/src/openssl30/crypto/ec/curve25519.c

Line	Count	Source
1		/*
2		* Copyright 2016-2021 The OpenSSL Project Authors. All Rights Reserved.
3		*
4		* Licensed under the Apache License 2.0 (the "License"). You may not use
5		* this file except in compliance with the License. You can obtain a copy
6		* in the file LICENSE in the source distribution or at
7		* https://www.openssl.org/source/license.html
8		*/
9
10		/*
11		* ECDSA low level APIs are deprecated for public use, but still ok for
12		* internal use.
13		*/
14		#include "internal/deprecated.h"
15
16		#include <string.h>
17		#include "crypto/ecx.h"
18		#include "ec_local.h"
19		#include <openssl/evp.h>
20		#include <openssl/sha.h>
21
22		#include "internal/numbers.h"
23
24		#if defined(X25519_ASM) && (defined(__x86_64) \|\| defined(__x86_64__) \|\| defined(_M_AMD64) \|\| defined(_M_X64))
25
26		#define BASE_2_64_IMPLEMENTED
27
28		typedef uint64_t fe64[4];
29
30		int x25519_fe64_eligible(void);
31
32		/*
33		* Following subroutines perform corresponding operations modulo
34		* 2^256-38, i.e. double the curve modulus. However, inputs and
35		* outputs are permitted to be partially reduced, i.e. to remain
36		* in [0..2^256) range. It's all tied up in final fe64_tobytes
37		* that performs full reduction modulo 2^255-19.
38		*
39		* There are no reference C implementations for these.
40		*/
41		void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
42		void x25519_fe64_sqr(fe64 h, const fe64 f);
43		void x25519_fe64_mul121666(fe64 h, fe64 f);
44		void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
45		void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
46		void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
47	41.4M	#define fe64_mul x25519_fe64_mul
48	41.0M	#define fe64_sqr x25519_fe64_sqr
49	8.21M	#define fe64_mul121666 x25519_fe64_mul121666
50	32.8M	#define fe64_add x25519_fe64_add
51	32.8M	#define fe64_sub x25519_fe64_sub
52	32.2k	#define fe64_tobytes x25519_fe64_tobytes
53
54		static uint64_t load_8(const uint8_t *in)
55	128k	{
56	128k	uint64_t result;
57
58	128k	result = in[0];
59	128k	result \|= ((uint64_t)in[1]) << 8;
60	128k	result \|= ((uint64_t)in[2]) << 16;
61	128k	result \|= ((uint64_t)in[3]) << 24;
62	128k	result \|= ((uint64_t)in[4]) << 32;
63	128k	result \|= ((uint64_t)in[5]) << 40;
64	128k	result \|= ((uint64_t)in[6]) << 48;
65	128k	result \|= ((uint64_t)in[7]) << 56;
66
67	128k	return result;
68	128k	}
69
70		static void fe64_frombytes(fe64 h, const uint8_t *s)
71	32.2k	{
72	32.2k	h[0] = load_8(s);
73	32.2k	h[1] = load_8(s + 8);
74	32.2k	h[2] = load_8(s + 16);
75	32.2k	h[3] = load_8(s + 24) & 0x7fffffffffffffff;
76	32.2k	}
77
78		static void fe64_0(fe64 h)
79	32.2k	{
80	32.2k	h[0] = 0;
81	32.2k	h[1] = 0;
82	32.2k	h[2] = 0;
83	32.2k	h[3] = 0;
84	32.2k	}
85
86		static void fe64_1(fe64 h)
87	64.4k	{
88	64.4k	h[0] = 1;
89	64.4k	h[1] = 0;
90	64.4k	h[2] = 0;
91	64.4k	h[3] = 0;
92	64.4k	}
93
94		static void fe64_copy(fe64 h, const fe64 f)
95	32.2k	{
96	32.2k	h[0] = f[0];
97	32.2k	h[1] = f[1];
98	32.2k	h[2] = f[2];
99	32.2k	h[3] = f[3];
100	32.2k	}
101
102		static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
103	16.4M	{
104	16.4M	int i;
105	16.4M	uint64_t mask = 0 - (uint64_t)b;
106
107	82.1M	for (i = 0; i < 4; i++) {
108	65.7M	uint64_t x = f[i] ^ g[i];
109	65.7M	x &= mask;
110	65.7M	f[i] ^= x;
111	65.7M	g[i] ^= x;
112	65.7M	}
113	16.4M	}
114
115		static void fe64_invert(fe64 out, const fe64 z)
116	32.2k	{
117	32.2k	fe64 t0;
118	32.2k	fe64 t1;
119	32.2k	fe64 t2;
120	32.2k	fe64 t3;
121	32.2k	int i;
122
123		/*
124		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
125		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
126		*/
127
128		/* t0 = z ** 2 */
129	32.2k	fe64_sqr(t0, z);
130
131		/* t1 = t0 (2 2) = z ** 8 */
132	32.2k	fe64_sqr(t1, t0);
133	32.2k	fe64_sqr(t1, t1);
134
135		/* t1 = z * t1 = z ** 9 */
136	32.2k	fe64_mul(t1, z, t1);
137		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
138	32.2k	fe64_mul(t0, t0, t1);
139
140		/* t2 = t0 2 = z 22 */
141	32.2k	fe64_sqr(t2, t0);
142
143		/* t1 = t1 * t2 = z (2 5 - 1) */
144	32.2k	fe64_mul(t1, t1, t2);
145
146		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
147	32.2k	fe64_sqr(t2, t1);
148	161k	for (i = 1; i < 5; ++i)
149	128k	fe64_sqr(t2, t2);
150
151		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
152	32.2k	fe64_mul(t1, t2, t1);
153
154		/* Continuing similarly... */
155
156		/* t2 = z (2 20 - 1) */
157	32.2k	fe64_sqr(t2, t1);
158	322k	for (i = 1; i < 10; ++i)
159	290k	fe64_sqr(t2, t2);
160
161	32.2k	fe64_mul(t2, t2, t1);
162
163		/* t2 = z (2 40 - 1) */
164	32.2k	fe64_sqr(t3, t2);
165	644k	for (i = 1; i < 20; ++i)
166	612k	fe64_sqr(t3, t3);
167
168	32.2k	fe64_mul(t2, t3, t2);
169
170		/* t2 = z (2 10) * (2 ** 40 - 1) */
171	354k	for (i = 0; i < 10; ++i)
172	322k	fe64_sqr(t2, t2);
173
174		/* t1 = z (2 50 - 1) */
175	32.2k	fe64_mul(t1, t2, t1);
176
177		/* t2 = z (2 100 - 1) */
178	32.2k	fe64_sqr(t2, t1);
179	1.61M	for (i = 1; i < 50; ++i)
180	1.57M	fe64_sqr(t2, t2);
181
182	32.2k	fe64_mul(t2, t2, t1);
183
184		/* t2 = z (2 200 - 1) */
185	32.2k	fe64_sqr(t3, t2);
186	3.22M	for (i = 1; i < 100; ++i)
187	3.19M	fe64_sqr(t3, t3);
188
189	32.2k	fe64_mul(t2, t3, t2);
190
191		/* t2 = z ((2 50) * (2 ** 200 - 1) */
192	1.64M	for (i = 0; i < 50; ++i)
193	1.61M	fe64_sqr(t2, t2);
194
195		/* t1 = z (2 250 - 1) */
196	32.2k	fe64_mul(t1, t2, t1);
197
198		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
199	193k	for (i = 0; i < 5; ++i)
200	161k	fe64_sqr(t1, t1);
201
202		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
203	32.2k	fe64_mul(out, t1, t0);
204	32.2k	}
205
206		/*
207		* Duplicate of original x25519_scalar_mult_generic, but using
208		* fe64_* subroutines.
209		*/
210		static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
211		const uint8_t point[32])
212	32.2k	{
213	32.2k	fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
214	32.2k	uint8_t e[32];
215	32.2k	unsigned swap = 0;
216	32.2k	int pos;
217
218	32.2k	memcpy(e, scalar, 32);
219	32.2k	e[0] &= 0xf8;
220	32.2k	e[31] &= 0x7f;
221	32.2k	e[31] \|= 0x40;
222	32.2k	fe64_frombytes(x1, point);
223	32.2k	fe64_1(x2);
224	32.2k	fe64_0(z2);
225	32.2k	fe64_copy(x3, x1);
226	32.2k	fe64_1(z3);
227
228	8.25M	for (pos = 254; pos >= 0; --pos) {
229	8.21M	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
230
231	8.21M	swap ^= b;
232	8.21M	fe64_cswap(x2, x3, swap);
233	8.21M	fe64_cswap(z2, z3, swap);
234	8.21M	swap = b;
235	8.21M	fe64_sub(tmp0, x3, z3);
236	8.21M	fe64_sub(tmp1, x2, z2);
237	8.21M	fe64_add(x2, x2, z2);
238	8.21M	fe64_add(z2, x3, z3);
239	8.21M	fe64_mul(z3, x2, tmp0);
240	8.21M	fe64_mul(z2, z2, tmp1);
241	8.21M	fe64_sqr(tmp0, tmp1);
242	8.21M	fe64_sqr(tmp1, x2);
243	8.21M	fe64_add(x3, z3, z2);
244	8.21M	fe64_sub(z2, z3, z2);
245	8.21M	fe64_mul(x2, tmp1, tmp0);
246	8.21M	fe64_sub(tmp1, tmp1, tmp0);
247	8.21M	fe64_sqr(z2, z2);
248	8.21M	fe64_mul121666(z3, tmp1);
249	8.21M	fe64_sqr(x3, x3);
250	8.21M	fe64_add(tmp0, tmp0, z3);
251	8.21M	fe64_mul(z3, x1, z2);
252	8.21M	fe64_mul(z2, tmp1, tmp0);
253	8.21M	}
254
255	32.2k	fe64_invert(z2, z2);
256	32.2k	fe64_mul(x2, x2, z2);
257	32.2k	fe64_tobytes(out, x2);
258
259	32.2k	OPENSSL_cleanse(e, sizeof(e));
260	32.2k	}
261		#endif
262
263		#if defined(X25519_ASM) \
264		\|\| (defined(INT128_MAX) \
265		&& !defined(__sparc__) \
266		&& (!defined(__SIZEOF_LONG__) \|\| (__SIZEOF_LONG__ == 8)) \
267		&& !(defined(__ANDROID__) && !defined(__clang__)))
268		/*
269		* Base 2^51 implementation. It's virtually no different from reference
270		* base 2^25.5 implementation in respect to lax boundary conditions for
271		* intermediate values and even individual limbs. So that whatever you
272		* know about the reference, applies even here...
273		*/
274		#define BASE_2_51_IMPLEMENTED
275
276		typedef uint64_t fe51[5];
277
278		static const uint64_t MASK51 = 0x7ffffffffffff;
279
280		static uint64_t load_7(const uint8_t *in)
281	0	{
282	0	uint64_t result;
283
284	0	result = in[0];
285	0	result \|= ((uint64_t)in[1]) << 8;
286	0	result \|= ((uint64_t)in[2]) << 16;
287	0	result \|= ((uint64_t)in[3]) << 24;
288	0	result \|= ((uint64_t)in[4]) << 32;
289	0	result \|= ((uint64_t)in[5]) << 40;
290	0	result \|= ((uint64_t)in[6]) << 48;
291
292	0	return result;
293	0	}
294
295		static uint64_t load_6(const uint8_t *in)
296	0	{
297	0	uint64_t result;
298
299	0	result = in[0];
300	0	result \|= ((uint64_t)in[1]) << 8;
301	0	result \|= ((uint64_t)in[2]) << 16;
302	0	result \|= ((uint64_t)in[3]) << 24;
303	0	result \|= ((uint64_t)in[4]) << 32;
304	0	result \|= ((uint64_t)in[5]) << 40;
305
306	0	return result;
307	0	}
308
309		static void fe51_frombytes(fe51 h, const uint8_t *s)
310	0	{
311	0	uint64_t h0 = load_7(s); /* 56 bits */
312	0	uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
313	0	uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
314	0	uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
315	0	uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
316
317	0	h1 \|= h0 >> 51;
318	0	h0 &= MASK51;
319	0	h2 \|= h1 >> 51;
320	0	h1 &= MASK51;
321	0	h3 \|= h2 >> 51;
322	0	h2 &= MASK51;
323	0	h4 \|= h3 >> 51;
324	0	h3 &= MASK51;
325
326	0	h[0] = h0;
327	0	h[1] = h1;
328	0	h[2] = h2;
329	0	h[3] = h3;
330	0	h[4] = h4;
331	0	}
332
333		static void fe51_tobytes(uint8_t *s, const fe51 h)
334	0	{
335	0	uint64_t h0 = h[0];
336	0	uint64_t h1 = h[1];
337	0	uint64_t h2 = h[2];
338	0	uint64_t h3 = h[3];
339	0	uint64_t h4 = h[4];
340	0	uint64_t q;
341
342		/* compare to modulus */
343	0	q = (h0 + 19) >> 51;
344	0	q = (h1 + q) >> 51;
345	0	q = (h2 + q) >> 51;
346	0	q = (h3 + q) >> 51;
347	0	q = (h4 + q) >> 51;
348
349		/* full reduce */
350	0	h0 += 19 * q;
351	0	h1 += h0 >> 51;
352	0	h0 &= MASK51;
353	0	h2 += h1 >> 51;
354	0	h1 &= MASK51;
355	0	h3 += h2 >> 51;
356	0	h2 &= MASK51;
357	0	h4 += h3 >> 51;
358	0	h3 &= MASK51;
359	0	h4 &= MASK51;
360
361		/* smash */
362	0	s[0] = (uint8_t)(h0 >> 0);
363	0	s[1] = (uint8_t)(h0 >> 8);
364	0	s[2] = (uint8_t)(h0 >> 16);
365	0	s[3] = (uint8_t)(h0 >> 24);
366	0	s[4] = (uint8_t)(h0 >> 32);
367	0	s[5] = (uint8_t)(h0 >> 40);
368	0	s[6] = (uint8_t)((h0 >> 48) \| ((uint32_t)h1 << 3));
369	0	s[7] = (uint8_t)(h1 >> 5);
370	0	s[8] = (uint8_t)(h1 >> 13);
371	0	s[9] = (uint8_t)(h1 >> 21);
372	0	s[10] = (uint8_t)(h1 >> 29);
373	0	s[11] = (uint8_t)(h1 >> 37);
374	0	s[12] = (uint8_t)((h1 >> 45) \| ((uint32_t)h2 << 6));
375	0	s[13] = (uint8_t)(h2 >> 2);
376	0	s[14] = (uint8_t)(h2 >> 10);
377	0	s[15] = (uint8_t)(h2 >> 18);
378	0	s[16] = (uint8_t)(h2 >> 26);
379	0	s[17] = (uint8_t)(h2 >> 34);
380	0	s[18] = (uint8_t)(h2 >> 42);
381	0	s[19] = (uint8_t)((h2 >> 50) \| ((uint32_t)h3 << 1));
382	0	s[20] = (uint8_t)(h3 >> 7);
383	0	s[21] = (uint8_t)(h3 >> 15);
384	0	s[22] = (uint8_t)(h3 >> 23);
385	0	s[23] = (uint8_t)(h3 >> 31);
386	0	s[24] = (uint8_t)(h3 >> 39);
387	0	s[25] = (uint8_t)((h3 >> 47) \| ((uint32_t)h4 << 4));
388	0	s[26] = (uint8_t)(h4 >> 4);
389	0	s[27] = (uint8_t)(h4 >> 12);
390	0	s[28] = (uint8_t)(h4 >> 20);
391	0	s[29] = (uint8_t)(h4 >> 28);
392	0	s[30] = (uint8_t)(h4 >> 36);
393	0	s[31] = (uint8_t)(h4 >> 44);
394	0	}
395
396		#if defined(X25519_ASM)
397		void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
398		void x25519_fe51_sqr(fe51 h, const fe51 f);
399		void x25519_fe51_mul121666(fe51 h, fe51 f);
400	0	#define fe51_mul x25519_fe51_mul
401	0	#define fe51_sq x25519_fe51_sqr
402	0	#define fe51_mul121666 x25519_fe51_mul121666
403		#else
404
405		typedef uint128_t u128;
406
407		static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
408		{
409		u128 h0, h1, h2, h3, h4;
410		uint64_t f_i, g0, g1, g2, g3, g4;
411
412		f_i = f[0];
413		h0 = (u128)f_i * (g0 = g[0]);
414		h1 = (u128)f_i * (g1 = g[1]);
415		h2 = (u128)f_i * (g2 = g[2]);
416		h3 = (u128)f_i * (g3 = g[3]);
417		h4 = (u128)f_i * (g4 = g[4]);
418
419		f_i = f[1];
420		h0 += (u128)f_i * (g4 *= 19);
421		h1 += (u128)f_i * g0;
422		h2 += (u128)f_i * g1;
423		h3 += (u128)f_i * g2;
424		h4 += (u128)f_i * g3;
425
426		f_i = f[2];
427		h0 += (u128)f_i * (g3 *= 19);
428		h1 += (u128)f_i * g4;
429		h2 += (u128)f_i * g0;
430		h3 += (u128)f_i * g1;
431		h4 += (u128)f_i * g2;
432
433		f_i = f[3];
434		h0 += (u128)f_i * (g2 *= 19);
435		h1 += (u128)f_i * g3;
436		h2 += (u128)f_i * g4;
437		h3 += (u128)f_i * g0;
438		h4 += (u128)f_i * g1;
439
440		f_i = f[4];
441		h0 += (u128)f_i * (g1 *= 19);
442		h1 += (u128)f_i * g2;
443		h2 += (u128)f_i * g3;
444		h3 += (u128)f_i * g4;
445		h4 += (u128)f_i * g0;
446
447		/* partial [lazy] reduction */
448		h3 += (uint64_t)(h2 >> 51);
449		g2 = (uint64_t)h2 & MASK51;
450		h1 += (uint64_t)(h0 >> 51);
451		g0 = (uint64_t)h0 & MASK51;
452
453		h4 += (uint64_t)(h3 >> 51);
454		g3 = (uint64_t)h3 & MASK51;
455		g2 += (uint64_t)(h1 >> 51);
456		g1 = (uint64_t)h1 & MASK51;
457
458		g0 += (uint64_t)(h4 >> 51) * 19;
459		g4 = (uint64_t)h4 & MASK51;
460		g3 += g2 >> 51;
461		g2 &= MASK51;
462		g1 += g0 >> 51;
463		g0 &= MASK51;
464
465		h[0] = g0;
466		h[1] = g1;
467		h[2] = g2;
468		h[3] = g3;
469		h[4] = g4;
470		}
471
472		static void fe51_sq(fe51 h, const fe51 f)
473		{
474		#if defined(OPENSSL_SMALL_FOOTPRINT)
475		fe51_mul(h, f, f);
476		#else
477		/* dedicated squaring gives 16-25% overall improvement */
478		uint64_t g0 = f[0];
479		uint64_t g1 = f[1];
480		uint64_t g2 = f[2];
481		uint64_t g3 = f[3];
482		uint64_t g4 = f[4];
483		u128 h0, h1, h2, h3, h4;
484
485		h0 = (u128)g0 * g0;
486		g0 *= 2;
487		h1 = (u128)g0 * g1;
488		h2 = (u128)g0 * g2;
489		h3 = (u128)g0 * g3;
490		h4 = (u128)g0 * g4;
491
492		g0 = g4; /* borrow g0 */
493		h3 += (u128)g0 * (g4 *= 19);
494
495		h2 += (u128)g1 * g1;
496		g1 *= 2;
497		h3 += (u128)g1 * g2;
498		h4 += (u128)g1 * g3;
499		h0 += (u128)g1 * g4;
500
501		g0 = g3; /* borrow g0 */
502		h1 += (u128)g0 * (g3 *= 19);
503		h2 += (u128)(g0 * 2) * g4;
504
505		h4 += (u128)g2 * g2;
506		g2 *= 2;
507		h0 += (u128)g2 * g3;
508		h1 += (u128)g2 * g4;
509
510		/* partial [lazy] reduction */
511		h3 += (uint64_t)(h2 >> 51);
512		g2 = (uint64_t)h2 & MASK51;
513		h1 += (uint64_t)(h0 >> 51);
514		g0 = (uint64_t)h0 & MASK51;
515
516		h4 += (uint64_t)(h3 >> 51);
517		g3 = (uint64_t)h3 & MASK51;
518		g2 += (uint64_t)(h1 >> 51);
519		g1 = (uint64_t)h1 & MASK51;
520
521		g0 += (uint64_t)(h4 >> 51) * 19;
522		g4 = (uint64_t)h4 & MASK51;
523		g3 += g2 >> 51;
524		g2 &= MASK51;
525		g1 += g0 >> 51;
526		g0 &= MASK51;
527
528		h[0] = g0;
529		h[1] = g1;
530		h[2] = g2;
531		h[3] = g3;
532		h[4] = g4;
533		#endif
534		}
535
536		static void fe51_mul121666(fe51 h, fe51 f)
537		{
538		u128 h0 = f[0] * (u128)121666;
539		u128 h1 = f[1] * (u128)121666;
540		u128 h2 = f[2] * (u128)121666;
541		u128 h3 = f[3] * (u128)121666;
542		u128 h4 = f[4] * (u128)121666;
543		uint64_t g0, g1, g2, g3, g4;
544
545		h3 += (uint64_t)(h2 >> 51);
546		g2 = (uint64_t)h2 & MASK51;
547		h1 += (uint64_t)(h0 >> 51);
548		g0 = (uint64_t)h0 & MASK51;
549
550		h4 += (uint64_t)(h3 >> 51);
551		g3 = (uint64_t)h3 & MASK51;
552		g2 += (uint64_t)(h1 >> 51);
553		g1 = (uint64_t)h1 & MASK51;
554
555		g0 += (uint64_t)(h4 >> 51) * 19;
556		g4 = (uint64_t)h4 & MASK51;
557		g3 += g2 >> 51;
558		g2 &= MASK51;
559		g1 += g0 >> 51;
560		g0 &= MASK51;
561
562		h[0] = g0;
563		h[1] = g1;
564		h[2] = g2;
565		h[3] = g3;
566		h[4] = g4;
567		}
568		#endif
569
570		static void fe51_add(fe51 h, const fe51 f, const fe51 g)
571	0	{
572	0	h[0] = f[0] + g[0];
573	0	h[1] = f[1] + g[1];
574	0	h[2] = f[2] + g[2];
575	0	h[3] = f[3] + g[3];
576	0	h[4] = f[4] + g[4];
577	0	}
578
579		static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
580	0	{
581		/*
582		* Add 2*modulus to ensure that result remains positive
583		* even if subtrahend is partially reduced.
584		*/
585	0	h[0] = (f[0] + 0xfffffffffffda) - g[0];
586	0	h[1] = (f[1] + 0xffffffffffffe) - g[1];
587	0	h[2] = (f[2] + 0xffffffffffffe) - g[2];
588	0	h[3] = (f[3] + 0xffffffffffffe) - g[3];
589	0	h[4] = (f[4] + 0xffffffffffffe) - g[4];
590	0	}
591
592		static void fe51_0(fe51 h)
593	0	{
594	0	h[0] = 0;
595	0	h[1] = 0;
596	0	h[2] = 0;
597	0	h[3] = 0;
598	0	h[4] = 0;
599	0	}
600
601		static void fe51_1(fe51 h)
602	0	{
603	0	h[0] = 1;
604	0	h[1] = 0;
605	0	h[2] = 0;
606	0	h[3] = 0;
607	0	h[4] = 0;
608	0	}
609
610		static void fe51_copy(fe51 h, const fe51 f)
611	0	{
612	0	h[0] = f[0];
613	0	h[1] = f[1];
614	0	h[2] = f[2];
615	0	h[3] = f[3];
616	0	h[4] = f[4];
617	0	}
618
619		static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
620	0	{
621	0	int i;
622	0	uint64_t mask = 0 - (uint64_t)b;
623
624	0	for (i = 0; i < 5; i++) {
625	0	int64_t x = f[i] ^ g[i];
626	0	x &= mask;
627	0	f[i] ^= x;
628	0	g[i] ^= x;
629	0	}
630	0	}
631
632		static void fe51_invert(fe51 out, const fe51 z)
633	0	{
634	0	fe51 t0;
635	0	fe51 t1;
636	0	fe51 t2;
637	0	fe51 t3;
638	0	int i;
639
640		/*
641		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
642		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
643		*/
644
645		/* t0 = z ** 2 */
646	0	fe51_sq(t0, z);
647
648		/* t1 = t0 (2 2) = z ** 8 */
649	0	fe51_sq(t1, t0);
650	0	fe51_sq(t1, t1);
651
652		/* t1 = z * t1 = z ** 9 */
653	0	fe51_mul(t1, z, t1);
654		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
655	0	fe51_mul(t0, t0, t1);
656
657		/* t2 = t0 2 = z 22 */
658	0	fe51_sq(t2, t0);
659
660		/* t1 = t1 * t2 = z (2 5 - 1) */
661	0	fe51_mul(t1, t1, t2);
662
663		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
664	0	fe51_sq(t2, t1);
665	0	for (i = 1; i < 5; ++i)
666	0	fe51_sq(t2, t2);
667
668		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
669	0	fe51_mul(t1, t2, t1);
670
671		/* Continuing similarly... */
672
673		/* t2 = z (2 20 - 1) */
674	0	fe51_sq(t2, t1);
675	0	for (i = 1; i < 10; ++i)
676	0	fe51_sq(t2, t2);
677
678	0	fe51_mul(t2, t2, t1);
679
680		/* t2 = z (2 40 - 1) */
681	0	fe51_sq(t3, t2);
682	0	for (i = 1; i < 20; ++i)
683	0	fe51_sq(t3, t3);
684
685	0	fe51_mul(t2, t3, t2);
686
687		/* t2 = z (2 10) * (2 ** 40 - 1) */
688	0	for (i = 0; i < 10; ++i)
689	0	fe51_sq(t2, t2);
690
691		/* t1 = z (2 50 - 1) */
692	0	fe51_mul(t1, t2, t1);
693
694		/* t2 = z (2 100 - 1) */
695	0	fe51_sq(t2, t1);
696	0	for (i = 1; i < 50; ++i)
697	0	fe51_sq(t2, t2);
698
699	0	fe51_mul(t2, t2, t1);
700
701		/* t2 = z (2 200 - 1) */
702	0	fe51_sq(t3, t2);
703	0	for (i = 1; i < 100; ++i)
704	0	fe51_sq(t3, t3);
705
706	0	fe51_mul(t2, t3, t2);
707
708		/* t2 = z ((2 50) * (2 ** 200 - 1) */
709	0	for (i = 0; i < 50; ++i)
710	0	fe51_sq(t2, t2);
711
712		/* t1 = z (2 250 - 1) */
713	0	fe51_mul(t1, t2, t1);
714
715		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
716	0	for (i = 0; i < 5; ++i)
717	0	fe51_sq(t1, t1);
718
719		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
720	0	fe51_mul(out, t1, t0);
721	0	}
722
723		/*
724		* Duplicate of original x25519_scalar_mult_generic, but using
725		* fe51_* subroutines.
726		*/
727		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
728		const uint8_t point[32])
729	32.2k	{
730	32.2k	fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
731	32.2k	uint8_t e[32];
732	32.2k	unsigned swap = 0;
733	32.2k	int pos;
734
735	32.2k	#ifdef BASE_2_64_IMPLEMENTED
736	32.2k	if (x25519_fe64_eligible()) {
737	32.2k	x25519_scalar_mulx(out, scalar, point);
738	32.2k	return;
739	32.2k	}
740	0	#endif
741
742	0	memcpy(e, scalar, 32);
743	0	e[0] &= 0xf8;
744	0	e[31] &= 0x7f;
745	0	e[31] \|= 0x40;
746	0	fe51_frombytes(x1, point);
747	0	fe51_1(x2);
748	0	fe51_0(z2);
749	0	fe51_copy(x3, x1);
750	0	fe51_1(z3);
751
752	0	for (pos = 254; pos >= 0; --pos) {
753	0	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
754
755	0	swap ^= b;
756	0	fe51_cswap(x2, x3, swap);
757	0	fe51_cswap(z2, z3, swap);
758	0	swap = b;
759	0	fe51_sub(tmp0, x3, z3);
760	0	fe51_sub(tmp1, x2, z2);
761	0	fe51_add(x2, x2, z2);
762	0	fe51_add(z2, x3, z3);
763	0	fe51_mul(z3, tmp0, x2);
764	0	fe51_mul(z2, z2, tmp1);
765	0	fe51_sq(tmp0, tmp1);
766	0	fe51_sq(tmp1, x2);
767	0	fe51_add(x3, z3, z2);
768	0	fe51_sub(z2, z3, z2);
769	0	fe51_mul(x2, tmp1, tmp0);
770	0	fe51_sub(tmp1, tmp1, tmp0);
771	0	fe51_sq(z2, z2);
772	0	fe51_mul121666(z3, tmp1);
773	0	fe51_sq(x3, x3);
774	0	fe51_add(tmp0, tmp0, z3);
775	0	fe51_mul(z3, x1, z2);
776	0	fe51_mul(z2, tmp1, tmp0);
777	0	}
778
779	0	fe51_invert(z2, z2);
780	0	fe51_mul(x2, x2, z2);
781	0	fe51_tobytes(out, x2);
782
783	0	OPENSSL_cleanse(e, sizeof(e));
784	0	}
785		#endif
786
787		/*
788		* Reference base 2^25.5 implementation.
789		*
790		* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
791		* 20141124 (http://bench.cr.yp.to/supercop.html).
792		*
793		* The field functions are shared by Ed25519 and X25519 where possible.
794		*/
795
796		/*
797		* fe means field element. Here the field is \Z/(2^255-19). An element t,
798		* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
799		* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
800		* context.
801		*/
802		typedef int32_t fe[10];
803
804		static const int64_t kBottom21Bits = 0x1fffffLL;
805		static const int64_t kBottom25Bits = 0x1ffffffLL;
806		static const int64_t kBottom26Bits = 0x3ffffffLL;
807		static const int64_t kTop39Bits = 0xfffffffffe000000LL;
808		static const int64_t kTop38Bits = 0xfffffffffc000000LL;
809
810		static uint64_t load_3(const uint8_t *in)
811	2.22k	{
812	2.22k	uint64_t result;
813
814	2.22k	result = ((uint64_t)in[0]);
815	2.22k	result \|= ((uint64_t)in[1]) << 8;
816	2.22k	result \|= ((uint64_t)in[2]) << 16;
817	2.22k	return result;
818	2.22k	}
819
820		static uint64_t load_4(const uint8_t *in)
821	1.74k	{
822	1.74k	uint64_t result;
823
824	1.74k	result = ((uint64_t)in[0]);
825	1.74k	result \|= ((uint64_t)in[1]) << 8;
826	1.74k	result \|= ((uint64_t)in[2]) << 16;
827	1.74k	result \|= ((uint64_t)in[3]) << 24;
828	1.74k	return result;
829	1.74k	}
830
831		static void fe_frombytes(fe h, const uint8_t *s)
832	119	{
833		/* Ignores top bit of h. */
834	119	int64_t h0 = load_4(s);
835	119	int64_t h1 = load_3(s + 4) << 6;
836	119	int64_t h2 = load_3(s + 7) << 5;
837	119	int64_t h3 = load_3(s + 10) << 3;
838	119	int64_t h4 = load_3(s + 13) << 2;
839	119	int64_t h5 = load_4(s + 16);
840	119	int64_t h6 = load_3(s + 20) << 7;
841	119	int64_t h7 = load_3(s + 23) << 5;
842	119	int64_t h8 = load_3(s + 26) << 4;
843	119	int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
844	119	int64_t carry0;
845	119	int64_t carry1;
846	119	int64_t carry2;
847	119	int64_t carry3;
848	119	int64_t carry4;
849	119	int64_t carry5;
850	119	int64_t carry6;
851	119	int64_t carry7;
852	119	int64_t carry8;
853	119	int64_t carry9;
854
855	119	carry9 = h9 + (1 << 24);
856	119	h0 += (carry9 >> 25) * 19;
857	119	h9 -= carry9 & kTop39Bits;
858	119	carry1 = h1 + (1 << 24);
859	119	h2 += carry1 >> 25;
860	119	h1 -= carry1 & kTop39Bits;
861	119	carry3 = h3 + (1 << 24);
862	119	h4 += carry3 >> 25;
863	119	h3 -= carry3 & kTop39Bits;
864	119	carry5 = h5 + (1 << 24);
865	119	h6 += carry5 >> 25;
866	119	h5 -= carry5 & kTop39Bits;
867	119	carry7 = h7 + (1 << 24);
868	119	h8 += carry7 >> 25;
869	119	h7 -= carry7 & kTop39Bits;
870
871	119	carry0 = h0 + (1 << 25);
872	119	h1 += carry0 >> 26;
873	119	h0 -= carry0 & kTop38Bits;
874	119	carry2 = h2 + (1 << 25);
875	119	h3 += carry2 >> 26;
876	119	h2 -= carry2 & kTop38Bits;
877	119	carry4 = h4 + (1 << 25);
878	119	h5 += carry4 >> 26;
879	119	h4 -= carry4 & kTop38Bits;
880	119	carry6 = h6 + (1 << 25);
881	119	h7 += carry6 >> 26;
882	119	h6 -= carry6 & kTop38Bits;
883	119	carry8 = h8 + (1 << 25);
884	119	h9 += carry8 >> 26;
885	119	h8 -= carry8 & kTop38Bits;
886
887	119	h[0] = (int32_t)h0;
888	119	h[1] = (int32_t)h1;
889	119	h[2] = (int32_t)h2;
890	119	h[3] = (int32_t)h3;
891	119	h[4] = (int32_t)h4;
892	119	h[5] = (int32_t)h5;
893	119	h[6] = (int32_t)h6;
894	119	h[7] = (int32_t)h7;
895	119	h[8] = (int32_t)h8;
896	119	h[9] = (int32_t)h9;
897	119	}
898
899		/*
900		* Preconditions:
901		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
902		*
903		* Write p=2^255-19; q=floor(h/p).
904		* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
905		*
906		* Proof:
907		* Have \|h\|<=p so \|q\|<=1 so \|19^2 2^(-255) q\|<1/4.
908		* Also have \|h-2^230 h9\|<2^231 so \|19 2^(-255)(h-2^230 h9)\|<1/4.
909		*
910		* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
911		* Then 0<y<1.
912		*
913		* Write r=h-pq.
914		* Have 0<=r<=p-1=2^255-20.
915		* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
916		*
917		* Write x=r+19(2^-255)r+y.
918		* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
919		*
920		* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
921		* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
922		*/
923		static void fe_tobytes(uint8_t *s, const fe h)
924	147k	{
925	147k	int32_t h0 = h[0];
926	147k	int32_t h1 = h[1];
927	147k	int32_t h2 = h[2];
928	147k	int32_t h3 = h[3];
929	147k	int32_t h4 = h[4];
930	147k	int32_t h5 = h[5];
931	147k	int32_t h6 = h[6];
932	147k	int32_t h7 = h[7];
933	147k	int32_t h8 = h[8];
934	147k	int32_t h9 = h[9];
935	147k	int32_t q;
936
937	147k	q = (19 * h9 + (((int32_t)1) << 24)) >> 25;
938	147k	q = (h0 + q) >> 26;
939	147k	q = (h1 + q) >> 25;
940	147k	q = (h2 + q) >> 26;
941	147k	q = (h3 + q) >> 25;
942	147k	q = (h4 + q) >> 26;
943	147k	q = (h5 + q) >> 25;
944	147k	q = (h6 + q) >> 26;
945	147k	q = (h7 + q) >> 25;
946	147k	q = (h8 + q) >> 26;
947	147k	q = (h9 + q) >> 25;
948
949		/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
950	147k	h0 += 19 * q;
951		/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
952
953	147k	h1 += h0 >> 26;
954	147k	h0 &= kBottom26Bits;
955	147k	h2 += h1 >> 25;
956	147k	h1 &= kBottom25Bits;
957	147k	h3 += h2 >> 26;
958	147k	h2 &= kBottom26Bits;
959	147k	h4 += h3 >> 25;
960	147k	h3 &= kBottom25Bits;
961	147k	h5 += h4 >> 26;
962	147k	h4 &= kBottom26Bits;
963	147k	h6 += h5 >> 25;
964	147k	h5 &= kBottom25Bits;
965	147k	h7 += h6 >> 26;
966	147k	h6 &= kBottom26Bits;
967	147k	h8 += h7 >> 25;
968	147k	h7 &= kBottom25Bits;
969	147k	h9 += h8 >> 26;
970	147k	h8 &= kBottom26Bits;
971	147k	h9 &= kBottom25Bits;
972		/* h10 = carry9 */
973
974		/*
975		* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
976		* Have h0+...+2^230 h9 between 0 and 2^255-1;
977		* evidently 2^255 h10-2^255 q = 0.
978		* Goal: Output h0+...+2^230 h9.
979		*/
980	147k	s[0] = (uint8_t)(h0 >> 0);
981	147k	s[1] = (uint8_t)(h0 >> 8);
982	147k	s[2] = (uint8_t)(h0 >> 16);
983	147k	s[3] = (uint8_t)((h0 >> 24) \| ((uint32_t)(h1) << 2));
984	147k	s[4] = (uint8_t)(h1 >> 6);
985	147k	s[5] = (uint8_t)(h1 >> 14);
986	147k	s[6] = (uint8_t)((h1 >> 22) \| ((uint32_t)(h2) << 3));
987	147k	s[7] = (uint8_t)(h2 >> 5);
988	147k	s[8] = (uint8_t)(h2 >> 13);
989	147k	s[9] = (uint8_t)((h2 >> 21) \| ((uint32_t)(h3) << 5));
990	147k	s[10] = (uint8_t)(h3 >> 3);
991	147k	s[11] = (uint8_t)(h3 >> 11);
992	147k	s[12] = (uint8_t)((h3 >> 19) \| ((uint32_t)(h4) << 6));
993	147k	s[13] = (uint8_t)(h4 >> 2);
994	147k	s[14] = (uint8_t)(h4 >> 10);
995	147k	s[15] = (uint8_t)(h4 >> 18);
996	147k	s[16] = (uint8_t)(h5 >> 0);
997	147k	s[17] = (uint8_t)(h5 >> 8);
998	147k	s[18] = (uint8_t)(h5 >> 16);
999	147k	s[19] = (uint8_t)((h5 >> 24) \| ((uint32_t)(h6) << 1));
1000	147k	s[20] = (uint8_t)(h6 >> 7);
1001	147k	s[21] = (uint8_t)(h6 >> 15);
1002	147k	s[22] = (uint8_t)((h6 >> 23) \| ((uint32_t)(h7) << 3));
1003	147k	s[23] = (uint8_t)(h7 >> 5);
1004	147k	s[24] = (uint8_t)(h7 >> 13);
1005	147k	s[25] = (uint8_t)((h7 >> 21) \| ((uint32_t)(h8) << 4));
1006	147k	s[26] = (uint8_t)(h8 >> 4);
1007	147k	s[27] = (uint8_t)(h8 >> 12);
1008	147k	s[28] = (uint8_t)((h8 >> 20) \| ((uint32_t)(h9) << 6));
1009	147k	s[29] = (uint8_t)(h9 >> 2);
1010	147k	s[30] = (uint8_t)(h9 >> 10);
1011	147k	s[31] = (uint8_t)(h9 >> 18);
1012	147k	}
1013
1014		/* h = f */
1015		static void fe_copy(fe h, const fe f)
1016	19.3M	{
1017	19.3M	memmove(h, f, sizeof(int32_t) * 10);
1018	19.3M	}
1019
1020		/* h = 0 */
1021		static void fe_0(fe h)
1022	9.72M	{
1023	9.72M	memset(h, 0, sizeof(int32_t) * 10);
1024	9.72M	}
1025
1026		/* h = 1 */
1027		static void fe_1(fe h)
1028	19.1M	{
1029	19.1M	memset(h, 0, sizeof(int32_t) * 10);
1030	19.1M	h[0] = 1;
1031	19.1M	}
1032
1033		/*
1034		* h = f + g
1035		*
1036		* Can overlap h with f or g.
1037		*
1038		* Preconditions:
1039		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1040		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1041		*
1042		* Postconditions:
1043		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1044		*/
1045		static void fe_add(fe h, const fe f, const fe g)
1046	39.1M	{
1047	39.1M	unsigned i;
1048
1049	430M	for (i = 0; i < 10; i++) {
1050	391M	h[i] = f[i] + g[i];
1051	391M	}
1052	39.1M	}
1053
1054		/*
1055		* h = f - g
1056		*
1057		* Can overlap h with f or g.
1058		*
1059		* Preconditions:
1060		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1061		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1062		*
1063		* Postconditions:
1064		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1065		*/
1066		static void fe_sub(fe h, const fe f, const fe g)
1067	30.3M	{
1068	30.3M	unsigned i;
1069
1070	333M	for (i = 0; i < 10; i++) {
1071	303M	h[i] = f[i] - g[i];
1072	303M	}
1073	30.3M	}
1074
1075		/*
1076		* h = f * g
1077		*
1078		* Can overlap h with f or g.
1079		*
1080		* Preconditions:
1081		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1082		* \|g\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1083		*
1084		* Postconditions:
1085		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1086		*
1087		* Notes on implementation strategy:
1088		*
1089		* Using schoolbook multiplication.
1090		* Karatsuba would save a little in some cost models.
1091		*
1092		* Most multiplications by 2 and 19 are 32-bit precomputations;
1093		* cheaper than 64-bit postcomputations.
1094		*
1095		* There is one remaining multiplication by 19 in the carry chain;
1096		* one *19 precomputation can be merged into this,
1097		* but the resulting data flow is considerably less clean.
1098		*
1099		* There are 12 carries below.
1100		* 10 of them are 2-way parallelizable and vectorizable.
1101		* Can get away with 11 carries, but then data flow is much deeper.
1102		*
1103		* With tighter constraints on inputs can squeeze carries into int32.
1104		*/
1105		static void fe_mul(fe h, const fe f, const fe g)
1106	69.8M	{
1107	69.8M	int32_t f0 = f[0];
1108	69.8M	int32_t f1 = f[1];
1109	69.8M	int32_t f2 = f[2];
1110	69.8M	int32_t f3 = f[3];
1111	69.8M	int32_t f4 = f[4];
1112	69.8M	int32_t f5 = f[5];
1113	69.8M	int32_t f6 = f[6];
1114	69.8M	int32_t f7 = f[7];
1115	69.8M	int32_t f8 = f[8];
1116	69.8M	int32_t f9 = f[9];
1117	69.8M	int32_t g0 = g[0];
1118	69.8M	int32_t g1 = g[1];
1119	69.8M	int32_t g2 = g[2];
1120	69.8M	int32_t g3 = g[3];
1121	69.8M	int32_t g4 = g[4];
1122	69.8M	int32_t g5 = g[5];
1123	69.8M	int32_t g6 = g[6];
1124	69.8M	int32_t g7 = g[7];
1125	69.8M	int32_t g8 = g[8];
1126	69.8M	int32_t g9 = g[9];
1127	69.8M	int32_t g1_19 = 19 * g1; /* 1.9593752^29 /
1128	69.8M	int32_t g2_19 = 19 * g2; /* 1.9593752^30; still ok /
1129	69.8M	int32_t g3_19 = 19 * g3;
1130	69.8M	int32_t g4_19 = 19 * g4;
1131	69.8M	int32_t g5_19 = 19 * g5;
1132	69.8M	int32_t g6_19 = 19 * g6;
1133	69.8M	int32_t g7_19 = 19 * g7;
1134	69.8M	int32_t g8_19 = 19 * g8;
1135	69.8M	int32_t g9_19 = 19 * g9;
1136	69.8M	int32_t f1_2 = 2 * f1;
1137	69.8M	int32_t f3_2 = 2 * f3;
1138	69.8M	int32_t f5_2 = 2 * f5;
1139	69.8M	int32_t f7_2 = 2 * f7;
1140	69.8M	int32_t f9_2 = 2 * f9;
1141	69.8M	int64_t f0g0 = f0 * (int64_t)g0;
1142	69.8M	int64_t f0g1 = f0 * (int64_t)g1;
1143	69.8M	int64_t f0g2 = f0 * (int64_t)g2;
1144	69.8M	int64_t f0g3 = f0 * (int64_t)g3;
1145	69.8M	int64_t f0g4 = f0 * (int64_t)g4;
1146	69.8M	int64_t f0g5 = f0 * (int64_t)g5;
1147	69.8M	int64_t f0g6 = f0 * (int64_t)g6;
1148	69.8M	int64_t f0g7 = f0 * (int64_t)g7;
1149	69.8M	int64_t f0g8 = f0 * (int64_t)g8;
1150	69.8M	int64_t f0g9 = f0 * (int64_t)g9;
1151	69.8M	int64_t f1g0 = f1 * (int64_t)g0;
1152	69.8M	int64_t f1g1_2 = f1_2 * (int64_t)g1;
1153	69.8M	int64_t f1g2 = f1 * (int64_t)g2;
1154	69.8M	int64_t f1g3_2 = f1_2 * (int64_t)g3;
1155	69.8M	int64_t f1g4 = f1 * (int64_t)g4;
1156	69.8M	int64_t f1g5_2 = f1_2 * (int64_t)g5;
1157	69.8M	int64_t f1g6 = f1 * (int64_t)g6;
1158	69.8M	int64_t f1g7_2 = f1_2 * (int64_t)g7;
1159	69.8M	int64_t f1g8 = f1 * (int64_t)g8;
1160	69.8M	int64_t f1g9_38 = f1_2 * (int64_t)g9_19;
1161	69.8M	int64_t f2g0 = f2 * (int64_t)g0;
1162	69.8M	int64_t f2g1 = f2 * (int64_t)g1;
1163	69.8M	int64_t f2g2 = f2 * (int64_t)g2;
1164	69.8M	int64_t f2g3 = f2 * (int64_t)g3;
1165	69.8M	int64_t f2g4 = f2 * (int64_t)g4;
1166	69.8M	int64_t f2g5 = f2 * (int64_t)g5;
1167	69.8M	int64_t f2g6 = f2 * (int64_t)g6;
1168	69.8M	int64_t f2g7 = f2 * (int64_t)g7;
1169	69.8M	int64_t f2g8_19 = f2 * (int64_t)g8_19;
1170	69.8M	int64_t f2g9_19 = f2 * (int64_t)g9_19;
1171	69.8M	int64_t f3g0 = f3 * (int64_t)g0;
1172	69.8M	int64_t f3g1_2 = f3_2 * (int64_t)g1;
1173	69.8M	int64_t f3g2 = f3 * (int64_t)g2;
1174	69.8M	int64_t f3g3_2 = f3_2 * (int64_t)g3;
1175	69.8M	int64_t f3g4 = f3 * (int64_t)g4;
1176	69.8M	int64_t f3g5_2 = f3_2 * (int64_t)g5;
1177	69.8M	int64_t f3g6 = f3 * (int64_t)g6;
1178	69.8M	int64_t f3g7_38 = f3_2 * (int64_t)g7_19;
1179	69.8M	int64_t f3g8_19 = f3 * (int64_t)g8_19;
1180	69.8M	int64_t f3g9_38 = f3_2 * (int64_t)g9_19;
1181	69.8M	int64_t f4g0 = f4 * (int64_t)g0;
1182	69.8M	int64_t f4g1 = f4 * (int64_t)g1;
1183	69.8M	int64_t f4g2 = f4 * (int64_t)g2;
1184	69.8M	int64_t f4g3 = f4 * (int64_t)g3;
1185	69.8M	int64_t f4g4 = f4 * (int64_t)g4;
1186	69.8M	int64_t f4g5 = f4 * (int64_t)g5;
1187	69.8M	int64_t f4g6_19 = f4 * (int64_t)g6_19;
1188	69.8M	int64_t f4g7_19 = f4 * (int64_t)g7_19;
1189	69.8M	int64_t f4g8_19 = f4 * (int64_t)g8_19;
1190	69.8M	int64_t f4g9_19 = f4 * (int64_t)g9_19;
1191	69.8M	int64_t f5g0 = f5 * (int64_t)g0;
1192	69.8M	int64_t f5g1_2 = f5_2 * (int64_t)g1;
1193	69.8M	int64_t f5g2 = f5 * (int64_t)g2;
1194	69.8M	int64_t f5g3_2 = f5_2 * (int64_t)g3;
1195	69.8M	int64_t f5g4 = f5 * (int64_t)g4;
1196	69.8M	int64_t f5g5_38 = f5_2 * (int64_t)g5_19;
1197	69.8M	int64_t f5g6_19 = f5 * (int64_t)g6_19;
1198	69.8M	int64_t f5g7_38 = f5_2 * (int64_t)g7_19;
1199	69.8M	int64_t f5g8_19 = f5 * (int64_t)g8_19;
1200	69.8M	int64_t f5g9_38 = f5_2 * (int64_t)g9_19;
1201	69.8M	int64_t f6g0 = f6 * (int64_t)g0;
1202	69.8M	int64_t f6g1 = f6 * (int64_t)g1;
1203	69.8M	int64_t f6g2 = f6 * (int64_t)g2;
1204	69.8M	int64_t f6g3 = f6 * (int64_t)g3;
1205	69.8M	int64_t f6g4_19 = f6 * (int64_t)g4_19;
1206	69.8M	int64_t f6g5_19 = f6 * (int64_t)g5_19;
1207	69.8M	int64_t f6g6_19 = f6 * (int64_t)g6_19;
1208	69.8M	int64_t f6g7_19 = f6 * (int64_t)g7_19;
1209	69.8M	int64_t f6g8_19 = f6 * (int64_t)g8_19;
1210	69.8M	int64_t f6g9_19 = f6 * (int64_t)g9_19;
1211	69.8M	int64_t f7g0 = f7 * (int64_t)g0;
1212	69.8M	int64_t f7g1_2 = f7_2 * (int64_t)g1;
1213	69.8M	int64_t f7g2 = f7 * (int64_t)g2;
1214	69.8M	int64_t f7g3_38 = f7_2 * (int64_t)g3_19;
1215	69.8M	int64_t f7g4_19 = f7 * (int64_t)g4_19;
1216	69.8M	int64_t f7g5_38 = f7_2 * (int64_t)g5_19;
1217	69.8M	int64_t f7g6_19 = f7 * (int64_t)g6_19;
1218	69.8M	int64_t f7g7_38 = f7_2 * (int64_t)g7_19;
1219	69.8M	int64_t f7g8_19 = f7 * (int64_t)g8_19;
1220	69.8M	int64_t f7g9_38 = f7_2 * (int64_t)g9_19;
1221	69.8M	int64_t f8g0 = f8 * (int64_t)g0;
1222	69.8M	int64_t f8g1 = f8 * (int64_t)g1;
1223	69.8M	int64_t f8g2_19 = f8 * (int64_t)g2_19;
1224	69.8M	int64_t f8g3_19 = f8 * (int64_t)g3_19;
1225	69.8M	int64_t f8g4_19 = f8 * (int64_t)g4_19;
1226	69.8M	int64_t f8g5_19 = f8 * (int64_t)g5_19;
1227	69.8M	int64_t f8g6_19 = f8 * (int64_t)g6_19;
1228	69.8M	int64_t f8g7_19 = f8 * (int64_t)g7_19;
1229	69.8M	int64_t f8g8_19 = f8 * (int64_t)g8_19;
1230	69.8M	int64_t f8g9_19 = f8 * (int64_t)g9_19;
1231	69.8M	int64_t f9g0 = f9 * (int64_t)g0;
1232	69.8M	int64_t f9g1_38 = f9_2 * (int64_t)g1_19;
1233	69.8M	int64_t f9g2_19 = f9 * (int64_t)g2_19;
1234	69.8M	int64_t f9g3_38 = f9_2 * (int64_t)g3_19;
1235	69.8M	int64_t f9g4_19 = f9 * (int64_t)g4_19;
1236	69.8M	int64_t f9g5_38 = f9_2 * (int64_t)g5_19;
1237	69.8M	int64_t f9g6_19 = f9 * (int64_t)g6_19;
1238	69.8M	int64_t f9g7_38 = f9_2 * (int64_t)g7_19;
1239	69.8M	int64_t f9g8_19 = f9 * (int64_t)g8_19;
1240	69.8M	int64_t f9g9_38 = f9_2 * (int64_t)g9_19;
1241	69.8M	int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1242	69.8M	int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1243	69.8M	int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1244	69.8M	int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1245	69.8M	int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1246	69.8M	int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1247	69.8M	int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
1248	69.8M	int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
1249	69.8M	int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
1250	69.8M	int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
1251	69.8M	int64_t carry0;
1252	69.8M	int64_t carry1;
1253	69.8M	int64_t carry2;
1254	69.8M	int64_t carry3;
1255	69.8M	int64_t carry4;
1256	69.8M	int64_t carry5;
1257	69.8M	int64_t carry6;
1258	69.8M	int64_t carry7;
1259	69.8M	int64_t carry8;
1260	69.8M	int64_t carry9;
1261
1262		/* \|h0\| <= (1.651.652^52(1+19+19+19+19)+1.651.652^50(38+38+38+38+38))
1263		* i.e. \|h0\| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1264		* \|h1\| <= (1.651.652^51*(1+1+19+19+19+19+19+19+19+19))
1265		* i.e. \|h1\| <= 1.72^59; narrower ranges for h3, h5, h7, h9 /
1266
1267	69.8M	carry0 = h0 + (1 << 25);
1268	69.8M	h1 += carry0 >> 26;
1269	69.8M	h0 -= carry0 & kTop38Bits;
1270	69.8M	carry4 = h4 + (1 << 25);
1271	69.8M	h5 += carry4 >> 26;
1272	69.8M	h4 -= carry4 & kTop38Bits;
1273		/* \|h0\| <= 2^25 */
1274		/* \|h4\| <= 2^25 */
1275		/* \|h1\| <= 1.712^59 /
1276		/* \|h5\| <= 1.712^59 /
1277
1278	69.8M	carry1 = h1 + (1 << 24);
1279	69.8M	h2 += carry1 >> 25;
1280	69.8M	h1 -= carry1 & kTop39Bits;
1281	69.8M	carry5 = h5 + (1 << 24);
1282	69.8M	h6 += carry5 >> 25;
1283	69.8M	h5 -= carry5 & kTop39Bits;
1284		/* \|h1\| <= 2^24; from now on fits into int32 */
1285		/* \|h5\| <= 2^24; from now on fits into int32 */
1286		/* \|h2\| <= 1.412^60 /
1287		/* \|h6\| <= 1.412^60 /
1288
1289	69.8M	carry2 = h2 + (1 << 25);
1290	69.8M	h3 += carry2 >> 26;
1291	69.8M	h2 -= carry2 & kTop38Bits;
1292	69.8M	carry6 = h6 + (1 << 25);
1293	69.8M	h7 += carry6 >> 26;
1294	69.8M	h6 -= carry6 & kTop38Bits;
1295		/* \|h2\| <= 2^25; from now on fits into int32 unchanged */
1296		/* \|h6\| <= 2^25; from now on fits into int32 unchanged */
1297		/* \|h3\| <= 1.712^59 /
1298		/* \|h7\| <= 1.712^59 /
1299
1300	69.8M	carry3 = h3 + (1 << 24);
1301	69.8M	h4 += carry3 >> 25;
1302	69.8M	h3 -= carry3 & kTop39Bits;
1303	69.8M	carry7 = h7 + (1 << 24);
1304	69.8M	h8 += carry7 >> 25;
1305	69.8M	h7 -= carry7 & kTop39Bits;
1306		/* \|h3\| <= 2^24; from now on fits into int32 unchanged */
1307		/* \|h7\| <= 2^24; from now on fits into int32 unchanged */
1308		/* \|h4\| <= 1.722^34 /
1309		/* \|h8\| <= 1.412^60 /
1310
1311	69.8M	carry4 = h4 + (1 << 25);
1312	69.8M	h5 += carry4 >> 26;
1313	69.8M	h4 -= carry4 & kTop38Bits;
1314	69.8M	carry8 = h8 + (1 << 25);
1315	69.8M	h9 += carry8 >> 26;
1316	69.8M	h8 -= carry8 & kTop38Bits;
1317		/* \|h4\| <= 2^25; from now on fits into int32 unchanged */
1318		/* \|h8\| <= 2^25; from now on fits into int32 unchanged */
1319		/* \|h5\| <= 1.012^24 /
1320		/* \|h9\| <= 1.712^59 /
1321
1322	69.8M	carry9 = h9 + (1 << 24);
1323	69.8M	h0 += (carry9 >> 25) * 19;
1324	69.8M	h9 -= carry9 & kTop39Bits;
1325		/* \|h9\| <= 2^24; from now on fits into int32 unchanged */
1326		/* \|h0\| <= 1.12^39 /
1327
1328	69.8M	carry0 = h0 + (1 << 25);
1329	69.8M	h1 += carry0 >> 26;
1330	69.8M	h0 -= carry0 & kTop38Bits;
1331		/* \|h0\| <= 2^25; from now on fits into int32 unchanged */
1332		/* \|h1\| <= 1.012^24 /
1333
1334	69.8M	h[0] = (int32_t)h0;
1335	69.8M	h[1] = (int32_t)h1;
1336	69.8M	h[2] = (int32_t)h2;
1337	69.8M	h[3] = (int32_t)h3;
1338	69.8M	h[4] = (int32_t)h4;
1339	69.8M	h[5] = (int32_t)h5;
1340	69.8M	h[6] = (int32_t)h6;
1341	69.8M	h[7] = (int32_t)h7;
1342	69.8M	h[8] = (int32_t)h8;
1343	69.8M	h[9] = (int32_t)h9;
1344	69.8M	}
1345
1346		/*
1347		* h = f * f
1348		*
1349		* Can overlap h with f.
1350		*
1351		* Preconditions:
1352		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1353		*
1354		* Postconditions:
1355		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1356		*
1357		* See fe_mul.c for discussion of implementation strategy.
1358		*/
1359		static void fe_sq(fe h, const fe f)
1360	39.3M	{
1361	39.3M	int32_t f0 = f[0];
1362	39.3M	int32_t f1 = f[1];
1363	39.3M	int32_t f2 = f[2];
1364	39.3M	int32_t f3 = f[3];
1365	39.3M	int32_t f4 = f[4];
1366	39.3M	int32_t f5 = f[5];
1367	39.3M	int32_t f6 = f[6];
1368	39.3M	int32_t f7 = f[7];
1369	39.3M	int32_t f8 = f[8];
1370	39.3M	int32_t f9 = f[9];
1371	39.3M	int32_t f0_2 = 2 * f0;
1372	39.3M	int32_t f1_2 = 2 * f1;
1373	39.3M	int32_t f2_2 = 2 * f2;
1374	39.3M	int32_t f3_2 = 2 * f3;
1375	39.3M	int32_t f4_2 = 2 * f4;
1376	39.3M	int32_t f5_2 = 2 * f5;
1377	39.3M	int32_t f6_2 = 2 * f6;
1378	39.3M	int32_t f7_2 = 2 * f7;
1379	39.3M	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1380	39.3M	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1381	39.3M	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1382	39.3M	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1383	39.3M	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1384	39.3M	int64_t f0f0 = f0 * (int64_t)f0;
1385	39.3M	int64_t f0f1_2 = f0_2 * (int64_t)f1;
1386	39.3M	int64_t f0f2_2 = f0_2 * (int64_t)f2;
1387	39.3M	int64_t f0f3_2 = f0_2 * (int64_t)f3;
1388	39.3M	int64_t f0f4_2 = f0_2 * (int64_t)f4;
1389	39.3M	int64_t f0f5_2 = f0_2 * (int64_t)f5;
1390	39.3M	int64_t f0f6_2 = f0_2 * (int64_t)f6;
1391	39.3M	int64_t f0f7_2 = f0_2 * (int64_t)f7;
1392	39.3M	int64_t f0f8_2 = f0_2 * (int64_t)f8;
1393	39.3M	int64_t f0f9_2 = f0_2 * (int64_t)f9;
1394	39.3M	int64_t f1f1_2 = f1_2 * (int64_t)f1;
1395	39.3M	int64_t f1f2_2 = f1_2 * (int64_t)f2;
1396	39.3M	int64_t f1f3_4 = f1_2 * (int64_t)f3_2;
1397	39.3M	int64_t f1f4_2 = f1_2 * (int64_t)f4;
1398	39.3M	int64_t f1f5_4 = f1_2 * (int64_t)f5_2;
1399	39.3M	int64_t f1f6_2 = f1_2 * (int64_t)f6;
1400	39.3M	int64_t f1f7_4 = f1_2 * (int64_t)f7_2;
1401	39.3M	int64_t f1f8_2 = f1_2 * (int64_t)f8;
1402	39.3M	int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
1403	39.3M	int64_t f2f2 = f2 * (int64_t)f2;
1404	39.3M	int64_t f2f3_2 = f2_2 * (int64_t)f3;
1405	39.3M	int64_t f2f4_2 = f2_2 * (int64_t)f4;
1406	39.3M	int64_t f2f5_2 = f2_2 * (int64_t)f5;
1407	39.3M	int64_t f2f6_2 = f2_2 * (int64_t)f6;
1408	39.3M	int64_t f2f7_2 = f2_2 * (int64_t)f7;
1409	39.3M	int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
1410	39.3M	int64_t f2f9_38 = f2 * (int64_t)f9_38;
1411	39.3M	int64_t f3f3_2 = f3_2 * (int64_t)f3;
1412	39.3M	int64_t f3f4_2 = f3_2 * (int64_t)f4;
1413	39.3M	int64_t f3f5_4 = f3_2 * (int64_t)f5_2;
1414	39.3M	int64_t f3f6_2 = f3_2 * (int64_t)f6;
1415	39.3M	int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
1416	39.3M	int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
1417	39.3M	int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
1418	39.3M	int64_t f4f4 = f4 * (int64_t)f4;
1419	39.3M	int64_t f4f5_2 = f4_2 * (int64_t)f5;
1420	39.3M	int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
1421	39.3M	int64_t f4f7_38 = f4 * (int64_t)f7_38;
1422	39.3M	int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
1423	39.3M	int64_t f4f9_38 = f4 * (int64_t)f9_38;
1424	39.3M	int64_t f5f5_38 = f5 * (int64_t)f5_38;
1425	39.3M	int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
1426	39.3M	int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
1427	39.3M	int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
1428	39.3M	int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
1429	39.3M	int64_t f6f6_19 = f6 * (int64_t)f6_19;
1430	39.3M	int64_t f6f7_38 = f6 * (int64_t)f7_38;
1431	39.3M	int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
1432	39.3M	int64_t f6f9_38 = f6 * (int64_t)f9_38;
1433	39.3M	int64_t f7f7_38 = f7 * (int64_t)f7_38;
1434	39.3M	int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
1435	39.3M	int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
1436	39.3M	int64_t f8f8_19 = f8 * (int64_t)f8_19;
1437	39.3M	int64_t f8f9_38 = f8 * (int64_t)f9_38;
1438	39.3M	int64_t f9f9_38 = f9 * (int64_t)f9_38;
1439	39.3M	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1440	39.3M	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1441	39.3M	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1442	39.3M	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1443	39.3M	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1444	39.3M	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1445	39.3M	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1446	39.3M	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1447	39.3M	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1448	39.3M	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1449	39.3M	int64_t carry0;
1450	39.3M	int64_t carry1;
1451	39.3M	int64_t carry2;
1452	39.3M	int64_t carry3;
1453	39.3M	int64_t carry4;
1454	39.3M	int64_t carry5;
1455	39.3M	int64_t carry6;
1456	39.3M	int64_t carry7;
1457	39.3M	int64_t carry8;
1458	39.3M	int64_t carry9;
1459
1460	39.3M	carry0 = h0 + (1 << 25);
1461	39.3M	h1 += carry0 >> 26;
1462	39.3M	h0 -= carry0 & kTop38Bits;
1463	39.3M	carry4 = h4 + (1 << 25);
1464	39.3M	h5 += carry4 >> 26;
1465	39.3M	h4 -= carry4 & kTop38Bits;
1466
1467	39.3M	carry1 = h1 + (1 << 24);
1468	39.3M	h2 += carry1 >> 25;
1469	39.3M	h1 -= carry1 & kTop39Bits;
1470	39.3M	carry5 = h5 + (1 << 24);
1471	39.3M	h6 += carry5 >> 25;
1472	39.3M	h5 -= carry5 & kTop39Bits;
1473
1474	39.3M	carry2 = h2 + (1 << 25);
1475	39.3M	h3 += carry2 >> 26;
1476	39.3M	h2 -= carry2 & kTop38Bits;
1477	39.3M	carry6 = h6 + (1 << 25);
1478	39.3M	h7 += carry6 >> 26;
1479	39.3M	h6 -= carry6 & kTop38Bits;
1480
1481	39.3M	carry3 = h3 + (1 << 24);
1482	39.3M	h4 += carry3 >> 25;
1483	39.3M	h3 -= carry3 & kTop39Bits;
1484	39.3M	carry7 = h7 + (1 << 24);
1485	39.3M	h8 += carry7 >> 25;
1486	39.3M	h7 -= carry7 & kTop39Bits;
1487
1488	39.3M	carry4 = h4 + (1 << 25);
1489	39.3M	h5 += carry4 >> 26;
1490	39.3M	h4 -= carry4 & kTop38Bits;
1491	39.3M	carry8 = h8 + (1 << 25);
1492	39.3M	h9 += carry8 >> 26;
1493	39.3M	h8 -= carry8 & kTop38Bits;
1494
1495	39.3M	carry9 = h9 + (1 << 24);
1496	39.3M	h0 += (carry9 >> 25) * 19;
1497	39.3M	h9 -= carry9 & kTop39Bits;
1498
1499	39.3M	carry0 = h0 + (1 << 25);
1500	39.3M	h1 += carry0 >> 26;
1501	39.3M	h0 -= carry0 & kTop38Bits;
1502
1503	39.3M	h[0] = (int32_t)h0;
1504	39.3M	h[1] = (int32_t)h1;
1505	39.3M	h[2] = (int32_t)h2;
1506	39.3M	h[3] = (int32_t)h3;
1507	39.3M	h[4] = (int32_t)h4;
1508	39.3M	h[5] = (int32_t)h5;
1509	39.3M	h[6] = (int32_t)h6;
1510	39.3M	h[7] = (int32_t)h7;
1511	39.3M	h[8] = (int32_t)h8;
1512	39.3M	h[9] = (int32_t)h9;
1513	39.3M	}
1514
1515		static void fe_invert(fe out, const fe z)
1516	147k	{
1517	147k	fe t0;
1518	147k	fe t1;
1519	147k	fe t2;
1520	147k	fe t3;
1521	147k	int i;
1522
1523		/*
1524		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
1525		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
1526		*/
1527
1528		/* t0 = z ** 2 */
1529	147k	fe_sq(t0, z);
1530
1531		/* t1 = t0 (2 2) = z ** 8 */
1532	147k	fe_sq(t1, t0);
1533	147k	fe_sq(t1, t1);
1534
1535		/* t1 = z * t1 = z ** 9 */
1536	147k	fe_mul(t1, z, t1);
1537		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1538	147k	fe_mul(t0, t0, t1);
1539
1540		/* t2 = t0 2 = z 22 */
1541	147k	fe_sq(t2, t0);
1542
1543		/* t1 = t1 * t2 = z (2 5 - 1) */
1544	147k	fe_mul(t1, t1, t2);
1545
1546		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
1547	147k	fe_sq(t2, t1);
1548	737k	for (i = 1; i < 5; ++i) {
1549	589k	fe_sq(t2, t2);
1550	589k	}
1551
1552		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
1553	147k	fe_mul(t1, t2, t1);
1554
1555		/* Continuing similarly... */
1556
1557		/* t2 = z (2 20 - 1) */
1558	147k	fe_sq(t2, t1);
1559	1.47M	for (i = 1; i < 10; ++i) {
1560	1.32M	fe_sq(t2, t2);
1561	1.32M	}
1562	147k	fe_mul(t2, t2, t1);
1563
1564		/* t2 = z (2 40 - 1) */
1565	147k	fe_sq(t3, t2);
1566	2.94M	for (i = 1; i < 20; ++i) {
1567	2.80M	fe_sq(t3, t3);
1568	2.80M	}
1569	147k	fe_mul(t2, t3, t2);
1570
1571		/* t2 = z (2 10) * (2 ** 40 - 1) */
1572	1.62M	for (i = 0; i < 10; ++i) {
1573	1.47M	fe_sq(t2, t2);
1574	1.47M	}
1575		/* t1 = z (2 50 - 1) */
1576	147k	fe_mul(t1, t2, t1);
1577
1578		/* t2 = z (2 100 - 1) */
1579	147k	fe_sq(t2, t1);
1580	7.37M	for (i = 1; i < 50; ++i) {
1581	7.22M	fe_sq(t2, t2);
1582	7.22M	}
1583	147k	fe_mul(t2, t2, t1);
1584
1585		/* t2 = z (2 200 - 1) */
1586	147k	fe_sq(t3, t2);
1587	14.7M	for (i = 1; i < 100; ++i) {
1588	14.6M	fe_sq(t3, t3);
1589	14.6M	}
1590	147k	fe_mul(t2, t3, t2);
1591
1592		/* t2 = z ((2 50) * (2 ** 200 - 1) */
1593	147k	fe_sq(t2, t2);
1594	7.37M	for (i = 1; i < 50; ++i) {
1595	7.22M	fe_sq(t2, t2);
1596	7.22M	}
1597
1598		/* t1 = z (2 250 - 1) */
1599	147k	fe_mul(t1, t2, t1);
1600
1601		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
1602	147k	fe_sq(t1, t1);
1603	737k	for (i = 1; i < 5; ++i) {
1604	589k	fe_sq(t1, t1);
1605	589k	}
1606
1607		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
1608	147k	fe_mul(out, t1, t0);
1609	147k	}
1610
1611		/*
1612		* h = -f
1613		*
1614		* Preconditions:
1615		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1616		*
1617		* Postconditions:
1618		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1619		*/
1620		static void fe_neg(fe h, const fe f)
1621	9.43M	{
1622	9.43M	unsigned i;
1623
1624	103M	for (i = 0; i < 10; i++) {
1625	94.3M	h[i] = -f[i];
1626	94.3M	}
1627	9.43M	}
1628
1629		/*
1630		* Replace (f,g) with (g,g) if b == 1;
1631		* replace (f,g) with (f,g) if b == 0.
1632		*
1633		* Preconditions: b in {0,1}.
1634		*/
1635		static void fe_cmov(fe f, const fe g, unsigned b)
1636	254M	{
1637	254M	size_t i;
1638
1639	254M	b = 0 - b;
1640	2.80G	for (i = 0; i < 10; i++) {
1641	2.54G	int32_t x = f[i] ^ g[i];
1642	2.54G	x &= b;
1643	2.54G	f[i] ^= x;
1644	2.54G	}
1645	254M	}
1646
1647		/*
1648		* return 0 if f == 0
1649		* return 1 if f != 0
1650		*
1651		* Preconditions:
1652		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1653		*/
1654		static int fe_isnonzero(const fe f)
1655	172	{
1656	172	uint8_t s[32];
1657	172	static const uint8_t zero[32] = { 0 };
1658
1659	172	fe_tobytes(s, f);
1660
1661	172	return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1662	172	}
1663
1664		/*
1665		* return 1 if f is in {1,3,5,...,q-2}
1666		* return 0 if f is in {0,2,4,...,q-1}
1667		*
1668		* Preconditions:
1669		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1670		*/
1671		static int fe_isnegative(const fe f)
1672	254	{
1673	254	uint8_t s[32];
1674
1675	254	fe_tobytes(s, f);
1676	254	return s[0] & 1;
1677	254	}
1678
1679		/*
1680		* h = 2 * f * f
1681		*
1682		* Can overlap h with f.
1683		*
1684		* Preconditions:
1685		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1686		*
1687		* Postconditions:
1688		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1689		*
1690		* See fe_mul.c for discussion of implementation strategy.
1691		*/
1692		static void fe_sq2(fe h, const fe f)
1693	618k	{
1694	618k	int32_t f0 = f[0];
1695	618k	int32_t f1 = f[1];
1696	618k	int32_t f2 = f[2];
1697	618k	int32_t f3 = f[3];
1698	618k	int32_t f4 = f[4];
1699	618k	int32_t f5 = f[5];
1700	618k	int32_t f6 = f[6];
1701	618k	int32_t f7 = f[7];
1702	618k	int32_t f8 = f[8];
1703	618k	int32_t f9 = f[9];
1704	618k	int32_t f0_2 = 2 * f0;
1705	618k	int32_t f1_2 = 2 * f1;
1706	618k	int32_t f2_2 = 2 * f2;
1707	618k	int32_t f3_2 = 2 * f3;
1708	618k	int32_t f4_2 = 2 * f4;
1709	618k	int32_t f5_2 = 2 * f5;
1710	618k	int32_t f6_2 = 2 * f6;
1711	618k	int32_t f7_2 = 2 * f7;
1712	618k	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1713	618k	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1714	618k	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1715	618k	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1716	618k	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1717	618k	int64_t f0f0 = f0 * (int64_t)f0;
1718	618k	int64_t f0f1_2 = f0_2 * (int64_t)f1;
1719	618k	int64_t f0f2_2 = f0_2 * (int64_t)f2;
1720	618k	int64_t f0f3_2 = f0_2 * (int64_t)f3;
1721	618k	int64_t f0f4_2 = f0_2 * (int64_t)f4;
1722	618k	int64_t f0f5_2 = f0_2 * (int64_t)f5;
1723	618k	int64_t f0f6_2 = f0_2 * (int64_t)f6;
1724	618k	int64_t f0f7_2 = f0_2 * (int64_t)f7;
1725	618k	int64_t f0f8_2 = f0_2 * (int64_t)f8;
1726	618k	int64_t f0f9_2 = f0_2 * (int64_t)f9;
1727	618k	int64_t f1f1_2 = f1_2 * (int64_t)f1;
1728	618k	int64_t f1f2_2 = f1_2 * (int64_t)f2;
1729	618k	int64_t f1f3_4 = f1_2 * (int64_t)f3_2;
1730	618k	int64_t f1f4_2 = f1_2 * (int64_t)f4;
1731	618k	int64_t f1f5_4 = f1_2 * (int64_t)f5_2;
1732	618k	int64_t f1f6_2 = f1_2 * (int64_t)f6;
1733	618k	int64_t f1f7_4 = f1_2 * (int64_t)f7_2;
1734	618k	int64_t f1f8_2 = f1_2 * (int64_t)f8;
1735	618k	int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
1736	618k	int64_t f2f2 = f2 * (int64_t)f2;
1737	618k	int64_t f2f3_2 = f2_2 * (int64_t)f3;
1738	618k	int64_t f2f4_2 = f2_2 * (int64_t)f4;
1739	618k	int64_t f2f5_2 = f2_2 * (int64_t)f5;
1740	618k	int64_t f2f6_2 = f2_2 * (int64_t)f6;
1741	618k	int64_t f2f7_2 = f2_2 * (int64_t)f7;
1742	618k	int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
1743	618k	int64_t f2f9_38 = f2 * (int64_t)f9_38;
1744	618k	int64_t f3f3_2 = f3_2 * (int64_t)f3;
1745	618k	int64_t f3f4_2 = f3_2 * (int64_t)f4;
1746	618k	int64_t f3f5_4 = f3_2 * (int64_t)f5_2;
1747	618k	int64_t f3f6_2 = f3_2 * (int64_t)f6;
1748	618k	int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
1749	618k	int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
1750	618k	int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
1751	618k	int64_t f4f4 = f4 * (int64_t)f4;
1752	618k	int64_t f4f5_2 = f4_2 * (int64_t)f5;
1753	618k	int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
1754	618k	int64_t f4f7_38 = f4 * (int64_t)f7_38;
1755	618k	int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
1756	618k	int64_t f4f9_38 = f4 * (int64_t)f9_38;
1757	618k	int64_t f5f5_38 = f5 * (int64_t)f5_38;
1758	618k	int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
1759	618k	int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
1760	618k	int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
1761	618k	int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
1762	618k	int64_t f6f6_19 = f6 * (int64_t)f6_19;
1763	618k	int64_t f6f7_38 = f6 * (int64_t)f7_38;
1764	618k	int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
1765	618k	int64_t f6f9_38 = f6 * (int64_t)f9_38;
1766	618k	int64_t f7f7_38 = f7 * (int64_t)f7_38;
1767	618k	int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
1768	618k	int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
1769	618k	int64_t f8f8_19 = f8 * (int64_t)f8_19;
1770	618k	int64_t f8f9_38 = f8 * (int64_t)f9_38;
1771	618k	int64_t f9f9_38 = f9 * (int64_t)f9_38;
1772	618k	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1773	618k	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1774	618k	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1775	618k	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1776	618k	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1777	618k	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1778	618k	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1779	618k	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1780	618k	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1781	618k	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1782	618k	int64_t carry0;
1783	618k	int64_t carry1;
1784	618k	int64_t carry2;
1785	618k	int64_t carry3;
1786	618k	int64_t carry4;
1787	618k	int64_t carry5;
1788	618k	int64_t carry6;
1789	618k	int64_t carry7;
1790	618k	int64_t carry8;
1791	618k	int64_t carry9;
1792
1793	618k	h0 += h0;
1794	618k	h1 += h1;
1795	618k	h2 += h2;
1796	618k	h3 += h3;
1797	618k	h4 += h4;
1798	618k	h5 += h5;
1799	618k	h6 += h6;
1800	618k	h7 += h7;
1801	618k	h8 += h8;
1802	618k	h9 += h9;
1803
1804	618k	carry0 = h0 + (1 << 25);
1805	618k	h1 += carry0 >> 26;
1806	618k	h0 -= carry0 & kTop38Bits;
1807	618k	carry4 = h4 + (1 << 25);
1808	618k	h5 += carry4 >> 26;
1809	618k	h4 -= carry4 & kTop38Bits;
1810
1811	618k	carry1 = h1 + (1 << 24);
1812	618k	h2 += carry1 >> 25;
1813	618k	h1 -= carry1 & kTop39Bits;
1814	618k	carry5 = h5 + (1 << 24);
1815	618k	h6 += carry5 >> 25;
1816	618k	h5 -= carry5 & kTop39Bits;
1817
1818	618k	carry2 = h2 + (1 << 25);
1819	618k	h3 += carry2 >> 26;
1820	618k	h2 -= carry2 & kTop38Bits;
1821	618k	carry6 = h6 + (1 << 25);
1822	618k	h7 += carry6 >> 26;
1823	618k	h6 -= carry6 & kTop38Bits;
1824
1825	618k	carry3 = h3 + (1 << 24);
1826	618k	h4 += carry3 >> 25;
1827	618k	h3 -= carry3 & kTop39Bits;
1828	618k	carry7 = h7 + (1 << 24);
1829	618k	h8 += carry7 >> 25;
1830	618k	h7 -= carry7 & kTop39Bits;
1831
1832	618k	carry4 = h4 + (1 << 25);
1833	618k	h5 += carry4 >> 26;
1834	618k	h4 -= carry4 & kTop38Bits;
1835	618k	carry8 = h8 + (1 << 25);
1836	618k	h9 += carry8 >> 26;
1837	618k	h8 -= carry8 & kTop38Bits;
1838
1839	618k	carry9 = h9 + (1 << 24);
1840	618k	h0 += (carry9 >> 25) * 19;
1841	618k	h9 -= carry9 & kTop39Bits;
1842
1843	618k	carry0 = h0 + (1 << 25);
1844	618k	h1 += carry0 >> 26;
1845	618k	h0 -= carry0 & kTop38Bits;
1846
1847	618k	h[0] = (int32_t)h0;
1848	618k	h[1] = (int32_t)h1;
1849	618k	h[2] = (int32_t)h2;
1850	618k	h[3] = (int32_t)h3;
1851	618k	h[4] = (int32_t)h4;
1852	618k	h[5] = (int32_t)h5;
1853	618k	h[6] = (int32_t)h6;
1854	618k	h[7] = (int32_t)h7;
1855	618k	h[8] = (int32_t)h8;
1856	618k	h[9] = (int32_t)h9;
1857	618k	}
1858
1859		static void fe_pow22523(fe out, const fe z)
1860	119	{
1861	119	fe t0;
1862	119	fe t1;
1863	119	fe t2;
1864	119	int i;
1865
1866	119	fe_sq(t0, z);
1867	119	fe_sq(t1, t0);
1868	238	for (i = 1; i < 2; ++i) {
1869	119	fe_sq(t1, t1);
1870	119	}
1871	119	fe_mul(t1, z, t1);
1872	119	fe_mul(t0, t0, t1);
1873	119	fe_sq(t0, t0);
1874	119	fe_mul(t0, t1, t0);
1875	119	fe_sq(t1, t0);
1876	595	for (i = 1; i < 5; ++i) {
1877	476	fe_sq(t1, t1);
1878	476	}
1879	119	fe_mul(t0, t1, t0);
1880	119	fe_sq(t1, t0);
1881	1.19k	for (i = 1; i < 10; ++i) {
1882	1.07k	fe_sq(t1, t1);
1883	1.07k	}
1884	119	fe_mul(t1, t1, t0);
1885	119	fe_sq(t2, t1);
1886	2.38k	for (i = 1; i < 20; ++i) {
1887	2.26k	fe_sq(t2, t2);
1888	2.26k	}
1889	119	fe_mul(t1, t2, t1);
1890	119	fe_sq(t1, t1);
1891	1.19k	for (i = 1; i < 10; ++i) {
1892	1.07k	fe_sq(t1, t1);
1893	1.07k	}
1894	119	fe_mul(t0, t1, t0);
1895	119	fe_sq(t1, t0);
1896	5.95k	for (i = 1; i < 50; ++i) {
1897	5.83k	fe_sq(t1, t1);
1898	5.83k	}
1899	119	fe_mul(t1, t1, t0);
1900	119	fe_sq(t2, t1);
1901	11.9k	for (i = 1; i < 100; ++i) {
1902	11.7k	fe_sq(t2, t2);
1903	11.7k	}
1904	119	fe_mul(t1, t2, t1);
1905	119	fe_sq(t1, t1);
1906	5.95k	for (i = 1; i < 50; ++i) {
1907	5.83k	fe_sq(t1, t1);
1908	5.83k	}
1909	119	fe_mul(t0, t1, t0);
1910	119	fe_sq(t0, t0);
1911	238	for (i = 1; i < 2; ++i) {
1912	119	fe_sq(t0, t0);
1913	119	}
1914	119	fe_mul(out, t0, z);
1915	119	}
1916
1917		/*
1918		* ge means group element.
1919		*
1920		* Here the group is the set of pairs (x,y) of field elements (see fe.h)
1921		* satisfying -x^2 + y^2 = 1 + d x^2y^2
1922		* where d = -121665/121666.
1923		*
1924		* Representations:
1925		* ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1926		* ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1927		* ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1928		* ge_precomp (Duif): (y+x,y-x,2dxy)
1929		*/
1930		typedef struct {
1931		fe X;
1932		fe Y;
1933		fe Z;
1934		} ge_p2;
1935
1936		typedef struct {
1937		fe X;
1938		fe Y;
1939		fe Z;
1940		fe T;
1941		} ge_p3;
1942
1943		typedef struct {
1944		fe X;
1945		fe Y;
1946		fe Z;
1947		fe T;
1948		} ge_p1p1;
1949
1950		typedef struct {
1951		fe yplusx;
1952		fe yminusx;
1953		fe xy2d;
1954		} ge_precomp;
1955
1956		typedef struct {
1957		fe YplusX;
1958		fe YminusX;
1959		fe Z;
1960		fe T2d;
1961		} ge_cached;
1962
1963		static void ge_tobytes(uint8_t s, const ge_p2 h)
1964	116	{
1965	116	fe recip;
1966	116	fe x;
1967	116	fe y;
1968
1969	116	fe_invert(recip, h->Z);
1970	116	fe_mul(x, h->X, recip);
1971	116	fe_mul(y, h->Y, recip);
1972	116	fe_tobytes(s, y);
1973	116	s[31] ^= fe_isnegative(x) << 7;
1974	116	}
1975
1976		static void ge_p3_tobytes(uint8_t s, const ge_p3 h)
1977	22	{
1978	22	fe recip;
1979	22	fe x;
1980	22	fe y;
1981
1982	22	fe_invert(recip, h->Z);
1983	22	fe_mul(x, h->X, recip);
1984	22	fe_mul(y, h->Y, recip);
1985	22	fe_tobytes(s, y);
1986	22	s[31] ^= fe_isnegative(x) << 7;
1987	22	}
1988
1989		static const fe d = {
1990		-10913610, 13857413, -15372611, 6949391, 114729,
1991		-8787816, -6275908, -3247719, -18696448, -12055116
1992		};
1993
1994		static const fe sqrtm1 = {
1995		-32595792, -7943725, 9377950, 3500415, 12389472,
1996		-272473, -25146209, -2005654, 326686, 11406482
1997		};
1998
1999		static int ge_frombytes_vartime(ge_p3 h, const uint8_t s)
2000	119	{
2001	119	fe u;
2002	119	fe v;
2003	119	fe v3;
2004	119	fe vxx;
2005	119	fe check;
2006
2007	119	fe_frombytes(h->Y, s);
2008	119	fe_1(h->Z);
2009	119	fe_sq(u, h->Y);
2010	119	fe_mul(v, u, d);
2011	119	fe_sub(u, u, h->Z); /* u = y^2-1 */
2012	119	fe_add(v, v, h->Z); /* v = dy^2+1 */
2013
2014	119	fe_sq(v3, v);
2015	119	fe_mul(v3, v3, v); /* v3 = v^3 */
2016	119	fe_sq(h->X, v3);
2017	119	fe_mul(h->X, h->X, v);
2018	119	fe_mul(h->X, h->X, u); /* x = uv^7 */
2019
2020	119	fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
2021	119	fe_mul(h->X, h->X, v3);
2022	119	fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
2023
2024	119	fe_sq(vxx, h->X);
2025	119	fe_mul(vxx, vxx, v);
2026	119	fe_sub(check, vxx, u); /* vx^2-u */
2027	119	if (fe_isnonzero(check)) {
2028	53	fe_add(check, vxx, u); /* vx^2+u */
2029	53	if (fe_isnonzero(check)) {
2030	3	return -1;
2031	3	}
2032	50	fe_mul(h->X, h->X, sqrtm1);
2033	50	}
2034
2035	116	if (fe_isnegative(h->X) != (s[31] >> 7)) {
2036	22	fe_neg(h->X, h->X);
2037	22	}
2038
2039	116	fe_mul(h->T, h->X, h->Y);
2040	116	return 0;
2041	119	}
2042
2043		static void ge_p2_0(ge_p2 *h)
2044	116	{
2045	116	fe_0(h->X);
2046	116	fe_1(h->Y);
2047	116	fe_1(h->Z);
2048	116	}
2049
2050		static void ge_p3_0(ge_p3 *h)
2051	147k	{
2052	147k	fe_0(h->X);
2053	147k	fe_1(h->Y);
2054	147k	fe_1(h->Z);
2055	147k	fe_0(h->T);
2056	147k	}
2057
2058		static void ge_precomp_0(ge_precomp *h)
2059	9.43M	{
2060	9.43M	fe_1(h->yplusx);
2061	9.43M	fe_1(h->yminusx);
2062	9.43M	fe_0(h->xy2d);
2063	9.43M	}
2064
2065		/* r = p */
2066		static void ge_p3_to_p2(ge_p2 r, const ge_p3 p)
2067	147k	{
2068	147k	fe_copy(r->X, p->X);
2069	147k	fe_copy(r->Y, p->Y);
2070	147k	fe_copy(r->Z, p->Z);
2071	147k	}
2072
2073		static const fe d2 = {
2074		-21827239, -5839606, -30745221, 13898782, 229458,
2075		15978800, -12551817, -6495438, 29715968, 9444199
2076		};
2077
2078		/* r = p */
2079		static void ge_p3_to_cached(ge_cached r, const ge_p3 p)
2080	928	{
2081	928	fe_add(r->YplusX, p->Y, p->X);
2082	928	fe_sub(r->YminusX, p->Y, p->X);
2083	928	fe_copy(r->Z, p->Z);
2084	928	fe_mul(r->T2d, p->T, d2);
2085	928	}
2086
2087		/* r = p */
2088		static void ge_p1p1_to_p2(ge_p2 r, const ge_p1p1 p)
2089	471k	{
2090	471k	fe_mul(r->X, p->X, p->T);
2091	471k	fe_mul(r->Y, p->Y, p->Z);
2092	471k	fe_mul(r->Z, p->Z, p->T);
2093	471k	}
2094
2095		/* r = p */
2096		static void ge_p1p1_to_p3(ge_p3 r, const ge_p1p1 p)
2097	9.58M	{
2098	9.58M	fe_mul(r->X, p->X, p->T);
2099	9.58M	fe_mul(r->Y, p->Y, p->Z);
2100	9.58M	fe_mul(r->Z, p->Z, p->T);
2101	9.58M	fe_mul(r->T, p->X, p->Y);
2102	9.58M	}
2103
2104		/* r = 2 * p */
2105		static void ge_p2_dbl(ge_p1p1 r, const ge_p2 p)
2106	618k	{
2107	618k	fe t0;
2108
2109	618k	fe_sq(r->X, p->X);
2110	618k	fe_sq(r->Z, p->Y);
2111	618k	fe_sq2(r->T, p->Z);
2112	618k	fe_add(r->Y, p->X, p->Y);
2113	618k	fe_sq(t0, r->Y);
2114	618k	fe_add(r->Y, r->Z, r->X);
2115	618k	fe_sub(r->Z, r->Z, r->X);
2116	618k	fe_sub(r->X, t0, r->Y);
2117	618k	fe_sub(r->T, r->T, r->Z);
2118	618k	}
2119
2120		/* r = 2 * p */
2121		static void ge_p3_dbl(ge_p1p1 r, const ge_p3 p)
2122	147k	{
2123	147k	ge_p2 q;
2124	147k	ge_p3_to_p2(&q, p);
2125	147k	ge_p2_dbl(r, &q);
2126	147k	}
2127
2128		/* r = p + q */
2129		static void ge_madd(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2130	9.43M	{
2131	9.43M	fe t0;
2132
2133	9.43M	fe_add(r->X, p->Y, p->X);
2134	9.43M	fe_sub(r->Y, p->Y, p->X);
2135	9.43M	fe_mul(r->Z, r->X, q->yplusx);
2136	9.43M	fe_mul(r->Y, r->Y, q->yminusx);
2137	9.43M	fe_mul(r->T, q->xy2d, p->T);
2138	9.43M	fe_add(t0, p->Z, p->Z);
2139	9.43M	fe_sub(r->X, r->Z, r->Y);
2140	9.43M	fe_add(r->Y, r->Z, r->Y);
2141	9.43M	fe_add(r->Z, t0, r->T);
2142	9.43M	fe_sub(r->T, t0, r->T);
2143	9.43M	}
2144
2145		/* r = p - q */
2146		static void ge_msub(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2147	588	{
2148	588	fe t0;
2149
2150	588	fe_add(r->X, p->Y, p->X);
2151	588	fe_sub(r->Y, p->Y, p->X);
2152	588	fe_mul(r->Z, r->X, q->yminusx);
2153	588	fe_mul(r->Y, r->Y, q->yplusx);
2154	588	fe_mul(r->T, q->xy2d, p->T);
2155	588	fe_add(t0, p->Z, p->Z);
2156	588	fe_sub(r->X, r->Z, r->Y);
2157	588	fe_add(r->Y, r->Z, r->Y);
2158	588	fe_sub(r->Z, t0, r->T);
2159	588	fe_add(r->T, t0, r->T);
2160	588	}
2161
2162		/* r = p + q */
2163		static void ge_add(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2164	3.25k	{
2165	3.25k	fe t0;
2166
2167	3.25k	fe_add(r->X, p->Y, p->X);
2168	3.25k	fe_sub(r->Y, p->Y, p->X);
2169	3.25k	fe_mul(r->Z, r->X, q->YplusX);
2170	3.25k	fe_mul(r->Y, r->Y, q->YminusX);
2171	3.25k	fe_mul(r->T, q->T2d, p->T);
2172	3.25k	fe_mul(r->X, p->Z, q->Z);
2173	3.25k	fe_add(t0, r->X, r->X);
2174	3.25k	fe_sub(r->X, r->Z, r->Y);
2175	3.25k	fe_add(r->Y, r->Z, r->Y);
2176	3.25k	fe_add(r->Z, t0, r->T);
2177	3.25k	fe_sub(r->T, t0, r->T);
2178	3.25k	}
2179
2180		/* r = p - q */
2181		static void ge_sub(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2182	2.47k	{
2183	2.47k	fe t0;
2184
2185	2.47k	fe_add(r->X, p->Y, p->X);
2186	2.47k	fe_sub(r->Y, p->Y, p->X);
2187	2.47k	fe_mul(r->Z, r->X, q->YminusX);
2188	2.47k	fe_mul(r->Y, r->Y, q->YplusX);
2189	2.47k	fe_mul(r->T, q->T2d, p->T);
2190	2.47k	fe_mul(r->X, p->Z, q->Z);
2191	2.47k	fe_add(t0, r->X, r->X);
2192	2.47k	fe_sub(r->X, r->Z, r->Y);
2193	2.47k	fe_add(r->Y, r->Z, r->Y);
2194	2.47k	fe_sub(r->Z, t0, r->T);
2195	2.47k	fe_add(r->T, t0, r->T);
2196	2.47k	}
2197
2198		static uint8_t equal(signed char b, signed char c)
2199	75.4M	{
2200	75.4M	uint8_t ub = b;
2201	75.4M	uint8_t uc = c;
2202	75.4M	uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2203	75.4M	uint32_t y = x; /* 0: yes; 1..255: no */
2204	75.4M	y -= 1; /* 4294967295: yes; 0..254: no */
2205	75.4M	y >>= 31; /* 1: yes; 0: no */
2206	75.4M	return y;
2207	75.4M	}
2208
2209		static void cmov(ge_precomp t, const ge_precomp u, uint8_t b)
2210	84.8M	{
2211	84.8M	fe_cmov(t->yplusx, u->yplusx, b);
2212	84.8M	fe_cmov(t->yminusx, u->yminusx, b);
2213	84.8M	fe_cmov(t->xy2d, u->xy2d, b);
2214	84.8M	}
2215
2216		/* k25519Precomp[i][j] = (j+1)256^iB */
2217		static const ge_precomp k25519Precomp[32][8] = {
2218		{
2219		{
2220		{ 25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2221		27544626, -11754271, -6079156, 2047605 },
2222		{ -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2223		5043384, 19500929, -15469378 },
2224		{ -8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2225		29287919, 11864899, -24514362, -4438546 },
2226		},
2227		{
2228		{ -12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2229		-11717903, -3814571, -358445, -10211303 },
2230		{ -21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2231		-15616551, 11189268, -26829678, -5319081 },
2232		{ 26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2233		-3128826, -9541118, -15472047, -4166697 },
2234		},
2235		{
2236		{ 15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2237		27787600, -14772189, 28944400, -1550024 },
2238		{ 16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2239		16354577, -11775962, 7689662, 11199574 },
2240		{ 30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2241		7512774, 10017326, -17749093, -9920357 },
2242		},
2243		{
2244		{ -17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2245		-28926210, 15006023, 3284568, -6276540 },
2246		{ 23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2247		7464579, 9656445, 13059162, 10374397 },
2248		{ 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2249		-3839045, -641708, -101325 },
2250		},
2251		{
2252		{ 10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2253		32867885, 14515107, -15438304, 10819380 },
2254		{ 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2255		12483688, -12668491, 5581306 },
2256		{ 19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2257		28542350, 13850243, -23678021, -15815942 },
2258		},
2259		{
2260		{ -15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2261		-19188627, -15224819, -9818940, -12085777 },
2262		{ -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2263		-15689887, 1762328, 14866737 },
2264		{ -18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2265		-28236412, 3959421, 27914454, 4383652 },
2266		},
2267		{
2268		{ 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2269		5230134, -23952439, -15175766 },
2270		{ -30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2271		20654025, 16520125, 30598449, 7715701 },
2272		{ 28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2273		-31400660, 1370708, 29794553, -1409300 },
2274		},
2275		{
2276		{ 14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2277		30290735, 10876454, -33154098, 2381726 },
2278		{ -7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2279		-6236617, 3696005, -32300832, 15351955 },
2280		{ 27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2281		-32961401, -2970515, 29551813, 10109425 },
2282		},
2283		},
2284		{
2285		{
2286		{ -13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2287		-2378284, -1627556, 10092783, -4764171 },
2288		{ 27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2289		-32508754, 12005538, -17810127, 12803510 },
2290		{ 17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2291		30364213, -9038194, 18016357, 4397660 },
2292		},
2293		{
2294		{ -10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2295		-26619106, 14544525, -17477504, 982639 },
2296		{ 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2297		-4120128, -21047696, 9934963 },
2298		{ 5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2299		-14747930, 4559895, -30123922, -10897950 },
2300		},
2301		{
2302		{ -27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2303		24191034, 4541697, -13338309, 5500568 },
2304		{ 12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2305		-17430592, 12264343, 10874051, 13524335 },
2306		{ 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2307		5080568, -22528059, 5376628 },
2308		},
2309		{
2310		{ -26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2311		-22321305, -9447443, 4535768, 1569007 },
2312		{ -2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2313		-30494562, 3044290, 31848280, 12543772 },
2314		{ -22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2315		-27377195, -2062731, 7718482, 14474653 },
2316		},
2317		{
2318		{ 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2319		-7236665, 24316168, -5253567 },
2320		{ 13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2321		33040651, -13424532, -20729456, 8321686 },
2322		{ 21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
2323		23845965, -11874838, -9984458, 608372 },
2324		},
2325		{
2326		{ -13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
2327		1123968, -6780577, 27229399, 23887 },
2328		{ -23244140, -294205, -11744728, 14712571, -29465699, -2029617,
2329		12797024, -6440308, -1633405, 16678954 },
2330		{ -29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
2331		-1508144, -4795045, -17169265, 4904953 },
2332		},
2333		{
2334		{ 24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
2335		5169211, 16191880, 2128236, -4326833 },
2336		{ -16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
2337		-29806336, 916033, -6882542, -2986532 },
2338		{ -22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
2339		285431, 2763829, 15736322, 4143876 },
2340		},
2341		{
2342		{ 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
2343		-14594663, 23527084, -16458268 },
2344		{ 33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
2345		-32625340, 4087881, -15188911, -14416214 },
2346		{ 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
2347		4357868, -4774191, -16323038 },
2348		},
2349		},
2350		{
2351		{
2352		{ 6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
2353		23365147, -3949732, 7390890, 2759800 },
2354		{ 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
2355		-4264057, 1244380, -12919645 },
2356		{ -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
2357		9208236, 15886429, 16489664 },
2358		},
2359		{
2360		{ 1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
2361		-13693198, 398369, -30606455, -712933 },
2362		{ -25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
2363		13348553, 12076947, -30836462, 5113182 },
2364		{ -17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
2365		-30341101, -7336386, 13847711, 5387222 },
2366		},
2367		{
2368		{ -18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
2369		8763061, 3617786, -19600662, 10370991 },
2370		{ 20246567, -14369378, 22358229, -543712, 18507283, -10413996,
2371		14554437, -8746092, 32232924, 16763880 },
2372		{ 9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
2373		11094161, 15689506, 3140038, -16510092 },
2374		},
2375		{
2376		{ -16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
2377		-27224800, 9448613, -28774454, 366295 },
2378		{ 19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
2379		28344573, 8041113, 719605, 11671788 },
2380		{ 8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
2381		-15266516, 27000813, -10195553 },
2382		},
2383		{
2384		{ -15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
2385		5336097, 6750977, -14521026 },
2386		{ 11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
2387		1695823, -8819122, 8169720, 16220347 },
2388		{ -18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
2389		-11144307, -2627664, -5990708, -14166033 },
2390		},
2391		{
2392		{ -23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
2393		27884329, 2847284, 2655861, 1738395 },
2394		{ -27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
2395		21651608, -3239336, -19087449, -11005278 },
2396		{ 1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
2397		5821408, 10478196, 8544890 },
2398		},
2399		{
2400		{ 32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
2401		19270449, 12217473, 17789017, -3395995 },
2402		{ -30552961, -2228401, -15578829, -10147201, 13243889, 517024,
2403		15479401, -3853233, 30460520, 1052596 },
2404		{ -11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
2405		27491595, -4612359, 3179268, -9478891 },
2406		},
2407		{
2408		{ 31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
2409		-14756777, -16411740, 19072640, -9511060 },
2410		{ 11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
2411		5977896, -5215017, 473099, 5040608 },
2412		{ -20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
2413		28326862, 1721092, -19558642, -3131606 },
2414		},
2415		},
2416		{
2417		{
2418		{ 7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
2419		8076149, -27868496, 11538389 },
2420		{ -19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
2421		8754525, 7446702, -5676054, 5797016 },
2422		{ -11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
2423		2014099, -9050574, -2369172, -5877341 },
2424		},
2425		{
2426		{ -22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
2427		1192730, -3714199, 15123619, 10811505 },
2428		{ 14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
2429		15776356, -28886779, -11974553 },
2430		{ -28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
2431		-20654173, -16484855, 4714547, -9600655 },
2432		},
2433		{
2434		{ 15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
2435		24611599, -4543832, -11745876, 12340220 },
2436		{ 12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
2437		9613953, 8241152, 15370987, 9608631 },
2438		{ -4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
2439		15866074, -28210621, -8814099 },
2440		},
2441		{
2442		{ 26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
2443		858697, 20571223, 8420556 },
2444		{ 14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
2445		33531827, 12516406, -21574435, -12476749 },
2446		{ 236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
2447		7256740, 8791136, 15069930 },
2448		},
2449		{
2450		{ 1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
2451		14711875, 4874229, -30663140, -2331391 },
2452		{ 5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
2453		-7912378, -33069337, 9234253 },
2454		{ 20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
2455		31559055, -11609587, 18979186, 13396066 },
2456		},
2457		{
2458		{ 24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
2459		-18816887, 13594782, 33514650, 7021958 },
2460		{ -11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
2461		-25948728, -3916677, -21480480, 12868082 },
2462		{ -28635013, 13504661, 19988037, -2132761, 21078225, 6443208,
2463		-21446107, 2244500, -12455797, -8089383 },
2464		},
2465		{
2466		{ -30595528, 13793479, -5852820, 319136, -25723172, -6263899,
2467		33086546, 8957937, -15233648, 5540521 },
2468		{ -11630176, -11503902, -8119500, -7643073, 2620056, 1022908,
2469		-23710744, -1568984, -16128528, -14962807 },
2470		{ 23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819,
2471		892185, -11513277, -15205948 },
2472		},
2473		{
2474		{ 9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819,
2475		4763127, -19179614, 5867134 },
2476		{ -32765025, 1927590, 31726409, -4753295, 23962434, -16019500,
2477		27846559, 5931263, -29749703, -16108455 },
2478		{ 27461885, -2977536, 22380810, 1815854, -23033753, -3031938,
2479		7283490, -15148073, -19526700, 7734629 },
2480		},
2481		},
2482		{
2483		{
2484		{ -8010264, -9590817, -11120403, 6196038, 29344158, -13430885,
2485		7585295, -3176626, 18549497, 15302069 },
2486		{ -32658337, -6171222, -7672793, -11051681, 6258878, 13504381,
2487		10458790, -6418461, -8872242, 8424746 },
2488		{ 24687205, 8613276, -30667046, -3233545, 1863892, -1830544,
2489		19206234, 7134917, -11284482, -828919 },
2490		},
2491		{
2492		{ 11334899, -9218022, 8025293, 12707519, 17523892, -10476071,
2493		10243738, -14685461, -5066034, 16498837 },
2494		{ 8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
2495		-14124238, 6536641, 10543906 },
2496		{ -28946384, 15479763, -17466835, 568876, -1497683, 11223454,
2497		-2669190, -16625574, -27235709, 8876771 },
2498		},
2499		{
2500		{ -25742899, -12566864, -15649966, -846607, -33026686, -796288,
2501		-33481822, 15824474, -604426, -9039817 },
2502		{ 10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697,
2503		-4890037, 1657394, 3084098 },
2504		{ 10477963, -7470260, 12119566, -13250805, 29016247, -5365589,
2505		31280319, 14396151, -30233575, 15272409 },
2506		},
2507		{
2508		{ -12288309, 3169463, 28813183, 16658753, 25116432, -5630466,
2509		-25173957, -12636138, -25014757, 1950504 },
2510		{ -26180358, 9489187, 11053416, -14746161, -31053720, 5825630,
2511		-8384306, -8767532, 15341279, 8373727 },
2512		{ 28685821, 7759505, -14378516, -12002860, -31971820, 4079242,
2513		298136, -10232602, -2878207, 15190420 },
2514		},
2515		{
2516		{ -32932876, 13806336, -14337485, -15794431, -24004620, 10940928,
2517		8669718, 2742393, -26033313, -6875003 },
2518		{ -1580388, -11729417, -25979658, -11445023, -17411874, -10912854,
2519		9291594, -16247779, -12154742, 6048605 },
2520		{ -30305315, 14843444, 1539301, 11864366, 20201677, 1900163,
2521		13934231, 5128323, 11213262, 9168384 },
2522		},
2523		{
2524		{ -26280513, 11007847, 19408960, -940758, -18592965, -4328580,
2525		-5088060, -11105150, 20470157, -16398701 },
2526		{ -23136053, 9282192, 14855179, -15390078, -7362815, -14408560,
2527		-22783952, 14461608, 14042978, 5230683 },
2528		{ 29969567, -2741594, -16711867, -8552442, 9175486, -2468974,
2529		21556951, 3506042, -5933891, -12449708 },
2530		},
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4239		{
4240		{ 30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
4241		-23827587, 5096219, 22740376, -7303417 },
4242		{ 2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
4243		24051124, 13742383, -15637599, 13295222 },
4244		{ 33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
4245		-17720195, -4612972, -4451357, -14669444 },
4246		},
4247		{
4248		{ -20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
4249		-2469266, -4141880, 7770569, 9620597 },
4250		{ 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
4251		-1694323, -33502340, -14767970 },
4252		{ 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
4253		1220118, 30494170, -11440799 },
4254		},
4255		{
4256		{ -5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
4257		-26739026, 926050, -1684339, -13333647 },
4258		{ 13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
4259		9021034, 9078865, 3353509, 4033511 },
4260		{ -29663431, -15113610, 32259991, -344482, 24295849, -12912123,
4261		23161163, 8839127, 27485041, 7356032 },
4262		},
4263		},
4264		{
4265		{
4266		{ 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
4267		2625015, 28431036, -16771834 },
4268		{ -23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
4269		-22545972, 14150565, 15970762, 4099461 },
4270		{ 29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
4271		13617293, -9937143, 11465739, 8317062 },
4272		},
4273		{
4274		{ -25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
4275		14898637, 3848455, 20969334, -5157516 },
4276		{ -20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
4277		-21610826, -3649888, 11177095, 14989547 },
4278		{ -24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
4279		13515641, 2581286, -28487508, 9930240 },
4280		},
4281		{
4282		{ -17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
4283		18345767, -13403753, 16291481, -5314038 },
4284		{ -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
4285		6957617, 4368891, 9788741 },
4286		{ 16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
4287		-21722536, -8613148, 16250552, -11111103 },
4288		},
4289		{
4290		{ -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
4291		10604807, -30190403, 4782747 },
4292		{ -1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
4293		-9981571, 4383045, 22546403, 437323 },
4294		{ 31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
4295		27343084, 2786261, -30633590, -14097016 },
4296		},
4297		{
4298		{ -14467279, -683715, -33374107, 7448552, 19294360, 14334329,
4299		-19690631, 2355319, -19284671, -6114373 },
4300		{ 15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
4301		18952177, 15496498, -29380133, 11754228 },
4302		{ -2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
4303		7141596, 11724556, 22761615, -10134141 },
4304		},
4305		{
4306		{ 16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
4307		-28741185, -12227393, 32851222, 11717399 },
4308		{ 11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
4309		31474879, 3483633, -1193175, -4030831 },
4310		{ -185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4311		33142652, 6546660, -19985279, -3948376 },
4312		},
4313		{
4314		{ -32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4315		-8537131, -12833048, -30772034, -15486313 },
4316		{ -18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4317		-31135347, -16049879, 10928917, 3011958 },
4318		{ -6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4319		-30831056, -12805180, 18008031, 10258577 },
4320		},
4321		{
4322		{ -22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4323		-1853465, 1367120, 25127874, 6671743 },
4324		{ 29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4325		21382910, 11042292, 25838796, 4642684 },
4326		{ -20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4327		30468147, -13900640, 18423289, 4177476 },
4328		},
4329		},
4330		};
4331
4332		static uint8_t negative(signed char b)
4333	9.43M	{
4334	9.43M	uint32_t x = b;
4335
4336	9.43M	x >>= 31; /* 1: yes; 0: no */
4337	9.43M	return x;
4338	9.43M	}
4339
4340		static void table_select(ge_precomp *t, int pos, signed char b)
4341	9.43M	{
4342	9.43M	ge_precomp minust;
4343	9.43M	uint8_t bnegative = negative(b);
4344	9.43M	uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4345
4346	9.43M	ge_precomp_0(t);
4347	9.43M	cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4348	9.43M	cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4349	9.43M	cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4350	9.43M	cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4351	9.43M	cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4352	9.43M	cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4353	9.43M	cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4354	9.43M	cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4355	9.43M	fe_copy(minust.yplusx, t->yminusx);
4356	9.43M	fe_copy(minust.yminusx, t->yplusx);
4357	9.43M	fe_neg(minust.xy2d, t->xy2d);
4358	9.43M	cmov(t, &minust, bnegative);
4359	9.43M	}
4360
4361		/*
4362		* h = a * B
4363		*
4364		* where a = a[0]+256*a[1]+...+256^31 a[31]
4365		* B is the Ed25519 base point (x,4/5) with x positive.
4366		*
4367		* Preconditions:
4368		* a[31] <= 127
4369		*/
4370		static void ge_scalarmult_base(ge_p3 h, const uint8_t a)
4371	147k	{
4372	147k	signed char e[64];
4373	147k	signed char carry;
4374	147k	ge_p1p1 r;
4375	147k	ge_p2 s;
4376	147k	ge_precomp t;
4377	147k	int i;
4378
4379	4.86M	for (i = 0; i < 32; ++i) {
4380	4.71M	e[2 * i + 0] = (a[i] >> 0) & 15;
4381	4.71M	e[2 * i + 1] = (a[i] >> 4) & 15;
4382	4.71M	}
4383		/* each e[i] is between 0 and 15 */
4384		/* e[63] is between 0 and 7 */
4385
4386	147k	carry = 0;
4387	9.43M	for (i = 0; i < 63; ++i) {
4388	9.28M	e[i] += carry;
4389	9.28M	carry = e[i] + 8;
4390	9.28M	carry >>= 4;
4391	9.28M	e[i] -= carry << 4;
4392	9.28M	}
4393	147k	e[63] += carry;
4394		/* each e[i] is between -8 and 8 */
4395
4396	147k	ge_p3_0(h);
4397	4.86M	for (i = 1; i < 64; i += 2) {
4398	4.71M	table_select(&t, i / 2, e[i]);
4399	4.71M	ge_madd(&r, h, &t);
4400	4.71M	ge_p1p1_to_p3(h, &r);
4401	4.71M	}
4402
4403	147k	ge_p3_dbl(&r, h);
4404	147k	ge_p1p1_to_p2(&s, &r);
4405	147k	ge_p2_dbl(&r, &s);
4406	147k	ge_p1p1_to_p2(&s, &r);
4407	147k	ge_p2_dbl(&r, &s);
4408	147k	ge_p1p1_to_p2(&s, &r);
4409	147k	ge_p2_dbl(&r, &s);
4410	147k	ge_p1p1_to_p3(h, &r);
4411
4412	4.86M	for (i = 0; i < 64; i += 2) {
4413	4.71M	table_select(&t, i / 2, e[i]);
4414	4.71M	ge_madd(&r, h, &t);
4415	4.71M	ge_p1p1_to_p3(h, &r);
4416	4.71M	}
4417
4418	147k	OPENSSL_cleanse(e, sizeof(e));
4419	147k	}
4420
4421		#if !defined(BASE_2_51_IMPLEMENTED)
4422		/*
4423		* Replace (f,g) with (g,f) if b == 1;
4424		* replace (f,g) with (f,g) if b == 0.
4425		*
4426		* Preconditions: b in {0,1}.
4427		*/
4428		static void fe_cswap(fe f, fe g, unsigned int b)
4429		{
4430		size_t i;
4431
4432		b = 0 - b;
4433		for (i = 0; i < 10; i++) {
4434		int32_t x = f[i] ^ g[i];
4435		x &= b;
4436		f[i] ^= x;
4437		g[i] ^= x;
4438		}
4439		}
4440
4441		/*
4442		* h = f * 121666
4443		*
4444		* Can overlap h with f.
4445		*
4446		* Preconditions:
4447		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
4448		*
4449		* Postconditions:
4450		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
4451		*/
4452		static void fe_mul121666(fe h, fe f)
4453		{
4454		int32_t f0 = f[0];
4455		int32_t f1 = f[1];
4456		int32_t f2 = f[2];
4457		int32_t f3 = f[3];
4458		int32_t f4 = f[4];
4459		int32_t f5 = f[5];
4460		int32_t f6 = f[6];
4461		int32_t f7 = f[7];
4462		int32_t f8 = f[8];
4463		int32_t f9 = f[9];
4464		int64_t h0 = f0 * (int64_t)121666;
4465		int64_t h1 = f1 * (int64_t)121666;
4466		int64_t h2 = f2 * (int64_t)121666;
4467		int64_t h3 = f3 * (int64_t)121666;
4468		int64_t h4 = f4 * (int64_t)121666;
4469		int64_t h5 = f5 * (int64_t)121666;
4470		int64_t h6 = f6 * (int64_t)121666;
4471		int64_t h7 = f7 * (int64_t)121666;
4472		int64_t h8 = f8 * (int64_t)121666;
4473		int64_t h9 = f9 * (int64_t)121666;
4474		int64_t carry0;
4475		int64_t carry1;
4476		int64_t carry2;
4477		int64_t carry3;
4478		int64_t carry4;
4479		int64_t carry5;
4480		int64_t carry6;
4481		int64_t carry7;
4482		int64_t carry8;
4483		int64_t carry9;
4484
4485		carry9 = h9 + (1 << 24);
4486		h0 += (carry9 >> 25) * 19;
4487		h9 -= carry9 & kTop39Bits;
4488		carry1 = h1 + (1 << 24);
4489		h2 += carry1 >> 25;
4490		h1 -= carry1 & kTop39Bits;
4491		carry3 = h3 + (1 << 24);
4492		h4 += carry3 >> 25;
4493		h3 -= carry3 & kTop39Bits;
4494		carry5 = h5 + (1 << 24);
4495		h6 += carry5 >> 25;
4496		h5 -= carry5 & kTop39Bits;
4497		carry7 = h7 + (1 << 24);
4498		h8 += carry7 >> 25;
4499		h7 -= carry7 & kTop39Bits;
4500
4501		carry0 = h0 + (1 << 25);
4502		h1 += carry0 >> 26;
4503		h0 -= carry0 & kTop38Bits;
4504		carry2 = h2 + (1 << 25);
4505		h3 += carry2 >> 26;
4506		h2 -= carry2 & kTop38Bits;
4507		carry4 = h4 + (1 << 25);
4508		h5 += carry4 >> 26;
4509		h4 -= carry4 & kTop38Bits;
4510		carry6 = h6 + (1 << 25);
4511		h7 += carry6 >> 26;
4512		h6 -= carry6 & kTop38Bits;
4513		carry8 = h8 + (1 << 25);
4514		h9 += carry8 >> 26;
4515		h8 -= carry8 & kTop38Bits;
4516
4517		h[0] = (int32_t)h0;
4518		h[1] = (int32_t)h1;
4519		h[2] = (int32_t)h2;
4520		h[3] = (int32_t)h3;
4521		h[4] = (int32_t)h4;
4522		h[5] = (int32_t)h5;
4523		h[6] = (int32_t)h6;
4524		h[7] = (int32_t)h7;
4525		h[8] = (int32_t)h8;
4526		h[9] = (int32_t)h9;
4527		}
4528
4529		static void x25519_scalar_mult_generic(uint8_t out[32],
4530		const uint8_t scalar[32],
4531		const uint8_t point[32])
4532		{
4533		fe x1, x2, z2, x3, z3, tmp0, tmp1;
4534		uint8_t e[32];
4535		unsigned swap = 0;
4536		int pos;
4537
4538		memcpy(e, scalar, 32);
4539		e[0] &= 248;
4540		e[31] &= 127;
4541		e[31] \|= 64;
4542		fe_frombytes(x1, point);
4543		fe_1(x2);
4544		fe_0(z2);
4545		fe_copy(x3, x1);
4546		fe_1(z3);
4547
4548		for (pos = 254; pos >= 0; --pos) {
4549		unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4550		swap ^= b;
4551		fe_cswap(x2, x3, swap);
4552		fe_cswap(z2, z3, swap);
4553		swap = b;
4554		fe_sub(tmp0, x3, z3);
4555		fe_sub(tmp1, x2, z2);
4556		fe_add(x2, x2, z2);
4557		fe_add(z2, x3, z3);
4558		fe_mul(z3, tmp0, x2);
4559		fe_mul(z2, z2, tmp1);
4560		fe_sq(tmp0, tmp1);
4561		fe_sq(tmp1, x2);
4562		fe_add(x3, z3, z2);
4563		fe_sub(z2, z3, z2);
4564		fe_mul(x2, tmp1, tmp0);
4565		fe_sub(tmp1, tmp1, tmp0);
4566		fe_sq(z2, z2);
4567		fe_mul121666(z3, tmp1);
4568		fe_sq(x3, x3);
4569		fe_add(tmp0, tmp0, z3);
4570		fe_mul(z3, x1, z2);
4571		fe_mul(z2, tmp1, tmp0);
4572		}
4573
4574		fe_invert(z2, z2);
4575		fe_mul(x2, x2, z2);
4576		fe_tobytes(out, x2);
4577
4578		OPENSSL_cleanse(e, sizeof(e));
4579		}
4580
4581		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4582		const uint8_t point[32])
4583		{
4584		x25519_scalar_mult_generic(out, scalar, point);
4585		}
4586		#endif
4587
4588		static void slide(signed char r, const uint8_t a)
4589	232	{
4590	232	int i;
4591	232	int b;
4592	232	int k;
4593
4594	59.6k	for (i = 0; i < 256; ++i) {
4595	59.3k	r[i] = 1 & (a[i >> 3] >> (i & 7));
4596	59.3k	}
4597
4598	59.6k	for (i = 0; i < 256; ++i) {
4599	59.3k	if (r[i]) {
4600	39.9k	for (b = 1; b <= 6 && i + b < 256; ++b) {
4601	37.5k	if (r[i + b]) {
4602	16.4k	if (r[i] + (r[i + b] << b) <= 15) {
4603	9.11k	r[i] += r[i + b] << b;
4604	9.11k	r[i + b] = 0;
4605	9.11k	} else if (r[i] - (r[i + b] << b) >= -15) {
4606	3.06k	r[i] -= r[i + b] << b;
4607	9.52k	for (k = i + b; k < 256; ++k) {
4608	9.52k	if (!r[k]) {
4609	3.06k	r[k] = 1;
4610	3.06k	break;
4611	3.06k	}
4612	6.46k	r[k] = 0;
4613	6.46k	}
4614	4.29k	} else {
4615	4.29k	break;
4616	4.29k	}
4617	16.4k	}
4618	37.5k	}
4619	6.75k	}
4620	59.3k	}
4621	232	}
4622
4623		static const ge_precomp Bi[8] = {
4624		{
4625		{ 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4626		-11754271, -6079156, 2047605 },
4627		{ -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4628		5043384, 19500929, -15469378 },
4629		{ -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4630		11864899, -24514362, -4438546 },
4631		},
4632		{
4633		{ 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4634		-14772189, 28944400, -1550024 },
4635		{ 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4636		-11775962, 7689662, 11199574 },
4637		{ 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4638		10017326, -17749093, -9920357 },
4639		},
4640		{
4641		{ 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4642		14515107, -15438304, 10819380 },
4643		{ 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4644		12483688, -12668491, 5581306 },
4645		{ 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4646		13850243, -23678021, -15815942 },
4647		},
4648		{
4649		{ 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4650		5230134, -23952439, -15175766 },
4651		{ -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4652		16520125, 30598449, 7715701 },
4653		{ 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4654		1370708, 29794553, -1409300 },
4655		},
4656		{
4657		{ -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4658		-1361450, -13062696, 13821877 },
4659		{ -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4660		-7212327, 18853322, -14220951 },
4661		{ 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4662		-10431137, 2207753, -3209784 },
4663		},
4664		{
4665		{ -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4666		-663000, -31111463, -16132436 },
4667		{ 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4668		15725684, 171356, 6466918 },
4669		{ 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4670		-14088058, -30714912, 16193877 },
4671		},
4672		{
4673		{ -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4674		4729455, -18074513, 9256800 },
4675		{ -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4676		9761698, -19827198, 630305 },
4677		{ -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4678		-15960994, -2449256, -14291300 },
4679		},
4680		{
4681		{ -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4682		15033784, 25105118, -7894876 },
4683		{ -24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4684		1573892, -2625887, 2198790, -15804619 },
4685		{ -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4686		-16236442, -32461234, -12290683 },
4687		},
4688		};
4689
4690		/*
4691		* r = a * A + b * B
4692		*
4693		* where a = a[0]+256*a[1]+...+256^31 a[31].
4694		* and b = b[0]+256*b[1]+...+256^31 b[31].
4695		* B is the Ed25519 base point (x,4/5) with x positive.
4696		*/
4697		static void ge_double_scalarmult_vartime(ge_p2 r, const uint8_t a,
4698		const ge_p3 A, const uint8_t b)
4699	116	{
4700	116	signed char aslide[256];
4701	116	signed char bslide[256];
4702	116	ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4703	116	ge_p1p1 t;
4704	116	ge_p3 u;
4705	116	ge_p3 A2;
4706	116	int i;
4707
4708	116	slide(aslide, a);
4709	116	slide(bslide, b);
4710
4711	116	ge_p3_to_cached(&Ai[0], A);
4712	116	ge_p3_dbl(&t, A);
4713	116	ge_p1p1_to_p3(&A2, &t);
4714	116	ge_add(&t, &A2, &Ai[0]);
4715	116	ge_p1p1_to_p3(&u, &t);
4716	116	ge_p3_to_cached(&Ai[1], &u);
4717	116	ge_add(&t, &A2, &Ai[1]);
4718	116	ge_p1p1_to_p3(&u, &t);
4719	116	ge_p3_to_cached(&Ai[2], &u);
4720	116	ge_add(&t, &A2, &Ai[2]);
4721	116	ge_p1p1_to_p3(&u, &t);
4722	116	ge_p3_to_cached(&Ai[3], &u);
4723	116	ge_add(&t, &A2, &Ai[3]);
4724	116	ge_p1p1_to_p3(&u, &t);
4725	116	ge_p3_to_cached(&Ai[4], &u);
4726	116	ge_add(&t, &A2, &Ai[4]);
4727	116	ge_p1p1_to_p3(&u, &t);
4728	116	ge_p3_to_cached(&Ai[5], &u);
4729	116	ge_add(&t, &A2, &Ai[5]);
4730	116	ge_p1p1_to_p3(&u, &t);
4731	116	ge_p3_to_cached(&Ai[6], &u);
4732	116	ge_add(&t, &A2, &Ai[6]);
4733	116	ge_p1p1_to_p3(&u, &t);
4734	116	ge_p3_to_cached(&Ai[7], &u);
4735
4736	116	ge_p2_0(r);
4737
4738	791	for (i = 255; i >= 0; --i) {
4739	791	if (aslide[i] \|\| bslide[i]) {
4740	116	break;
4741	116	}
4742	791	}
4743
4744	29.1k	for (; i >= 0; --i) {
4745	29.0k	ge_p2_dbl(&t, r);
4746
4747	29.0k	if (aslide[i] > 0) {
4748	2.44k	ge_p1p1_to_p3(&u, &t);
4749	2.44k	ge_add(&t, &u, &Ai[aslide[i] / 2]);
4750	26.5k	} else if (aslide[i] < 0) {
4751	2.47k	ge_p1p1_to_p3(&u, &t);
4752	2.47k	ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4753	2.47k	}
4754
4755	29.0k	if (bslide[i] > 0) {
4756	1.24k	ge_p1p1_to_p3(&u, &t);
4757	1.24k	ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4758	27.7k	} else if (bslide[i] < 0) {
4759	588	ge_p1p1_to_p3(&u, &t);
4760	588	ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4761	588	}
4762
4763	29.0k	ge_p1p1_to_p2(r, &t);
4764	29.0k	}
4765	116	}
4766
4767		/*
4768		* The set of scalars is \Z/l
4769		* where l = 2^252 + 27742317777372353535851937790883648493.
4770		*
4771		* Input:
4772		* s[0]+256s[1]+...+256^63s[63] = s
4773		*
4774		* Output:
4775		* s[0]+256s[1]+...+256^31s[31] = s mod l
4776		* where l = 2^252 + 27742317777372353535851937790883648493.
4777		* Overwrites s in place.
4778		*/
4779		static void x25519_sc_reduce(uint8_t *s)
4780	116	{
4781	116	int64_t s0 = kBottom21Bits & load_3(s);
4782	116	int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
4783	116	int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
4784	116	int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
4785	116	int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
4786	116	int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
4787	116	int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
4788	116	int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
4789	116	int64_t s8 = kBottom21Bits & load_3(s + 21);
4790	116	int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
4791	116	int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4792	116	int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4793	116	int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4794	116	int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4795	116	int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4796	116	int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4797	116	int64_t s16 = kBottom21Bits & load_3(s + 42);
4798	116	int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4799	116	int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4800	116	int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4801	116	int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4802	116	int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4803	116	int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4804	116	int64_t s23 = (load_4(s + 60) >> 3);
4805	116	int64_t carry0;
4806	116	int64_t carry1;
4807	116	int64_t carry2;
4808	116	int64_t carry3;
4809	116	int64_t carry4;
4810	116	int64_t carry5;
4811	116	int64_t carry6;
4812	116	int64_t carry7;
4813	116	int64_t carry8;
4814	116	int64_t carry9;
4815	116	int64_t carry10;
4816	116	int64_t carry11;
4817	116	int64_t carry12;
4818	116	int64_t carry13;
4819	116	int64_t carry14;
4820	116	int64_t carry15;
4821	116	int64_t carry16;
4822
4823	116	s11 += s23 * 666643;
4824	116	s12 += s23 * 470296;
4825	116	s13 += s23 * 654183;
4826	116	s14 -= s23 * 997805;
4827	116	s15 += s23 * 136657;
4828	116	s16 -= s23 * 683901;
4829	116	s23 = 0;
4830
4831	116	s10 += s22 * 666643;
4832	116	s11 += s22 * 470296;
4833	116	s12 += s22 * 654183;
4834	116	s13 -= s22 * 997805;
4835	116	s14 += s22 * 136657;
4836	116	s15 -= s22 * 683901;
4837	116	s22 = 0;
4838
4839	116	s9 += s21 * 666643;
4840	116	s10 += s21 * 470296;
4841	116	s11 += s21 * 654183;
4842	116	s12 -= s21 * 997805;
4843	116	s13 += s21 * 136657;
4844	116	s14 -= s21 * 683901;
4845	116	s21 = 0;
4846
4847	116	s8 += s20 * 666643;
4848	116	s9 += s20 * 470296;
4849	116	s10 += s20 * 654183;
4850	116	s11 -= s20 * 997805;
4851	116	s12 += s20 * 136657;
4852	116	s13 -= s20 * 683901;
4853	116	s20 = 0;
4854
4855	116	s7 += s19 * 666643;
4856	116	s8 += s19 * 470296;
4857	116	s9 += s19 * 654183;
4858	116	s10 -= s19 * 997805;
4859	116	s11 += s19 * 136657;
4860	116	s12 -= s19 * 683901;
4861	116	s19 = 0;
4862
4863	116	s6 += s18 * 666643;
4864	116	s7 += s18 * 470296;
4865	116	s8 += s18 * 654183;
4866	116	s9 -= s18 * 997805;
4867	116	s10 += s18 * 136657;
4868	116	s11 -= s18 * 683901;
4869	116	s18 = 0;
4870
4871	116	carry6 = (s6 + (1 << 20)) >> 21;
4872	116	s7 += carry6;
4873	116	s6 -= carry6 * (1 << 21);
4874	116	carry8 = (s8 + (1 << 20)) >> 21;
4875	116	s9 += carry8;
4876	116	s8 -= carry8 * (1 << 21);
4877	116	carry10 = (s10 + (1 << 20)) >> 21;
4878	116	s11 += carry10;
4879	116	s10 -= carry10 * (1 << 21);
4880	116	carry12 = (s12 + (1 << 20)) >> 21;
4881	116	s13 += carry12;
4882	116	s12 -= carry12 * (1 << 21);
4883	116	carry14 = (s14 + (1 << 20)) >> 21;
4884	116	s15 += carry14;
4885	116	s14 -= carry14 * (1 << 21);
4886	116	carry16 = (s16 + (1 << 20)) >> 21;
4887	116	s17 += carry16;
4888	116	s16 -= carry16 * (1 << 21);
4889
4890	116	carry7 = (s7 + (1 << 20)) >> 21;
4891	116	s8 += carry7;
4892	116	s7 -= carry7 * (1 << 21);
4893	116	carry9 = (s9 + (1 << 20)) >> 21;
4894	116	s10 += carry9;
4895	116	s9 -= carry9 * (1 << 21);
4896	116	carry11 = (s11 + (1 << 20)) >> 21;
4897	116	s12 += carry11;
4898	116	s11 -= carry11 * (1 << 21);
4899	116	carry13 = (s13 + (1 << 20)) >> 21;
4900	116	s14 += carry13;
4901	116	s13 -= carry13 * (1 << 21);
4902	116	carry15 = (s15 + (1 << 20)) >> 21;
4903	116	s16 += carry15;
4904	116	s15 -= carry15 * (1 << 21);
4905
4906	116	s5 += s17 * 666643;
4907	116	s6 += s17 * 470296;
4908	116	s7 += s17 * 654183;
4909	116	s8 -= s17 * 997805;
4910	116	s9 += s17 * 136657;
4911	116	s10 -= s17 * 683901;
4912	116	s17 = 0;
4913
4914	116	s4 += s16 * 666643;
4915	116	s5 += s16 * 470296;
4916	116	s6 += s16 * 654183;
4917	116	s7 -= s16 * 997805;
4918	116	s8 += s16 * 136657;
4919	116	s9 -= s16 * 683901;
4920	116	s16 = 0;
4921
4922	116	s3 += s15 * 666643;
4923	116	s4 += s15 * 470296;
4924	116	s5 += s15 * 654183;
4925	116	s6 -= s15 * 997805;
4926	116	s7 += s15 * 136657;
4927	116	s8 -= s15 * 683901;
4928	116	s15 = 0;
4929
4930	116	s2 += s14 * 666643;
4931	116	s3 += s14 * 470296;
4932	116	s4 += s14 * 654183;
4933	116	s5 -= s14 * 997805;
4934	116	s6 += s14 * 136657;
4935	116	s7 -= s14 * 683901;
4936	116	s14 = 0;
4937
4938	116	s1 += s13 * 666643;
4939	116	s2 += s13 * 470296;
4940	116	s3 += s13 * 654183;
4941	116	s4 -= s13 * 997805;
4942	116	s5 += s13 * 136657;
4943	116	s6 -= s13 * 683901;
4944	116	s13 = 0;
4945
4946	116	s0 += s12 * 666643;
4947	116	s1 += s12 * 470296;
4948	116	s2 += s12 * 654183;
4949	116	s3 -= s12 * 997805;
4950	116	s4 += s12 * 136657;
4951	116	s5 -= s12 * 683901;
4952	116	s12 = 0;
4953
4954	116	carry0 = (s0 + (1 << 20)) >> 21;
4955	116	s1 += carry0;
4956	116	s0 -= carry0 * (1 << 21);
4957	116	carry2 = (s2 + (1 << 20)) >> 21;
4958	116	s3 += carry2;
4959	116	s2 -= carry2 * (1 << 21);
4960	116	carry4 = (s4 + (1 << 20)) >> 21;
4961	116	s5 += carry4;
4962	116	s4 -= carry4 * (1 << 21);
4963	116	carry6 = (s6 + (1 << 20)) >> 21;
4964	116	s7 += carry6;
4965	116	s6 -= carry6 * (1 << 21);
4966	116	carry8 = (s8 + (1 << 20)) >> 21;
4967	116	s9 += carry8;
4968	116	s8 -= carry8 * (1 << 21);
4969	116	carry10 = (s10 + (1 << 20)) >> 21;
4970	116	s11 += carry10;
4971	116	s10 -= carry10 * (1 << 21);
4972
4973	116	carry1 = (s1 + (1 << 20)) >> 21;
4974	116	s2 += carry1;
4975	116	s1 -= carry1 * (1 << 21);
4976	116	carry3 = (s3 + (1 << 20)) >> 21;
4977	116	s4 += carry3;
4978	116	s3 -= carry3 * (1 << 21);
4979	116	carry5 = (s5 + (1 << 20)) >> 21;
4980	116	s6 += carry5;
4981	116	s5 -= carry5 * (1 << 21);
4982	116	carry7 = (s7 + (1 << 20)) >> 21;
4983	116	s8 += carry7;
4984	116	s7 -= carry7 * (1 << 21);
4985	116	carry9 = (s9 + (1 << 20)) >> 21;
4986	116	s10 += carry9;
4987	116	s9 -= carry9 * (1 << 21);
4988	116	carry11 = (s11 + (1 << 20)) >> 21;
4989	116	s12 += carry11;
4990	116	s11 -= carry11 * (1 << 21);
4991
4992	116	s0 += s12 * 666643;
4993	116	s1 += s12 * 470296;
4994	116	s2 += s12 * 654183;
4995	116	s3 -= s12 * 997805;
4996	116	s4 += s12 * 136657;
4997	116	s5 -= s12 * 683901;
4998	116	s12 = 0;
4999
5000	116	carry0 = s0 >> 21;
5001	116	s1 += carry0;
5002	116	s0 -= carry0 * (1 << 21);
5003	116	carry1 = s1 >> 21;
5004	116	s2 += carry1;
5005	116	s1 -= carry1 * (1 << 21);
5006	116	carry2 = s2 >> 21;
5007	116	s3 += carry2;
5008	116	s2 -= carry2 * (1 << 21);
5009	116	carry3 = s3 >> 21;
5010	116	s4 += carry3;
5011	116	s3 -= carry3 * (1 << 21);
5012	116	carry4 = s4 >> 21;
5013	116	s5 += carry4;
5014	116	s4 -= carry4 * (1 << 21);
5015	116	carry5 = s5 >> 21;
5016	116	s6 += carry5;
5017	116	s5 -= carry5 * (1 << 21);
5018	116	carry6 = s6 >> 21;
5019	116	s7 += carry6;
5020	116	s6 -= carry6 * (1 << 21);
5021	116	carry7 = s7 >> 21;
5022	116	s8 += carry7;
5023	116	s7 -= carry7 * (1 << 21);
5024	116	carry8 = s8 >> 21;
5025	116	s9 += carry8;
5026	116	s8 -= carry8 * (1 << 21);
5027	116	carry9 = s9 >> 21;
5028	116	s10 += carry9;
5029	116	s9 -= carry9 * (1 << 21);
5030	116	carry10 = s10 >> 21;
5031	116	s11 += carry10;
5032	116	s10 -= carry10 * (1 << 21);
5033	116	carry11 = s11 >> 21;
5034	116	s12 += carry11;
5035	116	s11 -= carry11 * (1 << 21);
5036
5037	116	s0 += s12 * 666643;
5038	116	s1 += s12 * 470296;
5039	116	s2 += s12 * 654183;
5040	116	s3 -= s12 * 997805;
5041	116	s4 += s12 * 136657;
5042	116	s5 -= s12 * 683901;
5043	116	s12 = 0;
5044
5045	116	carry0 = s0 >> 21;
5046	116	s1 += carry0;
5047	116	s0 -= carry0 * (1 << 21);
5048	116	carry1 = s1 >> 21;
5049	116	s2 += carry1;
5050	116	s1 -= carry1 * (1 << 21);
5051	116	carry2 = s2 >> 21;
5052	116	s3 += carry2;
5053	116	s2 -= carry2 * (1 << 21);
5054	116	carry3 = s3 >> 21;
5055	116	s4 += carry3;
5056	116	s3 -= carry3 * (1 << 21);
5057	116	carry4 = s4 >> 21;
5058	116	s5 += carry4;
5059	116	s4 -= carry4 * (1 << 21);
5060	116	carry5 = s5 >> 21;
5061	116	s6 += carry5;
5062	116	s5 -= carry5 * (1 << 21);
5063	116	carry6 = s6 >> 21;
5064	116	s7 += carry6;
5065	116	s6 -= carry6 * (1 << 21);
5066	116	carry7 = s7 >> 21;
5067	116	s8 += carry7;
5068	116	s7 -= carry7 * (1 << 21);
5069	116	carry8 = s8 >> 21;
5070	116	s9 += carry8;
5071	116	s8 -= carry8 * (1 << 21);
5072	116	carry9 = s9 >> 21;
5073	116	s10 += carry9;
5074	116	s9 -= carry9 * (1 << 21);
5075	116	carry10 = s10 >> 21;
5076	116	s11 += carry10;
5077	116	s10 -= carry10 * (1 << 21);
5078
5079	116	s[0] = (uint8_t)(s0 >> 0);
5080	116	s[1] = (uint8_t)(s0 >> 8);
5081	116	s[2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5082	116	s[3] = (uint8_t)(s1 >> 3);
5083	116	s[4] = (uint8_t)(s1 >> 11);
5084	116	s[5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5085	116	s[6] = (uint8_t)(s2 >> 6);
5086	116	s[7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5087	116	s[8] = (uint8_t)(s3 >> 1);
5088	116	s[9] = (uint8_t)(s3 >> 9);
5089	116	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5090	116	s[11] = (uint8_t)(s4 >> 4);
5091	116	s[12] = (uint8_t)(s4 >> 12);
5092	116	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5093	116	s[14] = (uint8_t)(s5 >> 7);
5094	116	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5095	116	s[16] = (uint8_t)(s6 >> 2);
5096	116	s[17] = (uint8_t)(s6 >> 10);
5097	116	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5098	116	s[19] = (uint8_t)(s7 >> 5);
5099	116	s[20] = (uint8_t)(s7 >> 13);
5100	116	s[21] = (uint8_t)(s8 >> 0);
5101	116	s[22] = (uint8_t)(s8 >> 8);
5102	116	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5103	116	s[24] = (uint8_t)(s9 >> 3);
5104	116	s[25] = (uint8_t)(s9 >> 11);
5105	116	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5106	116	s[27] = (uint8_t)(s10 >> 6);
5107	116	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5108	116	s[29] = (uint8_t)(s11 >> 1);
5109	116	s[30] = (uint8_t)(s11 >> 9);
5110	116	s[31] = (uint8_t)(s11 >> 17);
5111	116	}
5112
5113		/*
5114		* Input:
5115		* a[0]+256a[1]+...+256^31a[31] = a
5116		* b[0]+256b[1]+...+256^31b[31] = b
5117		* c[0]+256c[1]+...+256^31c[31] = c
5118		*
5119		* Output:
5120		* s[0]+256s[1]+...+256^31s[31] = (ab+c) mod l
5121		* where l = 2^252 + 27742317777372353535851937790883648493.
5122		*/
5123		static void sc_muladd(uint8_t s, const uint8_t a, const uint8_t *b,
5124		const uint8_t *c)
5125	0	{
5126	0	int64_t a0 = kBottom21Bits & load_3(a);
5127	0	int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
5128	0	int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
5129	0	int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
5130	0	int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
5131	0	int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
5132	0	int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
5133	0	int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
5134	0	int64_t a8 = kBottom21Bits & load_3(a + 21);
5135	0	int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
5136	0	int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
5137	0	int64_t a11 = (load_4(a + 28) >> 7);
5138	0	int64_t b0 = kBottom21Bits & load_3(b);
5139	0	int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
5140	0	int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
5141	0	int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
5142	0	int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
5143	0	int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
5144	0	int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
5145	0	int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
5146	0	int64_t b8 = kBottom21Bits & load_3(b + 21);
5147	0	int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
5148	0	int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
5149	0	int64_t b11 = (load_4(b + 28) >> 7);
5150	0	int64_t c0 = kBottom21Bits & load_3(c);
5151	0	int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
5152	0	int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
5153	0	int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
5154	0	int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
5155	0	int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
5156	0	int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
5157	0	int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
5158	0	int64_t c8 = kBottom21Bits & load_3(c + 21);
5159	0	int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
5160	0	int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
5161	0	int64_t c11 = (load_4(c + 28) >> 7);
5162	0	int64_t s0;
5163	0	int64_t s1;
5164	0	int64_t s2;
5165	0	int64_t s3;
5166	0	int64_t s4;
5167	0	int64_t s5;
5168	0	int64_t s6;
5169	0	int64_t s7;
5170	0	int64_t s8;
5171	0	int64_t s9;
5172	0	int64_t s10;
5173	0	int64_t s11;
5174	0	int64_t s12;
5175	0	int64_t s13;
5176	0	int64_t s14;
5177	0	int64_t s15;
5178	0	int64_t s16;
5179	0	int64_t s17;
5180	0	int64_t s18;
5181	0	int64_t s19;
5182	0	int64_t s20;
5183	0	int64_t s21;
5184	0	int64_t s22;
5185	0	int64_t s23;
5186	0	int64_t carry0;
5187	0	int64_t carry1;
5188	0	int64_t carry2;
5189	0	int64_t carry3;
5190	0	int64_t carry4;
5191	0	int64_t carry5;
5192	0	int64_t carry6;
5193	0	int64_t carry7;
5194	0	int64_t carry8;
5195	0	int64_t carry9;
5196	0	int64_t carry10;
5197	0	int64_t carry11;
5198	0	int64_t carry12;
5199	0	int64_t carry13;
5200	0	int64_t carry14;
5201	0	int64_t carry15;
5202	0	int64_t carry16;
5203	0	int64_t carry17;
5204	0	int64_t carry18;
5205	0	int64_t carry19;
5206	0	int64_t carry20;
5207	0	int64_t carry21;
5208	0	int64_t carry22;
5209
5210	0	s0 = c0 + a0 * b0;
5211	0	s1 = c1 + a0 * b1 + a1 * b0;
5212	0	s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
5213	0	s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
5214	0	s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
5215	0	s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
5216	0	s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
5217	0	s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
5218	0	s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
5219	0	s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
5220	0	s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
5221	0	s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
5222	0	s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
5223	0	s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
5224	0	s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
5225	0	s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
5226	0	s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
5227	0	s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
5228	0	s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
5229	0	s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
5230	0	s20 = a9 * b11 + a10 * b10 + a11 * b9;
5231	0	s21 = a10 * b11 + a11 * b10;
5232	0	s22 = a11 * b11;
5233	0	s23 = 0;
5234
5235	0	carry0 = (s0 + (1 << 20)) >> 21;
5236	0	s1 += carry0;
5237	0	s0 -= carry0 * (1 << 21);
5238	0	carry2 = (s2 + (1 << 20)) >> 21;
5239	0	s3 += carry2;
5240	0	s2 -= carry2 * (1 << 21);
5241	0	carry4 = (s4 + (1 << 20)) >> 21;
5242	0	s5 += carry4;
5243	0	s4 -= carry4 * (1 << 21);
5244	0	carry6 = (s6 + (1 << 20)) >> 21;
5245	0	s7 += carry6;
5246	0	s6 -= carry6 * (1 << 21);
5247	0	carry8 = (s8 + (1 << 20)) >> 21;
5248	0	s9 += carry8;
5249	0	s8 -= carry8 * (1 << 21);
5250	0	carry10 = (s10 + (1 << 20)) >> 21;
5251	0	s11 += carry10;
5252	0	s10 -= carry10 * (1 << 21);
5253	0	carry12 = (s12 + (1 << 20)) >> 21;
5254	0	s13 += carry12;
5255	0	s12 -= carry12 * (1 << 21);
5256	0	carry14 = (s14 + (1 << 20)) >> 21;
5257	0	s15 += carry14;
5258	0	s14 -= carry14 * (1 << 21);
5259	0	carry16 = (s16 + (1 << 20)) >> 21;
5260	0	s17 += carry16;
5261	0	s16 -= carry16 * (1 << 21);
5262	0	carry18 = (s18 + (1 << 20)) >> 21;
5263	0	s19 += carry18;
5264	0	s18 -= carry18 * (1 << 21);
5265	0	carry20 = (s20 + (1 << 20)) >> 21;
5266	0	s21 += carry20;
5267	0	s20 -= carry20 * (1 << 21);
5268	0	carry22 = (s22 + (1 << 20)) >> 21;
5269	0	s23 += carry22;
5270	0	s22 -= carry22 * (1 << 21);
5271
5272	0	carry1 = (s1 + (1 << 20)) >> 21;
5273	0	s2 += carry1;
5274	0	s1 -= carry1 * (1 << 21);
5275	0	carry3 = (s3 + (1 << 20)) >> 21;
5276	0	s4 += carry3;
5277	0	s3 -= carry3 * (1 << 21);
5278	0	carry5 = (s5 + (1 << 20)) >> 21;
5279	0	s6 += carry5;
5280	0	s5 -= carry5 * (1 << 21);
5281	0	carry7 = (s7 + (1 << 20)) >> 21;
5282	0	s8 += carry7;
5283	0	s7 -= carry7 * (1 << 21);
5284	0	carry9 = (s9 + (1 << 20)) >> 21;
5285	0	s10 += carry9;
5286	0	s9 -= carry9 * (1 << 21);
5287	0	carry11 = (s11 + (1 << 20)) >> 21;
5288	0	s12 += carry11;
5289	0	s11 -= carry11 * (1 << 21);
5290	0	carry13 = (s13 + (1 << 20)) >> 21;
5291	0	s14 += carry13;
5292	0	s13 -= carry13 * (1 << 21);
5293	0	carry15 = (s15 + (1 << 20)) >> 21;
5294	0	s16 += carry15;
5295	0	s15 -= carry15 * (1 << 21);
5296	0	carry17 = (s17 + (1 << 20)) >> 21;
5297	0	s18 += carry17;
5298	0	s17 -= carry17 * (1 << 21);
5299	0	carry19 = (s19 + (1 << 20)) >> 21;
5300	0	s20 += carry19;
5301	0	s19 -= carry19 * (1 << 21);
5302	0	carry21 = (s21 + (1 << 20)) >> 21;
5303	0	s22 += carry21;
5304	0	s21 -= carry21 * (1 << 21);
5305
5306	0	s11 += s23 * 666643;
5307	0	s12 += s23 * 470296;
5308	0	s13 += s23 * 654183;
5309	0	s14 -= s23 * 997805;
5310	0	s15 += s23 * 136657;
5311	0	s16 -= s23 * 683901;
5312	0	s23 = 0;
5313
5314	0	s10 += s22 * 666643;
5315	0	s11 += s22 * 470296;
5316	0	s12 += s22 * 654183;
5317	0	s13 -= s22 * 997805;
5318	0	s14 += s22 * 136657;
5319	0	s15 -= s22 * 683901;
5320	0	s22 = 0;
5321
5322	0	s9 += s21 * 666643;
5323	0	s10 += s21 * 470296;
5324	0	s11 += s21 * 654183;
5325	0	s12 -= s21 * 997805;
5326	0	s13 += s21 * 136657;
5327	0	s14 -= s21 * 683901;
5328	0	s21 = 0;
5329
5330	0	s8 += s20 * 666643;
5331	0	s9 += s20 * 470296;
5332	0	s10 += s20 * 654183;
5333	0	s11 -= s20 * 997805;
5334	0	s12 += s20 * 136657;
5335	0	s13 -= s20 * 683901;
5336	0	s20 = 0;
5337
5338	0	s7 += s19 * 666643;
5339	0	s8 += s19 * 470296;
5340	0	s9 += s19 * 654183;
5341	0	s10 -= s19 * 997805;
5342	0	s11 += s19 * 136657;
5343	0	s12 -= s19 * 683901;
5344	0	s19 = 0;
5345
5346	0	s6 += s18 * 666643;
5347	0	s7 += s18 * 470296;
5348	0	s8 += s18 * 654183;
5349	0	s9 -= s18 * 997805;
5350	0	s10 += s18 * 136657;
5351	0	s11 -= s18 * 683901;
5352	0	s18 = 0;
5353
5354	0	carry6 = (s6 + (1 << 20)) >> 21;
5355	0	s7 += carry6;
5356	0	s6 -= carry6 * (1 << 21);
5357	0	carry8 = (s8 + (1 << 20)) >> 21;
5358	0	s9 += carry8;
5359	0	s8 -= carry8 * (1 << 21);
5360	0	carry10 = (s10 + (1 << 20)) >> 21;
5361	0	s11 += carry10;
5362	0	s10 -= carry10 * (1 << 21);
5363	0	carry12 = (s12 + (1 << 20)) >> 21;
5364	0	s13 += carry12;
5365	0	s12 -= carry12 * (1 << 21);
5366	0	carry14 = (s14 + (1 << 20)) >> 21;
5367	0	s15 += carry14;
5368	0	s14 -= carry14 * (1 << 21);
5369	0	carry16 = (s16 + (1 << 20)) >> 21;
5370	0	s17 += carry16;
5371	0	s16 -= carry16 * (1 << 21);
5372
5373	0	carry7 = (s7 + (1 << 20)) >> 21;
5374	0	s8 += carry7;
5375	0	s7 -= carry7 * (1 << 21);
5376	0	carry9 = (s9 + (1 << 20)) >> 21;
5377	0	s10 += carry9;
5378	0	s9 -= carry9 * (1 << 21);
5379	0	carry11 = (s11 + (1 << 20)) >> 21;
5380	0	s12 += carry11;
5381	0	s11 -= carry11 * (1 << 21);
5382	0	carry13 = (s13 + (1 << 20)) >> 21;
5383	0	s14 += carry13;
5384	0	s13 -= carry13 * (1 << 21);
5385	0	carry15 = (s15 + (1 << 20)) >> 21;
5386	0	s16 += carry15;
5387	0	s15 -= carry15 * (1 << 21);
5388
5389	0	s5 += s17 * 666643;
5390	0	s6 += s17 * 470296;
5391	0	s7 += s17 * 654183;
5392	0	s8 -= s17 * 997805;
5393	0	s9 += s17 * 136657;
5394	0	s10 -= s17 * 683901;
5395	0	s17 = 0;
5396
5397	0	s4 += s16 * 666643;
5398	0	s5 += s16 * 470296;
5399	0	s6 += s16 * 654183;
5400	0	s7 -= s16 * 997805;
5401	0	s8 += s16 * 136657;
5402	0	s9 -= s16 * 683901;
5403	0	s16 = 0;
5404
5405	0	s3 += s15 * 666643;
5406	0	s4 += s15 * 470296;
5407	0	s5 += s15 * 654183;
5408	0	s6 -= s15 * 997805;
5409	0	s7 += s15 * 136657;
5410	0	s8 -= s15 * 683901;
5411	0	s15 = 0;
5412
5413	0	s2 += s14 * 666643;
5414	0	s3 += s14 * 470296;
5415	0	s4 += s14 * 654183;
5416	0	s5 -= s14 * 997805;
5417	0	s6 += s14 * 136657;
5418	0	s7 -= s14 * 683901;
5419	0	s14 = 0;
5420
5421	0	s1 += s13 * 666643;
5422	0	s2 += s13 * 470296;
5423	0	s3 += s13 * 654183;
5424	0	s4 -= s13 * 997805;
5425	0	s5 += s13 * 136657;
5426	0	s6 -= s13 * 683901;
5427	0	s13 = 0;
5428
5429	0	s0 += s12 * 666643;
5430	0	s1 += s12 * 470296;
5431	0	s2 += s12 * 654183;
5432	0	s3 -= s12 * 997805;
5433	0	s4 += s12 * 136657;
5434	0	s5 -= s12 * 683901;
5435	0	s12 = 0;
5436
5437	0	carry0 = (s0 + (1 << 20)) >> 21;
5438	0	s1 += carry0;
5439	0	s0 -= carry0 * (1 << 21);
5440	0	carry2 = (s2 + (1 << 20)) >> 21;
5441	0	s3 += carry2;
5442	0	s2 -= carry2 * (1 << 21);
5443	0	carry4 = (s4 + (1 << 20)) >> 21;
5444	0	s5 += carry4;
5445	0	s4 -= carry4 * (1 << 21);
5446	0	carry6 = (s6 + (1 << 20)) >> 21;
5447	0	s7 += carry6;
5448	0	s6 -= carry6 * (1 << 21);
5449	0	carry8 = (s8 + (1 << 20)) >> 21;
5450	0	s9 += carry8;
5451	0	s8 -= carry8 * (1 << 21);
5452	0	carry10 = (s10 + (1 << 20)) >> 21;
5453	0	s11 += carry10;
5454	0	s10 -= carry10 * (1 << 21);
5455
5456	0	carry1 = (s1 + (1 << 20)) >> 21;
5457	0	s2 += carry1;
5458	0	s1 -= carry1 * (1 << 21);
5459	0	carry3 = (s3 + (1 << 20)) >> 21;
5460	0	s4 += carry3;
5461	0	s3 -= carry3 * (1 << 21);
5462	0	carry5 = (s5 + (1 << 20)) >> 21;
5463	0	s6 += carry5;
5464	0	s5 -= carry5 * (1 << 21);
5465	0	carry7 = (s7 + (1 << 20)) >> 21;
5466	0	s8 += carry7;
5467	0	s7 -= carry7 * (1 << 21);
5468	0	carry9 = (s9 + (1 << 20)) >> 21;
5469	0	s10 += carry9;
5470	0	s9 -= carry9 * (1 << 21);
5471	0	carry11 = (s11 + (1 << 20)) >> 21;
5472	0	s12 += carry11;
5473	0	s11 -= carry11 * (1 << 21);
5474
5475	0	s0 += s12 * 666643;
5476	0	s1 += s12 * 470296;
5477	0	s2 += s12 * 654183;
5478	0	s3 -= s12 * 997805;
5479	0	s4 += s12 * 136657;
5480	0	s5 -= s12 * 683901;
5481	0	s12 = 0;
5482
5483	0	carry0 = s0 >> 21;
5484	0	s1 += carry0;
5485	0	s0 -= carry0 * (1 << 21);
5486	0	carry1 = s1 >> 21;
5487	0	s2 += carry1;
5488	0	s1 -= carry1 * (1 << 21);
5489	0	carry2 = s2 >> 21;
5490	0	s3 += carry2;
5491	0	s2 -= carry2 * (1 << 21);
5492	0	carry3 = s3 >> 21;
5493	0	s4 += carry3;
5494	0	s3 -= carry3 * (1 << 21);
5495	0	carry4 = s4 >> 21;
5496	0	s5 += carry4;
5497	0	s4 -= carry4 * (1 << 21);
5498	0	carry5 = s5 >> 21;
5499	0	s6 += carry5;
5500	0	s5 -= carry5 * (1 << 21);
5501	0	carry6 = s6 >> 21;
5502	0	s7 += carry6;
5503	0	s6 -= carry6 * (1 << 21);
5504	0	carry7 = s7 >> 21;
5505	0	s8 += carry7;
5506	0	s7 -= carry7 * (1 << 21);
5507	0	carry8 = s8 >> 21;
5508	0	s9 += carry8;
5509	0	s8 -= carry8 * (1 << 21);
5510	0	carry9 = s9 >> 21;
5511	0	s10 += carry9;
5512	0	s9 -= carry9 * (1 << 21);
5513	0	carry10 = s10 >> 21;
5514	0	s11 += carry10;
5515	0	s10 -= carry10 * (1 << 21);
5516	0	carry11 = s11 >> 21;
5517	0	s12 += carry11;
5518	0	s11 -= carry11 * (1 << 21);
5519
5520	0	s0 += s12 * 666643;
5521	0	s1 += s12 * 470296;
5522	0	s2 += s12 * 654183;
5523	0	s3 -= s12 * 997805;
5524	0	s4 += s12 * 136657;
5525	0	s5 -= s12 * 683901;
5526	0	s12 = 0;
5527
5528	0	carry0 = s0 >> 21;
5529	0	s1 += carry0;
5530	0	s0 -= carry0 * (1 << 21);
5531	0	carry1 = s1 >> 21;
5532	0	s2 += carry1;
5533	0	s1 -= carry1 * (1 << 21);
5534	0	carry2 = s2 >> 21;
5535	0	s3 += carry2;
5536	0	s2 -= carry2 * (1 << 21);
5537	0	carry3 = s3 >> 21;
5538	0	s4 += carry3;
5539	0	s3 -= carry3 * (1 << 21);
5540	0	carry4 = s4 >> 21;
5541	0	s5 += carry4;
5542	0	s4 -= carry4 * (1 << 21);
5543	0	carry5 = s5 >> 21;
5544	0	s6 += carry5;
5545	0	s5 -= carry5 * (1 << 21);
5546	0	carry6 = s6 >> 21;
5547	0	s7 += carry6;
5548	0	s6 -= carry6 * (1 << 21);
5549	0	carry7 = s7 >> 21;
5550	0	s8 += carry7;
5551	0	s7 -= carry7 * (1 << 21);
5552	0	carry8 = s8 >> 21;
5553	0	s9 += carry8;
5554	0	s8 -= carry8 * (1 << 21);
5555	0	carry9 = s9 >> 21;
5556	0	s10 += carry9;
5557	0	s9 -= carry9 * (1 << 21);
5558	0	carry10 = s10 >> 21;
5559	0	s11 += carry10;
5560	0	s10 -= carry10 * (1 << 21);
5561
5562	0	s[0] = (uint8_t)(s0 >> 0);
5563	0	s[1] = (uint8_t)(s0 >> 8);
5564	0	s[2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5565	0	s[3] = (uint8_t)(s1 >> 3);
5566	0	s[4] = (uint8_t)(s1 >> 11);
5567	0	s[5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5568	0	s[6] = (uint8_t)(s2 >> 6);
5569	0	s[7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5570	0	s[8] = (uint8_t)(s3 >> 1);
5571	0	s[9] = (uint8_t)(s3 >> 9);
5572	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5573	0	s[11] = (uint8_t)(s4 >> 4);
5574	0	s[12] = (uint8_t)(s4 >> 12);
5575	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5576	0	s[14] = (uint8_t)(s5 >> 7);
5577	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5578	0	s[16] = (uint8_t)(s6 >> 2);
5579	0	s[17] = (uint8_t)(s6 >> 10);
5580	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5581	0	s[19] = (uint8_t)(s7 >> 5);
5582	0	s[20] = (uint8_t)(s7 >> 13);
5583	0	s[21] = (uint8_t)(s8 >> 0);
5584	0	s[22] = (uint8_t)(s8 >> 8);
5585	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5586	0	s[24] = (uint8_t)(s9 >> 3);
5587	0	s[25] = (uint8_t)(s9 >> 11);
5588	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5589	0	s[27] = (uint8_t)(s10 >> 6);
5590	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5591	0	s[29] = (uint8_t)(s11 >> 1);
5592	0	s[30] = (uint8_t)(s11 >> 9);
5593	0	s[31] = (uint8_t)(s11 >> 17);
5594	0	}
5595
5596		int ossl_ed25519_sign(uint8_t out_sig, const uint8_t message, size_t message_len,
5597		const uint8_t public_key[32], const uint8_t private_key[32],
5598		OSSL_LIB_CTX libctx, const char propq)
5599	0	{
5600	0	uint8_t az[SHA512_DIGEST_LENGTH];
5601	0	uint8_t nonce[SHA512_DIGEST_LENGTH];
5602	0	ge_p3 R;
5603	0	uint8_t hram[SHA512_DIGEST_LENGTH];
5604	0	EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5605	0	EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
5606	0	unsigned int sz;
5607	0	int res = 0;
5608
5609	0	if (sha512 == NULL \|\| hash_ctx == NULL)
5610	0	goto err;
5611
5612	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5613	0	\|\| !EVP_DigestUpdate(hash_ctx, private_key, 32)
5614	0	\|\| !EVP_DigestFinal_ex(hash_ctx, az, &sz))
5615	0	goto err;
5616
5617	0	az[0] &= 248;
5618	0	az[31] &= 63;
5619	0	az[31] \|= 64;
5620
5621	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5622	0	\|\| !EVP_DigestUpdate(hash_ctx, az + 32, 32)
5623	0	\|\| !EVP_DigestUpdate(hash_ctx, message, message_len)
5624	0	\|\| !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
5625	0	goto err;
5626
5627	0	x25519_sc_reduce(nonce);
5628	0	ge_scalarmult_base(&R, nonce);
5629	0	ge_p3_tobytes(out_sig, &R);
5630
5631	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5632	0	\|\| !EVP_DigestUpdate(hash_ctx, out_sig, 32)
5633	0	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5634	0	\|\| !EVP_DigestUpdate(hash_ctx, message, message_len)
5635	0	\|\| !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
5636	0	goto err;
5637
5638	0	x25519_sc_reduce(hram);
5639	0	sc_muladd(out_sig + 32, hram, az, nonce);
5640
5641	0	res = 1;
5642	0	err:
5643	0	OPENSSL_cleanse(nonce, sizeof(nonce));
5644	0	OPENSSL_cleanse(az, sizeof(az));
5645	0	EVP_MD_free(sha512);
5646	0	EVP_MD_CTX_free(hash_ctx);
5647	0	return res;
5648	0	}
5649
5650		static const char allzeroes[15];
5651
5652		int ossl_ed25519_verify(const uint8_t *message, size_t message_len,
5653		const uint8_t signature[64], const uint8_t public_key[32],
5654		OSSL_LIB_CTX libctx, const char propq)
5655	137	{
5656	137	int i;
5657	137	ge_p3 A;
5658	137	const uint8_t r, s;
5659	137	EVP_MD *sha512;
5660	137	EVP_MD_CTX *hash_ctx = NULL;
5661	137	unsigned int sz;
5662	137	int res = 0;
5663	137	ge_p2 R;
5664	137	uint8_t rcheck[32];
5665	137	uint8_t h[SHA512_DIGEST_LENGTH];
5666		/* 27742317777372353535851937790883648493 in little endian format */
5667	137	const uint8_t l_low[16] = {
5668	137	0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5669	137	0xDE, 0xF9, 0xDE, 0x14
5670	137	};
5671
5672	137	r = signature;
5673	137	s = signature + 32;
5674
5675		/*
5676		* Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5677		*
5678		* If not the signature is publicly invalid. Since it's public we can do the
5679		* check in variable time.
5680		*
5681		* First check the most significant byte
5682		*/
5683	137	if (s[31] > 0x10)
5684	1	return 0;
5685	136	if (s[31] == 0x10) {
5686		/*
5687		* Most significant byte indicates a value close to 2^252 so check the
5688		* rest
5689		*/
5690	23	if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5691	8	return 0;
5692	35	for (i = 15; i >= 0; i--) {
5693	35	if (s[i] < l_low[i])
5694	6	break;
5695	29	if (s[i] > l_low[i])
5696	9	return 0;
5697	29	}
5698	6	if (i < 0)
5699	0	return 0;
5700	6	}
5701
5702	119	if (ge_frombytes_vartime(&A, public_key) != 0) {
5703	3	return 0;
5704	3	}
5705
5706	116	fe_neg(A.X, A.X);
5707	116	fe_neg(A.T, A.T);
5708
5709	116	sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5710	116	if (sha512 == NULL)
5711	0	return 0;
5712	116	hash_ctx = EVP_MD_CTX_new();
5713	116	if (hash_ctx == NULL)
5714	0	goto err;
5715
5716	116	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5717	116	\|\| !EVP_DigestUpdate(hash_ctx, r, 32)
5718	116	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5719	116	\|\| !EVP_DigestUpdate(hash_ctx, message, message_len)
5720	116	\|\| !EVP_DigestFinal_ex(hash_ctx, h, &sz))
5721	0	goto err;
5722
5723	116	x25519_sc_reduce(h);
5724
5725	116	ge_double_scalarmult_vartime(&R, h, &A, s);
5726
5727	116	ge_tobytes(rcheck, &R);
5728
5729	116	res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5730	116	err:
5731	116	EVP_MD_free(sha512);
5732	116	EVP_MD_CTX_free(hash_ctx);
5733	116	return res;
5734	116	}
5735
5736		int ossl_ed25519_public_from_private(OSSL_LIB_CTX *ctx, uint8_t out_public_key[32],
5737		const uint8_t private_key[32],
5738		const char *propq)
5739	22	{
5740	22	uint8_t az[SHA512_DIGEST_LENGTH];
5741	22	ge_p3 A;
5742	22	int r;
5743	22	EVP_MD *sha512 = NULL;
5744
5745	22	sha512 = EVP_MD_fetch(ctx, SN_sha512, propq);
5746	22	if (sha512 == NULL)
5747	0	return 0;
5748	22	r = EVP_Digest(private_key, 32, az, NULL, sha512, NULL);
5749	22	EVP_MD_free(sha512);
5750	22	if (!r) {
5751	0	OPENSSL_cleanse(az, sizeof(az));
5752	0	return 0;
5753	0	}
5754
5755	22	az[0] &= 248;
5756	22	az[31] &= 63;
5757	22	az[31] \|= 64;
5758
5759	22	ge_scalarmult_base(&A, az);
5760	22	ge_p3_tobytes(out_public_key, &A);
5761
5762	22	OPENSSL_cleanse(az, sizeof(az));
5763	22	return 1;
5764	22	}
5765
5766		int ossl_x25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5767		const uint8_t peer_public_value[32])
5768	32.2k	{
5769	32.2k	static const uint8_t kZeros[32] = { 0 };
5770	32.2k	x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5771		/* The all-zero output results when the input is a point of small order. */
5772	32.2k	return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5773	32.2k	}
5774
5775		void ossl_x25519_public_from_private(uint8_t out_public_value[32],
5776		const uint8_t private_key[32])
5777	147k	{
5778	147k	uint8_t e[32];
5779	147k	ge_p3 A;
5780	147k	fe zplusy, zminusy, zminusy_inv;
5781
5782	147k	memcpy(e, private_key, 32);
5783	147k	e[0] &= 248;
5784	147k	e[31] &= 127;
5785	147k	e[31] \|= 64;
5786
5787	147k	ge_scalarmult_base(&A, e);
5788
5789		/*
5790		* We only need the u-coordinate of the curve25519 point.
5791		* The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5792		* u=(Z+Y)/(Z-Y).
5793		*/
5794	147k	fe_add(zplusy, A.Z, A.Y);
5795	147k	fe_sub(zminusy, A.Z, A.Y);
5796	147k	fe_invert(zminusy_inv, zminusy);
5797	147k	fe_mul(zplusy, zplusy, zminusy_inv);
5798	147k	fe_tobytes(out_public_value, zplusy);
5799
5800	147k	OPENSSL_cleanse(e, sizeof(e));
5801	147k	}

Coverage Report

Created: 2025-12-31 06:58