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

Line	Count	Source (jump to first uncovered line)
1		/*
2		* Copyright 2016-2021 The OpenSSL Project Authors. All Rights Reserved.
3		*
4		* Licensed under the Apache License 2.0 (the "License"). You may not use
5		* this file except in compliance with the License. You can obtain a copy
6		* in the file LICENSE in the source distribution or at
7		* https://www.openssl.org/source/license.html
8		*/
9
10		/*
11		* ECDSA low level APIs are deprecated for public use, but still ok for
12		* internal use.
13		*/
14		#include "internal/deprecated.h"
15
16		#include <string.h>
17		#include "crypto/ecx.h"
18		#include "ec_local.h"
19		#include <openssl/evp.h>
20		#include <openssl/sha.h>
21
22		#include "internal/numbers.h"
23
24		#if defined(X25519_ASM) && (defined(__x86_64) \|\| defined(__x86_64__) \|\| \
25		defined(_M_AMD64) \|\| defined(_M_X64))
26
27		# define BASE_2_64_IMPLEMENTED
28
29		typedef uint64_t fe64[4];
30
31		int x25519_fe64_eligible(void);
32
33		/*
34		* Following subroutines perform corresponding operations modulo
35		* 2^256-38, i.e. double the curve modulus. However, inputs and
36		* outputs are permitted to be partially reduced, i.e. to remain
37		* in [0..2^256) range. It's all tied up in final fe64_tobytes
38		* that performs full reduction modulo 2^255-19.
39		*
40		* There are no reference C implementations for these.
41		*/
42		void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
43		void x25519_fe64_sqr(fe64 h, const fe64 f);
44		void x25519_fe64_mul121666(fe64 h, fe64 f);
45		void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
46		void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
47		void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
48	20.8M	# define fe64_mul x25519_fe64_mul
49	20.6M	# define fe64_sqr x25519_fe64_sqr
50	4.13M	# define fe64_mul121666 x25519_fe64_mul121666
51	16.5M	# define fe64_add x25519_fe64_add
52	16.5M	# define fe64_sub x25519_fe64_sub
53	16.2k	# define fe64_tobytes x25519_fe64_tobytes
54
55		static uint64_t load_8(const uint8_t *in)
56	64.9k	{
57	64.9k	uint64_t result;
58
59	64.9k	result = in[0];
60	64.9k	result \|= ((uint64_t)in[1]) << 8;
61	64.9k	result \|= ((uint64_t)in[2]) << 16;
62	64.9k	result \|= ((uint64_t)in[3]) << 24;
63	64.9k	result \|= ((uint64_t)in[4]) << 32;
64	64.9k	result \|= ((uint64_t)in[5]) << 40;
65	64.9k	result \|= ((uint64_t)in[6]) << 48;
66	64.9k	result \|= ((uint64_t)in[7]) << 56;
67
68	64.9k	return result;
69	64.9k	}
70
71		static void fe64_frombytes(fe64 h, const uint8_t *s)
72	16.2k	{
73	16.2k	h[0] = load_8(s);
74	16.2k	h[1] = load_8(s + 8);
75	16.2k	h[2] = load_8(s + 16);
76	16.2k	h[3] = load_8(s + 24) & 0x7fffffffffffffff;
77	16.2k	}
78
79		static void fe64_0(fe64 h)
80	16.2k	{
81	16.2k	h[0] = 0;
82	16.2k	h[1] = 0;
83	16.2k	h[2] = 0;
84	16.2k	h[3] = 0;
85	16.2k	}
86
87		static void fe64_1(fe64 h)
88	32.4k	{
89	32.4k	h[0] = 1;
90	32.4k	h[1] = 0;
91	32.4k	h[2] = 0;
92	32.4k	h[3] = 0;
93	32.4k	}
94
95		static void fe64_copy(fe64 h, const fe64 f)
96	16.2k	{
97	16.2k	h[0] = f[0];
98	16.2k	h[1] = f[1];
99	16.2k	h[2] = f[2];
100	16.2k	h[3] = f[3];
101	16.2k	}
102
103		static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
104	8.27M	{
105	8.27M	int i;
106	8.27M	uint64_t mask = 0 - (uint64_t)b;
107
108	41.3M	for (i = 0; i < 4; i++) {
109	33.1M	uint64_t x = f[i] ^ g[i];
110	33.1M	x &= mask;
111	33.1M	f[i] ^= x;
112	33.1M	g[i] ^= x;
113	33.1M	}
114	8.27M	}
115
116		static void fe64_invert(fe64 out, const fe64 z)
117	16.2k	{
118	16.2k	fe64 t0;
119	16.2k	fe64 t1;
120	16.2k	fe64 t2;
121	16.2k	fe64 t3;
122	16.2k	int i;
123
124		/*
125		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
126		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
127		*/
128
129		/* t0 = z ** 2 */
130	16.2k	fe64_sqr(t0, z);
131
132		/* t1 = t0 (2 2) = z ** 8 */
133	16.2k	fe64_sqr(t1, t0);
134	16.2k	fe64_sqr(t1, t1);
135
136		/* t1 = z * t1 = z ** 9 */
137	16.2k	fe64_mul(t1, z, t1);
138		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
139	16.2k	fe64_mul(t0, t0, t1);
140
141		/* t2 = t0 2 = z 22 */
142	16.2k	fe64_sqr(t2, t0);
143
144		/* t1 = t1 * t2 = z (2 5 - 1) */
145	16.2k	fe64_mul(t1, t1, t2);
146
147		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
148	16.2k	fe64_sqr(t2, t1);
149	81.1k	for (i = 1; i < 5; ++i)
150	64.9k	fe64_sqr(t2, t2);
151
152		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
153	16.2k	fe64_mul(t1, t2, t1);
154
155		/* Continuing similarly... */
156
157		/* t2 = z (2 20 - 1) */
158	16.2k	fe64_sqr(t2, t1);
159	162k	for (i = 1; i < 10; ++i)
160	146k	fe64_sqr(t2, t2);
161
162	16.2k	fe64_mul(t2, t2, t1);
163
164		/* t2 = z (2 40 - 1) */
165	16.2k	fe64_sqr(t3, t2);
166	324k	for (i = 1; i < 20; ++i)
167	308k	fe64_sqr(t3, t3);
168
169	16.2k	fe64_mul(t2, t3, t2);
170
171		/* t2 = z (2 10) * (2 ** 40 - 1) */
172	178k	for (i = 0; i < 10; ++i)
173	162k	fe64_sqr(t2, t2);
174
175		/* t1 = z (2 50 - 1) */
176	16.2k	fe64_mul(t1, t2, t1);
177
178		/* t2 = z (2 100 - 1) */
179	16.2k	fe64_sqr(t2, t1);
180	811k	for (i = 1; i < 50; ++i)
181	795k	fe64_sqr(t2, t2);
182
183	16.2k	fe64_mul(t2, t2, t1);
184
185		/* t2 = z (2 200 - 1) */
186	16.2k	fe64_sqr(t3, t2);
187	1.62M	for (i = 1; i < 100; ++i)
188	1.60M	fe64_sqr(t3, t3);
189
190	16.2k	fe64_mul(t2, t3, t2);
191
192		/* t2 = z ((2 50) * (2 ** 200 - 1) */
193	827k	for (i = 0; i < 50; ++i)
194	811k	fe64_sqr(t2, t2);
195
196		/* t1 = z (2 250 - 1) */
197	16.2k	fe64_mul(t1, t2, t1);
198
199		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
200	97.3k	for (i = 0; i < 5; ++i)
201	81.1k	fe64_sqr(t1, t1);
202
203		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
204	16.2k	fe64_mul(out, t1, t0);
205	16.2k	}
206
207		/*
208		* Duplicate of original x25519_scalar_mult_generic, but using
209		* fe64_* subroutines.
210		*/
211		static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
212		const uint8_t point[32])
213	16.2k	{
214	16.2k	fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
215	16.2k	uint8_t e[32];
216	16.2k	unsigned swap = 0;
217	16.2k	int pos;
218
219	16.2k	memcpy(e, scalar, 32);
220	16.2k	e[0] &= 0xf8;
221	16.2k	e[31] &= 0x7f;
222	16.2k	e[31] \|= 0x40;
223	16.2k	fe64_frombytes(x1, point);
224	16.2k	fe64_1(x2);
225	16.2k	fe64_0(z2);
226	16.2k	fe64_copy(x3, x1);
227	16.2k	fe64_1(z3);
228
229	4.15M	for (pos = 254; pos >= 0; --pos) {
230	4.13M	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
231
232	4.13M	swap ^= b;
233	4.13M	fe64_cswap(x2, x3, swap);
234	4.13M	fe64_cswap(z2, z3, swap);
235	4.13M	swap = b;
236	4.13M	fe64_sub(tmp0, x3, z3);
237	4.13M	fe64_sub(tmp1, x2, z2);
238	4.13M	fe64_add(x2, x2, z2);
239	4.13M	fe64_add(z2, x3, z3);
240	4.13M	fe64_mul(z3, x2, tmp0);
241	4.13M	fe64_mul(z2, z2, tmp1);
242	4.13M	fe64_sqr(tmp0, tmp1);
243	4.13M	fe64_sqr(tmp1, x2);
244	4.13M	fe64_add(x3, z3, z2);
245	4.13M	fe64_sub(z2, z3, z2);
246	4.13M	fe64_mul(x2, tmp1, tmp0);
247	4.13M	fe64_sub(tmp1, tmp1, tmp0);
248	4.13M	fe64_sqr(z2, z2);
249	4.13M	fe64_mul121666(z3, tmp1);
250	4.13M	fe64_sqr(x3, x3);
251	4.13M	fe64_add(tmp0, tmp0, z3);
252	4.13M	fe64_mul(z3, x1, z2);
253	4.13M	fe64_mul(z2, tmp1, tmp0);
254	4.13M	}
255
256	16.2k	fe64_invert(z2, z2);
257	16.2k	fe64_mul(x2, x2, z2);
258	16.2k	fe64_tobytes(out, x2);
259
260	16.2k	OPENSSL_cleanse(e, sizeof(e));
261	16.2k	}
262		#endif
263
264		#if defined(X25519_ASM) \
265		\|\| ( defined(INT128_MAX) \
266		&& !defined(__sparc__) \
267		&& (!defined(__SIZEOF_LONG__) \|\| (__SIZEOF_LONG__ == 8)) \
268		&& !(defined(__ANDROID__) && !defined(__clang__)) )
269		/*
270		* Base 2^51 implementation. It's virtually no different from reference
271		* base 2^25.5 implementation in respect to lax boundary conditions for
272		* intermediate values and even individual limbs. So that whatever you
273		* know about the reference, applies even here...
274		*/
275		# define BASE_2_51_IMPLEMENTED
276
277		typedef uint64_t fe51[5];
278
279		static const uint64_t MASK51 = 0x7ffffffffffff;
280
281		static uint64_t load_7(const uint8_t *in)
282	0	{
283	0	uint64_t result;
284
285	0	result = in[0];
286	0	result \|= ((uint64_t)in[1]) << 8;
287	0	result \|= ((uint64_t)in[2]) << 16;
288	0	result \|= ((uint64_t)in[3]) << 24;
289	0	result \|= ((uint64_t)in[4]) << 32;
290	0	result \|= ((uint64_t)in[5]) << 40;
291	0	result \|= ((uint64_t)in[6]) << 48;
292
293	0	return result;
294	0	}
295
296		static uint64_t load_6(const uint8_t *in)
297	0	{
298	0	uint64_t result;
299
300	0	result = in[0];
301	0	result \|= ((uint64_t)in[1]) << 8;
302	0	result \|= ((uint64_t)in[2]) << 16;
303	0	result \|= ((uint64_t)in[3]) << 24;
304	0	result \|= ((uint64_t)in[4]) << 32;
305	0	result \|= ((uint64_t)in[5]) << 40;
306
307	0	return result;
308	0	}
309
310		static void fe51_frombytes(fe51 h, const uint8_t *s)
311	0	{
312	0	uint64_t h0 = load_7(s); /* 56 bits */
313	0	uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
314	0	uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
315	0	uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
316	0	uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
317
318	0	h1 \|= h0 >> 51; h0 &= MASK51;
319	0	h2 \|= h1 >> 51; h1 &= MASK51;
320	0	h3 \|= h2 >> 51; h2 &= MASK51;
321	0	h4 \|= h3 >> 51; h3 &= MASK51;
322
323	0	h[0] = h0;
324	0	h[1] = h1;
325	0	h[2] = h2;
326	0	h[3] = h3;
327	0	h[4] = h4;
328	0	}
329
330		static void fe51_tobytes(uint8_t *s, const fe51 h)
331	0	{
332	0	uint64_t h0 = h[0];
333	0	uint64_t h1 = h[1];
334	0	uint64_t h2 = h[2];
335	0	uint64_t h3 = h[3];
336	0	uint64_t h4 = h[4];
337	0	uint64_t q;
338
339		/* compare to modulus */
340	0	q = (h0 + 19) >> 51;
341	0	q = (h1 + q) >> 51;
342	0	q = (h2 + q) >> 51;
343	0	q = (h3 + q) >> 51;
344	0	q = (h4 + q) >> 51;
345
346		/* full reduce */
347	0	h0 += 19 * q;
348	0	h1 += h0 >> 51; h0 &= MASK51;
349	0	h2 += h1 >> 51; h1 &= MASK51;
350	0	h3 += h2 >> 51; h2 &= MASK51;
351	0	h4 += h3 >> 51; h3 &= MASK51;
352	0	h4 &= MASK51;
353
354		/* smash */
355	0	s[0] = (uint8_t)(h0 >> 0);
356	0	s[1] = (uint8_t)(h0 >> 8);
357	0	s[2] = (uint8_t)(h0 >> 16);
358	0	s[3] = (uint8_t)(h0 >> 24);
359	0	s[4] = (uint8_t)(h0 >> 32);
360	0	s[5] = (uint8_t)(h0 >> 40);
361	0	s[6] = (uint8_t)((h0 >> 48) \| ((uint32_t)h1 << 3));
362	0	s[7] = (uint8_t)(h1 >> 5);
363	0	s[8] = (uint8_t)(h1 >> 13);
364	0	s[9] = (uint8_t)(h1 >> 21);
365	0	s[10] = (uint8_t)(h1 >> 29);
366	0	s[11] = (uint8_t)(h1 >> 37);
367	0	s[12] = (uint8_t)((h1 >> 45) \| ((uint32_t)h2 << 6));
368	0	s[13] = (uint8_t)(h2 >> 2);
369	0	s[14] = (uint8_t)(h2 >> 10);
370	0	s[15] = (uint8_t)(h2 >> 18);
371	0	s[16] = (uint8_t)(h2 >> 26);
372	0	s[17] = (uint8_t)(h2 >> 34);
373	0	s[18] = (uint8_t)(h2 >> 42);
374	0	s[19] = (uint8_t)((h2 >> 50) \| ((uint32_t)h3 << 1));
375	0	s[20] = (uint8_t)(h3 >> 7);
376	0	s[21] = (uint8_t)(h3 >> 15);
377	0	s[22] = (uint8_t)(h3 >> 23);
378	0	s[23] = (uint8_t)(h3 >> 31);
379	0	s[24] = (uint8_t)(h3 >> 39);
380	0	s[25] = (uint8_t)((h3 >> 47) \| ((uint32_t)h4 << 4));
381	0	s[26] = (uint8_t)(h4 >> 4);
382	0	s[27] = (uint8_t)(h4 >> 12);
383	0	s[28] = (uint8_t)(h4 >> 20);
384	0	s[29] = (uint8_t)(h4 >> 28);
385	0	s[30] = (uint8_t)(h4 >> 36);
386	0	s[31] = (uint8_t)(h4 >> 44);
387	0	}
388
389		# if defined(X25519_ASM)
390		void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
391		void x25519_fe51_sqr(fe51 h, const fe51 f);
392		void x25519_fe51_mul121666(fe51 h, fe51 f);
393	0	# define fe51_mul x25519_fe51_mul
394	0	# define fe51_sq x25519_fe51_sqr
395	0	# define fe51_mul121666 x25519_fe51_mul121666
396		# else
397
398		typedef uint128_t u128;
399
400		static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
401		{
402		u128 h0, h1, h2, h3, h4;
403		uint64_t f_i, g0, g1, g2, g3, g4;
404
405		f_i = f[0];
406		h0 = (u128)f_i * (g0 = g[0]);
407		h1 = (u128)f_i * (g1 = g[1]);
408		h2 = (u128)f_i * (g2 = g[2]);
409		h3 = (u128)f_i * (g3 = g[3]);
410		h4 = (u128)f_i * (g4 = g[4]);
411
412		f_i = f[1];
413		h0 += (u128)f_i * (g4 *= 19);
414		h1 += (u128)f_i * g0;
415		h2 += (u128)f_i * g1;
416		h3 += (u128)f_i * g2;
417		h4 += (u128)f_i * g3;
418
419		f_i = f[2];
420		h0 += (u128)f_i * (g3 *= 19);
421		h1 += (u128)f_i * g4;
422		h2 += (u128)f_i * g0;
423		h3 += (u128)f_i * g1;
424		h4 += (u128)f_i * g2;
425
426		f_i = f[3];
427		h0 += (u128)f_i * (g2 *= 19);
428		h1 += (u128)f_i * g3;
429		h2 += (u128)f_i * g4;
430		h3 += (u128)f_i * g0;
431		h4 += (u128)f_i * g1;
432
433		f_i = f[4];
434		h0 += (u128)f_i * (g1 *= 19);
435		h1 += (u128)f_i * g2;
436		h2 += (u128)f_i * g3;
437		h3 += (u128)f_i * g4;
438		h4 += (u128)f_i * g0;
439
440		/* partial [lazy] reduction */
441		h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
442		h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
443
444		h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
445		g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
446
447		g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
448		g3 += g2 >> 51; g2 &= MASK51;
449		g1 += g0 >> 51; g0 &= MASK51;
450
451		h[0] = g0;
452		h[1] = g1;
453		h[2] = g2;
454		h[3] = g3;
455		h[4] = g4;
456		}
457
458		static void fe51_sq(fe51 h, const fe51 f)
459		{
460		# if defined(OPENSSL_SMALL_FOOTPRINT)
461		fe51_mul(h, f, f);
462		# else
463		/* dedicated squaring gives 16-25% overall improvement */
464		uint64_t g0 = f[0];
465		uint64_t g1 = f[1];
466		uint64_t g2 = f[2];
467		uint64_t g3 = f[3];
468		uint64_t g4 = f[4];
469		u128 h0, h1, h2, h3, h4;
470
471		h0 = (u128)g0 * g0; g0 *= 2;
472		h1 = (u128)g0 * g1;
473		h2 = (u128)g0 * g2;
474		h3 = (u128)g0 * g3;
475		h4 = (u128)g0 * g4;
476
477		g0 = g4; /* borrow g0 */
478		h3 += (u128)g0 * (g4 *= 19);
479
480		h2 += (u128)g1 * g1; g1 *= 2;
481		h3 += (u128)g1 * g2;
482		h4 += (u128)g1 * g3;
483		h0 += (u128)g1 * g4;
484
485		g0 = g3; /* borrow g0 */
486		h1 += (u128)g0 * (g3 *= 19);
487		h2 += (u128)(g0 * 2) * g4;
488
489		h4 += (u128)g2 * g2; g2 *= 2;
490		h0 += (u128)g2 * g3;
491		h1 += (u128)g2 * g4;
492
493		/* partial [lazy] reduction */
494		h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
495		h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
496
497		h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
498		g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
499
500		g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
501		g3 += g2 >> 51; g2 &= MASK51;
502		g1 += g0 >> 51; g0 &= MASK51;
503
504		h[0] = g0;
505		h[1] = g1;
506		h[2] = g2;
507		h[3] = g3;
508		h[4] = g4;
509		# endif
510		}
511
512		static void fe51_mul121666(fe51 h, fe51 f)
513		{
514		u128 h0 = f[0] * (u128)121666;
515		u128 h1 = f[1] * (u128)121666;
516		u128 h2 = f[2] * (u128)121666;
517		u128 h3 = f[3] * (u128)121666;
518		u128 h4 = f[4] * (u128)121666;
519		uint64_t g0, g1, g2, g3, g4;
520
521		h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
522		h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
523
524		h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
525		g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
526
527		g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
528		g3 += g2 >> 51; g2 &= MASK51;
529		g1 += g0 >> 51; g0 &= MASK51;
530
531		h[0] = g0;
532		h[1] = g1;
533		h[2] = g2;
534		h[3] = g3;
535		h[4] = g4;
536		}
537		# endif
538
539		static void fe51_add(fe51 h, const fe51 f, const fe51 g)
540	0	{
541	0	h[0] = f[0] + g[0];
542	0	h[1] = f[1] + g[1];
543	0	h[2] = f[2] + g[2];
544	0	h[3] = f[3] + g[3];
545	0	h[4] = f[4] + g[4];
546	0	}
547
548		static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
549	0	{
550		/*
551		* Add 2*modulus to ensure that result remains positive
552		* even if subtrahend is partially reduced.
553		*/
554	0	h[0] = (f[0] + 0xfffffffffffda) - g[0];
555	0	h[1] = (f[1] + 0xffffffffffffe) - g[1];
556	0	h[2] = (f[2] + 0xffffffffffffe) - g[2];
557	0	h[3] = (f[3] + 0xffffffffffffe) - g[3];
558	0	h[4] = (f[4] + 0xffffffffffffe) - g[4];
559	0	}
560
561		static void fe51_0(fe51 h)
562	0	{
563	0	h[0] = 0;
564	0	h[1] = 0;
565	0	h[2] = 0;
566	0	h[3] = 0;
567	0	h[4] = 0;
568	0	}
569
570		static void fe51_1(fe51 h)
571	0	{
572	0	h[0] = 1;
573	0	h[1] = 0;
574	0	h[2] = 0;
575	0	h[3] = 0;
576	0	h[4] = 0;
577	0	}
578
579		static void fe51_copy(fe51 h, const fe51 f)
580	0	{
581	0	h[0] = f[0];
582	0	h[1] = f[1];
583	0	h[2] = f[2];
584	0	h[3] = f[3];
585	0	h[4] = f[4];
586	0	}
587
588		static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
589	0	{
590	0	int i;
591	0	uint64_t mask = 0 - (uint64_t)b;
592
593	0	for (i = 0; i < 5; i++) {
594	0	int64_t x = f[i] ^ g[i];
595	0	x &= mask;
596	0	f[i] ^= x;
597	0	g[i] ^= x;
598	0	}
599	0	}
600
601		static void fe51_invert(fe51 out, const fe51 z)
602	0	{
603	0	fe51 t0;
604	0	fe51 t1;
605	0	fe51 t2;
606	0	fe51 t3;
607	0	int i;
608
609		/*
610		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
611		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
612		*/
613
614		/* t0 = z ** 2 */
615	0	fe51_sq(t0, z);
616
617		/* t1 = t0 (2 2) = z ** 8 */
618	0	fe51_sq(t1, t0);
619	0	fe51_sq(t1, t1);
620
621		/* t1 = z * t1 = z ** 9 */
622	0	fe51_mul(t1, z, t1);
623		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
624	0	fe51_mul(t0, t0, t1);
625
626		/* t2 = t0 2 = z 22 */
627	0	fe51_sq(t2, t0);
628
629		/* t1 = t1 * t2 = z (2 5 - 1) */
630	0	fe51_mul(t1, t1, t2);
631
632		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
633	0	fe51_sq(t2, t1);
634	0	for (i = 1; i < 5; ++i)
635	0	fe51_sq(t2, t2);
636
637		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
638	0	fe51_mul(t1, t2, t1);
639
640		/* Continuing similarly... */
641
642		/* t2 = z (2 20 - 1) */
643	0	fe51_sq(t2, t1);
644	0	for (i = 1; i < 10; ++i)
645	0	fe51_sq(t2, t2);
646
647	0	fe51_mul(t2, t2, t1);
648
649		/* t2 = z (2 40 - 1) */
650	0	fe51_sq(t3, t2);
651	0	for (i = 1; i < 20; ++i)
652	0	fe51_sq(t3, t3);
653
654	0	fe51_mul(t2, t3, t2);
655
656		/* t2 = z (2 10) * (2 ** 40 - 1) */
657	0	for (i = 0; i < 10; ++i)
658	0	fe51_sq(t2, t2);
659
660		/* t1 = z (2 50 - 1) */
661	0	fe51_mul(t1, t2, t1);
662
663		/* t2 = z (2 100 - 1) */
664	0	fe51_sq(t2, t1);
665	0	for (i = 1; i < 50; ++i)
666	0	fe51_sq(t2, t2);
667
668	0	fe51_mul(t2, t2, t1);
669
670		/* t2 = z (2 200 - 1) */
671	0	fe51_sq(t3, t2);
672	0	for (i = 1; i < 100; ++i)
673	0	fe51_sq(t3, t3);
674
675	0	fe51_mul(t2, t3, t2);
676
677		/* t2 = z ((2 50) * (2 ** 200 - 1) */
678	0	for (i = 0; i < 50; ++i)
679	0	fe51_sq(t2, t2);
680
681		/* t1 = z (2 250 - 1) */
682	0	fe51_mul(t1, t2, t1);
683
684		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
685	0	for (i = 0; i < 5; ++i)
686	0	fe51_sq(t1, t1);
687
688		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
689	0	fe51_mul(out, t1, t0);
690	0	}
691
692		/*
693		* Duplicate of original x25519_scalar_mult_generic, but using
694		* fe51_* subroutines.
695		*/
696		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
697		const uint8_t point[32])
698	16.2k	{
699	16.2k	fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
700	16.2k	uint8_t e[32];
701	16.2k	unsigned swap = 0;
702	16.2k	int pos;
703
704	16.2k	# ifdef BASE_2_64_IMPLEMENTED
705	16.2k	if (x25519_fe64_eligible()) {
706	16.2k	x25519_scalar_mulx(out, scalar, point);
707	16.2k	return;
708	16.2k	}
709	0	# endif
710
711	0	memcpy(e, scalar, 32);
712	0	e[0] &= 0xf8;
713	0	e[31] &= 0x7f;
714	0	e[31] \|= 0x40;
715	0	fe51_frombytes(x1, point);
716	0	fe51_1(x2);
717	0	fe51_0(z2);
718	0	fe51_copy(x3, x1);
719	0	fe51_1(z3);
720
721	0	for (pos = 254; pos >= 0; --pos) {
722	0	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
723
724	0	swap ^= b;
725	0	fe51_cswap(x2, x3, swap);
726	0	fe51_cswap(z2, z3, swap);
727	0	swap = b;
728	0	fe51_sub(tmp0, x3, z3);
729	0	fe51_sub(tmp1, x2, z2);
730	0	fe51_add(x2, x2, z2);
731	0	fe51_add(z2, x3, z3);
732	0	fe51_mul(z3, tmp0, x2);
733	0	fe51_mul(z2, z2, tmp1);
734	0	fe51_sq(tmp0, tmp1);
735	0	fe51_sq(tmp1, x2);
736	0	fe51_add(x3, z3, z2);
737	0	fe51_sub(z2, z3, z2);
738	0	fe51_mul(x2, tmp1, tmp0);
739	0	fe51_sub(tmp1, tmp1, tmp0);
740	0	fe51_sq(z2, z2);
741	0	fe51_mul121666(z3, tmp1);
742	0	fe51_sq(x3, x3);
743	0	fe51_add(tmp0, tmp0, z3);
744	0	fe51_mul(z3, x1, z2);
745	0	fe51_mul(z2, tmp1, tmp0);
746	0	}
747
748	0	fe51_invert(z2, z2);
749	0	fe51_mul(x2, x2, z2);
750	0	fe51_tobytes(out, x2);
751
752	0	OPENSSL_cleanse(e, sizeof(e));
753	0	}
754		#endif
755
756		/*
757		* Reference base 2^25.5 implementation.
758		*
759		* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
760		* 20141124 (http://bench.cr.yp.to/supercop.html).
761		*
762		* The field functions are shared by Ed25519 and X25519 where possible.
763		*/
764
765		/*
766		* fe means field element. Here the field is \Z/(2^255-19). An element t,
767		* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
768		* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
769		* context.
770		*/
771		typedef int32_t fe[10];
772
773		static const int64_t kBottom21Bits = 0x1fffffLL;
774		static const int64_t kBottom25Bits = 0x1ffffffLL;
775		static const int64_t kBottom26Bits = 0x3ffffffLL;
776		static const int64_t kTop39Bits = 0xfffffffffe000000LL;
777		static const int64_t kTop38Bits = 0xfffffffffc000000LL;
778
779		static uint64_t load_3(const uint8_t *in)
780	1.84k	{
781	1.84k	uint64_t result;
782
783	1.84k	result = ((uint64_t)in[0]);
784	1.84k	result \|= ((uint64_t)in[1]) << 8;
785	1.84k	result \|= ((uint64_t)in[2]) << 16;
786	1.84k	return result;
787	1.84k	}
788
789		static uint64_t load_4(const uint8_t *in)
790	1.44k	{
791	1.44k	uint64_t result;
792
793	1.44k	result = ((uint64_t)in[0]);
794	1.44k	result \|= ((uint64_t)in[1]) << 8;
795	1.44k	result \|= ((uint64_t)in[2]) << 16;
796	1.44k	result \|= ((uint64_t)in[3]) << 24;
797	1.44k	return result;
798	1.44k	}
799
800		static void fe_frombytes(fe h, const uint8_t *s)
801	98	{
802		/* Ignores top bit of h. */
803	98	int64_t h0 = load_4(s);
804	98	int64_t h1 = load_3(s + 4) << 6;
805	98	int64_t h2 = load_3(s + 7) << 5;
806	98	int64_t h3 = load_3(s + 10) << 3;
807	98	int64_t h4 = load_3(s + 13) << 2;
808	98	int64_t h5 = load_4(s + 16);
809	98	int64_t h6 = load_3(s + 20) << 7;
810	98	int64_t h7 = load_3(s + 23) << 5;
811	98	int64_t h8 = load_3(s + 26) << 4;
812	98	int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
813	98	int64_t carry0;
814	98	int64_t carry1;
815	98	int64_t carry2;
816	98	int64_t carry3;
817	98	int64_t carry4;
818	98	int64_t carry5;
819	98	int64_t carry6;
820	98	int64_t carry7;
821	98	int64_t carry8;
822	98	int64_t carry9;
823
824	98	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
825	98	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
826	98	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
827	98	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
828	98	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
829
830	98	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
831	98	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
832	98	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
833	98	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
834	98	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
835
836	98	h[0] = (int32_t)h0;
837	98	h[1] = (int32_t)h1;
838	98	h[2] = (int32_t)h2;
839	98	h[3] = (int32_t)h3;
840	98	h[4] = (int32_t)h4;
841	98	h[5] = (int32_t)h5;
842	98	h[6] = (int32_t)h6;
843	98	h[7] = (int32_t)h7;
844	98	h[8] = (int32_t)h8;
845	98	h[9] = (int32_t)h9;
846	98	}
847
848		/*
849		* Preconditions:
850		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
851		*
852		* Write p=2^255-19; q=floor(h/p).
853		* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
854		*
855		* Proof:
856		* Have \|h\|<=p so \|q\|<=1 so \|19^2 2^(-255) q\|<1/4.
857		* Also have \|h-2^230 h9\|<2^231 so \|19 2^(-255)(h-2^230 h9)\|<1/4.
858		*
859		* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
860		* Then 0<y<1.
861		*
862		* Write r=h-pq.
863		* Have 0<=r<=p-1=2^255-20.
864		* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
865		*
866		* Write x=r+19(2^-255)r+y.
867		* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
868		*
869		* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
870		* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
871		*/
872		static void fe_tobytes(uint8_t *s, const fe h)
873	74.6k	{
874	74.6k	int32_t h0 = h[0];
875	74.6k	int32_t h1 = h[1];
876	74.6k	int32_t h2 = h[2];
877	74.6k	int32_t h3 = h[3];
878	74.6k	int32_t h4 = h[4];
879	74.6k	int32_t h5 = h[5];
880	74.6k	int32_t h6 = h[6];
881	74.6k	int32_t h7 = h[7];
882	74.6k	int32_t h8 = h[8];
883	74.6k	int32_t h9 = h[9];
884	74.6k	int32_t q;
885
886	74.6k	q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
887	74.6k	q = (h0 + q) >> 26;
888	74.6k	q = (h1 + q) >> 25;
889	74.6k	q = (h2 + q) >> 26;
890	74.6k	q = (h3 + q) >> 25;
891	74.6k	q = (h4 + q) >> 26;
892	74.6k	q = (h5 + q) >> 25;
893	74.6k	q = (h6 + q) >> 26;
894	74.6k	q = (h7 + q) >> 25;
895	74.6k	q = (h8 + q) >> 26;
896	74.6k	q = (h9 + q) >> 25;
897
898		/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
899	74.6k	h0 += 19 * q;
900		/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
901
902	74.6k	h1 += h0 >> 26; h0 &= kBottom26Bits;
903	74.6k	h2 += h1 >> 25; h1 &= kBottom25Bits;
904	74.6k	h3 += h2 >> 26; h2 &= kBottom26Bits;
905	74.6k	h4 += h3 >> 25; h3 &= kBottom25Bits;
906	74.6k	h5 += h4 >> 26; h4 &= kBottom26Bits;
907	74.6k	h6 += h5 >> 25; h5 &= kBottom25Bits;
908	74.6k	h7 += h6 >> 26; h6 &= kBottom26Bits;
909	74.6k	h8 += h7 >> 25; h7 &= kBottom25Bits;
910	74.6k	h9 += h8 >> 26; h8 &= kBottom26Bits;
911	74.6k	h9 &= kBottom25Bits;
912		/* h10 = carry9 */
913
914		/*
915		* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
916		* Have h0+...+2^230 h9 between 0 and 2^255-1;
917		* evidently 2^255 h10-2^255 q = 0.
918		* Goal: Output h0+...+2^230 h9.
919		*/
920	74.6k	s[ 0] = (uint8_t) (h0 >> 0);
921	74.6k	s[ 1] = (uint8_t) (h0 >> 8);
922	74.6k	s[ 2] = (uint8_t) (h0 >> 16);
923	74.6k	s[ 3] = (uint8_t)((h0 >> 24) \| ((uint32_t)(h1) << 2));
924	74.6k	s[ 4] = (uint8_t) (h1 >> 6);
925	74.6k	s[ 5] = (uint8_t) (h1 >> 14);
926	74.6k	s[ 6] = (uint8_t)((h1 >> 22) \| ((uint32_t)(h2) << 3));
927	74.6k	s[ 7] = (uint8_t) (h2 >> 5);
928	74.6k	s[ 8] = (uint8_t) (h2 >> 13);
929	74.6k	s[ 9] = (uint8_t)((h2 >> 21) \| ((uint32_t)(h3) << 5));
930	74.6k	s[10] = (uint8_t) (h3 >> 3);
931	74.6k	s[11] = (uint8_t) (h3 >> 11);
932	74.6k	s[12] = (uint8_t)((h3 >> 19) \| ((uint32_t)(h4) << 6));
933	74.6k	s[13] = (uint8_t) (h4 >> 2);
934	74.6k	s[14] = (uint8_t) (h4 >> 10);
935	74.6k	s[15] = (uint8_t) (h4 >> 18);
936	74.6k	s[16] = (uint8_t) (h5 >> 0);
937	74.6k	s[17] = (uint8_t) (h5 >> 8);
938	74.6k	s[18] = (uint8_t) (h5 >> 16);
939	74.6k	s[19] = (uint8_t)((h5 >> 24) \| ((uint32_t)(h6) << 1));
940	74.6k	s[20] = (uint8_t) (h6 >> 7);
941	74.6k	s[21] = (uint8_t) (h6 >> 15);
942	74.6k	s[22] = (uint8_t)((h6 >> 23) \| ((uint32_t)(h7) << 3));
943	74.6k	s[23] = (uint8_t) (h7 >> 5);
944	74.6k	s[24] = (uint8_t) (h7 >> 13);
945	74.6k	s[25] = (uint8_t)((h7 >> 21) \| ((uint32_t)(h8) << 4));
946	74.6k	s[26] = (uint8_t) (h8 >> 4);
947	74.6k	s[27] = (uint8_t) (h8 >> 12);
948	74.6k	s[28] = (uint8_t)((h8 >> 20) \| ((uint32_t)(h9) << 6));
949	74.6k	s[29] = (uint8_t) (h9 >> 2);
950	74.6k	s[30] = (uint8_t) (h9 >> 10);
951	74.6k	s[31] = (uint8_t) (h9 >> 18);
952	74.6k	}
953
954		/* h = f */
955		static void fe_copy(fe h, const fe f)
956	9.72M	{
957	9.72M	memmove(h, f, sizeof(int32_t) * 10);
958	9.72M	}
959
960		/* h = 0 */
961		static void fe_0(fe h)
962	4.89M	{
963	4.89M	memset(h, 0, sizeof(int32_t) * 10);
964	4.89M	}
965
966		/* h = 1 */
967		static void fe_1(fe h)
968	9.64M	{
969	9.64M	memset(h, 0, sizeof(int32_t) * 10);
970	9.64M	h[0] = 1;
971	9.64M	}
972
973		/*
974		* h = f + g
975		*
976		* Can overlap h with f or g.
977		*
978		* Preconditions:
979		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
980		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
981		*
982		* Postconditions:
983		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
984		*/
985		static void fe_add(fe h, const fe f, const fe g)
986	19.7M	{
987	19.7M	unsigned i;
988
989	217M	for (i = 0; i < 10; i++) {
990	197M	h[i] = f[i] + g[i];
991	197M	}
992	19.7M	}
993
994		/*
995		* h = f - g
996		*
997		* Can overlap h with f or g.
998		*
999		* Preconditions:
1000		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1001		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1002		*
1003		* Postconditions:
1004		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1005		*/
1006		static void fe_sub(fe h, const fe f, const fe g)
1007	15.3M	{
1008	15.3M	unsigned i;
1009
1010	168M	for (i = 0; i < 10; i++) {
1011	153M	h[i] = f[i] - g[i];
1012	153M	}
1013	15.3M	}
1014
1015		/*
1016		* h = f * g
1017		*
1018		* Can overlap h with f or g.
1019		*
1020		* Preconditions:
1021		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1022		* \|g\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1023		*
1024		* Postconditions:
1025		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1026		*
1027		* Notes on implementation strategy:
1028		*
1029		* Using schoolbook multiplication.
1030		* Karatsuba would save a little in some cost models.
1031		*
1032		* Most multiplications by 2 and 19 are 32-bit precomputations;
1033		* cheaper than 64-bit postcomputations.
1034		*
1035		* There is one remaining multiplication by 19 in the carry chain;
1036		* one *19 precomputation can be merged into this,
1037		* but the resulting data flow is considerably less clean.
1038		*
1039		* There are 12 carries below.
1040		* 10 of them are 2-way parallelizable and vectorizable.
1041		* Can get away with 11 carries, but then data flow is much deeper.
1042		*
1043		* With tighter constraints on inputs can squeeze carries into int32.
1044		*/
1045		static void fe_mul(fe h, const fe f, const fe g)
1046	35.2M	{
1047	35.2M	int32_t f0 = f[0];
1048	35.2M	int32_t f1 = f[1];
1049	35.2M	int32_t f2 = f[2];
1050	35.2M	int32_t f3 = f[3];
1051	35.2M	int32_t f4 = f[4];
1052	35.2M	int32_t f5 = f[5];
1053	35.2M	int32_t f6 = f[6];
1054	35.2M	int32_t f7 = f[7];
1055	35.2M	int32_t f8 = f[8];
1056	35.2M	int32_t f9 = f[9];
1057	35.2M	int32_t g0 = g[0];
1058	35.2M	int32_t g1 = g[1];
1059	35.2M	int32_t g2 = g[2];
1060	35.2M	int32_t g3 = g[3];
1061	35.2M	int32_t g4 = g[4];
1062	35.2M	int32_t g5 = g[5];
1063	35.2M	int32_t g6 = g[6];
1064	35.2M	int32_t g7 = g[7];
1065	35.2M	int32_t g8 = g[8];
1066	35.2M	int32_t g9 = g[9];
1067	35.2M	int32_t g1_19 = 19 * g1; /* 1.9593752^29 /
1068	35.2M	int32_t g2_19 = 19 * g2; /* 1.9593752^30; still ok /
1069	35.2M	int32_t g3_19 = 19 * g3;
1070	35.2M	int32_t g4_19 = 19 * g4;
1071	35.2M	int32_t g5_19 = 19 * g5;
1072	35.2M	int32_t g6_19 = 19 * g6;
1073	35.2M	int32_t g7_19 = 19 * g7;
1074	35.2M	int32_t g8_19 = 19 * g8;
1075	35.2M	int32_t g9_19 = 19 * g9;
1076	35.2M	int32_t f1_2 = 2 * f1;
1077	35.2M	int32_t f3_2 = 2 * f3;
1078	35.2M	int32_t f5_2 = 2 * f5;
1079	35.2M	int32_t f7_2 = 2 * f7;
1080	35.2M	int32_t f9_2 = 2 * f9;
1081	35.2M	int64_t f0g0 = f0 * (int64_t) g0;
1082	35.2M	int64_t f0g1 = f0 * (int64_t) g1;
1083	35.2M	int64_t f0g2 = f0 * (int64_t) g2;
1084	35.2M	int64_t f0g3 = f0 * (int64_t) g3;
1085	35.2M	int64_t f0g4 = f0 * (int64_t) g4;
1086	35.2M	int64_t f0g5 = f0 * (int64_t) g5;
1087	35.2M	int64_t f0g6 = f0 * (int64_t) g6;
1088	35.2M	int64_t f0g7 = f0 * (int64_t) g7;
1089	35.2M	int64_t f0g8 = f0 * (int64_t) g8;
1090	35.2M	int64_t f0g9 = f0 * (int64_t) g9;
1091	35.2M	int64_t f1g0 = f1 * (int64_t) g0;
1092	35.2M	int64_t f1g1_2 = f1_2 * (int64_t) g1;
1093	35.2M	int64_t f1g2 = f1 * (int64_t) g2;
1094	35.2M	int64_t f1g3_2 = f1_2 * (int64_t) g3;
1095	35.2M	int64_t f1g4 = f1 * (int64_t) g4;
1096	35.2M	int64_t f1g5_2 = f1_2 * (int64_t) g5;
1097	35.2M	int64_t f1g6 = f1 * (int64_t) g6;
1098	35.2M	int64_t f1g7_2 = f1_2 * (int64_t) g7;
1099	35.2M	int64_t f1g8 = f1 * (int64_t) g8;
1100	35.2M	int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
1101	35.2M	int64_t f2g0 = f2 * (int64_t) g0;
1102	35.2M	int64_t f2g1 = f2 * (int64_t) g1;
1103	35.2M	int64_t f2g2 = f2 * (int64_t) g2;
1104	35.2M	int64_t f2g3 = f2 * (int64_t) g3;
1105	35.2M	int64_t f2g4 = f2 * (int64_t) g4;
1106	35.2M	int64_t f2g5 = f2 * (int64_t) g5;
1107	35.2M	int64_t f2g6 = f2 * (int64_t) g6;
1108	35.2M	int64_t f2g7 = f2 * (int64_t) g7;
1109	35.2M	int64_t f2g8_19 = f2 * (int64_t) g8_19;
1110	35.2M	int64_t f2g9_19 = f2 * (int64_t) g9_19;
1111	35.2M	int64_t f3g0 = f3 * (int64_t) g0;
1112	35.2M	int64_t f3g1_2 = f3_2 * (int64_t) g1;
1113	35.2M	int64_t f3g2 = f3 * (int64_t) g2;
1114	35.2M	int64_t f3g3_2 = f3_2 * (int64_t) g3;
1115	35.2M	int64_t f3g4 = f3 * (int64_t) g4;
1116	35.2M	int64_t f3g5_2 = f3_2 * (int64_t) g5;
1117	35.2M	int64_t f3g6 = f3 * (int64_t) g6;
1118	35.2M	int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
1119	35.2M	int64_t f3g8_19 = f3 * (int64_t) g8_19;
1120	35.2M	int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
1121	35.2M	int64_t f4g0 = f4 * (int64_t) g0;
1122	35.2M	int64_t f4g1 = f4 * (int64_t) g1;
1123	35.2M	int64_t f4g2 = f4 * (int64_t) g2;
1124	35.2M	int64_t f4g3 = f4 * (int64_t) g3;
1125	35.2M	int64_t f4g4 = f4 * (int64_t) g4;
1126	35.2M	int64_t f4g5 = f4 * (int64_t) g5;
1127	35.2M	int64_t f4g6_19 = f4 * (int64_t) g6_19;
1128	35.2M	int64_t f4g7_19 = f4 * (int64_t) g7_19;
1129	35.2M	int64_t f4g8_19 = f4 * (int64_t) g8_19;
1130	35.2M	int64_t f4g9_19 = f4 * (int64_t) g9_19;
1131	35.2M	int64_t f5g0 = f5 * (int64_t) g0;
1132	35.2M	int64_t f5g1_2 = f5_2 * (int64_t) g1;
1133	35.2M	int64_t f5g2 = f5 * (int64_t) g2;
1134	35.2M	int64_t f5g3_2 = f5_2 * (int64_t) g3;
1135	35.2M	int64_t f5g4 = f5 * (int64_t) g4;
1136	35.2M	int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
1137	35.2M	int64_t f5g6_19 = f5 * (int64_t) g6_19;
1138	35.2M	int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
1139	35.2M	int64_t f5g8_19 = f5 * (int64_t) g8_19;
1140	35.2M	int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
1141	35.2M	int64_t f6g0 = f6 * (int64_t) g0;
1142	35.2M	int64_t f6g1 = f6 * (int64_t) g1;
1143	35.2M	int64_t f6g2 = f6 * (int64_t) g2;
1144	35.2M	int64_t f6g3 = f6 * (int64_t) g3;
1145	35.2M	int64_t f6g4_19 = f6 * (int64_t) g4_19;
1146	35.2M	int64_t f6g5_19 = f6 * (int64_t) g5_19;
1147	35.2M	int64_t f6g6_19 = f6 * (int64_t) g6_19;
1148	35.2M	int64_t f6g7_19 = f6 * (int64_t) g7_19;
1149	35.2M	int64_t f6g8_19 = f6 * (int64_t) g8_19;
1150	35.2M	int64_t f6g9_19 = f6 * (int64_t) g9_19;
1151	35.2M	int64_t f7g0 = f7 * (int64_t) g0;
1152	35.2M	int64_t f7g1_2 = f7_2 * (int64_t) g1;
1153	35.2M	int64_t f7g2 = f7 * (int64_t) g2;
1154	35.2M	int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
1155	35.2M	int64_t f7g4_19 = f7 * (int64_t) g4_19;
1156	35.2M	int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
1157	35.2M	int64_t f7g6_19 = f7 * (int64_t) g6_19;
1158	35.2M	int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
1159	35.2M	int64_t f7g8_19 = f7 * (int64_t) g8_19;
1160	35.2M	int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
1161	35.2M	int64_t f8g0 = f8 * (int64_t) g0;
1162	35.2M	int64_t f8g1 = f8 * (int64_t) g1;
1163	35.2M	int64_t f8g2_19 = f8 * (int64_t) g2_19;
1164	35.2M	int64_t f8g3_19 = f8 * (int64_t) g3_19;
1165	35.2M	int64_t f8g4_19 = f8 * (int64_t) g4_19;
1166	35.2M	int64_t f8g5_19 = f8 * (int64_t) g5_19;
1167	35.2M	int64_t f8g6_19 = f8 * (int64_t) g6_19;
1168	35.2M	int64_t f8g7_19 = f8 * (int64_t) g7_19;
1169	35.2M	int64_t f8g8_19 = f8 * (int64_t) g8_19;
1170	35.2M	int64_t f8g9_19 = f8 * (int64_t) g9_19;
1171	35.2M	int64_t f9g0 = f9 * (int64_t) g0;
1172	35.2M	int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
1173	35.2M	int64_t f9g2_19 = f9 * (int64_t) g2_19;
1174	35.2M	int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
1175	35.2M	int64_t f9g4_19 = f9 * (int64_t) g4_19;
1176	35.2M	int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
1177	35.2M	int64_t f9g6_19 = f9 * (int64_t) g6_19;
1178	35.2M	int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
1179	35.2M	int64_t f9g8_19 = f9 * (int64_t) g8_19;
1180	35.2M	int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
1181	35.2M	int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1182	35.2M	int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1183	35.2M	int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1184	35.2M	int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1185	35.2M	int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1186	35.2M	int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1187	35.2M	int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
1188	35.2M	int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
1189	35.2M	int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
1190	35.2M	int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ;
1191	35.2M	int64_t carry0;
1192	35.2M	int64_t carry1;
1193	35.2M	int64_t carry2;
1194	35.2M	int64_t carry3;
1195	35.2M	int64_t carry4;
1196	35.2M	int64_t carry5;
1197	35.2M	int64_t carry6;
1198	35.2M	int64_t carry7;
1199	35.2M	int64_t carry8;
1200	35.2M	int64_t carry9;
1201
1202		/* \|h0\| <= (1.651.652^52(1+19+19+19+19)+1.651.652^50(38+38+38+38+38))
1203		* i.e. \|h0\| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1204		* \|h1\| <= (1.651.652^51*(1+1+19+19+19+19+19+19+19+19))
1205		* i.e. \|h1\| <= 1.72^59; narrower ranges for h3, h5, h7, h9 /
1206
1207	35.2M	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1208	35.2M	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1209		/* \|h0\| <= 2^25 */
1210		/* \|h4\| <= 2^25 */
1211		/* \|h1\| <= 1.712^59 /
1212		/* \|h5\| <= 1.712^59 /
1213
1214	35.2M	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1215	35.2M	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1216		/* \|h1\| <= 2^24; from now on fits into int32 */
1217		/* \|h5\| <= 2^24; from now on fits into int32 */
1218		/* \|h2\| <= 1.412^60 /
1219		/* \|h6\| <= 1.412^60 /
1220
1221	35.2M	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1222	35.2M	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1223		/* \|h2\| <= 2^25; from now on fits into int32 unchanged */
1224		/* \|h6\| <= 2^25; from now on fits into int32 unchanged */
1225		/* \|h3\| <= 1.712^59 /
1226		/* \|h7\| <= 1.712^59 /
1227
1228	35.2M	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1229	35.2M	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1230		/* \|h3\| <= 2^24; from now on fits into int32 unchanged */
1231		/* \|h7\| <= 2^24; from now on fits into int32 unchanged */
1232		/* \|h4\| <= 1.722^34 /
1233		/* \|h8\| <= 1.412^60 /
1234
1235	35.2M	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1236	35.2M	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1237		/* \|h4\| <= 2^25; from now on fits into int32 unchanged */
1238		/* \|h8\| <= 2^25; from now on fits into int32 unchanged */
1239		/* \|h5\| <= 1.012^24 /
1240		/* \|h9\| <= 1.712^59 /
1241
1242	35.2M	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1243		/* \|h9\| <= 2^24; from now on fits into int32 unchanged */
1244		/* \|h0\| <= 1.12^39 /
1245
1246	35.2M	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1247		/* \|h0\| <= 2^25; from now on fits into int32 unchanged */
1248		/* \|h1\| <= 1.012^24 /
1249
1250	35.2M	h[0] = (int32_t)h0;
1251	35.2M	h[1] = (int32_t)h1;
1252	35.2M	h[2] = (int32_t)h2;
1253	35.2M	h[3] = (int32_t)h3;
1254	35.2M	h[4] = (int32_t)h4;
1255	35.2M	h[5] = (int32_t)h5;
1256	35.2M	h[6] = (int32_t)h6;
1257	35.2M	h[7] = (int32_t)h7;
1258	35.2M	h[8] = (int32_t)h8;
1259	35.2M	h[9] = (int32_t)h9;
1260	35.2M	}
1261
1262		/*
1263		* h = f * f
1264		*
1265		* Can overlap h with f.
1266		*
1267		* Preconditions:
1268		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1269		*
1270		* Postconditions:
1271		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1272		*
1273		* See fe_mul.c for discussion of implementation strategy.
1274		*/
1275		static void fe_sq(fe h, const fe f)
1276	19.8M	{
1277	19.8M	int32_t f0 = f[0];
1278	19.8M	int32_t f1 = f[1];
1279	19.8M	int32_t f2 = f[2];
1280	19.8M	int32_t f3 = f[3];
1281	19.8M	int32_t f4 = f[4];
1282	19.8M	int32_t f5 = f[5];
1283	19.8M	int32_t f6 = f[6];
1284	19.8M	int32_t f7 = f[7];
1285	19.8M	int32_t f8 = f[8];
1286	19.8M	int32_t f9 = f[9];
1287	19.8M	int32_t f0_2 = 2 * f0;
1288	19.8M	int32_t f1_2 = 2 * f1;
1289	19.8M	int32_t f2_2 = 2 * f2;
1290	19.8M	int32_t f3_2 = 2 * f3;
1291	19.8M	int32_t f4_2 = 2 * f4;
1292	19.8M	int32_t f5_2 = 2 * f5;
1293	19.8M	int32_t f6_2 = 2 * f6;
1294	19.8M	int32_t f7_2 = 2 * f7;
1295	19.8M	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1296	19.8M	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1297	19.8M	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1298	19.8M	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1299	19.8M	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1300	19.8M	int64_t f0f0 = f0 * (int64_t) f0;
1301	19.8M	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1302	19.8M	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1303	19.8M	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1304	19.8M	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1305	19.8M	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1306	19.8M	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1307	19.8M	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1308	19.8M	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1309	19.8M	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1310	19.8M	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1311	19.8M	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1312	19.8M	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1313	19.8M	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1314	19.8M	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1315	19.8M	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1316	19.8M	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1317	19.8M	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1318	19.8M	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1319	19.8M	int64_t f2f2 = f2 * (int64_t) f2;
1320	19.8M	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1321	19.8M	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1322	19.8M	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1323	19.8M	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1324	19.8M	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1325	19.8M	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1326	19.8M	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1327	19.8M	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1328	19.8M	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1329	19.8M	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1330	19.8M	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1331	19.8M	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1332	19.8M	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1333	19.8M	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1334	19.8M	int64_t f4f4 = f4 * (int64_t) f4;
1335	19.8M	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1336	19.8M	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1337	19.8M	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1338	19.8M	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1339	19.8M	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1340	19.8M	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1341	19.8M	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1342	19.8M	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1343	19.8M	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1344	19.8M	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1345	19.8M	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1346	19.8M	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1347	19.8M	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1348	19.8M	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1349	19.8M	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1350	19.8M	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1351	19.8M	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1352	19.8M	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1353	19.8M	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1354	19.8M	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1355	19.8M	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1356	19.8M	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1357	19.8M	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1358	19.8M	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1359	19.8M	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1360	19.8M	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1361	19.8M	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1362	19.8M	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1363	19.8M	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1364	19.8M	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1365	19.8M	int64_t carry0;
1366	19.8M	int64_t carry1;
1367	19.8M	int64_t carry2;
1368	19.8M	int64_t carry3;
1369	19.8M	int64_t carry4;
1370	19.8M	int64_t carry5;
1371	19.8M	int64_t carry6;
1372	19.8M	int64_t carry7;
1373	19.8M	int64_t carry8;
1374	19.8M	int64_t carry9;
1375
1376	19.8M	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1377	19.8M	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1378
1379	19.8M	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1380	19.8M	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1381
1382	19.8M	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1383	19.8M	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1384
1385	19.8M	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1386	19.8M	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1387
1388	19.8M	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1389	19.8M	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1390
1391	19.8M	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1392
1393	19.8M	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1394
1395	19.8M	h[0] = (int32_t)h0;
1396	19.8M	h[1] = (int32_t)h1;
1397	19.8M	h[2] = (int32_t)h2;
1398	19.8M	h[3] = (int32_t)h3;
1399	19.8M	h[4] = (int32_t)h4;
1400	19.8M	h[5] = (int32_t)h5;
1401	19.8M	h[6] = (int32_t)h6;
1402	19.8M	h[7] = (int32_t)h7;
1403	19.8M	h[8] = (int32_t)h8;
1404	19.8M	h[9] = (int32_t)h9;
1405	19.8M	}
1406
1407		static void fe_invert(fe out, const fe z)
1408	74.2k	{
1409	74.2k	fe t0;
1410	74.2k	fe t1;
1411	74.2k	fe t2;
1412	74.2k	fe t3;
1413	74.2k	int i;
1414
1415		/*
1416		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
1417		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
1418		*/
1419
1420		/* t0 = z ** 2 */
1421	74.2k	fe_sq(t0, z);
1422
1423		/* t1 = t0 (2 2) = z ** 8 */
1424	74.2k	fe_sq(t1, t0);
1425	74.2k	fe_sq(t1, t1);
1426
1427		/* t1 = z * t1 = z ** 9 */
1428	74.2k	fe_mul(t1, z, t1);
1429		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1430	74.2k	fe_mul(t0, t0, t1);
1431
1432		/* t2 = t0 2 = z 22 */
1433	74.2k	fe_sq(t2, t0);
1434
1435		/* t1 = t1 * t2 = z (2 5 - 1) */
1436	74.2k	fe_mul(t1, t1, t2);
1437
1438		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
1439	74.2k	fe_sq(t2, t1);
1440	371k	for (i = 1; i < 5; ++i) {
1441	297k	fe_sq(t2, t2);
1442	297k	}
1443
1444		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
1445	74.2k	fe_mul(t1, t2, t1);
1446
1447		/* Continuing similarly... */
1448
1449		/* t2 = z (2 20 - 1) */
1450	74.2k	fe_sq(t2, t1);
1451	742k	for (i = 1; i < 10; ++i) {
1452	668k	fe_sq(t2, t2);
1453	668k	}
1454	74.2k	fe_mul(t2, t2, t1);
1455
1456		/* t2 = z (2 40 - 1) */
1457	74.2k	fe_sq(t3, t2);
1458	1.48M	for (i = 1; i < 20; ++i) {
1459	1.41M	fe_sq(t3, t3);
1460	1.41M	}
1461	74.2k	fe_mul(t2, t3, t2);
1462
1463		/* t2 = z (2 10) * (2 ** 40 - 1) */
1464	817k	for (i = 0; i < 10; ++i) {
1465	742k	fe_sq(t2, t2);
1466	742k	}
1467		/* t1 = z (2 50 - 1) */
1468	74.2k	fe_mul(t1, t2, t1);
1469
1470		/* t2 = z (2 100 - 1) */
1471	74.2k	fe_sq(t2, t1);
1472	3.71M	for (i = 1; i < 50; ++i) {
1473	3.64M	fe_sq(t2, t2);
1474	3.64M	}
1475	74.2k	fe_mul(t2, t2, t1);
1476
1477		/* t2 = z (2 200 - 1) */
1478	74.2k	fe_sq(t3, t2);
1479	7.42M	for (i = 1; i < 100; ++i) {
1480	7.35M	fe_sq(t3, t3);
1481	7.35M	}
1482	74.2k	fe_mul(t2, t3, t2);
1483
1484		/* t2 = z ((2 50) * (2 ** 200 - 1) */
1485	74.2k	fe_sq(t2, t2);
1486	3.71M	for (i = 1; i < 50; ++i) {
1487	3.64M	fe_sq(t2, t2);
1488	3.64M	}
1489
1490		/* t1 = z (2 250 - 1) */
1491	74.2k	fe_mul(t1, t2, t1);
1492
1493		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
1494	74.2k	fe_sq(t1, t1);
1495	371k	for (i = 1; i < 5; ++i) {
1496	297k	fe_sq(t1, t1);
1497	297k	}
1498
1499		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
1500	74.2k	fe_mul(out, t1, t0);
1501	74.2k	}
1502
1503		/*
1504		* h = -f
1505		*
1506		* Preconditions:
1507		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1508		*
1509		* Postconditions:
1510		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1511		*/
1512		static void fe_neg(fe h, const fe f)
1513	4.74M	{
1514	4.74M	unsigned i;
1515
1516	52.2M	for (i = 0; i < 10; i++) {
1517	47.4M	h[i] = -f[i];
1518	47.4M	}
1519	4.74M	}
1520
1521		/*
1522		* Replace (f,g) with (g,g) if b == 1;
1523		* replace (f,g) with (f,g) if b == 0.
1524		*
1525		* Preconditions: b in {0,1}.
1526		*/
1527		static void fe_cmov(fe f, const fe g, unsigned b)
1528	128M	{
1529	128M	size_t i;
1530
1531	128M	b = 0-b;
1532	1.41G	for (i = 0; i < 10; i++) {
1533	1.28G	int32_t x = f[i] ^ g[i];
1534	1.28G	x &= b;
1535	1.28G	f[i] ^= x;
1536	1.28G	}
1537	128M	}
1538
1539		/*
1540		* return 0 if f == 0
1541		* return 1 if f != 0
1542		*
1543		* Preconditions:
1544		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1545		*/
1546		static int fe_isnonzero(const fe f)
1547	172	{
1548	172	uint8_t s[32];
1549	172	static const uint8_t zero[32] = {0};
1550
1551	172	fe_tobytes(s, f);
1552
1553	172	return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1554	172	}
1555
1556		/*
1557		* return 1 if f is in {1,3,5,...,q-2}
1558		* return 0 if f is in {0,2,4,...,q-1}
1559		*
1560		* Preconditions:
1561		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1562		*/
1563		static int fe_isnegative(const fe f)
1564	211	{
1565	211	uint8_t s[32];
1566
1567	211	fe_tobytes(s, f);
1568	211	return s[0] & 1;
1569	211	}
1570
1571		/*
1572		* h = 2 * f * f
1573		*
1574		* Can overlap h with f.
1575		*
1576		* Preconditions:
1577		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1578		*
1579		* Postconditions:
1580		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1581		*
1582		* See fe_mul.c for discussion of implementation strategy.
1583		*/
1584		static void fe_sq2(fe h, const fe f)
1585	320k	{
1586	320k	int32_t f0 = f[0];
1587	320k	int32_t f1 = f[1];
1588	320k	int32_t f2 = f[2];
1589	320k	int32_t f3 = f[3];
1590	320k	int32_t f4 = f[4];
1591	320k	int32_t f5 = f[5];
1592	320k	int32_t f6 = f[6];
1593	320k	int32_t f7 = f[7];
1594	320k	int32_t f8 = f[8];
1595	320k	int32_t f9 = f[9];
1596	320k	int32_t f0_2 = 2 * f0;
1597	320k	int32_t f1_2 = 2 * f1;
1598	320k	int32_t f2_2 = 2 * f2;
1599	320k	int32_t f3_2 = 2 * f3;
1600	320k	int32_t f4_2 = 2 * f4;
1601	320k	int32_t f5_2 = 2 * f5;
1602	320k	int32_t f6_2 = 2 * f6;
1603	320k	int32_t f7_2 = 2 * f7;
1604	320k	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1605	320k	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1606	320k	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1607	320k	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1608	320k	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1609	320k	int64_t f0f0 = f0 * (int64_t) f0;
1610	320k	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1611	320k	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1612	320k	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1613	320k	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1614	320k	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1615	320k	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1616	320k	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1617	320k	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1618	320k	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1619	320k	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1620	320k	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1621	320k	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1622	320k	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1623	320k	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1624	320k	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1625	320k	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1626	320k	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1627	320k	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1628	320k	int64_t f2f2 = f2 * (int64_t) f2;
1629	320k	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1630	320k	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1631	320k	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1632	320k	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1633	320k	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1634	320k	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1635	320k	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1636	320k	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1637	320k	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1638	320k	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1639	320k	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1640	320k	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1641	320k	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1642	320k	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1643	320k	int64_t f4f4 = f4 * (int64_t) f4;
1644	320k	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1645	320k	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1646	320k	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1647	320k	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1648	320k	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1649	320k	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1650	320k	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1651	320k	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1652	320k	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1653	320k	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1654	320k	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1655	320k	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1656	320k	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1657	320k	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1658	320k	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1659	320k	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1660	320k	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1661	320k	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1662	320k	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1663	320k	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1664	320k	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1665	320k	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1666	320k	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1667	320k	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1668	320k	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1669	320k	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1670	320k	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1671	320k	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1672	320k	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1673	320k	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1674	320k	int64_t carry0;
1675	320k	int64_t carry1;
1676	320k	int64_t carry2;
1677	320k	int64_t carry3;
1678	320k	int64_t carry4;
1679	320k	int64_t carry5;
1680	320k	int64_t carry6;
1681	320k	int64_t carry7;
1682	320k	int64_t carry8;
1683	320k	int64_t carry9;
1684
1685	320k	h0 += h0;
1686	320k	h1 += h1;
1687	320k	h2 += h2;
1688	320k	h3 += h3;
1689	320k	h4 += h4;
1690	320k	h5 += h5;
1691	320k	h6 += h6;
1692	320k	h7 += h7;
1693	320k	h8 += h8;
1694	320k	h9 += h9;
1695
1696	320k	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1697	320k	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1698
1699	320k	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1700	320k	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1701
1702	320k	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1703	320k	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1704
1705	320k	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1706	320k	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1707
1708	320k	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1709	320k	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1710
1711	320k	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1712
1713	320k	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1714
1715	320k	h[0] = (int32_t)h0;
1716	320k	h[1] = (int32_t)h1;
1717	320k	h[2] = (int32_t)h2;
1718	320k	h[3] = (int32_t)h3;
1719	320k	h[4] = (int32_t)h4;
1720	320k	h[5] = (int32_t)h5;
1721	320k	h[6] = (int32_t)h6;
1722	320k	h[7] = (int32_t)h7;
1723	320k	h[8] = (int32_t)h8;
1724	320k	h[9] = (int32_t)h9;
1725	320k	}
1726
1727		static void fe_pow22523(fe out, const fe z)
1728	98	{
1729	98	fe t0;
1730	98	fe t1;
1731	98	fe t2;
1732	98	int i;
1733
1734	98	fe_sq(t0, z);
1735	98	fe_sq(t1, t0);
1736	196	for (i = 1; i < 2; ++i) {
1737	98	fe_sq(t1, t1);
1738	98	}
1739	98	fe_mul(t1, z, t1);
1740	98	fe_mul(t0, t0, t1);
1741	98	fe_sq(t0, t0);
1742	98	fe_mul(t0, t1, t0);
1743	98	fe_sq(t1, t0);
1744	490	for (i = 1; i < 5; ++i) {
1745	392	fe_sq(t1, t1);
1746	392	}
1747	98	fe_mul(t0, t1, t0);
1748	98	fe_sq(t1, t0);
1749	980	for (i = 1; i < 10; ++i) {
1750	882	fe_sq(t1, t1);
1751	882	}
1752	98	fe_mul(t1, t1, t0);
1753	98	fe_sq(t2, t1);
1754	1.96k	for (i = 1; i < 20; ++i) {
1755	1.86k	fe_sq(t2, t2);
1756	1.86k	}
1757	98	fe_mul(t1, t2, t1);
1758	98	fe_sq(t1, t1);
1759	980	for (i = 1; i < 10; ++i) {
1760	882	fe_sq(t1, t1);
1761	882	}
1762	98	fe_mul(t0, t1, t0);
1763	98	fe_sq(t1, t0);
1764	4.90k	for (i = 1; i < 50; ++i) {
1765	4.80k	fe_sq(t1, t1);
1766	4.80k	}
1767	98	fe_mul(t1, t1, t0);
1768	98	fe_sq(t2, t1);
1769	9.80k	for (i = 1; i < 100; ++i) {
1770	9.70k	fe_sq(t2, t2);
1771	9.70k	}
1772	98	fe_mul(t1, t2, t1);
1773	98	fe_sq(t1, t1);
1774	4.90k	for (i = 1; i < 50; ++i) {
1775	4.80k	fe_sq(t1, t1);
1776	4.80k	}
1777	98	fe_mul(t0, t1, t0);
1778	98	fe_sq(t0, t0);
1779	196	for (i = 1; i < 2; ++i) {
1780	98	fe_sq(t0, t0);
1781	98	}
1782	98	fe_mul(out, t0, z);
1783	98	}
1784
1785		/*
1786		* ge means group element.
1787		*
1788		* Here the group is the set of pairs (x,y) of field elements (see fe.h)
1789		* satisfying -x^2 + y^2 = 1 + d x^2y^2
1790		* where d = -121665/121666.
1791		*
1792		* Representations:
1793		* ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1794		* ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1795		* ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1796		* ge_precomp (Duif): (y+x,y-x,2dxy)
1797		*/
1798		typedef struct {
1799		fe X;
1800		fe Y;
1801		fe Z;
1802		} ge_p2;
1803
1804		typedef struct {
1805		fe X;
1806		fe Y;
1807		fe Z;
1808		fe T;
1809		} ge_p3;
1810
1811		typedef struct {
1812		fe X;
1813		fe Y;
1814		fe Z;
1815		fe T;
1816		} ge_p1p1;
1817
1818		typedef struct {
1819		fe yplusx;
1820		fe yminusx;
1821		fe xy2d;
1822		} ge_precomp;
1823
1824		typedef struct {
1825		fe YplusX;
1826		fe YminusX;
1827		fe Z;
1828		fe T2d;
1829		} ge_cached;
1830
1831		static void ge_tobytes(uint8_t s, const ge_p2 h)
1832	96	{
1833	96	fe recip;
1834	96	fe x;
1835	96	fe y;
1836
1837	96	fe_invert(recip, h->Z);
1838	96	fe_mul(x, h->X, recip);
1839	96	fe_mul(y, h->Y, recip);
1840	96	fe_tobytes(s, y);
1841	96	s[31] ^= fe_isnegative(x) << 7;
1842	96	}
1843
1844		static void ge_p3_tobytes(uint8_t s, const ge_p3 h)
1845	19	{
1846	19	fe recip;
1847	19	fe x;
1848	19	fe y;
1849
1850	19	fe_invert(recip, h->Z);
1851	19	fe_mul(x, h->X, recip);
1852	19	fe_mul(y, h->Y, recip);
1853	19	fe_tobytes(s, y);
1854	19	s[31] ^= fe_isnegative(x) << 7;
1855	19	}
1856
1857		static const fe d = {
1858		-10913610, 13857413, -15372611, 6949391, 114729,
1859		-8787816, -6275908, -3247719, -18696448, -12055116
1860		};
1861
1862		static const fe sqrtm1 = {
1863		-32595792, -7943725, 9377950, 3500415, 12389472,
1864		-272473, -25146209, -2005654, 326686, 11406482
1865		};
1866
1867		static int ge_frombytes_vartime(ge_p3 h, const uint8_t s)
1868	98	{
1869	98	fe u;
1870	98	fe v;
1871	98	fe v3;
1872	98	fe vxx;
1873	98	fe check;
1874
1875	98	fe_frombytes(h->Y, s);
1876	98	fe_1(h->Z);
1877	98	fe_sq(u, h->Y);
1878	98	fe_mul(v, u, d);
1879	98	fe_sub(u, u, h->Z); /* u = y^2-1 */
1880	98	fe_add(v, v, h->Z); /* v = dy^2+1 */
1881
1882	98	fe_sq(v3, v);
1883	98	fe_mul(v3, v3, v); /* v3 = v^3 */
1884	98	fe_sq(h->X, v3);
1885	98	fe_mul(h->X, h->X, v);
1886	98	fe_mul(h->X, h->X, u); /* x = uv^7 */
1887
1888	98	fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
1889	98	fe_mul(h->X, h->X, v3);
1890	98	fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
1891
1892	98	fe_sq(vxx, h->X);
1893	98	fe_mul(vxx, vxx, v);
1894	98	fe_sub(check, vxx, u); /* vx^2-u */
1895	98	if (fe_isnonzero(check)) {
1896	74	fe_add(check, vxx, u); /* vx^2+u */
1897	74	if (fe_isnonzero(check)) {
1898	2	return -1;
1899	2	}
1900	72	fe_mul(h->X, h->X, sqrtm1);
1901	72	}
1902
1903	96	if (fe_isnegative(h->X) != (s[31] >> 7)) {
1904	57	fe_neg(h->X, h->X);
1905	57	}
1906
1907	96	fe_mul(h->T, h->X, h->Y);
1908	96	return 0;
1909	98	}
1910
1911		static void ge_p2_0(ge_p2 *h)
1912	96	{
1913	96	fe_0(h->X);
1914	96	fe_1(h->Y);
1915	96	fe_1(h->Z);
1916	96	}
1917
1918		static void ge_p3_0(ge_p3 *h)
1919	74.2k	{
1920	74.2k	fe_0(h->X);
1921	74.2k	fe_1(h->Y);
1922	74.2k	fe_1(h->Z);
1923	74.2k	fe_0(h->T);
1924	74.2k	}
1925
1926		static void ge_precomp_0(ge_precomp *h)
1927	4.74M	{
1928	4.74M	fe_1(h->yplusx);
1929	4.74M	fe_1(h->yminusx);
1930	4.74M	fe_0(h->xy2d);
1931	4.74M	}
1932
1933		/* r = p */
1934		static void ge_p3_to_p2(ge_p2 r, const ge_p3 p)
1935	74.2k	{
1936	74.2k	fe_copy(r->X, p->X);
1937	74.2k	fe_copy(r->Y, p->Y);
1938	74.2k	fe_copy(r->Z, p->Z);
1939	74.2k	}
1940
1941		static const fe d2 = {
1942		-21827239, -5839606, -30745221, 13898782, 229458,
1943		15978800, -12551817, -6495438, 29715968, 9444199
1944		};
1945
1946		/* r = p */
1947		static void ge_p3_to_cached(ge_cached r, const ge_p3 p)
1948	768	{
1949	768	fe_add(r->YplusX, p->Y, p->X);
1950	768	fe_sub(r->YminusX, p->Y, p->X);
1951	768	fe_copy(r->Z, p->Z);
1952	768	fe_mul(r->T2d, p->T, d2);
1953	768	}
1954
1955		/* r = p */
1956		static void ge_p1p1_to_p2(ge_p2 r, const ge_p1p1 p)
1957	246k	{
1958	246k	fe_mul(r->X, p->X, p->T);
1959	246k	fe_mul(r->Y, p->Y, p->Z);
1960	246k	fe_mul(r->Z, p->Z, p->T);
1961	246k	}
1962
1963		/* r = p */
1964		static void ge_p1p1_to_p3(ge_p3 r, const ge_p1p1 p)
1965	4.82M	{
1966	4.82M	fe_mul(r->X, p->X, p->T);
1967	4.82M	fe_mul(r->Y, p->Y, p->Z);
1968	4.82M	fe_mul(r->Z, p->Z, p->T);
1969	4.82M	fe_mul(r->T, p->X, p->Y);
1970	4.82M	}
1971
1972		/* r = 2 * p */
1973		static void ge_p2_dbl(ge_p1p1 r, const ge_p2 p)
1974	320k	{
1975	320k	fe t0;
1976
1977	320k	fe_sq(r->X, p->X);
1978	320k	fe_sq(r->Z, p->Y);
1979	320k	fe_sq2(r->T, p->Z);
1980	320k	fe_add(r->Y, p->X, p->Y);
1981	320k	fe_sq(t0, r->Y);
1982	320k	fe_add(r->Y, r->Z, r->X);
1983	320k	fe_sub(r->Z, r->Z, r->X);
1984	320k	fe_sub(r->X, t0, r->Y);
1985	320k	fe_sub(r->T, r->T, r->Z);
1986	320k	}
1987
1988		/* r = 2 * p */
1989		static void ge_p3_dbl(ge_p1p1 r, const ge_p3 p)
1990	74.2k	{
1991	74.2k	ge_p2 q;
1992	74.2k	ge_p3_to_p2(&q, p);
1993	74.2k	ge_p2_dbl(r, &q);
1994	74.2k	}
1995
1996		/* r = p + q */
1997		static void ge_madd(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
1998	4.75M	{
1999	4.75M	fe t0;
2000
2001	4.75M	fe_add(r->X, p->Y, p->X);
2002	4.75M	fe_sub(r->Y, p->Y, p->X);
2003	4.75M	fe_mul(r->Z, r->X, q->yplusx);
2004	4.75M	fe_mul(r->Y, r->Y, q->yminusx);
2005	4.75M	fe_mul(r->T, q->xy2d, p->T);
2006	4.75M	fe_add(t0, p->Z, p->Z);
2007	4.75M	fe_sub(r->X, r->Z, r->Y);
2008	4.75M	fe_add(r->Y, r->Z, r->Y);
2009	4.75M	fe_add(r->Z, t0, r->T);
2010	4.75M	fe_sub(r->T, t0, r->T);
2011	4.75M	}
2012
2013		/* r = p - q */
2014		static void ge_msub(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2015	519	{
2016	519	fe t0;
2017
2018	519	fe_add(r->X, p->Y, p->X);
2019	519	fe_sub(r->Y, p->Y, p->X);
2020	519	fe_mul(r->Z, r->X, q->yminusx);
2021	519	fe_mul(r->Y, r->Y, q->yplusx);
2022	519	fe_mul(r->T, q->xy2d, p->T);
2023	519	fe_add(t0, p->Z, p->Z);
2024	519	fe_sub(r->X, r->Z, r->Y);
2025	519	fe_add(r->Y, r->Z, r->Y);
2026	519	fe_sub(r->Z, t0, r->T);
2027	519	fe_add(r->T, t0, r->T);
2028	519	}
2029
2030		/* r = p + q */
2031		static void ge_add(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2032	2.71k	{
2033	2.71k	fe t0;
2034
2035	2.71k	fe_add(r->X, p->Y, p->X);
2036	2.71k	fe_sub(r->Y, p->Y, p->X);
2037	2.71k	fe_mul(r->Z, r->X, q->YplusX);
2038	2.71k	fe_mul(r->Y, r->Y, q->YminusX);
2039	2.71k	fe_mul(r->T, q->T2d, p->T);
2040	2.71k	fe_mul(r->X, p->Z, q->Z);
2041	2.71k	fe_add(t0, r->X, r->X);
2042	2.71k	fe_sub(r->X, r->Z, r->Y);
2043	2.71k	fe_add(r->Y, r->Z, r->Y);
2044	2.71k	fe_add(r->Z, t0, r->T);
2045	2.71k	fe_sub(r->T, t0, r->T);
2046	2.71k	}
2047
2048		/* r = p - q */
2049		static void ge_sub(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2050	2.00k	{
2051	2.00k	fe t0;
2052
2053	2.00k	fe_add(r->X, p->Y, p->X);
2054	2.00k	fe_sub(r->Y, p->Y, p->X);
2055	2.00k	fe_mul(r->Z, r->X, q->YminusX);
2056	2.00k	fe_mul(r->Y, r->Y, q->YplusX);
2057	2.00k	fe_mul(r->T, q->T2d, p->T);
2058	2.00k	fe_mul(r->X, p->Z, q->Z);
2059	2.00k	fe_add(t0, r->X, r->X);
2060	2.00k	fe_sub(r->X, r->Z, r->Y);
2061	2.00k	fe_add(r->Y, r->Z, r->Y);
2062	2.00k	fe_sub(r->Z, t0, r->T);
2063	2.00k	fe_add(r->T, t0, r->T);
2064	2.00k	}
2065
2066		static uint8_t equal(signed char b, signed char c)
2067	37.9M	{
2068	37.9M	uint8_t ub = b;
2069	37.9M	uint8_t uc = c;
2070	37.9M	uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2071	37.9M	uint32_t y = x; /* 0: yes; 1..255: no */
2072	37.9M	y -= 1; /* 4294967295: yes; 0..254: no */
2073	37.9M	y >>= 31; /* 1: yes; 0: no */
2074	37.9M	return y;
2075	37.9M	}
2076
2077		static void cmov(ge_precomp t, const ge_precomp u, uint8_t b)
2078	42.7M	{
2079	42.7M	fe_cmov(t->yplusx, u->yplusx, b);
2080	42.7M	fe_cmov(t->yminusx, u->yminusx, b);
2081	42.7M	fe_cmov(t->xy2d, u->xy2d, b);
2082	42.7M	}
2083
2084		/* k25519Precomp[i][j] = (j+1)256^iB */
2085		static const ge_precomp k25519Precomp[32][8] = {
2086		{
2087		{
2088		{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2089		27544626, -11754271, -6079156, 2047605},
2090		{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2091		5043384, 19500929, -15469378},
2092		{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2093		29287919, 11864899, -24514362, -4438546},
2094		},
2095		{
2096		{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2097		-11717903, -3814571, -358445, -10211303},
2098		{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2099		-15616551, 11189268, -26829678, -5319081},
2100		{26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2101		-3128826, -9541118, -15472047, -4166697},
2102		},
2103		{
2104		{15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2105		27787600, -14772189, 28944400, -1550024},
2106		{16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2107		16354577, -11775962, 7689662, 11199574},
2108		{30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2109		7512774, 10017326, -17749093, -9920357},
2110		},
2111		{
2112		{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2113		-28926210, 15006023, 3284568, -6276540},
2114		{23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2115		7464579, 9656445, 13059162, 10374397},
2116		{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2117		-3839045, -641708, -101325},
2118		},
2119		{
2120		{10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2121		32867885, 14515107, -15438304, 10819380},
2122		{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2123		12483688, -12668491, 5581306},
2124		{19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2125		28542350, 13850243, -23678021, -15815942},
2126		},
2127		{
2128		{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2129		-19188627, -15224819, -9818940, -12085777},
2130		{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2131		-15689887, 1762328, 14866737},
2132		{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2133		-28236412, 3959421, 27914454, 4383652},
2134		},
2135		{
2136		{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2137		5230134, -23952439, -15175766},
2138		{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2139		20654025, 16520125, 30598449, 7715701},
2140		{28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2141		-31400660, 1370708, 29794553, -1409300},
2142		},
2143		{
2144		{14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2145		30290735, 10876454, -33154098, 2381726},
2146		{-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2147		-6236617, 3696005, -32300832, 15351955},
2148		{27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2149		-32961401, -2970515, 29551813, 10109425},
2150		},
2151		},
2152		{
2153		{
2154		{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2155		-2378284, -1627556, 10092783, -4764171},
2156		{27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2157		-32508754, 12005538, -17810127, 12803510},
2158		{17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2159		30364213, -9038194, 18016357, 4397660},
2160		},
2161		{
2162		{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2163		-26619106, 14544525, -17477504, 982639},
2164		{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2165		-4120128, -21047696, 9934963},
2166		{5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2167		-14747930, 4559895, -30123922, -10897950},
2168		},
2169		{
2170		{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2171		24191034, 4541697, -13338309, 5500568},
2172		{12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2173		-17430592, 12264343, 10874051, 13524335},
2174		{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2175		5080568, -22528059, 5376628},
2176		},
2177		{
2178		{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2179		-22321305, -9447443, 4535768, 1569007},
2180		{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2181		-30494562, 3044290, 31848280, 12543772},
2182		{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2183		-27377195, -2062731, 7718482, 14474653},
2184		},
2185		{
2186		{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2187		-7236665, 24316168, -5253567},
2188		{13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2189		33040651, -13424532, -20729456, 8321686},
2190		{21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
2191		23845965, -11874838, -9984458, 608372},
2192		},
2193		{
2194		{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
2195		1123968, -6780577, 27229399, 23887},
2196		{-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
2197		12797024, -6440308, -1633405, 16678954},
2198		{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
2199		-1508144, -4795045, -17169265, 4904953},
2200		},
2201		{
2202		{24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
2203		5169211, 16191880, 2128236, -4326833},
2204		{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
2205		-29806336, 916033, -6882542, -2986532},
2206		{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
2207		285431, 2763829, 15736322, 4143876},
2208		},
2209		{
2210		{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
2211		-14594663, 23527084, -16458268},
2212		{33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
2213		-32625340, 4087881, -15188911, -14416214},
2214		{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
2215		4357868, -4774191, -16323038},
2216		},
2217		},
2218		{
2219		{
2220		{6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
2221		23365147, -3949732, 7390890, 2759800},
2222		{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
2223		-4264057, 1244380, -12919645},
2224		{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
2225		9208236, 15886429, 16489664},
2226		},
2227		{
2228		{1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
2229		-13693198, 398369, -30606455, -712933},
2230		{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
2231		13348553, 12076947, -30836462, 5113182},
2232		{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
2233		-30341101, -7336386, 13847711, 5387222},
2234		},
2235		{
2236		{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
2237		8763061, 3617786, -19600662, 10370991},
2238		{20246567, -14369378, 22358229, -543712, 18507283, -10413996,
2239		14554437, -8746092, 32232924, 16763880},
2240		{9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
2241		11094161, 15689506, 3140038, -16510092},
2242		},
2243		{
2244		{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
2245		-27224800, 9448613, -28774454, 366295},
2246		{19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
2247		28344573, 8041113, 719605, 11671788},
2248		{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
2249		-15266516, 27000813, -10195553},
2250		},
2251		{
2252		{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
2253		5336097, 6750977, -14521026},
2254		{11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
2255		1695823, -8819122, 8169720, 16220347},
2256		{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
2257		-11144307, -2627664, -5990708, -14166033},
2258		},
2259		{
2260		{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
2261		27884329, 2847284, 2655861, 1738395},
2262		{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
2263		21651608, -3239336, -19087449, -11005278},
2264		{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
2265		5821408, 10478196, 8544890},
2266		},
2267		{
2268		{32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
2269		19270449, 12217473, 17789017, -3395995},
2270		{-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
2271		15479401, -3853233, 30460520, 1052596},
2272		{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
2273		27491595, -4612359, 3179268, -9478891},
2274		},
2275		{
2276		{31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
2277		-14756777, -16411740, 19072640, -9511060},
2278		{11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
2279		5977896, -5215017, 473099, 5040608},
2280		{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
2281		28326862, 1721092, -19558642, -3131606},
2282		},
2283		},
2284		{
2285		{
2286		{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
2287		8076149, -27868496, 11538389},
2288		{-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
2289		8754525, 7446702, -5676054, 5797016},
2290		{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
2291		2014099, -9050574, -2369172, -5877341},
2292		},
2293		{
2294		{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
2295		1192730, -3714199, 15123619, 10811505},
2296		{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
2297		15776356, -28886779, -11974553},
2298		{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
2299		-20654173, -16484855, 4714547, -9600655},
2300		},
2301		{
2302		{15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
2303		24611599, -4543832, -11745876, 12340220},
2304		{12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
2305		9613953, 8241152, 15370987, 9608631},
2306		{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
2307		15866074, -28210621, -8814099},
2308		},
2309		{
2310		{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
2311		858697, 20571223, 8420556},
2312		{14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
2313		33531827, 12516406, -21574435, -12476749},
2314		{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
2315		7256740, 8791136, 15069930},
2316		},
2317		{
2318		{1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
2319		14711875, 4874229, -30663140, -2331391},
2320		{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
2321		-7912378, -33069337, 9234253},
2322		{20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
2323		31559055, -11609587, 18979186, 13396066},
2324		},
2325		{
2326		{24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
2327		-18816887, 13594782, 33514650, 7021958},
2328		{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
2329		-25948728, -3916677, -21480480, 12868082},
2330		{-28635013, 13504661, 19988037, -2132761, 21078225, 6443208,
2331		-21446107, 2244500, -12455797, -8089383},
2332		},
2333		{
2334		{-30595528, 13793479, -5852820, 319136, -25723172, -6263899,
2335		33086546, 8957937, -15233648, 5540521},
2336		{-11630176, -11503902, -8119500, -7643073, 2620056, 1022908,
2337		-23710744, -1568984, -16128528, -14962807},
2338		{23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819,
2339		892185, -11513277, -15205948},
2340		},
2341		{
2342		{9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819,
2343		4763127, -19179614, 5867134},
2344		{-32765025, 1927590, 31726409, -4753295, 23962434, -16019500,
2345		27846559, 5931263, -29749703, -16108455},
2346		{27461885, -2977536, 22380810, 1815854, -23033753, -3031938,
2347		7283490, -15148073, -19526700, 7734629},
2348		},
2349		},
2350		{
2351		{
2352		{-8010264, -9590817, -11120403, 6196038, 29344158, -13430885,
2353		7585295, -3176626, 18549497, 15302069},
2354		{-32658337, -6171222, -7672793, -11051681, 6258878, 13504381,
2355		10458790, -6418461, -8872242, 8424746},
2356		{24687205, 8613276, -30667046, -3233545, 1863892, -1830544,
2357		19206234, 7134917, -11284482, -828919},
2358		},
2359		{
2360		{11334899, -9218022, 8025293, 12707519, 17523892, -10476071,
2361		10243738, -14685461, -5066034, 16498837},
2362		{8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
2363		-14124238, 6536641, 10543906},
2364		{-28946384, 15479763, -17466835, 568876, -1497683, 11223454,
2365		-2669190, -16625574, -27235709, 8876771},
2366		},
2367		{
2368		{-25742899, -12566864, -15649966, -846607, -33026686, -796288,
2369		-33481822, 15824474, -604426, -9039817},
2370		{10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697,
2371		-4890037, 1657394, 3084098},
2372		{10477963, -7470260, 12119566, -13250805, 29016247, -5365589,
2373		31280319, 14396151, -30233575, 15272409},
2374		},
2375		{
2376		{-12288309, 3169463, 28813183, 16658753, 25116432, -5630466,
2377		-25173957, -12636138, -25014757, 1950504},
2378		{-26180358, 9489187, 11053416, -14746161, -31053720, 5825630,
2379		-8384306, -8767532, 15341279, 8373727},
2380		{28685821, 7759505, -14378516, -12002860, -31971820, 4079242,
2381		298136, -10232602, -2878207, 15190420},
2382		},
2383		{
2384		{-32932876, 13806336, -14337485, -15794431, -24004620, 10940928,
2385		8669718, 2742393, -26033313, -6875003},
2386		{-1580388, -11729417, -25979658, -11445023, -17411874, -10912854,
2387		9291594, -16247779, -12154742, 6048605},
2388		{-30305315, 14843444, 1539301, 11864366, 20201677, 1900163,
2389		13934231, 5128323, 11213262, 9168384},
2390		},
2391		{
2392		{-26280513, 11007847, 19408960, -940758, -18592965, -4328580,
2393		-5088060, -11105150, 20470157, -16398701},
2394		{-23136053, 9282192, 14855179, -15390078, -7362815, -14408560,
2395		-22783952, 14461608, 14042978, 5230683},
2396		{29969567, -2741594, -16711867, -8552442, 9175486, -2468974,
2397		21556951, 3506042, -5933891, -12449708},
2398		},
2399		{
2400		{-3144746, 8744661, 19704003, 4581278, -20430686, 6830683,
2401		-21284170, 8971513, -28539189, 15326563},
2402		{-19464629, 10110288, -17262528, -3503892, -23500387, 1355669,
2403		-15523050, 15300988, -20514118, 9168260},
2404		{-5353335, 4488613, -23803248, 16314347, 7780487, -15638939,
2405		-28948358, 9601605, 33087103, -9011387},
2406		},
2407		{
2408		{-19443170, -15512900, -20797467, -12445323, -29824447, 10229461,
2409		-27444329, -15000531, -5996870, 15664672},
2410		{23294591, -16632613, -22650781, -8470978, 27844204, 11461195,
2411		13099750, -2460356, 18151676, 13417686},
2412		{-24722913, -4176517, -31150679, 5988919, -26858785, 6685065,
2413		1661597, -12551441, 15271676, -15452665},
2414		},
2415		},
2416		{
2417		{
2418		{11433042, -13228665, 8239631, -5279517, -1985436, -725718,
2419		-18698764, 2167544, -6921301, -13440182},
2420		{-31436171, 15575146, 30436815, 12192228, -22463353, 9395379,
2421		-9917708, -8638997, 12215110, 12028277},
2422		{14098400, 6555944, 23007258, 5757252, -15427832, -12950502,
2423		30123440, 4617780, -16900089, -655628},
2424		},
2425		{
2426		{-4026201, -15240835, 11893168, 13718664, -14809462, 1847385,
2427		-15819999, 10154009, 23973261, -12684474},
2428		{-26531820, -3695990, -1908898, 2534301, -31870557, -16550355,
2429		18341390, -11419951, 32013174, -10103539},
2430		{-25479301, 10876443, -11771086, -14625140, -12369567, 1838104,
2431		21911214, 6354752, 4425632, -837822},
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2968		},
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3000		},
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3007		-5061276, -2144373, 17846988, -13971927},
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3010		{
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3074		},
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3076		{
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3092		},
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3100		},
3101		{
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3107		-26745169, 10942115, -25888931, -14884697},
3108		},
3109		{
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3112		{-25574376, 11967826, 29233242, 12948236, -6754465, 4713227,
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3116		},
3117		{
3118		{11630004, 12144454, 2116339, 13606037, 27378885, 15676917,
3119		-17408753, -13504373, -14395196, 8070818},
3120		{27117696, -10007378, -31282771, -5570088, 1127282, 12772488,
3121		-29845906, 10483306, -11552749, -1028714},
3122		{10637467, -5688064, 5674781, 1072708, -26343588, -6982302,
3123		-1683975, 9177853, -27493162, 15431203},
3124		},
3125		{
3126		{20525145, 10892566, -12742472, 12779443, -29493034, 16150075,
3127		-28240519, 14943142, -15056790, -7935931},
3128		{-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767,
3129		-3239766, -3356550, 9594024},
3130		{-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683,
3131		-6492290, 13352335, -10977084},
3132		},
3133		{
3134		{-1931799, -5407458, 3304649, -12884869, 17015806, -4877091,
3135		-29783850, -7752482, -13215537, -319204},
3136		{20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742,
3137		15077870, -22750759, 14523817},
3138		{27406042, -6041657, 27423596, -4497394, 4996214, 10002360,
3139		-28842031, -4545494, -30172742, -4805667},
3140		},
3141		},
3142		{
3143		{
3144		{11374242, 12660715, 17861383, -12540833, 10935568, 1099227,
3145		-13886076, -9091740, -27727044, 11358504},
3146		{-12730809, 10311867, 1510375, 10778093, -2119455, -9145702,
3147		32676003, 11149336, -26123651, 4985768},
3148		{-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043,
3149		13794114, -19414307, -15621255},
3150		},
3151		{
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3153		6970005, -1691065, -9004790},
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3157		-20571065, -7007978, -99853, -10237333},
3158		},
3159		{
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3162		{31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999,
3163		-3744247, 4882242, -10626905},
3164		{29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198,
3165		3272828, -5190932, -4162409},
3166		},
3167		{
3168		{12501286, 4044383, -8612957, -13392385, -32430052, 5136599,
3169		-19230378, -3529697, 330070, -3659409},
3170		{6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522,
3171		-8573892, -271295, 12071499},
3172		{-8365515, -4042521, 25133448, -4517355, -6211027, 2265927,
3173		-32769618, 1936675, -5159697, 3829363},
3174		},
3175		{
3176		{28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550,
3177		-6567787, 26333140, 14267664},
3178		{-11067219, 11871231, 27385719, -10559544, -4585914, -11189312,
3179		10004786, -8709488, -21761224, 8930324},
3180		{-21197785, -16396035, 25654216, -1725397, 12282012, 11008919,
3181		1541940, 4757911, -26491501, -16408940},
3182		},
3183		{
3184		{13537262, -7759490, -20604840, 10961927, -5922820, -13218065,
3185		-13156584, 6217254, -15943699, 13814990},
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3187		9257833, -1956526, -1776914},
3188		{-25045300, -10191966, 15366585, 15166509, -13105086, 8423556,
3189		-29171540, 12361135, -18685978, 4578290},
3190		},
3191		{
3192		{24579768, 3711570, 1342322, -11180126, -27005135, 14124956,
3193		-22544529, 14074919, 21964432, 8235257},
3194		{-6528613, -2411497, 9442966, -5925588, 12025640, -1487420,
3195		-2981514, -1669206, 13006806, 2355433},
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3197		27202044, 1719366, 1141648, -12796236},
3198		},
3199		{
3200		{-12863944, -13219986, -8318266, -11018091, -6810145, -4843894,
3201		13475066, -3133972, 32674895, 13715045},
3202		{11423335, -5468059, 32344216, 8962751, 24989809, 9241752,
3203		-13265253, 16086212, -28740881, -15642093},
3204		{-1409668, 12530728, -6368726, 10847387, 19531186, -14132160,
3205		-11709148, 7791794, -27245943, 4383347},
3206		},
3207		},
3208		{
3209		{
3210		{-28970898, 5271447, -1266009, -9736989, -12455236, 16732599,
3211		-4862407, -4906449, 27193557, 6245191},
3212		{-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898,
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3214		{-12632451, 11257346, -32692994, 13548177, -721004, 10879011,
3215		31168030, 13952092, -29571492, -3635906},
3216		},
3217		{
3218		{3877321, -9572739, 32416692, 5405324, -11004407, -13656635,
3219		3759769, 11935320, 5611860, 8164018},
3220		{-16275802, 14667797, 15906460, 12155291, -22111149, -9039718,
3221		32003002, -8832289, 5773085, -8422109},
3222		{-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725,
3223		12376320, 31632953, 190926},
3224		},
3225		{
3226		{-24593607, -16138885, -8423991, 13378746, 14162407, 6901328,
3227		-8288749, 4508564, -25341555, -3627528},
3228		{8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941,
3229		-14786005, -1672488, 827625},
3230		{-32720583, -16289296, -32503547, 7101210, 13354605, 2659080,
3231		-1800575, -14108036, -24878478, 1541286},
3232		},
3233		{
3234		{2901347, -1117687, 3880376, -10059388, -17620940, -3612781,
3235		-21802117, -3567481, 20456845, -1885033},
3236		{27019610, 12299467, -13658288, -1603234, -12861660, -4861471,
3237		-19540150, -5016058, 29439641, 15138866},
3238		{21536104, -6626420, -32447818, -10690208, -22408077, 5175814,
3239		-5420040, -16361163, 7779328, 109896},
3240		},
3241		{
3242		{30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390,
3243		12180118, 23177719, -554075},
3244		{26572847, 3405927, -31701700, 12890905, -19265668, 5335866,
3245		-6493768, 2378492, 4439158, -13279347},
3246		{-22716706, 3489070, -9225266, -332753, 18875722, -1140095,
3247		14819434, -12731527, -17717757, -5461437},
3248		},
3249		{
3250		{-5056483, 16566551, 15953661, 3767752, -10436499, 15627060,
3251		-820954, 2177225, 8550082, -15114165},
3252		{-18473302, 16596775, -381660, 15663611, 22860960, 15585581,
3253		-27844109, -3582739, -23260460, -8428588},
3254		{-32480551, 15707275, -8205912, -5652081, 29464558, 2713815,
3255		-22725137, 15860482, -21902570, 1494193},
3256		},
3257		{
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3259		21923482, 16529112, 8742704, 12967017},
3260		{-28464899, 1553205, 32536856, -10473729, -24691605, -406174,
3261		-8914625, -2933896, -29903758, 15553883},
3262		{21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572,
3263		14513274, 19375923, -12647961},
3264		},
3265		{
3266		{8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818,
3267		-6222716, 2862653, 9455043},
3268		{29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124,
3269		-2990080, 15511449, 4789663},
3270		{-20679756, 7004547, 8824831, -9434977, -4045704, -3750736,
3271		-5754762, 108893, 23513200, 16652362},
3272		},
3273		},
3274		{
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3276		{-33256173, 4144782, -4476029, -6579123, 10770039, -7155542,
3277		-6650416, -12936300, -18319198, 10212860},
3278		{2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801,
3279		2600940, -9988298, -12506466},
3280		{-24645692, 13317462, -30449259, -15653928, 21365574, -10869657,
3281		11344424, 864440, -2499677, -16710063},
3282		},
3283		{
3284		{-26432803, 6148329, -17184412, -14474154, 18782929, -275997,
3285		-22561534, 211300, 2719757, 4940997},
3286		{-1323882, 3911313, -6948744, 14759765, -30027150, 7851207,
3287		21690126, 8518463, 26699843, 5276295},
3288		{-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586,
3289		149635, -15452774, 7159369},
3290		},
3291		{
3292		{9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009,
3293		8312176, 22477218, -8403385},
3294		{18155857, -16504990, 19744716, 9006923, 15154154, -10538976,
3295		24256460, -4864995, -22548173, 9334109},
3296		{2986088, -4911893, 10776628, -3473844, 10620590, -7083203,
3297		-21413845, 14253545, -22587149, 536906},
3298		},
3299		{
3300		{4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551,
3301		10589625, 10838060, -15420424},
3302		{-19342404, 867880, 9277171, -3218459, -14431572, -1986443,
3303		19295826, -15796950, 6378260, 699185},
3304		{7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039,
3305		15693155, -5045064, -13373962},
3306		},
3307		{
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3309		31730678, -10962840, -3918636, -9669325},
3310		{10188286, -15770834, -7336361, 13427543, 22223443, 14896287,
3311		30743455, 7116568, -21786507, 5427593},
3312		{696102, 13206899, 27047647, -10632082, 15285305, -9853179,
3313		10798490, -4578720, 19236243, 12477404},
3314		},
3315		{
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3317		-3897669, 11180504, -23169516, 7733644},
3318		{17800790, -14036179, -27000429, -11766671, 23887827, 3149671,
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3320		{26246234, 11968874, 32263343, -5468728, 6830755, -13323031,
3321		-15794704, -101982, -24449242, 10890804},
3322		},
3323		{
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3325		-14982212, 16484931, 25180797, -5334884},
3326		{-586574, 10376444, -32586414, -11286356, 19801893, 10997610,
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3328		{-9882808, -4510367, -2115506, 16457136, -11100081, 11674996,
3329		30756178, -7515054, 30696930, -3712849},
3330		},
3331		{
3332		{32988917, -9603412, 12499366, 7910787, -10617257, -11931514,
3333		-7342816, -9985397, -32349517, 7392473},
3334		{-8855661, 15927861, 9866406, -3649411, -2396914, -16655781,
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3336		{-2504044, -436966, 25621774, -5678772, 15085042, -5479877,
3337		-24884878, -13526194, 5537438, -13914319},
3338		},
3339		},
3340		{
3341		{
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3343		-14876251, -1729667, 31234590, 6090599},
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3346		{-27757857, 247744, -15194774, -9002551, 23288161, -10011936,
3347		-23869595, 6503646, 20650474, 1804084},
3348		},
3349		{
3350		{-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995,
3351		-10329713, 27842616, -202328},
3352		{-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656,
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3356		},
3357		{
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3362		{-21389266, 421932, 26597266, 6860826, 22486084, -6737172,
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3364		},
3365		{
3366		{-20184622, 2338216, 19788685, -9620956, -4001265, -8740893,
3367		-20271184, 4733254, 3727144, -12934448},
3368		{6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594,
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3370		{30069250, -11435332, 30434654, 2958439, 18399564, -976289,
3371		12296869, 9204260, -16432438, 9648165},
3372		},
3373		{
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3376		{17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711,
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3378		{-1172927, -7558695, -4366770, -4287744, -21346413, -8434326,
3379		32087529, -1222777, 32247248, -14389861},
3380		},
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3386		{18510800, 15337574, 26171504, 981392, -22241552, 7827556,
3387		-23491134, -11323352, 3059833, -11782870},
3388		},
3389		{
3390		{10141598, 6082907, 17829293, -1947643, 9830092, 13613136,
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3396		},
3397		{
3398		{30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294,
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3403		-19172240, -16046376, 8764035, 12309598},
3404		},
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3406		{
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3409		-23665757, 1228319, 17544096, -10593782},
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3414		},
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3422		},
3423		{
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3428		{-8574695, 16099415, 4629974, -16340524, -20786213, -6005432,
3429		-10018363, 9276971, 11329923, 1862132},
3430		},
3431		{
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3436		{15214962, 3537601, -26238722, -14058872, 4418657, -15230761,
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3438		},
3439		{
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3442		{-12466472, 4195084, -9211532, 550904, -15565337, 12917920,
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3445		-10051775, 12493932, -5409317},
3446		},
3447		{
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3452		{-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645,
3453		960770, 12121869, 16648078},
3454		},
3455		{
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3457		-31504922, -7882064, 20237806, 2838411},
3458		{-19288047, 4453152, 15298546, -16178388, 22115043, -15972604,
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3462		},
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3800		},
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3802		{
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3807		254968, 7168080, 21676107, -1943028},
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3810		},
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3818		},
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3866		},
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3868		{
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3934		{
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3969		-8570186, -9689599, -3031667},
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3973		11879682, 5400171, 519526, -1235876},
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3980		{-21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
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3990		},
3991		{
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3998		},
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4000		{
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4008		},
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4064		},
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4066		{
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4098		},
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4130		},
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4132		{
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4140		},
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4148		},
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4151		18345767, -13403753, 16291481, -5314038},
4152		{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
4153		6957617, 4368891, 9788741},
4154		{16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
4155		-21722536, -8613148, 16250552, -11111103},
4156		},
4157		{
4158		{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
4159		10604807, -30190403, 4782747},
4160		{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
4161		-9981571, 4383045, 22546403, 437323},
4162		{31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
4163		27343084, 2786261, -30633590, -14097016},
4164		},
4165		{
4166		{-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
4167		-19690631, 2355319, -19284671, -6114373},
4168		{15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
4169		18952177, 15496498, -29380133, 11754228},
4170		{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
4171		7141596, 11724556, 22761615, -10134141},
4172		},
4173		{
4174		{16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
4175		-28741185, -12227393, 32851222, 11717399},
4176		{11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
4177		31474879, 3483633, -1193175, -4030831},
4178		{-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4179		33142652, 6546660, -19985279, -3948376},
4180		},
4181		{
4182		{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4183		-8537131, -12833048, -30772034, -15486313},
4184		{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4185		-31135347, -16049879, 10928917, 3011958},
4186		{-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4187		-30831056, -12805180, 18008031, 10258577},
4188		},
4189		{
4190		{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4191		-1853465, 1367120, 25127874, 6671743},
4192		{29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4193		21382910, 11042292, 25838796, 4642684},
4194		{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4195		30468147, -13900640, 18423289, 4177476},
4196		},
4197		},
4198		};
4199
4200		static uint8_t negative(signed char b)
4201	4.74M	{
4202	4.74M	uint32_t x = b;
4203
4204	4.74M	x >>= 31; /* 1: yes; 0: no */
4205	4.74M	return x;
4206	4.74M	}
4207
4208		static void table_select(ge_precomp *t, int pos, signed char b)
4209	4.74M	{
4210	4.74M	ge_precomp minust;
4211	4.74M	uint8_t bnegative = negative(b);
4212	4.74M	uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4213
4214	4.74M	ge_precomp_0(t);
4215	4.74M	cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4216	4.74M	cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4217	4.74M	cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4218	4.74M	cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4219	4.74M	cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4220	4.74M	cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4221	4.74M	cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4222	4.74M	cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4223	4.74M	fe_copy(minust.yplusx, t->yminusx);
4224	4.74M	fe_copy(minust.yminusx, t->yplusx);
4225	4.74M	fe_neg(minust.xy2d, t->xy2d);
4226	4.74M	cmov(t, &minust, bnegative);
4227	4.74M	}
4228
4229		/*
4230		* h = a * B
4231		*
4232		* where a = a[0]+256*a[1]+...+256^31 a[31]
4233		* B is the Ed25519 base point (x,4/5) with x positive.
4234		*
4235		* Preconditions:
4236		* a[31] <= 127
4237		*/
4238		static void ge_scalarmult_base(ge_p3 h, const uint8_t a)
4239	74.2k	{
4240	74.2k	signed char e[64];
4241	74.2k	signed char carry;
4242	74.2k	ge_p1p1 r;
4243	74.2k	ge_p2 s;
4244	74.2k	ge_precomp t;
4245	74.2k	int i;
4246
4247	2.44M	for (i = 0; i < 32; ++i) {
4248	2.37M	e[2 * i + 0] = (a[i] >> 0) & 15;
4249	2.37M	e[2 * i + 1] = (a[i] >> 4) & 15;
4250	2.37M	}
4251		/* each e[i] is between 0 and 15 */
4252		/* e[63] is between 0 and 7 */
4253
4254	74.2k	carry = 0;
4255	4.74M	for (i = 0; i < 63; ++i) {
4256	4.67M	e[i] += carry;
4257	4.67M	carry = e[i] + 8;
4258	4.67M	carry >>= 4;
4259	4.67M	e[i] -= carry << 4;
4260	4.67M	}
4261	74.2k	e[63] += carry;
4262		/* each e[i] is between -8 and 8 */
4263
4264	74.2k	ge_p3_0(h);
4265	2.44M	for (i = 1; i < 64; i += 2) {
4266	2.37M	table_select(&t, i / 2, e[i]);
4267	2.37M	ge_madd(&r, h, &t);
4268	2.37M	ge_p1p1_to_p3(h, &r);
4269	2.37M	}
4270
4271	74.2k	ge_p3_dbl(&r, h);
4272	74.2k	ge_p1p1_to_p2(&s, &r);
4273	74.2k	ge_p2_dbl(&r, &s);
4274	74.2k	ge_p1p1_to_p2(&s, &r);
4275	74.2k	ge_p2_dbl(&r, &s);
4276	74.2k	ge_p1p1_to_p2(&s, &r);
4277	74.2k	ge_p2_dbl(&r, &s);
4278	74.2k	ge_p1p1_to_p3(h, &r);
4279
4280	2.44M	for (i = 0; i < 64; i += 2) {
4281	2.37M	table_select(&t, i / 2, e[i]);
4282	2.37M	ge_madd(&r, h, &t);
4283	2.37M	ge_p1p1_to_p3(h, &r);
4284	2.37M	}
4285
4286	74.2k	OPENSSL_cleanse(e, sizeof(e));
4287	74.2k	}
4288
4289		#if !defined(BASE_2_51_IMPLEMENTED)
4290		/*
4291		* Replace (f,g) with (g,f) if b == 1;
4292		* replace (f,g) with (f,g) if b == 0.
4293		*
4294		* Preconditions: b in {0,1}.
4295		*/
4296		static void fe_cswap(fe f, fe g, unsigned int b)
4297		{
4298		size_t i;
4299
4300		b = 0-b;
4301		for (i = 0; i < 10; i++) {
4302		int32_t x = f[i] ^ g[i];
4303		x &= b;
4304		f[i] ^= x;
4305		g[i] ^= x;
4306		}
4307		}
4308
4309		/*
4310		* h = f * 121666
4311		*
4312		* Can overlap h with f.
4313		*
4314		* Preconditions:
4315		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
4316		*
4317		* Postconditions:
4318		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
4319		*/
4320		static void fe_mul121666(fe h, fe f)
4321		{
4322		int32_t f0 = f[0];
4323		int32_t f1 = f[1];
4324		int32_t f2 = f[2];
4325		int32_t f3 = f[3];
4326		int32_t f4 = f[4];
4327		int32_t f5 = f[5];
4328		int32_t f6 = f[6];
4329		int32_t f7 = f[7];
4330		int32_t f8 = f[8];
4331		int32_t f9 = f[9];
4332		int64_t h0 = f0 * (int64_t) 121666;
4333		int64_t h1 = f1 * (int64_t) 121666;
4334		int64_t h2 = f2 * (int64_t) 121666;
4335		int64_t h3 = f3 * (int64_t) 121666;
4336		int64_t h4 = f4 * (int64_t) 121666;
4337		int64_t h5 = f5 * (int64_t) 121666;
4338		int64_t h6 = f6 * (int64_t) 121666;
4339		int64_t h7 = f7 * (int64_t) 121666;
4340		int64_t h8 = f8 * (int64_t) 121666;
4341		int64_t h9 = f9 * (int64_t) 121666;
4342		int64_t carry0;
4343		int64_t carry1;
4344		int64_t carry2;
4345		int64_t carry3;
4346		int64_t carry4;
4347		int64_t carry5;
4348		int64_t carry6;
4349		int64_t carry7;
4350		int64_t carry8;
4351		int64_t carry9;
4352
4353		carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
4354		carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
4355		carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
4356		carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
4357		carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
4358
4359		carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
4360		carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
4361		carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
4362		carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
4363		carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
4364
4365		h[0] = (int32_t)h0;
4366		h[1] = (int32_t)h1;
4367		h[2] = (int32_t)h2;
4368		h[3] = (int32_t)h3;
4369		h[4] = (int32_t)h4;
4370		h[5] = (int32_t)h5;
4371		h[6] = (int32_t)h6;
4372		h[7] = (int32_t)h7;
4373		h[8] = (int32_t)h8;
4374		h[9] = (int32_t)h9;
4375		}
4376
4377		static void x25519_scalar_mult_generic(uint8_t out[32],
4378		const uint8_t scalar[32],
4379		const uint8_t point[32]) {
4380		fe x1, x2, z2, x3, z3, tmp0, tmp1;
4381		uint8_t e[32];
4382		unsigned swap = 0;
4383		int pos;
4384
4385		memcpy(e, scalar, 32);
4386		e[0] &= 248;
4387		e[31] &= 127;
4388		e[31] \|= 64;
4389		fe_frombytes(x1, point);
4390		fe_1(x2);
4391		fe_0(z2);
4392		fe_copy(x3, x1);
4393		fe_1(z3);
4394
4395		for (pos = 254; pos >= 0; --pos) {
4396		unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4397		swap ^= b;
4398		fe_cswap(x2, x3, swap);
4399		fe_cswap(z2, z3, swap);
4400		swap = b;
4401		fe_sub(tmp0, x3, z3);
4402		fe_sub(tmp1, x2, z2);
4403		fe_add(x2, x2, z2);
4404		fe_add(z2, x3, z3);
4405		fe_mul(z3, tmp0, x2);
4406		fe_mul(z2, z2, tmp1);
4407		fe_sq(tmp0, tmp1);
4408		fe_sq(tmp1, x2);
4409		fe_add(x3, z3, z2);
4410		fe_sub(z2, z3, z2);
4411		fe_mul(x2, tmp1, tmp0);
4412		fe_sub(tmp1, tmp1, tmp0);
4413		fe_sq(z2, z2);
4414		fe_mul121666(z3, tmp1);
4415		fe_sq(x3, x3);
4416		fe_add(tmp0, tmp0, z3);
4417		fe_mul(z3, x1, z2);
4418		fe_mul(z2, tmp1, tmp0);
4419		}
4420
4421		fe_invert(z2, z2);
4422		fe_mul(x2, x2, z2);
4423		fe_tobytes(out, x2);
4424
4425		OPENSSL_cleanse(e, sizeof(e));
4426		}
4427
4428		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4429		const uint8_t point[32]) {
4430		x25519_scalar_mult_generic(out, scalar, point);
4431		}
4432		#endif
4433
4434		static void slide(signed char r, const uint8_t a)
4435	192	{
4436	192	int i;
4437	192	int b;
4438	192	int k;
4439
4440	49.3k	for (i = 0; i < 256; ++i) {
4441	49.1k	r[i] = 1 & (a[i >> 3] >> (i & 7));
4442	49.1k	}
4443
4444	49.3k	for (i = 0; i < 256; ++i) {
4445	49.1k	if (r[i]) {
4446	34.9k	for (b = 1; b <= 6 && i + b < 256; ++b) {
4447	32.8k	if (r[i + b]) {
4448	14.1k	if (r[i] + (r[i + b] << b) <= 15) {
4449	7.93k	r[i] += r[i + b] << b;
4450	7.93k	r[i + b] = 0;
4451	7.93k	} else if (r[i] - (r[i + b] << b) >= -15) {
4452	2.52k	r[i] -= r[i + b] << b;
4453	8.08k	for (k = i + b; k < 256; ++k) {
4454	8.08k	if (!r[k]) {
4455	2.52k	r[k] = 1;
4456	2.52k	break;
4457	2.52k	}
4458	5.56k	r[k] = 0;
4459	5.56k	}
4460	3.71k	} else {
4461	3.71k	break;
4462	3.71k	}
4463	14.1k	}
4464	32.8k	}
4465	5.90k	}
4466	49.1k	}
4467	192	}
4468
4469		static const ge_precomp Bi[8] = {
4470		{
4471		{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4472		-11754271, -6079156, 2047605},
4473		{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4474		5043384, 19500929, -15469378},
4475		{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4476		11864899, -24514362, -4438546},
4477		},
4478		{
4479		{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4480		-14772189, 28944400, -1550024},
4481		{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4482		-11775962, 7689662, 11199574},
4483		{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4484		10017326, -17749093, -9920357},
4485		},
4486		{
4487		{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4488		14515107, -15438304, 10819380},
4489		{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4490		12483688, -12668491, 5581306},
4491		{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4492		13850243, -23678021, -15815942},
4493		},
4494		{
4495		{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4496		5230134, -23952439, -15175766},
4497		{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4498		16520125, 30598449, 7715701},
4499		{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4500		1370708, 29794553, -1409300},
4501		},
4502		{
4503		{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4504		-1361450, -13062696, 13821877},
4505		{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4506		-7212327, 18853322, -14220951},
4507		{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4508		-10431137, 2207753, -3209784},
4509		},
4510		{
4511		{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4512		-663000, -31111463, -16132436},
4513		{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4514		15725684, 171356, 6466918},
4515		{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4516		-14088058, -30714912, 16193877},
4517		},
4518		{
4519		{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4520		4729455, -18074513, 9256800},
4521		{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4522		9761698, -19827198, 630305},
4523		{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4524		-15960994, -2449256, -14291300},
4525		},
4526		{
4527		{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4528		15033784, 25105118, -7894876},
4529		{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4530		1573892, -2625887, 2198790, -15804619},
4531		{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4532		-16236442, -32461234, -12290683},
4533		},
4534		};
4535
4536		/*
4537		* r = a * A + b * B
4538		*
4539		* where a = a[0]+256*a[1]+...+256^31 a[31].
4540		* and b = b[0]+256*b[1]+...+256^31 b[31].
4541		* B is the Ed25519 base point (x,4/5) with x positive.
4542		*/
4543		static void ge_double_scalarmult_vartime(ge_p2 r, const uint8_t a,
4544		const ge_p3 A, const uint8_t b)
4545	96	{
4546	96	signed char aslide[256];
4547	96	signed char bslide[256];
4548	96	ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4549	96	ge_p1p1 t;
4550	96	ge_p3 u;
4551	96	ge_p3 A2;
4552	96	int i;
4553
4554	96	slide(aslide, a);
4555	96	slide(bslide, b);
4556
4557	96	ge_p3_to_cached(&Ai[0], A);
4558	96	ge_p3_dbl(&t, A);
4559	96	ge_p1p1_to_p3(&A2, &t);
4560	96	ge_add(&t, &A2, &Ai[0]);
4561	96	ge_p1p1_to_p3(&u, &t);
4562	96	ge_p3_to_cached(&Ai[1], &u);
4563	96	ge_add(&t, &A2, &Ai[1]);
4564	96	ge_p1p1_to_p3(&u, &t);
4565	96	ge_p3_to_cached(&Ai[2], &u);
4566	96	ge_add(&t, &A2, &Ai[2]);
4567	96	ge_p1p1_to_p3(&u, &t);
4568	96	ge_p3_to_cached(&Ai[3], &u);
4569	96	ge_add(&t, &A2, &Ai[3]);
4570	96	ge_p1p1_to_p3(&u, &t);
4571	96	ge_p3_to_cached(&Ai[4], &u);
4572	96	ge_add(&t, &A2, &Ai[4]);
4573	96	ge_p1p1_to_p3(&u, &t);
4574	96	ge_p3_to_cached(&Ai[5], &u);
4575	96	ge_add(&t, &A2, &Ai[5]);
4576	96	ge_p1p1_to_p3(&u, &t);
4577	96	ge_p3_to_cached(&Ai[6], &u);
4578	96	ge_add(&t, &A2, &Ai[6]);
4579	96	ge_p1p1_to_p3(&u, &t);
4580	96	ge_p3_to_cached(&Ai[7], &u);
4581
4582	96	ge_p2_0(r);
4583
4584	750	for (i = 255; i >= 0; --i) {
4585	750	if (aslide[i] \|\| bslide[i]) {
4586	96	break;
4587	96	}
4588	750	}
4589
4590	24.0k	for (; i >= 0; --i) {
4591	23.9k	ge_p2_dbl(&t, r);
4592
4593	23.9k	if (aslide[i] > 0) {
4594	2.04k	ge_p1p1_to_p3(&u, &t);
4595	2.04k	ge_add(&t, &u, &Ai[aslide[i] / 2]);
4596	21.8k	} else if (aslide[i] < 0) {
4597	2.00k	ge_p1p1_to_p3(&u, &t);
4598	2.00k	ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4599	2.00k	}
4600
4601	23.9k	if (bslide[i] > 0) {
4602	1.34k	ge_p1p1_to_p3(&u, &t);
4603	1.34k	ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4604	22.5k	} else if (bslide[i] < 0) {
4605	519	ge_p1p1_to_p3(&u, &t);
4606	519	ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4607	519	}
4608
4609	23.9k	ge_p1p1_to_p2(r, &t);
4610	23.9k	}
4611	96	}
4612
4613		/*
4614		* The set of scalars is \Z/l
4615		* where l = 2^252 + 27742317777372353535851937790883648493.
4616		*
4617		* Input:
4618		* s[0]+256s[1]+...+256^63s[63] = s
4619		*
4620		* Output:
4621		* s[0]+256s[1]+...+256^31s[31] = s mod l
4622		* where l = 2^252 + 27742317777372353535851937790883648493.
4623		* Overwrites s in place.
4624		*/
4625		static void x25519_sc_reduce(uint8_t *s)
4626	96	{
4627	96	int64_t s0 = kBottom21Bits & load_3(s);
4628	96	int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
4629	96	int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
4630	96	int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
4631	96	int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
4632	96	int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
4633	96	int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
4634	96	int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
4635	96	int64_t s8 = kBottom21Bits & load_3(s + 21);
4636	96	int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
4637	96	int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4638	96	int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4639	96	int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4640	96	int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4641	96	int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4642	96	int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4643	96	int64_t s16 = kBottom21Bits & load_3(s + 42);
4644	96	int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4645	96	int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4646	96	int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4647	96	int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4648	96	int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4649	96	int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4650	96	int64_t s23 = (load_4(s + 60) >> 3);
4651	96	int64_t carry0;
4652	96	int64_t carry1;
4653	96	int64_t carry2;
4654	96	int64_t carry3;
4655	96	int64_t carry4;
4656	96	int64_t carry5;
4657	96	int64_t carry6;
4658	96	int64_t carry7;
4659	96	int64_t carry8;
4660	96	int64_t carry9;
4661	96	int64_t carry10;
4662	96	int64_t carry11;
4663	96	int64_t carry12;
4664	96	int64_t carry13;
4665	96	int64_t carry14;
4666	96	int64_t carry15;
4667	96	int64_t carry16;
4668
4669	96	s11 += s23 * 666643;
4670	96	s12 += s23 * 470296;
4671	96	s13 += s23 * 654183;
4672	96	s14 -= s23 * 997805;
4673	96	s15 += s23 * 136657;
4674	96	s16 -= s23 * 683901;
4675	96	s23 = 0;
4676
4677	96	s10 += s22 * 666643;
4678	96	s11 += s22 * 470296;
4679	96	s12 += s22 * 654183;
4680	96	s13 -= s22 * 997805;
4681	96	s14 += s22 * 136657;
4682	96	s15 -= s22 * 683901;
4683	96	s22 = 0;
4684
4685	96	s9 += s21 * 666643;
4686	96	s10 += s21 * 470296;
4687	96	s11 += s21 * 654183;
4688	96	s12 -= s21 * 997805;
4689	96	s13 += s21 * 136657;
4690	96	s14 -= s21 * 683901;
4691	96	s21 = 0;
4692
4693	96	s8 += s20 * 666643;
4694	96	s9 += s20 * 470296;
4695	96	s10 += s20 * 654183;
4696	96	s11 -= s20 * 997805;
4697	96	s12 += s20 * 136657;
4698	96	s13 -= s20 * 683901;
4699	96	s20 = 0;
4700
4701	96	s7 += s19 * 666643;
4702	96	s8 += s19 * 470296;
4703	96	s9 += s19 * 654183;
4704	96	s10 -= s19 * 997805;
4705	96	s11 += s19 * 136657;
4706	96	s12 -= s19 * 683901;
4707	96	s19 = 0;
4708
4709	96	s6 += s18 * 666643;
4710	96	s7 += s18 * 470296;
4711	96	s8 += s18 * 654183;
4712	96	s9 -= s18 * 997805;
4713	96	s10 += s18 * 136657;
4714	96	s11 -= s18 * 683901;
4715	96	s18 = 0;
4716
4717	96	carry6 = (s6 + (1 << 20)) >> 21;
4718	96	s7 += carry6;
4719	96	s6 -= carry6 * (1 << 21);
4720	96	carry8 = (s8 + (1 << 20)) >> 21;
4721	96	s9 += carry8;
4722	96	s8 -= carry8 * (1 << 21);
4723	96	carry10 = (s10 + (1 << 20)) >> 21;
4724	96	s11 += carry10;
4725	96	s10 -= carry10 * (1 << 21);
4726	96	carry12 = (s12 + (1 << 20)) >> 21;
4727	96	s13 += carry12;
4728	96	s12 -= carry12 * (1 << 21);
4729	96	carry14 = (s14 + (1 << 20)) >> 21;
4730	96	s15 += carry14;
4731	96	s14 -= carry14 * (1 << 21);
4732	96	carry16 = (s16 + (1 << 20)) >> 21;
4733	96	s17 += carry16;
4734	96	s16 -= carry16 * (1 << 21);
4735
4736	96	carry7 = (s7 + (1 << 20)) >> 21;
4737	96	s8 += carry7;
4738	96	s7 -= carry7 * (1 << 21);
4739	96	carry9 = (s9 + (1 << 20)) >> 21;
4740	96	s10 += carry9;
4741	96	s9 -= carry9 * (1 << 21);
4742	96	carry11 = (s11 + (1 << 20)) >> 21;
4743	96	s12 += carry11;
4744	96	s11 -= carry11 * (1 << 21);
4745	96	carry13 = (s13 + (1 << 20)) >> 21;
4746	96	s14 += carry13;
4747	96	s13 -= carry13 * (1 << 21);
4748	96	carry15 = (s15 + (1 << 20)) >> 21;
4749	96	s16 += carry15;
4750	96	s15 -= carry15 * (1 << 21);
4751
4752	96	s5 += s17 * 666643;
4753	96	s6 += s17 * 470296;
4754	96	s7 += s17 * 654183;
4755	96	s8 -= s17 * 997805;
4756	96	s9 += s17 * 136657;
4757	96	s10 -= s17 * 683901;
4758	96	s17 = 0;
4759
4760	96	s4 += s16 * 666643;
4761	96	s5 += s16 * 470296;
4762	96	s6 += s16 * 654183;
4763	96	s7 -= s16 * 997805;
4764	96	s8 += s16 * 136657;
4765	96	s9 -= s16 * 683901;
4766	96	s16 = 0;
4767
4768	96	s3 += s15 * 666643;
4769	96	s4 += s15 * 470296;
4770	96	s5 += s15 * 654183;
4771	96	s6 -= s15 * 997805;
4772	96	s7 += s15 * 136657;
4773	96	s8 -= s15 * 683901;
4774	96	s15 = 0;
4775
4776	96	s2 += s14 * 666643;
4777	96	s3 += s14 * 470296;
4778	96	s4 += s14 * 654183;
4779	96	s5 -= s14 * 997805;
4780	96	s6 += s14 * 136657;
4781	96	s7 -= s14 * 683901;
4782	96	s14 = 0;
4783
4784	96	s1 += s13 * 666643;
4785	96	s2 += s13 * 470296;
4786	96	s3 += s13 * 654183;
4787	96	s4 -= s13 * 997805;
4788	96	s5 += s13 * 136657;
4789	96	s6 -= s13 * 683901;
4790	96	s13 = 0;
4791
4792	96	s0 += s12 * 666643;
4793	96	s1 += s12 * 470296;
4794	96	s2 += s12 * 654183;
4795	96	s3 -= s12 * 997805;
4796	96	s4 += s12 * 136657;
4797	96	s5 -= s12 * 683901;
4798	96	s12 = 0;
4799
4800	96	carry0 = (s0 + (1 << 20)) >> 21;
4801	96	s1 += carry0;
4802	96	s0 -= carry0 * (1 << 21);
4803	96	carry2 = (s2 + (1 << 20)) >> 21;
4804	96	s3 += carry2;
4805	96	s2 -= carry2 * (1 << 21);
4806	96	carry4 = (s4 + (1 << 20)) >> 21;
4807	96	s5 += carry4;
4808	96	s4 -= carry4 * (1 << 21);
4809	96	carry6 = (s6 + (1 << 20)) >> 21;
4810	96	s7 += carry6;
4811	96	s6 -= carry6 * (1 << 21);
4812	96	carry8 = (s8 + (1 << 20)) >> 21;
4813	96	s9 += carry8;
4814	96	s8 -= carry8 * (1 << 21);
4815	96	carry10 = (s10 + (1 << 20)) >> 21;
4816	96	s11 += carry10;
4817	96	s10 -= carry10 * (1 << 21);
4818
4819	96	carry1 = (s1 + (1 << 20)) >> 21;
4820	96	s2 += carry1;
4821	96	s1 -= carry1 * (1 << 21);
4822	96	carry3 = (s3 + (1 << 20)) >> 21;
4823	96	s4 += carry3;
4824	96	s3 -= carry3 * (1 << 21);
4825	96	carry5 = (s5 + (1 << 20)) >> 21;
4826	96	s6 += carry5;
4827	96	s5 -= carry5 * (1 << 21);
4828	96	carry7 = (s7 + (1 << 20)) >> 21;
4829	96	s8 += carry7;
4830	96	s7 -= carry7 * (1 << 21);
4831	96	carry9 = (s9 + (1 << 20)) >> 21;
4832	96	s10 += carry9;
4833	96	s9 -= carry9 * (1 << 21);
4834	96	carry11 = (s11 + (1 << 20)) >> 21;
4835	96	s12 += carry11;
4836	96	s11 -= carry11 * (1 << 21);
4837
4838	96	s0 += s12 * 666643;
4839	96	s1 += s12 * 470296;
4840	96	s2 += s12 * 654183;
4841	96	s3 -= s12 * 997805;
4842	96	s4 += s12 * 136657;
4843	96	s5 -= s12 * 683901;
4844	96	s12 = 0;
4845
4846	96	carry0 = s0 >> 21;
4847	96	s1 += carry0;
4848	96	s0 -= carry0 * (1 << 21);
4849	96	carry1 = s1 >> 21;
4850	96	s2 += carry1;
4851	96	s1 -= carry1 * (1 << 21);
4852	96	carry2 = s2 >> 21;
4853	96	s3 += carry2;
4854	96	s2 -= carry2 * (1 << 21);
4855	96	carry3 = s3 >> 21;
4856	96	s4 += carry3;
4857	96	s3 -= carry3 * (1 << 21);
4858	96	carry4 = s4 >> 21;
4859	96	s5 += carry4;
4860	96	s4 -= carry4 * (1 << 21);
4861	96	carry5 = s5 >> 21;
4862	96	s6 += carry5;
4863	96	s5 -= carry5 * (1 << 21);
4864	96	carry6 = s6 >> 21;
4865	96	s7 += carry6;
4866	96	s6 -= carry6 * (1 << 21);
4867	96	carry7 = s7 >> 21;
4868	96	s8 += carry7;
4869	96	s7 -= carry7 * (1 << 21);
4870	96	carry8 = s8 >> 21;
4871	96	s9 += carry8;
4872	96	s8 -= carry8 * (1 << 21);
4873	96	carry9 = s9 >> 21;
4874	96	s10 += carry9;
4875	96	s9 -= carry9 * (1 << 21);
4876	96	carry10 = s10 >> 21;
4877	96	s11 += carry10;
4878	96	s10 -= carry10 * (1 << 21);
4879	96	carry11 = s11 >> 21;
4880	96	s12 += carry11;
4881	96	s11 -= carry11 * (1 << 21);
4882
4883	96	s0 += s12 * 666643;
4884	96	s1 += s12 * 470296;
4885	96	s2 += s12 * 654183;
4886	96	s3 -= s12 * 997805;
4887	96	s4 += s12 * 136657;
4888	96	s5 -= s12 * 683901;
4889	96	s12 = 0;
4890
4891	96	carry0 = s0 >> 21;
4892	96	s1 += carry0;
4893	96	s0 -= carry0 * (1 << 21);
4894	96	carry1 = s1 >> 21;
4895	96	s2 += carry1;
4896	96	s1 -= carry1 * (1 << 21);
4897	96	carry2 = s2 >> 21;
4898	96	s3 += carry2;
4899	96	s2 -= carry2 * (1 << 21);
4900	96	carry3 = s3 >> 21;
4901	96	s4 += carry3;
4902	96	s3 -= carry3 * (1 << 21);
4903	96	carry4 = s4 >> 21;
4904	96	s5 += carry4;
4905	96	s4 -= carry4 * (1 << 21);
4906	96	carry5 = s5 >> 21;
4907	96	s6 += carry5;
4908	96	s5 -= carry5 * (1 << 21);
4909	96	carry6 = s6 >> 21;
4910	96	s7 += carry6;
4911	96	s6 -= carry6 * (1 << 21);
4912	96	carry7 = s7 >> 21;
4913	96	s8 += carry7;
4914	96	s7 -= carry7 * (1 << 21);
4915	96	carry8 = s8 >> 21;
4916	96	s9 += carry8;
4917	96	s8 -= carry8 * (1 << 21);
4918	96	carry9 = s9 >> 21;
4919	96	s10 += carry9;
4920	96	s9 -= carry9 * (1 << 21);
4921	96	carry10 = s10 >> 21;
4922	96	s11 += carry10;
4923	96	s10 -= carry10 * (1 << 21);
4924
4925	96	s[ 0] = (uint8_t) (s0 >> 0);
4926	96	s[ 1] = (uint8_t) (s0 >> 8);
4927	96	s[ 2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
4928	96	s[ 3] = (uint8_t) (s1 >> 3);
4929	96	s[ 4] = (uint8_t) (s1 >> 11);
4930	96	s[ 5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
4931	96	s[ 6] = (uint8_t) (s2 >> 6);
4932	96	s[ 7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
4933	96	s[ 8] = (uint8_t) (s3 >> 1);
4934	96	s[ 9] = (uint8_t) (s3 >> 9);
4935	96	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
4936	96	s[11] = (uint8_t) (s4 >> 4);
4937	96	s[12] = (uint8_t) (s4 >> 12);
4938	96	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
4939	96	s[14] = (uint8_t) (s5 >> 7);
4940	96	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
4941	96	s[16] = (uint8_t) (s6 >> 2);
4942	96	s[17] = (uint8_t) (s6 >> 10);
4943	96	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
4944	96	s[19] = (uint8_t) (s7 >> 5);
4945	96	s[20] = (uint8_t) (s7 >> 13);
4946	96	s[21] = (uint8_t) (s8 >> 0);
4947	96	s[22] = (uint8_t) (s8 >> 8);
4948	96	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
4949	96	s[24] = (uint8_t) (s9 >> 3);
4950	96	s[25] = (uint8_t) (s9 >> 11);
4951	96	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
4952	96	s[27] = (uint8_t) (s10 >> 6);
4953	96	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
4954	96	s[29] = (uint8_t) (s11 >> 1);
4955	96	s[30] = (uint8_t) (s11 >> 9);
4956	96	s[31] = (uint8_t) (s11 >> 17);
4957	96	}
4958
4959		/*
4960		* Input:
4961		* a[0]+256a[1]+...+256^31a[31] = a
4962		* b[0]+256b[1]+...+256^31b[31] = b
4963		* c[0]+256c[1]+...+256^31c[31] = c
4964		*
4965		* Output:
4966		* s[0]+256s[1]+...+256^31s[31] = (ab+c) mod l
4967		* where l = 2^252 + 27742317777372353535851937790883648493.
4968		*/
4969		static void sc_muladd(uint8_t s, const uint8_t a, const uint8_t *b,
4970		const uint8_t *c)
4971	0	{
4972	0	int64_t a0 = kBottom21Bits & load_3(a);
4973	0	int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
4974	0	int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
4975	0	int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
4976	0	int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
4977	0	int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
4978	0	int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
4979	0	int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
4980	0	int64_t a8 = kBottom21Bits & load_3(a + 21);
4981	0	int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
4982	0	int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
4983	0	int64_t a11 = (load_4(a + 28) >> 7);
4984	0	int64_t b0 = kBottom21Bits & load_3(b);
4985	0	int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
4986	0	int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
4987	0	int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
4988	0	int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
4989	0	int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
4990	0	int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
4991	0	int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
4992	0	int64_t b8 = kBottom21Bits & load_3(b + 21);
4993	0	int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
4994	0	int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
4995	0	int64_t b11 = (load_4(b + 28) >> 7);
4996	0	int64_t c0 = kBottom21Bits & load_3(c);
4997	0	int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
4998	0	int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
4999	0	int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
5000	0	int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
5001	0	int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
5002	0	int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
5003	0	int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
5004	0	int64_t c8 = kBottom21Bits & load_3(c + 21);
5005	0	int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
5006	0	int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
5007	0	int64_t c11 = (load_4(c + 28) >> 7);
5008	0	int64_t s0;
5009	0	int64_t s1;
5010	0	int64_t s2;
5011	0	int64_t s3;
5012	0	int64_t s4;
5013	0	int64_t s5;
5014	0	int64_t s6;
5015	0	int64_t s7;
5016	0	int64_t s8;
5017	0	int64_t s9;
5018	0	int64_t s10;
5019	0	int64_t s11;
5020	0	int64_t s12;
5021	0	int64_t s13;
5022	0	int64_t s14;
5023	0	int64_t s15;
5024	0	int64_t s16;
5025	0	int64_t s17;
5026	0	int64_t s18;
5027	0	int64_t s19;
5028	0	int64_t s20;
5029	0	int64_t s21;
5030	0	int64_t s22;
5031	0	int64_t s23;
5032	0	int64_t carry0;
5033	0	int64_t carry1;
5034	0	int64_t carry2;
5035	0	int64_t carry3;
5036	0	int64_t carry4;
5037	0	int64_t carry5;
5038	0	int64_t carry6;
5039	0	int64_t carry7;
5040	0	int64_t carry8;
5041	0	int64_t carry9;
5042	0	int64_t carry10;
5043	0	int64_t carry11;
5044	0	int64_t carry12;
5045	0	int64_t carry13;
5046	0	int64_t carry14;
5047	0	int64_t carry15;
5048	0	int64_t carry16;
5049	0	int64_t carry17;
5050	0	int64_t carry18;
5051	0	int64_t carry19;
5052	0	int64_t carry20;
5053	0	int64_t carry21;
5054	0	int64_t carry22;
5055
5056	0	s0 = c0 + a0 * b0;
5057	0	s1 = c1 + a0 * b1 + a1 * b0;
5058	0	s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
5059	0	s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
5060	0	s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
5061	0	s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
5062	0	s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
5063	0	s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
5064	0	s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
5065	0	s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
5066	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;
5067	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;
5068	0	s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
5069	0	s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
5070	0	s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
5071	0	s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
5072	0	s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
5073	0	s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
5074	0	s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
5075	0	s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
5076	0	s20 = a9 * b11 + a10 * b10 + a11 * b9;
5077	0	s21 = a10 * b11 + a11 * b10;
5078	0	s22 = a11 * b11;
5079	0	s23 = 0;
5080
5081	0	carry0 = (s0 + (1 << 20)) >> 21;
5082	0	s1 += carry0;
5083	0	s0 -= carry0 * (1 << 21);
5084	0	carry2 = (s2 + (1 << 20)) >> 21;
5085	0	s3 += carry2;
5086	0	s2 -= carry2 * (1 << 21);
5087	0	carry4 = (s4 + (1 << 20)) >> 21;
5088	0	s5 += carry4;
5089	0	s4 -= carry4 * (1 << 21);
5090	0	carry6 = (s6 + (1 << 20)) >> 21;
5091	0	s7 += carry6;
5092	0	s6 -= carry6 * (1 << 21);
5093	0	carry8 = (s8 + (1 << 20)) >> 21;
5094	0	s9 += carry8;
5095	0	s8 -= carry8 * (1 << 21);
5096	0	carry10 = (s10 + (1 << 20)) >> 21;
5097	0	s11 += carry10;
5098	0	s10 -= carry10 * (1 << 21);
5099	0	carry12 = (s12 + (1 << 20)) >> 21;
5100	0	s13 += carry12;
5101	0	s12 -= carry12 * (1 << 21);
5102	0	carry14 = (s14 + (1 << 20)) >> 21;
5103	0	s15 += carry14;
5104	0	s14 -= carry14 * (1 << 21);
5105	0	carry16 = (s16 + (1 << 20)) >> 21;
5106	0	s17 += carry16;
5107	0	s16 -= carry16 * (1 << 21);
5108	0	carry18 = (s18 + (1 << 20)) >> 21;
5109	0	s19 += carry18;
5110	0	s18 -= carry18 * (1 << 21);
5111	0	carry20 = (s20 + (1 << 20)) >> 21;
5112	0	s21 += carry20;
5113	0	s20 -= carry20 * (1 << 21);
5114	0	carry22 = (s22 + (1 << 20)) >> 21;
5115	0	s23 += carry22;
5116	0	s22 -= carry22 * (1 << 21);
5117
5118	0	carry1 = (s1 + (1 << 20)) >> 21;
5119	0	s2 += carry1;
5120	0	s1 -= carry1 * (1 << 21);
5121	0	carry3 = (s3 + (1 << 20)) >> 21;
5122	0	s4 += carry3;
5123	0	s3 -= carry3 * (1 << 21);
5124	0	carry5 = (s5 + (1 << 20)) >> 21;
5125	0	s6 += carry5;
5126	0	s5 -= carry5 * (1 << 21);
5127	0	carry7 = (s7 + (1 << 20)) >> 21;
5128	0	s8 += carry7;
5129	0	s7 -= carry7 * (1 << 21);
5130	0	carry9 = (s9 + (1 << 20)) >> 21;
5131	0	s10 += carry9;
5132	0	s9 -= carry9 * (1 << 21);
5133	0	carry11 = (s11 + (1 << 20)) >> 21;
5134	0	s12 += carry11;
5135	0	s11 -= carry11 * (1 << 21);
5136	0	carry13 = (s13 + (1 << 20)) >> 21;
5137	0	s14 += carry13;
5138	0	s13 -= carry13 * (1 << 21);
5139	0	carry15 = (s15 + (1 << 20)) >> 21;
5140	0	s16 += carry15;
5141	0	s15 -= carry15 * (1 << 21);
5142	0	carry17 = (s17 + (1 << 20)) >> 21;
5143	0	s18 += carry17;
5144	0	s17 -= carry17 * (1 << 21);
5145	0	carry19 = (s19 + (1 << 20)) >> 21;
5146	0	s20 += carry19;
5147	0	s19 -= carry19 * (1 << 21);
5148	0	carry21 = (s21 + (1 << 20)) >> 21;
5149	0	s22 += carry21;
5150	0	s21 -= carry21 * (1 << 21);
5151
5152	0	s11 += s23 * 666643;
5153	0	s12 += s23 * 470296;
5154	0	s13 += s23 * 654183;
5155	0	s14 -= s23 * 997805;
5156	0	s15 += s23 * 136657;
5157	0	s16 -= s23 * 683901;
5158	0	s23 = 0;
5159
5160	0	s10 += s22 * 666643;
5161	0	s11 += s22 * 470296;
5162	0	s12 += s22 * 654183;
5163	0	s13 -= s22 * 997805;
5164	0	s14 += s22 * 136657;
5165	0	s15 -= s22 * 683901;
5166	0	s22 = 0;
5167
5168	0	s9 += s21 * 666643;
5169	0	s10 += s21 * 470296;
5170	0	s11 += s21 * 654183;
5171	0	s12 -= s21 * 997805;
5172	0	s13 += s21 * 136657;
5173	0	s14 -= s21 * 683901;
5174	0	s21 = 0;
5175
5176	0	s8 += s20 * 666643;
5177	0	s9 += s20 * 470296;
5178	0	s10 += s20 * 654183;
5179	0	s11 -= s20 * 997805;
5180	0	s12 += s20 * 136657;
5181	0	s13 -= s20 * 683901;
5182	0	s20 = 0;
5183
5184	0	s7 += s19 * 666643;
5185	0	s8 += s19 * 470296;
5186	0	s9 += s19 * 654183;
5187	0	s10 -= s19 * 997805;
5188	0	s11 += s19 * 136657;
5189	0	s12 -= s19 * 683901;
5190	0	s19 = 0;
5191
5192	0	s6 += s18 * 666643;
5193	0	s7 += s18 * 470296;
5194	0	s8 += s18 * 654183;
5195	0	s9 -= s18 * 997805;
5196	0	s10 += s18 * 136657;
5197	0	s11 -= s18 * 683901;
5198	0	s18 = 0;
5199
5200	0	carry6 = (s6 + (1 << 20)) >> 21;
5201	0	s7 += carry6;
5202	0	s6 -= carry6 * (1 << 21);
5203	0	carry8 = (s8 + (1 << 20)) >> 21;
5204	0	s9 += carry8;
5205	0	s8 -= carry8 * (1 << 21);
5206	0	carry10 = (s10 + (1 << 20)) >> 21;
5207	0	s11 += carry10;
5208	0	s10 -= carry10 * (1 << 21);
5209	0	carry12 = (s12 + (1 << 20)) >> 21;
5210	0	s13 += carry12;
5211	0	s12 -= carry12 * (1 << 21);
5212	0	carry14 = (s14 + (1 << 20)) >> 21;
5213	0	s15 += carry14;
5214	0	s14 -= carry14 * (1 << 21);
5215	0	carry16 = (s16 + (1 << 20)) >> 21;
5216	0	s17 += carry16;
5217	0	s16 -= carry16 * (1 << 21);
5218
5219	0	carry7 = (s7 + (1 << 20)) >> 21;
5220	0	s8 += carry7;
5221	0	s7 -= carry7 * (1 << 21);
5222	0	carry9 = (s9 + (1 << 20)) >> 21;
5223	0	s10 += carry9;
5224	0	s9 -= carry9 * (1 << 21);
5225	0	carry11 = (s11 + (1 << 20)) >> 21;
5226	0	s12 += carry11;
5227	0	s11 -= carry11 * (1 << 21);
5228	0	carry13 = (s13 + (1 << 20)) >> 21;
5229	0	s14 += carry13;
5230	0	s13 -= carry13 * (1 << 21);
5231	0	carry15 = (s15 + (1 << 20)) >> 21;
5232	0	s16 += carry15;
5233	0	s15 -= carry15 * (1 << 21);
5234
5235	0	s5 += s17 * 666643;
5236	0	s6 += s17 * 470296;
5237	0	s7 += s17 * 654183;
5238	0	s8 -= s17 * 997805;
5239	0	s9 += s17 * 136657;
5240	0	s10 -= s17 * 683901;
5241	0	s17 = 0;
5242
5243	0	s4 += s16 * 666643;
5244	0	s5 += s16 * 470296;
5245	0	s6 += s16 * 654183;
5246	0	s7 -= s16 * 997805;
5247	0	s8 += s16 * 136657;
5248	0	s9 -= s16 * 683901;
5249	0	s16 = 0;
5250
5251	0	s3 += s15 * 666643;
5252	0	s4 += s15 * 470296;
5253	0	s5 += s15 * 654183;
5254	0	s6 -= s15 * 997805;
5255	0	s7 += s15 * 136657;
5256	0	s8 -= s15 * 683901;
5257	0	s15 = 0;
5258
5259	0	s2 += s14 * 666643;
5260	0	s3 += s14 * 470296;
5261	0	s4 += s14 * 654183;
5262	0	s5 -= s14 * 997805;
5263	0	s6 += s14 * 136657;
5264	0	s7 -= s14 * 683901;
5265	0	s14 = 0;
5266
5267	0	s1 += s13 * 666643;
5268	0	s2 += s13 * 470296;
5269	0	s3 += s13 * 654183;
5270	0	s4 -= s13 * 997805;
5271	0	s5 += s13 * 136657;
5272	0	s6 -= s13 * 683901;
5273	0	s13 = 0;
5274
5275	0	s0 += s12 * 666643;
5276	0	s1 += s12 * 470296;
5277	0	s2 += s12 * 654183;
5278	0	s3 -= s12 * 997805;
5279	0	s4 += s12 * 136657;
5280	0	s5 -= s12 * 683901;
5281	0	s12 = 0;
5282
5283	0	carry0 = (s0 + (1 << 20)) >> 21;
5284	0	s1 += carry0;
5285	0	s0 -= carry0 * (1 << 21);
5286	0	carry2 = (s2 + (1 << 20)) >> 21;
5287	0	s3 += carry2;
5288	0	s2 -= carry2 * (1 << 21);
5289	0	carry4 = (s4 + (1 << 20)) >> 21;
5290	0	s5 += carry4;
5291	0	s4 -= carry4 * (1 << 21);
5292	0	carry6 = (s6 + (1 << 20)) >> 21;
5293	0	s7 += carry6;
5294	0	s6 -= carry6 * (1 << 21);
5295	0	carry8 = (s8 + (1 << 20)) >> 21;
5296	0	s9 += carry8;
5297	0	s8 -= carry8 * (1 << 21);
5298	0	carry10 = (s10 + (1 << 20)) >> 21;
5299	0	s11 += carry10;
5300	0	s10 -= carry10 * (1 << 21);
5301
5302	0	carry1 = (s1 + (1 << 20)) >> 21;
5303	0	s2 += carry1;
5304	0	s1 -= carry1 * (1 << 21);
5305	0	carry3 = (s3 + (1 << 20)) >> 21;
5306	0	s4 += carry3;
5307	0	s3 -= carry3 * (1 << 21);
5308	0	carry5 = (s5 + (1 << 20)) >> 21;
5309	0	s6 += carry5;
5310	0	s5 -= carry5 * (1 << 21);
5311	0	carry7 = (s7 + (1 << 20)) >> 21;
5312	0	s8 += carry7;
5313	0	s7 -= carry7 * (1 << 21);
5314	0	carry9 = (s9 + (1 << 20)) >> 21;
5315	0	s10 += carry9;
5316	0	s9 -= carry9 * (1 << 21);
5317	0	carry11 = (s11 + (1 << 20)) >> 21;
5318	0	s12 += carry11;
5319	0	s11 -= carry11 * (1 << 21);
5320
5321	0	s0 += s12 * 666643;
5322	0	s1 += s12 * 470296;
5323	0	s2 += s12 * 654183;
5324	0	s3 -= s12 * 997805;
5325	0	s4 += s12 * 136657;
5326	0	s5 -= s12 * 683901;
5327	0	s12 = 0;
5328
5329	0	carry0 = s0 >> 21;
5330	0	s1 += carry0;
5331	0	s0 -= carry0 * (1 << 21);
5332	0	carry1 = s1 >> 21;
5333	0	s2 += carry1;
5334	0	s1 -= carry1 * (1 << 21);
5335	0	carry2 = s2 >> 21;
5336	0	s3 += carry2;
5337	0	s2 -= carry2 * (1 << 21);
5338	0	carry3 = s3 >> 21;
5339	0	s4 += carry3;
5340	0	s3 -= carry3 * (1 << 21);
5341	0	carry4 = s4 >> 21;
5342	0	s5 += carry4;
5343	0	s4 -= carry4 * (1 << 21);
5344	0	carry5 = s5 >> 21;
5345	0	s6 += carry5;
5346	0	s5 -= carry5 * (1 << 21);
5347	0	carry6 = s6 >> 21;
5348	0	s7 += carry6;
5349	0	s6 -= carry6 * (1 << 21);
5350	0	carry7 = s7 >> 21;
5351	0	s8 += carry7;
5352	0	s7 -= carry7 * (1 << 21);
5353	0	carry8 = s8 >> 21;
5354	0	s9 += carry8;
5355	0	s8 -= carry8 * (1 << 21);
5356	0	carry9 = s9 >> 21;
5357	0	s10 += carry9;
5358	0	s9 -= carry9 * (1 << 21);
5359	0	carry10 = s10 >> 21;
5360	0	s11 += carry10;
5361	0	s10 -= carry10 * (1 << 21);
5362	0	carry11 = s11 >> 21;
5363	0	s12 += carry11;
5364	0	s11 -= carry11 * (1 << 21);
5365
5366	0	s0 += s12 * 666643;
5367	0	s1 += s12 * 470296;
5368	0	s2 += s12 * 654183;
5369	0	s3 -= s12 * 997805;
5370	0	s4 += s12 * 136657;
5371	0	s5 -= s12 * 683901;
5372	0	s12 = 0;
5373
5374	0	carry0 = s0 >> 21;
5375	0	s1 += carry0;
5376	0	s0 -= carry0 * (1 << 21);
5377	0	carry1 = s1 >> 21;
5378	0	s2 += carry1;
5379	0	s1 -= carry1 * (1 << 21);
5380	0	carry2 = s2 >> 21;
5381	0	s3 += carry2;
5382	0	s2 -= carry2 * (1 << 21);
5383	0	carry3 = s3 >> 21;
5384	0	s4 += carry3;
5385	0	s3 -= carry3 * (1 << 21);
5386	0	carry4 = s4 >> 21;
5387	0	s5 += carry4;
5388	0	s4 -= carry4 * (1 << 21);
5389	0	carry5 = s5 >> 21;
5390	0	s6 += carry5;
5391	0	s5 -= carry5 * (1 << 21);
5392	0	carry6 = s6 >> 21;
5393	0	s7 += carry6;
5394	0	s6 -= carry6 * (1 << 21);
5395	0	carry7 = s7 >> 21;
5396	0	s8 += carry7;
5397	0	s7 -= carry7 * (1 << 21);
5398	0	carry8 = s8 >> 21;
5399	0	s9 += carry8;
5400	0	s8 -= carry8 * (1 << 21);
5401	0	carry9 = s9 >> 21;
5402	0	s10 += carry9;
5403	0	s9 -= carry9 * (1 << 21);
5404	0	carry10 = s10 >> 21;
5405	0	s11 += carry10;
5406	0	s10 -= carry10 * (1 << 21);
5407
5408	0	s[ 0] = (uint8_t) (s0 >> 0);
5409	0	s[ 1] = (uint8_t) (s0 >> 8);
5410	0	s[ 2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5411	0	s[ 3] = (uint8_t) (s1 >> 3);
5412	0	s[ 4] = (uint8_t) (s1 >> 11);
5413	0	s[ 5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5414	0	s[ 6] = (uint8_t) (s2 >> 6);
5415	0	s[ 7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5416	0	s[ 8] = (uint8_t) (s3 >> 1);
5417	0	s[ 9] = (uint8_t) (s3 >> 9);
5418	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5419	0	s[11] = (uint8_t) (s4 >> 4);
5420	0	s[12] = (uint8_t) (s4 >> 12);
5421	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5422	0	s[14] = (uint8_t) (s5 >> 7);
5423	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5424	0	s[16] = (uint8_t) (s6 >> 2);
5425	0	s[17] = (uint8_t) (s6 >> 10);
5426	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5427	0	s[19] = (uint8_t) (s7 >> 5);
5428	0	s[20] = (uint8_t) (s7 >> 13);
5429	0	s[21] = (uint8_t) (s8 >> 0);
5430	0	s[22] = (uint8_t) (s8 >> 8);
5431	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5432	0	s[24] = (uint8_t) (s9 >> 3);
5433	0	s[25] = (uint8_t) (s9 >> 11);
5434	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5435	0	s[27] = (uint8_t) (s10 >> 6);
5436	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5437	0	s[29] = (uint8_t) (s11 >> 1);
5438	0	s[30] = (uint8_t) (s11 >> 9);
5439	0	s[31] = (uint8_t) (s11 >> 17);
5440	0	}
5441
5442		int
5443		ossl_ed25519_sign(uint8_t out_sig, const uint8_t message, size_t message_len,
5444		const uint8_t public_key[32], const uint8_t private_key[32],
5445		OSSL_LIB_CTX libctx, const char propq)
5446	0	{
5447	0	uint8_t az[SHA512_DIGEST_LENGTH];
5448	0	uint8_t nonce[SHA512_DIGEST_LENGTH];
5449	0	ge_p3 R;
5450	0	uint8_t hram[SHA512_DIGEST_LENGTH];
5451	0	EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5452	0	EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
5453	0	unsigned int sz;
5454	0	int res = 0;
5455
5456	0	if (sha512 == NULL \|\| hash_ctx == NULL)
5457	0	goto err;
5458
5459	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5460	0	\|\| !EVP_DigestUpdate(hash_ctx, private_key, 32)
5461	0	\|\| !EVP_DigestFinal_ex(hash_ctx, az, &sz))
5462	0	goto err;
5463
5464	0	az[0] &= 248;
5465	0	az[31] &= 63;
5466	0	az[31] \|= 64;
5467
5468	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5469	0	\|\| !EVP_DigestUpdate(hash_ctx, az + 32, 32)
5470	0	\|\| !EVP_DigestUpdate(hash_ctx, message, message_len)
5471	0	\|\| !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
5472	0	goto err;
5473
5474	0	x25519_sc_reduce(nonce);
5475	0	ge_scalarmult_base(&R, nonce);
5476	0	ge_p3_tobytes(out_sig, &R);
5477
5478	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5479	0	\|\| !EVP_DigestUpdate(hash_ctx, out_sig, 32)
5480	0	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5481	0	\|\| !EVP_DigestUpdate(hash_ctx, message, message_len)
5482	0	\|\| !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
5483	0	goto err;
5484
5485	0	x25519_sc_reduce(hram);
5486	0	sc_muladd(out_sig + 32, hram, az, nonce);
5487
5488	0	res = 1;
5489	0	err:
5490	0	OPENSSL_cleanse(nonce, sizeof(nonce));
5491	0	OPENSSL_cleanse(az, sizeof(az));
5492	0	EVP_MD_free(sha512);
5493	0	EVP_MD_CTX_free(hash_ctx);
5494	0	return res;
5495	0	}
5496
5497		static const char allzeroes[15];
5498
5499		int
5500		ossl_ed25519_verify(const uint8_t *message, size_t message_len,
5501		const uint8_t signature[64], const uint8_t public_key[32],
5502		OSSL_LIB_CTX libctx, const char propq)
5503	111	{
5504	111	int i;
5505	111	ge_p3 A;
5506	111	const uint8_t r, s;
5507	111	EVP_MD *sha512;
5508	111	EVP_MD_CTX *hash_ctx = NULL;
5509	111	unsigned int sz;
5510	111	int res = 0;
5511	111	ge_p2 R;
5512	111	uint8_t rcheck[32];
5513	111	uint8_t h[SHA512_DIGEST_LENGTH];
5514		/* 27742317777372353535851937790883648493 in little endian format */
5515	111	const uint8_t l_low[16] = {
5516	111	0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5517	111	0xDE, 0xF9, 0xDE, 0x14
5518	111	};
5519
5520	111	r = signature;
5521	111	s = signature + 32;
5522
5523		/*
5524		* Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5525		*
5526		* If not the signature is publicly invalid. Since it's public we can do the
5527		* check in variable time.
5528		*
5529		* First check the most significant byte
5530		*/
5531	111	if (s[31] > 0x10)
5532	4	return 0;
5533	107	if (s[31] == 0x10) {
5534		/*
5535		* Most significant byte indicates a value close to 2^252 so check the
5536		* rest
5537		*/
5538	12	if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5539	5	return 0;
5540	17	for (i = 15; i >= 0; i--) {
5541	17	if (s[i] < l_low[i])
5542	3	break;
5543	14	if (s[i] > l_low[i])
5544	4	return 0;
5545	14	}
5546	3	if (i < 0)
5547	0	return 0;
5548	3	}
5549
5550	98	if (ge_frombytes_vartime(&A, public_key) != 0) {
5551	2	return 0;
5552	2	}
5553
5554	96	fe_neg(A.X, A.X);
5555	96	fe_neg(A.T, A.T);
5556
5557	96	sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5558	96	if (sha512 == NULL)
5559	0	return 0;
5560	96	hash_ctx = EVP_MD_CTX_new();
5561	96	if (hash_ctx == NULL)
5562	0	goto err;
5563
5564	96	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5565	96	\|\| !EVP_DigestUpdate(hash_ctx, r, 32)
5566	96	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5567	96	\|\| !EVP_DigestUpdate(hash_ctx, message, message_len)
5568	96	\|\| !EVP_DigestFinal_ex(hash_ctx, h, &sz))
5569	0	goto err;
5570
5571	96	x25519_sc_reduce(h);
5572
5573	96	ge_double_scalarmult_vartime(&R, h, &A, s);
5574
5575	96	ge_tobytes(rcheck, &R);
5576
5577	96	res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5578	96	err:
5579	96	EVP_MD_free(sha512);
5580	96	EVP_MD_CTX_free(hash_ctx);
5581	96	return res;
5582	96	}
5583
5584		int
5585		ossl_ed25519_public_from_private(OSSL_LIB_CTX *ctx, uint8_t out_public_key[32],
5586		const uint8_t private_key[32],
5587		const char *propq)
5588	19	{
5589	19	uint8_t az[SHA512_DIGEST_LENGTH];
5590	19	ge_p3 A;
5591	19	int r;
5592	19	EVP_MD *sha512 = NULL;
5593
5594	19	sha512 = EVP_MD_fetch(ctx, SN_sha512, propq);
5595	19	if (sha512 == NULL)
5596	0	return 0;
5597	19	r = EVP_Digest(private_key, 32, az, NULL, sha512, NULL);
5598	19	EVP_MD_free(sha512);
5599	19	if (!r) {
5600	0	OPENSSL_cleanse(az, sizeof(az));
5601	0	return 0;
5602	0	}
5603
5604	19	az[0] &= 248;
5605	19	az[31] &= 63;
5606	19	az[31] \|= 64;
5607
5608	19	ge_scalarmult_base(&A, az);
5609	19	ge_p3_tobytes(out_public_key, &A);
5610
5611	19	OPENSSL_cleanse(az, sizeof(az));
5612	19	return 1;
5613	19	}
5614
5615		int
5616		ossl_x25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5617		const uint8_t peer_public_value[32])
5618	16.2k	{
5619	16.2k	static const uint8_t kZeros[32] = {0};
5620	16.2k	x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5621		/* The all-zero output results when the input is a point of small order. */
5622	16.2k	return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5623	16.2k	}
5624
5625		void
5626		ossl_x25519_public_from_private(uint8_t out_public_value[32],
5627		const uint8_t private_key[32])
5628	74.1k	{
5629	74.1k	uint8_t e[32];
5630	74.1k	ge_p3 A;
5631	74.1k	fe zplusy, zminusy, zminusy_inv;
5632
5633	74.1k	memcpy(e, private_key, 32);
5634	74.1k	e[0] &= 248;
5635	74.1k	e[31] &= 127;
5636	74.1k	e[31] \|= 64;
5637
5638	74.1k	ge_scalarmult_base(&A, e);
5639
5640		/*
5641		* We only need the u-coordinate of the curve25519 point.
5642		* The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5643		* u=(Z+Y)/(Z-Y).
5644		*/
5645	74.1k	fe_add(zplusy, A.Z, A.Y);
5646	74.1k	fe_sub(zminusy, A.Z, A.Y);
5647	74.1k	fe_invert(zminusy_inv, zminusy);
5648	74.1k	fe_mul(zplusy, zplusy, zminusy_inv);
5649	74.1k	fe_tobytes(out_public_value, zplusy);
5650
5651	74.1k	OPENSSL_cleanse(e, sizeof(e));
5652	74.1k	}

Coverage Report

Created: 2025-06-13 06:58