curve25519.c@ 101665

Last change on this file since 101665 was 101211, checked in by vboxsync, 14 months ago
openssl-3.1.3: Applied and adjusted our OpenSSL changes to 3.1.2. bugref:10527
File size: 198.2 KB

Line
1	/*
2	* Copyright 2016-2022 The OpenSSL Project Authors. All Rights Reserved.
3	*
4	* Licensed under the Apache License 2.0 (the "License"). You may not use
5	* this file except in compliance with the License. You can obtain a copy
6	* in the file LICENSE in the source distribution or at
7	* https://www.openssl.org/source/license.html
8	*/
9
10	/*
11	* ECDSA low level APIs are deprecated for public use, but still ok for
12	* internal use.
13	*/
14	#include "internal/deprecated.h"
15
16	#include <string.h>
17	#include "crypto/ecx.h"
18	#include "ec_local.h"
19	#include <openssl/evp.h>
20	#include <openssl/sha.h>
21
22	#include "internal/numbers.h"
23
24	#if defined(X25519_ASM) && (defined(__x86_64) \|\| defined(__x86_64__) \|\| \
25	defined(_M_AMD64) \|\| defined(_M_X64))
26
27	# define BASE_2_64_IMPLEMENTED
28
29	typedef uint64_t fe64[4];
30
31	int x25519_fe64_eligible(void);
32
33	/*
34	* Following subroutines perform corresponding operations modulo
35	* 2^256-38, i.e. double the curve modulus. However, inputs and
36	* outputs are permitted to be partially reduced, i.e. to remain
37	* in [0..2^256) range. It's all tied up in final fe64_tobytes
38	* that performs full reduction modulo 2^255-19.
39	*
40	* There are no reference C implementations for these.
41	*/
42	void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
43	void x25519_fe64_sqr(fe64 h, const fe64 f);
44	void x25519_fe64_mul121666(fe64 h, fe64 f);
45	void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
46	void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
47	void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
48	# define fe64_mul x25519_fe64_mul
49	# define fe64_sqr x25519_fe64_sqr
50	# define fe64_mul121666 x25519_fe64_mul121666
51	# define fe64_add x25519_fe64_add
52	# define fe64_sub x25519_fe64_sub
53	# define fe64_tobytes x25519_fe64_tobytes
54
55	static uint64_t load_8(const uint8_t *in)
56	{
57	uint64_t result;
58
59	result = in[0];
60	result \|= ((uint64_t)in[1]) << 8;
61	result \|= ((uint64_t)in[2]) << 16;
62	result \|= ((uint64_t)in[3]) << 24;
63	result \|= ((uint64_t)in[4]) << 32;
64	result \|= ((uint64_t)in[5]) << 40;
65	result \|= ((uint64_t)in[6]) << 48;
66	result \|= ((uint64_t)in[7]) << 56;
67
68	return result;
69	}
70
71	static void fe64_frombytes(fe64 h, const uint8_t *s)
72	{
73	h[0] = load_8(s);
74	h[1] = load_8(s + 8);
75	h[2] = load_8(s + 16);
76	h[3] = load_8(s + 24) & 0x7fffffffffffffff;
77	}
78
79	static void fe64_0(fe64 h)
80	{
81	h[0] = 0;
82	h[1] = 0;
83	h[2] = 0;
84	h[3] = 0;
85	}
86
87	static void fe64_1(fe64 h)
88	{
89	h[0] = 1;
90	h[1] = 0;
91	h[2] = 0;
92	h[3] = 0;
93	}
94
95	static void fe64_copy(fe64 h, const fe64 f)
96	{
97	h[0] = f[0];
98	h[1] = f[1];
99	h[2] = f[2];
100	h[3] = f[3];
101	}
102
103	static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
104	{
105	int i;
106	uint64_t mask = 0 - (uint64_t)b;
107
108	for (i = 0; i < 4; i++) {
109	uint64_t x = f[i] ^ g[i];
110	x &= mask;
111	f[i] ^= x;
112	g[i] ^= x;
113	}
114	}
115
116	static void fe64_invert(fe64 out, const fe64 z)
117	{
118	fe64 t0;
119	fe64 t1;
120	fe64 t2;
121	fe64 t3;
122	int i;
123
124	/*
125	* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
126	* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
127	*/
128
129	/* t0 = z ** 2 */
130	fe64_sqr(t0, z);
131
132	/* t1 = t0 (2 2) = z ** 8 */
133	fe64_sqr(t1, t0);
134	fe64_sqr(t1, t1);
135
136	/* t1 = z * t1 = z ** 9 */
137	fe64_mul(t1, z, t1);
138	/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
139	fe64_mul(t0, t0, t1);
140
141	/* t2 = t0 2 = z 22 */
142	fe64_sqr(t2, t0);
143
144	/* t1 = t1 * t2 = z (2 5 - 1) */
145	fe64_mul(t1, t1, t2);
146
147	/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
148	fe64_sqr(t2, t1);
149	for (i = 1; i < 5; ++i)
150	fe64_sqr(t2, t2);
151
152	/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
153	fe64_mul(t1, t2, t1);
154
155	/* Continuing similarly... */
156
157	/* t2 = z (2 20 - 1) */
158	fe64_sqr(t2, t1);
159	for (i = 1; i < 10; ++i)
160	fe64_sqr(t2, t2);
161
162	fe64_mul(t2, t2, t1);
163
164	/* t2 = z (2 40 - 1) */
165	fe64_sqr(t3, t2);
166	for (i = 1; i < 20; ++i)
167	fe64_sqr(t3, t3);
168
169	fe64_mul(t2, t3, t2);
170
171	/* t2 = z (2 10) * (2 ** 40 - 1) */
172	for (i = 0; i < 10; ++i)
173	fe64_sqr(t2, t2);
174
175	/* t1 = z (2 50 - 1) */
176	fe64_mul(t1, t2, t1);
177
178	/* t2 = z (2 100 - 1) */
179	fe64_sqr(t2, t1);
180	for (i = 1; i < 50; ++i)
181	fe64_sqr(t2, t2);
182
183	fe64_mul(t2, t2, t1);
184
185	/* t2 = z (2 200 - 1) */
186	fe64_sqr(t3, t2);
187	for (i = 1; i < 100; ++i)
188	fe64_sqr(t3, t3);
189
190	fe64_mul(t2, t3, t2);
191
192	/* t2 = z ((2 50) * (2 ** 200 - 1) */
193	for (i = 0; i < 50; ++i)
194	fe64_sqr(t2, t2);
195
196	/* t1 = z (2 250 - 1) */
197	fe64_mul(t1, t2, t1);
198
199	/* t1 = z ((2 5) * (2 ** 250 - 1)) */
200	for (i = 0; i < 5; ++i)
201	fe64_sqr(t1, t1);
202
203	/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
204	fe64_mul(out, t1, t0);
205	}
206
207	/*
208	* Duplicate of original x25519_scalar_mult_generic, but using
209	* fe64_* subroutines.
210	*/
211	static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
212	const uint8_t point[32])
213	{
214	fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
215	uint8_t e[32];
216	unsigned swap = 0;
217	int pos;
218
219	memcpy(e, scalar, 32);
220	e[0] &= 0xf8;
221	e[31] &= 0x7f;
222	e[31] \|= 0x40;
223	fe64_frombytes(x1, point);
224	fe64_1(x2);
225	fe64_0(z2);
226	fe64_copy(x3, x1);
227	fe64_1(z3);
228
229	for (pos = 254; pos >= 0; --pos) {
230	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
231
232	swap ^= b;
233	fe64_cswap(x2, x3, swap);
234	fe64_cswap(z2, z3, swap);
235	swap = b;
236	fe64_sub(tmp0, x3, z3);
237	fe64_sub(tmp1, x2, z2);
238	fe64_add(x2, x2, z2);
239	fe64_add(z2, x3, z3);
240	fe64_mul(z3, x2, tmp0);
241	fe64_mul(z2, z2, tmp1);
242	fe64_sqr(tmp0, tmp1);
243	fe64_sqr(tmp1, x2);
244	fe64_add(x3, z3, z2);
245	fe64_sub(z2, z3, z2);
246	fe64_mul(x2, tmp1, tmp0);
247	fe64_sub(tmp1, tmp1, tmp0);
248	fe64_sqr(z2, z2);
249	fe64_mul121666(z3, tmp1);
250	fe64_sqr(x3, x3);
251	fe64_add(tmp0, tmp0, z3);
252	fe64_mul(z3, x1, z2);
253	fe64_mul(z2, tmp1, tmp0);
254	}
255
256	fe64_invert(z2, z2);
257	fe64_mul(x2, x2, z2);
258	fe64_tobytes(out, x2);
259
260	OPENSSL_cleanse(e, sizeof(e));
261	}
262	#endif
263
264	#if defined(X25519_ASM) \
265	\|\| ( defined(INT128_MAX) \
266	&& !defined(__sparc__) \
267	&& (!defined(__SIZEOF_LONG__) \|\| (__SIZEOF_LONG__ == 8)) \
268	&& !(defined(__ANDROID__) && !defined(__clang__)) )
269	/*
270	* Base 2^51 implementation. It's virtually no different from reference
271	* base 2^25.5 implementation in respect to lax boundary conditions for
272	* intermediate values and even individual limbs. So that whatever you
273	* know about the reference, applies even here...
274	*/
275	# define BASE_2_51_IMPLEMENTED
276
277	typedef uint64_t fe51[5];
278
279	static const uint64_t MASK51 = 0x7ffffffffffff;
280
281	static uint64_t load_7(const uint8_t *in)
282	{
283	uint64_t result;
284
285	result = in[0];
286	result \|= ((uint64_t)in[1]) << 8;
287	result \|= ((uint64_t)in[2]) << 16;
288	result \|= ((uint64_t)in[3]) << 24;
289	result \|= ((uint64_t)in[4]) << 32;
290	result \|= ((uint64_t)in[5]) << 40;
291	result \|= ((uint64_t)in[6]) << 48;
292
293	return result;
294	}
295
296	static uint64_t load_6(const uint8_t *in)
297	{
298	uint64_t result;
299
300	result = in[0];
301	result \|= ((uint64_t)in[1]) << 8;
302	result \|= ((uint64_t)in[2]) << 16;
303	result \|= ((uint64_t)in[3]) << 24;
304	result \|= ((uint64_t)in[4]) << 32;
305	result \|= ((uint64_t)in[5]) << 40;
306
307	return result;
308	}
309
310	static void fe51_frombytes(fe51 h, const uint8_t *s)
311	{
312	uint64_t h0 = load_7(s); /* 56 bits */
313	uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
314	uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
315	uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
316	uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
317
318	h1 \|= h0 >> 51; h0 &= MASK51;
319	h2 \|= h1 >> 51; h1 &= MASK51;
320	h3 \|= h2 >> 51; h2 &= MASK51;
321	h4 \|= h3 >> 51; h3 &= MASK51;
322
323	h[0] = h0;
324	h[1] = h1;
325	h[2] = h2;
326	h[3] = h3;
327	h[4] = h4;
328	}
329
330	static void fe51_tobytes(uint8_t *s, const fe51 h)
331	{
332	uint64_t h0 = h[0];
333	uint64_t h1 = h[1];
334	uint64_t h2 = h[2];
335	uint64_t h3 = h[3];
336	uint64_t h4 = h[4];
337	uint64_t q;
338
339	/* compare to modulus */
340	q = (h0 + 19) >> 51;
341	q = (h1 + q) >> 51;
342	q = (h2 + q) >> 51;
343	q = (h3 + q) >> 51;
344	q = (h4 + q) >> 51;
345
346	/* full reduce */
347	h0 += 19 * q;
348	h1 += h0 >> 51; h0 &= MASK51;
349	h2 += h1 >> 51; h1 &= MASK51;
350	h3 += h2 >> 51; h2 &= MASK51;
351	h4 += h3 >> 51; h3 &= MASK51;
352	h4 &= MASK51;
353
354	/* smash */
355	s[0] = (uint8_t)(h0 >> 0);
356	s[1] = (uint8_t)(h0 >> 8);
357	s[2] = (uint8_t)(h0 >> 16);
358	s[3] = (uint8_t)(h0 >> 24);
359	s[4] = (uint8_t)(h0 >> 32);
360	s[5] = (uint8_t)(h0 >> 40);
361	s[6] = (uint8_t)((h0 >> 48) \| ((uint32_t)h1 << 3));
362	s[7] = (uint8_t)(h1 >> 5);
363	s[8] = (uint8_t)(h1 >> 13);
364	s[9] = (uint8_t)(h1 >> 21);
365	s[10] = (uint8_t)(h1 >> 29);
366	s[11] = (uint8_t)(h1 >> 37);
367	s[12] = (uint8_t)((h1 >> 45) \| ((uint32_t)h2 << 6));
368	s[13] = (uint8_t)(h2 >> 2);
369	s[14] = (uint8_t)(h2 >> 10);
370	s[15] = (uint8_t)(h2 >> 18);
371	s[16] = (uint8_t)(h2 >> 26);
372	s[17] = (uint8_t)(h2 >> 34);
373	s[18] = (uint8_t)(h2 >> 42);
374	s[19] = (uint8_t)((h2 >> 50) \| ((uint32_t)h3 << 1));
375	s[20] = (uint8_t)(h3 >> 7);
376	s[21] = (uint8_t)(h3 >> 15);
377	s[22] = (uint8_t)(h3 >> 23);
378	s[23] = (uint8_t)(h3 >> 31);
379	s[24] = (uint8_t)(h3 >> 39);
380	s[25] = (uint8_t)((h3 >> 47) \| ((uint32_t)h4 << 4));
381	s[26] = (uint8_t)(h4 >> 4);
382	s[27] = (uint8_t)(h4 >> 12);
383	s[28] = (uint8_t)(h4 >> 20);
384	s[29] = (uint8_t)(h4 >> 28);
385	s[30] = (uint8_t)(h4 >> 36);
386	s[31] = (uint8_t)(h4 >> 44);
387	}
388
389	# if defined(X25519_ASM)
390	void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
391	void x25519_fe51_sqr(fe51 h, const fe51 f);
392	void x25519_fe51_mul121666(fe51 h, fe51 f);
393	# define fe51_mul x25519_fe51_mul
394	# define fe51_sq x25519_fe51_sqr
395	# define fe51_mul121666 x25519_fe51_mul121666
396	# else
397
398	typedef uint128_t u128;
399
400	static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
401	{
402	u128 h0, h1, h2, h3, h4;
403	uint64_t f_i, g0, g1, g2, g3, g4;
404
405	f_i = f[0];
406	h0 = (u128)f_i * (g0 = g[0]);
407	h1 = (u128)f_i * (g1 = g[1]);
408	h2 = (u128)f_i * (g2 = g[2]);
409	h3 = (u128)f_i * (g3 = g[3]);
410	h4 = (u128)f_i * (g4 = g[4]);
411
412	f_i = f[1];
413	h0 += (u128)f_i * (g4 *= 19);
414	h1 += (u128)f_i * g0;
415	h2 += (u128)f_i * g1;
416	h3 += (u128)f_i * g2;
417	h4 += (u128)f_i * g3;
418
419	f_i = f[2];
420	h0 += (u128)f_i * (g3 *= 19);
421	h1 += (u128)f_i * g4;
422	h2 += (u128)f_i * g0;
423	h3 += (u128)f_i * g1;
424	h4 += (u128)f_i * g2;
425
426	f_i = f[3];
427	h0 += (u128)f_i * (g2 *= 19);
428	h1 += (u128)f_i * g3;
429	h2 += (u128)f_i * g4;
430	h3 += (u128)f_i * g0;
431	h4 += (u128)f_i * g1;
432
433	f_i = f[4];
434	h0 += (u128)f_i * (g1 *= 19);
435	h1 += (u128)f_i * g2;
436	h2 += (u128)f_i * g3;
437	h3 += (u128)f_i * g4;
438	h4 += (u128)f_i * g0;
439
440	/* partial [lazy] reduction */
441	h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
442	h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
443
444	h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
445	g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
446
447	g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
448	g3 += g2 >> 51; g2 &= MASK51;
449	g1 += g0 >> 51; g0 &= MASK51;
450
451	h[0] = g0;
452	h[1] = g1;
453	h[2] = g2;
454	h[3] = g3;
455	h[4] = g4;
456	}
457
458	static void fe51_sq(fe51 h, const fe51 f)
459	{
460	# if defined(OPENSSL_SMALL_FOOTPRINT)
461	fe51_mul(h, f, f);
462	# else
463	/* dedicated squaring gives 16-25% overall improvement */
464	uint64_t g0 = f[0];
465	uint64_t g1 = f[1];
466	uint64_t g2 = f[2];
467	uint64_t g3 = f[3];
468	uint64_t g4 = f[4];
469	u128 h0, h1, h2, h3, h4;
470
471	h0 = (u128)g0 * g0; g0 *= 2;
472	h1 = (u128)g0 * g1;
473	h2 = (u128)g0 * g2;
474	h3 = (u128)g0 * g3;
475	h4 = (u128)g0 * g4;
476
477	g0 = g4; /* borrow g0 */
478	h3 += (u128)g0 * (g4 *= 19);
479
480	h2 += (u128)g1 * g1; g1 *= 2;
481	h3 += (u128)g1 * g2;
482	h4 += (u128)g1 * g3;
483	h0 += (u128)g1 * g4;
484
485	g0 = g3; /* borrow g0 */
486	h1 += (u128)g0 * (g3 *= 19);
487	h2 += (u128)(g0 * 2) * g4;
488
489	h4 += (u128)g2 * g2; g2 *= 2;
490	h0 += (u128)g2 * g3;
491	h1 += (u128)g2 * g4;
492
493	/* partial [lazy] reduction */
494	h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
495	h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
496
497	h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
498	g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
499
500	g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
501	g3 += g2 >> 51; g2 &= MASK51;
502	g1 += g0 >> 51; g0 &= MASK51;
503
504	h[0] = g0;
505	h[1] = g1;
506	h[2] = g2;
507	h[3] = g3;
508	h[4] = g4;
509	# endif
510	}
511
512	static void fe51_mul121666(fe51 h, fe51 f)
513	{
514	u128 h0 = f[0] * (u128)121666;
515	u128 h1 = f[1] * (u128)121666;
516	u128 h2 = f[2] * (u128)121666;
517	u128 h3 = f[3] * (u128)121666;
518	u128 h4 = f[4] * (u128)121666;
519	uint64_t g0, g1, g2, g3, g4;
520
521	h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
522	h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
523
524	h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
525	g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
526
527	g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
528	g3 += g2 >> 51; g2 &= MASK51;
529	g1 += g0 >> 51; g0 &= MASK51;
530
531	h[0] = g0;
532	h[1] = g1;
533	h[2] = g2;
534	h[3] = g3;
535	h[4] = g4;
536	}
537	# endif
538
539	static void fe51_add(fe51 h, const fe51 f, const fe51 g)
540	{
541	h[0] = f[0] + g[0];
542	h[1] = f[1] + g[1];
543	h[2] = f[2] + g[2];
544	h[3] = f[3] + g[3];
545	h[4] = f[4] + g[4];
546	}
547
548	static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
549	{
550	/*
551	* Add 2*modulus to ensure that result remains positive
552	* even if subtrahend is partially reduced.
553	*/
554	h[0] = (f[0] + 0xfffffffffffda) - g[0];
555	h[1] = (f[1] + 0xffffffffffffe) - g[1];
556	h[2] = (f[2] + 0xffffffffffffe) - g[2];
557	h[3] = (f[3] + 0xffffffffffffe) - g[3];
558	h[4] = (f[4] + 0xffffffffffffe) - g[4];
559	}
560
561	static void fe51_0(fe51 h)
562	{
563	h[0] = 0;
564	h[1] = 0;
565	h[2] = 0;
566	h[3] = 0;
567	h[4] = 0;
568	}
569
570	static void fe51_1(fe51 h)
571	{
572	h[0] = 1;
573	h[1] = 0;
574	h[2] = 0;
575	h[3] = 0;
576	h[4] = 0;
577	}
578
579	static void fe51_copy(fe51 h, const fe51 f)
580	{
581	h[0] = f[0];
582	h[1] = f[1];
583	h[2] = f[2];
584	h[3] = f[3];
585	h[4] = f[4];
586	}
587
588	static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
589	{
590	int i;
591	uint64_t mask = 0 - (uint64_t)b;
592
593	for (i = 0; i < 5; i++) {
594	int64_t x = f[i] ^ g[i];
595	x &= mask;
596	f[i] ^= x;
597	g[i] ^= x;
598	}
599	}
600
601	static void fe51_invert(fe51 out, const fe51 z)
602	{
603	fe51 t0;
604	fe51 t1;
605	fe51 t2;
606	fe51 t3;
607	int i;
608
609	/*
610	* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
611	* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
612	*/
613
614	/* t0 = z ** 2 */
615	fe51_sq(t0, z);
616
617	/* t1 = t0 (2 2) = z ** 8 */
618	fe51_sq(t1, t0);
619	fe51_sq(t1, t1);
620
621	/* t1 = z * t1 = z ** 9 */
622	fe51_mul(t1, z, t1);
623	/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
624	fe51_mul(t0, t0, t1);
625
626	/* t2 = t0 2 = z 22 */
627	fe51_sq(t2, t0);
628
629	/* t1 = t1 * t2 = z (2 5 - 1) */
630	fe51_mul(t1, t1, t2);
631
632	/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
633	fe51_sq(t2, t1);
634	for (i = 1; i < 5; ++i)
635	fe51_sq(t2, t2);
636
637	/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
638	fe51_mul(t1, t2, t1);
639
640	/* Continuing similarly... */
641
642	/* t2 = z (2 20 - 1) */
643	fe51_sq(t2, t1);
644	for (i = 1; i < 10; ++i)
645	fe51_sq(t2, t2);
646
647	fe51_mul(t2, t2, t1);
648
649	/* t2 = z (2 40 - 1) */
650	fe51_sq(t3, t2);
651	for (i = 1; i < 20; ++i)
652	fe51_sq(t3, t3);
653
654	fe51_mul(t2, t3, t2);
655
656	/* t2 = z (2 10) * (2 ** 40 - 1) */
657	for (i = 0; i < 10; ++i)
658	fe51_sq(t2, t2);
659
660	/* t1 = z (2 50 - 1) */
661	fe51_mul(t1, t2, t1);
662
663	/* t2 = z (2 100 - 1) */
664	fe51_sq(t2, t1);
665	for (i = 1; i < 50; ++i)
666	fe51_sq(t2, t2);
667
668	fe51_mul(t2, t2, t1);
669
670	/* t2 = z (2 200 - 1) */
671	fe51_sq(t3, t2);
672	for (i = 1; i < 100; ++i)
673	fe51_sq(t3, t3);
674
675	fe51_mul(t2, t3, t2);
676
677	/* t2 = z ((2 50) * (2 ** 200 - 1) */
678	for (i = 0; i < 50; ++i)
679	fe51_sq(t2, t2);
680
681	/* t1 = z (2 250 - 1) */
682	fe51_mul(t1, t2, t1);
683
684	/* t1 = z ((2 5) * (2 ** 250 - 1)) */
685	for (i = 0; i < 5; ++i)
686	fe51_sq(t1, t1);
687
688	/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
689	fe51_mul(out, t1, t0);
690	}
691
692	/*
693	* Duplicate of original x25519_scalar_mult_generic, but using
694	* fe51_* subroutines.
695	*/
696	static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
697	const uint8_t point[32])
698	{
699	fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
700	uint8_t e[32];
701	unsigned swap = 0;
702	int pos;
703
704	# ifdef BASE_2_64_IMPLEMENTED
705	if (x25519_fe64_eligible()) {
706	x25519_scalar_mulx(out, scalar, point);
707	return;
708	}
709	# endif
710
711	memcpy(e, scalar, 32);
712	e[0] &= 0xf8;
713	e[31] &= 0x7f;
714	e[31] \|= 0x40;
715	fe51_frombytes(x1, point);
716	fe51_1(x2);
717	fe51_0(z2);
718	fe51_copy(x3, x1);
719	fe51_1(z3);
720
721	for (pos = 254; pos >= 0; --pos) {
722	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
723
724	swap ^= b;
725	fe51_cswap(x2, x3, swap);
726	fe51_cswap(z2, z3, swap);
727	swap = b;
728	fe51_sub(tmp0, x3, z3);
729	fe51_sub(tmp1, x2, z2);
730	fe51_add(x2, x2, z2);
731	fe51_add(z2, x3, z3);
732	fe51_mul(z3, tmp0, x2);
733	fe51_mul(z2, z2, tmp1);
734	fe51_sq(tmp0, tmp1);
735	fe51_sq(tmp1, x2);
736	fe51_add(x3, z3, z2);
737	fe51_sub(z2, z3, z2);
738	fe51_mul(x2, tmp1, tmp0);
739	fe51_sub(tmp1, tmp1, tmp0);
740	fe51_sq(z2, z2);
741	fe51_mul121666(z3, tmp1);
742	fe51_sq(x3, x3);
743	fe51_add(tmp0, tmp0, z3);
744	fe51_mul(z3, x1, z2);
745	fe51_mul(z2, tmp1, tmp0);
746	}
747
748	fe51_invert(z2, z2);
749	fe51_mul(x2, x2, z2);
750	fe51_tobytes(out, x2);
751
752	OPENSSL_cleanse(e, sizeof(e));
753	}
754	#endif
755
756	/*
757	* Reference base 2^25.5 implementation.
758	*
759	* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
760	* 20141124 (http://bench.cr.yp.to/supercop.html).
761	*
762	* The field functions are shared by Ed25519 and X25519 where possible.
763	*/
764
765	/*
766	* fe means field element. Here the field is \Z/(2^255-19). An element t,
767	* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
768	* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
769	* context.
770	*/
771	typedef int32_t fe[10];
772
773	static const int64_t kBottom21Bits = 0x1fffffLL;
774	static const int64_t kBottom25Bits = 0x1ffffffLL;
775	static const int64_t kBottom26Bits = 0x3ffffffLL;
776	static const int64_t kTop39Bits = 0xfffffffffe000000LL;
777	static const int64_t kTop38Bits = 0xfffffffffc000000LL;
778
779	static uint64_t load_3(const uint8_t *in)
780	{
781	uint64_t result;
782
783	result = ((uint64_t)in[0]);
784	result \|= ((uint64_t)in[1]) << 8;
785	result \|= ((uint64_t)in[2]) << 16;
786	return result;
787	}
788
789	static uint64_t load_4(const uint8_t *in)
790	{
791	uint64_t result;
792
793	result = ((uint64_t)in[0]);
794	result \|= ((uint64_t)in[1]) << 8;
795	result \|= ((uint64_t)in[2]) << 16;
796	result \|= ((uint64_t)in[3]) << 24;
797	return result;
798	}
799
800	static void fe_frombytes(fe h, const uint8_t *s)
801	{
802	/* Ignores top bit of h. */
803	int64_t h0 = load_4(s);
804	int64_t h1 = load_3(s + 4) << 6;
805	int64_t h2 = load_3(s + 7) << 5;
806	int64_t h3 = load_3(s + 10) << 3;
807	int64_t h4 = load_3(s + 13) << 2;
808	int64_t h5 = load_4(s + 16);
809	int64_t h6 = load_3(s + 20) << 7;
810	int64_t h7 = load_3(s + 23) << 5;
811	int64_t h8 = load_3(s + 26) << 4;
812	int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
813	int64_t carry0;
814	int64_t carry1;
815	int64_t carry2;
816	int64_t carry3;
817	int64_t carry4;
818	int64_t carry5;
819	int64_t carry6;
820	int64_t carry7;
821	int64_t carry8;
822	int64_t carry9;
823
824	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
825	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
826	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
827	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
828	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
829
830	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
831	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
832	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
833	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
834	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
835
836	h[0] = (int32_t)h0;
837	h[1] = (int32_t)h1;
838	h[2] = (int32_t)h2;
839	h[3] = (int32_t)h3;
840	h[4] = (int32_t)h4;
841	h[5] = (int32_t)h5;
842	h[6] = (int32_t)h6;
843	h[7] = (int32_t)h7;
844	h[8] = (int32_t)h8;
845	h[9] = (int32_t)h9;
846	}
847
848	/*
849	* Preconditions:
850	* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
851	*
852	* Write p=2^255-19; q=floor(h/p).
853	* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
854	*
855	* Proof:
856	* Have \|h\|<=p so \|q\|<=1 so \|19^2 2^(-255) q\|<1/4.
857	* Also have \|h-2^230 h9\|<2^231 so \|19 2^(-255)(h-2^230 h9)\|<1/4.
858	*
859	* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
860	* Then 0<y<1.
861	*
862	* Write r=h-pq.
863	* Have 0<=r<=p-1=2^255-20.
864	* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
865	*
866	* Write x=r+19(2^-255)r+y.
867	* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
868	*
869	* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
870	* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
871	*/
872	static void fe_tobytes(uint8_t *s, const fe h)
873	{
874	int32_t h0 = h[0];
875	int32_t h1 = h[1];
876	int32_t h2 = h[2];
877	int32_t h3 = h[3];
878	int32_t h4 = h[4];
879	int32_t h5 = h[5];
880	int32_t h6 = h[6];
881	int32_t h7 = h[7];
882	int32_t h8 = h[8];
883	int32_t h9 = h[9];
884	int32_t q;
885
886	q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
887	q = (h0 + q) >> 26;
888	q = (h1 + q) >> 25;
889	q = (h2 + q) >> 26;
890	q = (h3 + q) >> 25;
891	q = (h4 + q) >> 26;
892	q = (h5 + q) >> 25;
893	q = (h6 + q) >> 26;
894	q = (h7 + q) >> 25;
895	q = (h8 + q) >> 26;
896	q = (h9 + q) >> 25;
897
898	/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
899	h0 += 19 * q;
900	/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
901
902	h1 += h0 >> 26; h0 &= kBottom26Bits;
903	h2 += h1 >> 25; h1 &= kBottom25Bits;
904	h3 += h2 >> 26; h2 &= kBottom26Bits;
905	h4 += h3 >> 25; h3 &= kBottom25Bits;
906	h5 += h4 >> 26; h4 &= kBottom26Bits;
907	h6 += h5 >> 25; h5 &= kBottom25Bits;
908	h7 += h6 >> 26; h6 &= kBottom26Bits;
909	h8 += h7 >> 25; h7 &= kBottom25Bits;
910	h9 += h8 >> 26; h8 &= kBottom26Bits;
911	h9 &= kBottom25Bits;
912	/* h10 = carry9 */
913
914	/*
915	* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
916	* Have h0+...+2^230 h9 between 0 and 2^255-1;
917	* evidently 2^255 h10-2^255 q = 0.
918	* Goal: Output h0+...+2^230 h9.
919	*/
920	s[ 0] = (uint8_t) (h0 >> 0);
921	s[ 1] = (uint8_t) (h0 >> 8);
922	s[ 2] = (uint8_t) (h0 >> 16);
923	s[ 3] = (uint8_t)((h0 >> 24) \| ((uint32_t)(h1) << 2));
924	s[ 4] = (uint8_t) (h1 >> 6);
925	s[ 5] = (uint8_t) (h1 >> 14);
926	s[ 6] = (uint8_t)((h1 >> 22) \| ((uint32_t)(h2) << 3));
927	s[ 7] = (uint8_t) (h2 >> 5);
928	s[ 8] = (uint8_t) (h2 >> 13);
929	s[ 9] = (uint8_t)((h2 >> 21) \| ((uint32_t)(h3) << 5));
930	s[10] = (uint8_t) (h3 >> 3);
931	s[11] = (uint8_t) (h3 >> 11);
932	s[12] = (uint8_t)((h3 >> 19) \| ((uint32_t)(h4) << 6));
933	s[13] = (uint8_t) (h4 >> 2);
934	s[14] = (uint8_t) (h4 >> 10);
935	s[15] = (uint8_t) (h4 >> 18);
936	s[16] = (uint8_t) (h5 >> 0);
937	s[17] = (uint8_t) (h5 >> 8);
938	s[18] = (uint8_t) (h5 >> 16);
939	s[19] = (uint8_t)((h5 >> 24) \| ((uint32_t)(h6) << 1));
940	s[20] = (uint8_t) (h6 >> 7);
941	s[21] = (uint8_t) (h6 >> 15);
942	s[22] = (uint8_t)((h6 >> 23) \| ((uint32_t)(h7) << 3));
943	s[23] = (uint8_t) (h7 >> 5);
944	s[24] = (uint8_t) (h7 >> 13);
945	s[25] = (uint8_t)((h7 >> 21) \| ((uint32_t)(h8) << 4));
946	s[26] = (uint8_t) (h8 >> 4);
947	s[27] = (uint8_t) (h8 >> 12);
948	s[28] = (uint8_t)((h8 >> 20) \| ((uint32_t)(h9) << 6));
949	s[29] = (uint8_t) (h9 >> 2);
950	s[30] = (uint8_t) (h9 >> 10);
951	s[31] = (uint8_t) (h9 >> 18);
952	}
953
954	/* h = f */
955	static void fe_copy(fe h, const fe f)
956	{
957	memmove(h, f, sizeof(int32_t) * 10);
958	}
959
960	/* h = 0 */
961	static void fe_0(fe h)
962	{
963	memset(h, 0, sizeof(int32_t) * 10);
964	}
965
966	/* h = 1 */
967	static void fe_1(fe h)
968	{
969	memset(h, 0, sizeof(int32_t) * 10);
970	h[0] = 1;
971	}
972
973	/*
974	* h = f + g
975	*
976	* Can overlap h with f or g.
977	*
978	* Preconditions:
979	* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
980	* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
981	*
982	* Postconditions:
983	* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
984	*/
985	static void fe_add(fe h, const fe f, const fe g)
986	{
987	unsigned i;
988
989	for (i = 0; i < 10; i++) {
990	h[i] = f[i] + g[i];
991	}
992	}
993
994	/*
995	* h = f - g
996	*
997	* Can overlap h with f or g.
998	*
999	* Preconditions:
1000	* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1001	* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1002	*
1003	* Postconditions:
1004	* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1005	*/
1006	static void fe_sub(fe h, const fe f, const fe g)
1007	{
1008	unsigned i;
1009
1010	for (i = 0; i < 10; i++) {
1011	h[i] = f[i] - g[i];
1012	}
1013	}
1014
1015	/*
1016	* h = f * g
1017	*
1018	* Can overlap h with f or g.
1019	*
1020	* Preconditions:
1021	* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1022	* \|g\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1023	*
1024	* Postconditions:
1025	* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1026	*
1027	* Notes on implementation strategy:
1028	*
1029	* Using schoolbook multiplication.
1030	* Karatsuba would save a little in some cost models.
1031	*
1032	* Most multiplications by 2 and 19 are 32-bit precomputations;
1033	* cheaper than 64-bit postcomputations.
1034	*
1035	* There is one remaining multiplication by 19 in the carry chain;
1036	* one *19 precomputation can be merged into this,
1037	* but the resulting data flow is considerably less clean.
1038	*
1039	* There are 12 carries below.
1040	* 10 of them are 2-way parallelizable and vectorizable.
1041	* Can get away with 11 carries, but then data flow is much deeper.
1042	*
1043	* With tighter constraints on inputs can squeeze carries into int32.
1044	*/
1045	static void fe_mul(fe h, const fe f, const fe g)
1046	{
1047	int32_t f0 = f[0];
1048	int32_t f1 = f[1];
1049	int32_t f2 = f[2];
1050	int32_t f3 = f[3];
1051	int32_t f4 = f[4];
1052	int32_t f5 = f[5];
1053	int32_t f6 = f[6];
1054	int32_t f7 = f[7];
1055	int32_t f8 = f[8];
1056	int32_t f9 = f[9];
1057	int32_t g0 = g[0];
1058	int32_t g1 = g[1];
1059	int32_t g2 = g[2];
1060	int32_t g3 = g[3];
1061	int32_t g4 = g[4];
1062	int32_t g5 = g[5];
1063	int32_t g6 = g[6];
1064	int32_t g7 = g[7];
1065	int32_t g8 = g[8];
1066	int32_t g9 = g[9];
1067	int32_t g1_19 = 19 * g1; /* 1.9593752^29 /
1068	int32_t g2_19 = 19 * g2; /* 1.9593752^30; still ok /
1069	int32_t g3_19 = 19 * g3;
1070	int32_t g4_19 = 19 * g4;
1071	int32_t g5_19 = 19 * g5;
1072	int32_t g6_19 = 19 * g6;
1073	int32_t g7_19 = 19 * g7;
1074	int32_t g8_19 = 19 * g8;
1075	int32_t g9_19 = 19 * g9;
1076	int32_t f1_2 = 2 * f1;
1077	int32_t f3_2 = 2 * f3;
1078	int32_t f5_2 = 2 * f5;
1079	int32_t f7_2 = 2 * f7;
1080	int32_t f9_2 = 2 * f9;
1081	int64_t f0g0 = f0 * (int64_t) g0;
1082	int64_t f0g1 = f0 * (int64_t) g1;
1083	int64_t f0g2 = f0 * (int64_t) g2;
1084	int64_t f0g3 = f0 * (int64_t) g3;
1085	int64_t f0g4 = f0 * (int64_t) g4;
1086	int64_t f0g5 = f0 * (int64_t) g5;
1087	int64_t f0g6 = f0 * (int64_t) g6;
1088	int64_t f0g7 = f0 * (int64_t) g7;
1089	int64_t f0g8 = f0 * (int64_t) g8;
1090	int64_t f0g9 = f0 * (int64_t) g9;
1091	int64_t f1g0 = f1 * (int64_t) g0;
1092	int64_t f1g1_2 = f1_2 * (int64_t) g1;
1093	int64_t f1g2 = f1 * (int64_t) g2;
1094	int64_t f1g3_2 = f1_2 * (int64_t) g3;
1095	int64_t f1g4 = f1 * (int64_t) g4;
1096	int64_t f1g5_2 = f1_2 * (int64_t) g5;
1097	int64_t f1g6 = f1 * (int64_t) g6;
1098	int64_t f1g7_2 = f1_2 * (int64_t) g7;
1099	int64_t f1g8 = f1 * (int64_t) g8;
1100	int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
1101	int64_t f2g0 = f2 * (int64_t) g0;
1102	int64_t f2g1 = f2 * (int64_t) g1;
1103	int64_t f2g2 = f2 * (int64_t) g2;
1104	int64_t f2g3 = f2 * (int64_t) g3;
1105	int64_t f2g4 = f2 * (int64_t) g4;
1106	int64_t f2g5 = f2 * (int64_t) g5;
1107	int64_t f2g6 = f2 * (int64_t) g6;
1108	int64_t f2g7 = f2 * (int64_t) g7;
1109	int64_t f2g8_19 = f2 * (int64_t) g8_19;
1110	int64_t f2g9_19 = f2 * (int64_t) g9_19;
1111	int64_t f3g0 = f3 * (int64_t) g0;
1112	int64_t f3g1_2 = f3_2 * (int64_t) g1;
1113	int64_t f3g2 = f3 * (int64_t) g2;
1114	int64_t f3g3_2 = f3_2 * (int64_t) g3;
1115	int64_t f3g4 = f3 * (int64_t) g4;
1116	int64_t f3g5_2 = f3_2 * (int64_t) g5;
1117	int64_t f3g6 = f3 * (int64_t) g6;
1118	int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
1119	int64_t f3g8_19 = f3 * (int64_t) g8_19;
1120	int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
1121	int64_t f4g0 = f4 * (int64_t) g0;
1122	int64_t f4g1 = f4 * (int64_t) g1;
1123	int64_t f4g2 = f4 * (int64_t) g2;
1124	int64_t f4g3 = f4 * (int64_t) g3;
1125	int64_t f4g4 = f4 * (int64_t) g4;
1126	int64_t f4g5 = f4 * (int64_t) g5;
1127	int64_t f4g6_19 = f4 * (int64_t) g6_19;
1128	int64_t f4g7_19 = f4 * (int64_t) g7_19;
1129	int64_t f4g8_19 = f4 * (int64_t) g8_19;
1130	int64_t f4g9_19 = f4 * (int64_t) g9_19;
1131	int64_t f5g0 = f5 * (int64_t) g0;
1132	int64_t f5g1_2 = f5_2 * (int64_t) g1;
1133	int64_t f5g2 = f5 * (int64_t) g2;
1134	int64_t f5g3_2 = f5_2 * (int64_t) g3;
1135	int64_t f5g4 = f5 * (int64_t) g4;
1136	int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
1137	int64_t f5g6_19 = f5 * (int64_t) g6_19;
1138	int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
1139	int64_t f5g8_19 = f5 * (int64_t) g8_19;
1140	int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
1141	int64_t f6g0 = f6 * (int64_t) g0;
1142	int64_t f6g1 = f6 * (int64_t) g1;
1143	int64_t f6g2 = f6 * (int64_t) g2;
1144	int64_t f6g3 = f6 * (int64_t) g3;
1145	int64_t f6g4_19 = f6 * (int64_t) g4_19;
1146	int64_t f6g5_19 = f6 * (int64_t) g5_19;
1147	int64_t f6g6_19 = f6 * (int64_t) g6_19;
1148	int64_t f6g7_19 = f6 * (int64_t) g7_19;
1149	int64_t f6g8_19 = f6 * (int64_t) g8_19;
1150	int64_t f6g9_19 = f6 * (int64_t) g9_19;
1151	int64_t f7g0 = f7 * (int64_t) g0;
1152	int64_t f7g1_2 = f7_2 * (int64_t) g1;
1153	int64_t f7g2 = f7 * (int64_t) g2;
1154	int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
1155	int64_t f7g4_19 = f7 * (int64_t) g4_19;
1156	int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
1157	int64_t f7g6_19 = f7 * (int64_t) g6_19;
1158	int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
1159	int64_t f7g8_19 = f7 * (int64_t) g8_19;
1160	int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
1161	int64_t f8g0 = f8 * (int64_t) g0;
1162	int64_t f8g1 = f8 * (int64_t) g1;
1163	int64_t f8g2_19 = f8 * (int64_t) g2_19;
1164	int64_t f8g3_19 = f8 * (int64_t) g3_19;
1165	int64_t f8g4_19 = f8 * (int64_t) g4_19;
1166	int64_t f8g5_19 = f8 * (int64_t) g5_19;
1167	int64_t f8g6_19 = f8 * (int64_t) g6_19;
1168	int64_t f8g7_19 = f8 * (int64_t) g7_19;
1169	int64_t f8g8_19 = f8 * (int64_t) g8_19;
1170	int64_t f8g9_19 = f8 * (int64_t) g9_19;
1171	int64_t f9g0 = f9 * (int64_t) g0;
1172	int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
1173	int64_t f9g2_19 = f9 * (int64_t) g2_19;
1174	int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
1175	int64_t f9g4_19 = f9 * (int64_t) g4_19;
1176	int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
1177	int64_t f9g6_19 = f9 * (int64_t) g6_19;
1178	int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
1179	int64_t f9g8_19 = f9 * (int64_t) g8_19;
1180	int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
1181	int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1182	int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1183	int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1184	int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1185	int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1186	int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1187	int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
1188	int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
1189	int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
1190	int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ;
1191	int64_t carry0;
1192	int64_t carry1;
1193	int64_t carry2;
1194	int64_t carry3;
1195	int64_t carry4;
1196	int64_t carry5;
1197	int64_t carry6;
1198	int64_t carry7;
1199	int64_t carry8;
1200	int64_t carry9;
1201
1202	/* \|h0\| <= (1.651.652^52(1+19+19+19+19)+1.651.652^50(38+38+38+38+38))
1203	* i.e. \|h0\| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1204	* \|h1\| <= (1.651.652^51*(1+1+19+19+19+19+19+19+19+19))
1205	* i.e. \|h1\| <= 1.72^59; narrower ranges for h3, h5, h7, h9 /
1206
1207	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1208	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1209	/* \|h0\| <= 2^25 */
1210	/* \|h4\| <= 2^25 */
1211	/* \|h1\| <= 1.712^59 /
1212	/* \|h5\| <= 1.712^59 /
1213
1214	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1215	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1216	/* \|h1\| <= 2^24; from now on fits into int32 */
1217	/* \|h5\| <= 2^24; from now on fits into int32 */
1218	/* \|h2\| <= 1.412^60 /
1219	/* \|h6\| <= 1.412^60 /
1220
1221	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1222	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1223	/* \|h2\| <= 2^25; from now on fits into int32 unchanged */
1224	/* \|h6\| <= 2^25; from now on fits into int32 unchanged */
1225	/* \|h3\| <= 1.712^59 /
1226	/* \|h7\| <= 1.712^59 /
1227
1228	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1229	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1230	/* \|h3\| <= 2^24; from now on fits into int32 unchanged */
1231	/* \|h7\| <= 2^24; from now on fits into int32 unchanged */
1232	/* \|h4\| <= 1.722^34 /
1233	/* \|h8\| <= 1.412^60 /
1234
1235	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1236	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1237	/* \|h4\| <= 2^25; from now on fits into int32 unchanged */
1238	/* \|h8\| <= 2^25; from now on fits into int32 unchanged */
1239	/* \|h5\| <= 1.012^24 /
1240	/* \|h9\| <= 1.712^59 /
1241
1242	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1243	/* \|h9\| <= 2^24; from now on fits into int32 unchanged */
1244	/* \|h0\| <= 1.12^39 /
1245
1246	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1247	/* \|h0\| <= 2^25; from now on fits into int32 unchanged */
1248	/* \|h1\| <= 1.012^24 /
1249
1250	h[0] = (int32_t)h0;
1251	h[1] = (int32_t)h1;
1252	h[2] = (int32_t)h2;
1253	h[3] = (int32_t)h3;
1254	h[4] = (int32_t)h4;
1255	h[5] = (int32_t)h5;
1256	h[6] = (int32_t)h6;
1257	h[7] = (int32_t)h7;
1258	h[8] = (int32_t)h8;
1259	h[9] = (int32_t)h9;
1260	}
1261
1262	/*
1263	* h = f * f
1264	*
1265	* Can overlap h with f.
1266	*
1267	* Preconditions:
1268	* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1269	*
1270	* Postconditions:
1271	* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1272	*
1273	* See fe_mul.c for discussion of implementation strategy.
1274	*/
1275	static void fe_sq(fe h, const fe f)
1276	{
1277	int32_t f0 = f[0];
1278	int32_t f1 = f[1];
1279	int32_t f2 = f[2];
1280	int32_t f3 = f[3];
1281	int32_t f4 = f[4];
1282	int32_t f5 = f[5];
1283	int32_t f6 = f[6];
1284	int32_t f7 = f[7];
1285	int32_t f8 = f[8];
1286	int32_t f9 = f[9];
1287	int32_t f0_2 = 2 * f0;
1288	int32_t f1_2 = 2 * f1;
1289	int32_t f2_2 = 2 * f2;
1290	int32_t f3_2 = 2 * f3;
1291	int32_t f4_2 = 2 * f4;
1292	int32_t f5_2 = 2 * f5;
1293	int32_t f6_2 = 2 * f6;
1294	int32_t f7_2 = 2 * f7;
1295	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1296	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1297	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1298	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1299	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1300	int64_t f0f0 = f0 * (int64_t) f0;
1301	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1302	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1303	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1304	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1305	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1306	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1307	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1308	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1309	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1310	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1311	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1312	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1313	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1314	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1315	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1316	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1317	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1318	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1319	int64_t f2f2 = f2 * (int64_t) f2;
1320	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1321	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1322	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1323	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1324	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1325	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1326	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1327	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1328	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1329	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1330	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1331	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1332	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1333	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1334	int64_t f4f4 = f4 * (int64_t) f4;
1335	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1336	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1337	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1338	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1339	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1340	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1341	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1342	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1343	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1344	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1345	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1346	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1347	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1348	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1349	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1350	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1351	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1352	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1353	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1354	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1355	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1356	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1357	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1358	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1359	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1360	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1361	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1362	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1363	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1364	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1365	int64_t carry0;
1366	int64_t carry1;
1367	int64_t carry2;
1368	int64_t carry3;
1369	int64_t carry4;
1370	int64_t carry5;
1371	int64_t carry6;
1372	int64_t carry7;
1373	int64_t carry8;
1374	int64_t carry9;
1375
1376	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1377	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1378
1379	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1380	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1381
1382	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1383	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1384
1385	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1386	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1387
1388	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1389	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1390
1391	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1392
1393	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1394
1395	h[0] = (int32_t)h0;
1396	h[1] = (int32_t)h1;
1397	h[2] = (int32_t)h2;
1398	h[3] = (int32_t)h3;
1399	h[4] = (int32_t)h4;
1400	h[5] = (int32_t)h5;
1401	h[6] = (int32_t)h6;
1402	h[7] = (int32_t)h7;
1403	h[8] = (int32_t)h8;
1404	h[9] = (int32_t)h9;
1405	}
1406
1407	static void fe_invert(fe out, const fe z)
1408	{
1409	fe t0;
1410	fe t1;
1411	fe t2;
1412	fe t3;
1413	int i;
1414
1415	/*
1416	* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
1417	* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
1418	*/
1419
1420	/* t0 = z ** 2 */
1421	fe_sq(t0, z);
1422
1423	/* t1 = t0 (2 2) = z ** 8 */
1424	fe_sq(t1, t0);
1425	fe_sq(t1, t1);
1426
1427	/* t1 = z * t1 = z ** 9 */
1428	fe_mul(t1, z, t1);
1429	/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1430	fe_mul(t0, t0, t1);
1431
1432	/* t2 = t0 2 = z 22 */
1433	fe_sq(t2, t0);
1434
1435	/* t1 = t1 * t2 = z (2 5 - 1) */
1436	fe_mul(t1, t1, t2);
1437
1438	/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
1439	fe_sq(t2, t1);
1440	for (i = 1; i < 5; ++i) {
1441	fe_sq(t2, t2);
1442	}
1443
1444	/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
1445	fe_mul(t1, t2, t1);
1446
1447	/* Continuing similarly... */
1448
1449	/* t2 = z (2 20 - 1) */
1450	fe_sq(t2, t1);
1451	for (i = 1; i < 10; ++i) {
1452	fe_sq(t2, t2);
1453	}
1454	fe_mul(t2, t2, t1);
1455
1456	/* t2 = z (2 40 - 1) */
1457	fe_sq(t3, t2);
1458	for (i = 1; i < 20; ++i) {
1459	fe_sq(t3, t3);
1460	}
1461	fe_mul(t2, t3, t2);
1462
1463	/* t2 = z (2 10) * (2 ** 40 - 1) */
1464	for (i = 0; i < 10; ++i) {
1465	fe_sq(t2, t2);
1466	}
1467	/* t1 = z (2 50 - 1) */
1468	fe_mul(t1, t2, t1);
1469
1470	/* t2 = z (2 100 - 1) */
1471	fe_sq(t2, t1);
1472	for (i = 1; i < 50; ++i) {
1473	fe_sq(t2, t2);
1474	}
1475	fe_mul(t2, t2, t1);
1476
1477	/* t2 = z (2 200 - 1) */
1478	fe_sq(t3, t2);
1479	for (i = 1; i < 100; ++i) {
1480	fe_sq(t3, t3);
1481	}
1482	fe_mul(t2, t3, t2);
1483
1484	/* t2 = z ((2 50) * (2 ** 200 - 1) */
1485	fe_sq(t2, t2);
1486	for (i = 1; i < 50; ++i) {
1487	fe_sq(t2, t2);
1488	}
1489
1490	/* t1 = z (2 250 - 1) */
1491	fe_mul(t1, t2, t1);
1492
1493	/* t1 = z ((2 5) * (2 ** 250 - 1)) */
1494	fe_sq(t1, t1);
1495	for (i = 1; i < 5; ++i) {
1496	fe_sq(t1, t1);
1497	}
1498
1499	/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
1500	fe_mul(out, t1, t0);
1501	}
1502
1503	/*
1504	* h = -f
1505	*
1506	* Preconditions:
1507	* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1508	*
1509	* Postconditions:
1510	* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1511	*/
1512	static void fe_neg(fe h, const fe f)
1513	{
1514	unsigned i;
1515
1516	for (i = 0; i < 10; i++) {
1517	h[i] = -f[i];
1518	}
1519	}
1520
1521	/*
1522	* Replace (f,g) with (g,g) if b == 1;
1523	* replace (f,g) with (f,g) if b == 0.
1524	*
1525	* Preconditions: b in {0,1}.
1526	*/
1527	static void fe_cmov(fe f, const fe g, unsigned b)
1528	{
1529	size_t i;
1530
1531	b = 0-b;
1532	for (i = 0; i < 10; i++) {
1533	int32_t x = f[i] ^ g[i];
1534	x &= b;
1535	f[i] ^= x;
1536	}
1537	}
1538
1539	/*
1540	* return 0 if f == 0
1541	* return 1 if f != 0
1542	*
1543	* Preconditions:
1544	* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1545	*/
1546	static int fe_isnonzero(const fe f)
1547	{
1548	uint8_t s[32];
1549	static const uint8_t zero[32] = {0};
1550
1551	fe_tobytes(s, f);
1552
1553	return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1554	}
1555
1556	/*
1557	* return 1 if f is in {1,3,5,...,q-2}
1558	* return 0 if f is in {0,2,4,...,q-1}
1559	*
1560	* Preconditions:
1561	* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1562	*/
1563	static int fe_isnegative(const fe f)
1564	{
1565	uint8_t s[32];
1566
1567	fe_tobytes(s, f);
1568	return s[0] & 1;
1569	}
1570
1571	/*
1572	* h = 2 * f * f
1573	*
1574	* Can overlap h with f.
1575	*
1576	* Preconditions:
1577	* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1578	*
1579	* Postconditions:
1580	* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1581	*
1582	* See fe_mul.c for discussion of implementation strategy.
1583	*/
1584	static void fe_sq2(fe h, const fe f)
1585	{
1586	int32_t f0 = f[0];
1587	int32_t f1 = f[1];
1588	int32_t f2 = f[2];
1589	int32_t f3 = f[3];
1590	int32_t f4 = f[4];
1591	int32_t f5 = f[5];
1592	int32_t f6 = f[6];
1593	int32_t f7 = f[7];
1594	int32_t f8 = f[8];
1595	int32_t f9 = f[9];
1596	int32_t f0_2 = 2 * f0;
1597	int32_t f1_2 = 2 * f1;
1598	int32_t f2_2 = 2 * f2;
1599	int32_t f3_2 = 2 * f3;
1600	int32_t f4_2 = 2 * f4;
1601	int32_t f5_2 = 2 * f5;
1602	int32_t f6_2 = 2 * f6;
1603	int32_t f7_2 = 2 * f7;
1604	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1605	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1606	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1607	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1608	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1609	int64_t f0f0 = f0 * (int64_t) f0;
1610	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1611	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1612	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1613	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1614	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1615	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1616	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1617	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1618	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1619	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1620	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1621	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1622	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1623	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1624	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1625	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1626	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1627	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1628	int64_t f2f2 = f2 * (int64_t) f2;
1629	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1630	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1631	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1632	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1633	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1634	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1635	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1636	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1637	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1638	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1639	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1640	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1641	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1642	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1643	int64_t f4f4 = f4 * (int64_t) f4;
1644	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1645	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1646	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1647	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1648	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1649	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1650	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1651	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1652	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1653	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1654	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1655	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1656	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1657	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1658	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1659	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1660	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1661	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1662	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1663	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1664	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1665	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1666	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1667	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1668	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1669	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1670	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1671	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1672	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1673	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1674	int64_t carry0;
1675	int64_t carry1;
1676	int64_t carry2;
1677	int64_t carry3;
1678	int64_t carry4;
1679	int64_t carry5;
1680	int64_t carry6;
1681	int64_t carry7;
1682	int64_t carry8;
1683	int64_t carry9;
1684
1685	h0 += h0;
1686	h1 += h1;
1687	h2 += h2;
1688	h3 += h3;
1689	h4 += h4;
1690	h5 += h5;
1691	h6 += h6;
1692	h7 += h7;
1693	h8 += h8;
1694	h9 += h9;
1695
1696	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1697	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1698
1699	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1700	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1701
1702	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1703	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1704
1705	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1706	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1707
1708	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1709	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1710
1711	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1712
1713	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1714
1715	h[0] = (int32_t)h0;
1716	h[1] = (int32_t)h1;
1717	h[2] = (int32_t)h2;
1718	h[3] = (int32_t)h3;
1719	h[4] = (int32_t)h4;
1720	h[5] = (int32_t)h5;
1721	h[6] = (int32_t)h6;
1722	h[7] = (int32_t)h7;
1723	h[8] = (int32_t)h8;
1724	h[9] = (int32_t)h9;
1725	}
1726
1727	static void fe_pow22523(fe out, const fe z)
1728	{
1729	fe t0;
1730	fe t1;
1731	fe t2;
1732	int i;
1733
1734	fe_sq(t0, z);
1735	fe_sq(t1, t0);
1736	for (i = 1; i < 2; ++i) {
1737	fe_sq(t1, t1);
1738	}
1739	fe_mul(t1, z, t1);
1740	fe_mul(t0, t0, t1);
1741	fe_sq(t0, t0);
1742	fe_mul(t0, t1, t0);
1743	fe_sq(t1, t0);
1744	for (i = 1; i < 5; ++i) {
1745	fe_sq(t1, t1);
1746	}
1747	fe_mul(t0, t1, t0);
1748	fe_sq(t1, t0);
1749	for (i = 1; i < 10; ++i) {
1750	fe_sq(t1, t1);
1751	}
1752	fe_mul(t1, t1, t0);
1753	fe_sq(t2, t1);
1754	for (i = 1; i < 20; ++i) {
1755	fe_sq(t2, t2);
1756	}
1757	fe_mul(t1, t2, t1);
1758	fe_sq(t1, t1);
1759	for (i = 1; i < 10; ++i) {
1760	fe_sq(t1, t1);
1761	}
1762	fe_mul(t0, t1, t0);
1763	fe_sq(t1, t0);
1764	for (i = 1; i < 50; ++i) {
1765	fe_sq(t1, t1);
1766	}
1767	fe_mul(t1, t1, t0);
1768	fe_sq(t2, t1);
1769	for (i = 1; i < 100; ++i) {
1770	fe_sq(t2, t2);
1771	}
1772	fe_mul(t1, t2, t1);
1773	fe_sq(t1, t1);
1774	for (i = 1; i < 50; ++i) {
1775	fe_sq(t1, t1);
1776	}
1777	fe_mul(t0, t1, t0);
1778	fe_sq(t0, t0);
1779	for (i = 1; i < 2; ++i) {
1780	fe_sq(t0, t0);
1781	}
1782	fe_mul(out, t0, z);
1783	}
1784
1785	/*
1786	* ge means group element.
1787	*
1788	* Here the group is the set of pairs (x,y) of field elements (see fe.h)
1789	* satisfying -x^2 + y^2 = 1 + d x^2y^2
1790	* where d = -121665/121666.
1791	*
1792	* Representations:
1793	* ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1794	* ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1795	* ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1796	* ge_precomp (Duif): (y+x,y-x,2dxy)
1797	*/
1798	typedef struct {
1799	fe X;
1800	fe Y;
1801	fe Z;
1802	} ge_p2;
1803
1804	typedef struct {
1805	fe X;
1806	fe Y;
1807	fe Z;
1808	fe T;
1809	} ge_p3;
1810
1811	typedef struct {
1812	fe X;
1813	fe Y;
1814	fe Z;
1815	fe T;
1816	} ge_p1p1;
1817
1818	typedef struct {
1819	fe yplusx;
1820	fe yminusx;
1821	fe xy2d;
1822	} ge_precomp;
1823
1824	typedef struct {
1825	fe YplusX;
1826	fe YminusX;
1827	fe Z;
1828	fe T2d;
1829	} ge_cached;
1830
1831	static void ge_tobytes(uint8_t s, const ge_p2 h)
1832	{
1833	fe recip;
1834	fe x;
1835	fe y;
1836
1837	fe_invert(recip, h->Z);
1838	fe_mul(x, h->X, recip);
1839	fe_mul(y, h->Y, recip);
1840	fe_tobytes(s, y);
1841	s[31] ^= fe_isnegative(x) << 7;
1842	}
1843
1844	static void ge_p3_tobytes(uint8_t s, const ge_p3 h)
1845	{
1846	fe recip;
1847	fe x;
1848	fe y;
1849
1850	fe_invert(recip, h->Z);
1851	fe_mul(x, h->X, recip);
1852	fe_mul(y, h->Y, recip);
1853	fe_tobytes(s, y);
1854	s[31] ^= fe_isnegative(x) << 7;
1855	}
1856
1857	static const fe d = {
1858	-10913610, 13857413, -15372611, 6949391, 114729,
1859	-8787816, -6275908, -3247719, -18696448, -12055116
1860	};
1861
1862	static const fe sqrtm1 = {
1863	-32595792, -7943725, 9377950, 3500415, 12389472,
1864	-272473, -25146209, -2005654, 326686, 11406482
1865	};
1866
1867	static int ge_frombytes_vartime(ge_p3 h, const uint8_t s)
1868	{
1869	fe u;
1870	fe v;
1871	fe w;
1872	fe vxx;
1873	fe check;
1874
1875	fe_frombytes(h->Y, s);
1876	fe_1(h->Z);
1877	fe_sq(u, h->Y);
1878	fe_mul(v, u, d);
1879	fe_sub(u, u, h->Z); /* u = y^2-1 */
1880	fe_add(v, v, h->Z); /* v = dy^2+1 */
1881
1882	fe_mul(w, u, v); /* w = uv /
1883
1884	fe_pow22523(h->X, w); /* x = w^((q-5)/8) */
1885	fe_mul(h->X, h->X, u); /* x = u * w^((q-5)/8) */
1886
1887	fe_sq(vxx, h->X);
1888	fe_mul(vxx, vxx, v);
1889	fe_sub(check, vxx, u); /* vx^2-u */
1890	if (fe_isnonzero(check)) {
1891	fe_add(check, vxx, u); /* vx^2+u */
1892	if (fe_isnonzero(check)) {
1893	return -1;
1894	}
1895	fe_mul(h->X, h->X, sqrtm1);
1896	}
1897
1898	if (fe_isnegative(h->X) != (s[31] >> 7)) {
1899	fe_neg(h->X, h->X);
1900	}
1901
1902	fe_mul(h->T, h->X, h->Y);
1903	return 0;
1904	}
1905
1906	static void ge_p2_0(ge_p2 *h)
1907	{
1908	fe_0(h->X);
1909	fe_1(h->Y);
1910	fe_1(h->Z);
1911	}
1912
1913	static void ge_p3_0(ge_p3 *h)
1914	{
1915	fe_0(h->X);
1916	fe_1(h->Y);
1917	fe_1(h->Z);
1918	fe_0(h->T);
1919	}
1920
1921	static void ge_precomp_0(ge_precomp *h)
1922	{
1923	fe_1(h->yplusx);
1924	fe_1(h->yminusx);
1925	fe_0(h->xy2d);
1926	}
1927
1928	/* r = p */
1929	static void ge_p3_to_p2(ge_p2 r, const ge_p3 p)
1930	{
1931	fe_copy(r->X, p->X);
1932	fe_copy(r->Y, p->Y);
1933	fe_copy(r->Z, p->Z);
1934	}
1935
1936	static const fe d2 = {
1937	-21827239, -5839606, -30745221, 13898782, 229458,
1938	15978800, -12551817, -6495438, 29715968, 9444199
1939	};
1940
1941	/* r = p */
1942	static void ge_p3_to_cached(ge_cached r, const ge_p3 p)
1943	{
1944	fe_add(r->YplusX, p->Y, p->X);
1945	fe_sub(r->YminusX, p->Y, p->X);
1946	fe_copy(r->Z, p->Z);
1947	fe_mul(r->T2d, p->T, d2);
1948	}
1949
1950	/* r = p */
1951	static void ge_p1p1_to_p2(ge_p2 r, const ge_p1p1 p)
1952	{
1953	fe_mul(r->X, p->X, p->T);
1954	fe_mul(r->Y, p->Y, p->Z);
1955	fe_mul(r->Z, p->Z, p->T);
1956	}
1957
1958	/* r = p */
1959	static void ge_p1p1_to_p3(ge_p3 r, const ge_p1p1 p)
1960	{
1961	fe_mul(r->X, p->X, p->T);
1962	fe_mul(r->Y, p->Y, p->Z);
1963	fe_mul(r->Z, p->Z, p->T);
1964	fe_mul(r->T, p->X, p->Y);
1965	}
1966
1967	/* r = 2 * p */
1968	static void ge_p2_dbl(ge_p1p1 r, const ge_p2 p)
1969	{
1970	fe t0;
1971
1972	fe_sq(r->X, p->X);
1973	fe_sq(r->Z, p->Y);
1974	fe_sq2(r->T, p->Z);
1975	fe_add(r->Y, p->X, p->Y);
1976	fe_sq(t0, r->Y);
1977	fe_add(r->Y, r->Z, r->X);
1978	fe_sub(r->Z, r->Z, r->X);
1979	fe_sub(r->X, t0, r->Y);
1980	fe_sub(r->T, r->T, r->Z);
1981	}
1982
1983	/* r = 2 * p */
1984	static void ge_p3_dbl(ge_p1p1 r, const ge_p3 p)
1985	{
1986	ge_p2 q;
1987	ge_p3_to_p2(&q, p);
1988	ge_p2_dbl(r, &q);
1989	}
1990
1991	/* r = p + q */
1992	static void ge_madd(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
1993	{
1994	fe t0;
1995
1996	fe_add(r->X, p->Y, p->X);
1997	fe_sub(r->Y, p->Y, p->X);
1998	fe_mul(r->Z, r->X, q->yplusx);
1999	fe_mul(r->Y, r->Y, q->yminusx);
2000	fe_mul(r->T, q->xy2d, p->T);
2001	fe_add(t0, p->Z, p->Z);
2002	fe_sub(r->X, r->Z, r->Y);
2003	fe_add(r->Y, r->Z, r->Y);
2004	fe_add(r->Z, t0, r->T);
2005	fe_sub(r->T, t0, r->T);
2006	}
2007
2008	/* r = p - q */
2009	static void ge_msub(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2010	{
2011	fe t0;
2012
2013	fe_add(r->X, p->Y, p->X);
2014	fe_sub(r->Y, p->Y, p->X);
2015	fe_mul(r->Z, r->X, q->yminusx);
2016	fe_mul(r->Y, r->Y, q->yplusx);
2017	fe_mul(r->T, q->xy2d, p->T);
2018	fe_add(t0, p->Z, p->Z);
2019	fe_sub(r->X, r->Z, r->Y);
2020	fe_add(r->Y, r->Z, r->Y);
2021	fe_sub(r->Z, t0, r->T);
2022	fe_add(r->T, t0, r->T);
2023	}
2024
2025	/* r = p + q */
2026	static void ge_add(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2027	{
2028	fe t0;
2029
2030	fe_add(r->X, p->Y, p->X);
2031	fe_sub(r->Y, p->Y, p->X);
2032	fe_mul(r->Z, r->X, q->YplusX);
2033	fe_mul(r->Y, r->Y, q->YminusX);
2034	fe_mul(r->T, q->T2d, p->T);
2035	fe_mul(r->X, p->Z, q->Z);
2036	fe_add(t0, r->X, r->X);
2037	fe_sub(r->X, r->Z, r->Y);
2038	fe_add(r->Y, r->Z, r->Y);
2039	fe_add(r->Z, t0, r->T);
2040	fe_sub(r->T, t0, r->T);
2041	}
2042
2043	/* r = p - q */
2044	static void ge_sub(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2045	{
2046	fe t0;
2047
2048	fe_add(r->X, p->Y, p->X);
2049	fe_sub(r->Y, p->Y, p->X);
2050	fe_mul(r->Z, r->X, q->YminusX);
2051	fe_mul(r->Y, r->Y, q->YplusX);
2052	fe_mul(r->T, q->T2d, p->T);
2053	fe_mul(r->X, p->Z, q->Z);
2054	fe_add(t0, r->X, r->X);
2055	fe_sub(r->X, r->Z, r->Y);
2056	fe_add(r->Y, r->Z, r->Y);
2057	fe_sub(r->Z, t0, r->T);
2058	fe_add(r->T, t0, r->T);
2059	}
2060
2061	static uint8_t equal(signed char b, signed char c)
2062	{
2063	uint8_t ub = b;
2064	uint8_t uc = c;
2065	uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2066	uint32_t y = x; /* 0: yes; 1..255: no */
2067	y -= 1; /* 4294967295: yes; 0..254: no */
2068	y >>= 31; /* 1: yes; 0: no */
2069	return y;
2070	}
2071
2072	static void cmov(ge_precomp t, const ge_precomp u, uint8_t b)
2073	{
2074	fe_cmov(t->yplusx, u->yplusx, b);
2075	fe_cmov(t->yminusx, u->yminusx, b);
2076	fe_cmov(t->xy2d, u->xy2d, b);
2077	}
2078
2079	/* k25519Precomp[i][j] = (j+1)256^iB */
2080	static const ge_precomp k25519Precomp[32][8] = {
2081	{
2082	{
2083	{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2084	27544626, -11754271, -6079156, 2047605},
2085	{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2086	5043384, 19500929, -15469378},
2087	{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2088	29287919, 11864899, -24514362, -4438546},
2089	},
2090	{
2091	{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2092	-11717903, -3814571, -358445, -10211303},
2093	{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2094	-15616551, 11189268, -26829678, -5319081},
2095	{26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2096	-3128826, -9541118, -15472047, -4166697},
2097	},
2098	{
2099	{15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2100	27787600, -14772189, 28944400, -1550024},
2101	{16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2102	16354577, -11775962, 7689662, 11199574},
2103	{30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2104	7512774, 10017326, -17749093, -9920357},
2105	},
2106	{
2107	{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2108	-28926210, 15006023, 3284568, -6276540},
2109	{23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2110	7464579, 9656445, 13059162, 10374397},
2111	{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2112	-3839045, -641708, -101325},
2113	},
2114	{
2115	{10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2116	32867885, 14515107, -15438304, 10819380},
2117	{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2118	12483688, -12668491, 5581306},
2119	{19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2120	28542350, 13850243, -23678021, -15815942},
2121	},
2122	{
2123	{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2124	-19188627, -15224819, -9818940, -12085777},
2125	{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2126	-15689887, 1762328, 14866737},
2127	{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2128	-28236412, 3959421, 27914454, 4383652},
2129	},
2130	{
2131	{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2132	5230134, -23952439, -15175766},
2133	{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2134	20654025, 16520125, 30598449, 7715701},
2135	{28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2136	-31400660, 1370708, 29794553, -1409300},
2137	},
2138	{
2139	{14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2140	30290735, 10876454, -33154098, 2381726},
2141	{-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2142	-6236617, 3696005, -32300832, 15351955},
2143	{27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2144	-32961401, -2970515, 29551813, 10109425},
2145	},
2146	},
2147	{
2148	{
2149	{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2150	-2378284, -1627556, 10092783, -4764171},
2151	{27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2152	-32508754, 12005538, -17810127, 12803510},
2153	{17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2154	30364213, -9038194, 18016357, 4397660},
2155	},
2156	{
2157	{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2158	-26619106, 14544525, -17477504, 982639},
2159	{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2160	-4120128, -21047696, 9934963},
2161	{5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2162	-14747930, 4559895, -30123922, -10897950},
2163	},
2164	{
2165	{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2166	24191034, 4541697, -13338309, 5500568},
2167	{12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2168	-17430592, 12264343, 10874051, 13524335},
2169	{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2170	5080568, -22528059, 5376628},
2171	},
2172	{
2173	{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2174	-22321305, -9447443, 4535768, 1569007},
2175	{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2176	-30494562, 3044290, 31848280, 12543772},
2177	{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2178	-27377195, -2062731, 7718482, 14474653},
2179	},
2180	{
2181	{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2182	-7236665, 24316168, -5253567},
2183	{13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2184	33040651, -13424532, -20729456, 8321686},
2185	{21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
2186	23845965, -11874838, -9984458, 608372},
2187	},
2188	{
2189	{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
2190	1123968, -6780577, 27229399, 23887},
2191	{-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
2192	12797024, -6440308, -1633405, 16678954},
2193	{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
2194	-1508144, -4795045, -17169265, 4904953},
2195	},
2196	{
2197	{24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
2198	5169211, 16191880, 2128236, -4326833},
2199	{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
2200	-29806336, 916033, -6882542, -2986532},
2201	{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
2202	285431, 2763829, 15736322, 4143876},
2203	},
2204	{
2205	{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
2206	-14594663, 23527084, -16458268},
2207	{33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
2208	-32625340, 4087881, -15188911, -14416214},
2209	{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
2210	4357868, -4774191, -16323038},
2211	},
2212	},
2213	{
2214	{
2215	{6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
2216	23365147, -3949732, 7390890, 2759800},
2217	{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
2218	-4264057, 1244380, -12919645},
2219	{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
2220	9208236, 15886429, 16489664},
2221	},
2222	{
2223	{1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
2224	-13693198, 398369, -30606455, -712933},
2225	{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
2226	13348553, 12076947, -30836462, 5113182},
2227	{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
2228	-30341101, -7336386, 13847711, 5387222},
2229	},
2230	{
2231	{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
2232	8763061, 3617786, -19600662, 10370991},
2233	{20246567, -14369378, 22358229, -543712, 18507283, -10413996,
2234	14554437, -8746092, 32232924, 16763880},
2235	{9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
2236	11094161, 15689506, 3140038, -16510092},
2237	},
2238	{
2239	{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
2240	-27224800, 9448613, -28774454, 366295},
2241	{19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
2242	28344573, 8041113, 719605, 11671788},
2243	{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
2244	-15266516, 27000813, -10195553},
2245	},
2246	{
2247	{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
2248	5336097, 6750977, -14521026},
2249	{11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
2250	1695823, -8819122, 8169720, 16220347},
2251	{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
2252	-11144307, -2627664, -5990708, -14166033},
2253	},
2254	{
2255	{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
2256	27884329, 2847284, 2655861, 1738395},
2257	{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
2258	21651608, -3239336, -19087449, -11005278},
2259	{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
2260	5821408, 10478196, 8544890},
2261	},
2262	{
2263	{32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
2264	19270449, 12217473, 17789017, -3395995},
2265	{-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
2266	15479401, -3853233, 30460520, 1052596},
2267	{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
2268	27491595, -4612359, 3179268, -9478891},
2269	},
2270	{
2271	{31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
2272	-14756777, -16411740, 19072640, -9511060},
2273	{11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
2274	5977896, -5215017, 473099, 5040608},
2275	{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
2276	28326862, 1721092, -19558642, -3131606},
2277	},
2278	},
2279	{
2280	{
2281	{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
2282	8076149, -27868496, 11538389},
2283	{-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
2284	8754525, 7446702, -5676054, 5797016},
2285	{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
2286	2014099, -9050574, -2369172, -5877341},
2287	},
2288	{
2289	{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
2290	1192730, -3714199, 15123619, 10811505},
2291	{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
2292	15776356, -28886779, -11974553},
2293	{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
2294	-20654173, -16484855, 4714547, -9600655},
2295	},
2296	{
2297	{15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
2298	24611599, -4543832, -11745876, 12340220},
2299	{12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
2300	9613953, 8241152, 15370987, 9608631},
2301	{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
2302	15866074, -28210621, -8814099},
2303	},
2304	{
2305	{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
2306	858697, 20571223, 8420556},
2307	{14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
2308	33531827, 12516406, -21574435, -12476749},
2309	{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
2310	7256740, 8791136, 15069930},
2311	},
2312	{
2313	{1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
2314	14711875, 4874229, -30663140, -2331391},
2315	{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
2316	-7912378, -33069337, 9234253},
2317	{20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
2318	31559055, -11609587, 18979186, 13396066},
2319	},
2320	{
2321	{24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
2322	-18816887, 13594782, 33514650, 7021958},
2323	{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
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4122	9021034, 9078865, 3353509, 4033511},
4123	{-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
4124	23161163, 8839127, 27485041, 7356032},
4125	},
4126	},
4127	{
4128	{
4129	{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
4130	2625015, 28431036, -16771834},
4131	{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
4132	-22545972, 14150565, 15970762, 4099461},
4133	{29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
4134	13617293, -9937143, 11465739, 8317062},
4135	},
4136	{
4137	{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
4138	14898637, 3848455, 20969334, -5157516},
4139	{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
4140	-21610826, -3649888, 11177095, 14989547},
4141	{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
4142	13515641, 2581286, -28487508, 9930240},
4143	},
4144	{
4145	{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
4146	18345767, -13403753, 16291481, -5314038},
4147	{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
4148	6957617, 4368891, 9788741},
4149	{16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
4150	-21722536, -8613148, 16250552, -11111103},
4151	},
4152	{
4153	{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
4154	10604807, -30190403, 4782747},
4155	{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
4156	-9981571, 4383045, 22546403, 437323},
4157	{31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
4158	27343084, 2786261, -30633590, -14097016},
4159	},
4160	{
4161	{-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
4162	-19690631, 2355319, -19284671, -6114373},
4163	{15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
4164	18952177, 15496498, -29380133, 11754228},
4165	{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
4166	7141596, 11724556, 22761615, -10134141},
4167	},
4168	{
4169	{16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
4170	-28741185, -12227393, 32851222, 11717399},
4171	{11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
4172	31474879, 3483633, -1193175, -4030831},
4173	{-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4174	33142652, 6546660, -19985279, -3948376},
4175	},
4176	{
4177	{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4178	-8537131, -12833048, -30772034, -15486313},
4179	{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4180	-31135347, -16049879, 10928917, 3011958},
4181	{-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4182	-30831056, -12805180, 18008031, 10258577},
4183	},
4184	{
4185	{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4186	-1853465, 1367120, 25127874, 6671743},
4187	{29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4188	21382910, 11042292, 25838796, 4642684},
4189	{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4190	30468147, -13900640, 18423289, 4177476},
4191	},
4192	},
4193	};
4194
4195	static uint8_t negative(signed char b)
4196	{
4197	uint32_t x = b;
4198
4199	x >>= 31; /* 1: yes; 0: no */
4200	return x;
4201	}
4202
4203	static void table_select(ge_precomp *t, int pos, signed char b)
4204	{
4205	ge_precomp minust;
4206	uint8_t bnegative = negative(b);
4207	uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4208
4209	ge_precomp_0(t);
4210	cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4211	cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4212	cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4213	cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4214	cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4215	cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4216	cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4217	cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4218	fe_copy(minust.yplusx, t->yminusx);
4219	fe_copy(minust.yminusx, t->yplusx);
4220	fe_neg(minust.xy2d, t->xy2d);
4221	cmov(t, &minust, bnegative);
4222	}
4223
4224	/*
4225	* h = a * B
4226	*
4227	* where a = a[0]+256*a[1]+...+256^31 a[31]
4228	* B is the Ed25519 base point (x,4/5) with x positive.
4229	*
4230	* Preconditions:
4231	* a[31] <= 127
4232	*/
4233	static void ge_scalarmult_base(ge_p3 h, const uint8_t a)
4234	{
4235	signed char e[64];
4236	signed char carry;
4237	ge_p1p1 r;
4238	ge_p2 s;
4239	ge_precomp t;
4240	int i;
4241
4242	for (i = 0; i < 32; ++i) {
4243	e[2 * i + 0] = (a[i] >> 0) & 15;
4244	e[2 * i + 1] = (a[i] >> 4) & 15;
4245	}
4246	/* each e[i] is between 0 and 15 */
4247	/* e[63] is between 0 and 7 */
4248
4249	carry = 0;
4250	for (i = 0; i < 63; ++i) {
4251	e[i] += carry;
4252	carry = e[i] + 8;
4253	carry >>= 4;
4254	e[i] -= carry << 4;
4255	}
4256	e[63] += carry;
4257	/* each e[i] is between -8 and 8 */
4258
4259	ge_p3_0(h);
4260	for (i = 1; i < 64; i += 2) {
4261	table_select(&t, i / 2, e[i]);
4262	ge_madd(&r, h, &t);
4263	ge_p1p1_to_p3(h, &r);
4264	}
4265
4266	ge_p3_dbl(&r, h);
4267	ge_p1p1_to_p2(&s, &r);
4268	ge_p2_dbl(&r, &s);
4269	ge_p1p1_to_p2(&s, &r);
4270	ge_p2_dbl(&r, &s);
4271	ge_p1p1_to_p2(&s, &r);
4272	ge_p2_dbl(&r, &s);
4273	ge_p1p1_to_p3(h, &r);
4274
4275	for (i = 0; i < 64; i += 2) {
4276	table_select(&t, i / 2, e[i]);
4277	ge_madd(&r, h, &t);
4278	ge_p1p1_to_p3(h, &r);
4279	}
4280
4281	OPENSSL_cleanse(e, sizeof(e));
4282	}
4283
4284	#if !defined(BASE_2_51_IMPLEMENTED)
4285	/*
4286	* Replace (f,g) with (g,f) if b == 1;
4287	* replace (f,g) with (f,g) if b == 0.
4288	*
4289	* Preconditions: b in {0,1}.
4290	*/
4291	static void fe_cswap(fe f, fe g, unsigned int b)
4292	{
4293	size_t i;
4294
4295	b = 0-b;
4296	for (i = 0; i < 10; i++) {
4297	int32_t x = f[i] ^ g[i];
4298	x &= b;
4299	f[i] ^= x;
4300	g[i] ^= x;
4301	}
4302	}
4303
4304	/*
4305	* h = f * 121666
4306	*
4307	* Can overlap h with f.
4308	*
4309	* Preconditions:
4310	* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
4311	*
4312	* Postconditions:
4313	* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
4314	*/
4315	static void fe_mul121666(fe h, fe f)
4316	{
4317	int32_t f0 = f[0];
4318	int32_t f1 = f[1];
4319	int32_t f2 = f[2];
4320	int32_t f3 = f[3];
4321	int32_t f4 = f[4];
4322	int32_t f5 = f[5];
4323	int32_t f6 = f[6];
4324	int32_t f7 = f[7];
4325	int32_t f8 = f[8];
4326	int32_t f9 = f[9];
4327	int64_t h0 = f0 * (int64_t) 121666;
4328	int64_t h1 = f1 * (int64_t) 121666;
4329	int64_t h2 = f2 * (int64_t) 121666;
4330	int64_t h3 = f3 * (int64_t) 121666;
4331	int64_t h4 = f4 * (int64_t) 121666;
4332	int64_t h5 = f5 * (int64_t) 121666;
4333	int64_t h6 = f6 * (int64_t) 121666;
4334	int64_t h7 = f7 * (int64_t) 121666;
4335	int64_t h8 = f8 * (int64_t) 121666;
4336	int64_t h9 = f9 * (int64_t) 121666;
4337	int64_t carry0;
4338	int64_t carry1;
4339	int64_t carry2;
4340	int64_t carry3;
4341	int64_t carry4;
4342	int64_t carry5;
4343	int64_t carry6;
4344	int64_t carry7;
4345	int64_t carry8;
4346	int64_t carry9;
4347
4348	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
4349	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
4350	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
4351	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
4352	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
4353
4354	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
4355	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
4356	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
4357	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
4358	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
4359
4360	h[0] = (int32_t)h0;
4361	h[1] = (int32_t)h1;
4362	h[2] = (int32_t)h2;
4363	h[3] = (int32_t)h3;
4364	h[4] = (int32_t)h4;
4365	h[5] = (int32_t)h5;
4366	h[6] = (int32_t)h6;
4367	h[7] = (int32_t)h7;
4368	h[8] = (int32_t)h8;
4369	h[9] = (int32_t)h9;
4370	}
4371
4372	static void x25519_scalar_mult_generic(uint8_t out[32],
4373	const uint8_t scalar[32],
4374	const uint8_t point[32]) {
4375	fe x1, x2, z2, x3, z3, tmp0, tmp1;
4376	uint8_t e[32];
4377	unsigned swap = 0;
4378	int pos;
4379
4380	memcpy(e, scalar, 32);
4381	e[0] &= 248;
4382	e[31] &= 127;
4383	e[31] \|= 64;
4384	fe_frombytes(x1, point);
4385	fe_1(x2);
4386	fe_0(z2);
4387	fe_copy(x3, x1);
4388	fe_1(z3);
4389
4390	for (pos = 254; pos >= 0; --pos) {
4391	unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4392	swap ^= b;
4393	fe_cswap(x2, x3, swap);
4394	fe_cswap(z2, z3, swap);
4395	swap = b;
4396	fe_sub(tmp0, x3, z3);
4397	fe_sub(tmp1, x2, z2);
4398	fe_add(x2, x2, z2);
4399	fe_add(z2, x3, z3);
4400	fe_mul(z3, tmp0, x2);
4401	fe_mul(z2, z2, tmp1);
4402	fe_sq(tmp0, tmp1);
4403	fe_sq(tmp1, x2);
4404	fe_add(x3, z3, z2);
4405	fe_sub(z2, z3, z2);
4406	fe_mul(x2, tmp1, tmp0);
4407	fe_sub(tmp1, tmp1, tmp0);
4408	fe_sq(z2, z2);
4409	fe_mul121666(z3, tmp1);
4410	fe_sq(x3, x3);
4411	fe_add(tmp0, tmp0, z3);
4412	fe_mul(z3, x1, z2);
4413	fe_mul(z2, tmp1, tmp0);
4414	}
4415
4416	fe_invert(z2, z2);
4417	fe_mul(x2, x2, z2);
4418	fe_tobytes(out, x2);
4419
4420	OPENSSL_cleanse(e, sizeof(e));
4421	}
4422
4423	static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4424	const uint8_t point[32]) {
4425	x25519_scalar_mult_generic(out, scalar, point);
4426	}
4427	#endif
4428
4429	static void slide(signed char r, const uint8_t a)
4430	{
4431	int i;
4432	int b;
4433	int k;
4434
4435	for (i = 0; i < 256; ++i) {
4436	r[i] = 1 & (a[i >> 3] >> (i & 7));
4437	}
4438
4439	for (i = 0; i < 256; ++i) {
4440	if (r[i]) {
4441	for (b = 1; b <= 6 && i + b < 256; ++b) {
4442	if (r[i + b]) {
4443	if (r[i] + (r[i + b] << b) <= 15) {
4444	r[i] += r[i + b] << b;
4445	r[i + b] = 0;
4446	} else if (r[i] - (r[i + b] << b) >= -15) {
4447	r[i] -= r[i + b] << b;
4448	for (k = i + b; k < 256; ++k) {
4449	if (!r[k]) {
4450	r[k] = 1;
4451	break;
4452	}
4453	r[k] = 0;
4454	}
4455	} else {
4456	break;
4457	}
4458	}
4459	}
4460	}
4461	}
4462	}
4463
4464	static const ge_precomp Bi[8] = {
4465	{
4466	{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4467	-11754271, -6079156, 2047605},
4468	{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4469	5043384, 19500929, -15469378},
4470	{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4471	11864899, -24514362, -4438546},
4472	},
4473	{
4474	{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4475	-14772189, 28944400, -1550024},
4476	{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4477	-11775962, 7689662, 11199574},
4478	{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4479	10017326, -17749093, -9920357},
4480	},
4481	{
4482	{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4483	14515107, -15438304, 10819380},
4484	{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4485	12483688, -12668491, 5581306},
4486	{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4487	13850243, -23678021, -15815942},
4488	},
4489	{
4490	{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4491	5230134, -23952439, -15175766},
4492	{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4493	16520125, 30598449, 7715701},
4494	{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4495	1370708, 29794553, -1409300},
4496	},
4497	{
4498	{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4499	-1361450, -13062696, 13821877},
4500	{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4501	-7212327, 18853322, -14220951},
4502	{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4503	-10431137, 2207753, -3209784},
4504	},
4505	{
4506	{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4507	-663000, -31111463, -16132436},
4508	{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4509	15725684, 171356, 6466918},
4510	{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4511	-14088058, -30714912, 16193877},
4512	},
4513	{
4514	{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4515	4729455, -18074513, 9256800},
4516	{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4517	9761698, -19827198, 630305},
4518	{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4519	-15960994, -2449256, -14291300},
4520	},
4521	{
4522	{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4523	15033784, 25105118, -7894876},
4524	{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4525	1573892, -2625887, 2198790, -15804619},
4526	{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4527	-16236442, -32461234, -12290683},
4528	},
4529	};
4530
4531	/*
4532	* r = a * A + b * B
4533	*
4534	* where a = a[0]+256*a[1]+...+256^31 a[31].
4535	* and b = b[0]+256*b[1]+...+256^31 b[31].
4536	* B is the Ed25519 base point (x,4/5) with x positive.
4537	*/
4538	static void ge_double_scalarmult_vartime(ge_p2 r, const uint8_t a,
4539	const ge_p3 A, const uint8_t b)
4540	{
4541	signed char aslide[256];
4542	signed char bslide[256];
4543	ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4544	ge_p1p1 t;
4545	ge_p3 u;
4546	ge_p3 A2;
4547	int i;
4548
4549	slide(aslide, a);
4550	slide(bslide, b);
4551
4552	ge_p3_to_cached(&Ai[0], A);
4553	ge_p3_dbl(&t, A);
4554	ge_p1p1_to_p3(&A2, &t);
4555	ge_add(&t, &A2, &Ai[0]);
4556	ge_p1p1_to_p3(&u, &t);
4557	ge_p3_to_cached(&Ai[1], &u);
4558	ge_add(&t, &A2, &Ai[1]);
4559	ge_p1p1_to_p3(&u, &t);
4560	ge_p3_to_cached(&Ai[2], &u);
4561	ge_add(&t, &A2, &Ai[2]);
4562	ge_p1p1_to_p3(&u, &t);
4563	ge_p3_to_cached(&Ai[3], &u);
4564	ge_add(&t, &A2, &Ai[3]);
4565	ge_p1p1_to_p3(&u, &t);
4566	ge_p3_to_cached(&Ai[4], &u);
4567	ge_add(&t, &A2, &Ai[4]);
4568	ge_p1p1_to_p3(&u, &t);
4569	ge_p3_to_cached(&Ai[5], &u);
4570	ge_add(&t, &A2, &Ai[5]);
4571	ge_p1p1_to_p3(&u, &t);
4572	ge_p3_to_cached(&Ai[6], &u);
4573	ge_add(&t, &A2, &Ai[6]);
4574	ge_p1p1_to_p3(&u, &t);
4575	ge_p3_to_cached(&Ai[7], &u);
4576
4577	ge_p2_0(r);
4578
4579	for (i = 255; i >= 0; --i) {
4580	if (aslide[i] \|\| bslide[i]) {
4581	break;
4582	}
4583	}
4584
4585	for (; i >= 0; --i) {
4586	ge_p2_dbl(&t, r);
4587
4588	if (aslide[i] > 0) {
4589	ge_p1p1_to_p3(&u, &t);
4590	ge_add(&t, &u, &Ai[aslide[i] / 2]);
4591	} else if (aslide[i] < 0) {
4592	ge_p1p1_to_p3(&u, &t);
4593	ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4594	}
4595
4596	if (bslide[i] > 0) {
4597	ge_p1p1_to_p3(&u, &t);
4598	ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4599	} else if (bslide[i] < 0) {
4600	ge_p1p1_to_p3(&u, &t);
4601	ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4602	}
4603
4604	ge_p1p1_to_p2(r, &t);
4605	}
4606	}
4607
4608	/*
4609	* The set of scalars is \Z/l
4610	* where l = 2^252 + 27742317777372353535851937790883648493.
4611	*
4612	* Input:
4613	* s[0]+256s[1]+...+256^63s[63] = s
4614	*
4615	* Output:
4616	* s[0]+256s[1]+...+256^31s[31] = s mod l
4617	* where l = 2^252 + 27742317777372353535851937790883648493.
4618	* Overwrites s in place.
4619	*/
4620	static void x25519_sc_reduce(uint8_t *s)
4621	{
4622	int64_t s0 = kBottom21Bits & load_3(s);
4623	int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
4624	int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
4625	int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
4626	int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
4627	int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
4628	int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
4629	int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
4630	int64_t s8 = kBottom21Bits & load_3(s + 21);
4631	int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
4632	int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4633	int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4634	int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4635	int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4636	int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4637	int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4638	int64_t s16 = kBottom21Bits & load_3(s + 42);
4639	int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4640	int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4641	int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4642	int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4643	int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4644	int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4645	int64_t s23 = (load_4(s + 60) >> 3);
4646	int64_t carry0;
4647	int64_t carry1;
4648	int64_t carry2;
4649	int64_t carry3;
4650	int64_t carry4;
4651	int64_t carry5;
4652	int64_t carry6;
4653	int64_t carry7;
4654	int64_t carry8;
4655	int64_t carry9;
4656	int64_t carry10;
4657	int64_t carry11;
4658	int64_t carry12;
4659	int64_t carry13;
4660	int64_t carry14;
4661	int64_t carry15;
4662	int64_t carry16;
4663
4664	s11 += s23 * 666643;
4665	s12 += s23 * 470296;
4666	s13 += s23 * 654183;
4667	s14 -= s23 * 997805;
4668	s15 += s23 * 136657;
4669	s16 -= s23 * 683901;
4670	s23 = 0;
4671
4672	s10 += s22 * 666643;
4673	s11 += s22 * 470296;
4674	s12 += s22 * 654183;
4675	s13 -= s22 * 997805;
4676	s14 += s22 * 136657;
4677	s15 -= s22 * 683901;
4678	s22 = 0;
4679
4680	s9 += s21 * 666643;
4681	s10 += s21 * 470296;
4682	s11 += s21 * 654183;
4683	s12 -= s21 * 997805;
4684	s13 += s21 * 136657;
4685	s14 -= s21 * 683901;
4686	s21 = 0;
4687
4688	s8 += s20 * 666643;
4689	s9 += s20 * 470296;
4690	s10 += s20 * 654183;
4691	s11 -= s20 * 997805;
4692	s12 += s20 * 136657;
4693	s13 -= s20 * 683901;
4694	s20 = 0;
4695
4696	s7 += s19 * 666643;
4697	s8 += s19 * 470296;
4698	s9 += s19 * 654183;
4699	s10 -= s19 * 997805;
4700	s11 += s19 * 136657;
4701	s12 -= s19 * 683901;
4702	s19 = 0;
4703
4704	s6 += s18 * 666643;
4705	s7 += s18 * 470296;
4706	s8 += s18 * 654183;
4707	s9 -= s18 * 997805;
4708	s10 += s18 * 136657;
4709	s11 -= s18 * 683901;
4710	s18 = 0;
4711
4712	carry6 = (s6 + (1 << 20)) >> 21;
4713	s7 += carry6;
4714	s6 -= carry6 * (1 << 21);
4715	carry8 = (s8 + (1 << 20)) >> 21;
4716	s9 += carry8;
4717	s8 -= carry8 * (1 << 21);
4718	carry10 = (s10 + (1 << 20)) >> 21;
4719	s11 += carry10;
4720	s10 -= carry10 * (1 << 21);
4721	carry12 = (s12 + (1 << 20)) >> 21;
4722	s13 += carry12;
4723	s12 -= carry12 * (1 << 21);
4724	carry14 = (s14 + (1 << 20)) >> 21;
4725	s15 += carry14;
4726	s14 -= carry14 * (1 << 21);
4727	carry16 = (s16 + (1 << 20)) >> 21;
4728	s17 += carry16;
4729	s16 -= carry16 * (1 << 21);
4730
4731	carry7 = (s7 + (1 << 20)) >> 21;
4732	s8 += carry7;
4733	s7 -= carry7 * (1 << 21);
4734	carry9 = (s9 + (1 << 20)) >> 21;
4735	s10 += carry9;
4736	s9 -= carry9 * (1 << 21);
4737	carry11 = (s11 + (1 << 20)) >> 21;
4738	s12 += carry11;
4739	s11 -= carry11 * (1 << 21);
4740	carry13 = (s13 + (1 << 20)) >> 21;
4741	s14 += carry13;
4742	s13 -= carry13 * (1 << 21);
4743	carry15 = (s15 + (1 << 20)) >> 21;
4744	s16 += carry15;
4745	s15 -= carry15 * (1 << 21);
4746
4747	s5 += s17 * 666643;
4748	s6 += s17 * 470296;
4749	s7 += s17 * 654183;
4750	s8 -= s17 * 997805;
4751	s9 += s17 * 136657;
4752	s10 -= s17 * 683901;
4753	s17 = 0;
4754
4755	s4 += s16 * 666643;
4756	s5 += s16 * 470296;
4757	s6 += s16 * 654183;
4758	s7 -= s16 * 997805;
4759	s8 += s16 * 136657;
4760	s9 -= s16 * 683901;
4761	s16 = 0;
4762
4763	s3 += s15 * 666643;
4764	s4 += s15 * 470296;
4765	s5 += s15 * 654183;
4766	s6 -= s15 * 997805;
4767	s7 += s15 * 136657;
4768	s8 -= s15 * 683901;
4769	s15 = 0;
4770
4771	s2 += s14 * 666643;
4772	s3 += s14 * 470296;
4773	s4 += s14 * 654183;
4774	s5 -= s14 * 997805;
4775	s6 += s14 * 136657;
4776	s7 -= s14 * 683901;
4777	s14 = 0;
4778
4779	s1 += s13 * 666643;
4780	s2 += s13 * 470296;
4781	s3 += s13 * 654183;
4782	s4 -= s13 * 997805;
4783	s5 += s13 * 136657;
4784	s6 -= s13 * 683901;
4785	s13 = 0;
4786
4787	s0 += s12 * 666643;
4788	s1 += s12 * 470296;
4789	s2 += s12 * 654183;
4790	s3 -= s12 * 997805;
4791	s4 += s12 * 136657;
4792	s5 -= s12 * 683901;
4793	s12 = 0;
4794
4795	carry0 = (s0 + (1 << 20)) >> 21;
4796	s1 += carry0;
4797	s0 -= carry0 * (1 << 21);
4798	carry2 = (s2 + (1 << 20)) >> 21;
4799	s3 += carry2;
4800	s2 -= carry2 * (1 << 21);
4801	carry4 = (s4 + (1 << 20)) >> 21;
4802	s5 += carry4;
4803	s4 -= carry4 * (1 << 21);
4804	carry6 = (s6 + (1 << 20)) >> 21;
4805	s7 += carry6;
4806	s6 -= carry6 * (1 << 21);
4807	carry8 = (s8 + (1 << 20)) >> 21;
4808	s9 += carry8;
4809	s8 -= carry8 * (1 << 21);
4810	carry10 = (s10 + (1 << 20)) >> 21;
4811	s11 += carry10;
4812	s10 -= carry10 * (1 << 21);
4813
4814	carry1 = (s1 + (1 << 20)) >> 21;
4815	s2 += carry1;
4816	s1 -= carry1 * (1 << 21);
4817	carry3 = (s3 + (1 << 20)) >> 21;
4818	s4 += carry3;
4819	s3 -= carry3 * (1 << 21);
4820	carry5 = (s5 + (1 << 20)) >> 21;
4821	s6 += carry5;
4822	s5 -= carry5 * (1 << 21);
4823	carry7 = (s7 + (1 << 20)) >> 21;
4824	s8 += carry7;
4825	s7 -= carry7 * (1 << 21);
4826	carry9 = (s9 + (1 << 20)) >> 21;
4827	s10 += carry9;
4828	s9 -= carry9 * (1 << 21);
4829	carry11 = (s11 + (1 << 20)) >> 21;
4830	s12 += carry11;
4831	s11 -= carry11 * (1 << 21);
4832
4833	s0 += s12 * 666643;
4834	s1 += s12 * 470296;
4835	s2 += s12 * 654183;
4836	s3 -= s12 * 997805;
4837	s4 += s12 * 136657;
4838	s5 -= s12 * 683901;
4839	s12 = 0;
4840
4841	carry0 = s0 >> 21;
4842	s1 += carry0;
4843	s0 -= carry0 * (1 << 21);
4844	carry1 = s1 >> 21;
4845	s2 += carry1;
4846	s1 -= carry1 * (1 << 21);
4847	carry2 = s2 >> 21;
4848	s3 += carry2;
4849	s2 -= carry2 * (1 << 21);
4850	carry3 = s3 >> 21;
4851	s4 += carry3;
4852	s3 -= carry3 * (1 << 21);
4853	carry4 = s4 >> 21;
4854	s5 += carry4;
4855	s4 -= carry4 * (1 << 21);
4856	carry5 = s5 >> 21;
4857	s6 += carry5;
4858	s5 -= carry5 * (1 << 21);
4859	carry6 = s6 >> 21;
4860	s7 += carry6;
4861	s6 -= carry6 * (1 << 21);
4862	carry7 = s7 >> 21;
4863	s8 += carry7;
4864	s7 -= carry7 * (1 << 21);
4865	carry8 = s8 >> 21;
4866	s9 += carry8;
4867	s8 -= carry8 * (1 << 21);
4868	carry9 = s9 >> 21;
4869	s10 += carry9;
4870	s9 -= carry9 * (1 << 21);
4871	carry10 = s10 >> 21;
4872	s11 += carry10;
4873	s10 -= carry10 * (1 << 21);
4874	carry11 = s11 >> 21;
4875	s12 += carry11;
4876	s11 -= carry11 * (1 << 21);
4877
4878	s0 += s12 * 666643;
4879	s1 += s12 * 470296;
4880	s2 += s12 * 654183;
4881	s3 -= s12 * 997805;
4882	s4 += s12 * 136657;
4883	s5 -= s12 * 683901;
4884	s12 = 0;
4885
4886	carry0 = s0 >> 21;
4887	s1 += carry0;
4888	s0 -= carry0 * (1 << 21);
4889	carry1 = s1 >> 21;
4890	s2 += carry1;
4891	s1 -= carry1 * (1 << 21);
4892	carry2 = s2 >> 21;
4893	s3 += carry2;
4894	s2 -= carry2 * (1 << 21);
4895	carry3 = s3 >> 21;
4896	s4 += carry3;
4897	s3 -= carry3 * (1 << 21);
4898	carry4 = s4 >> 21;
4899	s5 += carry4;
4900	s4 -= carry4 * (1 << 21);
4901	carry5 = s5 >> 21;
4902	s6 += carry5;
4903	s5 -= carry5 * (1 << 21);
4904	carry6 = s6 >> 21;
4905	s7 += carry6;
4906	s6 -= carry6 * (1 << 21);
4907	carry7 = s7 >> 21;
4908	s8 += carry7;
4909	s7 -= carry7 * (1 << 21);
4910	carry8 = s8 >> 21;
4911	s9 += carry8;
4912	s8 -= carry8 * (1 << 21);
4913	carry9 = s9 >> 21;
4914	s10 += carry9;
4915	s9 -= carry9 * (1 << 21);
4916	carry10 = s10 >> 21;
4917	s11 += carry10;
4918	s10 -= carry10 * (1 << 21);
4919
4920	s[ 0] = (uint8_t) (s0 >> 0);
4921	s[ 1] = (uint8_t) (s0 >> 8);
4922	s[ 2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
4923	s[ 3] = (uint8_t) (s1 >> 3);
4924	s[ 4] = (uint8_t) (s1 >> 11);
4925	s[ 5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
4926	s[ 6] = (uint8_t) (s2 >> 6);
4927	s[ 7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
4928	s[ 8] = (uint8_t) (s3 >> 1);
4929	s[ 9] = (uint8_t) (s3 >> 9);
4930	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
4931	s[11] = (uint8_t) (s4 >> 4);
4932	s[12] = (uint8_t) (s4 >> 12);
4933	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
4934	s[14] = (uint8_t) (s5 >> 7);
4935	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
4936	s[16] = (uint8_t) (s6 >> 2);
4937	s[17] = (uint8_t) (s6 >> 10);
4938	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
4939	s[19] = (uint8_t) (s7 >> 5);
4940	s[20] = (uint8_t) (s7 >> 13);
4941	s[21] = (uint8_t) (s8 >> 0);
4942	s[22] = (uint8_t) (s8 >> 8);
4943	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
4944	s[24] = (uint8_t) (s9 >> 3);
4945	s[25] = (uint8_t) (s9 >> 11);
4946	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
4947	s[27] = (uint8_t) (s10 >> 6);
4948	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
4949	s[29] = (uint8_t) (s11 >> 1);
4950	s[30] = (uint8_t) (s11 >> 9);
4951	s[31] = (uint8_t) (s11 >> 17);
4952	}
4953
4954	/*
4955	* Input:
4956	* a[0]+256a[1]+...+256^31a[31] = a
4957	* b[0]+256b[1]+...+256^31b[31] = b
4958	* c[0]+256c[1]+...+256^31c[31] = c
4959	*
4960	* Output:
4961	* s[0]+256s[1]+...+256^31s[31] = (ab+c) mod l
4962	* where l = 2^252 + 27742317777372353535851937790883648493.
4963	*/
4964	static void sc_muladd(uint8_t s, const uint8_t a, const uint8_t *b,
4965	const uint8_t *c)
4966	{
4967	int64_t a0 = kBottom21Bits & load_3(a);
4968	int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
4969	int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
4970	int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
4971	int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
4972	int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
4973	int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
4974	int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
4975	int64_t a8 = kBottom21Bits & load_3(a + 21);
4976	int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
4977	int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
4978	int64_t a11 = (load_4(a + 28) >> 7);
4979	int64_t b0 = kBottom21Bits & load_3(b);
4980	int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
4981	int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
4982	int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
4983	int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
4984	int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
4985	int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
4986	int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
4987	int64_t b8 = kBottom21Bits & load_3(b + 21);
4988	int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
4989	int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
4990	int64_t b11 = (load_4(b + 28) >> 7);
4991	int64_t c0 = kBottom21Bits & load_3(c);
4992	int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
4993	int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
4994	int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
4995	int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
4996	int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
4997	int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
4998	int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
4999	int64_t c8 = kBottom21Bits & load_3(c + 21);
5000	int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
5001	int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
5002	int64_t c11 = (load_4(c + 28) >> 7);
5003	int64_t s0;
5004	int64_t s1;
5005	int64_t s2;
5006	int64_t s3;
5007	int64_t s4;
5008	int64_t s5;
5009	int64_t s6;
5010	int64_t s7;
5011	int64_t s8;
5012	int64_t s9;
5013	int64_t s10;
5014	int64_t s11;
5015	int64_t s12;
5016	int64_t s13;
5017	int64_t s14;
5018	int64_t s15;
5019	int64_t s16;
5020	int64_t s17;
5021	int64_t s18;
5022	int64_t s19;
5023	int64_t s20;
5024	int64_t s21;
5025	int64_t s22;
5026	int64_t s23;
5027	int64_t carry0;
5028	int64_t carry1;
5029	int64_t carry2;
5030	int64_t carry3;
5031	int64_t carry4;
5032	int64_t carry5;
5033	int64_t carry6;
5034	int64_t carry7;
5035	int64_t carry8;
5036	int64_t carry9;
5037	int64_t carry10;
5038	int64_t carry11;
5039	int64_t carry12;
5040	int64_t carry13;
5041	int64_t carry14;
5042	int64_t carry15;
5043	int64_t carry16;
5044	int64_t carry17;
5045	int64_t carry18;
5046	int64_t carry19;
5047	int64_t carry20;
5048	int64_t carry21;
5049	int64_t carry22;
5050
5051	s0 = c0 + a0 * b0;
5052	s1 = c1 + a0 * b1 + a1 * b0;
5053	s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
5054	s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
5055	s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
5056	s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
5057	s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
5058	s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
5059	s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
5060	s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
5061	s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
5062	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;
5063	s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
5064	s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
5065	s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
5066	s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
5067	s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
5068	s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
5069	s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
5070	s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
5071	s20 = a9 * b11 + a10 * b10 + a11 * b9;
5072	s21 = a10 * b11 + a11 * b10;
5073	s22 = a11 * b11;
5074	s23 = 0;
5075
5076	carry0 = (s0 + (1 << 20)) >> 21;
5077	s1 += carry0;
5078	s0 -= carry0 * (1 << 21);
5079	carry2 = (s2 + (1 << 20)) >> 21;
5080	s3 += carry2;
5081	s2 -= carry2 * (1 << 21);
5082	carry4 = (s4 + (1 << 20)) >> 21;
5083	s5 += carry4;
5084	s4 -= carry4 * (1 << 21);
5085	carry6 = (s6 + (1 << 20)) >> 21;
5086	s7 += carry6;
5087	s6 -= carry6 * (1 << 21);
5088	carry8 = (s8 + (1 << 20)) >> 21;
5089	s9 += carry8;
5090	s8 -= carry8 * (1 << 21);
5091	carry10 = (s10 + (1 << 20)) >> 21;
5092	s11 += carry10;
5093	s10 -= carry10 * (1 << 21);
5094	carry12 = (s12 + (1 << 20)) >> 21;
5095	s13 += carry12;
5096	s12 -= carry12 * (1 << 21);
5097	carry14 = (s14 + (1 << 20)) >> 21;
5098	s15 += carry14;
5099	s14 -= carry14 * (1 << 21);
5100	carry16 = (s16 + (1 << 20)) >> 21;
5101	s17 += carry16;
5102	s16 -= carry16 * (1 << 21);
5103	carry18 = (s18 + (1 << 20)) >> 21;
5104	s19 += carry18;
5105	s18 -= carry18 * (1 << 21);
5106	carry20 = (s20 + (1 << 20)) >> 21;
5107	s21 += carry20;
5108	s20 -= carry20 * (1 << 21);
5109	carry22 = (s22 + (1 << 20)) >> 21;
5110	s23 += carry22;
5111	s22 -= carry22 * (1 << 21);
5112
5113	carry1 = (s1 + (1 << 20)) >> 21;
5114	s2 += carry1;
5115	s1 -= carry1 * (1 << 21);
5116	carry3 = (s3 + (1 << 20)) >> 21;
5117	s4 += carry3;
5118	s3 -= carry3 * (1 << 21);
5119	carry5 = (s5 + (1 << 20)) >> 21;
5120	s6 += carry5;
5121	s5 -= carry5 * (1 << 21);
5122	carry7 = (s7 + (1 << 20)) >> 21;
5123	s8 += carry7;
5124	s7 -= carry7 * (1 << 21);
5125	carry9 = (s9 + (1 << 20)) >> 21;
5126	s10 += carry9;
5127	s9 -= carry9 * (1 << 21);
5128	carry11 = (s11 + (1 << 20)) >> 21;
5129	s12 += carry11;
5130	s11 -= carry11 * (1 << 21);
5131	carry13 = (s13 + (1 << 20)) >> 21;
5132	s14 += carry13;
5133	s13 -= carry13 * (1 << 21);
5134	carry15 = (s15 + (1 << 20)) >> 21;
5135	s16 += carry15;
5136	s15 -= carry15 * (1 << 21);
5137	carry17 = (s17 + (1 << 20)) >> 21;
5138	s18 += carry17;
5139	s17 -= carry17 * (1 << 21);
5140	carry19 = (s19 + (1 << 20)) >> 21;
5141	s20 += carry19;
5142	s19 -= carry19 * (1 << 21);
5143	carry21 = (s21 + (1 << 20)) >> 21;
5144	s22 += carry21;
5145	s21 -= carry21 * (1 << 21);
5146
5147	s11 += s23 * 666643;
5148	s12 += s23 * 470296;
5149	s13 += s23 * 654183;
5150	s14 -= s23 * 997805;
5151	s15 += s23 * 136657;
5152	s16 -= s23 * 683901;
5153	s23 = 0;
5154
5155	s10 += s22 * 666643;
5156	s11 += s22 * 470296;
5157	s12 += s22 * 654183;
5158	s13 -= s22 * 997805;
5159	s14 += s22 * 136657;
5160	s15 -= s22 * 683901;
5161	s22 = 0;
5162
5163	s9 += s21 * 666643;
5164	s10 += s21 * 470296;
5165	s11 += s21 * 654183;
5166	s12 -= s21 * 997805;
5167	s13 += s21 * 136657;
5168	s14 -= s21 * 683901;
5169	s21 = 0;
5170
5171	s8 += s20 * 666643;
5172	s9 += s20 * 470296;
5173	s10 += s20 * 654183;
5174	s11 -= s20 * 997805;
5175	s12 += s20 * 136657;
5176	s13 -= s20 * 683901;
5177	s20 = 0;
5178
5179	s7 += s19 * 666643;
5180	s8 += s19 * 470296;
5181	s9 += s19 * 654183;
5182	s10 -= s19 * 997805;
5183	s11 += s19 * 136657;
5184	s12 -= s19 * 683901;
5185	s19 = 0;
5186
5187	s6 += s18 * 666643;
5188	s7 += s18 * 470296;
5189	s8 += s18 * 654183;
5190	s9 -= s18 * 997805;
5191	s10 += s18 * 136657;
5192	s11 -= s18 * 683901;
5193	s18 = 0;
5194
5195	carry6 = (s6 + (1 << 20)) >> 21;
5196	s7 += carry6;
5197	s6 -= carry6 * (1 << 21);
5198	carry8 = (s8 + (1 << 20)) >> 21;
5199	s9 += carry8;
5200	s8 -= carry8 * (1 << 21);
5201	carry10 = (s10 + (1 << 20)) >> 21;
5202	s11 += carry10;
5203	s10 -= carry10 * (1 << 21);
5204	carry12 = (s12 + (1 << 20)) >> 21;
5205	s13 += carry12;
5206	s12 -= carry12 * (1 << 21);
5207	carry14 = (s14 + (1 << 20)) >> 21;
5208	s15 += carry14;
5209	s14 -= carry14 * (1 << 21);
5210	carry16 = (s16 + (1 << 20)) >> 21;
5211	s17 += carry16;
5212	s16 -= carry16 * (1 << 21);
5213
5214	carry7 = (s7 + (1 << 20)) >> 21;
5215	s8 += carry7;
5216	s7 -= carry7 * (1 << 21);
5217	carry9 = (s9 + (1 << 20)) >> 21;
5218	s10 += carry9;
5219	s9 -= carry9 * (1 << 21);
5220	carry11 = (s11 + (1 << 20)) >> 21;
5221	s12 += carry11;
5222	s11 -= carry11 * (1 << 21);
5223	carry13 = (s13 + (1 << 20)) >> 21;
5224	s14 += carry13;
5225	s13 -= carry13 * (1 << 21);
5226	carry15 = (s15 + (1 << 20)) >> 21;
5227	s16 += carry15;
5228	s15 -= carry15 * (1 << 21);
5229
5230	s5 += s17 * 666643;
5231	s6 += s17 * 470296;
5232	s7 += s17 * 654183;
5233	s8 -= s17 * 997805;
5234	s9 += s17 * 136657;
5235	s10 -= s17 * 683901;
5236	s17 = 0;
5237
5238	s4 += s16 * 666643;
5239	s5 += s16 * 470296;
5240	s6 += s16 * 654183;
5241	s7 -= s16 * 997805;
5242	s8 += s16 * 136657;
5243	s9 -= s16 * 683901;
5244	s16 = 0;
5245
5246	s3 += s15 * 666643;
5247	s4 += s15 * 470296;
5248	s5 += s15 * 654183;
5249	s6 -= s15 * 997805;
5250	s7 += s15 * 136657;
5251	s8 -= s15 * 683901;
5252	s15 = 0;
5253
5254	s2 += s14 * 666643;
5255	s3 += s14 * 470296;
5256	s4 += s14 * 654183;
5257	s5 -= s14 * 997805;
5258	s6 += s14 * 136657;
5259	s7 -= s14 * 683901;
5260	s14 = 0;
5261
5262	s1 += s13 * 666643;
5263	s2 += s13 * 470296;
5264	s3 += s13 * 654183;
5265	s4 -= s13 * 997805;
5266	s5 += s13 * 136657;
5267	s6 -= s13 * 683901;
5268	s13 = 0;
5269
5270	s0 += s12 * 666643;
5271	s1 += s12 * 470296;
5272	s2 += s12 * 654183;
5273	s3 -= s12 * 997805;
5274	s4 += s12 * 136657;
5275	s5 -= s12 * 683901;
5276	s12 = 0;
5277
5278	carry0 = (s0 + (1 << 20)) >> 21;
5279	s1 += carry0;
5280	s0 -= carry0 * (1 << 21);
5281	carry2 = (s2 + (1 << 20)) >> 21;
5282	s3 += carry2;
5283	s2 -= carry2 * (1 << 21);
5284	carry4 = (s4 + (1 << 20)) >> 21;
5285	s5 += carry4;
5286	s4 -= carry4 * (1 << 21);
5287	carry6 = (s6 + (1 << 20)) >> 21;
5288	s7 += carry6;
5289	s6 -= carry6 * (1 << 21);
5290	carry8 = (s8 + (1 << 20)) >> 21;
5291	s9 += carry8;
5292	s8 -= carry8 * (1 << 21);
5293	carry10 = (s10 + (1 << 20)) >> 21;
5294	s11 += carry10;
5295	s10 -= carry10 * (1 << 21);
5296
5297	carry1 = (s1 + (1 << 20)) >> 21;
5298	s2 += carry1;
5299	s1 -= carry1 * (1 << 21);
5300	carry3 = (s3 + (1 << 20)) >> 21;
5301	s4 += carry3;
5302	s3 -= carry3 * (1 << 21);
5303	carry5 = (s5 + (1 << 20)) >> 21;
5304	s6 += carry5;
5305	s5 -= carry5 * (1 << 21);
5306	carry7 = (s7 + (1 << 20)) >> 21;
5307	s8 += carry7;
5308	s7 -= carry7 * (1 << 21);
5309	carry9 = (s9 + (1 << 20)) >> 21;
5310	s10 += carry9;
5311	s9 -= carry9 * (1 << 21);
5312	carry11 = (s11 + (1 << 20)) >> 21;
5313	s12 += carry11;
5314	s11 -= carry11 * (1 << 21);
5315
5316	s0 += s12 * 666643;
5317	s1 += s12 * 470296;
5318	s2 += s12 * 654183;
5319	s3 -= s12 * 997805;
5320	s4 += s12 * 136657;
5321	s5 -= s12 * 683901;
5322	s12 = 0;
5323
5324	carry0 = s0 >> 21;
5325	s1 += carry0;
5326	s0 -= carry0 * (1 << 21);
5327	carry1 = s1 >> 21;
5328	s2 += carry1;
5329	s1 -= carry1 * (1 << 21);
5330	carry2 = s2 >> 21;
5331	s3 += carry2;
5332	s2 -= carry2 * (1 << 21);
5333	carry3 = s3 >> 21;
5334	s4 += carry3;
5335	s3 -= carry3 * (1 << 21);
5336	carry4 = s4 >> 21;
5337	s5 += carry4;
5338	s4 -= carry4 * (1 << 21);
5339	carry5 = s5 >> 21;
5340	s6 += carry5;
5341	s5 -= carry5 * (1 << 21);
5342	carry6 = s6 >> 21;
5343	s7 += carry6;
5344	s6 -= carry6 * (1 << 21);
5345	carry7 = s7 >> 21;
5346	s8 += carry7;
5347	s7 -= carry7 * (1 << 21);
5348	carry8 = s8 >> 21;
5349	s9 += carry8;
5350	s8 -= carry8 * (1 << 21);
5351	carry9 = s9 >> 21;
5352	s10 += carry9;
5353	s9 -= carry9 * (1 << 21);
5354	carry10 = s10 >> 21;
5355	s11 += carry10;
5356	s10 -= carry10 * (1 << 21);
5357	carry11 = s11 >> 21;
5358	s12 += carry11;
5359	s11 -= carry11 * (1 << 21);
5360
5361	s0 += s12 * 666643;
5362	s1 += s12 * 470296;
5363	s2 += s12 * 654183;
5364	s3 -= s12 * 997805;
5365	s4 += s12 * 136657;
5366	s5 -= s12 * 683901;
5367	s12 = 0;
5368
5369	carry0 = s0 >> 21;
5370	s1 += carry0;
5371	s0 -= carry0 * (1 << 21);
5372	carry1 = s1 >> 21;
5373	s2 += carry1;
5374	s1 -= carry1 * (1 << 21);
5375	carry2 = s2 >> 21;
5376	s3 += carry2;
5377	s2 -= carry2 * (1 << 21);
5378	carry3 = s3 >> 21;
5379	s4 += carry3;
5380	s3 -= carry3 * (1 << 21);
5381	carry4 = s4 >> 21;
5382	s5 += carry4;
5383	s4 -= carry4 * (1 << 21);
5384	carry5 = s5 >> 21;
5385	s6 += carry5;
5386	s5 -= carry5 * (1 << 21);
5387	carry6 = s6 >> 21;
5388	s7 += carry6;
5389	s6 -= carry6 * (1 << 21);
5390	carry7 = s7 >> 21;
5391	s8 += carry7;
5392	s7 -= carry7 * (1 << 21);
5393	carry8 = s8 >> 21;
5394	s9 += carry8;
5395	s8 -= carry8 * (1 << 21);
5396	carry9 = s9 >> 21;
5397	s10 += carry9;
5398	s9 -= carry9 * (1 << 21);
5399	carry10 = s10 >> 21;
5400	s11 += carry10;
5401	s10 -= carry10 * (1 << 21);
5402
5403	s[ 0] = (uint8_t) (s0 >> 0);
5404	s[ 1] = (uint8_t) (s0 >> 8);
5405	s[ 2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5406	s[ 3] = (uint8_t) (s1 >> 3);
5407	s[ 4] = (uint8_t) (s1 >> 11);
5408	s[ 5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5409	s[ 6] = (uint8_t) (s2 >> 6);
5410	s[ 7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5411	s[ 8] = (uint8_t) (s3 >> 1);
5412	s[ 9] = (uint8_t) (s3 >> 9);
5413	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5414	s[11] = (uint8_t) (s4 >> 4);
5415	s[12] = (uint8_t) (s4 >> 12);
5416	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5417	s[14] = (uint8_t) (s5 >> 7);
5418	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5419	s[16] = (uint8_t) (s6 >> 2);
5420	s[17] = (uint8_t) (s6 >> 10);
5421	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5422	s[19] = (uint8_t) (s7 >> 5);
5423	s[20] = (uint8_t) (s7 >> 13);
5424	s[21] = (uint8_t) (s8 >> 0);
5425	s[22] = (uint8_t) (s8 >> 8);
5426	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5427	s[24] = (uint8_t) (s9 >> 3);
5428	s[25] = (uint8_t) (s9 >> 11);
5429	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5430	s[27] = (uint8_t) (s10 >> 6);
5431	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5432	s[29] = (uint8_t) (s11 >> 1);
5433	s[30] = (uint8_t) (s11 >> 9);
5434	s[31] = (uint8_t) (s11 >> 17);
5435	}
5436
5437	int
5438	ossl_ed25519_sign(uint8_t out_sig, const uint8_t message, size_t message_len,
5439	const uint8_t public_key[32], const uint8_t private_key[32],
5440	OSSL_LIB_CTX libctx, const char propq)
5441	{
5442	uint8_t az[SHA512_DIGEST_LENGTH];
5443	uint8_t nonce[SHA512_DIGEST_LENGTH];
5444	ge_p3 R;
5445	uint8_t hram[SHA512_DIGEST_LENGTH];
5446	EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5447	EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
5448	unsigned int sz;
5449	int res = 0;
5450
5451	if (sha512 == NULL \|\| hash_ctx == NULL)
5452	goto err;
5453
5454	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5455	\|\| !EVP_DigestUpdate(hash_ctx, private_key, 32)
5456	\|\| !EVP_DigestFinal_ex(hash_ctx, az, &sz))
5457	goto err;
5458
5459	az[0] &= 248;
5460	az[31] &= 63;
5461	az[31] \|= 64;
5462
5463	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5464	\|\| !EVP_DigestUpdate(hash_ctx, az + 32, 32)
5465	\|\| !EVP_DigestUpdate(hash_ctx, message, message_len)
5466	\|\| !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
5467	goto err;
5468
5469	x25519_sc_reduce(nonce);
5470	ge_scalarmult_base(&R, nonce);
5471	ge_p3_tobytes(out_sig, &R);
5472
5473	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5474	\|\| !EVP_DigestUpdate(hash_ctx, out_sig, 32)
5475	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5476	\|\| !EVP_DigestUpdate(hash_ctx, message, message_len)
5477	\|\| !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
5478	goto err;
5479
5480	x25519_sc_reduce(hram);
5481	sc_muladd(out_sig + 32, hram, az, nonce);
5482
5483	res = 1;
5484	err:
5485	OPENSSL_cleanse(nonce, sizeof(nonce));
5486	OPENSSL_cleanse(az, sizeof(az));
5487	EVP_MD_free(sha512);
5488	EVP_MD_CTX_free(hash_ctx);
5489	return res;
5490	}
5491
5492	static const char allzeroes[15];
5493
5494	int
5495	ossl_ed25519_verify(const uint8_t *message, size_t message_len,
5496	const uint8_t signature[64], const uint8_t public_key[32],
5497	OSSL_LIB_CTX libctx, const char propq)
5498	{
5499	int i;
5500	ge_p3 A;
5501	const uint8_t r, s;
5502	EVP_MD *sha512;
5503	EVP_MD_CTX *hash_ctx = NULL;
5504	unsigned int sz;
5505	int res = 0;
5506	ge_p2 R;
5507	uint8_t rcheck[32];
5508	uint8_t h[SHA512_DIGEST_LENGTH];
5509	/* 27742317777372353535851937790883648493 in little endian format */
5510	const uint8_t l_low[16] = {
5511	0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5512	0xDE, 0xF9, 0xDE, 0x14
5513	};
5514
5515	r = signature;
5516	s = signature + 32;
5517
5518	/*
5519	* Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5520	*
5521	* If not the signature is publicly invalid. Since it's public we can do the
5522	* check in variable time.
5523	*
5524	* First check the most significant byte
5525	*/
5526	if (s[31] > 0x10)
5527	return 0;
5528	if (s[31] == 0x10) {
5529	/*
5530	* Most significant byte indicates a value close to 2^252 so check the
5531	* rest
5532	*/
5533	if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5534	return 0;
5535	for (i = 15; i >= 0; i--) {
5536	if (s[i] < l_low[i])
5537	break;
5538	if (s[i] > l_low[i])
5539	return 0;
5540	}
5541	if (i < 0)
5542	return 0;
5543	}
5544
5545	if (ge_frombytes_vartime(&A, public_key) != 0) {
5546	return 0;
5547	}
5548
5549	fe_neg(A.X, A.X);
5550	fe_neg(A.T, A.T);
5551
5552	sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5553	if (sha512 == NULL)
5554	return 0;
5555	hash_ctx = EVP_MD_CTX_new();
5556	if (hash_ctx == NULL)
5557	goto err;
5558
5559	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5560	\|\| !EVP_DigestUpdate(hash_ctx, r, 32)
5561	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5562	\|\| !EVP_DigestUpdate(hash_ctx, message, message_len)
5563	\|\| !EVP_DigestFinal_ex(hash_ctx, h, &sz))
5564	goto err;
5565
5566	x25519_sc_reduce(h);
5567
5568	ge_double_scalarmult_vartime(&R, h, &A, s);
5569
5570	ge_tobytes(rcheck, &R);
5571
5572	res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5573	err:
5574	EVP_MD_free(sha512);
5575	EVP_MD_CTX_free(hash_ctx);
5576	return res;
5577	}
5578
5579	int
5580	ossl_ed25519_public_from_private(OSSL_LIB_CTX *ctx, uint8_t out_public_key[32],
5581	const uint8_t private_key[32],
5582	const char *propq)
5583	{
5584	uint8_t az[SHA512_DIGEST_LENGTH];
5585	ge_p3 A;
5586	int r;
5587	EVP_MD *sha512 = NULL;
5588
5589	sha512 = EVP_MD_fetch(ctx, SN_sha512, propq);
5590	if (sha512 == NULL)
5591	return 0;
5592	r = EVP_Digest(private_key, 32, az, NULL, sha512, NULL);
5593	EVP_MD_free(sha512);
5594	if (!r) {
5595	OPENSSL_cleanse(az, sizeof(az));
5596	return 0;
5597	}
5598
5599	az[0] &= 248;
5600	az[31] &= 63;
5601	az[31] \|= 64;
5602
5603	ge_scalarmult_base(&A, az);
5604	ge_p3_tobytes(out_public_key, &A);
5605
5606	OPENSSL_cleanse(az, sizeof(az));
5607	return 1;
5608	}
5609
5610	int
5611	ossl_x25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5612	const uint8_t peer_public_value[32])
5613	{
5614	static const uint8_t kZeros[32] = {0};
5615	x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5616	/* The all-zero output results when the input is a point of small order. */
5617	return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5618	}
5619
5620	void
5621	ossl_x25519_public_from_private(uint8_t out_public_value[32],
5622	const uint8_t private_key[32])
5623	{
5624	uint8_t e[32];
5625	ge_p3 A;
5626	fe zplusy, zminusy, zminusy_inv;
5627
5628	memcpy(e, private_key, 32);
5629	e[0] &= 248;
5630	e[31] &= 127;
5631	e[31] \|= 64;
5632
5633	ge_scalarmult_base(&A, e);
5634
5635	/*
5636	* We only need the u-coordinate of the curve25519 point.
5637	* The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5638	* u=(Z+Y)/(Z-Y).
5639	*/
5640	fe_add(zplusy, A.Z, A.Y);
5641	fe_sub(zminusy, A.Z, A.Y);
5642	fe_invert(zminusy_inv, zminusy);
5643	fe_mul(zplusy, zplusy, zminusy_inv);
5644	fe_tobytes(out_public_value, zplusy);
5645
5646	OPENSSL_cleanse(e, sizeof(e));
5647	}

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source: vbox/trunk/src/libs/openssl-3.1.3/crypto/ec/curve25519.c@ 101665

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