry9 = s9 >> 21;
4917 s10 += carry9;
425dde5d 4918 s9 -= carry9 * (1 << 21);
3a17b9a4
DMSP		 4919 carry10 = s10 >> 21;
4920 s11 += carry10;
4921 s10 -= carry10 * (1 << 21);
4922
425dde5d
DMSP		 4923 s[ 0] = (uint8_t) (s0 >> 0);
4924 s[ 1] = (uint8_t) (s0 >> 8);
4925 s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5));
4926 s[ 3] = (uint8_t) (s1 >> 3);
4927 s[ 4] = (uint8_t) (s1 >> 11);
4928 s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2));
4929 s[ 6] = (uint8_t) (s2 >> 6);
4930 s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7));
4931 s[ 8] = (uint8_t) (s3 >> 1);
4932 s[ 9] = (uint8_t) (s3 >> 9);
4933 s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
4934 s[11] = (uint8_t) (s4 >> 4);
4935 s[12] = (uint8_t) (s4 >> 12);
4936 s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
4937 s[14] = (uint8_t) (s5 >> 7);
4938 s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
4939 s[16] = (uint8_t) (s6 >> 2);
4940 s[17] = (uint8_t) (s6 >> 10);
4941 s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
4942 s[19] = (uint8_t) (s7 >> 5);
4943 s[20] = (uint8_t) (s7 >> 13);
4944 s[21] = (uint8_t) (s8 >> 0);
4945 s[22] = (uint8_t) (s8 >> 8);
4946 s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
4947 s[24] = (uint8_t) (s9 >> 3);
4948 s[25] = (uint8_t) (s9 >> 11);
4949 s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
4950 s[27] = (uint8_t) (s10 >> 6);
4951 s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
4952 s[29] = (uint8_t) (s11 >> 1);
4953 s[30] = (uint8_t) (s11 >> 9);
4954 s[31] = (uint8_t) (s11 >> 17);
06c6d05f
DSH		 4955}
4956
3a17b9a4
DMSP		 4957/*
4958 * Input:
06c6d05f
DSH		 4959 * a[0]+256*a[1]+...+256^31*a[31] = a
4960 * b[0]+256*b[1]+...+256^31*b[31] = b
4961 * c[0]+256*c[1]+...+256^31*c[31] = c
4962 *
4963 * Output:
4964 * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
3a17b9a4
DMSP		 4965 * where l = 2^252 + 27742317777372353535851937790883648493.
4966 */
06c6d05f 4967static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
3a17b9a4
DMSP		 4968 const uint8_t *c)
4969{
425dde5d
DMSP		 4970 int64_t a0 = kBottom21Bits & load_3(a);
4971 int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
4972 int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
4973 int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
4974 int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
4975 int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
4976 int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
4977 int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
4978 int64_t a8 = kBottom21Bits & load_3(a + 21);
4979 int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
4980 int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
4981 int64_t a11 = (load_4(a + 28) >> 7);
4982 int64_t b0 = kBottom21Bits & load_3(b);
4983 int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
4984 int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
4985 int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
4986 int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
4987 int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
4988 int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
4989 int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
4990 int64_t b8 = kBottom21Bits & load_3(b + 21);
4991 int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
4992 int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
4993 int64_t b11 = (load_4(b + 28) >> 7);
4994 int64_t c0 = kBottom21Bits & load_3(c);
4995 int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
4996 int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
4997 int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
4998 int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
4999 int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
5000 int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
5001 int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
5002 int64_t c8 = kBottom21Bits & load_3(c + 21);
5003 int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
5004 int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
5005 int64_t c11 = (load_4(c + 28) >> 7);
3a17b9a4
DMSP		 5006 int64_t s0;
5007 int64_t s1;
5008 int64_t s2;
5009 int64_t s3;
5010 int64_t s4;
5011 int64_t s5;
5012 int64_t s6;
5013 int64_t s7;
5014 int64_t s8;
5015 int64_t s9;
5016 int64_t s10;
5017 int64_t s11;
5018 int64_t s12;
5019 int64_t s13;
5020 int64_t s14;
5021 int64_t s15;
5022 int64_t s16;
5023 int64_t s17;
5024 int64_t s18;
5025 int64_t s19;
5026 int64_t s20;
5027 int64_t s21;
5028 int64_t s22;
5029 int64_t s23;
5030 int64_t carry0;
5031 int64_t carry1;
5032 int64_t carry2;
5033 int64_t carry3;
5034 int64_t carry4;
5035 int64_t carry5;
5036 int64_t carry6;
5037 int64_t carry7;
5038 int64_t carry8;
5039 int64_t carry9;
5040 int64_t carry10;
5041 int64_t carry11;
5042 int64_t carry12;
5043 int64_t carry13;
5044 int64_t carry14;
5045 int64_t carry15;
5046 int64_t carry16;
5047 int64_t carry17;
5048 int64_t carry18;
5049 int64_t carry19;
5050 int64_t carry20;
5051 int64_t carry21;
5052 int64_t carry22;
5053
425dde5d
DMSP		 5054 s0 = c0 + a0 * b0;
5055 s1 = c1 + a0 * b1 + a1 * b0;
5056 s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
5057 s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
5058 s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
5059 s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
5060 s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
5061 s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
5062 s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
5063 s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
5064 s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
5065 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;
5066 s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
5067 s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
5068 s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
5069 s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
5070 s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
5071 s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
5072 s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
5073 s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
5074 s20 = a9 * b11 + a10 * b10 + a11 * b9;
5075 s21 = a10 * b11 + a11 * b10;
5076 s22 = a11 * b11;
5077 s23 = 0;
3a17b9a4
DMSP		 5078
5079 carry0 = (s0 + (1 << 20)) >> 21;
425dde5d
DMSP		 5080 s1 += carry0;
5081 s0 -= carry0 * (1 << 21);
3a17b9a4 5082 carry2 = (s2 + (1 << 20)) >> 21;
425dde5d
DMSP		 5083 s3 += carry2;
5084 s2 -= carry2 * (1 << 21);
3a17b9a4 5085 carry4 = (s4 + (1 << 20)) >> 21;
425dde5d
DMSP		 5086 s5 += carry4;
5087 s4 -= carry4 * (1 << 21);
3a17b9a4 5088 carry6 = (s6 + (1 << 20)) >> 21;
425dde5d
DMSP		 5089 s7 += carry6;
5090 s6 -= carry6 * (1 << 21);
3a17b9a4 5091 carry8 = (s8 + (1 << 20)) >> 21;
425dde5d
DMSP		 5092 s9 += carry8;
5093 s8 -= carry8 * (1 << 21);
3a17b9a4
DMSP		 5094 carry10 = (s10 + (1 << 20)) >> 21;
5095 s11 += carry10;
5096 s10 -= carry10 * (1 << 21);
5097 carry12 = (s12 + (1 << 20)) >> 21;
5098 s13 += carry12;
5099 s12 -= carry12 * (1 << 21);
5100 carry14 = (s14 + (1 << 20)) >> 21;
5101 s15 += carry14;
5102 s14 -= carry14 * (1 << 21);
5103 carry16 = (s16 + (1 << 20)) >> 21;
5104 s17 += carry16;
5105 s16 -= carry16 * (1 << 21);
5106 carry18 = (s18 + (1 << 20)) >> 21;
5107 s19 += carry18;
5108 s18 -= carry18 * (1 << 21);
5109 carry20 = (s20 + (1 << 20)) >> 21;
5110 s21 += carry20;
5111 s20 -= carry20 * (1 << 21);
5112 carry22 = (s22 + (1 << 20)) >> 21;
5113 s23 += carry22;
5114 s22 -= carry22 * (1 << 21);
5115
5116 carry1 = (s1 + (1 << 20)) >> 21;
425dde5d
DMSP		 5117 s2 += carry1;
5118 s1 -= carry1 * (1 << 21);
3a17b9a4 5119 carry3 = (s3 + (1 << 20)) >> 21;
425dde5d
DMSP		 5120 s4 += carry3;
5121 s3 -= carry3 * (1 << 21);
3a17b9a4 5122 carry5 = (s5 + (1 << 20)) >> 21;
425dde5d
DMSP		 5123 s6 += carry5;
5124 s5 -= carry5 * (1 << 21);
3a17b9a4 5125 carry7 = (s7 + (1 << 20)) >> 21;
425dde5d
DMSP		 5126 s8 += carry7;
5127 s7 -= carry7 * (1 << 21);
3a17b9a4
DMSP		 5128 carry9 = (s9 + (1 << 20)) >> 21;
5129 s10 += carry9;
425dde5d 5130 s9 -= carry9 * (1 << 21);
3a17b9a4
DMSP		 5131 carry11 = (s11 + (1 << 20)) >> 21;
5132 s12 += carry11;
5133 s11 -= carry11 * (1 << 21);
5134 carry13 = (s13 + (1 << 20)) >> 21;
5135 s14 += carry13;
5136 s13 -= carry13 * (1 << 21);
5137 carry15 = (s15 + (1 << 20)) >> 21;
5138 s16 += carry15;
5139 s15 -= carry15 * (1 << 21);
5140 carry17 = (s17 + (1 << 20)) >> 21;
5141 s18 += carry17;
5142 s17 -= carry17 * (1 << 21);
5143 carry19 = (s19 + (1 << 20)) >> 21;
5144 s20 += carry19;
5145 s19 -= carry19 * (1 << 21);
5146 carry21 = (s21 + (1 << 20)) >> 21;
5147 s22 += carry21;
5148 s21 -= carry21 * (1 << 21);
5149
5150 s11 += s23 * 666643;
5151 s12 += s23 * 470296;
5152 s13 += s23 * 654183;
5153 s14 -= s23 * 997805;
5154 s15 += s23 * 136657;
5155 s16 -= s23 * 683901;
425dde5d 5156 s23 = 0;
3a17b9a4
DMSP		 5157
5158 s10 += s22 * 666643;
5159 s11 += s22 * 470296;
5160 s12 += s22 * 654183;
5161 s13 -= s22 * 997805;
5162 s14 += s22 * 136657;
5163 s15 -= s22 * 683901;
425dde5d 5164 s22 = 0;
3a17b9a4 5165
425dde5d 5166 s9 += s21 * 666643;
3a17b9a4
DMSP		 5167 s10 += s21 * 470296;
5168 s11 += s21 * 654183;
5169 s12 -= s21 * 997805;
5170 s13 += s21 * 136657;
5171 s14 -= s21 * 683901;
425dde5d 5172 s21 = 0;
3a17b9a4 5173
425dde5d
DMSP		 5174 s8 += s20 * 666643;
5175 s9 += s20 * 470296;
3a17b9a4
DMSP		 5176 s10 += s20 * 654183;
5177 s11 -= s20 * 997805;
5178 s12 += s20 * 136657;
5179 s13 -= s20 * 683901;
425dde5d 5180 s20 = 0;
3a17b9a4 5181
425dde5d
DMSP		 5182 s7 += s19 * 666643;
5183 s8 += s19 * 470296;
5184 s9 += s19 * 654183;
3a17b9a4
DMSP		 5185 s10 -= s19 * 997805;
5186 s11 += s19 * 136657;
5187 s12 -= s19 * 683901;
425dde5d 5188 s19 = 0;
3a17b9a4 5189
425dde5d
DMSP		 5190 s6 += s18 * 666643;
5191 s7 += s18 * 470296;
5192 s8 += s18 * 654183;
5193 s9 -= s18 * 997805;
3a17b9a4
DMSP		 5194 s10 += s18 * 136657;
5195 s11 -= s18 * 683901;
425dde5d 5196 s18 = 0;
3a17b9a4
DMSP		 5197
5198 carry6 = (s6 + (1 << 20)) >> 21;
425dde5d
DMSP		 5199 s7 += carry6;
5200 s6 -= carry6 * (1 << 21);
3a17b9a4 5201 carry8 = (s8 + (1 << 20)) >> 21;
425dde5d
DMSP		 5202 s9 += carry8;
5203 s8 -= carry8 * (1 << 21);
3a17b9a4
DMSP		 5204 carry10 = (s10 + (1 << 20)) >> 21;
5205 s11 += carry10;
5206 s10 -= carry10 * (1 << 21);
5207 carry12 = (s12 + (1 << 20)) >> 21;
5208 s13 += carry12;
5209 s12 -= carry12 * (1 << 21);
5210 carry14 = (s14 + (1 << 20)) >> 21;
5211 s15 += carry14;
5212 s14 -= carry14 * (1 << 21);
5213 carry16 = (s16 + (1 << 20)) >> 21;
5214 s17 += carry16;
5215 s16 -= carry16 * (1 << 21);
5216
5217 carry7 = (s7 + (1 << 20)) >> 21;
425dde5d
DMSP		 5218 s8 += carry7;
5219 s7 -= carry7 * (1 << 21);
3a17b9a4
DMSP		 5220 carry9 = (s9 + (1 << 20)) >> 21;
5221 s10 += carry9;
425dde5d 5222 s9 -= carry9 * (1 << 21);
3a17b9a4
DMSP		 5223 carry11 = (s11 + (1 << 20)) >> 21;
5224 s12 += carry11;
5225 s11 -= carry11 * (1 << 21);
5226 carry13 = (s13 + (1 << 20)) >> 21;
5227 s14 += carry13;
5228 s13 -= carry13 * (1 << 21);
5229 carry15 = (s15 + (1 << 20)) >> 21;
5230 s16 += carry15;
5231 s15 -= carry15 * (1 << 21);
5232
425dde5d
DMSP		 5233 s5 += s17 * 666643;
5234 s6 += s17 * 470296;
5235 s7 += s17 * 654183;
5236 s8 -= s17 * 997805;
5237 s9 += s17 * 136657;
3a17b9a4 5238 s10 -= s17 * 683901;
425dde5d
DMSP		 5239 s17 = 0;
5240
5241 s4 += s16 * 666643;
5242 s5 += s16 * 470296;
5243 s6 += s16 * 654183;
5244 s7 -= s16 * 997805;
5245 s8 += s16 * 136657;
5246 s9 -= s16 * 683901;
5247 s16 = 0;
5248
5249 s3 += s15 * 666643;
5250 s4 += s15 * 470296;
5251 s5 += s15 * 654183;
5252 s6 -= s15 * 997805;
5253 s7 += s15 * 136657;
5254 s8 -= s15 * 683901;
5255 s15 = 0;
5256
5257 s2 += s14 * 666643;
5258 s3 += s14 * 470296;
5259 s4 += s14 * 654183;
5260 s5 -= s14 * 997805;
5261 s6 += s14 * 136657;
5262 s7 -= s14 * 683901;
5263 s14 = 0;
5264
5265 s1 += s13 * 666643;
5266 s2 += s13 * 470296;
5267 s3 += s13 * 654183;
5268 s4 -= s13 * 997805;
5269 s5 += s13 * 136657;
5270 s6 -= s13 * 683901;
5271 s13 = 0;
5272
5273 s0 += s12 * 666643;
5274 s1 += s12 * 470296;
5275 s2 += s12 * 654183;
5276 s3 -= s12 * 997805;
5277 s4 += s12 * 136657;
5278 s5 -= s12 * 683901;
3a17b9a4
DMSP		 5279 s12 = 0;
5280
5281 carry0 = (s0 + (1 << 20)) >> 21;
425dde5d
DMSP		 5282 s1 += carry0;
5283 s0 -= carry0 * (1 << 21);
3a17b9a4 5284 carry2 = (s2 + (1 << 20)) >> 21;
425dde5d
DMSP		 5285 s3 += carry2;
5286 s2 -= carry2 * (1 << 21);
3a17b9a4 5287 carry4 = (s4 + (1 << 20)) >> 21;
425dde5d
DMSP		 5288 s5 += carry4;
5289 s4 -= carry4 * (1 << 21);
3a17b9a4 5290 carry6 = (s6 + (1 << 20)) >> 21;
425dde5d
DMSP		 5291 s7 += carry6;
5292 s6 -= carry6 * (1 << 21);
3a17b9a4 5293 carry8 = (s8 + (1 << 20)) >> 21;
425dde5d
DMSP		 5294 s9 += carry8;
5295 s8 -= carry8 * (1 << 21);
3a17b9a4
DMSP		 5296 carry10 = (s10 + (1 << 20)) >> 21;
5297 s11 += carry10;
5298 s10 -= carry10 * (1 << 21);
5299
5300 carry1 = (s1 + (1 << 20)) >> 21;
425dde5d
DMSP		 5301 s2 += carry1;
5302 s1 -= carry1 * (1 << 21);
3a17b9a4 5303 carry3 = (s3 + (1 << 20)) >> 21;
425dde5d
DMSP		 5304 s4 += carry3;
5305 s3 -= carry3 * (1 << 21);
3a17b9a4 5306 carry5 = (s5 + (1 << 20)) >> 21;
425dde5d
DMSP		 5307 s6 += carry5;
5308 s5 -= carry5 * (1 << 21);
3a17b9a4 5309 carry7 = (s7 + (1 << 20)) >> 21;
425dde5d
DMSP		 5310 s8 += carry7;
5311 s7 -= carry7 * (1 << 21);
3a17b9a4
DMSP		 5312 carry9 = (s9 + (1 << 20)) >> 21;
5313 s10 += carry9;
425dde5d 5314 s9 -= carry9 * (1 << 21);
3a17b9a4
DMSP		 5315 carry11 = (s11 + (1 << 20)) >> 21;
5316 s12 += carry11;
5317 s11 -= carry11 * (1 << 21);
5318
425dde5d
DMSP		 5319 s0 += s12 * 666643;
5320 s1 += s12 * 470296;
5321 s2 += s12 * 654183;
5322 s3 -= s12 * 997805;
5323 s4 += s12 * 136657;
5324 s5 -= s12 * 683901;
5325 s12 = 0;
3a17b9a4
DMSP		 5326
5327 carry0 = s0 >> 21;
425dde5d
DMSP		 5328 s1 += carry0;
5329 s0 -= carry0 * (1 << 21);
3a17b9a4 5330 carry1 = s1 >> 21;
425dde5d
DMSP		 5331 s2 += carry1;
5332 s1 -= carry1 * (1 << 21);
3a17b9a4 5333 carry2 = s2 >> 21;
425dde5d
DMSP		 5334 s3 += carry2;
5335 s2 -= carry2 * (1 << 21);
3a17b9a4 5336 carry3 = s3 >> 21;
425dde5d
DMSP		 5337 s4 += carry3;
5338 s3 -= carry3 * (1 << 21);
3a17b9a4 5339 carry4 = s4 >> 21;
425dde5d
DMSP		 5340 s5 += carry4;
5341 s4 -= carry4 * (1 << 21);
3a17b9a4 5342 carry5 = s5 >> 21;
425dde5d
DMSP		 5343 s6 += carry5;
5344 s5 -= carry5 * (1 << 21);
3a17b9a4 5345 carry6 = s6 >> 21;
425dde5d
DMSP		 5346 s7 += carry6;
5347 s6 -= carry6 * (1 << 21);
3a17b9a4 5348 carry7 = s7 >> 21;
425dde5d
DMSP		 5349 s8 += carry7;
5350 s7 -= carry7 * (1 << 21);
3a17b9a4 5351 carry8 = s8 >> 21;
425dde5d
DMSP		 5352 s9 += carry8;
5353 s8 -= carry8 * (1 << 21);
3a17b9a4
DMSP		 5354 carry9 = s9 >> 21;
5355 s10 += carry9;
425dde5d 5356 s9 -= carry9 * (1 << 21);
3a17b9a4
DMSP		 5357 carry10 = s10 >> 21;
5358 s11 += carry10;
5359 s10 -= carry10 * (1 << 21);
5360 carry11 = s11 >> 21;
5361 s12 += carry11;
5362 s11 -= carry11 * (1 << 21);
5363
425dde5d
DMSP		 5364 s0 += s12 * 666643;
5365 s1 += s12 * 470296;
5366 s2 += s12 * 654183;
5367 s3 -= s12 * 997805;
5368 s4 += s12 * 136657;
5369 s5 -= s12 * 683901;
5370 s12 = 0;
3a17b9a4
DMSP		 5371
5372 carry0 = s0 >> 21;
425dde5d
DMSP		 5373 s1 += carry0;
5374 s0 -= carry0 * (1 << 21);
3a17b9a4 5375 carry1 = s1 >> 21;
425dde5d
DMSP		 5376 s2 += carry1;
5377 s1 -= carry1 * (1 << 21);
3a17b9a4 5378 carry2 = s2 >> 21;
425dde5d
DMSP		 5379 s3 += carry2;
5380 s2 -= carry2 * (1 << 21);
3a17b9a4 5381 carry3 = s3 >> 21;
425dde5d
DMSP		 5382 s4 += carry3;
5383 s3 -= carry3 * (1 << 21);
3a17b9a4 5384 carry4 = s4 >> 21;
425dde5d
DMSP		 5385 s5 += carry4;
5386 s4 -= carry4 * (1 << 21);
3a17b9a4 5387 carry5 = s5 >> 21;
425dde5d
DMSP		 5388 s6 += carry5;
5389 s5 -= carry5 * (1 << 21);
3a17b9a4 5390 carry6 = s6 >> 21;
425dde5d
DMSP		 5391 s7 += carry6;
5392 s6 -= carry6 * (1 << 21);
3a17b9a4 5393 carry7 = s7 >> 21;
425dde5d
DMSP		 5394 s8 += carry7;
5395 s7 -= carry7 * (1 << 21);
3a17b9a4 5396 carry8 = s8 >> 21;
425dde5d
DMSP		 5397 s9 += carry8;
5398 s8 -= carry8 * (1 << 21);
3a17b9a4
DMSP		 5399 carry9 = s9 >> 21;
5400 s10 += carry9;
425dde5d 5401 s9 -= carry9 * (1 << 21);
3a17b9a4
DMSP		 5402 carry10 = s10 >> 21;
5403 s11 += carry10;
5404 s10 -= carry10 * (1 << 21);
5405
425dde5d
DMSP		 5406 s[ 0] = (uint8_t) (s0 >> 0);
5407 s[ 1] = (uint8_t) (s0 >> 8);
5408 s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5));
5409 s[ 3] = (uint8_t) (s1 >> 3);
5410 s[ 4] = (uint8_t) (s1 >> 11);
5411 s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2));
5412 s[ 6] = (uint8_t) (s2 >> 6);
5413 s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7));
5414 s[ 8] = (uint8_t) (s3 >> 1);
5415 s[ 9] = (uint8_t) (s3 >> 9);
5416 s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
5417 s[11] = (uint8_t) (s4 >> 4);
5418 s[12] = (uint8_t) (s4 >> 12);
5419 s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
5420 s[14] = (uint8_t) (s5 >> 7);
5421 s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
5422 s[16] = (uint8_t) (s6 >> 2);
5423 s[17] = (uint8_t) (s6 >> 10);
5424 s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
5425 s[19] = (uint8_t) (s7 >> 5);
5426 s[20] = (uint8_t) (s7 >> 13);
5427 s[21] = (uint8_t) (s8 >> 0);
5428 s[22] = (uint8_t) (s8 >> 8);
5429 s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
5430 s[24] = (uint8_t) (s9 >> 3);
5431 s[25] = (uint8_t) (s9 >> 11);
5432 s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
5433 s[27] = (uint8_t) (s10 >> 6);
3a17b9a4 5434 s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
425dde5d
DMSP		 5435 s[29] = (uint8_t) (s11 >> 1);
5436 s[30] = (uint8_t) (s11 >> 9);
5437 s[31] = (uint8_t) (s11 >> 17);
06c6d05f 5438}
d4d001df 5439
06c6d05f 5440int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
5435044f
MC		 5441 const uint8_t public_key[32], const uint8_t private_key[32],
5442 OPENSSL_CTX *libctx, const char *propq)
3a17b9a4
DMSP		 5443{
5444 uint8_t az[SHA512_DIGEST_LENGTH];
5445 uint8_t nonce[SHA512_DIGEST_LENGTH];
5446 ge_p3 R;
5447 uint8_t hram[SHA512_DIGEST_LENGTH];
5435044f 5448 EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
85d843c8
P		 5449 EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
5450 unsigned int sz;
5451 int res = 0;
3a17b9a4 5452
85d843c8
P		 5453 if (sha512 == NULL || hash_ctx == NULL)
5454 goto err;
5455
5456 if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5457 || !EVP_DigestUpdate(hash_ctx, private_key, 32)
5458 || !EVP_DigestFinal_ex(hash_ctx, az, &sz))
5459 goto err;
3a17b9a4
DMSP		 5460
5461 az[0] &= 248;
5462 az[31] &= 63;
5463 az[31] |= 64;
5464
85d843c8
P		 5465 if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5466 || !EVP_DigestUpdate(hash_ctx, az + 32, 32)
5467 || !EVP_DigestUpdate(hash_ctx, message, message_len)
5468 || !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
5469 goto err;
3a17b9a4
DMSP		 5470
5471 x25519_sc_reduce(nonce);
5472 ge_scalarmult_base(&R, nonce);
5473 ge_p3_tobytes(out_sig, &R);
5474
85d843c8
P		 5475 if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5476 || !EVP_DigestUpdate(hash_ctx, out_sig, 32)
5477 || !EVP_DigestUpdate(hash_ctx, public_key, 32)
5478 || !EVP_DigestUpdate(hash_ctx, message, message_len)
5479 || !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
5480 goto err;
3a17b9a4
DMSP		 5481
5482 x25519_sc_reduce(hram);
5483 sc_muladd(out_sig + 32, hram, az, nonce);
5484
85d843c8
P		 5485 res = 1;
5486err:
3a17b9a4
DMSP		 5487 OPENSSL_cleanse(nonce, sizeof(nonce));
5488 OPENSSL_cleanse(az, sizeof(az));
85d843c8
P		 5489 EVP_MD_free(sha512);
5490 EVP_MD_CTX_free(hash_ctx);
5491 return res;
06c6d05f
DSH		 5492}
5493
0ac8f35c
MC		 5494static const char allzeroes[15];
5495
06c6d05f 5496int ED25519_verify(const uint8_t *message, size_t message_len,
5435044f
MC		 5497 const uint8_t signature[64], const uint8_t public_key[32],
5498 OPENSSL_CTX *libctx, const char *propq)
3a17b9a4
DMSP		 5499{
5500 int i;
5501 ge_p3 A;
5502 const uint8_t *r, *s;
85d843c8
P		 5503 EVP_MD *sha512;
5504 EVP_MD_CTX *hash_ctx = NULL;
5505 unsigned int sz;
5506 int res = 0;
3a17b9a4
DMSP		 5507 ge_p2 R;
5508 uint8_t rcheck[32];
5509 uint8_t h[SHA512_DIGEST_LENGTH];
5510 /* 27742317777372353535851937790883648493 in little endian format */
5511 const uint8_t l_low[16] = {
5512 0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5513 0xDE, 0xF9, 0xDE, 0x14
5514 };
5515
5516 r = signature;
5517 s = signature + 32;
5518
5519 /*
5520 * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5521 *
5522 * If not the signature is publicly invalid. Since it's public we can do the
5523 * check in variable time.
5524 *
5525 * First check the most significant byte
5526 */
5527 if (s[31] > 0x10)
0ac8f35c 5528 return 0;
3a17b9a4
DMSP		 5529 if (s[31] == 0x10) {
5530 /*
5531 * Most significant byte indicates a value close to 2^252 so check the
5532 * rest
5533 */
5534 if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
0ac8f35c 5535 return 0;
3a17b9a4
DMSP		 5536 for (i = 15; i >= 0; i--) {
5537 if (s[i] < l_low[i])
5538 break;
5539 if (s[i] > l_low[i])
5540 return 0;
5541 }
5542 if (i < 0)
5543 return 0;
5544 }
0ac8f35c 5545
3a17b9a4
DMSP		 5546 if (ge_frombytes_vartime(&A, public_key) != 0) {
5547 return 0;
5548 }
06c6d05f 5549
3a17b9a4
DMSP		 5550 fe_neg(A.X, A.X);
5551 fe_neg(A.T, A.T);
06c6d05f 5552
5435044f 5553 sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
85d843c8
P		 5554 if (sha512 == NULL)
5555 return 0;
5556 hash_ctx = EVP_MD_CTX_new();
5557 if (hash_ctx == NULL)
5558 goto err;
5559
5560 if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5561 || !EVP_DigestUpdate(hash_ctx, r, 32)
5562 || !EVP_DigestUpdate(hash_ctx, public_key, 32)
5563 || !EVP_DigestUpdate(hash_ctx, message, message_len)
5564 || !EVP_DigestFinal_ex(hash_ctx, h, &sz))
5565 goto err;
06c6d05f 5566
3a17b9a4 5567 x25519_sc_reduce(h);
06c6d05f 5568
3a17b9a4 5569 ge_double_scalarmult_vartime(&R, h, &A, s);
06c6d05f 5570
3a17b9a4 5571 ge_tobytes(rcheck, &R);
06c6d05f 5572
85d843c8
P		 5573 res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5574err:
5575 EVP_MD_free(sha512);
5576 EVP_MD_CTX_free(hash_ctx);
5577 return res;
06c6d05f
DSH		 5578}
5579
43cd3701
P		 5580int ED25519_public_from_private(OPENSSL_CTX *ctx, uint8_t out_public_key[32],
5581 const uint8_t private_key[32])
3a17b9a4
DMSP		 5582{
5583 uint8_t az[SHA512_DIGEST_LENGTH];
5584 ge_p3 A;
43cd3701
P		 5585 int r;
5586 EVP_MD *sha512 = NULL;
06c6d05f 5587
43cd3701
P		 5588 sha512 = EVP_MD_fetch(ctx, SN_sha512, NULL);
5589 if (sha512 == NULL)
5590 return 0;
5591 r = EVP_Digest(private_key, 32, az, NULL, sha512, NULL);
5592 EVP_MD_free(sha512);
5593 if (!r) {
5594 OPENSSL_cleanse(az, sizeof(az));
5595 return 0;
5596 }
06c6d05f 5597
3a17b9a4
DMSP		 5598 az[0] &= 248;
5599 az[31] &= 63;
5600 az[31] |= 64;
06c6d05f 5601
3a17b9a4
DMSP		 5602 ge_scalarmult_base(&A, az);
5603 ge_p3_tobytes(out_public_key, &A);
3790a2f6 5604
3a17b9a4 5605 OPENSSL_cleanse(az, sizeof(az));
43cd3701 5606 return 1;
06c6d05f
DSH		 5607}
5608
a90def6b 5609int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
3a17b9a4
DMSP		 5610 const uint8_t peer_public_value[32])
5611{
5612 static const uint8_t kZeros[32] = {0};
5613 x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5614 /* The all-zero output results when the input is a point of small order. */
5615 return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
a90def6b
DSH		 5616}
5617
a90def6b 5618void X25519_public_from_private(uint8_t out_public_value[32],
3a17b9a4
DMSP		 5619 const uint8_t private_key[32])
5620{
5621 uint8_t e[32];
5622 ge_p3 A;
5623 fe zplusy, zminusy, zminusy_inv;
5624
5625 memcpy(e, private_key, 32);
5626 e[0] &= 248;
5627 e[31] &= 127;
5628 e[31] |= 64;
5629
5630 ge_scalarmult_base(&A, e);
5631
5632 /*
5633 * We only need the u-coordinate of the curve25519 point.
5634 * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5635 * u=(Z+Y)/(Z-Y).
5636 */
5637 fe_add(zplusy, A.Z, A.Y);
5638 fe_sub(zminusy, A.Z, A.Y);
5639 fe_invert(zminusy_inv, zminusy);
5640 fe_mul(zplusy, zplusy, zminusy_inv);
5641 fe_tobytes(out_public_value, zplusy);
5642
5643 OPENSSL_cleanse(e, sizeof(e));
a90def6b 5644}
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