1/*
2 * Copyright 2016-2021 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the Apache License 2.0 (the "License").  You may not use
5 * this file except in compliance with the License.  You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
8 */
9
10/*
11 * ECDSA low level APIs are deprecated for public use, but still ok for
12 * internal use.
13 */
14#include "internal/deprecated.h"
15
16#include <string.h>
17#include "crypto/ecx.h"
18#include "ec_local.h"
19#include <openssl/evp.h>
20#include <openssl/sha.h>
21
22#include "internal/numbers.h"
23
24#if defined(X25519_ASM) && (defined(__x86_64) || defined(__x86_64__) || \
25                            defined(_M_AMD64) || defined(_M_X64))
26
27# define BASE_2_64_IMPLEMENTED
28
29typedef uint64_t fe64[4];
30
31int x25519_fe64_eligible(void);
32
33/*
34 * Following subroutines perform corresponding operations modulo
35 * 2^256-38, i.e. double the curve modulus. However, inputs and
36 * outputs are permitted to be partially reduced, i.e. to remain
37 * in [0..2^256) range. It's all tied up in final fe64_tobytes
38 * that performs full reduction modulo 2^255-19.
39 *
40 * There are no reference C implementations for these.
41 */
42void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
43void x25519_fe64_sqr(fe64 h, const fe64 f);
44void x25519_fe64_mul121666(fe64 h, fe64 f);
45void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
46void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
47void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
48# define fe64_mul x25519_fe64_mul
49# define fe64_sqr x25519_fe64_sqr
50# define fe64_mul121666 x25519_fe64_mul121666
51# define fe64_add x25519_fe64_add
52# define fe64_sub x25519_fe64_sub
53# define fe64_tobytes x25519_fe64_tobytes
54
55static uint64_t load_8(const uint8_t *in)
56{
57    uint64_t result;
58
59    result = in[0];
60    result |= ((uint64_t)in[1]) << 8;
61    result |= ((uint64_t)in[2]) << 16;
62    result |= ((uint64_t)in[3]) << 24;
63    result |= ((uint64_t)in[4]) << 32;
64    result |= ((uint64_t)in[5]) << 40;
65    result |= ((uint64_t)in[6]) << 48;
66    result |= ((uint64_t)in[7]) << 56;
67
68    return result;
69}
70
71static void fe64_frombytes(fe64 h, const uint8_t *s)
72{
73    h[0] = load_8(s);
74    h[1] = load_8(s + 8);
75    h[2] = load_8(s + 16);
76    h[3] = load_8(s + 24) & 0x7fffffffffffffff;
77}
78
79static void fe64_0(fe64 h)
80{
81    h[0] = 0;
82    h[1] = 0;
83    h[2] = 0;
84    h[3] = 0;
85}
86
87static void fe64_1(fe64 h)
88{
89    h[0] = 1;
90    h[1] = 0;
91    h[2] = 0;
92    h[3] = 0;
93}
94
95static void fe64_copy(fe64 h, const fe64 f)
96{
97    h[0] = f[0];
98    h[1] = f[1];
99    h[2] = f[2];
100    h[3] = f[3];
101}
102
103static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
104{
105    int i;
106    uint64_t mask = 0 - (uint64_t)b;
107
108    for (i = 0; i < 4; i++) {
109        uint64_t x = f[i] ^ g[i];
110        x &= mask;
111        f[i] ^= x;
112        g[i] ^= x;
113    }
114}
115
116static void fe64_invert(fe64 out, const fe64 z)
117{
118    fe64 t0;
119    fe64 t1;
120    fe64 t2;
121    fe64 t3;
122    int i;
123
124    /*
125     * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
126     * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
127     */
128
129    /* t0 = z ** 2 */
130    fe64_sqr(t0, z);
131
132    /* t1 = t0 ** (2 ** 2) = z ** 8 */
133    fe64_sqr(t1, t0);
134    fe64_sqr(t1, t1);
135
136    /* t1 = z * t1 = z ** 9 */
137    fe64_mul(t1, z, t1);
138    /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
139    fe64_mul(t0, t0, t1);
140
141    /* t2 = t0 ** 2 = z ** 22 */
142    fe64_sqr(t2, t0);
143
144    /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
145    fe64_mul(t1, t1, t2);
146
147    /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
148    fe64_sqr(t2, t1);
149    for (i = 1; i < 5; ++i)
150        fe64_sqr(t2, t2);
151
152    /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
153    fe64_mul(t1, t2, t1);
154
155    /* Continuing similarly... */
156
157    /* t2 = z ** (2 ** 20 - 1) */
158    fe64_sqr(t2, t1);
159    for (i = 1; i < 10; ++i)
160        fe64_sqr(t2, t2);
161
162    fe64_mul(t2, t2, t1);
163
164    /* t2 = z ** (2 ** 40 - 1) */
165    fe64_sqr(t3, t2);
166    for (i = 1; i < 20; ++i)
167        fe64_sqr(t3, t3);
168
169    fe64_mul(t2, t3, t2);
170
171    /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
172    for (i = 0; i < 10; ++i)
173        fe64_sqr(t2, t2);
174
175    /* t1 = z ** (2 ** 50 - 1) */
176    fe64_mul(t1, t2, t1);
177
178    /* t2 = z ** (2 ** 100 - 1) */
179    fe64_sqr(t2, t1);
180    for (i = 1; i < 50; ++i)
181        fe64_sqr(t2, t2);
182
183    fe64_mul(t2, t2, t1);
184
185    /* t2 = z ** (2 ** 200 - 1) */
186    fe64_sqr(t3, t2);
187    for (i = 1; i < 100; ++i)
188        fe64_sqr(t3, t3);
189
190    fe64_mul(t2, t3, t2);
191
192    /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
193    for (i = 0; i < 50; ++i)
194        fe64_sqr(t2, t2);
195
196    /* t1 = z ** (2 ** 250 - 1) */
197    fe64_mul(t1, t2, t1);
198
199    /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
200    for (i = 0; i < 5; ++i)
201        fe64_sqr(t1, t1);
202
203    /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
204    fe64_mul(out, t1, t0);
205}
206
207/*
208 * Duplicate of original x25519_scalar_mult_generic, but using
209 * fe64_* subroutines.
210 */
211static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
212                               const uint8_t point[32])
213{
214    fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
215    uint8_t e[32];
216    unsigned swap = 0;
217    int pos;
218
219    memcpy(e, scalar, 32);
220    e[0]  &= 0xf8;
221    e[31] &= 0x7f;
222    e[31] |= 0x40;
223    fe64_frombytes(x1, point);
224    fe64_1(x2);
225    fe64_0(z2);
226    fe64_copy(x3, x1);
227    fe64_1(z3);
228
229    for (pos = 254; pos >= 0; --pos) {
230        unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
231
232        swap ^= b;
233        fe64_cswap(x2, x3, swap);
234        fe64_cswap(z2, z3, swap);
235        swap = b;
236        fe64_sub(tmp0, x3, z3);
237        fe64_sub(tmp1, x2, z2);
238        fe64_add(x2, x2, z2);
239        fe64_add(z2, x3, z3);
240        fe64_mul(z3, x2, tmp0);
241        fe64_mul(z2, z2, tmp1);
242        fe64_sqr(tmp0, tmp1);
243        fe64_sqr(tmp1, x2);
244        fe64_add(x3, z3, z2);
245        fe64_sub(z2, z3, z2);
246        fe64_mul(x2, tmp1, tmp0);
247        fe64_sub(tmp1, tmp1, tmp0);
248        fe64_sqr(z2, z2);
249        fe64_mul121666(z3, tmp1);
250        fe64_sqr(x3, x3);
251        fe64_add(tmp0, tmp0, z3);
252        fe64_mul(z3, x1, z2);
253        fe64_mul(z2, tmp1, tmp0);
254    }
255
256    fe64_invert(z2, z2);
257    fe64_mul(x2, x2, z2);
258    fe64_tobytes(out, x2);
259
260    OPENSSL_cleanse(e, sizeof(e));
261}
262#endif
263
264#if defined(X25519_ASM) \
265    || ( defined(INT128_MAX) \
266         && !defined(__sparc__) \
267         && (!defined(__SIZEOF_LONG__) || (__SIZEOF_LONG__ == 8)) \
268         && !(defined(__ANDROID__) && !defined(__clang__)) )
269/*
270 * Base 2^51 implementation. It's virtually no different from reference
271 * base 2^25.5 implementation in respect to lax boundary conditions for
272 * intermediate values and even individual limbs. So that whatever you
273 * know about the reference, applies even here...
274 */
275# define BASE_2_51_IMPLEMENTED
276
277typedef uint64_t fe51[5];
278
279static const uint64_t MASK51 = 0x7ffffffffffff;
280
281static uint64_t load_7(const uint8_t *in)
282{
283    uint64_t result;
284
285    result = in[0];
286    result |= ((uint64_t)in[1]) << 8;
287    result |= ((uint64_t)in[2]) << 16;
288    result |= ((uint64_t)in[3]) << 24;
289    result |= ((uint64_t)in[4]) << 32;
290    result |= ((uint64_t)in[5]) << 40;
291    result |= ((uint64_t)in[6]) << 48;
292
293    return result;
294}
295
296static uint64_t load_6(const uint8_t *in)
297{
298    uint64_t result;
299
300    result = in[0];
301    result |= ((uint64_t)in[1]) << 8;
302    result |= ((uint64_t)in[2]) << 16;
303    result |= ((uint64_t)in[3]) << 24;
304    result |= ((uint64_t)in[4]) << 32;
305    result |= ((uint64_t)in[5]) << 40;
306
307    return result;
308}
309
310static void fe51_frombytes(fe51 h, const uint8_t *s)
311{
312    uint64_t h0 = load_7(s);                                /* 56 bits */
313    uint64_t h1 = load_6(s + 7) << 5;                       /* 53 bits */
314    uint64_t h2 = load_7(s + 13) << 2;                      /* 58 bits */
315    uint64_t h3 = load_6(s + 20) << 7;                      /* 55 bits */
316    uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4;   /* 51 bits */
317
318    h1 |= h0 >> 51; h0 &= MASK51;
319    h2 |= h1 >> 51; h1 &= MASK51;
320    h3 |= h2 >> 51; h2 &= MASK51;
321    h4 |= h3 >> 51; h3 &= MASK51;
322
323    h[0] = h0;
324    h[1] = h1;
325    h[2] = h2;
326    h[3] = h3;
327    h[4] = h4;
328}
329
330static void fe51_tobytes(uint8_t *s, const fe51 h)
331{
332    uint64_t h0 = h[0];
333    uint64_t h1 = h[1];
334    uint64_t h2 = h[2];
335    uint64_t h3 = h[3];
336    uint64_t h4 = h[4];
337    uint64_t q;
338
339    /* compare to modulus */
340    q = (h0 + 19) >> 51;
341    q = (h1 + q) >> 51;
342    q = (h2 + q) >> 51;
343    q = (h3 + q) >> 51;
344    q = (h4 + q) >> 51;
345
346    /* full reduce */
347    h0 += 19 * q;
348    h1 += h0 >> 51; h0 &= MASK51;
349    h2 += h1 >> 51; h1 &= MASK51;
350    h3 += h2 >> 51; h2 &= MASK51;
351    h4 += h3 >> 51; h3 &= MASK51;
352                    h4 &= MASK51;
353
354    /* smash */
355    s[0] = (uint8_t)(h0 >> 0);
356    s[1] = (uint8_t)(h0 >> 8);
357    s[2] = (uint8_t)(h0 >> 16);
358    s[3] = (uint8_t)(h0 >> 24);
359    s[4] = (uint8_t)(h0 >> 32);
360    s[5] = (uint8_t)(h0 >> 40);
361    s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3));
362    s[7] = (uint8_t)(h1 >> 5);
363    s[8] = (uint8_t)(h1 >> 13);
364    s[9] = (uint8_t)(h1 >> 21);
365    s[10] = (uint8_t)(h1 >> 29);
366    s[11] = (uint8_t)(h1 >> 37);
367    s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6));
368    s[13] = (uint8_t)(h2 >> 2);
369    s[14] = (uint8_t)(h2 >> 10);
370    s[15] = (uint8_t)(h2 >> 18);
371    s[16] = (uint8_t)(h2 >> 26);
372    s[17] = (uint8_t)(h2 >> 34);
373    s[18] = (uint8_t)(h2 >> 42);
374    s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1));
375    s[20] = (uint8_t)(h3 >> 7);
376    s[21] = (uint8_t)(h3 >> 15);
377    s[22] = (uint8_t)(h3 >> 23);
378    s[23] = (uint8_t)(h3 >> 31);
379    s[24] = (uint8_t)(h3 >> 39);
380    s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4));
381    s[26] = (uint8_t)(h4 >> 4);
382    s[27] = (uint8_t)(h4 >> 12);
383    s[28] = (uint8_t)(h4 >> 20);
384    s[29] = (uint8_t)(h4 >> 28);
385    s[30] = (uint8_t)(h4 >> 36);
386    s[31] = (uint8_t)(h4 >> 44);
387}
388
389# if defined(X25519_ASM)
390void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
391void x25519_fe51_sqr(fe51 h, const fe51 f);
392void x25519_fe51_mul121666(fe51 h, fe51 f);
393#  define fe51_mul x25519_fe51_mul
394#  define fe51_sq  x25519_fe51_sqr
395#  define fe51_mul121666 x25519_fe51_mul121666
396# else
397
398typedef uint128_t u128;
399
400static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
401{
402    u128 h0, h1, h2, h3, h4;
403    uint64_t f_i, g0, g1, g2, g3, g4;
404
405    f_i = f[0];
406    h0 = (u128)f_i * (g0 = g[0]);
407    h1 = (u128)f_i * (g1 = g[1]);
408    h2 = (u128)f_i * (g2 = g[2]);
409    h3 = (u128)f_i * (g3 = g[3]);
410    h4 = (u128)f_i * (g4 = g[4]);
411
412    f_i = f[1];
413    h0 += (u128)f_i * (g4 *= 19);
414    h1 += (u128)f_i * g0;
415    h2 += (u128)f_i * g1;
416    h3 += (u128)f_i * g2;
417    h4 += (u128)f_i * g3;
418
419    f_i = f[2];
420    h0 += (u128)f_i * (g3 *= 19);
421    h1 += (u128)f_i * g4;
422    h2 += (u128)f_i * g0;
423    h3 += (u128)f_i * g1;
424    h4 += (u128)f_i * g2;
425
426    f_i = f[3];
427    h0 += (u128)f_i * (g2 *= 19);
428    h1 += (u128)f_i * g3;
429    h2 += (u128)f_i * g4;
430    h3 += (u128)f_i * g0;
431    h4 += (u128)f_i * g1;
432
433    f_i = f[4];
434    h0 += (u128)f_i * (g1 *= 19);
435    h1 += (u128)f_i * g2;
436    h2 += (u128)f_i * g3;
437    h3 += (u128)f_i * g4;
438    h4 += (u128)f_i * g0;
439
440    /* partial [lazy] reduction */
441    h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
442    h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
443
444    h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
445    g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
446
447    g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
448    g3 += g2 >> 51; g2 &= MASK51;
449    g1 += g0 >> 51; g0 &= MASK51;
450
451    h[0] = g0;
452    h[1] = g1;
453    h[2] = g2;
454    h[3] = g3;
455    h[4] = g4;
456}
457
458static void fe51_sq(fe51 h, const fe51 f)
459{
460#  if defined(OPENSSL_SMALL_FOOTPRINT)
461    fe51_mul(h, f, f);
462#  else
463    /* dedicated squaring gives 16-25% overall improvement */
464    uint64_t g0 = f[0];
465    uint64_t g1 = f[1];
466    uint64_t g2 = f[2];
467    uint64_t g3 = f[3];
468    uint64_t g4 = f[4];
469    u128 h0, h1, h2, h3, h4;
470
471    h0 = (u128)g0 * g0;     g0 *= 2;
472    h1 = (u128)g0 * g1;
473    h2 = (u128)g0 * g2;
474    h3 = (u128)g0 * g3;
475    h4 = (u128)g0 * g4;
476
477    g0 = g4;                /* borrow g0 */
478    h3 += (u128)g0 * (g4 *= 19);
479
480    h2 += (u128)g1 * g1;    g1 *= 2;
481    h3 += (u128)g1 * g2;
482    h4 += (u128)g1 * g3;
483    h0 += (u128)g1 * g4;
484
485    g0 = g3;                /* borrow g0 */
486    h1 += (u128)g0 * (g3 *= 19);
487    h2 += (u128)(g0 * 2) * g4;
488
489    h4 += (u128)g2 * g2;    g2 *= 2;
490    h0 += (u128)g2 * g3;
491    h1 += (u128)g2 * g4;
492
493    /* partial [lazy] reduction */
494    h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
495    h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
496
497    h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
498    g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
499
500    g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
501    g3 += g2 >> 51; g2 &= MASK51;
502    g1 += g0 >> 51; g0 &= MASK51;
503
504    h[0] = g0;
505    h[1] = g1;
506    h[2] = g2;
507    h[3] = g3;
508    h[4] = g4;
509#  endif
510}
511
512static void fe51_mul121666(fe51 h, fe51 f)
513{
514    u128 h0 = f[0] * (u128)121666;
515    u128 h1 = f[1] * (u128)121666;
516    u128 h2 = f[2] * (u128)121666;
517    u128 h3 = f[3] * (u128)121666;
518    u128 h4 = f[4] * (u128)121666;
519    uint64_t g0, g1, g2, g3, g4;
520
521    h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
522    h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
523
524    h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
525    g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
526
527    g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
528    g3 += g2 >> 51; g2 &= MASK51;
529    g1 += g0 >> 51; g0 &= MASK51;
530
531    h[0] = g0;
532    h[1] = g1;
533    h[2] = g2;
534    h[3] = g3;
535    h[4] = g4;
536}
537# endif
538
539static void fe51_add(fe51 h, const fe51 f, const fe51 g)
540{
541    h[0] = f[0] + g[0];
542    h[1] = f[1] + g[1];
543    h[2] = f[2] + g[2];
544    h[3] = f[3] + g[3];
545    h[4] = f[4] + g[4];
546}
547
548static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
549{
550    /*
551     * Add 2*modulus to ensure that result remains positive
552     * even if subtrahend is partially reduced.
553     */
554    h[0] = (f[0] + 0xfffffffffffda) - g[0];
555    h[1] = (f[1] + 0xffffffffffffe) - g[1];
556    h[2] = (f[2] + 0xffffffffffffe) - g[2];
557    h[3] = (f[3] + 0xffffffffffffe) - g[3];
558    h[4] = (f[4] + 0xffffffffffffe) - g[4];
559}
560
561static void fe51_0(fe51 h)
562{
563    h[0] = 0;
564    h[1] = 0;
565    h[2] = 0;
566    h[3] = 0;
567    h[4] = 0;
568}
569
570static void fe51_1(fe51 h)
571{
572    h[0] = 1;
573    h[1] = 0;
574    h[2] = 0;
575    h[3] = 0;
576    h[4] = 0;
577}
578
579static void fe51_copy(fe51 h, const fe51 f)
580{
581    h[0] = f[0];
582    h[1] = f[1];
583    h[2] = f[2];
584    h[3] = f[3];
585    h[4] = f[4];
586}
587
588static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
589{
590    int i;
591    uint64_t mask = 0 - (uint64_t)b;
592
593    for (i = 0; i < 5; i++) {
594        int64_t x = f[i] ^ g[i];
595        x &= mask;
596        f[i] ^= x;
597        g[i] ^= x;
598    }
599}
600
601static void fe51_invert(fe51 out, const fe51 z)
602{
603    fe51 t0;
604    fe51 t1;
605    fe51 t2;
606    fe51 t3;
607    int i;
608
609    /*
610     * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
611     * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
612     */
613
614    /* t0 = z ** 2 */
615    fe51_sq(t0, z);
616
617    /* t1 = t0 ** (2 ** 2) = z ** 8 */
618    fe51_sq(t1, t0);
619    fe51_sq(t1, t1);
620
621    /* t1 = z * t1 = z ** 9 */
622    fe51_mul(t1, z, t1);
623    /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
624    fe51_mul(t0, t0, t1);
625
626    /* t2 = t0 ** 2 = z ** 22 */
627    fe51_sq(t2, t0);
628
629    /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
630    fe51_mul(t1, t1, t2);
631
632    /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
633    fe51_sq(t2, t1);
634    for (i = 1; i < 5; ++i)
635        fe51_sq(t2, t2);
636
637    /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
638    fe51_mul(t1, t2, t1);
639
640    /* Continuing similarly... */
641
642    /* t2 = z ** (2 ** 20 - 1) */
643    fe51_sq(t2, t1);
644    for (i = 1; i < 10; ++i)
645        fe51_sq(t2, t2);
646
647    fe51_mul(t2, t2, t1);
648
649    /* t2 = z ** (2 ** 40 - 1) */
650    fe51_sq(t3, t2);
651    for (i = 1; i < 20; ++i)
652        fe51_sq(t3, t3);
653
654    fe51_mul(t2, t3, t2);
655
656    /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
657    for (i = 0; i < 10; ++i)
658        fe51_sq(t2, t2);
659
660    /* t1 = z ** (2 ** 50 - 1) */
661    fe51_mul(t1, t2, t1);
662
663    /* t2 = z ** (2 ** 100 - 1) */
664    fe51_sq(t2, t1);
665    for (i = 1; i < 50; ++i)
666        fe51_sq(t2, t2);
667
668    fe51_mul(t2, t2, t1);
669
670    /* t2 = z ** (2 ** 200 - 1) */
671    fe51_sq(t3, t2);
672    for (i = 1; i < 100; ++i)
673        fe51_sq(t3, t3);
674
675    fe51_mul(t2, t3, t2);
676
677    /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
678    for (i = 0; i < 50; ++i)
679        fe51_sq(t2, t2);
680
681    /* t1 = z ** (2 ** 250 - 1) */
682    fe51_mul(t1, t2, t1);
683
684    /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
685    for (i = 0; i < 5; ++i)
686        fe51_sq(t1, t1);
687
688    /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
689    fe51_mul(out, t1, t0);
690}
691
692/*
693 * Duplicate of original x25519_scalar_mult_generic, but using
694 * fe51_* subroutines.
695 */
696static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
697                               const uint8_t point[32])
698{
699    fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
700    uint8_t e[32];
701    unsigned swap = 0;
702    int pos;
703
704# ifdef BASE_2_64_IMPLEMENTED
705    if (x25519_fe64_eligible()) {
706        x25519_scalar_mulx(out, scalar, point);
707        return;
708    }
709# endif
710
711    memcpy(e, scalar, 32);
712    e[0]  &= 0xf8;
713    e[31] &= 0x7f;
714    e[31] |= 0x40;
715    fe51_frombytes(x1, point);
716    fe51_1(x2);
717    fe51_0(z2);
718    fe51_copy(x3, x1);
719    fe51_1(z3);
720
721    for (pos = 254; pos >= 0; --pos) {
722        unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
723
724        swap ^= b;
725        fe51_cswap(x2, x3, swap);
726        fe51_cswap(z2, z3, swap);
727        swap = b;
728        fe51_sub(tmp0, x3, z3);
729        fe51_sub(tmp1, x2, z2);
730        fe51_add(x2, x2, z2);
731        fe51_add(z2, x3, z3);
732        fe51_mul(z3, tmp0, x2);
733        fe51_mul(z2, z2, tmp1);
734        fe51_sq(tmp0, tmp1);
735        fe51_sq(tmp1, x2);
736        fe51_add(x3, z3, z2);
737        fe51_sub(z2, z3, z2);
738        fe51_mul(x2, tmp1, tmp0);
739        fe51_sub(tmp1, tmp1, tmp0);
740        fe51_sq(z2, z2);
741        fe51_mul121666(z3, tmp1);
742        fe51_sq(x3, x3);
743        fe51_add(tmp0, tmp0, z3);
744        fe51_mul(z3, x1, z2);
745        fe51_mul(z2, tmp1, tmp0);
746    }
747
748    fe51_invert(z2, z2);
749    fe51_mul(x2, x2, z2);
750    fe51_tobytes(out, x2);
751
752    OPENSSL_cleanse(e, sizeof(e));
753}
754#endif
755
756/*
757 * Reference base 2^25.5 implementation.
758 *
759 * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
760 * 20141124 (http://bench.cr.yp.to/supercop.html).
761 *
762 * The field functions are shared by Ed25519 and X25519 where possible.
763 */
764
765/*
766 * fe means field element. Here the field is \Z/(2^255-19). An element t,
767 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
768 * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
769 * context.
770 */
771typedef int32_t fe[10];
772
773static const int64_t kBottom21Bits =  0x1fffffLL;
774static const int64_t kBottom25Bits = 0x1ffffffLL;
775static const int64_t kBottom26Bits = 0x3ffffffLL;
776static const int64_t kTop39Bits = 0xfffffffffe000000LL;
777static const int64_t kTop38Bits = 0xfffffffffc000000LL;
778
779static uint64_t load_3(const uint8_t *in)
780{
781    uint64_t result;
782
783    result  = ((uint64_t)in[0]);
784    result |= ((uint64_t)in[1]) << 8;
785    result |= ((uint64_t)in[2]) << 16;
786    return result;
787}
788
789static uint64_t load_4(const uint8_t *in)
790{
791    uint64_t result;
792
793    result  = ((uint64_t)in[0]);
794    result |= ((uint64_t)in[1]) << 8;
795    result |= ((uint64_t)in[2]) << 16;
796    result |= ((uint64_t)in[3]) << 24;
797    return result;
798}
799
800static void fe_frombytes(fe h, const uint8_t *s)
801{
802    /* Ignores top bit of h. */
803    int64_t h0 =  load_4(s);
804    int64_t h1 =  load_3(s +  4) << 6;
805    int64_t h2 =  load_3(s +  7) << 5;
806    int64_t h3 =  load_3(s + 10) << 3;
807    int64_t h4 =  load_3(s + 13) << 2;
808    int64_t h5 =  load_4(s + 16);
809    int64_t h6 =  load_3(s + 20) << 7;
810    int64_t h7 =  load_3(s + 23) << 5;
811    int64_t h8 =  load_3(s + 26) << 4;
812    int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
813    int64_t carry0;
814    int64_t carry1;
815    int64_t carry2;
816    int64_t carry3;
817    int64_t carry4;
818    int64_t carry5;
819    int64_t carry6;
820    int64_t carry7;
821    int64_t carry8;
822    int64_t carry9;
823
824    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
825    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
826    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
827    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
828    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
829
830    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
831    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
832    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
833    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
834    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
835
836    h[0] = (int32_t)h0;
837    h[1] = (int32_t)h1;
838    h[2] = (int32_t)h2;
839    h[3] = (int32_t)h3;
840    h[4] = (int32_t)h4;
841    h[5] = (int32_t)h5;
842    h[6] = (int32_t)h6;
843    h[7] = (int32_t)h7;
844    h[8] = (int32_t)h8;
845    h[9] = (int32_t)h9;
846}
847
848/*
849 * Preconditions:
850 *   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
851 *
852 * Write p=2^255-19; q=floor(h/p).
853 * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
854 *
855 * Proof:
856 *   Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
857 *   Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
858 *
859 *   Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
860 *   Then 0<y<1.
861 *
862 *   Write r=h-pq.
863 *   Have 0<=r<=p-1=2^255-20.
864 *   Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
865 *
866 *   Write x=r+19(2^-255)r+y.
867 *   Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
868 *
869 *   Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
870 *   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
871 */
872static void fe_tobytes(uint8_t *s, const fe h)
873{
874    int32_t h0 = h[0];
875    int32_t h1 = h[1];
876    int32_t h2 = h[2];
877    int32_t h3 = h[3];
878    int32_t h4 = h[4];
879    int32_t h5 = h[5];
880    int32_t h6 = h[6];
881    int32_t h7 = h[7];
882    int32_t h8 = h[8];
883    int32_t h9 = h[9];
884    int32_t q;
885
886    q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
887    q = (h0 + q) >> 26;
888    q = (h1 + q) >> 25;
889    q = (h2 + q) >> 26;
890    q = (h3 + q) >> 25;
891    q = (h4 + q) >> 26;
892    q = (h5 + q) >> 25;
893    q = (h6 + q) >> 26;
894    q = (h7 + q) >> 25;
895    q = (h8 + q) >> 26;
896    q = (h9 + q) >> 25;
897
898    /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
899    h0 += 19 * q;
900    /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
901
902    h1 += h0 >> 26; h0 &= kBottom26Bits;
903    h2 += h1 >> 25; h1 &= kBottom25Bits;
904    h3 += h2 >> 26; h2 &= kBottom26Bits;
905    h4 += h3 >> 25; h3 &= kBottom25Bits;
906    h5 += h4 >> 26; h4 &= kBottom26Bits;
907    h6 += h5 >> 25; h5 &= kBottom25Bits;
908    h7 += h6 >> 26; h6 &= kBottom26Bits;
909    h8 += h7 >> 25; h7 &= kBottom25Bits;
910    h9 += h8 >> 26; h8 &= kBottom26Bits;
911                    h9 &= kBottom25Bits;
912    /* h10 = carry9 */
913
914    /*
915     * Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
916     * Have h0+...+2^230 h9 between 0 and 2^255-1;
917     * evidently 2^255 h10-2^255 q = 0.
918     * Goal: Output h0+...+2^230 h9.
919     */
920    s[ 0] = (uint8_t) (h0 >>  0);
921    s[ 1] = (uint8_t) (h0 >>  8);
922    s[ 2] = (uint8_t) (h0 >> 16);
923    s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2));
924    s[ 4] = (uint8_t) (h1 >>  6);
925    s[ 5] = (uint8_t) (h1 >> 14);
926    s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3));
927    s[ 7] = (uint8_t) (h2 >>  5);
928    s[ 8] = (uint8_t) (h2 >> 13);
929    s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5));
930    s[10] = (uint8_t) (h3 >>  3);
931    s[11] = (uint8_t) (h3 >> 11);
932    s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6));
933    s[13] = (uint8_t) (h4 >>  2);
934    s[14] = (uint8_t) (h4 >> 10);
935    s[15] = (uint8_t) (h4 >> 18);
936    s[16] = (uint8_t) (h5 >>  0);
937    s[17] = (uint8_t) (h5 >>  8);
938    s[18] = (uint8_t) (h5 >> 16);
939    s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1));
940    s[20] = (uint8_t) (h6 >>  7);
941    s[21] = (uint8_t) (h6 >> 15);
942    s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3));
943    s[23] = (uint8_t) (h7 >>  5);
944    s[24] = (uint8_t) (h7 >> 13);
945    s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4));
946    s[26] = (uint8_t) (h8 >>  4);
947    s[27] = (uint8_t) (h8 >> 12);
948    s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6));
949    s[29] = (uint8_t) (h9 >>  2);
950    s[30] = (uint8_t) (h9 >> 10);
951    s[31] = (uint8_t) (h9 >> 18);
952}
953
954/* h = f */
955static void fe_copy(fe h, const fe f)
956{
957    memmove(h, f, sizeof(int32_t) * 10);
958}
959
960/* h = 0 */
961static void fe_0(fe h)
962{
963    memset(h, 0, sizeof(int32_t) * 10);
964}
965
966/* h = 1 */
967static void fe_1(fe h)
968{
969    memset(h, 0, sizeof(int32_t) * 10);
970    h[0] = 1;
971}
972
973/*
974 * h = f + g
975 *
976 * Can overlap h with f or g.
977 *
978 * Preconditions:
979 *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
980 *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
981 *
982 * Postconditions:
983 *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
984 */
985static void fe_add(fe h, const fe f, const fe g)
986{
987    unsigned i;
988
989    for (i = 0; i < 10; i++) {
990        h[i] = f[i] + g[i];
991    }
992}
993
994/*
995 * h = f - g
996 *
997 * Can overlap h with f or g.
998 *
999 * Preconditions:
1000 *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1001 *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1002 *
1003 * Postconditions:
1004 *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1005 */
1006static void fe_sub(fe h, const fe f, const fe g)
1007{
1008    unsigned i;
1009
1010    for (i = 0; i < 10; i++) {
1011        h[i] = f[i] - g[i];
1012    }
1013}
1014
1015/*
1016 * h = f * g
1017 *
1018 * Can overlap h with f or g.
1019 *
1020 * Preconditions:
1021 *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1022 *    |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1023 *
1024 * Postconditions:
1025 *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1026 *
1027 * Notes on implementation strategy:
1028 *
1029 * Using schoolbook multiplication.
1030 * Karatsuba would save a little in some cost models.
1031 *
1032 * Most multiplications by 2 and 19 are 32-bit precomputations;
1033 * cheaper than 64-bit postcomputations.
1034 *
1035 * There is one remaining multiplication by 19 in the carry chain;
1036 * one *19 precomputation can be merged into this,
1037 * but the resulting data flow is considerably less clean.
1038 *
1039 * There are 12 carries below.
1040 * 10 of them are 2-way parallelizable and vectorizable.
1041 * Can get away with 11 carries, but then data flow is much deeper.
1042 *
1043 * With tighter constraints on inputs can squeeze carries into int32.
1044 */
1045static void fe_mul(fe h, const fe f, const fe g)
1046{
1047    int32_t f0 = f[0];
1048    int32_t f1 = f[1];
1049    int32_t f2 = f[2];
1050    int32_t f3 = f[3];
1051    int32_t f4 = f[4];
1052    int32_t f5 = f[5];
1053    int32_t f6 = f[6];
1054    int32_t f7 = f[7];
1055    int32_t f8 = f[8];
1056    int32_t f9 = f[9];
1057    int32_t g0 = g[0];
1058    int32_t g1 = g[1];
1059    int32_t g2 = g[2];
1060    int32_t g3 = g[3];
1061    int32_t g4 = g[4];
1062    int32_t g5 = g[5];
1063    int32_t g6 = g[6];
1064    int32_t g7 = g[7];
1065    int32_t g8 = g[8];
1066    int32_t g9 = g[9];
1067    int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
1068    int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
1069    int32_t g3_19 = 19 * g3;
1070    int32_t g4_19 = 19 * g4;
1071    int32_t g5_19 = 19 * g5;
1072    int32_t g6_19 = 19 * g6;
1073    int32_t g7_19 = 19 * g7;
1074    int32_t g8_19 = 19 * g8;
1075    int32_t g9_19 = 19 * g9;
1076    int32_t f1_2 = 2 * f1;
1077    int32_t f3_2 = 2 * f3;
1078    int32_t f5_2 = 2 * f5;
1079    int32_t f7_2 = 2 * f7;
1080    int32_t f9_2 = 2 * f9;
1081    int64_t f0g0    = f0   * (int64_t) g0;
1082    int64_t f0g1    = f0   * (int64_t) g1;
1083    int64_t f0g2    = f0   * (int64_t) g2;
1084    int64_t f0g3    = f0   * (int64_t) g3;
1085    int64_t f0g4    = f0   * (int64_t) g4;
1086    int64_t f0g5    = f0   * (int64_t) g5;
1087    int64_t f0g6    = f0   * (int64_t) g6;
1088    int64_t f0g7    = f0   * (int64_t) g7;
1089    int64_t f0g8    = f0   * (int64_t) g8;
1090    int64_t f0g9    = f0   * (int64_t) g9;
1091    int64_t f1g0    = f1   * (int64_t) g0;
1092    int64_t f1g1_2  = f1_2 * (int64_t) g1;
1093    int64_t f1g2    = f1   * (int64_t) g2;
1094    int64_t f1g3_2  = f1_2 * (int64_t) g3;
1095    int64_t f1g4    = f1   * (int64_t) g4;
1096    int64_t f1g5_2  = f1_2 * (int64_t) g5;
1097    int64_t f1g6    = f1   * (int64_t) g6;
1098    int64_t f1g7_2  = f1_2 * (int64_t) g7;
1099    int64_t f1g8    = f1   * (int64_t) g8;
1100    int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
1101    int64_t f2g0    = f2   * (int64_t) g0;
1102    int64_t f2g1    = f2   * (int64_t) g1;
1103    int64_t f2g2    = f2   * (int64_t) g2;
1104    int64_t f2g3    = f2   * (int64_t) g3;
1105    int64_t f2g4    = f2   * (int64_t) g4;
1106    int64_t f2g5    = f2   * (int64_t) g5;
1107    int64_t f2g6    = f2   * (int64_t) g6;
1108    int64_t f2g7    = f2   * (int64_t) g7;
1109    int64_t f2g8_19 = f2   * (int64_t) g8_19;
1110    int64_t f2g9_19 = f2   * (int64_t) g9_19;
1111    int64_t f3g0    = f3   * (int64_t) g0;
1112    int64_t f3g1_2  = f3_2 * (int64_t) g1;
1113    int64_t f3g2    = f3   * (int64_t) g2;
1114    int64_t f3g3_2  = f3_2 * (int64_t) g3;
1115    int64_t f3g4    = f3   * (int64_t) g4;
1116    int64_t f3g5_2  = f3_2 * (int64_t) g5;
1117    int64_t f3g6    = f3   * (int64_t) g6;
1118    int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
1119    int64_t f3g8_19 = f3   * (int64_t) g8_19;
1120    int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
1121    int64_t f4g0    = f4   * (int64_t) g0;
1122    int64_t f4g1    = f4   * (int64_t) g1;
1123    int64_t f4g2    = f4   * (int64_t) g2;
1124    int64_t f4g3    = f4   * (int64_t) g3;
1125    int64_t f4g4    = f4   * (int64_t) g4;
1126    int64_t f4g5    = f4   * (int64_t) g5;
1127    int64_t f4g6_19 = f4   * (int64_t) g6_19;
1128    int64_t f4g7_19 = f4   * (int64_t) g7_19;
1129    int64_t f4g8_19 = f4   * (int64_t) g8_19;
1130    int64_t f4g9_19 = f4   * (int64_t) g9_19;
1131    int64_t f5g0    = f5   * (int64_t) g0;
1132    int64_t f5g1_2  = f5_2 * (int64_t) g1;
1133    int64_t f5g2    = f5   * (int64_t) g2;
1134    int64_t f5g3_2  = f5_2 * (int64_t) g3;
1135    int64_t f5g4    = f5   * (int64_t) g4;
1136    int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
1137    int64_t f5g6_19 = f5   * (int64_t) g6_19;
1138    int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
1139    int64_t f5g8_19 = f5   * (int64_t) g8_19;
1140    int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
1141    int64_t f6g0    = f6   * (int64_t) g0;
1142    int64_t f6g1    = f6   * (int64_t) g1;
1143    int64_t f6g2    = f6   * (int64_t) g2;
1144    int64_t f6g3    = f6   * (int64_t) g3;
1145    int64_t f6g4_19 = f6   * (int64_t) g4_19;
1146    int64_t f6g5_19 = f6   * (int64_t) g5_19;
1147    int64_t f6g6_19 = f6   * (int64_t) g6_19;
1148    int64_t f6g7_19 = f6   * (int64_t) g7_19;
1149    int64_t f6g8_19 = f6   * (int64_t) g8_19;
1150    int64_t f6g9_19 = f6   * (int64_t) g9_19;
1151    int64_t f7g0    = f7   * (int64_t) g0;
1152    int64_t f7g1_2  = f7_2 * (int64_t) g1;
1153    int64_t f7g2    = f7   * (int64_t) g2;
1154    int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
1155    int64_t f7g4_19 = f7   * (int64_t) g4_19;
1156    int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
1157    int64_t f7g6_19 = f7   * (int64_t) g6_19;
1158    int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
1159    int64_t f7g8_19 = f7   * (int64_t) g8_19;
1160    int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
1161    int64_t f8g0    = f8   * (int64_t) g0;
1162    int64_t f8g1    = f8   * (int64_t) g1;
1163    int64_t f8g2_19 = f8   * (int64_t) g2_19;
1164    int64_t f8g3_19 = f8   * (int64_t) g3_19;
1165    int64_t f8g4_19 = f8   * (int64_t) g4_19;
1166    int64_t f8g5_19 = f8   * (int64_t) g5_19;
1167    int64_t f8g6_19 = f8   * (int64_t) g6_19;
1168    int64_t f8g7_19 = f8   * (int64_t) g7_19;
1169    int64_t f8g8_19 = f8   * (int64_t) g8_19;
1170    int64_t f8g9_19 = f8   * (int64_t) g9_19;
1171    int64_t f9g0    = f9   * (int64_t) g0;
1172    int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
1173    int64_t f9g2_19 = f9   * (int64_t) g2_19;
1174    int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
1175    int64_t f9g4_19 = f9   * (int64_t) g4_19;
1176    int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
1177    int64_t f9g6_19 = f9   * (int64_t) g6_19;
1178    int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
1179    int64_t f9g8_19 = f9   * (int64_t) g8_19;
1180    int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
1181    int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1182    int64_t h1 = f0g1 + f1g0    + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1183    int64_t h2 = f0g2 + f1g1_2  + f2g0    + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1184    int64_t h3 = f0g3 + f1g2    + f2g1    + f3g0    + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1185    int64_t h4 = f0g4 + f1g3_2  + f2g2    + f3g1_2  + f4g0    + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1186    int64_t h5 = f0g5 + f1g4    + f2g3    + f3g2    + f4g1    + f5g0    + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1187    int64_t h6 = f0g6 + f1g5_2  + f2g4    + f3g3_2  + f4g2    + f5g1_2  + f6g0    + f7g9_38 + f8g8_19 + f9g7_38;
1188    int64_t h7 = f0g7 + f1g6    + f2g5    + f3g4    + f4g3    + f5g2    + f6g1    + f7g0    + f8g9_19 + f9g8_19;
1189    int64_t h8 = f0g8 + f1g7_2  + f2g6    + f3g5_2  + f4g4    + f5g3_2  + f6g2    + f7g1_2  + f8g0    + f9g9_38;
1190    int64_t h9 = f0g9 + f1g8    + f2g7    + f3g6    + f4g5    + f5g4    + f6g3    + f7g2    + f8g1    + f9g0   ;
1191    int64_t carry0;
1192    int64_t carry1;
1193    int64_t carry2;
1194    int64_t carry3;
1195    int64_t carry4;
1196    int64_t carry5;
1197    int64_t carry6;
1198    int64_t carry7;
1199    int64_t carry8;
1200    int64_t carry9;
1201
1202    /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
1203     *   i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1204     * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
1205     *   i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
1206
1207    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1208    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1209    /* |h0| <= 2^25 */
1210    /* |h4| <= 2^25 */
1211    /* |h1| <= 1.71*2^59 */
1212    /* |h5| <= 1.71*2^59 */
1213
1214    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1215    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1216    /* |h1| <= 2^24; from now on fits into int32 */
1217    /* |h5| <= 2^24; from now on fits into int32 */
1218    /* |h2| <= 1.41*2^60 */
1219    /* |h6| <= 1.41*2^60 */
1220
1221    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1222    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1223    /* |h2| <= 2^25; from now on fits into int32 unchanged */
1224    /* |h6| <= 2^25; from now on fits into int32 unchanged */
1225    /* |h3| <= 1.71*2^59 */
1226    /* |h7| <= 1.71*2^59 */
1227
1228    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1229    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1230    /* |h3| <= 2^24; from now on fits into int32 unchanged */
1231    /* |h7| <= 2^24; from now on fits into int32 unchanged */
1232    /* |h4| <= 1.72*2^34 */
1233    /* |h8| <= 1.41*2^60 */
1234
1235    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1236    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1237    /* |h4| <= 2^25; from now on fits into int32 unchanged */
1238    /* |h8| <= 2^25; from now on fits into int32 unchanged */
1239    /* |h5| <= 1.01*2^24 */
1240    /* |h9| <= 1.71*2^59 */
1241
1242    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1243    /* |h9| <= 2^24; from now on fits into int32 unchanged */
1244    /* |h0| <= 1.1*2^39 */
1245
1246    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1247    /* |h0| <= 2^25; from now on fits into int32 unchanged */
1248    /* |h1| <= 1.01*2^24 */
1249
1250    h[0] = (int32_t)h0;
1251    h[1] = (int32_t)h1;
1252    h[2] = (int32_t)h2;
1253    h[3] = (int32_t)h3;
1254    h[4] = (int32_t)h4;
1255    h[5] = (int32_t)h5;
1256    h[6] = (int32_t)h6;
1257    h[7] = (int32_t)h7;
1258    h[8] = (int32_t)h8;
1259    h[9] = (int32_t)h9;
1260}
1261
1262/*
1263 * h = f * f
1264 *
1265 * Can overlap h with f.
1266 *
1267 * Preconditions:
1268 *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1269 *
1270 * Postconditions:
1271 *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1272 *
1273 * See fe_mul.c for discussion of implementation strategy.
1274 */
1275static void fe_sq(fe h, const fe f)
1276{
1277    int32_t f0 = f[0];
1278    int32_t f1 = f[1];
1279    int32_t f2 = f[2];
1280    int32_t f3 = f[3];
1281    int32_t f4 = f[4];
1282    int32_t f5 = f[5];
1283    int32_t f6 = f[6];
1284    int32_t f7 = f[7];
1285    int32_t f8 = f[8];
1286    int32_t f9 = f[9];
1287    int32_t f0_2 = 2 * f0;
1288    int32_t f1_2 = 2 * f1;
1289    int32_t f2_2 = 2 * f2;
1290    int32_t f3_2 = 2 * f3;
1291    int32_t f4_2 = 2 * f4;
1292    int32_t f5_2 = 2 * f5;
1293    int32_t f6_2 = 2 * f6;
1294    int32_t f7_2 = 2 * f7;
1295    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
1296    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
1297    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
1298    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
1299    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
1300    int64_t f0f0    = f0   * (int64_t) f0;
1301    int64_t f0f1_2  = f0_2 * (int64_t) f1;
1302    int64_t f0f2_2  = f0_2 * (int64_t) f2;
1303    int64_t f0f3_2  = f0_2 * (int64_t) f3;
1304    int64_t f0f4_2  = f0_2 * (int64_t) f4;
1305    int64_t f0f5_2  = f0_2 * (int64_t) f5;
1306    int64_t f0f6_2  = f0_2 * (int64_t) f6;
1307    int64_t f0f7_2  = f0_2 * (int64_t) f7;
1308    int64_t f0f8_2  = f0_2 * (int64_t) f8;
1309    int64_t f0f9_2  = f0_2 * (int64_t) f9;
1310    int64_t f1f1_2  = f1_2 * (int64_t) f1;
1311    int64_t f1f2_2  = f1_2 * (int64_t) f2;
1312    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
1313    int64_t f1f4_2  = f1_2 * (int64_t) f4;
1314    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
1315    int64_t f1f6_2  = f1_2 * (int64_t) f6;
1316    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
1317    int64_t f1f8_2  = f1_2 * (int64_t) f8;
1318    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1319    int64_t f2f2    = f2   * (int64_t) f2;
1320    int64_t f2f3_2  = f2_2 * (int64_t) f3;
1321    int64_t f2f4_2  = f2_2 * (int64_t) f4;
1322    int64_t f2f5_2  = f2_2 * (int64_t) f5;
1323    int64_t f2f6_2  = f2_2 * (int64_t) f6;
1324    int64_t f2f7_2  = f2_2 * (int64_t) f7;
1325    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1326    int64_t f2f9_38 = f2   * (int64_t) f9_38;
1327    int64_t f3f3_2  = f3_2 * (int64_t) f3;
1328    int64_t f3f4_2  = f3_2 * (int64_t) f4;
1329    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
1330    int64_t f3f6_2  = f3_2 * (int64_t) f6;
1331    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1332    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1333    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1334    int64_t f4f4    = f4   * (int64_t) f4;
1335    int64_t f4f5_2  = f4_2 * (int64_t) f5;
1336    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1337    int64_t f4f7_38 = f4   * (int64_t) f7_38;
1338    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1339    int64_t f4f9_38 = f4   * (int64_t) f9_38;
1340    int64_t f5f5_38 = f5   * (int64_t) f5_38;
1341    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1342    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1343    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1344    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1345    int64_t f6f6_19 = f6   * (int64_t) f6_19;
1346    int64_t f6f7_38 = f6   * (int64_t) f7_38;
1347    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1348    int64_t f6f9_38 = f6   * (int64_t) f9_38;
1349    int64_t f7f7_38 = f7   * (int64_t) f7_38;
1350    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1351    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1352    int64_t f8f8_19 = f8   * (int64_t) f8_19;
1353    int64_t f8f9_38 = f8   * (int64_t) f9_38;
1354    int64_t f9f9_38 = f9   * (int64_t) f9_38;
1355    int64_t h0 = f0f0   + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1356    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1357    int64_t h2 = f0f2_2 + f1f1_2  + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1358    int64_t h3 = f0f3_2 + f1f2_2  + f4f9_38 + f5f8_38 + f6f7_38;
1359    int64_t h4 = f0f4_2 + f1f3_4  + f2f2    + f5f9_76 + f6f8_38 + f7f7_38;
1360    int64_t h5 = f0f5_2 + f1f4_2  + f2f3_2  + f6f9_38 + f7f8_38;
1361    int64_t h6 = f0f6_2 + f1f5_4  + f2f4_2  + f3f3_2  + f7f9_76 + f8f8_19;
1362    int64_t h7 = f0f7_2 + f1f6_2  + f2f5_2  + f3f4_2  + f8f9_38;
1363    int64_t h8 = f0f8_2 + f1f7_4  + f2f6_2  + f3f5_4  + f4f4    + f9f9_38;
1364    int64_t h9 = f0f9_2 + f1f8_2  + f2f7_2  + f3f6_2  + f4f5_2;
1365    int64_t carry0;
1366    int64_t carry1;
1367    int64_t carry2;
1368    int64_t carry3;
1369    int64_t carry4;
1370    int64_t carry5;
1371    int64_t carry6;
1372    int64_t carry7;
1373    int64_t carry8;
1374    int64_t carry9;
1375
1376    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1377    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1378
1379    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1380    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1381
1382    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1383    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1384
1385    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1386    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1387
1388    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1389    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1390
1391    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1392
1393    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1394
1395    h[0] = (int32_t)h0;
1396    h[1] = (int32_t)h1;
1397    h[2] = (int32_t)h2;
1398    h[3] = (int32_t)h3;
1399    h[4] = (int32_t)h4;
1400    h[5] = (int32_t)h5;
1401    h[6] = (int32_t)h6;
1402    h[7] = (int32_t)h7;
1403    h[8] = (int32_t)h8;
1404    h[9] = (int32_t)h9;
1405}
1406
1407static void fe_invert(fe out, const fe z)
1408{
1409    fe t0;
1410    fe t1;
1411    fe t2;
1412    fe t3;
1413    int i;
1414
1415    /*
1416     * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
1417     * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
1418     */
1419
1420    /* t0 = z ** 2 */
1421    fe_sq(t0, z);
1422
1423    /* t1 = t0 ** (2 ** 2) = z ** 8 */
1424    fe_sq(t1, t0);
1425    fe_sq(t1, t1);
1426
1427    /* t1 = z * t1 = z ** 9 */
1428    fe_mul(t1, z, t1);
1429    /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1430    fe_mul(t0, t0, t1);
1431
1432    /* t2 = t0 ** 2 = z ** 22 */
1433    fe_sq(t2, t0);
1434
1435    /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
1436    fe_mul(t1, t1, t2);
1437
1438    /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
1439    fe_sq(t2, t1);
1440    for (i = 1; i < 5; ++i) {
1441        fe_sq(t2, t2);
1442    }
1443
1444    /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
1445    fe_mul(t1, t2, t1);
1446
1447    /* Continuing similarly... */
1448
1449    /* t2 = z ** (2 ** 20 - 1) */
1450    fe_sq(t2, t1);
1451    for (i = 1; i < 10; ++i) {
1452        fe_sq(t2, t2);
1453    }
1454    fe_mul(t2, t2, t1);
1455
1456    /* t2 = z ** (2 ** 40 - 1) */
1457    fe_sq(t3, t2);
1458    for (i = 1; i < 20; ++i) {
1459        fe_sq(t3, t3);
1460    }
1461    fe_mul(t2, t3, t2);
1462
1463    /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
1464    for (i = 0; i < 10; ++i) {
1465        fe_sq(t2, t2);
1466    }
1467    /* t1 = z ** (2 ** 50 - 1) */
1468    fe_mul(t1, t2, t1);
1469
1470    /* t2 = z ** (2 ** 100 - 1) */
1471    fe_sq(t2, t1);
1472    for (i = 1; i < 50; ++i) {
1473        fe_sq(t2, t2);
1474    }
1475    fe_mul(t2, t2, t1);
1476
1477    /* t2 = z ** (2 ** 200 - 1) */
1478    fe_sq(t3, t2);
1479    for (i = 1; i < 100; ++i) {
1480        fe_sq(t3, t3);
1481    }
1482    fe_mul(t2, t3, t2);
1483
1484    /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
1485    fe_sq(t2, t2);
1486    for (i = 1; i < 50; ++i) {
1487        fe_sq(t2, t2);
1488    }
1489
1490    /* t1 = z ** (2 ** 250 - 1) */
1491    fe_mul(t1, t2, t1);
1492
1493    /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
1494    fe_sq(t1, t1);
1495    for (i = 1; i < 5; ++i) {
1496        fe_sq(t1, t1);
1497    }
1498
1499    /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
1500    fe_mul(out, t1, t0);
1501}
1502
1503/*
1504 * h = -f
1505 *
1506 * Preconditions:
1507 *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1508 *
1509 * Postconditions:
1510 *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1511 */
1512static void fe_neg(fe h, const fe f)
1513{
1514    unsigned i;
1515
1516    for (i = 0; i < 10; i++) {
1517        h[i] = -f[i];
1518    }
1519}
1520
1521/*
1522 * Replace (f,g) with (g,g) if b == 1;
1523 * replace (f,g) with (f,g) if b == 0.
1524 *
1525 * Preconditions: b in {0,1}.
1526 */
1527static void fe_cmov(fe f, const fe g, unsigned b)
1528{
1529    size_t i;
1530
1531    b = 0-b;
1532    for (i = 0; i < 10; i++) {
1533        int32_t x = f[i] ^ g[i];
1534        x &= b;
1535        f[i] ^= x;
1536    }
1537}
1538
1539/*
1540 * return 0 if f == 0
1541 * return 1 if f != 0
1542 *
1543 * Preconditions:
1544 *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1545 */
1546static int fe_isnonzero(const fe f)
1547{
1548    uint8_t s[32];
1549    static const uint8_t zero[32] = {0};
1550
1551    fe_tobytes(s, f);
1552
1553    return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1554}
1555
1556/*
1557 * return 1 if f is in {1,3,5,...,q-2}
1558 * return 0 if f is in {0,2,4,...,q-1}
1559 *
1560 * Preconditions:
1561 *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1562 */
1563static int fe_isnegative(const fe f)
1564{
1565    uint8_t s[32];
1566
1567    fe_tobytes(s, f);
1568    return s[0] & 1;
1569}
1570
1571/*
1572 * h = 2 * f * f
1573 *
1574 * Can overlap h with f.
1575 *
1576 * Preconditions:
1577 *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1578 *
1579 * Postconditions:
1580 *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1581 *
1582 * See fe_mul.c for discussion of implementation strategy.
1583 */
1584static void fe_sq2(fe h, const fe f)
1585{
1586    int32_t f0 = f[0];
1587    int32_t f1 = f[1];
1588    int32_t f2 = f[2];
1589    int32_t f3 = f[3];
1590    int32_t f4 = f[4];
1591    int32_t f5 = f[5];
1592    int32_t f6 = f[6];
1593    int32_t f7 = f[7];
1594    int32_t f8 = f[8];
1595    int32_t f9 = f[9];
1596    int32_t f0_2 = 2 * f0;
1597    int32_t f1_2 = 2 * f1;
1598    int32_t f2_2 = 2 * f2;
1599    int32_t f3_2 = 2 * f3;
1600    int32_t f4_2 = 2 * f4;
1601    int32_t f5_2 = 2 * f5;
1602    int32_t f6_2 = 2 * f6;
1603    int32_t f7_2 = 2 * f7;
1604    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
1605    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
1606    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
1607    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
1608    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
1609    int64_t f0f0    = f0   * (int64_t) f0;
1610    int64_t f0f1_2  = f0_2 * (int64_t) f1;
1611    int64_t f0f2_2  = f0_2 * (int64_t) f2;
1612    int64_t f0f3_2  = f0_2 * (int64_t) f3;
1613    int64_t f0f4_2  = f0_2 * (int64_t) f4;
1614    int64_t f0f5_2  = f0_2 * (int64_t) f5;
1615    int64_t f0f6_2  = f0_2 * (int64_t) f6;
1616    int64_t f0f7_2  = f0_2 * (int64_t) f7;
1617    int64_t f0f8_2  = f0_2 * (int64_t) f8;
1618    int64_t f0f9_2  = f0_2 * (int64_t) f9;
1619    int64_t f1f1_2  = f1_2 * (int64_t) f1;
1620    int64_t f1f2_2  = f1_2 * (int64_t) f2;
1621    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
1622    int64_t f1f4_2  = f1_2 * (int64_t) f4;
1623    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
1624    int64_t f1f6_2  = f1_2 * (int64_t) f6;
1625    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
1626    int64_t f1f8_2  = f1_2 * (int64_t) f8;
1627    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1628    int64_t f2f2    = f2   * (int64_t) f2;
1629    int64_t f2f3_2  = f2_2 * (int64_t) f3;
1630    int64_t f2f4_2  = f2_2 * (int64_t) f4;
1631    int64_t f2f5_2  = f2_2 * (int64_t) f5;
1632    int64_t f2f6_2  = f2_2 * (int64_t) f6;
1633    int64_t f2f7_2  = f2_2 * (int64_t) f7;
1634    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1635    int64_t f2f9_38 = f2   * (int64_t) f9_38;
1636    int64_t f3f3_2  = f3_2 * (int64_t) f3;
1637    int64_t f3f4_2  = f3_2 * (int64_t) f4;
1638    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
1639    int64_t f3f6_2  = f3_2 * (int64_t) f6;
1640    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1641    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1642    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1643    int64_t f4f4    = f4   * (int64_t) f4;
1644    int64_t f4f5_2  = f4_2 * (int64_t) f5;
1645    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1646    int64_t f4f7_38 = f4   * (int64_t) f7_38;
1647    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1648    int64_t f4f9_38 = f4   * (int64_t) f9_38;
1649    int64_t f5f5_38 = f5   * (int64_t) f5_38;
1650    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1651    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1652    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1653    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1654    int64_t f6f6_19 = f6   * (int64_t) f6_19;
1655    int64_t f6f7_38 = f6   * (int64_t) f7_38;
1656    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1657    int64_t f6f9_38 = f6   * (int64_t) f9_38;
1658    int64_t f7f7_38 = f7   * (int64_t) f7_38;
1659    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1660    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1661    int64_t f8f8_19 = f8   * (int64_t) f8_19;
1662    int64_t f8f9_38 = f8   * (int64_t) f9_38;
1663    int64_t f9f9_38 = f9   * (int64_t) f9_38;
1664    int64_t h0 = f0f0   + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1665    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1666    int64_t h2 = f0f2_2 + f1f1_2  + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1667    int64_t h3 = f0f3_2 + f1f2_2  + f4f9_38 + f5f8_38 + f6f7_38;
1668    int64_t h4 = f0f4_2 + f1f3_4  + f2f2    + f5f9_76 + f6f8_38 + f7f7_38;
1669    int64_t h5 = f0f5_2 + f1f4_2  + f2f3_2  + f6f9_38 + f7f8_38;
1670    int64_t h6 = f0f6_2 + f1f5_4  + f2f4_2  + f3f3_2  + f7f9_76 + f8f8_19;
1671    int64_t h7 = f0f7_2 + f1f6_2  + f2f5_2  + f3f4_2  + f8f9_38;
1672    int64_t h8 = f0f8_2 + f1f7_4  + f2f6_2  + f3f5_4  + f4f4    + f9f9_38;
1673    int64_t h9 = f0f9_2 + f1f8_2  + f2f7_2  + f3f6_2  + f4f5_2;
1674    int64_t carry0;
1675    int64_t carry1;
1676    int64_t carry2;
1677    int64_t carry3;
1678    int64_t carry4;
1679    int64_t carry5;
1680    int64_t carry6;
1681    int64_t carry7;
1682    int64_t carry8;
1683    int64_t carry9;
1684
1685    h0 += h0;
1686    h1 += h1;
1687    h2 += h2;
1688    h3 += h3;
1689    h4 += h4;
1690    h5 += h5;
1691    h6 += h6;
1692    h7 += h7;
1693    h8 += h8;
1694    h9 += h9;
1695
1696    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1697    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1698
1699    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1700    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1701
1702    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1703    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1704
1705    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1706    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1707
1708    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1709    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1710
1711    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1712
1713    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1714
1715    h[0] = (int32_t)h0;
1716    h[1] = (int32_t)h1;
1717    h[2] = (int32_t)h2;
1718    h[3] = (int32_t)h3;
1719    h[4] = (int32_t)h4;
1720    h[5] = (int32_t)h5;
1721    h[6] = (int32_t)h6;
1722    h[7] = (int32_t)h7;
1723    h[8] = (int32_t)h8;
1724    h[9] = (int32_t)h9;
1725}
1726
1727static void fe_pow22523(fe out, const fe z)
1728{
1729    fe t0;
1730    fe t1;
1731    fe t2;
1732    int i;
1733
1734    fe_sq(t0, z);
1735    fe_sq(t1, t0);
1736    for (i = 1; i < 2; ++i) {
1737        fe_sq(t1, t1);
1738    }
1739    fe_mul(t1, z, t1);
1740    fe_mul(t0, t0, t1);
1741    fe_sq(t0, t0);
1742    fe_mul(t0, t1, t0);
1743    fe_sq(t1, t0);
1744    for (i = 1; i < 5; ++i) {
1745        fe_sq(t1, t1);
1746    }
1747    fe_mul(t0, t1, t0);
1748    fe_sq(t1, t0);
1749    for (i = 1; i < 10; ++i) {
1750        fe_sq(t1, t1);
1751    }
1752    fe_mul(t1, t1, t0);
1753    fe_sq(t2, t1);
1754    for (i = 1; i < 20; ++i) {
1755        fe_sq(t2, t2);
1756    }
1757    fe_mul(t1, t2, t1);
1758    fe_sq(t1, t1);
1759    for (i = 1; i < 10; ++i) {
1760        fe_sq(t1, t1);
1761    }
1762    fe_mul(t0, t1, t0);
1763    fe_sq(t1, t0);
1764    for (i = 1; i < 50; ++i) {
1765        fe_sq(t1, t1);
1766    }
1767    fe_mul(t1, t1, t0);
1768    fe_sq(t2, t1);
1769    for (i = 1; i < 100; ++i) {
1770        fe_sq(t2, t2);
1771    }
1772    fe_mul(t1, t2, t1);
1773    fe_sq(t1, t1);
1774    for (i = 1; i < 50; ++i) {
1775        fe_sq(t1, t1);
1776    }
1777    fe_mul(t0, t1, t0);
1778    fe_sq(t0, t0);
1779    for (i = 1; i < 2; ++i) {
1780        fe_sq(t0, t0);
1781    }
1782    fe_mul(out, t0, z);
1783}
1784
1785/*
1786 * ge means group element.
1787 *
1788 * Here the group is the set of pairs (x,y) of field elements (see fe.h)
1789 * satisfying -x^2 + y^2 = 1 + d x^2y^2
1790 * where d = -121665/121666.
1791 *
1792 * Representations:
1793 *   ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1794 *   ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1795 *   ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1796 *   ge_precomp (Duif): (y+x,y-x,2dxy)
1797 */
1798typedef struct {
1799    fe X;
1800    fe Y;
1801    fe Z;
1802} ge_p2;
1803
1804typedef struct {
1805    fe X;
1806    fe Y;
1807    fe Z;
1808    fe T;
1809} ge_p3;
1810
1811typedef struct {
1812    fe X;
1813    fe Y;
1814    fe Z;
1815    fe T;
1816} ge_p1p1;
1817
1818typedef struct {
1819    fe yplusx;
1820    fe yminusx;
1821    fe xy2d;
1822} ge_precomp;
1823
1824typedef struct {
1825    fe YplusX;
1826    fe YminusX;
1827    fe Z;
1828    fe T2d;
1829} ge_cached;
1830
1831static void ge_tobytes(uint8_t *s, const ge_p2 *h)
1832{
1833    fe recip;
1834    fe x;
1835    fe y;
1836
1837    fe_invert(recip, h->Z);
1838    fe_mul(x, h->X, recip);
1839    fe_mul(y, h->Y, recip);
1840    fe_tobytes(s, y);
1841    s[31] ^= fe_isnegative(x) << 7;
1842}
1843
1844static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h)
1845{
1846    fe recip;
1847    fe x;
1848    fe y;
1849
1850    fe_invert(recip, h->Z);
1851    fe_mul(x, h->X, recip);
1852    fe_mul(y, h->Y, recip);
1853    fe_tobytes(s, y);
1854    s[31] ^= fe_isnegative(x) << 7;
1855}
1856
1857static const fe d = {
1858    -10913610, 13857413, -15372611, 6949391,   114729,
1859    -8787816,  -6275908, -3247719,  -18696448, -12055116
1860};
1861
1862static const fe sqrtm1 = {
1863    -32595792, -7943725,  9377950,  3500415, 12389472,
1864    -272473,   -25146209, -2005654, 326686,  11406482
1865};
1866
1867static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s)
1868{
1869    fe u;
1870    fe v;
1871    fe v3;
1872    fe vxx;
1873    fe check;
1874
1875    fe_frombytes(h->Y, s);
1876    fe_1(h->Z);
1877    fe_sq(u, h->Y);
1878    fe_mul(v, u, d);
1879    fe_sub(u, u, h->Z); /* u = y^2-1 */
1880    fe_add(v, v, h->Z); /* v = dy^2+1 */
1881
1882    fe_sq(v3, v);
1883    fe_mul(v3, v3, v); /* v3 = v^3 */
1884    fe_sq(h->X, v3);
1885    fe_mul(h->X, h->X, v);
1886    fe_mul(h->X, h->X, u); /* x = uv^7 */
1887
1888    fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
1889    fe_mul(h->X, h->X, v3);
1890    fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
1891
1892    fe_sq(vxx, h->X);
1893    fe_mul(vxx, vxx, v);
1894    fe_sub(check, vxx, u); /* vx^2-u */
1895    if (fe_isnonzero(check)) {
1896        fe_add(check, vxx, u); /* vx^2+u */
1897        if (fe_isnonzero(check)) {
1898            return -1;
1899        }
1900        fe_mul(h->X, h->X, sqrtm1);
1901    }
1902
1903    if (fe_isnegative(h->X) != (s[31] >> 7)) {
1904        fe_neg(h->X, h->X);
1905    }
1906
1907    fe_mul(h->T, h->X, h->Y);
1908    return 0;
1909}
1910
1911static void ge_p2_0(ge_p2 *h)
1912{
1913    fe_0(h->X);
1914    fe_1(h->Y);
1915    fe_1(h->Z);
1916}
1917
1918static void ge_p3_0(ge_p3 *h)
1919{
1920    fe_0(h->X);
1921    fe_1(h->Y);
1922    fe_1(h->Z);
1923    fe_0(h->T);
1924}
1925
1926static void ge_precomp_0(ge_precomp *h)
1927{
1928    fe_1(h->yplusx);
1929    fe_1(h->yminusx);
1930    fe_0(h->xy2d);
1931}
1932
1933/* r = p */
1934static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p)
1935{
1936    fe_copy(r->X, p->X);
1937    fe_copy(r->Y, p->Y);
1938    fe_copy(r->Z, p->Z);
1939}
1940
1941static const fe d2 = {
1942    -21827239, -5839606,  -30745221, 13898782, 229458,
1943    15978800,  -12551817, -6495438,  29715968, 9444199
1944};
1945
1946/* r = p */
1947static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p)
1948{
1949    fe_add(r->YplusX, p->Y, p->X);
1950    fe_sub(r->YminusX, p->Y, p->X);
1951    fe_copy(r->Z, p->Z);
1952    fe_mul(r->T2d, p->T, d2);
1953}
1954
1955/* r = p */
1956static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p)
1957{
1958    fe_mul(r->X, p->X, p->T);
1959    fe_mul(r->Y, p->Y, p->Z);
1960    fe_mul(r->Z, p->Z, p->T);
1961}
1962
1963/* r = p */
1964static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p)
1965{
1966    fe_mul(r->X, p->X, p->T);
1967    fe_mul(r->Y, p->Y, p->Z);
1968    fe_mul(r->Z, p->Z, p->T);
1969    fe_mul(r->T, p->X, p->Y);
1970}
1971
1972/* r = 2 * p */
1973static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p)
1974{
1975    fe t0;
1976
1977    fe_sq(r->X, p->X);
1978    fe_sq(r->Z, p->Y);
1979    fe_sq2(r->T, p->Z);
1980    fe_add(r->Y, p->X, p->Y);
1981    fe_sq(t0, r->Y);
1982    fe_add(r->Y, r->Z, r->X);
1983    fe_sub(r->Z, r->Z, r->X);
1984    fe_sub(r->X, t0, r->Y);
1985    fe_sub(r->T, r->T, r->Z);
1986}
1987
1988/* r = 2 * p */
1989static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p)
1990{
1991    ge_p2 q;
1992    ge_p3_to_p2(&q, p);
1993    ge_p2_dbl(r, &q);
1994}
1995
1996/* r = p + q */
1997static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
1998{
1999    fe t0;
2000
2001    fe_add(r->X, p->Y, p->X);
2002    fe_sub(r->Y, p->Y, p->X);
2003    fe_mul(r->Z, r->X, q->yplusx);
2004    fe_mul(r->Y, r->Y, q->yminusx);
2005    fe_mul(r->T, q->xy2d, p->T);
2006    fe_add(t0, p->Z, p->Z);
2007    fe_sub(r->X, r->Z, r->Y);
2008    fe_add(r->Y, r->Z, r->Y);
2009    fe_add(r->Z, t0, r->T);
2010    fe_sub(r->T, t0, r->T);
2011}
2012
2013/* r = p - q */
2014static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
2015{
2016    fe t0;
2017
2018    fe_add(r->X, p->Y, p->X);
2019    fe_sub(r->Y, p->Y, p->X);
2020    fe_mul(r->Z, r->X, q->yminusx);
2021    fe_mul(r->Y, r->Y, q->yplusx);
2022    fe_mul(r->T, q->xy2d, p->T);
2023    fe_add(t0, p->Z, p->Z);
2024    fe_sub(r->X, r->Z, r->Y);
2025    fe_add(r->Y, r->Z, r->Y);
2026    fe_sub(r->Z, t0, r->T);
2027    fe_add(r->T, t0, r->T);
2028}
2029
2030/* r = p + q */
2031static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
2032{
2033    fe t0;
2034
2035    fe_add(r->X, p->Y, p->X);
2036    fe_sub(r->Y, p->Y, p->X);
2037    fe_mul(r->Z, r->X, q->YplusX);
2038    fe_mul(r->Y, r->Y, q->YminusX);
2039    fe_mul(r->T, q->T2d, p->T);
2040    fe_mul(r->X, p->Z, q->Z);
2041    fe_add(t0, r->X, r->X);
2042    fe_sub(r->X, r->Z, r->Y);
2043    fe_add(r->Y, r->Z, r->Y);
2044    fe_add(r->Z, t0, r->T);
2045    fe_sub(r->T, t0, r->T);
2046}
2047
2048/* r = p - q */
2049static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
2050{
2051    fe t0;
2052
2053    fe_add(r->X, p->Y, p->X);
2054    fe_sub(r->Y, p->Y, p->X);
2055    fe_mul(r->Z, r->X, q->YminusX);
2056    fe_mul(r->Y, r->Y, q->YplusX);
2057    fe_mul(r->T, q->T2d, p->T);
2058    fe_mul(r->X, p->Z, q->Z);
2059    fe_add(t0, r->X, r->X);
2060    fe_sub(r->X, r->Z, r->Y);
2061    fe_add(r->Y, r->Z, r->Y);
2062    fe_sub(r->Z, t0, r->T);
2063    fe_add(r->T, t0, r->T);
2064}
2065
2066static uint8_t equal(signed char b, signed char c)
2067{
2068    uint8_t ub = b;
2069    uint8_t uc = c;
2070    uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2071    uint32_t y = x;      /* 0: yes; 1..255: no */
2072    y -= 1;              /* 4294967295: yes; 0..254: no */
2073    y >>= 31;            /* 1: yes; 0: no */
2074    return y;
2075}
2076
2077static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b)
2078{
2079    fe_cmov(t->yplusx, u->yplusx, b);
2080    fe_cmov(t->yminusx, u->yminusx, b);
2081    fe_cmov(t->xy2d, u->xy2d, b);
2082}
2083
2084/* k25519Precomp[i][j] = (j+1)*256^i*B */
2085static const ge_precomp k25519Precomp[32][8] = {
2086    {
2087        {
2088            {25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2089             27544626, -11754271, -6079156, 2047605},
2090            {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2091             5043384, 19500929, -15469378},
2092            {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2093             29287919, 11864899, -24514362, -4438546},
2094        },
2095        {
2096            {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2097             -11717903, -3814571, -358445, -10211303},
2098            {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2099             -15616551, 11189268, -26829678, -5319081},
2100            {26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2101             -3128826, -9541118, -15472047, -4166697},
2102        },
2103        {
2104            {15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2105             27787600, -14772189, 28944400, -1550024},
2106            {16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2107             16354577, -11775962, 7689662, 11199574},
2108            {30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2109             7512774, 10017326, -17749093, -9920357},
2110        },
2111        {
2112            {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2113             -28926210, 15006023, 3284568, -6276540},
2114            {23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2115             7464579, 9656445, 13059162, 10374397},
2116            {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2117             -3839045, -641708, -101325},
2118        },
2119        {
2120            {10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2121             32867885, 14515107, -15438304, 10819380},
2122            {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2123             12483688, -12668491, 5581306},
2124            {19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2125             28542350, 13850243, -23678021, -15815942},
2126        },
2127        {
2128            {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2129             -19188627, -15224819, -9818940, -12085777},
2130            {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2131             -15689887, 1762328, 14866737},
2132            {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2133             -28236412, 3959421, 27914454, 4383652},
2134        },
2135        {
2136            {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2137             5230134, -23952439, -15175766},
2138            {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2139             20654025, 16520125, 30598449, 7715701},
2140            {28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2141             -31400660, 1370708, 29794553, -1409300},
2142        },
2143        {
2144            {14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2145             30290735, 10876454, -33154098, 2381726},
2146            {-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2147             -6236617, 3696005, -32300832, 15351955},
2148            {27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2149             -32961401, -2970515, 29551813, 10109425},
2150        },
2151    },
2152    {
2153        {
2154            {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2155             -2378284, -1627556, 10092783, -4764171},
2156            {27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2157             -32508754, 12005538, -17810127, 12803510},
2158            {17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2159             30364213, -9038194, 18016357, 4397660},
2160        },
2161        {
2162            {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2163             -26619106, 14544525, -17477504, 982639},
2164            {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2165             -4120128, -21047696, 9934963},
2166            {5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2167             -14747930, 4559895, -30123922, -10897950},
2168        },
2169        {
2170            {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2171             24191034, 4541697, -13338309, 5500568},
2172            {12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2173             -17430592, 12264343, 10874051, 13524335},
2174            {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2175             5080568, -22528059, 5376628},
2176        },
2177        {
2178            {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2179             -22321305, -9447443, 4535768, 1569007},
2180            {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2181             -30494562, 3044290, 31848280, 12543772},
2182            {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2183             -27377195, -2062731, 7718482, 14474653},
2184        },
2185        {
2186            {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2187             -7236665, 24316168, -5253567},
2188            {13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2189             33040651, -13424532, -20729456, 8321686},
2190            {21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
2191             23845965, -11874838, -9984458, 608372},
2192        },
2193        {
2194            {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
2195             1123968, -6780577, 27229399, 23887},
2196            {-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
2197             12797024, -6440308, -1633405, 16678954},
2198            {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
2199             -1508144, -4795045, -17169265, 4904953},
2200        },
2201        {
2202            {24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
2203             5169211, 16191880, 2128236, -4326833},
2204            {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
2205             -29806336, 916033, -6882542, -2986532},
2206            {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
2207             285431, 2763829, 15736322, 4143876},
2208        },
2209        {
2210            {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
2211             -14594663, 23527084, -16458268},
2212            {33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
2213             -32625340, 4087881, -15188911, -14416214},
2214            {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
2215             4357868, -4774191, -16323038},
2216        },
2217    },
2218    {
2219        {
2220            {6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
2221             23365147, -3949732, 7390890, 2759800},
2222            {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
2223             -4264057, 1244380, -12919645},
2224            {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
2225             9208236, 15886429, 16489664},
2226        },
2227        {
2228            {1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
2229             -13693198, 398369, -30606455, -712933},
2230            {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
2231             13348553, 12076947, -30836462, 5113182},
2232            {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
2233             -30341101, -7336386, 13847711, 5387222},
2234        },
2235        {
2236            {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
2237             8763061, 3617786, -19600662, 10370991},
2238            {20246567, -14369378, 22358229, -543712, 18507283, -10413996,
2239             14554437, -8746092, 32232924, 16763880},
2240            {9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
2241             11094161, 15689506, 3140038, -16510092},
2242        },
2243        {
2244            {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
2245             -27224800, 9448613, -28774454, 366295},
2246            {19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
2247             28344573, 8041113, 719605, 11671788},
2248            {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
2249             -15266516, 27000813, -10195553},
2250        },
2251        {
2252            {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
2253             5336097, 6750977, -14521026},
2254            {11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
2255             1695823, -8819122, 8169720, 16220347},
2256            {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
2257             -11144307, -2627664, -5990708, -14166033},
2258        },
2259        {
2260            {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
2261             27884329, 2847284, 2655861, 1738395},
2262            {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
2263             21651608, -3239336, -19087449, -11005278},
2264            {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
2265             5821408, 10478196, 8544890},
2266        },
2267        {
2268            {32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
2269             19270449, 12217473, 17789017, -3395995},
2270            {-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
2271             15479401, -3853233, 30460520, 1052596},
2272            {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
2273             27491595, -4612359, 3179268, -9478891},
2274        },
2275        {
2276            {31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
2277             -14756777, -16411740, 19072640, -9511060},
2278            {11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
2279             5977896, -5215017, 473099, 5040608},
2280            {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
2281             28326862, 1721092, -19558642, -3131606},
2282        },
2283    },
2284    {
2285        {
2286            {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
2287             8076149, -27868496, 11538389},
2288            {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
2289             8754525, 7446702, -5676054, 5797016},
2290            {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
2291             2014099, -9050574, -2369172, -5877341},
2292        },
2293        {
2294            {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
2295             1192730, -3714199, 15123619, 10811505},
2296            {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
2297             15776356, -28886779, -11974553},
2298            {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
2299             -20654173, -16484855, 4714547, -9600655},
2300        },
2301        {
2302            {15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
2303             24611599, -4543832, -11745876, 12340220},
2304            {12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
2305             9613953, 8241152, 15370987, 9608631},
2306            {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
2307             15866074, -28210621, -8814099},
2308        },
2309        {
2310            {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
2311             858697, 20571223, 8420556},
2312            {14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
2313             33531827, 12516406, -21574435, -12476749},
2314            {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
2315             7256740, 8791136, 15069930},
2316        },
2317        {
2318            {1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
2319             14711875, 4874229, -30663140, -2331391},
2320            {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
2321             -7912378, -33069337, 9234253},
2322            {20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
2323             31559055, -11609587, 18979186, 13396066},
2324        },
2325        {
2326            {24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
2327             -18816887, 13594782, 33514650, 7021958},
2328            {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
2329             -25948728, -3916677, -21480480, 12868082},
2330            {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208,
2331             -21446107, 2244500, -12455797, -8089383},
2332        },
2333        {
2334            {-30595528, 13793479, -5852820, 319136, -25723172, -6263899,
2335             33086546, 8957937, -15233648, 5540521},
2336            {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908,
2337             -23710744, -1568984, -16128528, -14962807},
2338            {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819,
2339             892185, -11513277, -15205948},
2340        },
2341        {
2342            {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819,
2343             4763127, -19179614, 5867134},
2344            {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500,
2345             27846559, 5931263, -29749703, -16108455},
2346            {27461885, -2977536, 22380810, 1815854, -23033753, -3031938,
2347             7283490, -15148073, -19526700, 7734629},
2348        },
2349    },
2350    {
2351        {
2352            {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885,
2353             7585295, -3176626, 18549497, 15302069},
2354            {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381,
2355             10458790, -6418461, -8872242, 8424746},
2356            {24687205, 8613276, -30667046, -3233545, 1863892, -1830544,
2357             19206234, 7134917, -11284482, -828919},
2358        },
2359        {
2360            {11334899, -9218022, 8025293, 12707519, 17523892, -10476071,
2361             10243738, -14685461, -5066034, 16498837},
2362            {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
2363             -14124238, 6536641, 10543906},
2364            {-28946384, 15479763, -17466835, 568876, -1497683, 11223454,
2365             -2669190, -16625574, -27235709, 8876771},
2366        },
2367        {
2368            {-25742899, -12566864, -15649966, -846607, -33026686, -796288,
2369             -33481822, 15824474, -604426, -9039817},
2370            {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697,
2371             -4890037, 1657394, 3084098},
2372            {10477963, -7470260, 12119566, -13250805, 29016247, -5365589,
2373             31280319, 14396151, -30233575, 15272409},
2374        },
2375        {
2376            {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466,
2377             -25173957, -12636138, -25014757, 1950504},
2378            {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630,
2379             -8384306, -8767532, 15341279, 8373727},
2380            {28685821, 7759505, -14378516, -12002860, -31971820, 4079242,
2381             298136, -10232602, -2878207, 15190420},
2382        },
2383        {
2384            {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928,
2385             8669718, 2742393, -26033313, -6875003},
2386            {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854,
2387             9291594, -16247779, -12154742, 6048605},
2388            {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163,
2389             13934231, 5128323, 11213262, 9168384},
2390        },
2391        {
2392            {-26280513, 11007847, 19408960, -940758, -18592965, -4328580,
2393             -5088060, -11105150, 20470157, -16398701},
2394            {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560,
2395             -22783952, 14461608, 14042978, 5230683},
2396            {29969567, -2741594, -16711867, -8552442, 9175486, -2468974,
2397             21556951, 3506042, -5933891, -12449708},
2398        },
2399        {
2400            {-3144746, 8744661, 19704003, 4581278, -20430686, 6830683,
2401             -21284170, 8971513, -28539189, 15326563},
2402            {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669,
2403             -15523050, 15300988, -20514118, 9168260},
2404            {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939,
2405             -28948358, 9601605, 33087103, -9011387},
2406        },
2407        {
2408            {-19443170, -15512900, -20797467, -12445323, -29824447, 10229461,
2409             -27444329, -15000531, -5996870, 15664672},
2410            {23294591, -16632613, -22650781, -8470978, 27844204, 11461195,
2411             13099750, -2460356, 18151676, 13417686},
2412            {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065,
2413             1661597, -12551441, 15271676, -15452665},
2414        },
2415    },
2416    {
2417        {
2418            {11433042, -13228665, 8239631, -5279517, -1985436, -725718,
2419             -18698764, 2167544, -6921301, -13440182},
2420            {-31436171, 15575146, 30436815, 12192228, -22463353, 9395379,
2421             -9917708, -8638997, 12215110, 12028277},
2422            {14098400, 6555944, 23007258, 5757252, -15427832, -12950502,
2423             30123440, 4617780, -16900089, -655628},
2424        },
2425        {
2426            {-4026201, -15240835, 11893168, 13718664, -14809462, 1847385,
2427             -15819999, 10154009, 23973261, -12684474},
2428            {-26531820, -3695990, -1908898, 2534301, -31870557, -16550355,
2429             18341390, -11419951, 32013174, -10103539},
2430            {-25479301, 10876443, -11771086, -14625140, -12369567, 1838104,
2431             21911214, 6354752, 4425632, -837822},
2432        },
2433        {
2434            {-10433389, -14612966, 22229858, -3091047, -13191166, 776729,
2435             -17415375, -12020462, 4725005, 14044970},
2436            {19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390,
2437             -1411784, -19522291, -16109756},
2438            {-24864089, 12986008, -10898878, -5558584, -11312371, -148526,
2439             19541418, 8180106, 9282262, 10282508},
2440        },
2441        {
2442            {-26205082, 4428547, -8661196, -13194263, 4098402, -14165257,
2443             15522535, 8372215, 5542595, -10702683},
2444            {-10562541, 14895633, 26814552, -16673850, -17480754, -2489360,
2445             -2781891, 6993761, -18093885, 10114655},
2446            {-20107055, -929418, 31422704, 10427861, -7110749, 6150669,
2447             -29091755, -11529146, 25953725, -106158},
2448        },
2449        {
2450            {-4234397, -8039292, -9119125, 3046000, 2101609, -12607294,
2451             19390020, 6094296, -3315279, 12831125},
2452            {-15998678, 7578152, 5310217, 14408357, -33548620, -224739,
2453             31575954, 6326196, 7381791, -2421839},
2454            {-20902779, 3296811, 24736065, -16328389, 18374254, 7318640,
2455             6295303, 8082724, -15362489, 12339664},
2456        },
2457        {
2458            {27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414,
2459             15768922, 25091167, 14856294},
2460            {-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300,
2461             -12695493, -22182473, -9012899},
2462            {-11423429, -5421590, 11632845, 3405020, 30536730, -11674039,
2463             -27260765, 13866390, 30146206, 9142070},
2464        },
2465        {
2466            {3924129, -15307516, -13817122, -10054960, 12291820, -668366,
2467             -27702774, 9326384, -8237858, 4171294},
2468            {-15921940, 16037937, 6713787, 16606682, -21612135, 2790944,
2469             26396185, 3731949, 345228, -5462949},
2470            {-21327538, 13448259, 25284571, 1143661, 20614966, -8849387,
2471             2031539, -12391231, -16253183, -13582083},
2472        },
2473        {
2474            {31016211, -16722429, 26371392, -14451233, -5027349, 14854137,
2475             17477601, 3842657, 28012650, -16405420},
2476            {-5075835, 9368966, -8562079, -4600902, -15249953, 6970560,
2477             -9189873, 16292057, -8867157, 3507940},
2478            {29439664, 3537914, 23333589, 6997794, -17555561, -11018068,
2479             -15209202, -15051267, -9164929, 6580396},
2480        },
2481    },
2482    {
2483        {
2484            {-12185861, -7679788, 16438269, 10826160, -8696817, -6235611,
2485             17860444, -9273846, -2095802, 9304567},
2486            {20714564, -4336911, 29088195, 7406487, 11426967, -5095705,
2487             14792667, -14608617, 5289421, -477127},
2488            {-16665533, -10650790, -6160345, -13305760, 9192020, -1802462,
2489             17271490, 12349094, 26939669, -3752294},
2490        },
2491        {
2492            {-12889898, 9373458, 31595848, 16374215, 21471720, 13221525,
2493             -27283495, -12348559, -3698806, 117887},
2494            {22263325, -6560050, 3984570, -11174646, -15114008, -566785,
2495             28311253, 5358056, -23319780, 541964},
2496            {16259219, 3261970, 2309254, -15534474, -16885711, -4581916,
2497             24134070, -16705829, -13337066, -13552195},
2498        },
2499        {
2500            {9378160, -13140186, -22845982, -12745264, 28198281, -7244098,
2501             -2399684, -717351, 690426, 14876244},
2502            {24977353, -314384, -8223969, -13465086, 28432343, -1176353,
2503             -13068804, -12297348, -22380984, 6618999},
2504            {-1538174, 11685646, 12944378, 13682314, -24389511, -14413193,
2505             8044829, -13817328, 32239829, -5652762},
2506        },
2507        {
2508            {-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647,
2509             -10350059, 32779359, 5095274},
2510            {-33008130, -5214506, -32264887, -3685216, 9460461, -9327423,
2511             -24601656, 14506724, 21639561, -2630236},
2512            {-16400943, -13112215, 25239338, 15531969, 3987758, -4499318,
2513             -1289502, -6863535, 17874574, 558605},
2514        },
2515        {
2516            {-13600129, 10240081, 9171883, 16131053, -20869254, 9599700,
2517             33499487, 5080151, 2085892, 5119761},
2518            {-22205145, -2519528, -16381601, 414691, -25019550, 2170430,
2519             30634760, -8363614, -31999993, -5759884},
2520            {-6845704, 15791202, 8550074, -1312654, 29928809, -12092256,
2521             27534430, -7192145, -22351378, 12961482},
2522        },
2523        {
2524            {-24492060, -9570771, 10368194, 11582341, -23397293, -2245287,
2525             16533930, 8206996, -30194652, -5159638},
2526            {-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630,
2527             7031275, 7589640, 8945490},
2528            {-32152748, 8917967, 6661220, -11677616, -1192060, -15793393,
2529             7251489, -11182180, 24099109, -14456170},
2530        },
2531        {
2532            {5019558, -7907470, 4244127, -14714356, -26933272, 6453165,
2533             -19118182, -13289025, -6231896, -10280736},
2534            {10853594, 10721687, 26480089, 5861829, -22995819, 1972175,
2535             -1866647, -10557898, -3363451, -6441124},
2536            {-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661,
2537             -2008168, -13866408, 7421392},
2538        },
2539        {
2540            {8139927, -6546497, 32257646, -5890546, 30375719, 1886181,
2541             -21175108, 15441252, 28826358, -4123029},
2542            {6267086, 9695052, 7709135, -16603597, -32869068, -1886135,
2543             14795160, -7840124, 13746021, -1742048},
2544            {28584902, 7787108, -6732942, -15050729, 22846041, -7571236,
2545             -3181936, -363524, 4771362, -8419958},
2546        },
2547    },
2548    {
2549        {
2550            {24949256, 6376279, -27466481, -8174608, -18646154, -9930606,
2551             33543569, -12141695, 3569627, 11342593},
2552            {26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886,
2553             4608608, 7325975, -14801071},
2554            {-11618399, -14554430, -24321212, 7655128, -1369274, 5214312,
2555             -27400540, 10258390, -17646694, -8186692},
2556        },
2557        {
2558            {11431204, 15823007, 26570245, 14329124, 18029990, 4796082,
2559             -31446179, 15580664, 9280358, -3973687},
2560            {-160783, -10326257, -22855316, -4304997, -20861367, -13621002,
2561             -32810901, -11181622, -15545091, 4387441},
2562            {-20799378, 12194512, 3937617, -5805892, -27154820, 9340370,
2563             -24513992, 8548137, 20617071, -7482001},
2564        },
2565        {
2566            {-938825, -3930586, -8714311, 16124718, 24603125, -6225393,
2567             -13775352, -11875822, 24345683, 10325460},
2568            {-19855277, -1568885, -22202708, 8714034, 14007766, 6928528,
2569             16318175, -1010689, 4766743, 3552007},
2570            {-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514,
2571             14481909, 10988822, -3994762},
2572        },
2573        {
2574            {15564307, -14311570, 3101243, 5684148, 30446780, -8051356,
2575             12677127, -6505343, -8295852, 13296005},
2576            {-9442290, 6624296, -30298964, -11913677, -4670981, -2057379,
2577             31521204, 9614054, -30000824, 12074674},
2578            {4771191, -135239, 14290749, -13089852, 27992298, 14998318,
2579             -1413936, -1556716, 29832613, -16391035},
2580        },
2581        {
2582            {7064884, -7541174, -19161962, -5067537, -18891269, -2912736,
2583             25825242, 5293297, -27122660, 13101590},
2584            {-2298563, 2439670, -7466610, 1719965, -27267541, -16328445,
2585             32512469, -5317593, -30356070, -4190957},
2586            {-30006540, 10162316, -33180176, 3981723, -16482138, -13070044,
2587             14413974, 9515896, 19568978, 9628812},
2588        },
2589        {
2590            {33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894,
2591             -6106839, -6291786, 3437740},
2592            {-18978877, 3884493, 19469877, 12726490, 15913552, 13614290,
2593             -22961733, 70104, 7463304, 4176122},
2594            {-27124001, 10659917, 11482427, -16070381, 12771467, -6635117,
2595             -32719404, -5322751, 24216882, 5944158},
2596        },
2597        {
2598            {8894125, 7450974, -2664149, -9765752, -28080517, -12389115,
2599             19345746, 14680796, 11632993, 5847885},
2600            {26942781, -2315317, 9129564, -4906607, 26024105, 11769399,
2601             -11518837, 6367194, -9727230, 4782140},
2602            {19916461, -4828410, -22910704, -11414391, 25606324, -5972441,
2603             33253853, 8220911, 6358847, -1873857},
2604        },
2605        {
2606            {801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388,
2607             -4480480, -13538503, 1387155},
2608            {19646058, 5720633, -11416706, 12814209, 11607948, 12749789,
2609             14147075, 15156355, -21866831, 11835260},
2610            {19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523,
2611             15467869, -26560550, 5052483},
2612        },
2613    },
2614    {
2615        {
2616            {-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123,
2617             -12618185, 12228557, -7003677},
2618            {32944382, 14922211, -22844894, 5188528, 21913450, -8719943,
2619             4001465, 13238564, -6114803, 8653815},
2620            {22865569, -4652735, 27603668, -12545395, 14348958, 8234005,
2621             24808405, 5719875, 28483275, 2841751},
2622        },
2623        {
2624            {-16420968, -1113305, -327719, -12107856, 21886282, -15552774,
2625             -1887966, -315658, 19932058, -12739203},
2626            {-11656086, 10087521, -8864888, -5536143, -19278573, -3055912,
2627             3999228, 13239134, -4777469, -13910208},
2628            {1382174, -11694719, 17266790, 9194690, -13324356, 9720081,
2629             20403944, 11284705, -14013818, 3093230},
2630        },
2631        {
2632            {16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424,
2633             16271225, -24049421, -6691850},
2634            {-21911077, -5927941, -4611316, -5560156, -31744103, -10785293,
2635             24123614, 15193618, -21652117, -16739389},
2636            {-9935934, -4289447, -25279823, 4372842, 2087473, 10399484,
2637             31870908, 14690798, 17361620, 11864968},
2638        },
2639        {
2640            {-11307610, 6210372, 13206574, 5806320, -29017692, -13967200,
2641             -12331205, -7486601, -25578460, -16240689},
2642            {14668462, -12270235, 26039039, 15305210, 25515617, 4542480,
2643             10453892, 6577524, 9145645, -6443880},
2644            {5974874, 3053895, -9433049, -10385191, -31865124, 3225009,
2645             -7972642, 3936128, -5652273, -3050304},
2646        },
2647        {
2648            {30625386, -4729400, -25555961, -12792866, -20484575, 7695099,
2649             17097188, -16303496, -27999779, 1803632},
2650            {-3553091, 9865099, -5228566, 4272701, -5673832, -16689700,
2651             14911344, 12196514, -21405489, 7047412},
2652            {20093277, 9920966, -11138194, -5343857, 13161587, 12044805,
2653             -32856851, 4124601, -32343828, -10257566},
2654        },
2655        {
2656            {-20788824, 14084654, -13531713, 7842147, 19119038, -13822605,
2657             4752377, -8714640, -21679658, 2288038},
2658            {-26819236, -3283715, 29965059, 3039786, -14473765, 2540457,
2659             29457502, 14625692, -24819617, 12570232},
2660            {-1063558, -11551823, 16920318, 12494842, 1278292, -5869109,
2661             -21159943, -3498680, -11974704, 4724943},
2662        },
2663        {
2664            {17960970, -11775534, -4140968, -9702530, -8876562, -1410617,
2665             -12907383, -8659932, -29576300, 1903856},
2666            {23134274, -14279132, -10681997, -1611936, 20684485, 15770816,
2667             -12989750, 3190296, 26955097, 14109738},
2668            {15308788, 5320727, -30113809, -14318877, 22902008, 7767164,
2669             29425325, -11277562, 31960942, 11934971},
2670        },
2671        {
2672            {-27395711, 8435796, 4109644, 12222639, -24627868, 14818669,
2673             20638173, 4875028, 10491392, 1379718},
2674            {-13159415, 9197841, 3875503, -8936108, -1383712, -5879801,
2675             33518459, 16176658, 21432314, 12180697},
2676            {-11787308, 11500838, 13787581, -13832590, -22430679, 10140205,
2677             1465425, 12689540, -10301319, -13872883},
2678        },
2679    },
2680    {
2681        {
2682            {5414091, -15386041, -21007664, 9643570, 12834970, 1186149,
2683             -2622916, -1342231, 26128231, 6032912},
2684            {-26337395, -13766162, 32496025, -13653919, 17847801, -12669156,
2685             3604025, 8316894, -25875034, -10437358},
2686            {3296484, 6223048, 24680646, -12246460, -23052020, 5903205,
2687             -8862297, -4639164, 12376617, 3188849},
2688        },
2689        {
2690            {29190488, -14659046, 27549113, -1183516, 3520066, -10697301,
2691             32049515, -7309113, -16109234, -9852307},
2692            {-14744486, -9309156, 735818, -598978, -20407687, -5057904,
2693             25246078, -15795669, 18640741, -960977},
2694            {-6928835, -16430795, 10361374, 5642961, 4910474, 12345252,
2695             -31638386, -494430, 10530747, 1053335},
2696        },
2697        {
2698            {-29265967, -14186805, -13538216, -12117373, -19457059, -10655384,
2699             -31462369, -2948985, 24018831, 15026644},
2700            {-22592535, -3145277, -2289276, 5953843, -13440189, 9425631,
2701             25310643, 13003497, -2314791, -15145616},
2702            {-27419985, -603321, -8043984, -1669117, -26092265, 13987819,
2703             -27297622, 187899, -23166419, -2531735},
2704        },
2705        {
2706            {-21744398, -13810475, 1844840, 5021428, -10434399, -15911473,
2707             9716667, 16266922, -5070217, 726099},
2708            {29370922, -6053998, 7334071, -15342259, 9385287, 2247707,
2709             -13661962, -4839461, 30007388, -15823341},
2710            {-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109,
2711             730663, 9835848, 4555336},
2712        },
2713        {
2714            {-23376435, 1410446, -22253753, -12899614, 30867635, 15826977,
2715             17693930, 544696, -11985298, 12422646},
2716            {31117226, -12215734, -13502838, 6561947, -9876867, -12757670,
2717             -5118685, -4096706, 29120153, 13924425},
2718            {-17400879, -14233209, 19675799, -2734756, -11006962, -5858820,
2719             -9383939, -11317700, 7240931, -237388},
2720        },
2721        {
2722            {-31361739, -11346780, -15007447, -5856218, -22453340, -12152771,
2723             1222336, 4389483, 3293637, -15551743},
2724            {-16684801, -14444245, 11038544, 11054958, -13801175, -3338533,
2725             -24319580, 7733547, 12796905, -6335822},
2726            {-8759414, -10817836, -25418864, 10783769, -30615557, -9746811,
2727             -28253339, 3647836, 3222231, -11160462},
2728        },
2729        {
2730            {18606113, 1693100, -25448386, -15170272, 4112353, 10045021,
2731             23603893, -2048234, -7550776, 2484985},
2732            {9255317, -3131197, -12156162, -1004256, 13098013, -9214866,
2733             16377220, -2102812, -19802075, -3034702},
2734            {-22729289, 7496160, -5742199, 11329249, 19991973, -3347502,
2735             -31718148, 9936966, -30097688, -10618797},
2736        },
2737        {
2738            {21878590, -5001297, 4338336, 13643897, -3036865, 13160960,
2739             19708896, 5415497, -7360503, -4109293},
2740            {27736861, 10103576, 12500508, 8502413, -3413016, -9633558,
2741             10436918, -1550276, -23659143, -8132100},
2742            {19492550, -12104365, -29681976, -852630, -3208171, 12403437,
2743             30066266, 8367329, 13243957, 8709688},
2744        },
2745    },
2746    {
2747        {
2748            {12015105, 2801261, 28198131, 10151021, 24818120, -4743133,
2749             -11194191, -5645734, 5150968, 7274186},
2750            {2831366, -12492146, 1478975, 6122054, 23825128, -12733586,
2751             31097299, 6083058, 31021603, -9793610},
2752            {-2529932, -2229646, 445613, 10720828, -13849527, -11505937,
2753             -23507731, 16354465, 15067285, -14147707},
2754        },
2755        {
2756            {7840942, 14037873, -33364863, 15934016, -728213, -3642706,
2757             21403988, 1057586, -19379462, -12403220},
2758            {915865, -16469274, 15608285, -8789130, -24357026, 6060030,
2759             -17371319, 8410997, -7220461, 16527025},
2760            {32922597, -556987, 20336074, -16184568, 10903705, -5384487,
2761             16957574, 52992, 23834301, 6588044},
2762        },
2763        {
2764            {32752030, 11232950, 3381995, -8714866, 22652988, -10744103,
2765             17159699, 16689107, -20314580, -1305992},
2766            {-4689649, 9166776, -25710296, -10847306, 11576752, 12733943,
2767             7924251, -2752281, 1976123, -7249027},
2768            {21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041,
2769             -3371252, 12331345, -8237197},
2770        },
2771        {
2772            {8651614, -4477032, -16085636, -4996994, 13002507, 2950805,
2773             29054427, -5106970, 10008136, -4667901},
2774            {31486080, 15114593, -14261250, 12951354, 14369431, -7387845,
2775             16347321, -13662089, 8684155, -10532952},
2776            {19443825, 11385320, 24468943, -9659068, -23919258, 2187569,
2777             -26263207, -6086921, 31316348, 14219878},
2778        },
2779        {
2780            {-28594490, 1193785, 32245219, 11392485, 31092169, 15722801,
2781             27146014, 6992409, 29126555, 9207390},
2782            {32382935, 1110093, 18477781, 11028262, -27411763, -7548111,
2783             -4980517, 10843782, -7957600, -14435730},
2784            {2814918, 7836403, 27519878, -7868156, -20894015, -11553689,
2785             -21494559, 8550130, 28346258, 1994730},
2786        },
2787        {
2788            {-19578299, 8085545, -14000519, -3948622, 2785838, -16231307,
2789             -19516951, 7174894, 22628102, 8115180},
2790            {-30405132, 955511, -11133838, -15078069, -32447087, -13278079,
2791             -25651578, 3317160, -9943017, 930272},
2792            {-15303681, -6833769, 28856490, 1357446, 23421993, 1057177,
2793             24091212, -1388970, -22765376, -10650715},
2794        },
2795        {
2796            {-22751231, -5303997, -12907607, -12768866, -15811511, -7797053,
2797             -14839018, -16554220, -1867018, 8398970},
2798            {-31969310, 2106403, -4736360, 1362501, 12813763, 16200670,
2799             22981545, -6291273, 18009408, -15772772},
2800            {-17220923, -9545221, -27784654, 14166835, 29815394, 7444469,
2801             29551787, -3727419, 19288549, 1325865},
2802        },
2803        {
2804            {15100157, -15835752, -23923978, -1005098, -26450192, 15509408,
2805             12376730, -3479146, 33166107, -8042750},
2806            {20909231, 13023121, -9209752, 16251778, -5778415, -8094914,
2807             12412151, 10018715, 2213263, -13878373},
2808            {32529814, -11074689, 30361439, -16689753, -9135940, 1513226,
2809             22922121, 6382134, -5766928, 8371348},
2810        },
2811    },
2812    {
2813        {
2814            {9923462, 11271500, 12616794, 3544722, -29998368, -1721626,
2815             12891687, -8193132, -26442943, 10486144},
2816            {-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726,
2817             2610596, -23921530, -11455195},
2818            {5408411, -1136691, -4969122, 10561668, 24145918, 14240566,
2819             31319731, -4235541, 19985175, -3436086},
2820        },
2821        {
2822            {-13994457, 16616821, 14549246, 3341099, 32155958, 13648976,
2823             -17577068, 8849297, 65030, 8370684},
2824            {-8320926, -12049626, 31204563, 5839400, -20627288, -1057277,
2825             -19442942, 6922164, 12743482, -9800518},
2826            {-2361371, 12678785, 28815050, 4759974, -23893047, 4884717,
2827             23783145, 11038569, 18800704, 255233},
2828        },
2829        {
2830            {-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847,
2831             9066957, 19258688, -14753793},
2832            {-2936654, -10827535, -10432089, 14516793, -3640786, 4372541,
2833             -31934921, 2209390, -1524053, 2055794},
2834            {580882, 16705327, 5468415, -2683018, -30926419, -14696000,
2835             -7203346, -8994389, -30021019, 7394435},
2836        },
2837        {
2838            {23838809, 1822728, -15738443, 15242727, 8318092, -3733104,
2839             -21672180, -3492205, -4821741, 14799921},
2840            {13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804,
2841             13496856, -9056018, 7402518},
2842            {2286874, -4435931, -20042458, -2008336, -13696227, 5038122,
2843             11006906, -15760352, 8205061, 1607563},
2844        },
2845        {
2846            {14414086, -8002132, 3331830, -3208217, 22249151, -5594188,
2847             18364661, -2906958, 30019587, -9029278},
2848            {-27688051, 1585953, -10775053, 931069, -29120221, -11002319,
2849             -14410829, 12029093, 9944378, 8024},
2850            {4368715, -3709630, 29874200, -15022983, -20230386, -11410704,
2851             -16114594, -999085, -8142388, 5640030},
2852        },
2853        {
2854            {10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887,
2855             -16694564, 15219798, -14327783},
2856            {27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605,
2857             -1173195, -18342183, 9742717},
2858            {6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614,
2859             7406442, 12420155, 1994844},
2860        },
2861        {
2862            {14012521, -5024720, -18384453, -9578469, -26485342, -3936439,
2863             -13033478, -10909803, 24319929, -6446333},
2864            {16412690, -4507367, 10772641, 15929391, -17068788, -4658621,
2865             10555945, -10484049, -30102368, -4739048},
2866            {22397382, -7767684, -9293161, -12792868, 17166287, -9755136,
2867             -27333065, 6199366, 21880021, -12250760},
2868        },
2869        {
2870            {-4283307, 5368523, -31117018, 8163389, -30323063, 3209128,
2871             16557151, 8890729, 8840445, 4957760},
2872            {-15447727, 709327, -6919446, -10870178, -29777922, 6522332,
2873             -21720181, 12130072, -14796503, 5005757},
2874            {-2114751, -14308128, 23019042, 15765735, -25269683, 6002752,
2875             10183197, -13239326, -16395286, -2176112},
2876        },
2877    },
2878    {
2879        {
2880            {-19025756, 1632005, 13466291, -7995100, -23640451, 16573537,
2881             -32013908, -3057104, 22208662, 2000468},
2882            {3065073, -1412761, -25598674, -361432, -17683065, -5703415,
2883             -8164212, 11248527, -3691214, -7414184},
2884            {10379208, -6045554, 8877319, 1473647, -29291284, -12507580,
2885             16690915, 2553332, -3132688, 16400289},
2886        },
2887        {
2888            {15716668, 1254266, -18472690, 7446274, -8448918, 6344164,
2889             -22097271, -7285580, 26894937, 9132066},
2890            {24158887, 12938817, 11085297, -8177598, -28063478, -4457083,
2891             -30576463, 64452, -6817084, -2692882},
2892            {13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710,
2893             -3418511, -4688006, 2364226},
2894        },
2895        {
2896            {16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024,
2897             -11697457, 15445875, -7798101},
2898            {29004207, -7867081, 28661402, -640412, -12794003, -7943086,
2899             31863255, -4135540, -278050, -15759279},
2900            {-6122061, -14866665, -28614905, 14569919, -10857999, -3591829,
2901             10343412, -6976290, -29828287, -10815811},
2902        },
2903        {
2904            {27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636,
2905             15372179, 17293797, 960709},
2906            {20263915, 11434237, -5765435, 11236810, 13505955, -10857102,
2907             -16111345, 6493122, -19384511, 7639714},
2908            {-2830798, -14839232, 25403038, -8215196, -8317012, -16173699,
2909             18006287, -16043750, 29994677, -15808121},
2910        },
2911        {
2912            {9769828, 5202651, -24157398, -13631392, -28051003, -11561624,
2913             -24613141, -13860782, -31184575, 709464},
2914            {12286395, 13076066, -21775189, -1176622, -25003198, 4057652,
2915             -32018128, -8890874, 16102007, 13205847},
2916            {13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170,
2917             8525972, 10151379, 10394400},
2918        },
2919        {
2920            {4024660, -16137551, 22436262, 12276534, -9099015, -2686099,
2921             19698229, 11743039, -33302334, 8934414},
2922            {-15879800, -4525240, -8580747, -2934061, 14634845, -698278,
2923             -9449077, 3137094, -11536886, 11721158},
2924            {17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229,
2925             8835153, -9205489, -1280045},
2926        },
2927        {
2928            {-461409, -7830014, 20614118, 16688288, -7514766, -4807119,
2929             22300304, 505429, 6108462, -6183415},
2930            {-5070281, 12367917, -30663534, 3234473, 32617080, -8422642,
2931             29880583, -13483331, -26898490, -7867459},
2932            {-31975283, 5726539, 26934134, 10237677, -3173717, -605053,
2933             24199304, 3795095, 7592688, -14992079},
2934        },
2935        {
2936            {21594432, -14964228, 17466408, -4077222, 32537084, 2739898,
2937             6407723, 12018833, -28256052, 4298412},
2938            {-20650503, -11961496, -27236275, 570498, 3767144, -1717540,
2939             13891942, -1569194, 13717174, 10805743},
2940            {-14676630, -15644296, 15287174, 11927123, 24177847, -8175568,
2941             -796431, 14860609, -26938930, -5863836},
2942        },
2943    },
2944    {
2945        {
2946            {12962541, 5311799, -10060768, 11658280, 18855286, -7954201,
2947             13286263, -12808704, -4381056, 9882022},
2948            {18512079, 11319350, -20123124, 15090309, 18818594, 5271736,
2949             -22727904, 3666879, -23967430, -3299429},
2950            {-6789020, -3146043, 16192429, 13241070, 15898607, -14206114,
2951             -10084880, -6661110, -2403099, 5276065},
2952        },
2953        {
2954            {30169808, -5317648, 26306206, -11750859, 27814964, 7069267,
2955             7152851, 3684982, 1449224, 13082861},
2956            {10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382,
2957             15056736, -21016438, -8202000},
2958            {-33150110, 3261608, 22745853, 7948688, 19370557, -15177665,
2959             -26171976, 6482814, -10300080, -11060101},
2960        },
2961        {
2962            {32869458, -5408545, 25609743, 15678670, -10687769, -15471071,
2963             26112421, 2521008, -22664288, 6904815},
2964            {29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737,
2965             3841096, -29003639, -6657642},
2966            {10340844, -6630377, -18656632, -2278430, 12621151, -13339055,
2967             30878497, -11824370, -25584551, 5181966},
2968        },
2969        {
2970            {25940115, -12658025, 17324188, -10307374, -8671468, 15029094,
2971             24396252, -16450922, -2322852, -12388574},
2972            {-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390,
2973             12641087, 20603771, -6561742},
2974            {-18882287, -11673380, 24849422, 11501709, 13161720, -4768874,
2975             1925523, 11914390, 4662781, 7820689},
2976        },
2977        {
2978            {12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456,
2979             12172924, 16136752, 15264020},
2980            {-10349955, -14680563, -8211979, 2330220, -17662549, -14545780,
2981             10658213, 6671822, 19012087, 3772772},
2982            {3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732,
2983             -15762884, 20527771, 12988982},
2984        },
2985        {
2986            {-14822485, -5797269, -3707987, 12689773, -898983, -10914866,
2987             -24183046, -10564943, 3299665, -12424953},
2988            {-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197,
2989             6461331, -25583147, 8991218},
2990            {-17226263, 1816362, -1673288, -6086439, 31783888, -8175991,
2991             -32948145, 7417950, -30242287, 1507265},
2992        },
2993        {
2994            {29692663, 6829891, -10498800, 4334896, 20945975, -11906496,
2995             -28887608, 8209391, 14606362, -10647073},
2996            {-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695,
2997             9761487, 4170404, -2085325},
2998            {-11587470, 14855945, -4127778, -1531857, -26649089, 15084046,
2999             22186522, 16002000, -14276837, -8400798},
3000        },
3001        {
3002            {-4811456, 13761029, -31703877, -2483919, -3312471, 7869047,
3003             -7113572, -9620092, 13240845, 10965870},
3004            {-7742563, -8256762, -14768334, -13656260, -23232383, 12387166,
3005             4498947, 14147411, 29514390, 4302863},
3006            {-13413405, -12407859, 20757302, -13801832, 14785143, 8976368,
3007             -5061276, -2144373, 17846988, -13971927},
3008        },
3009    },
3010    {
3011        {
3012            {-2244452, -754728, -4597030, -1066309, -6247172, 1455299,
3013             -21647728, -9214789, -5222701, 12650267},
3014            {-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813,
3015             13770293, -19134326, 10958663},
3016            {22470984, 12369526, 23446014, -5441109, -21520802, -9698723,
3017             -11772496, -11574455, -25083830, 4271862},
3018        },
3019        {
3020            {-25169565, -10053642, -19909332, 15361595, -5984358, 2159192,
3021             75375, -4278529, -32526221, 8469673},
3022            {15854970, 4148314, -8893890, 7259002, 11666551, 13824734,
3023             -30531198, 2697372, 24154791, -9460943},
3024            {15446137, -15806644, 29759747, 14019369, 30811221, -9610191,
3025             -31582008, 12840104, 24913809, 9815020},
3026        },
3027        {
3028            {-4709286, -5614269, -31841498, -12288893, -14443537, 10799414,
3029             -9103676, 13438769, 18735128, 9466238},
3030            {11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821,
3031             -10896103, -22728655, 16199064},
3032            {14576810, 379472, -26786533, -8317236, -29426508, -10812974,
3033             -102766, 1876699, 30801119, 2164795},
3034        },
3035        {
3036            {15995086, 3199873, 13672555, 13712240, -19378835, -4647646,
3037             -13081610, -15496269, -13492807, 1268052},
3038            {-10290614, -3659039, -3286592, 10948818, 23037027, 3794475,
3039             -3470338, -12600221, -17055369, 3565904},
3040            {29210088, -9419337, -5919792, -4952785, 10834811, -13327726,
3041             -16512102, -10820713, -27162222, -14030531},
3042        },
3043        {
3044            {-13161890, 15508588, 16663704, -8156150, -28349942, 9019123,
3045             -29183421, -3769423, 2244111, -14001979},
3046            {-5152875, -3800936, -9306475, -6071583, 16243069, 14684434,
3047             -25673088, -16180800, 13491506, 4641841},
3048            {10813417, 643330, -19188515, -728916, 30292062, -16600078,
3049             27548447, -7721242, 14476989, -12767431},
3050        },
3051        {
3052            {10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937,
3053             -1644259, -27912810, 12651324},
3054            {-31185513, -813383, 22271204, 11835308, 10201545, 15351028,
3055             17099662, 3988035, 21721536, -3148940},
3056            {10202177, -6545839, -31373232, -9574638, -32150642, -8119683,
3057             -12906320, 3852694, 13216206, 14842320},
3058        },
3059        {
3060            {-15815640, -10601066, -6538952, -7258995, -6984659, -6581778,
3061             -31500847, 13765824, -27434397, 9900184},
3062            {14465505, -13833331, -32133984, -14738873, -27443187, 12990492,
3063             33046193, 15796406, -7051866, -8040114},
3064            {30924417, -8279620, 6359016, -12816335, 16508377, 9071735,
3065             -25488601, 15413635, 9524356, -7018878},
3066        },
3067        {
3068            {12274201, -13175547, 32627641, -1785326, 6736625, 13267305,
3069             5237659, -5109483, 15663516, 4035784},
3070            {-2951309, 8903985, 17349946, 601635, -16432815, -4612556,
3071             -13732739, -15889334, -22258478, 4659091},
3072            {-16916263, -4952973, -30393711, -15158821, 20774812, 15897498,
3073             5736189, 15026997, -2178256, -13455585},
3074        },
3075    },
3076    {
3077        {
3078            {-8858980, -2219056, 28571666, -10155518, -474467, -10105698,
3079             -3801496, 278095, 23440562, -290208},
3080            {10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275,
3081             11551483, -16571960, -7442864},
3082            {17932739, -12437276, -24039557, 10749060, 11316803, 7535897,
3083             22503767, 5561594, -3646624, 3898661},
3084        },
3085        {
3086            {7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531,
3087             7152530, 21831162, 1245233},
3088            {26958459, -14658026, 4314586, 8346991, -5677764, 11960072,
3089             -32589295, -620035, -30402091, -16716212},
3090            {-12165896, 9166947, 33491384, 13673479, 29787085, 13096535,
3091             6280834, 14587357, -22338025, 13987525},
3092        },
3093        {
3094            {-24349909, 7778775, 21116000, 15572597, -4833266, -5357778,
3095             -4300898, -5124639, -7469781, -2858068},
3096            {9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781,
3097             6439245, -14581012, 4091397},
3098            {-8426427, 1470727, -28109679, -1596990, 3978627, -5123623,
3099             -19622683, 12092163, 29077877, -14741988},
3100        },
3101        {
3102            {5269168, -6859726, -13230211, -8020715, 25932563, 1763552,
3103             -5606110, -5505881, -20017847, 2357889},
3104            {32264008, -15407652, -5387735, -1160093, -2091322, -3946900,
3105             23104804, -12869908, 5727338, 189038},
3106            {14609123, -8954470, -6000566, -16622781, -14577387, -7743898,
3107             -26745169, 10942115, -25888931, -14884697},
3108        },
3109        {
3110            {20513500, 5557931, -15604613, 7829531, 26413943, -2019404,
3111             -21378968, 7471781, 13913677, -5137875},
3112            {-25574376, 11967826, 29233242, 12948236, -6754465, 4713227,
3113             -8940970, 14059180, 12878652, 8511905},
3114            {-25656801, 3393631, -2955415, -7075526, -2250709, 9366908,
3115             -30223418, 6812974, 5568676, -3127656},
3116        },
3117        {
3118            {11630004, 12144454, 2116339, 13606037, 27378885, 15676917,
3119             -17408753, -13504373, -14395196, 8070818},
3120            {27117696, -10007378, -31282771, -5570088, 1127282, 12772488,
3121             -29845906, 10483306, -11552749, -1028714},
3122            {10637467, -5688064, 5674781, 1072708, -26343588, -6982302,
3123             -1683975, 9177853, -27493162, 15431203},
3124        },
3125        {
3126            {20525145, 10892566, -12742472, 12779443, -29493034, 16150075,
3127             -28240519, 14943142, -15056790, -7935931},
3128            {-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767,
3129             -3239766, -3356550, 9594024},
3130            {-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683,
3131             -6492290, 13352335, -10977084},
3132        },
3133        {
3134            {-1931799, -5407458, 3304649, -12884869, 17015806, -4877091,
3135             -29783850, -7752482, -13215537, -319204},
3136            {20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742,
3137             15077870, -22750759, 14523817},
3138            {27406042, -6041657, 27423596, -4497394, 4996214, 10002360,
3139             -28842031, -4545494, -30172742, -4805667},
3140        },
3141    },
3142    {
3143        {
3144            {11374242, 12660715, 17861383, -12540833, 10935568, 1099227,
3145             -13886076, -9091740, -27727044, 11358504},
3146            {-12730809, 10311867, 1510375, 10778093, -2119455, -9145702,
3147             32676003, 11149336, -26123651, 4985768},
3148            {-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043,
3149             13794114, -19414307, -15621255},
3150        },
3151        {
3152            {6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603,
3153             6970005, -1691065, -9004790},
3154            {1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622,
3155             -5475723, -16796596, -5031438},
3156            {-22273315, -13524424, -64685, -4334223, -18605636, -10921968,
3157             -20571065, -7007978, -99853, -10237333},
3158        },
3159        {
3160            {17747465, 10039260, 19368299, -4050591, -20630635, -16041286,
3161             31992683, -15857976, -29260363, -5511971},
3162            {31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999,
3163             -3744247, 4882242, -10626905},
3164            {29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198,
3165             3272828, -5190932, -4162409},
3166        },
3167        {
3168            {12501286, 4044383, -8612957, -13392385, -32430052, 5136599,
3169             -19230378, -3529697, 330070, -3659409},
3170            {6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522,
3171             -8573892, -271295, 12071499},
3172            {-8365515, -4042521, 25133448, -4517355, -6211027, 2265927,
3173             -32769618, 1936675, -5159697, 3829363},
3174        },
3175        {
3176            {28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550,
3177             -6567787, 26333140, 14267664},
3178            {-11067219, 11871231, 27385719, -10559544, -4585914, -11189312,
3179             10004786, -8709488, -21761224, 8930324},
3180            {-21197785, -16396035, 25654216, -1725397, 12282012, 11008919,
3181             1541940, 4757911, -26491501, -16408940},
3182        },
3183        {
3184            {13537262, -7759490, -20604840, 10961927, -5922820, -13218065,
3185             -13156584, 6217254, -15943699, 13814990},
3186            {-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681,
3187             9257833, -1956526, -1776914},
3188            {-25045300, -10191966, 15366585, 15166509, -13105086, 8423556,
3189             -29171540, 12361135, -18685978, 4578290},
3190        },
3191        {
3192            {24579768, 3711570, 1342322, -11180126, -27005135, 14124956,
3193             -22544529, 14074919, 21964432, 8235257},
3194            {-6528613, -2411497, 9442966, -5925588, 12025640, -1487420,
3195             -2981514, -1669206, 13006806, 2355433},
3196            {-16304899, -13605259, -6632427, -5142349, 16974359, -10911083,
3197             27202044, 1719366, 1141648, -12796236},
3198        },
3199        {
3200            {-12863944, -13219986, -8318266, -11018091, -6810145, -4843894,
3201             13475066, -3133972, 32674895, 13715045},
3202            {11423335, -5468059, 32344216, 8962751, 24989809, 9241752,
3203             -13265253, 16086212, -28740881, -15642093},
3204            {-1409668, 12530728, -6368726, 10847387, 19531186, -14132160,
3205             -11709148, 7791794, -27245943, 4383347},
3206        },
3207    },
3208    {
3209        {
3210            {-28970898, 5271447, -1266009, -9736989, -12455236, 16732599,
3211             -4862407, -4906449, 27193557, 6245191},
3212            {-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898,
3213             3260492, 22510453, 8577507},
3214            {-12632451, 11257346, -32692994, 13548177, -721004, 10879011,
3215             31168030, 13952092, -29571492, -3635906},
3216        },
3217        {
3218            {3877321, -9572739, 32416692, 5405324, -11004407, -13656635,
3219             3759769, 11935320, 5611860, 8164018},
3220            {-16275802, 14667797, 15906460, 12155291, -22111149, -9039718,
3221             32003002, -8832289, 5773085, -8422109},
3222            {-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725,
3223             12376320, 31632953, 190926},
3224        },
3225        {
3226            {-24593607, -16138885, -8423991, 13378746, 14162407, 6901328,
3227             -8288749, 4508564, -25341555, -3627528},
3228            {8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941,
3229             -14786005, -1672488, 827625},
3230            {-32720583, -16289296, -32503547, 7101210, 13354605, 2659080,
3231             -1800575, -14108036, -24878478, 1541286},
3232        },
3233        {
3234            {2901347, -1117687, 3880376, -10059388, -17620940, -3612781,
3235             -21802117, -3567481, 20456845, -1885033},
3236            {27019610, 12299467, -13658288, -1603234, -12861660, -4861471,
3237             -19540150, -5016058, 29439641, 15138866},
3238            {21536104, -6626420, -32447818, -10690208, -22408077, 5175814,
3239             -5420040, -16361163, 7779328, 109896},
3240        },
3241        {
3242            {30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390,
3243             12180118, 23177719, -554075},
3244            {26572847, 3405927, -31701700, 12890905, -19265668, 5335866,
3245             -6493768, 2378492, 4439158, -13279347},
3246            {-22716706, 3489070, -9225266, -332753, 18875722, -1140095,
3247             14819434, -12731527, -17717757, -5461437},
3248        },
3249        {
3250            {-5056483, 16566551, 15953661, 3767752, -10436499, 15627060,
3251             -820954, 2177225, 8550082, -15114165},
3252            {-18473302, 16596775, -381660, 15663611, 22860960, 15585581,
3253             -27844109, -3582739, -23260460, -8428588},
3254            {-32480551, 15707275, -8205912, -5652081, 29464558, 2713815,
3255             -22725137, 15860482, -21902570, 1494193},
3256        },
3257        {
3258            {-19562091, -14087393, -25583872, -9299552, 13127842, 759709,
3259             21923482, 16529112, 8742704, 12967017},
3260            {-28464899, 1553205, 32536856, -10473729, -24691605, -406174,
3261             -8914625, -2933896, -29903758, 15553883},
3262            {21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572,
3263             14513274, 19375923, -12647961},
3264        },
3265        {
3266            {8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818,
3267             -6222716, 2862653, 9455043},
3268            {29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124,
3269             -2990080, 15511449, 4789663},
3270            {-20679756, 7004547, 8824831, -9434977, -4045704, -3750736,
3271             -5754762, 108893, 23513200, 16652362},
3272        },
3273    },
3274    {
3275        {
3276            {-33256173, 4144782, -4476029, -6579123, 10770039, -7155542,
3277             -6650416, -12936300, -18319198, 10212860},
3278            {2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801,
3279             2600940, -9988298, -12506466},
3280            {-24645692, 13317462, -30449259, -15653928, 21365574, -10869657,
3281             11344424, 864440, -2499677, -16710063},
3282        },
3283        {
3284            {-26432803, 6148329, -17184412, -14474154, 18782929, -275997,
3285             -22561534, 211300, 2719757, 4940997},
3286            {-1323882, 3911313, -6948744, 14759765, -30027150, 7851207,
3287             21690126, 8518463, 26699843, 5276295},
3288            {-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586,
3289             149635, -15452774, 7159369},
3290        },
3291        {
3292            {9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009,
3293             8312176, 22477218, -8403385},
3294            {18155857, -16504990, 19744716, 9006923, 15154154, -10538976,
3295             24256460, -4864995, -22548173, 9334109},
3296            {2986088, -4911893, 10776628, -3473844, 10620590, -7083203,
3297             -21413845, 14253545, -22587149, 536906},
3298        },
3299        {
3300            {4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551,
3301             10589625, 10838060, -15420424},
3302            {-19342404, 867880, 9277171, -3218459, -14431572, -1986443,
3303             19295826, -15796950, 6378260, 699185},
3304            {7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039,
3305             15693155, -5045064, -13373962},
3306        },
3307        {
3308            {-7737563, -5869402, -14566319, -7406919, 11385654, 13201616,
3309             31730678, -10962840, -3918636, -9669325},
3310            {10188286, -15770834, -7336361, 13427543, 22223443, 14896287,
3311             30743455, 7116568, -21786507, 5427593},
3312            {696102, 13206899, 27047647, -10632082, 15285305, -9853179,
3313             10798490, -4578720, 19236243, 12477404},
3314        },
3315        {
3316            {-11229439, 11243796, -17054270, -8040865, -788228, -8167967,
3317             -3897669, 11180504, -23169516, 7733644},
3318            {17800790, -14036179, -27000429, -11766671, 23887827, 3149671,
3319             23466177, -10538171, 10322027, 15313801},
3320            {26246234, 11968874, 32263343, -5468728, 6830755, -13323031,
3321             -15794704, -101982, -24449242, 10890804},
3322        },
3323        {
3324            {-31365647, 10271363, -12660625, -6267268, 16690207, -13062544,
3325             -14982212, 16484931, 25180797, -5334884},
3326            {-586574, 10376444, -32586414, -11286356, 19801893, 10997610,
3327             2276632, 9482883, 316878, 13820577},
3328            {-9882808, -4510367, -2115506, 16457136, -11100081, 11674996,
3329             30756178, -7515054, 30696930, -3712849},
3330        },
3331        {
3332            {32988917, -9603412, 12499366, 7910787, -10617257, -11931514,
3333             -7342816, -9985397, -32349517, 7392473},
3334            {-8855661, 15927861, 9866406, -3649411, -2396914, -16655781,
3335             -30409476, -9134995, 25112947, -2926644},
3336            {-2504044, -436966, 25621774, -5678772, 15085042, -5479877,
3337             -24884878, -13526194, 5537438, -13914319},
3338        },
3339    },
3340    {
3341        {
3342            {-11225584, 2320285, -9584280, 10149187, -33444663, 5808648,
3343             -14876251, -1729667, 31234590, 6090599},
3344            {-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721,
3345             15878753, -6970405, -9034768},
3346            {-27757857, 247744, -15194774, -9002551, 23288161, -10011936,
3347             -23869595, 6503646, 20650474, 1804084},
3348        },
3349        {
3350            {-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995,
3351             -10329713, 27842616, -202328},
3352            {-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656,
3353             5031932, -11375082, 12714369},
3354            {20807691, -7270825, 29286141, 11421711, -27876523, -13868230,
3355             -21227475, 1035546, -19733229, 12796920},
3356        },
3357        {
3358            {12076899, -14301286, -8785001, -11848922, -25012791, 16400684,
3359             -17591495, -12899438, 3480665, -15182815},
3360            {-32361549, 5457597, 28548107, 7833186, 7303070, -11953545,
3361             -24363064, -15921875, -33374054, 2771025},
3362            {-21389266, 421932, 26597266, 6860826, 22486084, -6737172,
3363             -17137485, -4210226, -24552282, 15673397},
3364        },
3365        {
3366            {-20184622, 2338216, 19788685, -9620956, -4001265, -8740893,
3367             -20271184, 4733254, 3727144, -12934448},
3368            {6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594,
3369             7975683, 31123697, -10958981},
3370            {30069250, -11435332, 30434654, 2958439, 18399564, -976289,
3371             12296869, 9204260, -16432438, 9648165},
3372        },
3373        {
3374            {32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266,
3375             5248604, -26008332, -11377501},
3376            {17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711,
3377             15298639, 2662509, -16297073},
3378            {-1172927, -7558695, -4366770, -4287744, -21346413, -8434326,
3379             32087529, -1222777, 32247248, -14389861},
3380        },
3381        {
3382            {14312628, 1221556, 17395390, -8700143, -4945741, -8684635,
3383             -28197744, -9637817, -16027623, -13378845},
3384            {-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502,
3385             9803137, 17597934, 2346211},
3386            {18510800, 15337574, 26171504, 981392, -22241552, 7827556,
3387             -23491134, -11323352, 3059833, -11782870},
3388        },
3389        {
3390            {10141598, 6082907, 17829293, -1947643, 9830092, 13613136,
3391             -25556636, -5544586, -33502212, 3592096},
3392            {33114168, -15889352, -26525686, -13343397, 33076705, 8716171,
3393             1151462, 1521897, -982665, -6837803},
3394            {-32939165, -4255815, 23947181, -324178, -33072974, -12305637,
3395             -16637686, 3891704, 26353178, 693168},
3396        },
3397        {
3398            {30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294,
3399             -400668, 31375464, 14369965},
3400            {-14370654, -7772529, 1510301, 6434173, -18784789, -6262728,
3401             32732230, -13108839, 17901441, 16011505},
3402            {18171223, -11934626, -12500402, 15197122, -11038147, -15230035,
3403             -19172240, -16046376, 8764035, 12309598},
3404        },
3405    },
3406    {
3407        {
3408            {5975908, -5243188, -19459362, -9681747, -11541277, 14015782,
3409             -23665757, 1228319, 17544096, -10593782},
3410            {5811932, -1715293, 3442887, -2269310, -18367348, -8359541,
3411             -18044043, -15410127, -5565381, 12348900},
3412            {-31399660, 11407555, 25755363, 6891399, -3256938, 14872274,
3413             -24849353, 8141295, -10632534, -585479},
3414        },
3415        {
3416            {-12675304, 694026, -5076145, 13300344, 14015258, -14451394,
3417             -9698672, -11329050, 30944593, 1130208},
3418            {8247766, -6710942, -26562381, -7709309, -14401939, -14648910,
3419             4652152, 2488540, 23550156, -271232},
3420            {17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737,
3421             -5908146, -408818, -137719},
3422        },
3423        {
3424            {16091085, -16253926, 18599252, 7340678, 2137637, -1221657,
3425             -3364161, 14550936, 3260525, -7166271},
3426            {-4910104, -13332887, 18550887, 10864893, -16459325, -7291596,
3427             -23028869, -13204905, -12748722, 2701326},
3428            {-8574695, 16099415, 4629974, -16340524, -20786213, -6005432,
3429             -10018363, 9276971, 11329923, 1862132},
3430        },
3431        {
3432            {14763076, -15903608, -30918270, 3689867, 3511892, 10313526,
3433             -21951088, 12219231, -9037963, -940300},
3434            {8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216,
3435             -2909717, -15438168, 11595570},
3436            {15214962, 3537601, -26238722, -14058872, 4418657, -15230761,
3437             13947276, 10730794, -13489462, -4363670},
3438        },
3439        {
3440            {-2538306, 7682793, 32759013, 263109, -29984731, -7955452,
3441             -22332124, -10188635, 977108, 699994},
3442            {-12466472, 4195084, -9211532, 550904, -15565337, 12917920,
3443             19118110, -439841, -30534533, -14337913},
3444            {31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237,
3445             -10051775, 12493932, -5409317},
3446        },
3447        {
3448            {-25680606, 5260744, -19235809, -6284470, -3695942, 16566087,
3449             27218280, 2607121, 29375955, 6024730},
3450            {842132, -2794693, -4763381, -8722815, 26332018, -12405641,
3451             11831880, 6985184, -9940361, 2854096},
3452            {-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645,
3453             960770, 12121869, 16648078},
3454        },
3455        {
3456            {-15218652, 14667096, -13336229, 2013717, 30598287, -464137,
3457             -31504922, -7882064, 20237806, 2838411},
3458            {-19288047, 4453152, 15298546, -16178388, 22115043, -15972604,
3459             12544294, -13470457, 1068881, -12499905},
3460            {-9558883, -16518835, 33238498, 13506958, 30505848, -1114596,
3461             -8486907, -2630053, 12521378, 4845654},
3462        },
3463        {
3464            {-28198521, 10744108, -2958380, 10199664, 7759311, -13088600,
3465             3409348, -873400, -6482306, -12885870},
3466            {-23561822, 6230156, -20382013, 10655314, -24040585, -11621172,
3467             10477734, -1240216, -3113227, 13974498},
3468            {12966261, 15550616, -32038948, -1615346, 21025980, -629444,
3469             5642325, 7188737, 18895762, 12629579},
3470        },
3471    },
3472    {
3473        {
3474            {14741879, -14946887, 22177208, -11721237, 1279741, 8058600,
3475             11758140, 789443, 32195181, 3895677},
3476            {10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575,
3477             -3566119, -8982069, 4429647},
3478            {-2453894, 15725973, -20436342, -10410672, -5803908, -11040220,
3479             -7135870, -11642895, 18047436, -15281743},
3480        },
3481        {
3482            {-25173001, -11307165, 29759956, 11776784, -22262383, -15820455,
3483             10993114, -12850837, -17620701, -9408468},
3484            {21987233, 700364, -24505048, 14972008, -7774265, -5718395,
3485             32155026, 2581431, -29958985, 8773375},
3486            {-25568350, 454463, -13211935, 16126715, 25240068, 8594567,
3487             20656846, 12017935, -7874389, -13920155},
3488        },
3489        {
3490            {6028182, 6263078, -31011806, -11301710, -818919, 2461772,
3491             -31841174, -5468042, -1721788, -2776725},
3492            {-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845,
3493             -4166698, 28408820, 6816612},
3494            {-10358094, -8237829, 19549651, -12169222, 22082623, 16147817,
3495             20613181, 13982702, -10339570, 5067943},
3496        },
3497        {
3498            {-30505967, -3821767, 12074681, 13582412, -19877972, 2443951,
3499             -19719286, 12746132, 5331210, -10105944},
3500            {30528811, 3601899, -1957090, 4619785, -27361822, -15436388,
3501             24180793, -12570394, 27679908, -1648928},
3502            {9402404, -13957065, 32834043, 10838634, -26580150, -13237195,
3503             26653274, -8685565, 22611444, -12715406},
3504        },
3505        {
3506            {22190590, 1118029, 22736441, 15130463, -30460692, -5991321,
3507             19189625, -4648942, 4854859, 6622139},
3508            {-8310738, -2953450, -8262579, -3388049, -10401731, -271929,
3509             13424426, -3567227, 26404409, 13001963},
3510            {-31241838, -15415700, -2994250, 8939346, 11562230, -12840670,
3511             -26064365, -11621720, -15405155, 11020693},
3512        },
3513        {
3514            {1866042, -7949489, -7898649, -10301010, 12483315, 13477547,
3515             3175636, -12424163, 28761762, 1406734},
3516            {-448555, -1777666, 13018551, 3194501, -9580420, -11161737,
3517             24760585, -4347088, 25577411, -13378680},
3518            {-24290378, 4759345, -690653, -1852816, 2066747, 10693769,
3519             -29595790, 9884936, -9368926, 4745410},
3520        },
3521        {
3522            {-9141284, 6049714, -19531061, -4341411, -31260798, 9944276,
3523             -15462008, -11311852, 10931924, -11931931},
3524            {-16561513, 14112680, -8012645, 4817318, -8040464, -11414606,
3525             -22853429, 10856641, -20470770, 13434654},
3526            {22759489, -10073434, -16766264, -1871422, 13637442, -10168091,
3527             1765144, -12654326, 28445307, -5364710},
3528        },
3529        {
3530            {29875063, 12493613, 2795536, -3786330, 1710620, 15181182,
3531             -10195717, -8788675, 9074234, 1167180},
3532            {-26205683, 11014233, -9842651, -2635485, -26908120, 7532294,
3533             -18716888, -9535498, 3843903, 9367684},
3534            {-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123,
3535             8601684, -139197, 4242895},
3536        },
3537    },
3538    {
3539        {
3540            {22092954, -13191123, -2042793, -11968512, 32186753, -11517388,
3541             -6574341, 2470660, -27417366, 16625501},
3542            {-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857,
3543             2602725, -27351616, 14247413},
3544            {6314175, -10264892, -32772502, 15957557, -10157730, 168750,
3545             -8618807, 14290061, 27108877, -1180880},
3546        },
3547        {
3548            {-8586597, -7170966, 13241782, 10960156, -32991015, -13794596,
3549             33547976, -11058889, -27148451, 981874},
3550            {22833440, 9293594, -32649448, -13618667, -9136966, 14756819,
3551             -22928859, -13970780, -10479804, -16197962},
3552            {-7768587, 3326786, -28111797, 10783824, 19178761, 14905060,
3553             22680049, 13906969, -15933690, 3797899},
3554        },
3555        {
3556            {21721356, -4212746, -12206123, 9310182, -3882239, -13653110,
3557             23740224, -2709232, 20491983, -8042152},
3558            {9209270, -15135055, -13256557, -6167798, -731016, 15289673,
3559             25947805, 15286587, 30997318, -6703063},
3560            {7392032, 16618386, 23946583, -8039892, -13265164, -1533858,
3561             -14197445, -2321576, 17649998, -250080},
3562        },
3563        {
3564            {-9301088, -14193827, 30609526, -3049543, -25175069, -1283752,
3565             -15241566, -9525724, -2233253, 7662146},
3566            {-17558673, 1763594, -33114336, 15908610, -30040870, -12174295,
3567             7335080, -8472199, -3174674, 3440183},
3568            {-19889700, -5977008, -24111293, -9688870, 10799743, -16571957,
3569             40450, -4431835, 4862400, 1133},
3570        },
3571        {
3572            {-32856209, -7873957, -5422389, 14860950, -16319031, 7956142,
3573             7258061, 311861, -30594991, -7379421},
3574            {-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763,
3575             16527196, 18278453, 15405622},
3576            {-4381906, 8508652, -19898366, -3674424, -5984453, 15149970,
3577             -13313598, 843523, -21875062, 13626197},
3578        },
3579        {
3580            {2281448, -13487055, -10915418, -2609910, 1879358, 16164207,
3581             -10783882, 3953792, 13340839, 15928663},
3582            {31727126, -7179855, -18437503, -8283652, 2875793, -16390330,
3583             -25269894, -7014826, -23452306, 5964753},
3584            {4100420, -5959452, -17179337, 6017714, -18705837, 12227141,
3585             -26684835, 11344144, 2538215, -7570755},
3586        },
3587        {
3588            {-9433605, 6123113, 11159803, -2156608, 30016280, 14966241,
3589             -20474983, 1485421, -629256, -15958862},
3590            {-26804558, 4260919, 11851389, 9658551, -32017107, 16367492,
3591             -20205425, -13191288, 11659922, -11115118},
3592            {26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568,
3593             -10170080, 33100372, -1306171},
3594        },
3595        {
3596            {15121113, -5201871, -10389905, 15427821, -27509937, -15992507,
3597             21670947, 4486675, -5931810, -14466380},
3598            {16166486, -9483733, -11104130, 6023908, -31926798, -1364923,
3599             2340060, -16254968, -10735770, -10039824},
3600            {28042865, -3557089, -12126526, 12259706, -3717498, -6945899,
3601             6766453, -8689599, 18036436, 5803270},
3602        },
3603    },
3604    {
3605        {
3606            {-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391,
3607             4598332, -6159431, -14117438},
3608            {-31031306, -14256194, 17332029, -2383520, 31312682, -5967183,
3609             696309, 50292, -20095739, 11763584},
3610            {-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117,
3611             -12613632, -19773211, -10713562},
3612        },
3613        {
3614            {30464590, -11262872, -4127476, -12734478, 19835327, -7105613,
3615             -24396175, 2075773, -17020157, 992471},
3616            {18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841,
3617             8080033, -11574335, -10601610},
3618            {19598397, 10334610, 12555054, 2555664, 18821899, -10339780,
3619             21873263, 16014234, 26224780, 16452269},
3620        },
3621        {
3622            {-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804,
3623             -7618186, -20533829, 3698650},
3624            {14187449, 3448569, -10636236, -10810935, -22663880, -3433596,
3625             7268410, -10890444, 27394301, 12015369},
3626            {19695761, 16087646, 28032085, 12999827, 6817792, 11427614,
3627             20244189, -1312777, -13259127, -3402461},
3628        },
3629        {
3630            {30860103, 12735208, -1888245, -4699734, -16974906, 2256940,
3631             -8166013, 12298312, -8550524, -10393462},
3632            {-5719826, -11245325, -1910649, 15569035, 26642876, -7587760,
3633             -5789354, -15118654, -4976164, 12651793},
3634            {-2848395, 9953421, 11531313, -5282879, 26895123, -12697089,
3635             -13118820, -16517902, 9768698, -2533218},
3636        },
3637        {
3638            {-24719459, 1894651, -287698, -4704085, 15348719, -8156530,
3639             32767513, 12765450, 4940095, 10678226},
3640            {18860224, 15980149, -18987240, -1562570, -26233012, -11071856,
3641             -7843882, 13944024, -24372348, 16582019},
3642            {-15504260, 4970268, -29893044, 4175593, -20993212, -2199756,
3643             -11704054, 15444560, -11003761, 7989037},
3644        },
3645        {
3646            {31490452, 5568061, -2412803, 2182383, -32336847, 4531686,
3647             -32078269, 6200206, -19686113, -14800171},
3648            {-17308668, -15879940, -31522777, -2831, -32887382, 16375549,
3649             8680158, -16371713, 28550068, -6857132},
3650            {-28126887, -5688091, 16837845, -1820458, -6850681, 12700016,
3651             -30039981, 4364038, 1155602, 5988841},
3652        },
3653        {
3654            {21890435, -13272907, -12624011, 12154349, -7831873, 15300496,
3655             23148983, -4470481, 24618407, 8283181},
3656            {-33136107, -10512751, 9975416, 6841041, -31559793, 16356536,
3657             3070187, -7025928, 1466169, 10740210},
3658            {-1509399, -15488185, -13503385, -10655916, 32799044, 909394,
3659             -13938903, -5779719, -32164649, -15327040},
3660        },
3661        {
3662            {3960823, -14267803, -28026090, -15918051, -19404858, 13146868,
3663             15567327, 951507, -3260321, -573935},
3664            {24740841, 5052253, -30094131, 8961361, 25877428, 6165135,
3665             -24368180, 14397372, -7380369, -6144105},
3666            {-28888365, 3510803, -28103278, -1158478, -11238128, -10631454,
3667             -15441463, -14453128, -1625486, -6494814},
3668        },
3669    },
3670    {
3671        {
3672            {793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843,
3673             -4885251, -9906200, -621852},
3674            {5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374,
3675             1468826, -6171428, -15186581},
3676            {-4859255, -3779343, -2917758, -6748019, 7778750, 11688288,
3677             -30404353, -9871238, -1558923, -9863646},
3678        },
3679        {
3680            {10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958,
3681             14783338, -30581476, -15757844},
3682            {10566929, 12612572, -31944212, 11118703, -12633376, 12362879,
3683             21752402, 8822496, 24003793, 14264025},
3684            {27713862, -7355973, -11008240, 9227530, 27050101, 2504721,
3685             23886875, -13117525, 13958495, -5732453},
3686        },
3687        {
3688            {-23481610, 4867226, -27247128, 3900521, 29838369, -8212291,
3689             -31889399, -10041781, 7340521, -15410068},
3690            {4646514, -8011124, -22766023, -11532654, 23184553, 8566613,
3691             31366726, -1381061, -15066784, -10375192},
3692            {-17270517, 12723032, -16993061, 14878794, 21619651, -6197576,
3693             27584817, 3093888, -8843694, 3849921},
3694        },
3695        {
3696            {-9064912, 2103172, 25561640, -15125738, -5239824, 9582958,
3697             32477045, -9017955, 5002294, -15550259},
3698            {-12057553, -11177906, 21115585, -13365155, 8808712, -12030708,
3699             16489530, 13378448, -25845716, 12741426},
3700            {-5946367, 10645103, -30911586, 15390284, -3286982, -7118677,
3701             24306472, 15852464, 28834118, -7646072},
3702        },
3703        {
3704            {-17335748, -9107057, -24531279, 9434953, -8472084, -583362,
3705             -13090771, 455841, 20461858, 5491305},
3706            {13669248, -16095482, -12481974, -10203039, -14569770, -11893198,
3707             -24995986, 11293807, -28588204, -9421832},
3708            {28497928, 6272777, -33022994, 14470570, 8906179, -1225630,
3709             18504674, -14165166, 29867745, -8795943},
3710        },
3711        {
3712            {-16207023, 13517196, -27799630, -13697798, 24009064, -6373891,
3713             -6367600, -13175392, 22853429, -4012011},
3714            {24191378, 16712145, -13931797, 15217831, 14542237, 1646131,
3715             18603514, -11037887, 12876623, -2112447},
3716            {17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753,
3717             608397, 16031844, 3723494},
3718        },
3719        {
3720            {-28632773, 12763728, -20446446, 7577504, 33001348, -13017745,
3721             17558842, -7872890, 23896954, -4314245},
3722            {-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064,
3723             7229064, -9919646, -8826859},
3724            {28816045, 298879, -28165016, -15920938, 19000928, -1665890,
3725             -12680833, -2949325, -18051778, -2082915},
3726        },
3727        {
3728            {16000882, -344896, 3493092, -11447198, -29504595, -13159789,
3729             12577740, 16041268, -19715240, 7847707},
3730            {10151868, 10572098, 27312476, 7922682, 14825339, 4723128,
3731             -32855931, -6519018, -10020567, 3852848},
3732            {-11430470, 15697596, -21121557, -4420647, 5386314, 15063598,
3733             16514493, -15932110, 29330899, -15076224},
3734        },
3735    },
3736    {
3737        {
3738            {-25499735, -4378794, -15222908, -6901211, 16615731, 2051784,
3739             3303702, 15490, -27548796, 12314391},
3740            {15683520, -6003043, 18109120, -9980648, 15337968, -5997823,
3741             -16717435, 15921866, 16103996, -3731215},
3742            {-23169824, -10781249, 13588192, -1628807, -3798557, -1074929,
3743             -19273607, 5402699, -29815713, -9841101},
3744        },
3745        {
3746            {23190676, 2384583, -32714340, 3462154, -29903655, -1529132,
3747             -11266856, 8911517, -25205859, 2739713},
3748            {21374101, -3554250, -33524649, 9874411, 15377179, 11831242,
3749             -33529904, 6134907, 4931255, 11987849},
3750            {-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539,
3751             13861388, -30076310, 10117930},
3752        },
3753        {
3754            {-29501170, -10744872, -26163768, 13051539, -25625564, 5089643,
3755             -6325503, 6704079, 12890019, 15728940},
3756            {-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376,
3757             -10428139, 12885167, 8311031},
3758            {-17516482, 5352194, 10384213, -13811658, 7506451, 13453191,
3759             26423267, 4384730, 1888765, -5435404},
3760        },
3761        {
3762            {-25817338, -3107312, -13494599, -3182506, 30896459, -13921729,
3763             -32251644, -12707869, -19464434, -3340243},
3764            {-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245,
3765             14845197, 17151279, -9854116},
3766            {-24830458, -12733720, -15165978, 10367250, -29530908, -265356,
3767             22825805, -7087279, -16866484, 16176525},
3768        },
3769        {
3770            {-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182,
3771             -10363426, -28746253, -10197509},
3772            {-10626600, -4486402, -13320562, -5125317, 3432136, -6393229,
3773             23632037, -1940610, 32808310, 1099883},
3774            {15030977, 5768825, -27451236, -2887299, -6427378, -15361371,
3775             -15277896, -6809350, 2051441, -15225865},
3776        },
3777        {
3778            {-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398,
3779             -14154188, -22686354, 16633660},
3780            {4577086, -16752288, 13249841, -15304328, 19958763, -14537274,
3781             18559670, -10759549, 8402478, -9864273},
3782            {-28406330, -1051581, -26790155, -907698, -17212414, -11030789,
3783             9453451, -14980072, 17983010, 9967138},
3784        },
3785        {
3786            {-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990,
3787             7806337, 17507396, 3651560},
3788            {-10420457, -4118111, 14584639, 15971087, -15768321, 8861010,
3789             26556809, -5574557, -18553322, -11357135},
3790            {2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121,
3791             8459447, -5605463, -7621941},
3792        },
3793        {
3794            {-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813,
3795             -849066, 17258084, -7977739},
3796            {18164541, -10595176, -17154882, -1542417, 19237078, -9745295,
3797             23357533, -15217008, 26908270, 12150756},
3798            {-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168,
3799             -5537701, -32302074, 16215819},
3800        },
3801    },
3802    {
3803        {
3804            {-6898905, 9824394, -12304779, -4401089, -31397141, -6276835,
3805             32574489, 12532905, -7503072, -8675347},
3806            {-27343522, -16515468, -27151524, -10722951, 946346, 16291093,
3807             254968, 7168080, 21676107, -1943028},
3808            {21260961, -8424752, -16831886, -11920822, -23677961, 3968121,
3809             -3651949, -6215466, -3556191, -7913075},
3810        },
3811        {
3812            {16544754, 13250366, -16804428, 15546242, -4583003, 12757258,
3813             -2462308, -8680336, -18907032, -9662799},
3814            {-2415239, -15577728, 18312303, 4964443, -15272530, -12653564,
3815             26820651, 16690659, 25459437, -4564609},
3816            {-25144690, 11425020, 28423002, -11020557, -6144921, -15826224,
3817             9142795, -2391602, -6432418, -1644817},
3818        },
3819        {
3820            {-23104652, 6253476, 16964147, -3768872, -25113972, -12296437,
3821             -27457225, -16344658, 6335692, 7249989},
3822            {-30333227, 13979675, 7503222, -12368314, -11956721, -4621693,
3823             -30272269, 2682242, 25993170, -12478523},
3824            {4364628, 5930691, 32304656, -10044554, -8054781, 15091131,
3825             22857016, -10598955, 31820368, 15075278},
3826        },
3827        {
3828            {31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788,
3829             -9650886, -17970238, 12833045},
3830            {19073683, 14851414, -24403169, -11860168, 7625278, 11091125,
3831             -19619190, 2074449, -9413939, 14905377},
3832            {24483667, -11935567, -2518866, -11547418, -1553130, 15355506,
3833             -25282080, 9253129, 27628530, -7555480},
3834        },
3835        {
3836            {17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324,
3837             -9157582, -14110875, 15297016},
3838            {510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417,
3839             -11864220, 8683221, 2921426},
3840            {18606791, 11874196, 27155355, -5281482, -24031742, 6265446,
3841             -25178240, -1278924, 4674690, 13890525},
3842        },
3843        {
3844            {13609624, 13069022, -27372361, -13055908, 24360586, 9592974,
3845             14977157, 9835105, 4389687, 288396},
3846            {9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062,
3847             8317628, 23388070, 16052080},
3848            {12720016, 11937594, -31970060, -5028689, 26900120, 8561328,
3849             -20155687, -11632979, -14754271, -10812892},
3850        },
3851        {
3852            {15961858, 14150409, 26716931, -665832, -22794328, 13603569,
3853             11829573, 7467844, -28822128, 929275},
3854            {11038231, -11582396, -27310482, -7316562, -10498527, -16307831,
3855             -23479533, -9371869, -21393143, 2465074},
3856            {20017163, -4323226, 27915242, 1529148, 12396362, 15675764,
3857             13817261, -9658066, 2463391, -4622140},
3858        },
3859        {
3860            {-16358878, -12663911, -12065183, 4996454, -1256422, 1073572,
3861             9583558, 12851107, 4003896, 12673717},
3862            {-1731589, -15155870, -3262930, 16143082, 19294135, 13385325,
3863             14741514, -9103726, 7903886, 2348101},
3864            {24536016, -16515207, 12715592, -3862155, 1511293, 10047386,
3865             -3842346, -7129159, -28377538, 10048127},
3866        },
3867    },
3868    {
3869        {
3870            {-12622226, -6204820, 30718825, 2591312, -10617028, 12192840,
3871             18873298, -7297090, -32297756, 15221632},
3872            {-26478122, -11103864, 11546244, -1852483, 9180880, 7656409,
3873             -21343950, 2095755, 29769758, 6593415},
3874            {-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345,
3875             -6118678, 30958054, 8292160},
3876        },
3877        {
3878            {31429822, -13959116, 29173532, 15632448, 12174511, -2760094,
3879             32808831, 3977186, 26143136, -3148876},
3880            {22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633,
3881             -1674433, -3758243, -2304625},
3882            {-15491917, 8012313, -2514730, -12702462, -23965846, -10254029,
3883             -1612713, -1535569, -16664475, 8194478},
3884        },
3885        {
3886            {27338066, -7507420, -7414224, 10140405, -19026427, -6589889,
3887             27277191, 8855376, 28572286, 3005164},
3888            {26287124, 4821776, 25476601, -4145903, -3764513, -15788984,
3889             -18008582, 1182479, -26094821, -13079595},
3890            {-7171154, 3178080, 23970071, 6201893, -17195577, -4489192,
3891             -21876275, -13982627, 32208683, -1198248},
3892        },
3893        {
3894            {-16657702, 2817643, -10286362, 14811298, 6024667, 13349505,
3895             -27315504, -10497842, -27672585, -11539858},
3896            {15941029, -9405932, -21367050, 8062055, 31876073, -238629,
3897             -15278393, -1444429, 15397331, -4130193},
3898            {8934485, -13485467, -23286397, -13423241, -32446090, 14047986,
3899             31170398, -1441021, -27505566, 15087184},
3900        },
3901        {
3902            {-18357243, -2156491, 24524913, -16677868, 15520427, -6360776,
3903             -15502406, 11461896, 16788528, -5868942},
3904            {-1947386, 16013773, 21750665, 3714552, -17401782, -16055433,
3905             -3770287, -10323320, 31322514, -11615635},
3906            {21426655, -5650218, -13648287, -5347537, -28812189, -4920970,
3907             -18275391, -14621414, 13040862, -12112948},
3908        },
3909        {
3910            {11293895, 12478086, -27136401, 15083750, -29307421, 14748872,
3911             14555558, -13417103, 1613711, 4896935},
3912            {-25894883, 15323294, -8489791, -8057900, 25967126, -13425460,
3913             2825960, -4897045, -23971776, -11267415},
3914            {-15924766, -5229880, -17443532, 6410664, 3622847, 10243618,
3915             20615400, 12405433, -23753030, -8436416},
3916        },
3917        {
3918            {-7091295, 12556208, -20191352, 9025187, -17072479, 4333801,
3919             4378436, 2432030, 23097949, -566018},
3920            {4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264,
3921             10103221, -18512313, 2424778},
3922            {366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678,
3923             1344109, -3642553, 12412659},
3924        },
3925        {
3926            {-24001791, 7690286, 14929416, -168257, -32210835, -13412986,
3927             24162697, -15326504, -3141501, 11179385},
3928            {18289522, -14724954, 8056945, 16430056, -21729724, 7842514,
3929             -6001441, -1486897, -18684645, -11443503},
3930            {476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959,
3931             13403813, 11052904, 5219329},
3932        },
3933    },
3934    {
3935        {
3936            {20678546, -8375738, -32671898, 8849123, -5009758, 14574752,
3937             31186971, -3973730, 9014762, -8579056},
3938            {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600,
3939             -33102500, 9160280, 8473550, -3256838},
3940            {24900749, 14435722, 17209120, -15292541, -22592275, 9878983,
3941             -7689309, -16335821, -24568481, 11788948},
3942        },
3943        {
3944            {-3118155, -11395194, -13802089, 14797441, 9652448, -6845904,
3945             -20037437, 10410733, -24568470, -1458691},
3946            {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911,
3947             11871841, -12505194, -18513325, 8464118},
3948            {-23400612, 8348507, -14585951, -861714, -3950205, -6373419,
3949             14325289, 8628612, 33313881, -8370517},
3950        },
3951        {
3952            {-20186973, -4967935, 22367356, 5271547, -1097117, -4788838,
3953             -24805667, -10236854, -8940735, -5818269},
3954            {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245,
3955             15989197, -12838188, 28358192, -4253904},
3956            {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267,
3957             -16637684, 4072016, -5351664, 5596589},
3958        },
3959        {
3960            {-28236598, -3390048, 12312896, 6213178, 3117142, 16078565,
3961             29266239, 2557221, 1768301, 15373193},
3962            {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902,
3963             -4504991, -24660491, 3442910},
3964            {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093,
3965             22597931, 7176455, -18585478, 13365930},
3966        },
3967        {
3968            {-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107,
3969             -8570186, -9689599, -3031667},
3970            {25008904, -10771599, -4305031, -9638010, 16265036, 15721635,
3971             683793, -11823784, 15723479, -15163481},
3972            {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514,
3973             11879682, 5400171, 519526, -1235876},
3974        },
3975        {
3976            {22258397, -16332233, -7869817, 14613016, -22520255, -2950923,
3977             -20353881, 7315967, 16648397, 7605640},
3978            {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212,
3979             23994942, -5281555, -9468848, 4763278},
3980            {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
3981             31088447, -7764523, -11356529, 728112},
3982        },
3983        {
3984            {26047220, -11751471, -6900323, -16521798, 24092068, 9158119,
3985             -4273545, -12555558, -29365436, -5498272},
3986            {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007,
3987             12327945, 10750447, 10014012},
3988            {-10312768, 3936952, 9156313, -8897683, 16498692, -994647,
3989             -27481051, -666732, 3424691, 7540221},
3990        },
3991        {
3992            {30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422,
3993             -16317219, -9244265, 15258046},
3994            {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
3995             2711395, 1062915, -5136345},
3996            {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
3997             -6066489, 12194497, 32960380, 1459310},
3998        },
3999    },
4000    {
4001        {
4002            {19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
4003             -6101885, 18638003, -11174937},
4004            {31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
4005             9012486, -7584354, -6643087, -5442636},
4006            {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
4007             9677543, -32294889, -6456008},
4008        },
4009        {
4010            {-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
4011             -7839692, -7852844, -8138429},
4012            {-15236356, -15433509, 7766470, 746860, 26346930, -10221762,
4013             -27333451, 10754588, -9431476, 5203576},
4014            {31834314, 14135496, -770007, 5159118, 20917671, -16768096,
4015             -7467973, -7337524, 31809243, 7347066},
4016        },
4017        {
4018            {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
4019             19797970, -12211255, 15192876, -2087490},
4020            {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
4021             10609330, 12694420, 33473243, -13382104},
4022            {33184999, 11180355, 15832085, -11385430, -1633671, 225884,
4023             15089336, -11023903, -6135662, 14480053},
4024        },
4025        {
4026            {31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
4027             5496208, 13685227, 27595050, 8737275},
4028            {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
4029             -31008351, -12610604, 26498114, 66511},
4030            {22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
4031             30540766, -4286747, -13327787, -7515095},
4032        },
4033        {
4034            {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
4035             8205540, 13585437, -17127465, 15115439},
4036            {23711543, -672915, 31206561, -8362711, 6164647, -9709987,
4037             -33535882, -1426096, 8236921, 16492939},
4038            {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
4039             19574902, 10071562, 6708380, -6222424},
4040        },
4041        {
4042            {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
4043             9328700, 29955601, -11678310},
4044            {3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
4045             -25892142, -12635595, -9917575, 6216608},
4046            {-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
4047             24822830, -6146567, -26767480, 7525079},
4048        },
4049        {
4050            {-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
4051             -910336, -2782495, -19386633, 11994101},
4052            {21691500, -13624626, -641331, -14367021, 3285881, -3483596,
4053             -25064666, 9718258, -7477437, 13381418},
4054            {18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
4055             23111648, -6375247, 28535282, 15779576},
4056        },
4057        {
4058            {30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
4059             -14068454, 12021730, 9955285, -16303356},
4060            {9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
4061             -18426029, 9924399, 20194861, 13380996},
4062            {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
4063             -1984914, 15707771, 26342023, 10146099},
4064        },
4065    },
4066    {
4067        {
4068            {-26016874, -219943, 21339191, -41388, 19745256, -2878700,
4069             -29637280, 2227040, 21612326, -545728},
4070            {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
4071             25764461, 12243797, -20856566, 11649658},
4072            {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
4073             6114064, 33514190, 2333242},
4074        },
4075        {
4076            {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
4077             -6679750, -12670638, 24350578, -13450001},
4078            {-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
4079             -31536088, -10406836, 8317860, 12352766},
4080            {18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
4081             -23552096, -2287550, 20712163, 6719373},
4082        },
4083        {
4084            {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
4085             -3763210, 26224235, -3297458},
4086            {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
4087             21728352, 9493610, 18620611, -16428628},
4088            {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
4089             -5269471, -9725556, -30701573, -16479657},
4090        },
4091        {
4092            {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
4093             12248509, -5240639, 13735342, 1934062},
4094            {25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
4095             -15136294, -3765346, -21277997, 5473616},
4096            {31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
4097             -7125085, 12469656, 29111212, -5451014},
4098        },
4099        {
4100            {24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
4101             24367466, 6388839, -10295587, 452383},
4102            {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
4103             -24236251, -5915248, 15766062, 8407814},
4104            {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
4105             -8917023, -4388953, -8067909, 2276718},
4106        },
4107        {
4108            {30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
4109             -23827587, 5096219, 22740376, -7303417},
4110            {2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
4111             24051124, 13742383, -15637599, 13295222},
4112            {33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
4113             -17720195, -4612972, -4451357, -14669444},
4114        },
4115        {
4116            {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
4117             -2469266, -4141880, 7770569, 9620597},
4118            {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
4119             -1694323, -33502340, -14767970},
4120            {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
4121             1220118, 30494170, -11440799},
4122        },
4123        {
4124            {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
4125             -26739026, 926050, -1684339, -13333647},
4126            {13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
4127             9021034, 9078865, 3353509, 4033511},
4128            {-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
4129             23161163, 8839127, 27485041, 7356032},
4130        },
4131    },
4132    {
4133        {
4134            {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
4135             2625015, 28431036, -16771834},
4136            {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
4137             -22545972, 14150565, 15970762, 4099461},
4138            {29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
4139             13617293, -9937143, 11465739, 8317062},
4140        },
4141        {
4142            {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
4143             14898637, 3848455, 20969334, -5157516},
4144            {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
4145             -21610826, -3649888, 11177095, 14989547},
4146            {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
4147             13515641, 2581286, -28487508, 9930240},
4148        },
4149        {
4150            {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
4151             18345767, -13403753, 16291481, -5314038},
4152            {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
4153             6957617, 4368891, 9788741},
4154            {16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
4155             -21722536, -8613148, 16250552, -11111103},
4156        },
4157        {
4158            {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
4159             10604807, -30190403, 4782747},
4160            {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
4161             -9981571, 4383045, 22546403, 437323},
4162            {31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
4163             27343084, 2786261, -30633590, -14097016},
4164        },
4165        {
4166            {-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
4167             -19690631, 2355319, -19284671, -6114373},
4168            {15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
4169             18952177, 15496498, -29380133, 11754228},
4170            {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
4171             7141596, 11724556, 22761615, -10134141},
4172        },
4173        {
4174            {16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
4175             -28741185, -12227393, 32851222, 11717399},
4176            {11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
4177             31474879, 3483633, -1193175, -4030831},
4178            {-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4179             33142652, 6546660, -19985279, -3948376},
4180        },
4181        {
4182            {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4183             -8537131, -12833048, -30772034, -15486313},
4184            {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4185             -31135347, -16049879, 10928917, 3011958},
4186            {-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4187             -30831056, -12805180, 18008031, 10258577},
4188        },
4189        {
4190            {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4191             -1853465, 1367120, 25127874, 6671743},
4192            {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4193             21382910, 11042292, 25838796, 4642684},
4194            {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4195             30468147, -13900640, 18423289, 4177476},
4196        },
4197    },
4198};
4199
4200static uint8_t negative(signed char b)
4201{
4202    uint32_t x = b;
4203
4204    x >>= 31; /* 1: yes; 0: no */
4205    return x;
4206}
4207
4208static void table_select(ge_precomp *t, int pos, signed char b)
4209{
4210    ge_precomp minust;
4211    uint8_t bnegative = negative(b);
4212    uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4213
4214    ge_precomp_0(t);
4215    cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4216    cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4217    cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4218    cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4219    cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4220    cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4221    cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4222    cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4223    fe_copy(minust.yplusx, t->yminusx);
4224    fe_copy(minust.yminusx, t->yplusx);
4225    fe_neg(minust.xy2d, t->xy2d);
4226    cmov(t, &minust, bnegative);
4227}
4228
4229/*
4230 * h = a * B
4231 *
4232 * where a = a[0]+256*a[1]+...+256^31 a[31]
4233 * B is the Ed25519 base point (x,4/5) with x positive.
4234 *
4235 * Preconditions:
4236 *   a[31] <= 127
4237 */
4238static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a)
4239{
4240    signed char e[64];
4241    signed char carry;
4242    ge_p1p1 r;
4243    ge_p2 s;
4244    ge_precomp t;
4245    int i;
4246
4247    for (i = 0; i < 32; ++i) {
4248        e[2 * i + 0] = (a[i] >> 0) & 15;
4249        e[2 * i + 1] = (a[i] >> 4) & 15;
4250    }
4251    /* each e[i] is between 0 and 15 */
4252    /* e[63] is between 0 and 7 */
4253
4254    carry = 0;
4255    for (i = 0; i < 63; ++i) {
4256        e[i] += carry;
4257        carry = e[i] + 8;
4258        carry >>= 4;
4259        e[i] -= carry << 4;
4260    }
4261    e[63] += carry;
4262    /* each e[i] is between -8 and 8 */
4263
4264    ge_p3_0(h);
4265    for (i = 1; i < 64; i += 2) {
4266        table_select(&t, i / 2, e[i]);
4267        ge_madd(&r, h, &t);
4268        ge_p1p1_to_p3(h, &r);
4269    }
4270
4271    ge_p3_dbl(&r, h);
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);
4276    ge_p1p1_to_p2(&s, &r);
4277    ge_p2_dbl(&r, &s);
4278    ge_p1p1_to_p3(h, &r);
4279
4280    for (i = 0; i < 64; i += 2) {
4281        table_select(&t, i / 2, e[i]);
4282        ge_madd(&r, h, &t);
4283        ge_p1p1_to_p3(h, &r);
4284    }
4285
4286    OPENSSL_cleanse(e, sizeof(e));
4287}
4288
4289#if !defined(BASE_2_51_IMPLEMENTED)
4290/*
4291 * Replace (f,g) with (g,f) if b == 1;
4292 * replace (f,g) with (f,g) if b == 0.
4293 *
4294 * Preconditions: b in {0,1}.
4295 */
4296static void fe_cswap(fe f, fe g, unsigned int b)
4297{
4298    size_t i;
4299
4300    b = 0-b;
4301    for (i = 0; i < 10; i++) {
4302        int32_t x = f[i] ^ g[i];
4303        x &= b;
4304        f[i] ^= x;
4305        g[i] ^= x;
4306    }
4307}
4308
4309/*
4310 * h = f * 121666
4311 *
4312 * Can overlap h with f.
4313 *
4314 * Preconditions:
4315 *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
4316 *
4317 * Postconditions:
4318 *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
4319 */
4320static void fe_mul121666(fe h, fe f)
4321{
4322    int32_t f0 = f[0];
4323    int32_t f1 = f[1];
4324    int32_t f2 = f[2];
4325    int32_t f3 = f[3];
4326    int32_t f4 = f[4];
4327    int32_t f5 = f[5];
4328    int32_t f6 = f[6];
4329    int32_t f7 = f[7];
4330    int32_t f8 = f[8];
4331    int32_t f9 = f[9];
4332    int64_t h0 = f0 * (int64_t) 121666;
4333    int64_t h1 = f1 * (int64_t) 121666;
4334    int64_t h2 = f2 * (int64_t) 121666;
4335    int64_t h3 = f3 * (int64_t) 121666;
4336    int64_t h4 = f4 * (int64_t) 121666;
4337    int64_t h5 = f5 * (int64_t) 121666;
4338    int64_t h6 = f6 * (int64_t) 121666;
4339    int64_t h7 = f7 * (int64_t) 121666;
4340    int64_t h8 = f8 * (int64_t) 121666;
4341    int64_t h9 = f9 * (int64_t) 121666;
4342    int64_t carry0;
4343    int64_t carry1;
4344    int64_t carry2;
4345    int64_t carry3;
4346    int64_t carry4;
4347    int64_t carry5;
4348    int64_t carry6;
4349    int64_t carry7;
4350    int64_t carry8;
4351    int64_t carry9;
4352
4353    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
4354    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
4355    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
4356    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
4357    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
4358
4359    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
4360    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
4361    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
4362    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
4363    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
4364
4365    h[0] = (int32_t)h0;
4366    h[1] = (int32_t)h1;
4367    h[2] = (int32_t)h2;
4368    h[3] = (int32_t)h3;
4369    h[4] = (int32_t)h4;
4370    h[5] = (int32_t)h5;
4371    h[6] = (int32_t)h6;
4372    h[7] = (int32_t)h7;
4373    h[8] = (int32_t)h8;
4374    h[9] = (int32_t)h9;
4375}
4376
4377static void x25519_scalar_mult_generic(uint8_t out[32],
4378                                       const uint8_t scalar[32],
4379                                       const uint8_t point[32]) {
4380    fe x1, x2, z2, x3, z3, tmp0, tmp1;
4381    uint8_t e[32];
4382    unsigned swap = 0;
4383    int pos;
4384
4385    memcpy(e, scalar, 32);
4386    e[0] &= 248;
4387    e[31] &= 127;
4388    e[31] |= 64;
4389    fe_frombytes(x1, point);
4390    fe_1(x2);
4391    fe_0(z2);
4392    fe_copy(x3, x1);
4393    fe_1(z3);
4394
4395    for (pos = 254; pos >= 0; --pos) {
4396        unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4397        swap ^= b;
4398        fe_cswap(x2, x3, swap);
4399        fe_cswap(z2, z3, swap);
4400        swap = b;
4401        fe_sub(tmp0, x3, z3);
4402        fe_sub(tmp1, x2, z2);
4403        fe_add(x2, x2, z2);
4404        fe_add(z2, x3, z3);
4405        fe_mul(z3, tmp0, x2);
4406        fe_mul(z2, z2, tmp1);
4407        fe_sq(tmp0, tmp1);
4408        fe_sq(tmp1, x2);
4409        fe_add(x3, z3, z2);
4410        fe_sub(z2, z3, z2);
4411        fe_mul(x2, tmp1, tmp0);
4412        fe_sub(tmp1, tmp1, tmp0);
4413        fe_sq(z2, z2);
4414        fe_mul121666(z3, tmp1);
4415        fe_sq(x3, x3);
4416        fe_add(tmp0, tmp0, z3);
4417        fe_mul(z3, x1, z2);
4418        fe_mul(z2, tmp1, tmp0);
4419    }
4420
4421    fe_invert(z2, z2);
4422    fe_mul(x2, x2, z2);
4423    fe_tobytes(out, x2);
4424
4425    OPENSSL_cleanse(e, sizeof(e));
4426}
4427
4428static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4429                               const uint8_t point[32]) {
4430    x25519_scalar_mult_generic(out, scalar, point);
4431}
4432#endif
4433
4434static void slide(signed char *r, const uint8_t *a)
4435{
4436    int i;
4437    int b;
4438    int k;
4439
4440    for (i = 0; i < 256; ++i) {
4441        r[i] = 1 & (a[i >> 3] >> (i & 7));
4442    }
4443
4444    for (i = 0; i < 256; ++i) {
4445        if (r[i]) {
4446            for (b = 1; b <= 6 && i + b < 256; ++b) {
4447                if (r[i + b]) {
4448                    if (r[i] + (r[i + b] << b) <= 15) {
4449                        r[i] += r[i + b] << b;
4450                        r[i + b] = 0;
4451                    } else if (r[i] - (r[i + b] << b) >= -15) {
4452                        r[i] -= r[i + b] << b;
4453                        for (k = i + b; k < 256; ++k) {
4454                            if (!r[k]) {
4455                                r[k] = 1;
4456                                break;
4457                            }
4458                            r[k] = 0;
4459                        }
4460                    } else {
4461                        break;
4462                    }
4463                }
4464            }
4465        }
4466    }
4467}
4468
4469static const ge_precomp Bi[8] = {
4470    {
4471        {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4472         -11754271, -6079156, 2047605},
4473        {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4474         5043384, 19500929, -15469378},
4475        {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4476         11864899, -24514362, -4438546},
4477    },
4478    {
4479        {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4480         -14772189, 28944400, -1550024},
4481        {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4482         -11775962, 7689662, 11199574},
4483        {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4484         10017326, -17749093, -9920357},
4485    },
4486    {
4487        {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4488         14515107, -15438304, 10819380},
4489        {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4490         12483688, -12668491, 5581306},
4491        {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4492         13850243, -23678021, -15815942},
4493    },
4494    {
4495        {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4496         5230134, -23952439, -15175766},
4497        {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4498         16520125, 30598449, 7715701},
4499        {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4500         1370708, 29794553, -1409300},
4501    },
4502    {
4503        {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4504         -1361450, -13062696, 13821877},
4505        {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4506         -7212327, 18853322, -14220951},
4507        {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4508         -10431137, 2207753, -3209784},
4509    },
4510    {
4511        {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4512         -663000, -31111463, -16132436},
4513        {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4514         15725684, 171356, 6466918},
4515        {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4516         -14088058, -30714912, 16193877},
4517    },
4518    {
4519        {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4520         4729455, -18074513, 9256800},
4521        {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4522         9761698, -19827198, 630305},
4523        {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4524         -15960994, -2449256, -14291300},
4525    },
4526    {
4527        {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4528         15033784, 25105118, -7894876},
4529        {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4530         1573892, -2625887, 2198790, -15804619},
4531        {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4532         -16236442, -32461234, -12290683},
4533    },
4534};
4535
4536/*
4537 * r = a * A + b * B
4538 *
4539 * where a = a[0]+256*a[1]+...+256^31 a[31].
4540 * and b = b[0]+256*b[1]+...+256^31 b[31].
4541 * B is the Ed25519 base point (x,4/5) with x positive.
4542 */
4543static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
4544                                         const ge_p3 *A, const uint8_t *b)
4545{
4546    signed char aslide[256];
4547    signed char bslide[256];
4548    ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4549    ge_p1p1 t;
4550    ge_p3 u;
4551    ge_p3 A2;
4552    int i;
4553
4554    slide(aslide, a);
4555    slide(bslide, b);
4556
4557    ge_p3_to_cached(&Ai[0], A);
4558    ge_p3_dbl(&t, A);
4559    ge_p1p1_to_p3(&A2, &t);
4560    ge_add(&t, &A2, &Ai[0]);
4561    ge_p1p1_to_p3(&u, &t);
4562    ge_p3_to_cached(&Ai[1], &u);
4563    ge_add(&t, &A2, &Ai[1]);
4564    ge_p1p1_to_p3(&u, &t);
4565    ge_p3_to_cached(&Ai[2], &u);
4566    ge_add(&t, &A2, &Ai[2]);
4567    ge_p1p1_to_p3(&u, &t);
4568    ge_p3_to_cached(&Ai[3], &u);
4569    ge_add(&t, &A2, &Ai[3]);
4570    ge_p1p1_to_p3(&u, &t);
4571    ge_p3_to_cached(&Ai[4], &u);
4572    ge_add(&t, &A2, &Ai[4]);
4573    ge_p1p1_to_p3(&u, &t);
4574    ge_p3_to_cached(&Ai[5], &u);
4575    ge_add(&t, &A2, &Ai[5]);
4576    ge_p1p1_to_p3(&u, &t);
4577    ge_p3_to_cached(&Ai[6], &u);
4578    ge_add(&t, &A2, &Ai[6]);
4579    ge_p1p1_to_p3(&u, &t);
4580    ge_p3_to_cached(&Ai[7], &u);
4581
4582    ge_p2_0(r);
4583
4584    for (i = 255; i >= 0; --i) {
4585        if (aslide[i] || bslide[i]) {
4586            break;
4587        }
4588    }
4589
4590    for (; i >= 0; --i) {
4591        ge_p2_dbl(&t, r);
4592
4593        if (aslide[i] > 0) {
4594            ge_p1p1_to_p3(&u, &t);
4595            ge_add(&t, &u, &Ai[aslide[i] / 2]);
4596        } else if (aslide[i] < 0) {
4597            ge_p1p1_to_p3(&u, &t);
4598            ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4599        }
4600
4601        if (bslide[i] > 0) {
4602            ge_p1p1_to_p3(&u, &t);
4603            ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4604        } else if (bslide[i] < 0) {
4605            ge_p1p1_to_p3(&u, &t);
4606            ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4607        }
4608
4609        ge_p1p1_to_p2(r, &t);
4610    }
4611}
4612
4613/*
4614 * The set of scalars is \Z/l
4615 * where l = 2^252 + 27742317777372353535851937790883648493.
4616 *
4617 * Input:
4618 *   s[0]+256*s[1]+...+256^63*s[63] = s
4619 *
4620 * Output:
4621 *   s[0]+256*s[1]+...+256^31*s[31] = s mod l
4622 *   where l = 2^252 + 27742317777372353535851937790883648493.
4623 *   Overwrites s in place.
4624*/
4625static void x25519_sc_reduce(uint8_t *s)
4626{
4627    int64_t s0  = kBottom21Bits &  load_3(s);
4628    int64_t s1  = kBottom21Bits & (load_4(s +  2) >> 5);
4629    int64_t s2  = kBottom21Bits & (load_3(s +  5) >> 2);
4630    int64_t s3  = kBottom21Bits & (load_4(s +  7) >> 7);
4631    int64_t s4  = kBottom21Bits & (load_4(s + 10) >> 4);
4632    int64_t s5  = kBottom21Bits & (load_3(s + 13) >> 1);
4633    int64_t s6  = kBottom21Bits & (load_4(s + 15) >> 6);
4634    int64_t s7  = kBottom21Bits & (load_3(s + 18) >> 3);
4635    int64_t s8  = kBottom21Bits &  load_3(s + 21);
4636    int64_t s9  = kBottom21Bits & (load_4(s + 23) >> 5);
4637    int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4638    int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4639    int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4640    int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4641    int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4642    int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4643    int64_t s16 = kBottom21Bits &  load_3(s + 42);
4644    int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4645    int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4646    int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4647    int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4648    int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4649    int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4650    int64_t s23 =                 (load_4(s + 60) >> 3);
4651    int64_t carry0;
4652    int64_t carry1;
4653    int64_t carry2;
4654    int64_t carry3;
4655    int64_t carry4;
4656    int64_t carry5;
4657    int64_t carry6;
4658    int64_t carry7;
4659    int64_t carry8;
4660    int64_t carry9;
4661    int64_t carry10;
4662    int64_t carry11;
4663    int64_t carry12;
4664    int64_t carry13;
4665    int64_t carry14;
4666    int64_t carry15;
4667    int64_t carry16;
4668
4669    s11 += s23 * 666643;
4670    s12 += s23 * 470296;
4671    s13 += s23 * 654183;
4672    s14 -= s23 * 997805;
4673    s15 += s23 * 136657;
4674    s16 -= s23 * 683901;
4675    s23  = 0;
4676
4677    s10 += s22 * 666643;
4678    s11 += s22 * 470296;
4679    s12 += s22 * 654183;
4680    s13 -= s22 * 997805;
4681    s14 += s22 * 136657;
4682    s15 -= s22 * 683901;
4683    s22  = 0;
4684
4685    s9  += s21 * 666643;
4686    s10 += s21 * 470296;
4687    s11 += s21 * 654183;
4688    s12 -= s21 * 997805;
4689    s13 += s21 * 136657;
4690    s14 -= s21 * 683901;
4691    s21  = 0;
4692
4693    s8  += s20 * 666643;
4694    s9  += s20 * 470296;
4695    s10 += s20 * 654183;
4696    s11 -= s20 * 997805;
4697    s12 += s20 * 136657;
4698    s13 -= s20 * 683901;
4699    s20  = 0;
4700
4701    s7  += s19 * 666643;
4702    s8  += s19 * 470296;
4703    s9  += s19 * 654183;
4704    s10 -= s19 * 997805;
4705    s11 += s19 * 136657;
4706    s12 -= s19 * 683901;
4707    s19  = 0;
4708
4709    s6  += s18 * 666643;
4710    s7  += s18 * 470296;
4711    s8  += s18 * 654183;
4712    s9  -= s18 * 997805;
4713    s10 += s18 * 136657;
4714    s11 -= s18 * 683901;
4715    s18  = 0;
4716
4717    carry6 = (s6 + (1 << 20)) >> 21;
4718    s7  += carry6;
4719    s6  -= carry6 * (1 << 21);
4720    carry8 = (s8 + (1 << 20)) >> 21;
4721    s9  += carry8;
4722    s8  -= carry8 * (1 << 21);
4723    carry10 = (s10 + (1 << 20)) >> 21;
4724    s11 += carry10;
4725    s10 -= carry10 * (1 << 21);
4726    carry12 = (s12 + (1 << 20)) >> 21;
4727    s13 += carry12;
4728    s12 -= carry12 * (1 << 21);
4729    carry14 = (s14 + (1 << 20)) >> 21;
4730    s15 += carry14;
4731    s14 -= carry14 * (1 << 21);
4732    carry16 = (s16 + (1 << 20)) >> 21;
4733    s17 += carry16;
4734    s16 -= carry16 * (1 << 21);
4735
4736    carry7 = (s7 + (1 << 20)) >> 21;
4737    s8  += carry7;
4738    s7  -= carry7 * (1 << 21);
4739    carry9 = (s9 + (1 << 20)) >> 21;
4740    s10 += carry9;
4741    s9  -= carry9 * (1 << 21);
4742    carry11 = (s11 + (1 << 20)) >> 21;
4743    s12 += carry11;
4744    s11 -= carry11 * (1 << 21);
4745    carry13 = (s13 + (1 << 20)) >> 21;
4746    s14 += carry13;
4747    s13 -= carry13 * (1 << 21);
4748    carry15 = (s15 + (1 << 20)) >> 21;
4749    s16 += carry15;
4750    s15 -= carry15 * (1 << 21);
4751
4752    s5  += s17 * 666643;
4753    s6  += s17 * 470296;
4754    s7  += s17 * 654183;
4755    s8  -= s17 * 997805;
4756    s9  += s17 * 136657;
4757    s10 -= s17 * 683901;
4758    s17  = 0;
4759
4760    s4  += s16 * 666643;
4761    s5  += s16 * 470296;
4762    s6  += s16 * 654183;
4763    s7  -= s16 * 997805;
4764    s8  += s16 * 136657;
4765    s9  -= s16 * 683901;
4766    s16  = 0;
4767
4768    s3  += s15 * 666643;
4769    s4  += s15 * 470296;
4770    s5  += s15 * 654183;
4771    s6  -= s15 * 997805;
4772    s7  += s15 * 136657;
4773    s8  -= s15 * 683901;
4774    s15  = 0;
4775
4776    s2  += s14 * 666643;
4777    s3  += s14 * 470296;
4778    s4  += s14 * 654183;
4779    s5  -= s14 * 997805;
4780    s6  += s14 * 136657;
4781    s7  -= s14 * 683901;
4782    s14  = 0;
4783
4784    s1  += s13 * 666643;
4785    s2  += s13 * 470296;
4786    s3  += s13 * 654183;
4787    s4  -= s13 * 997805;
4788    s5  += s13 * 136657;
4789    s6  -= s13 * 683901;
4790    s13  = 0;
4791
4792    s0  += s12 * 666643;
4793    s1  += s12 * 470296;
4794    s2  += s12 * 654183;
4795    s3  -= s12 * 997805;
4796    s4  += s12 * 136657;
4797    s5  -= s12 * 683901;
4798    s12  = 0;
4799
4800    carry0 = (s0 + (1 << 20)) >> 21;
4801    s1  += carry0;
4802    s0  -= carry0 * (1 << 21);
4803    carry2 = (s2 + (1 << 20)) >> 21;
4804    s3  += carry2;
4805    s2  -= carry2 * (1 << 21);
4806    carry4 = (s4 + (1 << 20)) >> 21;
4807    s5  += carry4;
4808    s4  -= carry4 * (1 << 21);
4809    carry6 = (s6 + (1 << 20)) >> 21;
4810    s7 += carry6;
4811    s6 -= carry6 * (1 << 21);
4812    carry8 = (s8 + (1 << 20)) >> 21;
4813    s9  += carry8;
4814    s8  -= carry8 * (1 << 21);
4815    carry10 = (s10 + (1 << 20)) >> 21;
4816    s11 += carry10;
4817    s10 -= carry10 * (1 << 21);
4818
4819    carry1 = (s1 + (1 << 20)) >> 21;
4820    s2  += carry1;
4821    s1  -= carry1 * (1 << 21);
4822    carry3 = (s3 + (1 << 20)) >> 21;
4823    s4  += carry3;
4824    s3  -= carry3 * (1 << 21);
4825    carry5 = (s5 + (1 << 20)) >> 21;
4826    s6  += carry5;
4827    s5  -= carry5 * (1 << 21);
4828    carry7 = (s7 + (1 << 20)) >> 21;
4829    s8  += carry7;
4830    s7  -= carry7 * (1 << 21);
4831    carry9 = (s9 + (1 << 20)) >> 21;
4832    s10 += carry9;
4833    s9  -= carry9 * (1 << 21);
4834    carry11 = (s11 + (1 << 20)) >> 21;
4835    s12 += carry11;
4836    s11 -= carry11 * (1 << 21);
4837
4838    s0  += s12 * 666643;
4839    s1  += s12 * 470296;
4840    s2  += s12 * 654183;
4841    s3  -= s12 * 997805;
4842    s4  += s12 * 136657;
4843    s5  -= s12 * 683901;
4844    s12  = 0;
4845
4846    carry0 = s0 >> 21;
4847    s1  += carry0;
4848    s0  -= carry0 * (1 << 21);
4849    carry1 = s1 >> 21;
4850    s2  += carry1;
4851    s1  -= carry1 * (1 << 21);
4852    carry2 = s2 >> 21;
4853    s3  += carry2;
4854    s2  -= carry2 * (1 << 21);
4855    carry3 = s3 >> 21;
4856    s4  += carry3;
4857    s3  -= carry3 * (1 << 21);
4858    carry4 = s4 >> 21;
4859    s5  += carry4;
4860    s4  -= carry4 * (1 << 21);
4861    carry5 = s5 >> 21;
4862    s6  += carry5;
4863    s5  -= carry5 * (1 << 21);
4864    carry6 = s6 >> 21;
4865    s7  += carry6;
4866    s6  -= carry6 * (1 << 21);
4867    carry7 = s7 >> 21;
4868    s8  += carry7;
4869    s7  -= carry7 * (1 << 21);
4870    carry8 = s8 >> 21;
4871    s9  += carry8;
4872    s8  -= carry8 * (1 << 21);
4873    carry9 = s9 >> 21;
4874    s10 += carry9;
4875    s9  -= carry9 * (1 << 21);
4876    carry10 = s10 >> 21;
4877    s11 += carry10;
4878    s10 -= carry10 * (1 << 21);
4879    carry11 = s11 >> 21;
4880    s12 += carry11;
4881    s11 -= carry11 * (1 << 21);
4882
4883    s0  += s12 * 666643;
4884    s1  += s12 * 470296;
4885    s2  += s12 * 654183;
4886    s3  -= s12 * 997805;
4887    s4  += s12 * 136657;
4888    s5  -= s12 * 683901;
4889    s12  = 0;
4890
4891    carry0 = s0 >> 21;
4892    s1  += carry0;
4893    s0  -= carry0 * (1 << 21);
4894    carry1 = s1 >> 21;
4895    s2  += carry1;
4896    s1  -= carry1 * (1 << 21);
4897    carry2 = s2 >> 21;
4898    s3  += carry2;
4899    s2  -= carry2 * (1 << 21);
4900    carry3 = s3 >> 21;
4901    s4  += carry3;
4902    s3  -= carry3 * (1 << 21);
4903    carry4 = s4 >> 21;
4904    s5  += carry4;
4905    s4  -= carry4 * (1 << 21);
4906    carry5 = s5 >> 21;
4907    s6  += carry5;
4908    s5  -= carry5 * (1 << 21);
4909    carry6 = s6 >> 21;
4910    s7  += carry6;
4911    s6  -= carry6 * (1 << 21);
4912    carry7 = s7 >> 21;
4913    s8  += carry7;
4914    s7  -= carry7 * (1 << 21);
4915    carry8 = s8 >> 21;
4916    s9  += carry8;
4917    s8  -= carry8 * (1 << 21);
4918    carry9 = s9 >> 21;
4919    s10 += carry9;
4920    s9  -= carry9 * (1 << 21);
4921    carry10 = s10 >> 21;
4922    s11 += carry10;
4923    s10 -= carry10 * (1 << 21);
4924
4925    s[ 0] = (uint8_t) (s0  >>  0);
4926    s[ 1] = (uint8_t) (s0  >>  8);
4927    s[ 2] = (uint8_t)((s0  >> 16) | (s1  <<  5));
4928    s[ 3] = (uint8_t) (s1  >>  3);
4929    s[ 4] = (uint8_t) (s1  >> 11);
4930    s[ 5] = (uint8_t)((s1  >> 19) | (s2  <<  2));
4931    s[ 6] = (uint8_t) (s2  >>  6);
4932    s[ 7] = (uint8_t)((s2  >> 14) | (s3  <<  7));
4933    s[ 8] = (uint8_t) (s3  >>  1);
4934    s[ 9] = (uint8_t) (s3  >>  9);
4935    s[10] = (uint8_t)((s3  >> 17) | (s4  <<  4));
4936    s[11] = (uint8_t) (s4  >>  4);
4937    s[12] = (uint8_t) (s4  >> 12);
4938    s[13] = (uint8_t)((s4  >> 20) | (s5  <<  1));
4939    s[14] = (uint8_t) (s5  >>  7);
4940    s[15] = (uint8_t)((s5  >> 15) | (s6  <<  6));
4941    s[16] = (uint8_t) (s6  >>  2);
4942    s[17] = (uint8_t) (s6  >> 10);
4943    s[18] = (uint8_t)((s6  >> 18) | (s7  <<  3));
4944    s[19] = (uint8_t) (s7  >>  5);
4945    s[20] = (uint8_t) (s7  >> 13);
4946    s[21] = (uint8_t) (s8  >>  0);
4947    s[22] = (uint8_t) (s8  >>  8);
4948    s[23] = (uint8_t)((s8  >> 16) | (s9  <<  5));
4949    s[24] = (uint8_t) (s9  >>  3);
4950    s[25] = (uint8_t) (s9  >> 11);
4951    s[26] = (uint8_t)((s9  >> 19) | (s10 <<  2));
4952    s[27] = (uint8_t) (s10 >>  6);
4953    s[28] = (uint8_t)((s10 >> 14) | (s11 <<  7));
4954    s[29] = (uint8_t) (s11 >>  1);
4955    s[30] = (uint8_t) (s11 >>  9);
4956    s[31] = (uint8_t) (s11 >> 17);
4957}
4958
4959/*
4960 * Input:
4961 *   a[0]+256*a[1]+...+256^31*a[31] = a
4962 *   b[0]+256*b[1]+...+256^31*b[31] = b
4963 *   c[0]+256*c[1]+...+256^31*c[31] = c
4964 *
4965 * Output:
4966 *   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
4967 *   where l = 2^252 + 27742317777372353535851937790883648493.
4968 */
4969static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
4970                      const uint8_t *c)
4971{
4972    int64_t a0  = kBottom21Bits &  load_3(a);
4973    int64_t a1  = kBottom21Bits & (load_4(a +  2) >> 5);
4974    int64_t a2  = kBottom21Bits & (load_3(a +  5) >> 2);
4975    int64_t a3  = kBottom21Bits & (load_4(a +  7) >> 7);
4976    int64_t a4  = kBottom21Bits & (load_4(a + 10) >> 4);
4977    int64_t a5  = kBottom21Bits & (load_3(a + 13) >> 1);
4978    int64_t a6  = kBottom21Bits & (load_4(a + 15) >> 6);
4979    int64_t a7  = kBottom21Bits & (load_3(a + 18) >> 3);
4980    int64_t a8  = kBottom21Bits &  load_3(a + 21);
4981    int64_t a9  = kBottom21Bits & (load_4(a + 23) >> 5);
4982    int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
4983    int64_t a11 =                 (load_4(a + 28) >> 7);
4984    int64_t b0  = kBottom21Bits &  load_3(b);
4985    int64_t b1  = kBottom21Bits & (load_4(b +  2) >> 5);
4986    int64_t b2  = kBottom21Bits & (load_3(b +  5) >> 2);
4987    int64_t b3  = kBottom21Bits & (load_4(b +  7) >> 7);
4988    int64_t b4  = kBottom21Bits & (load_4(b + 10) >> 4);
4989    int64_t b5  = kBottom21Bits & (load_3(b + 13) >> 1);
4990    int64_t b6  = kBottom21Bits & (load_4(b + 15) >> 6);
4991    int64_t b7  = kBottom21Bits & (load_3(b + 18) >> 3);
4992    int64_t b8  = kBottom21Bits &  load_3(b + 21);
4993    int64_t b9  = kBottom21Bits & (load_4(b + 23) >> 5);
4994    int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
4995    int64_t b11 =                 (load_4(b + 28) >> 7);
4996    int64_t c0  = kBottom21Bits &  load_3(c);
4997    int64_t c1  = kBottom21Bits & (load_4(c +  2) >> 5);
4998    int64_t c2  = kBottom21Bits & (load_3(c +  5) >> 2);
4999    int64_t c3  = kBottom21Bits & (load_4(c +  7) >> 7);
5000    int64_t c4  = kBottom21Bits & (load_4(c + 10) >> 4);
5001    int64_t c5  = kBottom21Bits & (load_3(c + 13) >> 1);
5002    int64_t c6  = kBottom21Bits & (load_4(c + 15) >> 6);
5003    int64_t c7  = kBottom21Bits & (load_3(c + 18) >> 3);
5004    int64_t c8  = kBottom21Bits &  load_3(c + 21);
5005    int64_t c9  = kBottom21Bits & (load_4(c + 23) >> 5);
5006    int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
5007    int64_t c11 =                 (load_4(c + 28) >> 7);
5008    int64_t s0;
5009    int64_t s1;
5010    int64_t s2;
5011    int64_t s3;
5012    int64_t s4;
5013    int64_t s5;
5014    int64_t s6;
5015    int64_t s7;
5016    int64_t s8;
5017    int64_t s9;
5018    int64_t s10;
5019    int64_t s11;
5020    int64_t s12;
5021    int64_t s13;
5022    int64_t s14;
5023    int64_t s15;
5024    int64_t s16;
5025    int64_t s17;
5026    int64_t s18;
5027    int64_t s19;
5028    int64_t s20;
5029    int64_t s21;
5030    int64_t s22;
5031    int64_t s23;
5032    int64_t carry0;
5033    int64_t carry1;
5034    int64_t carry2;
5035    int64_t carry3;
5036    int64_t carry4;
5037    int64_t carry5;
5038    int64_t carry6;
5039    int64_t carry7;
5040    int64_t carry8;
5041    int64_t carry9;
5042    int64_t carry10;
5043    int64_t carry11;
5044    int64_t carry12;
5045    int64_t carry13;
5046    int64_t carry14;
5047    int64_t carry15;
5048    int64_t carry16;
5049    int64_t carry17;
5050    int64_t carry18;
5051    int64_t carry19;
5052    int64_t carry20;
5053    int64_t carry21;
5054    int64_t carry22;
5055
5056    s0  = c0   +   a0 * b0;
5057    s1  = c1   +   a0 * b1   +   a1 * b0;
5058    s2  = c2   +   a0 * b2   +   a1 * b1   +   a2 * b0;
5059    s3  = c3   +   a0 * b3   +   a1 * b2   +   a2 * b1  +   a3 * b0;
5060    s4  = c4   +   a0 * b4   +   a1 * b3   +   a2 * b2  +   a3 * b1  +   a4 * b0;
5061    s5  = c5   +   a0 * b5   +   a1 * b4   +   a2 * b3  +   a3 * b2  +   a4 * b1  +   a5 * b0;
5062    s6  = c6   +   a0 * b6   +   a1 * b5   +   a2 * b4  +   a3 * b3  +   a4 * b2  +   a5 * b1 +   a6 * b0;
5063    s7  = c7   +   a0 * b7   +   a1 * b6   +   a2 * b5  +   a3 * b4  +   a4 * b3  +   a5 * b2 +   a6 * b1   +   a7 * b0;
5064    s8  = c8   +   a0 * b8   +   a1 * b7   +   a2 * b6  +   a3 * b5  +   a4 * b4  +   a5 * b3 +   a6 * b2   +   a7 * b1   +   a8 * b0;
5065    s9  = c9   +   a0 * b9   +   a1 * b8   +   a2 * b7  +   a3 * b6  +   a4 * b5  +   a5 * b4 +   a6 * b3   +   a7 * b2   +   a8 * b1  +   a9 * b0;
5066    s10 = c10  +   a0 * b10  +   a1 * b9   +   a2 * b8  +   a3 * b7  +   a4 * b6  +   a5 * b5 +   a6 * b4   +   a7 * b3   +   a8 * b2  +   a9 * b1  +  a10 * b0;
5067    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;
5068    s12 =          a1 * b11  +   a2 * b10  +   a3 * b9  +   a4 * b8  +   a5 * b7  +   a6 * b6 +   a7 * b5   +   a8 * b4   +   a9 * b3  +  a10 * b2  +  a11 * b1;
5069    s13 =          a2 * b11  +   a3 * b10  +   a4 * b9  +   a5 * b8  +   a6 * b7  +   a7 * b6 +   a8 * b5   +   a9 * b4   +  a10 * b3  +  a11 * b2;
5070    s14 =          a3 * b11  +   a4 * b10  +   a5 * b9  +   a6 * b8  +   a7 * b7  +   a8 * b6 +   a9 * b5   +  a10 * b4   +  a11 * b3;
5071    s15 =          a4 * b11  +   a5 * b10  +   a6 * b9  +   a7 * b8  +   a8 * b7  +   a9 * b6 +  a10 * b5   +  a11 * b4;
5072    s16 =          a5 * b11  +   a6 * b10  +   a7 * b9  +   a8 * b8  +   a9 * b7  +  a10 * b6 +  a11 * b5;
5073    s17 =          a6 * b11  +   a7 * b10  +   a8 * b9  +   a9 * b8  +  a10 * b7  +  a11 * b6;
5074    s18 =          a7 * b11  +   a8 * b10  +   a9 * b9  +  a10 * b8  +  a11 * b7;
5075    s19 =          a8 * b11  +   a9 * b10  +  a10 * b9  +  a11 * b8;
5076    s20 =          a9 * b11  +  a10 * b10  +  a11 * b9;
5077    s21 =         a10 * b11  +  a11 * b10;
5078    s22 =         a11 * b11;
5079    s23 =         0;
5080
5081    carry0 = (s0 + (1 << 20)) >> 21;
5082    s1  += carry0;
5083    s0  -= carry0 * (1 << 21);
5084    carry2 = (s2 + (1 << 20)) >> 21;
5085    s3  += carry2;
5086    s2  -= carry2 * (1 << 21);
5087    carry4 = (s4 + (1 << 20)) >> 21;
5088    s5  += carry4;
5089    s4  -= carry4 * (1 << 21);
5090    carry6 = (s6 + (1 << 20)) >> 21;
5091    s7  += carry6;
5092    s6  -= carry6 * (1 << 21);
5093    carry8 = (s8 + (1 << 20)) >> 21;
5094    s9  += carry8;
5095    s8  -= carry8 * (1 << 21);
5096    carry10 = (s10 + (1 << 20)) >> 21;
5097    s11 += carry10;
5098    s10 -= carry10 * (1 << 21);
5099    carry12 = (s12 + (1 << 20)) >> 21;
5100    s13 += carry12;
5101    s12 -= carry12 * (1 << 21);
5102    carry14 = (s14 + (1 << 20)) >> 21;
5103    s15 += carry14;
5104    s14 -= carry14 * (1 << 21);
5105    carry16 = (s16 + (1 << 20)) >> 21;
5106    s17 += carry16;
5107    s16 -= carry16 * (1 << 21);
5108    carry18 = (s18 + (1 << 20)) >> 21;
5109    s19 += carry18;
5110    s18 -= carry18 * (1 << 21);
5111    carry20 = (s20 + (1 << 20)) >> 21;
5112    s21 += carry20;
5113    s20 -= carry20 * (1 << 21);
5114    carry22 = (s22 + (1 << 20)) >> 21;
5115    s23 += carry22;
5116    s22 -= carry22 * (1 << 21);
5117
5118    carry1 = (s1 + (1 << 20)) >> 21;
5119    s2  += carry1;
5120    s1  -= carry1 * (1 << 21);
5121    carry3 = (s3 + (1 << 20)) >> 21;
5122    s4  += carry3;
5123    s3  -= carry3 * (1 << 21);
5124    carry5 = (s5 + (1 << 20)) >> 21;
5125    s6  += carry5;
5126    s5  -= carry5 * (1 << 21);
5127    carry7 = (s7 + (1 << 20)) >> 21;
5128    s8  += carry7;
5129    s7  -= carry7 * (1 << 21);
5130    carry9 = (s9 + (1 << 20)) >> 21;
5131    s10 += carry9;
5132    s9  -= carry9 * (1 << 21);
5133    carry11 = (s11 + (1 << 20)) >> 21;
5134    s12 += carry11;
5135    s11 -= carry11 * (1 << 21);
5136    carry13 = (s13 + (1 << 20)) >> 21;
5137    s14 += carry13;
5138    s13 -= carry13 * (1 << 21);
5139    carry15 = (s15 + (1 << 20)) >> 21;
5140    s16 += carry15;
5141    s15 -= carry15 * (1 << 21);
5142    carry17 = (s17 + (1 << 20)) >> 21;
5143    s18 += carry17;
5144    s17 -= carry17 * (1 << 21);
5145    carry19 = (s19 + (1 << 20)) >> 21;
5146    s20 += carry19;
5147    s19 -= carry19 * (1 << 21);
5148    carry21 = (s21 + (1 << 20)) >> 21;
5149    s22 += carry21;
5150    s21 -= carry21 * (1 << 21);
5151
5152    s11 += s23 * 666643;
5153    s12 += s23 * 470296;
5154    s13 += s23 * 654183;
5155    s14 -= s23 * 997805;
5156    s15 += s23 * 136657;
5157    s16 -= s23 * 683901;
5158    s23  = 0;
5159
5160    s10 += s22 * 666643;
5161    s11 += s22 * 470296;
5162    s12 += s22 * 654183;
5163    s13 -= s22 * 997805;
5164    s14 += s22 * 136657;
5165    s15 -= s22 * 683901;
5166    s22  = 0;
5167
5168    s9  += s21 * 666643;
5169    s10 += s21 * 470296;
5170    s11 += s21 * 654183;
5171    s12 -= s21 * 997805;
5172    s13 += s21 * 136657;
5173    s14 -= s21 * 683901;
5174    s21  = 0;
5175
5176    s8  += s20 * 666643;
5177    s9  += s20 * 470296;
5178    s10 += s20 * 654183;
5179    s11 -= s20 * 997805;
5180    s12 += s20 * 136657;
5181    s13 -= s20 * 683901;
5182    s20  = 0;
5183
5184    s7  += s19 * 666643;
5185    s8  += s19 * 470296;
5186    s9  += s19 * 654183;
5187    s10 -= s19 * 997805;
5188    s11 += s19 * 136657;
5189    s12 -= s19 * 683901;
5190    s19  = 0;
5191
5192    s6  += s18 * 666643;
5193    s7  += s18 * 470296;
5194    s8  += s18 * 654183;
5195    s9  -= s18 * 997805;
5196    s10 += s18 * 136657;
5197    s11 -= s18 * 683901;
5198    s18  = 0;
5199
5200    carry6 = (s6 + (1 << 20)) >> 21;
5201    s7  += carry6;
5202    s6  -= carry6 * (1 << 21);
5203    carry8 = (s8 + (1 << 20)) >> 21;
5204    s9  += carry8;
5205    s8  -= carry8 * (1 << 21);
5206    carry10 = (s10 + (1 << 20)) >> 21;
5207    s11 += carry10;
5208    s10 -= carry10 * (1 << 21);
5209    carry12 = (s12 + (1 << 20)) >> 21;
5210    s13 += carry12;
5211    s12 -= carry12 * (1 << 21);
5212    carry14 = (s14 + (1 << 20)) >> 21;
5213    s15 += carry14;
5214    s14 -= carry14 * (1 << 21);
5215    carry16 = (s16 + (1 << 20)) >> 21;
5216    s17 += carry16;
5217    s16 -= carry16 * (1 << 21);
5218
5219    carry7 = (s7 + (1 << 20)) >> 21;
5220    s8  += carry7;
5221    s7  -= carry7 * (1 << 21);
5222    carry9 = (s9 + (1 << 20)) >> 21;
5223    s10 += carry9;
5224    s9  -= carry9 * (1 << 21);
5225    carry11 = (s11 + (1 << 20)) >> 21;
5226    s12 += carry11;
5227    s11 -= carry11 * (1 << 21);
5228    carry13 = (s13 + (1 << 20)) >> 21;
5229    s14 += carry13;
5230    s13 -= carry13 * (1 << 21);
5231    carry15 = (s15 + (1 << 20)) >> 21;
5232    s16 += carry15;
5233    s15 -= carry15 * (1 << 21);
5234
5235    s5  += s17 * 666643;
5236    s6  += s17 * 470296;
5237    s7  += s17 * 654183;
5238    s8  -= s17 * 997805;
5239    s9  += s17 * 136657;
5240    s10 -= s17 * 683901;
5241    s17  = 0;
5242
5243    s4  += s16 * 666643;
5244    s5  += s16 * 470296;
5245    s6  += s16 * 654183;
5246    s7  -= s16 * 997805;
5247    s8  += s16 * 136657;
5248    s9  -= s16 * 683901;
5249    s16  = 0;
5250
5251    s3  += s15 * 666643;
5252    s4  += s15 * 470296;
5253    s5  += s15 * 654183;
5254    s6  -= s15 * 997805;
5255    s7  += s15 * 136657;
5256    s8  -= s15 * 683901;
5257    s15  = 0;
5258
5259    s2  += s14 * 666643;
5260    s3  += s14 * 470296;
5261    s4  += s14 * 654183;
5262    s5  -= s14 * 997805;
5263    s6  += s14 * 136657;
5264    s7  -= s14 * 683901;
5265    s14  = 0;
5266
5267    s1  += s13 * 666643;
5268    s2  += s13 * 470296;
5269    s3  += s13 * 654183;
5270    s4  -= s13 * 997805;
5271    s5  += s13 * 136657;
5272    s6  -= s13 * 683901;
5273    s13  = 0;
5274
5275    s0  += s12 * 666643;
5276    s1  += s12 * 470296;
5277    s2  += s12 * 654183;
5278    s3  -= s12 * 997805;
5279    s4  += s12 * 136657;
5280    s5  -= s12 * 683901;
5281    s12 = 0;
5282
5283    carry0 = (s0 + (1 << 20)) >> 21;
5284    s1  += carry0;
5285    s0  -= carry0 * (1 << 21);
5286    carry2 = (s2 + (1 << 20)) >> 21;
5287    s3  += carry2;
5288    s2  -= carry2 * (1 << 21);
5289    carry4 = (s4 + (1 << 20)) >> 21;
5290    s5  += carry4;
5291    s4  -= carry4 * (1 << 21);
5292    carry6 = (s6 + (1 << 20)) >> 21;
5293    s7  += carry6;
5294    s6  -= carry6 * (1 << 21);
5295    carry8 = (s8 + (1 << 20)) >> 21;
5296    s9  += carry8;
5297    s8  -= carry8 * (1 << 21);
5298    carry10 = (s10 + (1 << 20)) >> 21;
5299    s11 += carry10;
5300    s10 -= carry10 * (1 << 21);
5301
5302    carry1 = (s1 + (1 << 20)) >> 21;
5303    s2  += carry1;
5304    s1  -= carry1 * (1 << 21);
5305    carry3 = (s3 + (1 << 20)) >> 21;
5306    s4  += carry3;
5307    s3  -= carry3 * (1 << 21);
5308    carry5 = (s5 + (1 << 20)) >> 21;
5309    s6  += carry5;
5310    s5  -= carry5 * (1 << 21);
5311    carry7 = (s7 + (1 << 20)) >> 21;
5312    s8  += carry7;
5313    s7  -= carry7 * (1 << 21);
5314    carry9 = (s9 + (1 << 20)) >> 21;
5315    s10 += carry9;
5316    s9  -= carry9 * (1 << 21);
5317    carry11 = (s11 + (1 << 20)) >> 21;
5318    s12 += carry11;
5319    s11 -= carry11 * (1 << 21);
5320
5321    s0  += s12 * 666643;
5322    s1  += s12 * 470296;
5323    s2  += s12 * 654183;
5324    s3  -= s12 * 997805;
5325    s4  += s12 * 136657;
5326    s5  -= s12 * 683901;
5327    s12  = 0;
5328
5329    carry0 = s0 >> 21;
5330    s1  += carry0;
5331    s0  -= carry0 * (1 << 21);
5332    carry1 = s1 >> 21;
5333    s2  += carry1;
5334    s1  -= carry1 * (1 << 21);
5335    carry2 = s2 >> 21;
5336    s3  += carry2;
5337    s2  -= carry2 * (1 << 21);
5338    carry3 = s3 >> 21;
5339    s4  += carry3;
5340    s3  -= carry3 * (1 << 21);
5341    carry4 = s4 >> 21;
5342    s5  += carry4;
5343    s4  -= carry4 * (1 << 21);
5344    carry5 = s5 >> 21;
5345    s6  += carry5;
5346    s5  -= carry5 * (1 << 21);
5347    carry6 = s6 >> 21;
5348    s7  += carry6;
5349    s6  -= carry6 * (1 << 21);
5350    carry7 = s7 >> 21;
5351    s8  += carry7;
5352    s7  -= carry7 * (1 << 21);
5353    carry8 = s8 >> 21;
5354    s9  += carry8;
5355    s8  -= carry8 * (1 << 21);
5356    carry9 = s9 >> 21;
5357    s10 += carry9;
5358    s9  -= carry9 * (1 << 21);
5359    carry10 = s10 >> 21;
5360    s11 += carry10;
5361    s10 -= carry10 * (1 << 21);
5362    carry11 = s11 >> 21;
5363    s12 += carry11;
5364    s11 -= carry11 * (1 << 21);
5365
5366    s0  += s12 * 666643;
5367    s1  += s12 * 470296;
5368    s2  += s12 * 654183;
5369    s3  -= s12 * 997805;
5370    s4  += s12 * 136657;
5371    s5  -= s12 * 683901;
5372    s12  = 0;
5373
5374    carry0 = s0 >> 21;
5375    s1  += carry0;
5376    s0  -= carry0 * (1 << 21);
5377    carry1 = s1 >> 21;
5378    s2  += carry1;
5379    s1  -= carry1 * (1 << 21);
5380    carry2 = s2 >> 21;
5381    s3  += carry2;
5382    s2  -= carry2 * (1 << 21);
5383    carry3 = s3 >> 21;
5384    s4  += carry3;
5385    s3  -= carry3 * (1 << 21);
5386    carry4 = s4 >> 21;
5387    s5  += carry4;
5388    s4  -= carry4 * (1 << 21);
5389    carry5 = s5 >> 21;
5390    s6  += carry5;
5391    s5  -= carry5 * (1 << 21);
5392    carry6 = s6 >> 21;
5393    s7  += carry6;
5394    s6  -= carry6 * (1 << 21);
5395    carry7 = s7 >> 21;
5396    s8  += carry7;
5397    s7  -= carry7 * (1 << 21);
5398    carry8 = s8 >> 21;
5399    s9  += carry8;
5400    s8  -= carry8 * (1 << 21);
5401    carry9 = s9 >> 21;
5402    s10 += carry9;
5403    s9  -= carry9 * (1 << 21);
5404    carry10 = s10 >> 21;
5405    s11 += carry10;
5406    s10 -= carry10 * (1 << 21);
5407
5408    s[ 0] = (uint8_t) (s0  >>  0);
5409    s[ 1] = (uint8_t) (s0  >>  8);
5410    s[ 2] = (uint8_t)((s0  >> 16) | (s1 << 5));
5411    s[ 3] = (uint8_t) (s1  >>  3);
5412    s[ 4] = (uint8_t) (s1  >> 11);
5413    s[ 5] = (uint8_t)((s1  >> 19) | (s2 << 2));
5414    s[ 6] = (uint8_t) (s2  >>  6);
5415    s[ 7] = (uint8_t)((s2  >> 14) | (s3 << 7));
5416    s[ 8] = (uint8_t) (s3  >>  1);
5417    s[ 9] = (uint8_t) (s3  >>  9);
5418    s[10] = (uint8_t)((s3  >> 17) | (s4 << 4));
5419    s[11] = (uint8_t) (s4  >>  4);
5420    s[12] = (uint8_t) (s4  >> 12);
5421    s[13] = (uint8_t)((s4  >> 20) | (s5 << 1));
5422    s[14] = (uint8_t) (s5  >>  7);
5423    s[15] = (uint8_t)((s5  >> 15) | (s6 << 6));
5424    s[16] = (uint8_t) (s6  >>  2);
5425    s[17] = (uint8_t) (s6  >> 10);
5426    s[18] = (uint8_t)((s6  >> 18) | (s7 << 3));
5427    s[19] = (uint8_t) (s7  >>  5);
5428    s[20] = (uint8_t) (s7  >> 13);
5429    s[21] = (uint8_t) (s8  >>  0);
5430    s[22] = (uint8_t) (s8  >>  8);
5431    s[23] = (uint8_t)((s8  >> 16) | (s9 << 5));
5432    s[24] = (uint8_t) (s9  >>  3);
5433    s[25] = (uint8_t) (s9  >> 11);
5434    s[26] = (uint8_t)((s9  >> 19) | (s10 << 2));
5435    s[27] = (uint8_t) (s10 >>  6);
5436    s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
5437    s[29] = (uint8_t) (s11 >>  1);
5438    s[30] = (uint8_t) (s11 >>  9);
5439    s[31] = (uint8_t) (s11 >> 17);
5440}
5441
5442int
5443ossl_ed25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
5444                  const uint8_t public_key[32], const uint8_t private_key[32],
5445                  OSSL_LIB_CTX *libctx, const char *propq)
5446{
5447    uint8_t az[SHA512_DIGEST_LENGTH];
5448    uint8_t nonce[SHA512_DIGEST_LENGTH];
5449    ge_p3 R;
5450    uint8_t hram[SHA512_DIGEST_LENGTH];
5451    EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5452    EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
5453    unsigned int sz;
5454    int res = 0;
5455
5456    if (sha512 == NULL || hash_ctx == NULL)
5457        goto err;
5458
5459    if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5460        || !EVP_DigestUpdate(hash_ctx, private_key, 32)
5461        || !EVP_DigestFinal_ex(hash_ctx, az, &sz))
5462        goto err;
5463
5464    az[0] &= 248;
5465    az[31] &= 63;
5466    az[31] |= 64;
5467
5468    if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5469        || !EVP_DigestUpdate(hash_ctx, az + 32, 32)
5470        || !EVP_DigestUpdate(hash_ctx, message, message_len)
5471        || !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
5472        goto err;
5473
5474    x25519_sc_reduce(nonce);
5475    ge_scalarmult_base(&R, nonce);
5476    ge_p3_tobytes(out_sig, &R);
5477
5478    if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5479        || !EVP_DigestUpdate(hash_ctx, out_sig, 32)
5480        || !EVP_DigestUpdate(hash_ctx, public_key, 32)
5481        || !EVP_DigestUpdate(hash_ctx, message, message_len)
5482        || !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
5483        goto err;
5484
5485    x25519_sc_reduce(hram);
5486    sc_muladd(out_sig + 32, hram, az, nonce);
5487
5488    res = 1;
5489err:
5490    OPENSSL_cleanse(nonce, sizeof(nonce));
5491    OPENSSL_cleanse(az, sizeof(az));
5492    EVP_MD_free(sha512);
5493    EVP_MD_CTX_free(hash_ctx);
5494    return res;
5495}
5496
5497static const char allzeroes[15];
5498
5499int
5500ossl_ed25519_verify(const uint8_t *message, size_t message_len,
5501                    const uint8_t signature[64], const uint8_t public_key[32],
5502                    OSSL_LIB_CTX *libctx, const char *propq)
5503{
5504    int i;
5505    ge_p3 A;
5506    const uint8_t *r, *s;
5507    EVP_MD *sha512;
5508    EVP_MD_CTX *hash_ctx = NULL;
5509    unsigned int sz;
5510    int res = 0;
5511    ge_p2 R;
5512    uint8_t rcheck[32];
5513    uint8_t h[SHA512_DIGEST_LENGTH];
5514    /* 27742317777372353535851937790883648493 in little endian format */
5515    const uint8_t l_low[16] = {
5516        0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5517        0xDE, 0xF9, 0xDE, 0x14
5518    };
5519
5520    r = signature;
5521    s = signature + 32;
5522
5523    /*
5524     * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5525     *
5526     * If not the signature is publicly invalid. Since it's public we can do the
5527     * check in variable time.
5528     *
5529     * First check the most significant byte
5530     */
5531    if (s[31] > 0x10)
5532        return 0;
5533    if (s[31] == 0x10) {
5534        /*
5535         * Most significant byte indicates a value close to 2^252 so check the
5536         * rest
5537         */
5538        if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5539            return 0;
5540        for (i = 15; i >= 0; i--) {
5541            if (s[i] < l_low[i])
5542                break;
5543            if (s[i] > l_low[i])
5544                return 0;
5545        }
5546        if (i < 0)
5547            return 0;
5548    }
5549
5550    if (ge_frombytes_vartime(&A, public_key) != 0) {
5551        return 0;
5552    }
5553
5554    fe_neg(A.X, A.X);
5555    fe_neg(A.T, A.T);
5556
5557    sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5558    if (sha512 == NULL)
5559        return 0;
5560    hash_ctx = EVP_MD_CTX_new();
5561    if (hash_ctx == NULL)
5562        goto err;
5563
5564    if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5565        || !EVP_DigestUpdate(hash_ctx, r, 32)
5566        || !EVP_DigestUpdate(hash_ctx, public_key, 32)
5567        || !EVP_DigestUpdate(hash_ctx, message, message_len)
5568        || !EVP_DigestFinal_ex(hash_ctx, h, &sz))
5569        goto err;
5570
5571    x25519_sc_reduce(h);
5572
5573    ge_double_scalarmult_vartime(&R, h, &A, s);
5574
5575    ge_tobytes(rcheck, &R);
5576
5577    res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5578err:
5579    EVP_MD_free(sha512);
5580    EVP_MD_CTX_free(hash_ctx);
5581    return res;
5582}
5583
5584int
5585ossl_ed25519_public_from_private(OSSL_LIB_CTX *ctx, uint8_t out_public_key[32],
5586                                 const uint8_t private_key[32],
5587                                 const char *propq)
5588{
5589    uint8_t az[SHA512_DIGEST_LENGTH];
5590    ge_p3 A;
5591    int r;
5592    EVP_MD *sha512 = NULL;
5593
5594    sha512 = EVP_MD_fetch(ctx, SN_sha512, propq);
5595    if (sha512 == NULL)
5596        return 0;
5597    r = EVP_Digest(private_key, 32, az, NULL, sha512, NULL);
5598    EVP_MD_free(sha512);
5599    if (!r) {
5600        OPENSSL_cleanse(az, sizeof(az));
5601        return 0;
5602    }
5603
5604    az[0] &= 248;
5605    az[31] &= 63;
5606    az[31] |= 64;
5607
5608    ge_scalarmult_base(&A, az);
5609    ge_p3_tobytes(out_public_key, &A);
5610
5611    OPENSSL_cleanse(az, sizeof(az));
5612    return 1;
5613}
5614
5615int
5616ossl_x25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5617            const uint8_t peer_public_value[32])
5618{
5619    static const uint8_t kZeros[32] = {0};
5620    x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5621    /* The all-zero output results when the input is a point of small order. */
5622    return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5623}
5624
5625void
5626ossl_x25519_public_from_private(uint8_t out_public_value[32],
5627                                const uint8_t private_key[32])
5628{
5629    uint8_t e[32];
5630    ge_p3 A;
5631    fe zplusy, zminusy, zminusy_inv;
5632
5633    memcpy(e, private_key, 32);
5634    e[0] &= 248;
5635    e[31] &= 127;
5636    e[31] |= 64;
5637
5638    ge_scalarmult_base(&A, e);
5639
5640    /*
5641     * We only need the u-coordinate of the curve25519 point.
5642     * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5643     * u=(Z+Y)/(Z-Y).
5644     */
5645    fe_add(zplusy, A.Z, A.Y);
5646    fe_sub(zminusy, A.Z, A.Y);
5647    fe_invert(zminusy_inv, zminusy);
5648    fe_mul(zplusy, zplusy, zminusy_inv);
5649    fe_tobytes(out_public_value, zplusy);
5650
5651    OPENSSL_cleanse(e, sizeof(e));
5652}
5653