curve25519.c@ 83531

Last change on this file since 83531 was 83531, checked in by vboxsync, 5 years ago
setting svn:sync-process=export for openssl-1.1.1f, all files except tests
File size: 196.9 KB

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1	/*
2	* Copyright 2016-2019 The OpenSSL Project Authors. All Rights Reserved.
3	*
4	* Licensed under the OpenSSL license (the "License"). You may not use
5	* this file except in compliance with the License. You can obtain a copy
6	* in the file LICENSE in the source distribution or at
7	* https://www.openssl.org/source/license.html
8	*/
9
10	#include <string.h>
11	#include "ec_local.h"
12	#include <openssl/sha.h>
13
14	#if defined(X25519_ASM) && (defined(__x86_64) \|\| defined(__x86_64__) \|\| \
15	defined(_M_AMD64) \|\| defined(_M_X64))
16
17	# define BASE_2_64_IMPLEMENTED
18
19	typedef uint64_t fe64[4];
20
21	int x25519_fe64_eligible(void);
22
23	/*
24	* Following subroutines perform corresponding operations modulo
25	* 2^256-38, i.e. double the curve modulus. However, inputs and
26	* outputs are permitted to be partially reduced, i.e. to remain
27	* in [0..2^256) range. It's all tied up in final fe64_tobytes
28	* that performs full reduction modulo 2^255-19.
29	*
30	* There are no reference C implementations for these.
31	*/
32	void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
33	void x25519_fe64_sqr(fe64 h, const fe64 f);
34	void x25519_fe64_mul121666(fe64 h, fe64 f);
35	void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
36	void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
37	void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
38	# define fe64_mul x25519_fe64_mul
39	# define fe64_sqr x25519_fe64_sqr
40	# define fe64_mul121666 x25519_fe64_mul121666
41	# define fe64_add x25519_fe64_add
42	# define fe64_sub x25519_fe64_sub
43	# define fe64_tobytes x25519_fe64_tobytes
44
45	static uint64_t load_8(const uint8_t *in)
46	{
47	uint64_t result;
48
49	result = in[0];
50	result \|= ((uint64_t)in[1]) << 8;
51	result \|= ((uint64_t)in[2]) << 16;
52	result \|= ((uint64_t)in[3]) << 24;
53	result \|= ((uint64_t)in[4]) << 32;
54	result \|= ((uint64_t)in[5]) << 40;
55	result \|= ((uint64_t)in[6]) << 48;
56	result \|= ((uint64_t)in[7]) << 56;
57
58	return result;
59	}
60
61	static void fe64_frombytes(fe64 h, const uint8_t *s)
62	{
63	h[0] = load_8(s);
64	h[1] = load_8(s + 8);
65	h[2] = load_8(s + 16);
66	h[3] = load_8(s + 24) & 0x7fffffffffffffff;
67	}
68
69	static void fe64_0(fe64 h)
70	{
71	h[0] = 0;
72	h[1] = 0;
73	h[2] = 0;
74	h[3] = 0;
75	}
76
77	static void fe64_1(fe64 h)
78	{
79	h[0] = 1;
80	h[1] = 0;
81	h[2] = 0;
82	h[3] = 0;
83	}
84
85	static void fe64_copy(fe64 h, const fe64 f)
86	{
87	h[0] = f[0];
88	h[1] = f[1];
89	h[2] = f[2];
90	h[3] = f[3];
91	}
92
93	static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
94	{
95	int i;
96	uint64_t mask = 0 - (uint64_t)b;
97
98	for (i = 0; i < 4; i++) {
99	uint64_t x = f[i] ^ g[i];
100	x &= mask;
101	f[i] ^= x;
102	g[i] ^= x;
103	}
104	}
105
106	static void fe64_invert(fe64 out, const fe64 z)
107	{
108	fe64 t0;
109	fe64 t1;
110	fe64 t2;
111	fe64 t3;
112	int i;
113
114	/*
115	* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
116	* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
117	*/
118
119	/* t0 = z ** 2 */
120	fe64_sqr(t0, z);
121
122	/* t1 = t0 (2 2) = z ** 8 */
123	fe64_sqr(t1, t0);
124	fe64_sqr(t1, t1);
125
126	/* t1 = z * t1 = z ** 9 */
127	fe64_mul(t1, z, t1);
128	/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
129	fe64_mul(t0, t0, t1);
130
131	/* t2 = t0 2 = z 22 */
132	fe64_sqr(t2, t0);
133
134	/* t1 = t1 * t2 = z (2 5 - 1) */
135	fe64_mul(t1, t1, t2);
136
137	/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
138	fe64_sqr(t2, t1);
139	for (i = 1; i < 5; ++i)
140	fe64_sqr(t2, t2);
141
142	/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
143	fe64_mul(t1, t2, t1);
144
145	/* Continuing similarly... */
146
147	/* t2 = z (2 20 - 1) */
148	fe64_sqr(t2, t1);
149	for (i = 1; i < 10; ++i)
150	fe64_sqr(t2, t2);
151
152	fe64_mul(t2, t2, t1);
153
154	/* t2 = z (2 40 - 1) */
155	fe64_sqr(t3, t2);
156	for (i = 1; i < 20; ++i)
157	fe64_sqr(t3, t3);
158
159	fe64_mul(t2, t3, t2);
160
161	/* t2 = z (2 10) * (2 ** 40 - 1) */
162	for (i = 0; i < 10; ++i)
163	fe64_sqr(t2, t2);
164
165	/* t1 = z (2 50 - 1) */
166	fe64_mul(t1, t2, t1);
167
168	/* t2 = z (2 100 - 1) */
169	fe64_sqr(t2, t1);
170	for (i = 1; i < 50; ++i)
171	fe64_sqr(t2, t2);
172
173	fe64_mul(t2, t2, t1);
174
175	/* t2 = z (2 200 - 1) */
176	fe64_sqr(t3, t2);
177	for (i = 1; i < 100; ++i)
178	fe64_sqr(t3, t3);
179
180	fe64_mul(t2, t3, t2);
181
182	/* t2 = z ((2 50) * (2 ** 200 - 1) */
183	for (i = 0; i < 50; ++i)
184	fe64_sqr(t2, t2);
185
186	/* t1 = z (2 250 - 1) */
187	fe64_mul(t1, t2, t1);
188
189	/* t1 = z ((2 5) * (2 ** 250 - 1)) */
190	for (i = 0; i < 5; ++i)
191	fe64_sqr(t1, t1);
192
193	/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
194	fe64_mul(out, t1, t0);
195	}
196
197	/*
198	* Duplicate of original x25519_scalar_mult_generic, but using
199	* fe64_* subroutines.
200	*/
201	static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
202	const uint8_t point[32])
203	{
204	fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
205	uint8_t e[32];
206	unsigned swap = 0;
207	int pos;
208
209	memcpy(e, scalar, 32);
210	e[0] &= 0xf8;
211	e[31] &= 0x7f;
212	e[31] \|= 0x40;
213	fe64_frombytes(x1, point);
214	fe64_1(x2);
215	fe64_0(z2);
216	fe64_copy(x3, x1);
217	fe64_1(z3);
218
219	for (pos = 254; pos >= 0; --pos) {
220	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
221
222	swap ^= b;
223	fe64_cswap(x2, x3, swap);
224	fe64_cswap(z2, z3, swap);
225	swap = b;
226	fe64_sub(tmp0, x3, z3);
227	fe64_sub(tmp1, x2, z2);
228	fe64_add(x2, x2, z2);
229	fe64_add(z2, x3, z3);
230	fe64_mul(z3, x2, tmp0);
231	fe64_mul(z2, z2, tmp1);
232	fe64_sqr(tmp0, tmp1);
233	fe64_sqr(tmp1, x2);
234	fe64_add(x3, z3, z2);
235	fe64_sub(z2, z3, z2);
236	fe64_mul(x2, tmp1, tmp0);
237	fe64_sub(tmp1, tmp1, tmp0);
238	fe64_sqr(z2, z2);
239	fe64_mul121666(z3, tmp1);
240	fe64_sqr(x3, x3);
241	fe64_add(tmp0, tmp0, z3);
242	fe64_mul(z3, x1, z2);
243	fe64_mul(z2, tmp1, tmp0);
244	}
245
246	fe64_invert(z2, z2);
247	fe64_mul(x2, x2, z2);
248	fe64_tobytes(out, x2);
249
250	OPENSSL_cleanse(e, sizeof(e));
251	}
252	#endif
253
254	#if defined(X25519_ASM) \
255	\|\| ( (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16) \
256	&& !defined(__sparc__) \
257	&& (!defined(__SIZEOF_LONG__) \|\| (__SIZEOF_LONG__ == 8)) \
258	&& !(defined(__ANDROID__) && !defined(__clang__)) )
259	/*
260	* Base 2^51 implementation. It's virtually no different from reference
261	* base 2^25.5 implementation in respect to lax boundary conditions for
262	* intermediate values and even individual limbs. So that whatever you
263	* know about the reference, applies even here...
264	*/
265	# define BASE_2_51_IMPLEMENTED
266
267	typedef uint64_t fe51[5];
268
269	static const uint64_t MASK51 = 0x7ffffffffffff;
270
271	static uint64_t load_7(const uint8_t *in)
272	{
273	uint64_t result;
274
275	result = in[0];
276	result \|= ((uint64_t)in[1]) << 8;
277	result \|= ((uint64_t)in[2]) << 16;
278	result \|= ((uint64_t)in[3]) << 24;
279	result \|= ((uint64_t)in[4]) << 32;
280	result \|= ((uint64_t)in[5]) << 40;
281	result \|= ((uint64_t)in[6]) << 48;
282
283	return result;
284	}
285
286	static uint64_t load_6(const uint8_t *in)
287	{
288	uint64_t result;
289
290	result = in[0];
291	result \|= ((uint64_t)in[1]) << 8;
292	result \|= ((uint64_t)in[2]) << 16;
293	result \|= ((uint64_t)in[3]) << 24;
294	result \|= ((uint64_t)in[4]) << 32;
295	result \|= ((uint64_t)in[5]) << 40;
296
297	return result;
298	}
299
300	static void fe51_frombytes(fe51 h, const uint8_t *s)
301	{
302	uint64_t h0 = load_7(s); /* 56 bits */
303	uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
304	uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
305	uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
306	uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
307
308	h1 \|= h0 >> 51; h0 &= MASK51;
309	h2 \|= h1 >> 51; h1 &= MASK51;
310	h3 \|= h2 >> 51; h2 &= MASK51;
311	h4 \|= h3 >> 51; h3 &= MASK51;
312
313	h[0] = h0;
314	h[1] = h1;
315	h[2] = h2;
316	h[3] = h3;
317	h[4] = h4;
318	}
319
320	static void fe51_tobytes(uint8_t *s, const fe51 h)
321	{
322	uint64_t h0 = h[0];
323	uint64_t h1 = h[1];
324	uint64_t h2 = h[2];
325	uint64_t h3 = h[3];
326	uint64_t h4 = h[4];
327	uint64_t q;
328
329	/* compare to modulus */
330	q = (h0 + 19) >> 51;
331	q = (h1 + q) >> 51;
332	q = (h2 + q) >> 51;
333	q = (h3 + q) >> 51;
334	q = (h4 + q) >> 51;
335
336	/* full reduce */
337	h0 += 19 * q;
338	h1 += h0 >> 51; h0 &= MASK51;
339	h2 += h1 >> 51; h1 &= MASK51;
340	h3 += h2 >> 51; h2 &= MASK51;
341	h4 += h3 >> 51; h3 &= MASK51;
342	h4 &= MASK51;
343
344	/* smash */
345	s[0] = (uint8_t)(h0 >> 0);
346	s[1] = (uint8_t)(h0 >> 8);
347	s[2] = (uint8_t)(h0 >> 16);
348	s[3] = (uint8_t)(h0 >> 24);
349	s[4] = (uint8_t)(h0 >> 32);
350	s[5] = (uint8_t)(h0 >> 40);
351	s[6] = (uint8_t)((h0 >> 48) \| ((uint32_t)h1 << 3));
352	s[7] = (uint8_t)(h1 >> 5);
353	s[8] = (uint8_t)(h1 >> 13);
354	s[9] = (uint8_t)(h1 >> 21);
355	s[10] = (uint8_t)(h1 >> 29);
356	s[11] = (uint8_t)(h1 >> 37);
357	s[12] = (uint8_t)((h1 >> 45) \| ((uint32_t)h2 << 6));
358	s[13] = (uint8_t)(h2 >> 2);
359	s[14] = (uint8_t)(h2 >> 10);
360	s[15] = (uint8_t)(h2 >> 18);
361	s[16] = (uint8_t)(h2 >> 26);
362	s[17] = (uint8_t)(h2 >> 34);
363	s[18] = (uint8_t)(h2 >> 42);
364	s[19] = (uint8_t)((h2 >> 50) \| ((uint32_t)h3 << 1));
365	s[20] = (uint8_t)(h3 >> 7);
366	s[21] = (uint8_t)(h3 >> 15);
367	s[22] = (uint8_t)(h3 >> 23);
368	s[23] = (uint8_t)(h3 >> 31);
369	s[24] = (uint8_t)(h3 >> 39);
370	s[25] = (uint8_t)((h3 >> 47) \| ((uint32_t)h4 << 4));
371	s[26] = (uint8_t)(h4 >> 4);
372	s[27] = (uint8_t)(h4 >> 12);
373	s[28] = (uint8_t)(h4 >> 20);
374	s[29] = (uint8_t)(h4 >> 28);
375	s[30] = (uint8_t)(h4 >> 36);
376	s[31] = (uint8_t)(h4 >> 44);
377	}
378
379	# if defined(X25519_ASM)
380	void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
381	void x25519_fe51_sqr(fe51 h, const fe51 f);
382	void x25519_fe51_mul121666(fe51 h, fe51 f);
383	# define fe51_mul x25519_fe51_mul
384	# define fe51_sq x25519_fe51_sqr
385	# define fe51_mul121666 x25519_fe51_mul121666
386	# else
387
388	typedef __uint128_t u128;
389
390	static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
391	{
392	u128 h0, h1, h2, h3, h4;
393	uint64_t f_i, g0, g1, g2, g3, g4;
394
395	f_i = f[0];
396	h0 = (u128)f_i * (g0 = g[0]);
397	h1 = (u128)f_i * (g1 = g[1]);
398	h2 = (u128)f_i * (g2 = g[2]);
399	h3 = (u128)f_i * (g3 = g[3]);
400	h4 = (u128)f_i * (g4 = g[4]);
401
402	f_i = f[1];
403	h0 += (u128)f_i * (g4 *= 19);
404	h1 += (u128)f_i * g0;
405	h2 += (u128)f_i * g1;
406	h3 += (u128)f_i * g2;
407	h4 += (u128)f_i * g3;
408
409	f_i = f[2];
410	h0 += (u128)f_i * (g3 *= 19);
411	h1 += (u128)f_i * g4;
412	h2 += (u128)f_i * g0;
413	h3 += (u128)f_i * g1;
414	h4 += (u128)f_i * g2;
415
416	f_i = f[3];
417	h0 += (u128)f_i * (g2 *= 19);
418	h1 += (u128)f_i * g3;
419	h2 += (u128)f_i * g4;
420	h3 += (u128)f_i * g0;
421	h4 += (u128)f_i * g1;
422
423	f_i = f[4];
424	h0 += (u128)f_i * (g1 *= 19);
425	h1 += (u128)f_i * g2;
426	h2 += (u128)f_i * g3;
427	h3 += (u128)f_i * g4;
428	h4 += (u128)f_i * g0;
429
430	/* partial [lazy] reduction */
431	h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
432	h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
433
434	h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
435	g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
436
437	g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
438	g3 += g2 >> 51; g2 &= MASK51;
439	g1 += g0 >> 51; g0 &= MASK51;
440
441	h[0] = g0;
442	h[1] = g1;
443	h[2] = g2;
444	h[3] = g3;
445	h[4] = g4;
446	}
447
448	static void fe51_sq(fe51 h, const fe51 f)
449	{
450	# if defined(OPENSSL_SMALL_FOOTPRINT)
451	fe51_mul(h, f, f);
452	# else
453	/* dedicated squaring gives 16-25% overall improvement */
454	uint64_t g0 = f[0];
455	uint64_t g1 = f[1];
456	uint64_t g2 = f[2];
457	uint64_t g3 = f[3];
458	uint64_t g4 = f[4];
459	u128 h0, h1, h2, h3, h4;
460
461	h0 = (u128)g0 * g0; g0 *= 2;
462	h1 = (u128)g0 * g1;
463	h2 = (u128)g0 * g2;
464	h3 = (u128)g0 * g3;
465	h4 = (u128)g0 * g4;
466
467	g0 = g4; /* borrow g0 */
468	h3 += (u128)g0 * (g4 *= 19);
469
470	h2 += (u128)g1 * g1; g1 *= 2;
471	h3 += (u128)g1 * g2;
472	h4 += (u128)g1 * g3;
473	h0 += (u128)g1 * g4;
474
475	g0 = g3; /* borrow g0 */
476	h1 += (u128)g0 * (g3 *= 19);
477	h2 += (u128)(g0 * 2) * g4;
478
479	h4 += (u128)g2 * g2; g2 *= 2;
480	h0 += (u128)g2 * g3;
481	h1 += (u128)g2 * g4;
482
483	/* partial [lazy] reduction */
484	h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
485	h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
486
487	h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
488	g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
489
490	g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
491	g3 += g2 >> 51; g2 &= MASK51;
492	g1 += g0 >> 51; g0 &= MASK51;
493
494	h[0] = g0;
495	h[1] = g1;
496	h[2] = g2;
497	h[3] = g3;
498	h[4] = g4;
499	# endif
500	}
501
502	static void fe51_mul121666(fe51 h, fe51 f)
503	{
504	u128 h0 = f[0] * (u128)121666;
505	u128 h1 = f[1] * (u128)121666;
506	u128 h2 = f[2] * (u128)121666;
507	u128 h3 = f[3] * (u128)121666;
508	u128 h4 = f[4] * (u128)121666;
509	uint64_t g0, g1, g2, g3, g4;
510
511	h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
512	h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
513
514	h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
515	g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
516
517	g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
518	g3 += g2 >> 51; g2 &= MASK51;
519	g1 += g0 >> 51; g0 &= MASK51;
520
521	h[0] = g0;
522	h[1] = g1;
523	h[2] = g2;
524	h[3] = g3;
525	h[4] = g4;
526	}
527	# endif
528
529	static void fe51_add(fe51 h, const fe51 f, const fe51 g)
530	{
531	h[0] = f[0] + g[0];
532	h[1] = f[1] + g[1];
533	h[2] = f[2] + g[2];
534	h[3] = f[3] + g[3];
535	h[4] = f[4] + g[4];
536	}
537
538	static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
539	{
540	/*
541	* Add 2*modulus to ensure that result remains positive
542	* even if subtrahend is partially reduced.
543	*/
544	h[0] = (f[0] + 0xfffffffffffda) - g[0];
545	h[1] = (f[1] + 0xffffffffffffe) - g[1];
546	h[2] = (f[2] + 0xffffffffffffe) - g[2];
547	h[3] = (f[3] + 0xffffffffffffe) - g[3];
548	h[4] = (f[4] + 0xffffffffffffe) - g[4];
549	}
550
551	static void fe51_0(fe51 h)
552	{
553	h[0] = 0;
554	h[1] = 0;
555	h[2] = 0;
556	h[3] = 0;
557	h[4] = 0;
558	}
559
560	static void fe51_1(fe51 h)
561	{
562	h[0] = 1;
563	h[1] = 0;
564	h[2] = 0;
565	h[3] = 0;
566	h[4] = 0;
567	}
568
569	static void fe51_copy(fe51 h, const fe51 f)
570	{
571	h[0] = f[0];
572	h[1] = f[1];
573	h[2] = f[2];
574	h[3] = f[3];
575	h[4] = f[4];
576	}
577
578	static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
579	{
580	int i;
581	uint64_t mask = 0 - (uint64_t)b;
582
583	for (i = 0; i < 5; i++) {
584	int64_t x = f[i] ^ g[i];
585	x &= mask;
586	f[i] ^= x;
587	g[i] ^= x;
588	}
589	}
590
591	static void fe51_invert(fe51 out, const fe51 z)
592	{
593	fe51 t0;
594	fe51 t1;
595	fe51 t2;
596	fe51 t3;
597	int i;
598
599	/*
600	* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
601	* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
602	*/
603
604	/* t0 = z ** 2 */
605	fe51_sq(t0, z);
606
607	/* t1 = t0 (2 2) = z ** 8 */
608	fe51_sq(t1, t0);
609	fe51_sq(t1, t1);
610
611	/* t1 = z * t1 = z ** 9 */
612	fe51_mul(t1, z, t1);
613	/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
614	fe51_mul(t0, t0, t1);
615
616	/* t2 = t0 2 = z 22 */
617	fe51_sq(t2, t0);
618
619	/* t1 = t1 * t2 = z (2 5 - 1) */
620	fe51_mul(t1, t1, t2);
621
622	/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
623	fe51_sq(t2, t1);
624	for (i = 1; i < 5; ++i)
625	fe51_sq(t2, t2);
626
627	/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
628	fe51_mul(t1, t2, t1);
629
630	/* Continuing similarly... */
631
632	/* t2 = z (2 20 - 1) */
633	fe51_sq(t2, t1);
634	for (i = 1; i < 10; ++i)
635	fe51_sq(t2, t2);
636
637	fe51_mul(t2, t2, t1);
638
639	/* t2 = z (2 40 - 1) */
640	fe51_sq(t3, t2);
641	for (i = 1; i < 20; ++i)
642	fe51_sq(t3, t3);
643
644	fe51_mul(t2, t3, t2);
645
646	/* t2 = z (2 10) * (2 ** 40 - 1) */
647	for (i = 0; i < 10; ++i)
648	fe51_sq(t2, t2);
649
650	/* t1 = z (2 50 - 1) */
651	fe51_mul(t1, t2, t1);
652
653	/* t2 = z (2 100 - 1) */
654	fe51_sq(t2, t1);
655	for (i = 1; i < 50; ++i)
656	fe51_sq(t2, t2);
657
658	fe51_mul(t2, t2, t1);
659
660	/* t2 = z (2 200 - 1) */
661	fe51_sq(t3, t2);
662	for (i = 1; i < 100; ++i)
663	fe51_sq(t3, t3);
664
665	fe51_mul(t2, t3, t2);
666
667	/* t2 = z ((2 50) * (2 ** 200 - 1) */
668	for (i = 0; i < 50; ++i)
669	fe51_sq(t2, t2);
670
671	/* t1 = z (2 250 - 1) */
672	fe51_mul(t1, t2, t1);
673
674	/* t1 = z ((2 5) * (2 ** 250 - 1)) */
675	for (i = 0; i < 5; ++i)
676	fe51_sq(t1, t1);
677
678	/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
679	fe51_mul(out, t1, t0);
680	}
681
682	/*
683	* Duplicate of original x25519_scalar_mult_generic, but using
684	* fe51_* subroutines.
685	*/
686	static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
687	const uint8_t point[32])
688	{
689	fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
690	uint8_t e[32];
691	unsigned swap = 0;
692	int pos;
693
694	# ifdef BASE_2_64_IMPLEMENTED
695	if (x25519_fe64_eligible()) {
696	x25519_scalar_mulx(out, scalar, point);
697	return;
698	}
699	# endif
700
701	memcpy(e, scalar, 32);
702	e[0] &= 0xf8;
703	e[31] &= 0x7f;
704	e[31] \|= 0x40;
705	fe51_frombytes(x1, point);
706	fe51_1(x2);
707	fe51_0(z2);
708	fe51_copy(x3, x1);
709	fe51_1(z3);
710
711	for (pos = 254; pos >= 0; --pos) {
712	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
713
714	swap ^= b;
715	fe51_cswap(x2, x3, swap);
716	fe51_cswap(z2, z3, swap);
717	swap = b;
718	fe51_sub(tmp0, x3, z3);
719	fe51_sub(tmp1, x2, z2);
720	fe51_add(x2, x2, z2);
721	fe51_add(z2, x3, z3);
722	fe51_mul(z3, tmp0, x2);
723	fe51_mul(z2, z2, tmp1);
724	fe51_sq(tmp0, tmp1);
725	fe51_sq(tmp1, x2);
726	fe51_add(x3, z3, z2);
727	fe51_sub(z2, z3, z2);
728	fe51_mul(x2, tmp1, tmp0);
729	fe51_sub(tmp1, tmp1, tmp0);
730	fe51_sq(z2, z2);
731	fe51_mul121666(z3, tmp1);
732	fe51_sq(x3, x3);
733	fe51_add(tmp0, tmp0, z3);
734	fe51_mul(z3, x1, z2);
735	fe51_mul(z2, tmp1, tmp0);
736	}
737
738	fe51_invert(z2, z2);
739	fe51_mul(x2, x2, z2);
740	fe51_tobytes(out, x2);
741
742	OPENSSL_cleanse(e, sizeof(e));
743	}
744	#endif
745
746	/*
747	* Reference base 2^25.5 implementation.
748	*
749	* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
750	* 20141124 (http://bench.cr.yp.to/supercop.html).
751	*
752	* The field functions are shared by Ed25519 and X25519 where possible.
753	*/
754
755	/*
756	* fe means field element. Here the field is \Z/(2^255-19). An element t,
757	* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
758	* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
759	* context.
760	*/
761	typedef int32_t fe[10];
762
763	static const int64_t kBottom21Bits = 0x1fffffLL;
764	static const int64_t kBottom25Bits = 0x1ffffffLL;
765	static const int64_t kBottom26Bits = 0x3ffffffLL;
766	static const int64_t kTop39Bits = 0xfffffffffe000000LL;
767	static const int64_t kTop38Bits = 0xfffffffffc000000LL;
768
769	static uint64_t load_3(const uint8_t *in)
770	{
771	uint64_t result;
772
773	result = ((uint64_t)in[0]);
774	result \|= ((uint64_t)in[1]) << 8;
775	result \|= ((uint64_t)in[2]) << 16;
776	return result;
777	}
778
779	static uint64_t load_4(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	result \|= ((uint64_t)in[3]) << 24;
787	return result;
788	}
789
790	static void fe_frombytes(fe h, const uint8_t *s)
791	{
792	/* Ignores top bit of h. */
793	int64_t h0 = load_4(s);
794	int64_t h1 = load_3(s + 4) << 6;
795	int64_t h2 = load_3(s + 7) << 5;
796	int64_t h3 = load_3(s + 10) << 3;
797	int64_t h4 = load_3(s + 13) << 2;
798	int64_t h5 = load_4(s + 16);
799	int64_t h6 = load_3(s + 20) << 7;
800	int64_t h7 = load_3(s + 23) << 5;
801	int64_t h8 = load_3(s + 26) << 4;
802	int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
803	int64_t carry0;
804	int64_t carry1;
805	int64_t carry2;
806	int64_t carry3;
807	int64_t carry4;
808	int64_t carry5;
809	int64_t carry6;
810	int64_t carry7;
811	int64_t carry8;
812	int64_t carry9;
813
814	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
815	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
816	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
817	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
818	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
819
820	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
821	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
822	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
823	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
824	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
825
826	h[0] = (int32_t)h0;
827	h[1] = (int32_t)h1;
828	h[2] = (int32_t)h2;
829	h[3] = (int32_t)h3;
830	h[4] = (int32_t)h4;
831	h[5] = (int32_t)h5;
832	h[6] = (int32_t)h6;
833	h[7] = (int32_t)h7;
834	h[8] = (int32_t)h8;
835	h[9] = (int32_t)h9;
836	}
837
838	/*
839	* Preconditions:
840	* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
841	*
842	* Write p=2^255-19; q=floor(h/p).
843	* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
844	*
845	* Proof:
846	* Have \|h\|<=p so \|q\|<=1 so \|19^2 2^(-255) q\|<1/4.
847	* Also have \|h-2^230 h9\|<2^231 so \|19 2^(-255)(h-2^230 h9)\|<1/4.
848	*
849	* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
850	* Then 0<y<1.
851	*
852	* Write r=h-pq.
853	* Have 0<=r<=p-1=2^255-20.
854	* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
855	*
856	* Write x=r+19(2^-255)r+y.
857	* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
858	*
859	* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
860	* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
861	*/
862	static void fe_tobytes(uint8_t *s, const fe h)
863	{
864	int32_t h0 = h[0];
865	int32_t h1 = h[1];
866	int32_t h2 = h[2];
867	int32_t h3 = h[3];
868	int32_t h4 = h[4];
869	int32_t h5 = h[5];
870	int32_t h6 = h[6];
871	int32_t h7 = h[7];
872	int32_t h8 = h[8];
873	int32_t h9 = h[9];
874	int32_t q;
875
876	q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
877	q = (h0 + q) >> 26;
878	q = (h1 + q) >> 25;
879	q = (h2 + q) >> 26;
880	q = (h3 + q) >> 25;
881	q = (h4 + q) >> 26;
882	q = (h5 + q) >> 25;
883	q = (h6 + q) >> 26;
884	q = (h7 + q) >> 25;
885	q = (h8 + q) >> 26;
886	q = (h9 + q) >> 25;
887
888	/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
889	h0 += 19 * q;
890	/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
891
892	h1 += h0 >> 26; h0 &= kBottom26Bits;
893	h2 += h1 >> 25; h1 &= kBottom25Bits;
894	h3 += h2 >> 26; h2 &= kBottom26Bits;
895	h4 += h3 >> 25; h3 &= kBottom25Bits;
896	h5 += h4 >> 26; h4 &= kBottom26Bits;
897	h6 += h5 >> 25; h5 &= kBottom25Bits;
898	h7 += h6 >> 26; h6 &= kBottom26Bits;
899	h8 += h7 >> 25; h7 &= kBottom25Bits;
900	h9 += h8 >> 26; h8 &= kBottom26Bits;
901	h9 &= kBottom25Bits;
902	/* h10 = carry9 */
903
904	/*
905	* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
906	* Have h0+...+2^230 h9 between 0 and 2^255-1;
907	* evidently 2^255 h10-2^255 q = 0.
908	* Goal: Output h0+...+2^230 h9.
909	*/
910	s[ 0] = (uint8_t) (h0 >> 0);
911	s[ 1] = (uint8_t) (h0 >> 8);
912	s[ 2] = (uint8_t) (h0 >> 16);
913	s[ 3] = (uint8_t)((h0 >> 24) \| ((uint32_t)(h1) << 2));
914	s[ 4] = (uint8_t) (h1 >> 6);
915	s[ 5] = (uint8_t) (h1 >> 14);
916	s[ 6] = (uint8_t)((h1 >> 22) \| ((uint32_t)(h2) << 3));
917	s[ 7] = (uint8_t) (h2 >> 5);
918	s[ 8] = (uint8_t) (h2 >> 13);
919	s[ 9] = (uint8_t)((h2 >> 21) \| ((uint32_t)(h3) << 5));
920	s[10] = (uint8_t) (h3 >> 3);
921	s[11] = (uint8_t) (h3 >> 11);
922	s[12] = (uint8_t)((h3 >> 19) \| ((uint32_t)(h4) << 6));
923	s[13] = (uint8_t) (h4 >> 2);
924	s[14] = (uint8_t) (h4 >> 10);
925	s[15] = (uint8_t) (h4 >> 18);
926	s[16] = (uint8_t) (h5 >> 0);
927	s[17] = (uint8_t) (h5 >> 8);
928	s[18] = (uint8_t) (h5 >> 16);
929	s[19] = (uint8_t)((h5 >> 24) \| ((uint32_t)(h6) << 1));
930	s[20] = (uint8_t) (h6 >> 7);
931	s[21] = (uint8_t) (h6 >> 15);
932	s[22] = (uint8_t)((h6 >> 23) \| ((uint32_t)(h7) << 3));
933	s[23] = (uint8_t) (h7 >> 5);
934	s[24] = (uint8_t) (h7 >> 13);
935	s[25] = (uint8_t)((h7 >> 21) \| ((uint32_t)(h8) << 4));
936	s[26] = (uint8_t) (h8 >> 4);
937	s[27] = (uint8_t) (h8 >> 12);
938	s[28] = (uint8_t)((h8 >> 20) \| ((uint32_t)(h9) << 6));
939	s[29] = (uint8_t) (h9 >> 2);
940	s[30] = (uint8_t) (h9 >> 10);
941	s[31] = (uint8_t) (h9 >> 18);
942	}
943
944	/* h = f */
945	static void fe_copy(fe h, const fe f)
946	{
947	memmove(h, f, sizeof(int32_t) * 10);
948	}
949
950	/* h = 0 */
951	static void fe_0(fe h)
952	{
953	memset(h, 0, sizeof(int32_t) * 10);
954	}
955
956	/* h = 1 */
957	static void fe_1(fe h)
958	{
959	memset(h, 0, sizeof(int32_t) * 10);
960	h[0] = 1;
961	}
962
963	/*
964	* h = f + g
965	*
966	* Can overlap h with f or g.
967	*
968	* Preconditions:
969	* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
970	* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
971	*
972	* Postconditions:
973	* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
974	*/
975	static void fe_add(fe h, const fe f, const fe g)
976	{
977	unsigned i;
978
979	for (i = 0; i < 10; i++) {
980	h[i] = f[i] + g[i];
981	}
982	}
983
984	/*
985	* h = f - g
986	*
987	* Can overlap h with f or g.
988	*
989	* Preconditions:
990	* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
991	* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
992	*
993	* Postconditions:
994	* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
995	*/
996	static void fe_sub(fe h, const fe f, const fe g)
997	{
998	unsigned i;
999
1000	for (i = 0; i < 10; i++) {
1001	h[i] = f[i] - g[i];
1002	}
1003	}
1004
1005	/*
1006	* h = f * g
1007	*
1008	* Can overlap h with f or g.
1009	*
1010	* Preconditions:
1011	* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1012	* \|g\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1013	*
1014	* Postconditions:
1015	* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1016	*
1017	* Notes on implementation strategy:
1018	*
1019	* Using schoolbook multiplication.
1020	* Karatsuba would save a little in some cost models.
1021	*
1022	* Most multiplications by 2 and 19 are 32-bit precomputations;
1023	* cheaper than 64-bit postcomputations.
1024	*
1025	* There is one remaining multiplication by 19 in the carry chain;
1026	* one *19 precomputation can be merged into this,
1027	* but the resulting data flow is considerably less clean.
1028	*
1029	* There are 12 carries below.
1030	* 10 of them are 2-way parallelizable and vectorizable.
1031	* Can get away with 11 carries, but then data flow is much deeper.
1032	*
1033	* With tighter constraints on inputs can squeeze carries into int32.
1034	*/
1035	static void fe_mul(fe h, const fe f, const fe g)
1036	{
1037	int32_t f0 = f[0];
1038	int32_t f1 = f[1];
1039	int32_t f2 = f[2];
1040	int32_t f3 = f[3];
1041	int32_t f4 = f[4];
1042	int32_t f5 = f[5];
1043	int32_t f6 = f[6];
1044	int32_t f7 = f[7];
1045	int32_t f8 = f[8];
1046	int32_t f9 = f[9];
1047	int32_t g0 = g[0];
1048	int32_t g1 = g[1];
1049	int32_t g2 = g[2];
1050	int32_t g3 = g[3];
1051	int32_t g4 = g[4];
1052	int32_t g5 = g[5];
1053	int32_t g6 = g[6];
1054	int32_t g7 = g[7];
1055	int32_t g8 = g[8];
1056	int32_t g9 = g[9];
1057	int32_t g1_19 = 19 * g1; /* 1.9593752^29 /
1058	int32_t g2_19 = 19 * g2; /* 1.9593752^30; still ok /
1059	int32_t g3_19 = 19 * g3;
1060	int32_t g4_19 = 19 * g4;
1061	int32_t g5_19 = 19 * g5;
1062	int32_t g6_19 = 19 * g6;
1063	int32_t g7_19 = 19 * g7;
1064	int32_t g8_19 = 19 * g8;
1065	int32_t g9_19 = 19 * g9;
1066	int32_t f1_2 = 2 * f1;
1067	int32_t f3_2 = 2 * f3;
1068	int32_t f5_2 = 2 * f5;
1069	int32_t f7_2 = 2 * f7;
1070	int32_t f9_2 = 2 * f9;
1071	int64_t f0g0 = f0 * (int64_t) g0;
1072	int64_t f0g1 = f0 * (int64_t) g1;
1073	int64_t f0g2 = f0 * (int64_t) g2;
1074	int64_t f0g3 = f0 * (int64_t) g3;
1075	int64_t f0g4 = f0 * (int64_t) g4;
1076	int64_t f0g5 = f0 * (int64_t) g5;
1077	int64_t f0g6 = f0 * (int64_t) g6;
1078	int64_t f0g7 = f0 * (int64_t) g7;
1079	int64_t f0g8 = f0 * (int64_t) g8;
1080	int64_t f0g9 = f0 * (int64_t) g9;
1081	int64_t f1g0 = f1 * (int64_t) g0;
1082	int64_t f1g1_2 = f1_2 * (int64_t) g1;
1083	int64_t f1g2 = f1 * (int64_t) g2;
1084	int64_t f1g3_2 = f1_2 * (int64_t) g3;
1085	int64_t f1g4 = f1 * (int64_t) g4;
1086	int64_t f1g5_2 = f1_2 * (int64_t) g5;
1087	int64_t f1g6 = f1 * (int64_t) g6;
1088	int64_t f1g7_2 = f1_2 * (int64_t) g7;
1089	int64_t f1g8 = f1 * (int64_t) g8;
1090	int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
1091	int64_t f2g0 = f2 * (int64_t) g0;
1092	int64_t f2g1 = f2 * (int64_t) g1;
1093	int64_t f2g2 = f2 * (int64_t) g2;
1094	int64_t f2g3 = f2 * (int64_t) g3;
1095	int64_t f2g4 = f2 * (int64_t) g4;
1096	int64_t f2g5 = f2 * (int64_t) g5;
1097	int64_t f2g6 = f2 * (int64_t) g6;
1098	int64_t f2g7 = f2 * (int64_t) g7;
1099	int64_t f2g8_19 = f2 * (int64_t) g8_19;
1100	int64_t f2g9_19 = f2 * (int64_t) g9_19;
1101	int64_t f3g0 = f3 * (int64_t) g0;
1102	int64_t f3g1_2 = f3_2 * (int64_t) g1;
1103	int64_t f3g2 = f3 * (int64_t) g2;
1104	int64_t f3g3_2 = f3_2 * (int64_t) g3;
1105	int64_t f3g4 = f3 * (int64_t) g4;
1106	int64_t f3g5_2 = f3_2 * (int64_t) g5;
1107	int64_t f3g6 = f3 * (int64_t) g6;
1108	int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
1109	int64_t f3g8_19 = f3 * (int64_t) g8_19;
1110	int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
1111	int64_t f4g0 = f4 * (int64_t) g0;
1112	int64_t f4g1 = f4 * (int64_t) g1;
1113	int64_t f4g2 = f4 * (int64_t) g2;
1114	int64_t f4g3 = f4 * (int64_t) g3;
1115	int64_t f4g4 = f4 * (int64_t) g4;
1116	int64_t f4g5 = f4 * (int64_t) g5;
1117	int64_t f4g6_19 = f4 * (int64_t) g6_19;
1118	int64_t f4g7_19 = f4 * (int64_t) g7_19;
1119	int64_t f4g8_19 = f4 * (int64_t) g8_19;
1120	int64_t f4g9_19 = f4 * (int64_t) g9_19;
1121	int64_t f5g0 = f5 * (int64_t) g0;
1122	int64_t f5g1_2 = f5_2 * (int64_t) g1;
1123	int64_t f5g2 = f5 * (int64_t) g2;
1124	int64_t f5g3_2 = f5_2 * (int64_t) g3;
1125	int64_t f5g4 = f5 * (int64_t) g4;
1126	int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
1127	int64_t f5g6_19 = f5 * (int64_t) g6_19;
1128	int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
1129	int64_t f5g8_19 = f5 * (int64_t) g8_19;
1130	int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
1131	int64_t f6g0 = f6 * (int64_t) g0;
1132	int64_t f6g1 = f6 * (int64_t) g1;
1133	int64_t f6g2 = f6 * (int64_t) g2;
1134	int64_t f6g3 = f6 * (int64_t) g3;
1135	int64_t f6g4_19 = f6 * (int64_t) g4_19;
1136	int64_t f6g5_19 = f6 * (int64_t) g5_19;
1137	int64_t f6g6_19 = f6 * (int64_t) g6_19;
1138	int64_t f6g7_19 = f6 * (int64_t) g7_19;
1139	int64_t f6g8_19 = f6 * (int64_t) g8_19;
1140	int64_t f6g9_19 = f6 * (int64_t) g9_19;
1141	int64_t f7g0 = f7 * (int64_t) g0;
1142	int64_t f7g1_2 = f7_2 * (int64_t) g1;
1143	int64_t f7g2 = f7 * (int64_t) g2;
1144	int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
1145	int64_t f7g4_19 = f7 * (int64_t) g4_19;
1146	int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
1147	int64_t f7g6_19 = f7 * (int64_t) g6_19;
1148	int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
1149	int64_t f7g8_19 = f7 * (int64_t) g8_19;
1150	int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
1151	int64_t f8g0 = f8 * (int64_t) g0;
1152	int64_t f8g1 = f8 * (int64_t) g1;
1153	int64_t f8g2_19 = f8 * (int64_t) g2_19;
1154	int64_t f8g3_19 = f8 * (int64_t) g3_19;
1155	int64_t f8g4_19 = f8 * (int64_t) g4_19;
1156	int64_t f8g5_19 = f8 * (int64_t) g5_19;
1157	int64_t f8g6_19 = f8 * (int64_t) g6_19;
1158	int64_t f8g7_19 = f8 * (int64_t) g7_19;
1159	int64_t f8g8_19 = f8 * (int64_t) g8_19;
1160	int64_t f8g9_19 = f8 * (int64_t) g9_19;
1161	int64_t f9g0 = f9 * (int64_t) g0;
1162	int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
1163	int64_t f9g2_19 = f9 * (int64_t) g2_19;
1164	int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
1165	int64_t f9g4_19 = f9 * (int64_t) g4_19;
1166	int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
1167	int64_t f9g6_19 = f9 * (int64_t) g6_19;
1168	int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
1169	int64_t f9g8_19 = f9 * (int64_t) g8_19;
1170	int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
1171	int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1172	int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1173	int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1174	int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1175	int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1176	int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1177	int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
1178	int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
1179	int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
1180	int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ;
1181	int64_t carry0;
1182	int64_t carry1;
1183	int64_t carry2;
1184	int64_t carry3;
1185	int64_t carry4;
1186	int64_t carry5;
1187	int64_t carry6;
1188	int64_t carry7;
1189	int64_t carry8;
1190	int64_t carry9;
1191
1192	/* \|h0\| <= (1.651.652^52(1+19+19+19+19)+1.651.652^50(38+38+38+38+38))
1193	* i.e. \|h0\| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1194	* \|h1\| <= (1.651.652^51*(1+1+19+19+19+19+19+19+19+19))
1195	* i.e. \|h1\| <= 1.72^59; narrower ranges for h3, h5, h7, h9 /
1196
1197	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1198	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1199	/* \|h0\| <= 2^25 */
1200	/* \|h4\| <= 2^25 */
1201	/* \|h1\| <= 1.712^59 /
1202	/* \|h5\| <= 1.712^59 /
1203
1204	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1205	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1206	/* \|h1\| <= 2^24; from now on fits into int32 */
1207	/* \|h5\| <= 2^24; from now on fits into int32 */
1208	/* \|h2\| <= 1.412^60 /
1209	/* \|h6\| <= 1.412^60 /
1210
1211	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1212	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1213	/* \|h2\| <= 2^25; from now on fits into int32 unchanged */
1214	/* \|h6\| <= 2^25; from now on fits into int32 unchanged */
1215	/* \|h3\| <= 1.712^59 /
1216	/* \|h7\| <= 1.712^59 /
1217
1218	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1219	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1220	/* \|h3\| <= 2^24; from now on fits into int32 unchanged */
1221	/* \|h7\| <= 2^24; from now on fits into int32 unchanged */
1222	/* \|h4\| <= 1.722^34 /
1223	/* \|h8\| <= 1.412^60 /
1224
1225	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1226	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1227	/* \|h4\| <= 2^25; from now on fits into int32 unchanged */
1228	/* \|h8\| <= 2^25; from now on fits into int32 unchanged */
1229	/* \|h5\| <= 1.012^24 /
1230	/* \|h9\| <= 1.712^59 /
1231
1232	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1233	/* \|h9\| <= 2^24; from now on fits into int32 unchanged */
1234	/* \|h0\| <= 1.12^39 /
1235
1236	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1237	/* \|h0\| <= 2^25; from now on fits into int32 unchanged */
1238	/* \|h1\| <= 1.012^24 /
1239
1240	h[0] = (int32_t)h0;
1241	h[1] = (int32_t)h1;
1242	h[2] = (int32_t)h2;
1243	h[3] = (int32_t)h3;
1244	h[4] = (int32_t)h4;
1245	h[5] = (int32_t)h5;
1246	h[6] = (int32_t)h6;
1247	h[7] = (int32_t)h7;
1248	h[8] = (int32_t)h8;
1249	h[9] = (int32_t)h9;
1250	}
1251
1252	/*
1253	* h = f * f
1254	*
1255	* Can overlap h with f.
1256	*
1257	* Preconditions:
1258	* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1259	*
1260	* Postconditions:
1261	* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1262	*
1263	* See fe_mul.c for discussion of implementation strategy.
1264	*/
1265	static void fe_sq(fe h, const fe f)
1266	{
1267	int32_t f0 = f[0];
1268	int32_t f1 = f[1];
1269	int32_t f2 = f[2];
1270	int32_t f3 = f[3];
1271	int32_t f4 = f[4];
1272	int32_t f5 = f[5];
1273	int32_t f6 = f[6];
1274	int32_t f7 = f[7];
1275	int32_t f8 = f[8];
1276	int32_t f9 = f[9];
1277	int32_t f0_2 = 2 * f0;
1278	int32_t f1_2 = 2 * f1;
1279	int32_t f2_2 = 2 * f2;
1280	int32_t f3_2 = 2 * f3;
1281	int32_t f4_2 = 2 * f4;
1282	int32_t f5_2 = 2 * f5;
1283	int32_t f6_2 = 2 * f6;
1284	int32_t f7_2 = 2 * f7;
1285	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1286	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1287	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1288	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1289	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1290	int64_t f0f0 = f0 * (int64_t) f0;
1291	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1292	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1293	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1294	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1295	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1296	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1297	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1298	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1299	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1300	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1301	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1302	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1303	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1304	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1305	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1306	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1307	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1308	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1309	int64_t f2f2 = f2 * (int64_t) f2;
1310	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1311	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1312	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1313	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1314	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1315	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1316	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1317	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1318	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1319	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1320	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1321	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1322	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1323	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1324	int64_t f4f4 = f4 * (int64_t) f4;
1325	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1326	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1327	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1328	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1329	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1330	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1331	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1332	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1333	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1334	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1335	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1336	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1337	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1338	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1339	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1340	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1341	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1342	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1343	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1344	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1345	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1346	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1347	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1348	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1349	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1350	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1351	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1352	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1353	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1354	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1355	int64_t carry0;
1356	int64_t carry1;
1357	int64_t carry2;
1358	int64_t carry3;
1359	int64_t carry4;
1360	int64_t carry5;
1361	int64_t carry6;
1362	int64_t carry7;
1363	int64_t carry8;
1364	int64_t carry9;
1365
1366	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1367	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1368
1369	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1370	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1371
1372	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1373	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1374
1375	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1376	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1377
1378	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1379	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1380
1381	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1382
1383	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1384
1385	h[0] = (int32_t)h0;
1386	h[1] = (int32_t)h1;
1387	h[2] = (int32_t)h2;
1388	h[3] = (int32_t)h3;
1389	h[4] = (int32_t)h4;
1390	h[5] = (int32_t)h5;
1391	h[6] = (int32_t)h6;
1392	h[7] = (int32_t)h7;
1393	h[8] = (int32_t)h8;
1394	h[9] = (int32_t)h9;
1395	}
1396
1397	static void fe_invert(fe out, const fe z)
1398	{
1399	fe t0;
1400	fe t1;
1401	fe t2;
1402	fe t3;
1403	int i;
1404
1405	/*
1406	* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
1407	* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
1408	*/
1409
1410	/* t0 = z ** 2 */
1411	fe_sq(t0, z);
1412
1413	/* t1 = t0 (2 2) = z ** 8 */
1414	fe_sq(t1, t0);
1415	fe_sq(t1, t1);
1416
1417	/* t1 = z * t1 = z ** 9 */
1418	fe_mul(t1, z, t1);
1419	/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1420	fe_mul(t0, t0, t1);
1421
1422	/* t2 = t0 2 = z 22 */
1423	fe_sq(t2, t0);
1424
1425	/* t1 = t1 * t2 = z (2 5 - 1) */
1426	fe_mul(t1, t1, t2);
1427
1428	/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
1429	fe_sq(t2, t1);
1430	for (i = 1; i < 5; ++i) {
1431	fe_sq(t2, t2);
1432	}
1433
1434	/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
1435	fe_mul(t1, t2, t1);
1436
1437	/* Continuing similarly... */
1438
1439	/* t2 = z (2 20 - 1) */
1440	fe_sq(t2, t1);
1441	for (i = 1; i < 10; ++i) {
1442	fe_sq(t2, t2);
1443	}
1444	fe_mul(t2, t2, t1);
1445
1446	/* t2 = z (2 40 - 1) */
1447	fe_sq(t3, t2);
1448	for (i = 1; i < 20; ++i) {
1449	fe_sq(t3, t3);
1450	}
1451	fe_mul(t2, t3, t2);
1452
1453	/* t2 = z (2 10) * (2 ** 40 - 1) */
1454	for (i = 0; i < 10; ++i) {
1455	fe_sq(t2, t2);
1456	}
1457	/* t1 = z (2 50 - 1) */
1458	fe_mul(t1, t2, t1);
1459
1460	/* t2 = z (2 100 - 1) */
1461	fe_sq(t2, t1);
1462	for (i = 1; i < 50; ++i) {
1463	fe_sq(t2, t2);
1464	}
1465	fe_mul(t2, t2, t1);
1466
1467	/* t2 = z (2 200 - 1) */
1468	fe_sq(t3, t2);
1469	for (i = 1; i < 100; ++i) {
1470	fe_sq(t3, t3);
1471	}
1472	fe_mul(t2, t3, t2);
1473
1474	/* t2 = z ((2 50) * (2 ** 200 - 1) */
1475	fe_sq(t2, t2);
1476	for (i = 1; i < 50; ++i) {
1477	fe_sq(t2, t2);
1478	}
1479
1480	/* t1 = z (2 250 - 1) */
1481	fe_mul(t1, t2, t1);
1482
1483	/* t1 = z ((2 5) * (2 ** 250 - 1)) */
1484	fe_sq(t1, t1);
1485	for (i = 1; i < 5; ++i) {
1486	fe_sq(t1, t1);
1487	}
1488
1489	/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
1490	fe_mul(out, t1, t0);
1491	}
1492
1493	/*
1494	* h = -f
1495	*
1496	* Preconditions:
1497	* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1498	*
1499	* Postconditions:
1500	* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1501	*/
1502	static void fe_neg(fe h, const fe f)
1503	{
1504	unsigned i;
1505
1506	for (i = 0; i < 10; i++) {
1507	h[i] = -f[i];
1508	}
1509	}
1510
1511	/*
1512	* Replace (f,g) with (g,g) if b == 1;
1513	* replace (f,g) with (f,g) if b == 0.
1514	*
1515	* Preconditions: b in {0,1}.
1516	*/
1517	static void fe_cmov(fe f, const fe g, unsigned b)
1518	{
1519	size_t i;
1520
1521	b = 0-b;
1522	for (i = 0; i < 10; i++) {
1523	int32_t x = f[i] ^ g[i];
1524	x &= b;
1525	f[i] ^= x;
1526	}
1527	}
1528
1529	/*
1530	* return 0 if f == 0
1531	* return 1 if f != 0
1532	*
1533	* Preconditions:
1534	* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1535	*/
1536	static int fe_isnonzero(const fe f)
1537	{
1538	uint8_t s[32];
1539	static const uint8_t zero[32] = {0};
1540
1541	fe_tobytes(s, f);
1542
1543	return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1544	}
1545
1546	/*
1547	* return 1 if f is in {1,3,5,...,q-2}
1548	* return 0 if f is in {0,2,4,...,q-1}
1549	*
1550	* Preconditions:
1551	* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1552	*/
1553	static int fe_isnegative(const fe f)
1554	{
1555	uint8_t s[32];
1556
1557	fe_tobytes(s, f);
1558	return s[0] & 1;
1559	}
1560
1561	/*
1562	* h = 2 * f * f
1563	*
1564	* Can overlap h with f.
1565	*
1566	* Preconditions:
1567	* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1568	*
1569	* Postconditions:
1570	* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1571	*
1572	* See fe_mul.c for discussion of implementation strategy.
1573	*/
1574	static void fe_sq2(fe h, const fe f)
1575	{
1576	int32_t f0 = f[0];
1577	int32_t f1 = f[1];
1578	int32_t f2 = f[2];
1579	int32_t f3 = f[3];
1580	int32_t f4 = f[4];
1581	int32_t f5 = f[5];
1582	int32_t f6 = f[6];
1583	int32_t f7 = f[7];
1584	int32_t f8 = f[8];
1585	int32_t f9 = f[9];
1586	int32_t f0_2 = 2 * f0;
1587	int32_t f1_2 = 2 * f1;
1588	int32_t f2_2 = 2 * f2;
1589	int32_t f3_2 = 2 * f3;
1590	int32_t f4_2 = 2 * f4;
1591	int32_t f5_2 = 2 * f5;
1592	int32_t f6_2 = 2 * f6;
1593	int32_t f7_2 = 2 * f7;
1594	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1595	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1596	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1597	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1598	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1599	int64_t f0f0 = f0 * (int64_t) f0;
1600	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1601	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1602	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1603	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1604	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1605	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1606	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1607	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1608	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1609	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1610	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1611	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1612	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1613	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1614	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1615	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1616	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1617	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1618	int64_t f2f2 = f2 * (int64_t) f2;
1619	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1620	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1621	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1622	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1623	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1624	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1625	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1626	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1627	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1628	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1629	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1630	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1631	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1632	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1633	int64_t f4f4 = f4 * (int64_t) f4;
1634	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1635	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1636	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1637	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1638	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1639	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1640	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1641	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1642	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1643	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1644	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1645	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1646	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1647	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1648	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1649	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1650	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1651	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1652	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1653	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1654	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1655	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1656	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1657	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1658	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1659	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1660	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1661	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1662	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1663	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1664	int64_t carry0;
1665	int64_t carry1;
1666	int64_t carry2;
1667	int64_t carry3;
1668	int64_t carry4;
1669	int64_t carry5;
1670	int64_t carry6;
1671	int64_t carry7;
1672	int64_t carry8;
1673	int64_t carry9;
1674
1675	h0 += h0;
1676	h1 += h1;
1677	h2 += h2;
1678	h3 += h3;
1679	h4 += h4;
1680	h5 += h5;
1681	h6 += h6;
1682	h7 += h7;
1683	h8 += h8;
1684	h9 += h9;
1685
1686	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1687	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1688
1689	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1690	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1691
1692	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1693	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1694
1695	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1696	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1697
1698	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1699	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1700
1701	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1702
1703	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1704
1705	h[0] = (int32_t)h0;
1706	h[1] = (int32_t)h1;
1707	h[2] = (int32_t)h2;
1708	h[3] = (int32_t)h3;
1709	h[4] = (int32_t)h4;
1710	h[5] = (int32_t)h5;
1711	h[6] = (int32_t)h6;
1712	h[7] = (int32_t)h7;
1713	h[8] = (int32_t)h8;
1714	h[9] = (int32_t)h9;
1715	}
1716
1717	static void fe_pow22523(fe out, const fe z)
1718	{
1719	fe t0;
1720	fe t1;
1721	fe t2;
1722	int i;
1723
1724	fe_sq(t0, z);
1725	fe_sq(t1, t0);
1726	for (i = 1; i < 2; ++i) {
1727	fe_sq(t1, t1);
1728	}
1729	fe_mul(t1, z, t1);
1730	fe_mul(t0, t0, t1);
1731	fe_sq(t0, t0);
1732	fe_mul(t0, t1, t0);
1733	fe_sq(t1, t0);
1734	for (i = 1; i < 5; ++i) {
1735	fe_sq(t1, t1);
1736	}
1737	fe_mul(t0, t1, t0);
1738	fe_sq(t1, t0);
1739	for (i = 1; i < 10; ++i) {
1740	fe_sq(t1, t1);
1741	}
1742	fe_mul(t1, t1, t0);
1743	fe_sq(t2, t1);
1744	for (i = 1; i < 20; ++i) {
1745	fe_sq(t2, t2);
1746	}
1747	fe_mul(t1, t2, t1);
1748	fe_sq(t1, t1);
1749	for (i = 1; i < 10; ++i) {
1750	fe_sq(t1, t1);
1751	}
1752	fe_mul(t0, t1, t0);
1753	fe_sq(t1, t0);
1754	for (i = 1; i < 50; ++i) {
1755	fe_sq(t1, t1);
1756	}
1757	fe_mul(t1, t1, t0);
1758	fe_sq(t2, t1);
1759	for (i = 1; i < 100; ++i) {
1760	fe_sq(t2, t2);
1761	}
1762	fe_mul(t1, t2, t1);
1763	fe_sq(t1, t1);
1764	for (i = 1; i < 50; ++i) {
1765	fe_sq(t1, t1);
1766	}
1767	fe_mul(t0, t1, t0);
1768	fe_sq(t0, t0);
1769	for (i = 1; i < 2; ++i) {
1770	fe_sq(t0, t0);
1771	}
1772	fe_mul(out, t0, z);
1773	}
1774
1775	/*
1776	* ge means group element.
1777	*
1778	* Here the group is the set of pairs (x,y) of field elements (see fe.h)
1779	* satisfying -x^2 + y^2 = 1 + d x^2y^2
1780	* where d = -121665/121666.
1781	*
1782	* Representations:
1783	* ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1784	* ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1785	* ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1786	* ge_precomp (Duif): (y+x,y-x,2dxy)
1787	*/
1788	typedef struct {
1789	fe X;
1790	fe Y;
1791	fe Z;
1792	} ge_p2;
1793
1794	typedef struct {
1795	fe X;
1796	fe Y;
1797	fe Z;
1798	fe T;
1799	} ge_p3;
1800
1801	typedef struct {
1802	fe X;
1803	fe Y;
1804	fe Z;
1805	fe T;
1806	} ge_p1p1;
1807
1808	typedef struct {
1809	fe yplusx;
1810	fe yminusx;
1811	fe xy2d;
1812	} ge_precomp;
1813
1814	typedef struct {
1815	fe YplusX;
1816	fe YminusX;
1817	fe Z;
1818	fe T2d;
1819	} ge_cached;
1820
1821	static void ge_tobytes(uint8_t s, const ge_p2 h)
1822	{
1823	fe recip;
1824	fe x;
1825	fe y;
1826
1827	fe_invert(recip, h->Z);
1828	fe_mul(x, h->X, recip);
1829	fe_mul(y, h->Y, recip);
1830	fe_tobytes(s, y);
1831	s[31] ^= fe_isnegative(x) << 7;
1832	}
1833
1834	static void ge_p3_tobytes(uint8_t s, const ge_p3 h)
1835	{
1836	fe recip;
1837	fe x;
1838	fe y;
1839
1840	fe_invert(recip, h->Z);
1841	fe_mul(x, h->X, recip);
1842	fe_mul(y, h->Y, recip);
1843	fe_tobytes(s, y);
1844	s[31] ^= fe_isnegative(x) << 7;
1845	}
1846
1847	static const fe d = {
1848	-10913610, 13857413, -15372611, 6949391, 114729,
1849	-8787816, -6275908, -3247719, -18696448, -12055116
1850	};
1851
1852	static const fe sqrtm1 = {
1853	-32595792, -7943725, 9377950, 3500415, 12389472,
1854	-272473, -25146209, -2005654, 326686, 11406482
1855	};
1856
1857	static int ge_frombytes_vartime(ge_p3 h, const uint8_t s)
1858	{
1859	fe u;
1860	fe v;
1861	fe v3;
1862	fe vxx;
1863	fe check;
1864
1865	fe_frombytes(h->Y, s);
1866	fe_1(h->Z);
1867	fe_sq(u, h->Y);
1868	fe_mul(v, u, d);
1869	fe_sub(u, u, h->Z); /* u = y^2-1 */
1870	fe_add(v, v, h->Z); /* v = dy^2+1 */
1871
1872	fe_sq(v3, v);
1873	fe_mul(v3, v3, v); /* v3 = v^3 */
1874	fe_sq(h->X, v3);
1875	fe_mul(h->X, h->X, v);
1876	fe_mul(h->X, h->X, u); /* x = uv^7 */
1877
1878	fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
1879	fe_mul(h->X, h->X, v3);
1880	fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
1881
1882	fe_sq(vxx, h->X);
1883	fe_mul(vxx, vxx, v);
1884	fe_sub(check, vxx, u); /* vx^2-u */
1885	if (fe_isnonzero(check)) {
1886	fe_add(check, vxx, u); /* vx^2+u */
1887	if (fe_isnonzero(check)) {
1888	return -1;
1889	}
1890	fe_mul(h->X, h->X, sqrtm1);
1891	}
1892
1893	if (fe_isnegative(h->X) != (s[31] >> 7)) {
1894	fe_neg(h->X, h->X);
1895	}
1896
1897	fe_mul(h->T, h->X, h->Y);
1898	return 0;
1899	}
1900
1901	static void ge_p2_0(ge_p2 *h)
1902	{
1903	fe_0(h->X);
1904	fe_1(h->Y);
1905	fe_1(h->Z);
1906	}
1907
1908	static void ge_p3_0(ge_p3 *h)
1909	{
1910	fe_0(h->X);
1911	fe_1(h->Y);
1912	fe_1(h->Z);
1913	fe_0(h->T);
1914	}
1915
1916	static void ge_precomp_0(ge_precomp *h)
1917	{
1918	fe_1(h->yplusx);
1919	fe_1(h->yminusx);
1920	fe_0(h->xy2d);
1921	}
1922
1923	/* r = p */
1924	static void ge_p3_to_p2(ge_p2 r, const ge_p3 p)
1925	{
1926	fe_copy(r->X, p->X);
1927	fe_copy(r->Y, p->Y);
1928	fe_copy(r->Z, p->Z);
1929	}
1930
1931	static const fe d2 = {
1932	-21827239, -5839606, -30745221, 13898782, 229458,
1933	15978800, -12551817, -6495438, 29715968, 9444199
1934	};
1935
1936	/* r = p */
1937	static void ge_p3_to_cached(ge_cached r, const ge_p3 p)
1938	{
1939	fe_add(r->YplusX, p->Y, p->X);
1940	fe_sub(r->YminusX, p->Y, p->X);
1941	fe_copy(r->Z, p->Z);
1942	fe_mul(r->T2d, p->T, d2);
1943	}
1944
1945	/* r = p */
1946	static void ge_p1p1_to_p2(ge_p2 r, const ge_p1p1 p)
1947	{
1948	fe_mul(r->X, p->X, p->T);
1949	fe_mul(r->Y, p->Y, p->Z);
1950	fe_mul(r->Z, p->Z, p->T);
1951	}
1952
1953	/* r = p */
1954	static void ge_p1p1_to_p3(ge_p3 r, const ge_p1p1 p)
1955	{
1956	fe_mul(r->X, p->X, p->T);
1957	fe_mul(r->Y, p->Y, p->Z);
1958	fe_mul(r->Z, p->Z, p->T);
1959	fe_mul(r->T, p->X, p->Y);
1960	}
1961
1962	/* r = 2 * p */
1963	static void ge_p2_dbl(ge_p1p1 r, const ge_p2 p)
1964	{
1965	fe t0;
1966
1967	fe_sq(r->X, p->X);
1968	fe_sq(r->Z, p->Y);
1969	fe_sq2(r->T, p->Z);
1970	fe_add(r->Y, p->X, p->Y);
1971	fe_sq(t0, r->Y);
1972	fe_add(r->Y, r->Z, r->X);
1973	fe_sub(r->Z, r->Z, r->X);
1974	fe_sub(r->X, t0, r->Y);
1975	fe_sub(r->T, r->T, r->Z);
1976	}
1977
1978	/* r = 2 * p */
1979	static void ge_p3_dbl(ge_p1p1 r, const ge_p3 p)
1980	{
1981	ge_p2 q;
1982	ge_p3_to_p2(&q, p);
1983	ge_p2_dbl(r, &q);
1984	}
1985
1986	/* r = p + q */
1987	static void ge_madd(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
1988	{
1989	fe t0;
1990
1991	fe_add(r->X, p->Y, p->X);
1992	fe_sub(r->Y, p->Y, p->X);
1993	fe_mul(r->Z, r->X, q->yplusx);
1994	fe_mul(r->Y, r->Y, q->yminusx);
1995	fe_mul(r->T, q->xy2d, p->T);
1996	fe_add(t0, p->Z, p->Z);
1997	fe_sub(r->X, r->Z, r->Y);
1998	fe_add(r->Y, r->Z, r->Y);
1999	fe_add(r->Z, t0, r->T);
2000	fe_sub(r->T, t0, r->T);
2001	}
2002
2003	/* r = p - q */
2004	static void ge_msub(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2005	{
2006	fe t0;
2007
2008	fe_add(r->X, p->Y, p->X);
2009	fe_sub(r->Y, p->Y, p->X);
2010	fe_mul(r->Z, r->X, q->yminusx);
2011	fe_mul(r->Y, r->Y, q->yplusx);
2012	fe_mul(r->T, q->xy2d, p->T);
2013	fe_add(t0, p->Z, p->Z);
2014	fe_sub(r->X, r->Z, r->Y);
2015	fe_add(r->Y, r->Z, r->Y);
2016	fe_sub(r->Z, t0, r->T);
2017	fe_add(r->T, t0, r->T);
2018	}
2019
2020	/* r = p + q */
2021	static void ge_add(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2022	{
2023	fe t0;
2024
2025	fe_add(r->X, p->Y, p->X);
2026	fe_sub(r->Y, p->Y, p->X);
2027	fe_mul(r->Z, r->X, q->YplusX);
2028	fe_mul(r->Y, r->Y, q->YminusX);
2029	fe_mul(r->T, q->T2d, p->T);
2030	fe_mul(r->X, p->Z, q->Z);
2031	fe_add(t0, r->X, r->X);
2032	fe_sub(r->X, r->Z, r->Y);
2033	fe_add(r->Y, r->Z, r->Y);
2034	fe_add(r->Z, t0, r->T);
2035	fe_sub(r->T, t0, r->T);
2036	}
2037
2038	/* r = p - q */
2039	static void ge_sub(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2040	{
2041	fe t0;
2042
2043	fe_add(r->X, p->Y, p->X);
2044	fe_sub(r->Y, p->Y, p->X);
2045	fe_mul(r->Z, r->X, q->YminusX);
2046	fe_mul(r->Y, r->Y, q->YplusX);
2047	fe_mul(r->T, q->T2d, p->T);
2048	fe_mul(r->X, p->Z, q->Z);
2049	fe_add(t0, r->X, r->X);
2050	fe_sub(r->X, r->Z, r->Y);
2051	fe_add(r->Y, r->Z, r->Y);
2052	fe_sub(r->Z, t0, r->T);
2053	fe_add(r->T, t0, r->T);
2054	}
2055
2056	static uint8_t equal(signed char b, signed char c)
2057	{
2058	uint8_t ub = b;
2059	uint8_t uc = c;
2060	uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2061	uint32_t y = x; /* 0: yes; 1..255: no */
2062	y -= 1; /* 4294967295: yes; 0..254: no */
2063	y >>= 31; /* 1: yes; 0: no */
2064	return y;
2065	}
2066
2067	static void cmov(ge_precomp t, const ge_precomp u, uint8_t b)
2068	{
2069	fe_cmov(t->yplusx, u->yplusx, b);
2070	fe_cmov(t->yminusx, u->yminusx, b);
2071	fe_cmov(t->xy2d, u->xy2d, b);
2072	}
2073
2074	/* k25519Precomp[i][j] = (j+1)256^iB */
2075	static const ge_precomp k25519Precomp[32][8] = {
2076	{
2077	{
2078	{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2079	27544626, -11754271, -6079156, 2047605},
2080	{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2081	5043384, 19500929, -15469378},
2082	{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2083	29287919, 11864899, -24514362, -4438546},
2084	},
2085	{
2086	{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2087	-11717903, -3814571, -358445, -10211303},
2088	{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2089	-15616551, 11189268, -26829678, -5319081},
2090	{26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2091	-3128826, -9541118, -15472047, -4166697},
2092	},
2093	{
2094	{15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2095	27787600, -14772189, 28944400, -1550024},
2096	{16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2097	16354577, -11775962, 7689662, 11199574},
2098	{30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2099	7512774, 10017326, -17749093, -9920357},
2100	},
2101	{
2102	{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2103	-28926210, 15006023, 3284568, -6276540},
2104	{23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2105	7464579, 9656445, 13059162, 10374397},
2106	{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2107	-3839045, -641708, -101325},
2108	},
2109	{
2110	{10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2111	32867885, 14515107, -15438304, 10819380},
2112	{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2113	12483688, -12668491, 5581306},
2114	{19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2115	28542350, 13850243, -23678021, -15815942},
2116	},
2117	{
2118	{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2119	-19188627, -15224819, -9818940, -12085777},
2120	{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2121	-15689887, 1762328, 14866737},
2122	{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2123	-28236412, 3959421, 27914454, 4383652},
2124	},
2125	{
2126	{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2127	5230134, -23952439, -15175766},
2128	{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2129	20654025, 16520125, 30598449, 7715701},
2130	{28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2131	-31400660, 1370708, 29794553, -1409300},
2132	},
2133	{
2134	{14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2135	30290735, 10876454, -33154098, 2381726},
2136	{-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2137	-6236617, 3696005, -32300832, 15351955},
2138	{27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2139	-32961401, -2970515, 29551813, 10109425},
2140	},
2141	},
2142	{
2143	{
2144	{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2145	-2378284, -1627556, 10092783, -4764171},
2146	{27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2147	-32508754, 12005538, -17810127, 12803510},
2148	{17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2149	30364213, -9038194, 18016357, 4397660},
2150	},
2151	{
2152	{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2153	-26619106, 14544525, -17477504, 982639},
2154	{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2155	-4120128, -21047696, 9934963},
2156	{5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2157	-14747930, 4559895, -30123922, -10897950},
2158	},
2159	{
2160	{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2161	24191034, 4541697, -13338309, 5500568},
2162	{12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2163	-17430592, 12264343, 10874051, 13524335},
2164	{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2165	5080568, -22528059, 5376628},
2166	},
2167	{
2168	{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2169	-22321305, -9447443, 4535768, 1569007},
2170	{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2171	-30494562, 3044290, 31848280, 12543772},
2172	{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2173	-27377195, -2062731, 7718482, 14474653},
2174	},
2175	{
2176	{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2177	-7236665, 24316168, -5253567},
2178	{13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2179	33040651, -13424532, -20729456, 8321686},
2180	{21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
2181	23845965, -11874838, -9984458, 608372},
2182	},
2183	{
2184	{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
2185	1123968, -6780577, 27229399, 23887},
2186	{-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
2187	12797024, -6440308, -1633405, 16678954},
2188	{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
2189	-1508144, -4795045, -17169265, 4904953},
2190	},
2191	{
2192	{24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
2193	5169211, 16191880, 2128236, -4326833},
2194	{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
2195	-29806336, 916033, -6882542, -2986532},
2196	{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
2197	285431, 2763829, 15736322, 4143876},
2198	},
2199	{
2200	{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
2201	-14594663, 23527084, -16458268},
2202	{33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
2203	-32625340, 4087881, -15188911, -14416214},
2204	{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
2205	4357868, -4774191, -16323038},
2206	},
2207	},
2208	{
2209	{
2210	{6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
2211	23365147, -3949732, 7390890, 2759800},
2212	{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
2213	-4264057, 1244380, -12919645},
2214	{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
2215	9208236, 15886429, 16489664},
2216	},
2217	{
2218	{1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
2219	-13693198, 398369, -30606455, -712933},
2220	{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
2221	13348553, 12076947, -30836462, 5113182},
2222	{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
2223	-30341101, -7336386, 13847711, 5387222},
2224	},
2225	{
2226	{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
2227	8763061, 3617786, -19600662, 10370991},
2228	{20246567, -14369378, 22358229, -543712, 18507283, -10413996,
2229	14554437, -8746092, 32232924, 16763880},
2230	{9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
2231	11094161, 15689506, 3140038, -16510092},
2232	},
2233	{
2234	{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
2235	-27224800, 9448613, -28774454, 366295},
2236	{19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
2237	28344573, 8041113, 719605, 11671788},
2238	{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
2239	-15266516, 27000813, -10195553},
2240	},
2241	{
2242	{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
2243	5336097, 6750977, -14521026},
2244	{11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
2245	1695823, -8819122, 8169720, 16220347},
2246	{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
2247	-11144307, -2627664, -5990708, -14166033},
2248	},
2249	{
2250	{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
2251	27884329, 2847284, 2655861, 1738395},
2252	{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
2253	21651608, -3239336, -19087449, -11005278},
2254	{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
2255	5821408, 10478196, 8544890},
2256	},
2257	{
2258	{32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
2259	19270449, 12217473, 17789017, -3395995},
2260	{-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
2261	15479401, -3853233, 30460520, 1052596},
2262	{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
2263	27491595, -4612359, 3179268, -9478891},
2264	},
2265	{
2266	{31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
2267	-14756777, -16411740, 19072640, -9511060},
2268	{11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
2269	5977896, -5215017, 473099, 5040608},
2270	{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
2271	28326862, 1721092, -19558642, -3131606},
2272	},
2273	},
2274	{
2275	{
2276	{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
2277	8076149, -27868496, 11538389},
2278	{-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
2279	8754525, 7446702, -5676054, 5797016},
2280	{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
2281	2014099, -9050574, -2369172, -5877341},
2282	},
2283	{
2284	{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
2285	1192730, -3714199, 15123619, 10811505},
2286	{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
2287	15776356, -28886779, -11974553},
2288	{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
2289	-20654173, -16484855, 4714547, -9600655},
2290	},
2291	{
2292	{15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
2293	24611599, -4543832, -11745876, 12340220},
2294	{12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
2295	9613953, 8241152, 15370987, 9608631},
2296	{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
2297	15866074, -28210621, -8814099},
2298	},
2299	{
2300	{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
2301	858697, 20571223, 8420556},
2302	{14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
2303	33531827, 12516406, -21574435, -12476749},
2304	{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
2305	7256740, 8791136, 15069930},
2306	},
2307	{
2308	{1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
2309	14711875, 4874229, -30663140, -2331391},
2310	{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
2311	-7912378, -33069337, 9234253},
2312	{20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
2313	31559055, -11609587, 18979186, 13396066},
2314	},
2315	{
2316	{24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
2317	-18816887, 13594782, 33514650, 7021958},
2318	{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
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4117	9021034, 9078865, 3353509, 4033511},
4118	{-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
4119	23161163, 8839127, 27485041, 7356032},
4120	},
4121	},
4122	{
4123	{
4124	{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
4125	2625015, 28431036, -16771834},
4126	{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
4127	-22545972, 14150565, 15970762, 4099461},
4128	{29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
4129	13617293, -9937143, 11465739, 8317062},
4130	},
4131	{
4132	{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
4133	14898637, 3848455, 20969334, -5157516},
4134	{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
4135	-21610826, -3649888, 11177095, 14989547},
4136	{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
4137	13515641, 2581286, -28487508, 9930240},
4138	},
4139	{
4140	{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
4141	18345767, -13403753, 16291481, -5314038},
4142	{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
4143	6957617, 4368891, 9788741},
4144	{16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
4145	-21722536, -8613148, 16250552, -11111103},
4146	},
4147	{
4148	{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
4149	10604807, -30190403, 4782747},
4150	{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
4151	-9981571, 4383045, 22546403, 437323},
4152	{31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
4153	27343084, 2786261, -30633590, -14097016},
4154	},
4155	{
4156	{-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
4157	-19690631, 2355319, -19284671, -6114373},
4158	{15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
4159	18952177, 15496498, -29380133, 11754228},
4160	{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
4161	7141596, 11724556, 22761615, -10134141},
4162	},
4163	{
4164	{16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
4165	-28741185, -12227393, 32851222, 11717399},
4166	{11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
4167	31474879, 3483633, -1193175, -4030831},
4168	{-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4169	33142652, 6546660, -19985279, -3948376},
4170	},
4171	{
4172	{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4173	-8537131, -12833048, -30772034, -15486313},
4174	{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4175	-31135347, -16049879, 10928917, 3011958},
4176	{-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4177	-30831056, -12805180, 18008031, 10258577},
4178	},
4179	{
4180	{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4181	-1853465, 1367120, 25127874, 6671743},
4182	{29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4183	21382910, 11042292, 25838796, 4642684},
4184	{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4185	30468147, -13900640, 18423289, 4177476},
4186	},
4187	},
4188	};
4189
4190	static uint8_t negative(signed char b)
4191	{
4192	uint32_t x = b;
4193
4194	x >>= 31; /* 1: yes; 0: no */
4195	return x;
4196	}
4197
4198	static void table_select(ge_precomp *t, int pos, signed char b)
4199	{
4200	ge_precomp minust;
4201	uint8_t bnegative = negative(b);
4202	uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4203
4204	ge_precomp_0(t);
4205	cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4206	cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4207	cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4208	cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4209	cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4210	cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4211	cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4212	cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4213	fe_copy(minust.yplusx, t->yminusx);
4214	fe_copy(minust.yminusx, t->yplusx);
4215	fe_neg(minust.xy2d, t->xy2d);
4216	cmov(t, &minust, bnegative);
4217	}
4218
4219	/*
4220	* h = a * B
4221	*
4222	* where a = a[0]+256*a[1]+...+256^31 a[31]
4223	* B is the Ed25519 base point (x,4/5) with x positive.
4224	*
4225	* Preconditions:
4226	* a[31] <= 127
4227	*/
4228	static void ge_scalarmult_base(ge_p3 h, const uint8_t a)
4229	{
4230	signed char e[64];
4231	signed char carry;
4232	ge_p1p1 r;
4233	ge_p2 s;
4234	ge_precomp t;
4235	int i;
4236
4237	for (i = 0; i < 32; ++i) {
4238	e[2 * i + 0] = (a[i] >> 0) & 15;
4239	e[2 * i + 1] = (a[i] >> 4) & 15;
4240	}
4241	/* each e[i] is between 0 and 15 */
4242	/* e[63] is between 0 and 7 */
4243
4244	carry = 0;
4245	for (i = 0; i < 63; ++i) {
4246	e[i] += carry;
4247	carry = e[i] + 8;
4248	carry >>= 4;
4249	e[i] -= carry << 4;
4250	}
4251	e[63] += carry;
4252	/* each e[i] is between -8 and 8 */
4253
4254	ge_p3_0(h);
4255	for (i = 1; i < 64; i += 2) {
4256	table_select(&t, i / 2, e[i]);
4257	ge_madd(&r, h, &t);
4258	ge_p1p1_to_p3(h, &r);
4259	}
4260
4261	ge_p3_dbl(&r, h);
4262	ge_p1p1_to_p2(&s, &r);
4263	ge_p2_dbl(&r, &s);
4264	ge_p1p1_to_p2(&s, &r);
4265	ge_p2_dbl(&r, &s);
4266	ge_p1p1_to_p2(&s, &r);
4267	ge_p2_dbl(&r, &s);
4268	ge_p1p1_to_p3(h, &r);
4269
4270	for (i = 0; i < 64; i += 2) {
4271	table_select(&t, i / 2, e[i]);
4272	ge_madd(&r, h, &t);
4273	ge_p1p1_to_p3(h, &r);
4274	}
4275
4276	OPENSSL_cleanse(e, sizeof(e));
4277	}
4278
4279	#if !defined(BASE_2_51_IMPLEMENTED)
4280	/*
4281	* Replace (f,g) with (g,f) if b == 1;
4282	* replace (f,g) with (f,g) if b == 0.
4283	*
4284	* Preconditions: b in {0,1}.
4285	*/
4286	static void fe_cswap(fe f, fe g, unsigned int b)
4287	{
4288	size_t i;
4289
4290	b = 0-b;
4291	for (i = 0; i < 10; i++) {
4292	int32_t x = f[i] ^ g[i];
4293	x &= b;
4294	f[i] ^= x;
4295	g[i] ^= x;
4296	}
4297	}
4298
4299	/*
4300	* h = f * 121666
4301	*
4302	* Can overlap h with f.
4303	*
4304	* Preconditions:
4305	* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
4306	*
4307	* Postconditions:
4308	* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
4309	*/
4310	static void fe_mul121666(fe h, fe f)
4311	{
4312	int32_t f0 = f[0];
4313	int32_t f1 = f[1];
4314	int32_t f2 = f[2];
4315	int32_t f3 = f[3];
4316	int32_t f4 = f[4];
4317	int32_t f5 = f[5];
4318	int32_t f6 = f[6];
4319	int32_t f7 = f[7];
4320	int32_t f8 = f[8];
4321	int32_t f9 = f[9];
4322	int64_t h0 = f0 * (int64_t) 121666;
4323	int64_t h1 = f1 * (int64_t) 121666;
4324	int64_t h2 = f2 * (int64_t) 121666;
4325	int64_t h3 = f3 * (int64_t) 121666;
4326	int64_t h4 = f4 * (int64_t) 121666;
4327	int64_t h5 = f5 * (int64_t) 121666;
4328	int64_t h6 = f6 * (int64_t) 121666;
4329	int64_t h7 = f7 * (int64_t) 121666;
4330	int64_t h8 = f8 * (int64_t) 121666;
4331	int64_t h9 = f9 * (int64_t) 121666;
4332	int64_t carry0;
4333	int64_t carry1;
4334	int64_t carry2;
4335	int64_t carry3;
4336	int64_t carry4;
4337	int64_t carry5;
4338	int64_t carry6;
4339	int64_t carry7;
4340	int64_t carry8;
4341	int64_t carry9;
4342
4343	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
4344	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
4345	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
4346	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
4347	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
4348
4349	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
4350	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
4351	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
4352	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
4353	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
4354
4355	h[0] = (int32_t)h0;
4356	h[1] = (int32_t)h1;
4357	h[2] = (int32_t)h2;
4358	h[3] = (int32_t)h3;
4359	h[4] = (int32_t)h4;
4360	h[5] = (int32_t)h5;
4361	h[6] = (int32_t)h6;
4362	h[7] = (int32_t)h7;
4363	h[8] = (int32_t)h8;
4364	h[9] = (int32_t)h9;
4365	}
4366
4367	static void x25519_scalar_mult_generic(uint8_t out[32],
4368	const uint8_t scalar[32],
4369	const uint8_t point[32]) {
4370	fe x1, x2, z2, x3, z3, tmp0, tmp1;
4371	uint8_t e[32];
4372	unsigned swap = 0;
4373	int pos;
4374
4375	memcpy(e, scalar, 32);
4376	e[0] &= 248;
4377	e[31] &= 127;
4378	e[31] \|= 64;
4379	fe_frombytes(x1, point);
4380	fe_1(x2);
4381	fe_0(z2);
4382	fe_copy(x3, x1);
4383	fe_1(z3);
4384
4385	for (pos = 254; pos >= 0; --pos) {
4386	unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4387	swap ^= b;
4388	fe_cswap(x2, x3, swap);
4389	fe_cswap(z2, z3, swap);
4390	swap = b;
4391	fe_sub(tmp0, x3, z3);
4392	fe_sub(tmp1, x2, z2);
4393	fe_add(x2, x2, z2);
4394	fe_add(z2, x3, z3);
4395	fe_mul(z3, tmp0, x2);
4396	fe_mul(z2, z2, tmp1);
4397	fe_sq(tmp0, tmp1);
4398	fe_sq(tmp1, x2);
4399	fe_add(x3, z3, z2);
4400	fe_sub(z2, z3, z2);
4401	fe_mul(x2, tmp1, tmp0);
4402	fe_sub(tmp1, tmp1, tmp0);
4403	fe_sq(z2, z2);
4404	fe_mul121666(z3, tmp1);
4405	fe_sq(x3, x3);
4406	fe_add(tmp0, tmp0, z3);
4407	fe_mul(z3, x1, z2);
4408	fe_mul(z2, tmp1, tmp0);
4409	}
4410
4411	fe_invert(z2, z2);
4412	fe_mul(x2, x2, z2);
4413	fe_tobytes(out, x2);
4414
4415	OPENSSL_cleanse(e, sizeof(e));
4416	}
4417
4418	static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4419	const uint8_t point[32]) {
4420	x25519_scalar_mult_generic(out, scalar, point);
4421	}
4422	#endif
4423
4424	static void slide(signed char r, const uint8_t a)
4425	{
4426	int i;
4427	int b;
4428	int k;
4429
4430	for (i = 0; i < 256; ++i) {
4431	r[i] = 1 & (a[i >> 3] >> (i & 7));
4432	}
4433
4434	for (i = 0; i < 256; ++i) {
4435	if (r[i]) {
4436	for (b = 1; b <= 6 && i + b < 256; ++b) {
4437	if (r[i + b]) {
4438	if (r[i] + (r[i + b] << b) <= 15) {
4439	r[i] += r[i + b] << b;
4440	r[i + b] = 0;
4441	} else if (r[i] - (r[i + b] << b) >= -15) {
4442	r[i] -= r[i + b] << b;
4443	for (k = i + b; k < 256; ++k) {
4444	if (!r[k]) {
4445	r[k] = 1;
4446	break;
4447	}
4448	r[k] = 0;
4449	}
4450	} else {
4451	break;
4452	}
4453	}
4454	}
4455	}
4456	}
4457	}
4458
4459	static const ge_precomp Bi[8] = {
4460	{
4461	{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4462	-11754271, -6079156, 2047605},
4463	{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4464	5043384, 19500929, -15469378},
4465	{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4466	11864899, -24514362, -4438546},
4467	},
4468	{
4469	{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4470	-14772189, 28944400, -1550024},
4471	{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4472	-11775962, 7689662, 11199574},
4473	{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4474	10017326, -17749093, -9920357},
4475	},
4476	{
4477	{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4478	14515107, -15438304, 10819380},
4479	{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4480	12483688, -12668491, 5581306},
4481	{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4482	13850243, -23678021, -15815942},
4483	},
4484	{
4485	{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4486	5230134, -23952439, -15175766},
4487	{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4488	16520125, 30598449, 7715701},
4489	{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4490	1370708, 29794553, -1409300},
4491	},
4492	{
4493	{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4494	-1361450, -13062696, 13821877},
4495	{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4496	-7212327, 18853322, -14220951},
4497	{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4498	-10431137, 2207753, -3209784},
4499	},
4500	{
4501	{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4502	-663000, -31111463, -16132436},
4503	{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4504	15725684, 171356, 6466918},
4505	{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4506	-14088058, -30714912, 16193877},
4507	},
4508	{
4509	{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4510	4729455, -18074513, 9256800},
4511	{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4512	9761698, -19827198, 630305},
4513	{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4514	-15960994, -2449256, -14291300},
4515	},
4516	{
4517	{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4518	15033784, 25105118, -7894876},
4519	{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4520	1573892, -2625887, 2198790, -15804619},
4521	{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4522	-16236442, -32461234, -12290683},
4523	},
4524	};
4525
4526	/*
4527	* r = a * A + b * B
4528	*
4529	* where a = a[0]+256*a[1]+...+256^31 a[31].
4530	* and b = b[0]+256*b[1]+...+256^31 b[31].
4531	* B is the Ed25519 base point (x,4/5) with x positive.
4532	*/
4533	static void ge_double_scalarmult_vartime(ge_p2 r, const uint8_t a,
4534	const ge_p3 A, const uint8_t b)
4535	{
4536	signed char aslide[256];
4537	signed char bslide[256];
4538	ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4539	ge_p1p1 t;
4540	ge_p3 u;
4541	ge_p3 A2;
4542	int i;
4543
4544	slide(aslide, a);
4545	slide(bslide, b);
4546
4547	ge_p3_to_cached(&Ai[0], A);
4548	ge_p3_dbl(&t, A);
4549	ge_p1p1_to_p3(&A2, &t);
4550	ge_add(&t, &A2, &Ai[0]);
4551	ge_p1p1_to_p3(&u, &t);
4552	ge_p3_to_cached(&Ai[1], &u);
4553	ge_add(&t, &A2, &Ai[1]);
4554	ge_p1p1_to_p3(&u, &t);
4555	ge_p3_to_cached(&Ai[2], &u);
4556	ge_add(&t, &A2, &Ai[2]);
4557	ge_p1p1_to_p3(&u, &t);
4558	ge_p3_to_cached(&Ai[3], &u);
4559	ge_add(&t, &A2, &Ai[3]);
4560	ge_p1p1_to_p3(&u, &t);
4561	ge_p3_to_cached(&Ai[4], &u);
4562	ge_add(&t, &A2, &Ai[4]);
4563	ge_p1p1_to_p3(&u, &t);
4564	ge_p3_to_cached(&Ai[5], &u);
4565	ge_add(&t, &A2, &Ai[5]);
4566	ge_p1p1_to_p3(&u, &t);
4567	ge_p3_to_cached(&Ai[6], &u);
4568	ge_add(&t, &A2, &Ai[6]);
4569	ge_p1p1_to_p3(&u, &t);
4570	ge_p3_to_cached(&Ai[7], &u);
4571
4572	ge_p2_0(r);
4573
4574	for (i = 255; i >= 0; --i) {
4575	if (aslide[i] \|\| bslide[i]) {
4576	break;
4577	}
4578	}
4579
4580	for (; i >= 0; --i) {
4581	ge_p2_dbl(&t, r);
4582
4583	if (aslide[i] > 0) {
4584	ge_p1p1_to_p3(&u, &t);
4585	ge_add(&t, &u, &Ai[aslide[i] / 2]);
4586	} else if (aslide[i] < 0) {
4587	ge_p1p1_to_p3(&u, &t);
4588	ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4589	}
4590
4591	if (bslide[i] > 0) {
4592	ge_p1p1_to_p3(&u, &t);
4593	ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4594	} else if (bslide[i] < 0) {
4595	ge_p1p1_to_p3(&u, &t);
4596	ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4597	}
4598
4599	ge_p1p1_to_p2(r, &t);
4600	}
4601	}
4602
4603	/*
4604	* The set of scalars is \Z/l
4605	* where l = 2^252 + 27742317777372353535851937790883648493.
4606	*
4607	* Input:
4608	* s[0]+256s[1]+...+256^63s[63] = s
4609	*
4610	* Output:
4611	* s[0]+256s[1]+...+256^31s[31] = s mod l
4612	* where l = 2^252 + 27742317777372353535851937790883648493.
4613	* Overwrites s in place.
4614	*/
4615	static void x25519_sc_reduce(uint8_t *s)
4616	{
4617	int64_t s0 = kBottom21Bits & load_3(s);
4618	int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
4619	int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
4620	int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
4621	int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
4622	int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
4623	int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
4624	int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
4625	int64_t s8 = kBottom21Bits & load_3(s + 21);
4626	int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
4627	int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4628	int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4629	int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4630	int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4631	int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4632	int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4633	int64_t s16 = kBottom21Bits & load_3(s + 42);
4634	int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4635	int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4636	int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4637	int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4638	int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4639	int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4640	int64_t s23 = (load_4(s + 60) >> 3);
4641	int64_t carry0;
4642	int64_t carry1;
4643	int64_t carry2;
4644	int64_t carry3;
4645	int64_t carry4;
4646	int64_t carry5;
4647	int64_t carry6;
4648	int64_t carry7;
4649	int64_t carry8;
4650	int64_t carry9;
4651	int64_t carry10;
4652	int64_t carry11;
4653	int64_t carry12;
4654	int64_t carry13;
4655	int64_t carry14;
4656	int64_t carry15;
4657	int64_t carry16;
4658
4659	s11 += s23 * 666643;
4660	s12 += s23 * 470296;
4661	s13 += s23 * 654183;
4662	s14 -= s23 * 997805;
4663	s15 += s23 * 136657;
4664	s16 -= s23 * 683901;
4665	s23 = 0;
4666
4667	s10 += s22 * 666643;
4668	s11 += s22 * 470296;
4669	s12 += s22 * 654183;
4670	s13 -= s22 * 997805;
4671	s14 += s22 * 136657;
4672	s15 -= s22 * 683901;
4673	s22 = 0;
4674
4675	s9 += s21 * 666643;
4676	s10 += s21 * 470296;
4677	s11 += s21 * 654183;
4678	s12 -= s21 * 997805;
4679	s13 += s21 * 136657;
4680	s14 -= s21 * 683901;
4681	s21 = 0;
4682
4683	s8 += s20 * 666643;
4684	s9 += s20 * 470296;
4685	s10 += s20 * 654183;
4686	s11 -= s20 * 997805;
4687	s12 += s20 * 136657;
4688	s13 -= s20 * 683901;
4689	s20 = 0;
4690
4691	s7 += s19 * 666643;
4692	s8 += s19 * 470296;
4693	s9 += s19 * 654183;
4694	s10 -= s19 * 997805;
4695	s11 += s19 * 136657;
4696	s12 -= s19 * 683901;
4697	s19 = 0;
4698
4699	s6 += s18 * 666643;
4700	s7 += s18 * 470296;
4701	s8 += s18 * 654183;
4702	s9 -= s18 * 997805;
4703	s10 += s18 * 136657;
4704	s11 -= s18 * 683901;
4705	s18 = 0;
4706
4707	carry6 = (s6 + (1 << 20)) >> 21;
4708	s7 += carry6;
4709	s6 -= carry6 * (1 << 21);
4710	carry8 = (s8 + (1 << 20)) >> 21;
4711	s9 += carry8;
4712	s8 -= carry8 * (1 << 21);
4713	carry10 = (s10 + (1 << 20)) >> 21;
4714	s11 += carry10;
4715	s10 -= carry10 * (1 << 21);
4716	carry12 = (s12 + (1 << 20)) >> 21;
4717	s13 += carry12;
4718	s12 -= carry12 * (1 << 21);
4719	carry14 = (s14 + (1 << 20)) >> 21;
4720	s15 += carry14;
4721	s14 -= carry14 * (1 << 21);
4722	carry16 = (s16 + (1 << 20)) >> 21;
4723	s17 += carry16;
4724	s16 -= carry16 * (1 << 21);
4725
4726	carry7 = (s7 + (1 << 20)) >> 21;
4727	s8 += carry7;
4728	s7 -= carry7 * (1 << 21);
4729	carry9 = (s9 + (1 << 20)) >> 21;
4730	s10 += carry9;
4731	s9 -= carry9 * (1 << 21);
4732	carry11 = (s11 + (1 << 20)) >> 21;
4733	s12 += carry11;
4734	s11 -= carry11 * (1 << 21);
4735	carry13 = (s13 + (1 << 20)) >> 21;
4736	s14 += carry13;
4737	s13 -= carry13 * (1 << 21);
4738	carry15 = (s15 + (1 << 20)) >> 21;
4739	s16 += carry15;
4740	s15 -= carry15 * (1 << 21);
4741
4742	s5 += s17 * 666643;
4743	s6 += s17 * 470296;
4744	s7 += s17 * 654183;
4745	s8 -= s17 * 997805;
4746	s9 += s17 * 136657;
4747	s10 -= s17 * 683901;
4748	s17 = 0;
4749
4750	s4 += s16 * 666643;
4751	s5 += s16 * 470296;
4752	s6 += s16 * 654183;
4753	s7 -= s16 * 997805;
4754	s8 += s16 * 136657;
4755	s9 -= s16 * 683901;
4756	s16 = 0;
4757
4758	s3 += s15 * 666643;
4759	s4 += s15 * 470296;
4760	s5 += s15 * 654183;
4761	s6 -= s15 * 997805;
4762	s7 += s15 * 136657;
4763	s8 -= s15 * 683901;
4764	s15 = 0;
4765
4766	s2 += s14 * 666643;
4767	s3 += s14 * 470296;
4768	s4 += s14 * 654183;
4769	s5 -= s14 * 997805;
4770	s6 += s14 * 136657;
4771	s7 -= s14 * 683901;
4772	s14 = 0;
4773
4774	s1 += s13 * 666643;
4775	s2 += s13 * 470296;
4776	s3 += s13 * 654183;
4777	s4 -= s13 * 997805;
4778	s5 += s13 * 136657;
4779	s6 -= s13 * 683901;
4780	s13 = 0;
4781
4782	s0 += s12 * 666643;
4783	s1 += s12 * 470296;
4784	s2 += s12 * 654183;
4785	s3 -= s12 * 997805;
4786	s4 += s12 * 136657;
4787	s5 -= s12 * 683901;
4788	s12 = 0;
4789
4790	carry0 = (s0 + (1 << 20)) >> 21;
4791	s1 += carry0;
4792	s0 -= carry0 * (1 << 21);
4793	carry2 = (s2 + (1 << 20)) >> 21;
4794	s3 += carry2;
4795	s2 -= carry2 * (1 << 21);
4796	carry4 = (s4 + (1 << 20)) >> 21;
4797	s5 += carry4;
4798	s4 -= carry4 * (1 << 21);
4799	carry6 = (s6 + (1 << 20)) >> 21;
4800	s7 += carry6;
4801	s6 -= carry6 * (1 << 21);
4802	carry8 = (s8 + (1 << 20)) >> 21;
4803	s9 += carry8;
4804	s8 -= carry8 * (1 << 21);
4805	carry10 = (s10 + (1 << 20)) >> 21;
4806	s11 += carry10;
4807	s10 -= carry10 * (1 << 21);
4808
4809	carry1 = (s1 + (1 << 20)) >> 21;
4810	s2 += carry1;
4811	s1 -= carry1 * (1 << 21);
4812	carry3 = (s3 + (1 << 20)) >> 21;
4813	s4 += carry3;
4814	s3 -= carry3 * (1 << 21);
4815	carry5 = (s5 + (1 << 20)) >> 21;
4816	s6 += carry5;
4817	s5 -= carry5 * (1 << 21);
4818	carry7 = (s7 + (1 << 20)) >> 21;
4819	s8 += carry7;
4820	s7 -= carry7 * (1 << 21);
4821	carry9 = (s9 + (1 << 20)) >> 21;
4822	s10 += carry9;
4823	s9 -= carry9 * (1 << 21);
4824	carry11 = (s11 + (1 << 20)) >> 21;
4825	s12 += carry11;
4826	s11 -= carry11 * (1 << 21);
4827
4828	s0 += s12 * 666643;
4829	s1 += s12 * 470296;
4830	s2 += s12 * 654183;
4831	s3 -= s12 * 997805;
4832	s4 += s12 * 136657;
4833	s5 -= s12 * 683901;
4834	s12 = 0;
4835
4836	carry0 = s0 >> 21;
4837	s1 += carry0;
4838	s0 -= carry0 * (1 << 21);
4839	carry1 = s1 >> 21;
4840	s2 += carry1;
4841	s1 -= carry1 * (1 << 21);
4842	carry2 = s2 >> 21;
4843	s3 += carry2;
4844	s2 -= carry2 * (1 << 21);
4845	carry3 = s3 >> 21;
4846	s4 += carry3;
4847	s3 -= carry3 * (1 << 21);
4848	carry4 = s4 >> 21;
4849	s5 += carry4;
4850	s4 -= carry4 * (1 << 21);
4851	carry5 = s5 >> 21;
4852	s6 += carry5;
4853	s5 -= carry5 * (1 << 21);
4854	carry6 = s6 >> 21;
4855	s7 += carry6;
4856	s6 -= carry6 * (1 << 21);
4857	carry7 = s7 >> 21;
4858	s8 += carry7;
4859	s7 -= carry7 * (1 << 21);
4860	carry8 = s8 >> 21;
4861	s9 += carry8;
4862	s8 -= carry8 * (1 << 21);
4863	carry9 = s9 >> 21;
4864	s10 += carry9;
4865	s9 -= carry9 * (1 << 21);
4866	carry10 = s10 >> 21;
4867	s11 += carry10;
4868	s10 -= carry10 * (1 << 21);
4869	carry11 = s11 >> 21;
4870	s12 += carry11;
4871	s11 -= carry11 * (1 << 21);
4872
4873	s0 += s12 * 666643;
4874	s1 += s12 * 470296;
4875	s2 += s12 * 654183;
4876	s3 -= s12 * 997805;
4877	s4 += s12 * 136657;
4878	s5 -= s12 * 683901;
4879	s12 = 0;
4880
4881	carry0 = s0 >> 21;
4882	s1 += carry0;
4883	s0 -= carry0 * (1 << 21);
4884	carry1 = s1 >> 21;
4885	s2 += carry1;
4886	s1 -= carry1 * (1 << 21);
4887	carry2 = s2 >> 21;
4888	s3 += carry2;
4889	s2 -= carry2 * (1 << 21);
4890	carry3 = s3 >> 21;
4891	s4 += carry3;
4892	s3 -= carry3 * (1 << 21);
4893	carry4 = s4 >> 21;
4894	s5 += carry4;
4895	s4 -= carry4 * (1 << 21);
4896	carry5 = s5 >> 21;
4897	s6 += carry5;
4898	s5 -= carry5 * (1 << 21);
4899	carry6 = s6 >> 21;
4900	s7 += carry6;
4901	s6 -= carry6 * (1 << 21);
4902	carry7 = s7 >> 21;
4903	s8 += carry7;
4904	s7 -= carry7 * (1 << 21);
4905	carry8 = s8 >> 21;
4906	s9 += carry8;
4907	s8 -= carry8 * (1 << 21);
4908	carry9 = s9 >> 21;
4909	s10 += carry9;
4910	s9 -= carry9 * (1 << 21);
4911	carry10 = s10 >> 21;
4912	s11 += carry10;
4913	s10 -= carry10 * (1 << 21);
4914
4915	s[ 0] = (uint8_t) (s0 >> 0);
4916	s[ 1] = (uint8_t) (s0 >> 8);
4917	s[ 2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
4918	s[ 3] = (uint8_t) (s1 >> 3);
4919	s[ 4] = (uint8_t) (s1 >> 11);
4920	s[ 5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
4921	s[ 6] = (uint8_t) (s2 >> 6);
4922	s[ 7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
4923	s[ 8] = (uint8_t) (s3 >> 1);
4924	s[ 9] = (uint8_t) (s3 >> 9);
4925	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
4926	s[11] = (uint8_t) (s4 >> 4);
4927	s[12] = (uint8_t) (s4 >> 12);
4928	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
4929	s[14] = (uint8_t) (s5 >> 7);
4930	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
4931	s[16] = (uint8_t) (s6 >> 2);
4932	s[17] = (uint8_t) (s6 >> 10);
4933	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
4934	s[19] = (uint8_t) (s7 >> 5);
4935	s[20] = (uint8_t) (s7 >> 13);
4936	s[21] = (uint8_t) (s8 >> 0);
4937	s[22] = (uint8_t) (s8 >> 8);
4938	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
4939	s[24] = (uint8_t) (s9 >> 3);
4940	s[25] = (uint8_t) (s9 >> 11);
4941	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
4942	s[27] = (uint8_t) (s10 >> 6);
4943	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
4944	s[29] = (uint8_t) (s11 >> 1);
4945	s[30] = (uint8_t) (s11 >> 9);
4946	s[31] = (uint8_t) (s11 >> 17);
4947	}
4948
4949	/*
4950	* Input:
4951	* a[0]+256a[1]+...+256^31a[31] = a
4952	* b[0]+256b[1]+...+256^31b[31] = b
4953	* c[0]+256c[1]+...+256^31c[31] = c
4954	*
4955	* Output:
4956	* s[0]+256s[1]+...+256^31s[31] = (ab+c) mod l
4957	* where l = 2^252 + 27742317777372353535851937790883648493.
4958	*/
4959	static void sc_muladd(uint8_t s, const uint8_t a, const uint8_t *b,
4960	const uint8_t *c)
4961	{
4962	int64_t a0 = kBottom21Bits & load_3(a);
4963	int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
4964	int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
4965	int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
4966	int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
4967	int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
4968	int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
4969	int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
4970	int64_t a8 = kBottom21Bits & load_3(a + 21);
4971	int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
4972	int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
4973	int64_t a11 = (load_4(a + 28) >> 7);
4974	int64_t b0 = kBottom21Bits & load_3(b);
4975	int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
4976	int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
4977	int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
4978	int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
4979	int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
4980	int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
4981	int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
4982	int64_t b8 = kBottom21Bits & load_3(b + 21);
4983	int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
4984	int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
4985	int64_t b11 = (load_4(b + 28) >> 7);
4986	int64_t c0 = kBottom21Bits & load_3(c);
4987	int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
4988	int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
4989	int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
4990	int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
4991	int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
4992	int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
4993	int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
4994	int64_t c8 = kBottom21Bits & load_3(c + 21);
4995	int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
4996	int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
4997	int64_t c11 = (load_4(c + 28) >> 7);
4998	int64_t s0;
4999	int64_t s1;
5000	int64_t s2;
5001	int64_t s3;
5002	int64_t s4;
5003	int64_t s5;
5004	int64_t s6;
5005	int64_t s7;
5006	int64_t s8;
5007	int64_t s9;
5008	int64_t s10;
5009	int64_t s11;
5010	int64_t s12;
5011	int64_t s13;
5012	int64_t s14;
5013	int64_t s15;
5014	int64_t s16;
5015	int64_t s17;
5016	int64_t s18;
5017	int64_t s19;
5018	int64_t s20;
5019	int64_t s21;
5020	int64_t s22;
5021	int64_t s23;
5022	int64_t carry0;
5023	int64_t carry1;
5024	int64_t carry2;
5025	int64_t carry3;
5026	int64_t carry4;
5027	int64_t carry5;
5028	int64_t carry6;
5029	int64_t carry7;
5030	int64_t carry8;
5031	int64_t carry9;
5032	int64_t carry10;
5033	int64_t carry11;
5034	int64_t carry12;
5035	int64_t carry13;
5036	int64_t carry14;
5037	int64_t carry15;
5038	int64_t carry16;
5039	int64_t carry17;
5040	int64_t carry18;
5041	int64_t carry19;
5042	int64_t carry20;
5043	int64_t carry21;
5044	int64_t carry22;
5045
5046	s0 = c0 + a0 * b0;
5047	s1 = c1 + a0 * b1 + a1 * b0;
5048	s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
5049	s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
5050	s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
5051	s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
5052	s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
5053	s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
5054	s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
5055	s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
5056	s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
5057	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;
5058	s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
5059	s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
5060	s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
5061	s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
5062	s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
5063	s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
5064	s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
5065	s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
5066	s20 = a9 * b11 + a10 * b10 + a11 * b9;
5067	s21 = a10 * b11 + a11 * b10;
5068	s22 = a11 * b11;
5069	s23 = 0;
5070
5071	carry0 = (s0 + (1 << 20)) >> 21;
5072	s1 += carry0;
5073	s0 -= carry0 * (1 << 21);
5074	carry2 = (s2 + (1 << 20)) >> 21;
5075	s3 += carry2;
5076	s2 -= carry2 * (1 << 21);
5077	carry4 = (s4 + (1 << 20)) >> 21;
5078	s5 += carry4;
5079	s4 -= carry4 * (1 << 21);
5080	carry6 = (s6 + (1 << 20)) >> 21;
5081	s7 += carry6;
5082	s6 -= carry6 * (1 << 21);
5083	carry8 = (s8 + (1 << 20)) >> 21;
5084	s9 += carry8;
5085	s8 -= carry8 * (1 << 21);
5086	carry10 = (s10 + (1 << 20)) >> 21;
5087	s11 += carry10;
5088	s10 -= carry10 * (1 << 21);
5089	carry12 = (s12 + (1 << 20)) >> 21;
5090	s13 += carry12;
5091	s12 -= carry12 * (1 << 21);
5092	carry14 = (s14 + (1 << 20)) >> 21;
5093	s15 += carry14;
5094	s14 -= carry14 * (1 << 21);
5095	carry16 = (s16 + (1 << 20)) >> 21;
5096	s17 += carry16;
5097	s16 -= carry16 * (1 << 21);
5098	carry18 = (s18 + (1 << 20)) >> 21;
5099	s19 += carry18;
5100	s18 -= carry18 * (1 << 21);
5101	carry20 = (s20 + (1 << 20)) >> 21;
5102	s21 += carry20;
5103	s20 -= carry20 * (1 << 21);
5104	carry22 = (s22 + (1 << 20)) >> 21;
5105	s23 += carry22;
5106	s22 -= carry22 * (1 << 21);
5107
5108	carry1 = (s1 + (1 << 20)) >> 21;
5109	s2 += carry1;
5110	s1 -= carry1 * (1 << 21);
5111	carry3 = (s3 + (1 << 20)) >> 21;
5112	s4 += carry3;
5113	s3 -= carry3 * (1 << 21);
5114	carry5 = (s5 + (1 << 20)) >> 21;
5115	s6 += carry5;
5116	s5 -= carry5 * (1 << 21);
5117	carry7 = (s7 + (1 << 20)) >> 21;
5118	s8 += carry7;
5119	s7 -= carry7 * (1 << 21);
5120	carry9 = (s9 + (1 << 20)) >> 21;
5121	s10 += carry9;
5122	s9 -= carry9 * (1 << 21);
5123	carry11 = (s11 + (1 << 20)) >> 21;
5124	s12 += carry11;
5125	s11 -= carry11 * (1 << 21);
5126	carry13 = (s13 + (1 << 20)) >> 21;
5127	s14 += carry13;
5128	s13 -= carry13 * (1 << 21);
5129	carry15 = (s15 + (1 << 20)) >> 21;
5130	s16 += carry15;
5131	s15 -= carry15 * (1 << 21);
5132	carry17 = (s17 + (1 << 20)) >> 21;
5133	s18 += carry17;
5134	s17 -= carry17 * (1 << 21);
5135	carry19 = (s19 + (1 << 20)) >> 21;
5136	s20 += carry19;
5137	s19 -= carry19 * (1 << 21);
5138	carry21 = (s21 + (1 << 20)) >> 21;
5139	s22 += carry21;
5140	s21 -= carry21 * (1 << 21);
5141
5142	s11 += s23 * 666643;
5143	s12 += s23 * 470296;
5144	s13 += s23 * 654183;
5145	s14 -= s23 * 997805;
5146	s15 += s23 * 136657;
5147	s16 -= s23 * 683901;
5148	s23 = 0;
5149
5150	s10 += s22 * 666643;
5151	s11 += s22 * 470296;
5152	s12 += s22 * 654183;
5153	s13 -= s22 * 997805;
5154	s14 += s22 * 136657;
5155	s15 -= s22 * 683901;
5156	s22 = 0;
5157
5158	s9 += s21 * 666643;
5159	s10 += s21 * 470296;
5160	s11 += s21 * 654183;
5161	s12 -= s21 * 997805;
5162	s13 += s21 * 136657;
5163	s14 -= s21 * 683901;
5164	s21 = 0;
5165
5166	s8 += s20 * 666643;
5167	s9 += s20 * 470296;
5168	s10 += s20 * 654183;
5169	s11 -= s20 * 997805;
5170	s12 += s20 * 136657;
5171	s13 -= s20 * 683901;
5172	s20 = 0;
5173
5174	s7 += s19 * 666643;
5175	s8 += s19 * 470296;
5176	s9 += s19 * 654183;
5177	s10 -= s19 * 997805;
5178	s11 += s19 * 136657;
5179	s12 -= s19 * 683901;
5180	s19 = 0;
5181
5182	s6 += s18 * 666643;
5183	s7 += s18 * 470296;
5184	s8 += s18 * 654183;
5185	s9 -= s18 * 997805;
5186	s10 += s18 * 136657;
5187	s11 -= s18 * 683901;
5188	s18 = 0;
5189
5190	carry6 = (s6 + (1 << 20)) >> 21;
5191	s7 += carry6;
5192	s6 -= carry6 * (1 << 21);
5193	carry8 = (s8 + (1 << 20)) >> 21;
5194	s9 += carry8;
5195	s8 -= carry8 * (1 << 21);
5196	carry10 = (s10 + (1 << 20)) >> 21;
5197	s11 += carry10;
5198	s10 -= carry10 * (1 << 21);
5199	carry12 = (s12 + (1 << 20)) >> 21;
5200	s13 += carry12;
5201	s12 -= carry12 * (1 << 21);
5202	carry14 = (s14 + (1 << 20)) >> 21;
5203	s15 += carry14;
5204	s14 -= carry14 * (1 << 21);
5205	carry16 = (s16 + (1 << 20)) >> 21;
5206	s17 += carry16;
5207	s16 -= carry16 * (1 << 21);
5208
5209	carry7 = (s7 + (1 << 20)) >> 21;
5210	s8 += carry7;
5211	s7 -= carry7 * (1 << 21);
5212	carry9 = (s9 + (1 << 20)) >> 21;
5213	s10 += carry9;
5214	s9 -= carry9 * (1 << 21);
5215	carry11 = (s11 + (1 << 20)) >> 21;
5216	s12 += carry11;
5217	s11 -= carry11 * (1 << 21);
5218	carry13 = (s13 + (1 << 20)) >> 21;
5219	s14 += carry13;
5220	s13 -= carry13 * (1 << 21);
5221	carry15 = (s15 + (1 << 20)) >> 21;
5222	s16 += carry15;
5223	s15 -= carry15 * (1 << 21);
5224
5225	s5 += s17 * 666643;
5226	s6 += s17 * 470296;
5227	s7 += s17 * 654183;
5228	s8 -= s17 * 997805;
5229	s9 += s17 * 136657;
5230	s10 -= s17 * 683901;
5231	s17 = 0;
5232
5233	s4 += s16 * 666643;
5234	s5 += s16 * 470296;
5235	s6 += s16 * 654183;
5236	s7 -= s16 * 997805;
5237	s8 += s16 * 136657;
5238	s9 -= s16 * 683901;
5239	s16 = 0;
5240
5241	s3 += s15 * 666643;
5242	s4 += s15 * 470296;
5243	s5 += s15 * 654183;
5244	s6 -= s15 * 997805;
5245	s7 += s15 * 136657;
5246	s8 -= s15 * 683901;
5247	s15 = 0;
5248
5249	s2 += s14 * 666643;
5250	s3 += s14 * 470296;
5251	s4 += s14 * 654183;
5252	s5 -= s14 * 997805;
5253	s6 += s14 * 136657;
5254	s7 -= s14 * 683901;
5255	s14 = 0;
5256
5257	s1 += s13 * 666643;
5258	s2 += s13 * 470296;
5259	s3 += s13 * 654183;
5260	s4 -= s13 * 997805;
5261	s5 += s13 * 136657;
5262	s6 -= s13 * 683901;
5263	s13 = 0;
5264
5265	s0 += s12 * 666643;
5266	s1 += s12 * 470296;
5267	s2 += s12 * 654183;
5268	s3 -= s12 * 997805;
5269	s4 += s12 * 136657;
5270	s5 -= s12 * 683901;
5271	s12 = 0;
5272
5273	carry0 = (s0 + (1 << 20)) >> 21;
5274	s1 += carry0;
5275	s0 -= carry0 * (1 << 21);
5276	carry2 = (s2 + (1 << 20)) >> 21;
5277	s3 += carry2;
5278	s2 -= carry2 * (1 << 21);
5279	carry4 = (s4 + (1 << 20)) >> 21;
5280	s5 += carry4;
5281	s4 -= carry4 * (1 << 21);
5282	carry6 = (s6 + (1 << 20)) >> 21;
5283	s7 += carry6;
5284	s6 -= carry6 * (1 << 21);
5285	carry8 = (s8 + (1 << 20)) >> 21;
5286	s9 += carry8;
5287	s8 -= carry8 * (1 << 21);
5288	carry10 = (s10 + (1 << 20)) >> 21;
5289	s11 += carry10;
5290	s10 -= carry10 * (1 << 21);
5291
5292	carry1 = (s1 + (1 << 20)) >> 21;
5293	s2 += carry1;
5294	s1 -= carry1 * (1 << 21);
5295	carry3 = (s3 + (1 << 20)) >> 21;
5296	s4 += carry3;
5297	s3 -= carry3 * (1 << 21);
5298	carry5 = (s5 + (1 << 20)) >> 21;
5299	s6 += carry5;
5300	s5 -= carry5 * (1 << 21);
5301	carry7 = (s7 + (1 << 20)) >> 21;
5302	s8 += carry7;
5303	s7 -= carry7 * (1 << 21);
5304	carry9 = (s9 + (1 << 20)) >> 21;
5305	s10 += carry9;
5306	s9 -= carry9 * (1 << 21);
5307	carry11 = (s11 + (1 << 20)) >> 21;
5308	s12 += carry11;
5309	s11 -= carry11 * (1 << 21);
5310
5311	s0 += s12 * 666643;
5312	s1 += s12 * 470296;
5313	s2 += s12 * 654183;
5314	s3 -= s12 * 997805;
5315	s4 += s12 * 136657;
5316	s5 -= s12 * 683901;
5317	s12 = 0;
5318
5319	carry0 = s0 >> 21;
5320	s1 += carry0;
5321	s0 -= carry0 * (1 << 21);
5322	carry1 = s1 >> 21;
5323	s2 += carry1;
5324	s1 -= carry1 * (1 << 21);
5325	carry2 = s2 >> 21;
5326	s3 += carry2;
5327	s2 -= carry2 * (1 << 21);
5328	carry3 = s3 >> 21;
5329	s4 += carry3;
5330	s3 -= carry3 * (1 << 21);
5331	carry4 = s4 >> 21;
5332	s5 += carry4;
5333	s4 -= carry4 * (1 << 21);
5334	carry5 = s5 >> 21;
5335	s6 += carry5;
5336	s5 -= carry5 * (1 << 21);
5337	carry6 = s6 >> 21;
5338	s7 += carry6;
5339	s6 -= carry6 * (1 << 21);
5340	carry7 = s7 >> 21;
5341	s8 += carry7;
5342	s7 -= carry7 * (1 << 21);
5343	carry8 = s8 >> 21;
5344	s9 += carry8;
5345	s8 -= carry8 * (1 << 21);
5346	carry9 = s9 >> 21;
5347	s10 += carry9;
5348	s9 -= carry9 * (1 << 21);
5349	carry10 = s10 >> 21;
5350	s11 += carry10;
5351	s10 -= carry10 * (1 << 21);
5352	carry11 = s11 >> 21;
5353	s12 += carry11;
5354	s11 -= carry11 * (1 << 21);
5355
5356	s0 += s12 * 666643;
5357	s1 += s12 * 470296;
5358	s2 += s12 * 654183;
5359	s3 -= s12 * 997805;
5360	s4 += s12 * 136657;
5361	s5 -= s12 * 683901;
5362	s12 = 0;
5363
5364	carry0 = s0 >> 21;
5365	s1 += carry0;
5366	s0 -= carry0 * (1 << 21);
5367	carry1 = s1 >> 21;
5368	s2 += carry1;
5369	s1 -= carry1 * (1 << 21);
5370	carry2 = s2 >> 21;
5371	s3 += carry2;
5372	s2 -= carry2 * (1 << 21);
5373	carry3 = s3 >> 21;
5374	s4 += carry3;
5375	s3 -= carry3 * (1 << 21);
5376	carry4 = s4 >> 21;
5377	s5 += carry4;
5378	s4 -= carry4 * (1 << 21);
5379	carry5 = s5 >> 21;
5380	s6 += carry5;
5381	s5 -= carry5 * (1 << 21);
5382	carry6 = s6 >> 21;
5383	s7 += carry6;
5384	s6 -= carry6 * (1 << 21);
5385	carry7 = s7 >> 21;
5386	s8 += carry7;
5387	s7 -= carry7 * (1 << 21);
5388	carry8 = s8 >> 21;
5389	s9 += carry8;
5390	s8 -= carry8 * (1 << 21);
5391	carry9 = s9 >> 21;
5392	s10 += carry9;
5393	s9 -= carry9 * (1 << 21);
5394	carry10 = s10 >> 21;
5395	s11 += carry10;
5396	s10 -= carry10 * (1 << 21);
5397
5398	s[ 0] = (uint8_t) (s0 >> 0);
5399	s[ 1] = (uint8_t) (s0 >> 8);
5400	s[ 2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5401	s[ 3] = (uint8_t) (s1 >> 3);
5402	s[ 4] = (uint8_t) (s1 >> 11);
5403	s[ 5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5404	s[ 6] = (uint8_t) (s2 >> 6);
5405	s[ 7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5406	s[ 8] = (uint8_t) (s3 >> 1);
5407	s[ 9] = (uint8_t) (s3 >> 9);
5408	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5409	s[11] = (uint8_t) (s4 >> 4);
5410	s[12] = (uint8_t) (s4 >> 12);
5411	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5412	s[14] = (uint8_t) (s5 >> 7);
5413	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5414	s[16] = (uint8_t) (s6 >> 2);
5415	s[17] = (uint8_t) (s6 >> 10);
5416	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5417	s[19] = (uint8_t) (s7 >> 5);
5418	s[20] = (uint8_t) (s7 >> 13);
5419	s[21] = (uint8_t) (s8 >> 0);
5420	s[22] = (uint8_t) (s8 >> 8);
5421	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5422	s[24] = (uint8_t) (s9 >> 3);
5423	s[25] = (uint8_t) (s9 >> 11);
5424	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5425	s[27] = (uint8_t) (s10 >> 6);
5426	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5427	s[29] = (uint8_t) (s11 >> 1);
5428	s[30] = (uint8_t) (s11 >> 9);
5429	s[31] = (uint8_t) (s11 >> 17);
5430	}
5431
5432	int ED25519_sign(uint8_t out_sig, const uint8_t message, size_t message_len,
5433	const uint8_t public_key[32], const uint8_t private_key[32])
5434	{
5435	uint8_t az[SHA512_DIGEST_LENGTH];
5436	uint8_t nonce[SHA512_DIGEST_LENGTH];
5437	ge_p3 R;
5438	uint8_t hram[SHA512_DIGEST_LENGTH];
5439	SHA512_CTX hash_ctx;
5440
5441	SHA512_Init(&hash_ctx);
5442	SHA512_Update(&hash_ctx, private_key, 32);
5443	SHA512_Final(az, &hash_ctx);
5444
5445	az[0] &= 248;
5446	az[31] &= 63;
5447	az[31] \|= 64;
5448
5449	SHA512_Init(&hash_ctx);
5450	SHA512_Update(&hash_ctx, az + 32, 32);
5451	SHA512_Update(&hash_ctx, message, message_len);
5452	SHA512_Final(nonce, &hash_ctx);
5453
5454	x25519_sc_reduce(nonce);
5455	ge_scalarmult_base(&R, nonce);
5456	ge_p3_tobytes(out_sig, &R);
5457
5458	SHA512_Init(&hash_ctx);
5459	SHA512_Update(&hash_ctx, out_sig, 32);
5460	SHA512_Update(&hash_ctx, public_key, 32);
5461	SHA512_Update(&hash_ctx, message, message_len);
5462	SHA512_Final(hram, &hash_ctx);
5463
5464	x25519_sc_reduce(hram);
5465	sc_muladd(out_sig + 32, hram, az, nonce);
5466
5467	OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx));
5468	OPENSSL_cleanse(nonce, sizeof(nonce));
5469	OPENSSL_cleanse(az, sizeof(az));
5470
5471	return 1;
5472	}
5473
5474	static const char allzeroes[15];
5475
5476	int ED25519_verify(const uint8_t *message, size_t message_len,
5477	const uint8_t signature[64], const uint8_t public_key[32])
5478	{
5479	int i;
5480	ge_p3 A;
5481	const uint8_t r, s;
5482	SHA512_CTX hash_ctx;
5483	ge_p2 R;
5484	uint8_t rcheck[32];
5485	uint8_t h[SHA512_DIGEST_LENGTH];
5486	/* 27742317777372353535851937790883648493 in little endian format */
5487	const uint8_t l_low[16] = {
5488	0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5489	0xDE, 0xF9, 0xDE, 0x14
5490	};
5491
5492	r = signature;
5493	s = signature + 32;
5494
5495	/*
5496	* Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5497	*
5498	* If not the signature is publicly invalid. Since it's public we can do the
5499	* check in variable time.
5500	*
5501	* First check the most significant byte
5502	*/
5503	if (s[31] > 0x10)
5504	return 0;
5505	if (s[31] == 0x10) {
5506	/*
5507	* Most significant byte indicates a value close to 2^252 so check the
5508	* rest
5509	*/
5510	if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5511	return 0;
5512	for (i = 15; i >= 0; i--) {
5513	if (s[i] < l_low[i])
5514	break;
5515	if (s[i] > l_low[i])
5516	return 0;
5517	}
5518	if (i < 0)
5519	return 0;
5520	}
5521
5522	if (ge_frombytes_vartime(&A, public_key) != 0) {
5523	return 0;
5524	}
5525
5526	fe_neg(A.X, A.X);
5527	fe_neg(A.T, A.T);
5528
5529	SHA512_Init(&hash_ctx);
5530	SHA512_Update(&hash_ctx, r, 32);
5531	SHA512_Update(&hash_ctx, public_key, 32);
5532	SHA512_Update(&hash_ctx, message, message_len);
5533	SHA512_Final(h, &hash_ctx);
5534
5535	x25519_sc_reduce(h);
5536
5537	ge_double_scalarmult_vartime(&R, h, &A, s);
5538
5539	ge_tobytes(rcheck, &R);
5540
5541	return CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5542	}
5543
5544	void ED25519_public_from_private(uint8_t out_public_key[32],
5545	const uint8_t private_key[32])
5546	{
5547	uint8_t az[SHA512_DIGEST_LENGTH];
5548	ge_p3 A;
5549
5550	SHA512(private_key, 32, az);
5551
5552	az[0] &= 248;
5553	az[31] &= 63;
5554	az[31] \|= 64;
5555
5556	ge_scalarmult_base(&A, az);
5557	ge_p3_tobytes(out_public_key, &A);
5558
5559	OPENSSL_cleanse(az, sizeof(az));
5560	}
5561
5562	int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5563	const uint8_t peer_public_value[32])
5564	{
5565	static const uint8_t kZeros[32] = {0};
5566	x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5567	/* The all-zero output results when the input is a point of small order. */
5568	return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5569	}
5570
5571	void X25519_public_from_private(uint8_t out_public_value[32],
5572	const uint8_t private_key[32])
5573	{
5574	uint8_t e[32];
5575	ge_p3 A;
5576	fe zplusy, zminusy, zminusy_inv;
5577
5578	memcpy(e, private_key, 32);
5579	e[0] &= 248;
5580	e[31] &= 127;
5581	e[31] \|= 64;
5582
5583	ge_scalarmult_base(&A, e);
5584
5585	/*
5586	* We only need the u-coordinate of the curve25519 point.
5587	* The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5588	* u=(Z+Y)/(Z-Y).
5589	*/
5590	fe_add(zplusy, A.Z, A.Y);
5591	fe_sub(zminusy, A.Z, A.Y);
5592	fe_invert(zminusy_inv, zminusy);
5593	fe_mul(zplusy, zplusy, zminusy_inv);
5594	fe_tobytes(out_public_value, zplusy);
5595
5596	OPENSSL_cleanse(e, sizeof(e));
5597	}

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source: vbox/trunk/src/libs/openssl-1.1.1f/crypto/ec/curve25519.c@ 83531

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