/src/openssl/crypto/ec/curve25519.c

Line	Count	Source (jump to first uncovered line)
1		/*
2		* Copyright 2016-2024 The OpenSSL Project Authors. All Rights Reserved.
3		*
4		* Licensed under the Apache License 2.0 (the "License"). You may not use
5		* this file except in compliance with the License. You can obtain a copy
6		* in the file LICENSE in the source distribution or at
7		* https://www.openssl.org/source/license.html
8		*/
9
10		/*
11		* ECDSA low level APIs are deprecated for public use, but still ok for
12		* internal use.
13		*/
14		#include "internal/deprecated.h"
15
16		#include <string.h>
17		#include "crypto/ecx.h"
18		#include "ec_local.h"
19		#include <openssl/evp.h>
20		#include <openssl/sha.h>
21
22		#include "internal/numbers.h"
23
24		#if defined(X25519_ASM) && (defined(__x86_64) \|\| defined(__x86_64__) \|\| \
25		defined(_M_AMD64) \|\| defined(_M_X64))
26
27		# define BASE_2_64_IMPLEMENTED
28
29		typedef uint64_t fe64[4];
30
31		int x25519_fe64_eligible(void);
32
33		/*
34		* Following subroutines perform corresponding operations modulo
35		* 2^256-38, i.e. double the curve modulus. However, inputs and
36		* outputs are permitted to be partially reduced, i.e. to remain
37		* in [0..2^256) range. It's all tied up in final fe64_tobytes
38		* that performs full reduction modulo 2^255-19.
39		*
40		* There are no reference C implementations for these.
41		*/
42		void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
43		void x25519_fe64_sqr(fe64 h, const fe64 f);
44		void x25519_fe64_mul121666(fe64 h, fe64 f);
45		void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
46		void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
47		void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
48		# define fe64_mul x25519_fe64_mul
49		# define fe64_sqr x25519_fe64_sqr
50		# define fe64_mul121666 x25519_fe64_mul121666
51		# define fe64_add x25519_fe64_add
52		# define fe64_sub x25519_fe64_sub
53		# define fe64_tobytes x25519_fe64_tobytes
54
55		static uint64_t load_8(const uint8_t *in)
56		{
57		uint64_t result;
58
59		result = in[0];
60		result \|= ((uint64_t)in[1]) << 8;
61		result \|= ((uint64_t)in[2]) << 16;
62		result \|= ((uint64_t)in[3]) << 24;
63		result \|= ((uint64_t)in[4]) << 32;
64		result \|= ((uint64_t)in[5]) << 40;
65		result \|= ((uint64_t)in[6]) << 48;
66		result \|= ((uint64_t)in[7]) << 56;
67
68		return result;
69		}
70
71		static void fe64_frombytes(fe64 h, const uint8_t *s)
72		{
73		h[0] = load_8(s);
74		h[1] = load_8(s + 8);
75		h[2] = load_8(s + 16);
76		h[3] = load_8(s + 24) & 0x7fffffffffffffff;
77		}
78
79		static void fe64_0(fe64 h)
80		{
81		h[0] = 0;
82		h[1] = 0;
83		h[2] = 0;
84		h[3] = 0;
85		}
86
87		static void fe64_1(fe64 h)
88		{
89		h[0] = 1;
90		h[1] = 0;
91		h[2] = 0;
92		h[3] = 0;
93		}
94
95		static void fe64_copy(fe64 h, const fe64 f)
96		{
97		h[0] = f[0];
98		h[1] = f[1];
99		h[2] = f[2];
100		h[3] = f[3];
101		}
102
103		static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
104		{
105		int i;
106		uint64_t mask = 0 - (uint64_t)b;
107
108		for (i = 0; i < 4; i++) {
109		uint64_t x = f[i] ^ g[i];
110		x &= mask;
111		f[i] ^= x;
112		g[i] ^= x;
113		}
114		}
115
116		static void fe64_invert(fe64 out, const fe64 z)
117		{
118		fe64 t0;
119		fe64 t1;
120		fe64 t2;
121		fe64 t3;
122		int i;
123
124		/*
125		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
126		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
127		*/
128
129		/* t0 = z ** 2 */
130		fe64_sqr(t0, z);
131
132		/* t1 = t0 (2 2) = z ** 8 */
133		fe64_sqr(t1, t0);
134		fe64_sqr(t1, t1);
135
136		/* t1 = z * t1 = z ** 9 */
137		fe64_mul(t1, z, t1);
138		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
139		fe64_mul(t0, t0, t1);
140
141		/* t2 = t0 2 = z 22 */
142		fe64_sqr(t2, t0);
143
144		/* t1 = t1 * t2 = z (2 5 - 1) */
145		fe64_mul(t1, t1, t2);
146
147		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
148		fe64_sqr(t2, t1);
149		for (i = 1; i < 5; ++i)
150		fe64_sqr(t2, t2);
151
152		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
153		fe64_mul(t1, t2, t1);
154
155		/* Continuing similarly... */
156
157		/* t2 = z (2 20 - 1) */
158		fe64_sqr(t2, t1);
159		for (i = 1; i < 10; ++i)
160		fe64_sqr(t2, t2);
161
162		fe64_mul(t2, t2, t1);
163
164		/* t2 = z (2 40 - 1) */
165		fe64_sqr(t3, t2);
166		for (i = 1; i < 20; ++i)
167		fe64_sqr(t3, t3);
168
169		fe64_mul(t2, t3, t2);
170
171		/* t2 = z (2 10) * (2 ** 40 - 1) */
172		for (i = 0; i < 10; ++i)
173		fe64_sqr(t2, t2);
174
175		/* t1 = z (2 50 - 1) */
176		fe64_mul(t1, t2, t1);
177
178		/* t2 = z (2 100 - 1) */
179		fe64_sqr(t2, t1);
180		for (i = 1; i < 50; ++i)
181		fe64_sqr(t2, t2);
182
183		fe64_mul(t2, t2, t1);
184
185		/* t2 = z (2 200 - 1) */
186		fe64_sqr(t3, t2);
187		for (i = 1; i < 100; ++i)
188		fe64_sqr(t3, t3);
189
190		fe64_mul(t2, t3, t2);
191
192		/* t2 = z ((2 50) * (2 ** 200 - 1) */
193		for (i = 0; i < 50; ++i)
194		fe64_sqr(t2, t2);
195
196		/* t1 = z (2 250 - 1) */
197		fe64_mul(t1, t2, t1);
198
199		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
200		for (i = 0; i < 5; ++i)
201		fe64_sqr(t1, t1);
202
203		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
204		fe64_mul(out, t1, t0);
205		}
206
207		/*
208		* Duplicate of original x25519_scalar_mult_generic, but using
209		* fe64_* subroutines.
210		*/
211		static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
212		const uint8_t point[32])
213		{
214		fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
215		uint8_t e[32];
216		unsigned swap = 0;
217		int pos;
218
219		memcpy(e, scalar, 32);
220		e[0] &= 0xf8;
221		e[31] &= 0x7f;
222		e[31] \|= 0x40;
223		fe64_frombytes(x1, point);
224		fe64_1(x2);
225		fe64_0(z2);
226		fe64_copy(x3, x1);
227		fe64_1(z3);
228
229		for (pos = 254; pos >= 0; --pos) {
230		unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
231
232		swap ^= b;
233		fe64_cswap(x2, x3, swap);
234		fe64_cswap(z2, z3, swap);
235		swap = b;
236		fe64_sub(tmp0, x3, z3);
237		fe64_sub(tmp1, x2, z2);
238		fe64_add(x2, x2, z2);
239		fe64_add(z2, x3, z3);
240		fe64_mul(z3, x2, tmp0);
241		fe64_mul(z2, z2, tmp1);
242		fe64_sqr(tmp0, tmp1);
243		fe64_sqr(tmp1, x2);
244		fe64_add(x3, z3, z2);
245		fe64_sub(z2, z3, z2);
246		fe64_mul(x2, tmp1, tmp0);
247		fe64_sub(tmp1, tmp1, tmp0);
248		fe64_sqr(z2, z2);
249		fe64_mul121666(z3, tmp1);
250		fe64_sqr(x3, x3);
251		fe64_add(tmp0, tmp0, z3);
252		fe64_mul(z3, x1, z2);
253		fe64_mul(z2, tmp1, tmp0);
254		}
255
256		fe64_invert(z2, z2);
257		fe64_mul(x2, x2, z2);
258		fe64_tobytes(out, x2);
259
260		OPENSSL_cleanse(e, sizeof(e));
261		}
262		#endif
263
264		#if defined(X25519_ASM) \
265		\|\| ( defined(INT128_MAX) \
266		&& !defined(__sparc__) \
267		&& (!defined(__SIZEOF_LONG__) \|\| (__SIZEOF_LONG__ == 8)) \
268		&& !(defined(__ANDROID__) && !defined(__clang__)) )
269		/*
270		* Base 2^51 implementation. It's virtually no different from reference
271		* base 2^25.5 implementation in respect to lax boundary conditions for
272		* intermediate values and even individual limbs. So that whatever you
273		* know about the reference, applies even here...
274		*/
275		# define BASE_2_51_IMPLEMENTED
276
277		typedef uint64_t fe51[5];
278
279		static const uint64_t MASK51 = 0x7ffffffffffff;
280
281		static uint64_t load_7(const uint8_t *in)
282	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		# define fe51_mul x25519_fe51_mul
394		# define fe51_sq x25519_fe51_sqr
395		# define fe51_mul121666 x25519_fe51_mul121666
396		# else
397
398		typedef uint128_t u128;
399
400		static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
401	0	{
402	0	u128 h0, h1, h2, h3, h4;
403	0	uint64_t f_i, g0, g1, g2, g3, g4;
404
405	0	f_i = f[0];
406	0	h0 = (u128)f_i * (g0 = g[0]);
407	0	h1 = (u128)f_i * (g1 = g[1]);
408	0	h2 = (u128)f_i * (g2 = g[2]);
409	0	h3 = (u128)f_i * (g3 = g[3]);
410	0	h4 = (u128)f_i * (g4 = g[4]);
411
412	0	f_i = f[1];
413	0	h0 += (u128)f_i * (g4 *= 19);
414	0	h1 += (u128)f_i * g0;
415	0	h2 += (u128)f_i * g1;
416	0	h3 += (u128)f_i * g2;
417	0	h4 += (u128)f_i * g3;
418
419	0	f_i = f[2];
420	0	h0 += (u128)f_i * (g3 *= 19);
421	0	h1 += (u128)f_i * g4;
422	0	h2 += (u128)f_i * g0;
423	0	h3 += (u128)f_i * g1;
424	0	h4 += (u128)f_i * g2;
425
426	0	f_i = f[3];
427	0	h0 += (u128)f_i * (g2 *= 19);
428	0	h1 += (u128)f_i * g3;
429	0	h2 += (u128)f_i * g4;
430	0	h3 += (u128)f_i * g0;
431	0	h4 += (u128)f_i * g1;
432
433	0	f_i = f[4];
434	0	h0 += (u128)f_i * (g1 *= 19);
435	0	h1 += (u128)f_i * g2;
436	0	h2 += (u128)f_i * g3;
437	0	h3 += (u128)f_i * g4;
438	0	h4 += (u128)f_i * g0;
439
440		/* partial [lazy] reduction */
441	0	h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
442	0	h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
443
444	0	h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
445	0	g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
446
447	0	g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
448	0	g3 += g2 >> 51; g2 &= MASK51;
449	0	g1 += g0 >> 51; g0 &= MASK51;
450
451	0	h[0] = g0;
452	0	h[1] = g1;
453	0	h[2] = g2;
454	0	h[3] = g3;
455	0	h[4] = g4;
456	0	}
457
458		static void fe51_sq(fe51 h, const fe51 f)
459	0	{
460		# if defined(OPENSSL_SMALL_FOOTPRINT)
461		fe51_mul(h, f, f);
462		# else
463		/* dedicated squaring gives 16-25% overall improvement */
464	0	uint64_t g0 = f[0];
465	0	uint64_t g1 = f[1];
466	0	uint64_t g2 = f[2];
467	0	uint64_t g3 = f[3];
468	0	uint64_t g4 = f[4];
469	0	u128 h0, h1, h2, h3, h4;
470
471	0	h0 = (u128)g0 * g0; g0 *= 2;
472	0	h1 = (u128)g0 * g1;
473	0	h2 = (u128)g0 * g2;
474	0	h3 = (u128)g0 * g3;
475	0	h4 = (u128)g0 * g4;
476
477	0	g0 = g4; /* borrow g0 */
478	0	h3 += (u128)g0 * (g4 *= 19);
479
480	0	h2 += (u128)g1 * g1; g1 *= 2;
481	0	h3 += (u128)g1 * g2;
482	0	h4 += (u128)g1 * g3;
483	0	h0 += (u128)g1 * g4;
484
485	0	g0 = g3; /* borrow g0 */
486	0	h1 += (u128)g0 * (g3 *= 19);
487	0	h2 += (u128)(g0 * 2) * g4;
488
489	0	h4 += (u128)g2 * g2; g2 *= 2;
490	0	h0 += (u128)g2 * g3;
491	0	h1 += (u128)g2 * g4;
492
493		/* partial [lazy] reduction */
494	0	h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
495	0	h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
496
497	0	h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
498	0	g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
499
500	0	g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
501	0	g3 += g2 >> 51; g2 &= MASK51;
502	0	g1 += g0 >> 51; g0 &= MASK51;
503
504	0	h[0] = g0;
505	0	h[1] = g1;
506	0	h[2] = g2;
507	0	h[3] = g3;
508	0	h[4] = g4;
509	0	# endif
510	0	}
511
512		static void fe51_mul121666(fe51 h, fe51 f)
513	0	{
514	0	u128 h0 = f[0] * (u128)121666;
515	0	u128 h1 = f[1] * (u128)121666;
516	0	u128 h2 = f[2] * (u128)121666;
517	0	u128 h3 = f[3] * (u128)121666;
518	0	u128 h4 = f[4] * (u128)121666;
519	0	uint64_t g0, g1, g2, g3, g4;
520
521	0	h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
522	0	h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
523
524	0	h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
525	0	g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
526
527	0	g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
528	0	g3 += g2 >> 51; g2 &= MASK51;
529	0	g1 += g0 >> 51; g0 &= MASK51;
530
531	0	h[0] = g0;
532	0	h[1] = g1;
533	0	h[2] = g2;
534	0	h[3] = g3;
535	0	h[4] = g4;
536	0	}
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	0	{
699	0	fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
700	0	uint8_t e[32];
701	0	unsigned swap = 0;
702	0	int pos;
703
704		# ifdef BASE_2_64_IMPLEMENTED
705		if (x25519_fe64_eligible()) {
706		x25519_scalar_mulx(out, scalar, point);
707		return;
708		}
709		# endif
710
711	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	0	{
781	0	uint64_t result;
782
783	0	result = ((uint64_t)in[0]);
784	0	result \|= ((uint64_t)in[1]) << 8;
785	0	result \|= ((uint64_t)in[2]) << 16;
786	0	return result;
787	0	}
788
789		static uint64_t load_4(const uint8_t *in)
790	0	{
791	0	uint64_t result;
792
793	0	result = ((uint64_t)in[0]);
794	0	result \|= ((uint64_t)in[1]) << 8;
795	0	result \|= ((uint64_t)in[2]) << 16;
796	0	result \|= ((uint64_t)in[3]) << 24;
797	0	return result;
798	0	}
799
800		static void fe_frombytes(fe h, const uint8_t *s)
801	0	{
802		/* Ignores top bit of h. */
803	0	int64_t h0 = load_4(s);
804	0	int64_t h1 = load_3(s + 4) << 6;
805	0	int64_t h2 = load_3(s + 7) << 5;
806	0	int64_t h3 = load_3(s + 10) << 3;
807	0	int64_t h4 = load_3(s + 13) << 2;
808	0	int64_t h5 = load_4(s + 16);
809	0	int64_t h6 = load_3(s + 20) << 7;
810	0	int64_t h7 = load_3(s + 23) << 5;
811	0	int64_t h8 = load_3(s + 26) << 4;
812	0	int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
813	0	int64_t carry0;
814	0	int64_t carry1;
815	0	int64_t carry2;
816	0	int64_t carry3;
817	0	int64_t carry4;
818	0	int64_t carry5;
819	0	int64_t carry6;
820	0	int64_t carry7;
821	0	int64_t carry8;
822	0	int64_t carry9;
823
824	0	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
825	0	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
826	0	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
827	0	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
828	0	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
829
830	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
831	0	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
832	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
833	0	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
834	0	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
835
836	0	h[0] = (int32_t)h0;
837	0	h[1] = (int32_t)h1;
838	0	h[2] = (int32_t)h2;
839	0	h[3] = (int32_t)h3;
840	0	h[4] = (int32_t)h4;
841	0	h[5] = (int32_t)h5;
842	0	h[6] = (int32_t)h6;
843	0	h[7] = (int32_t)h7;
844	0	h[8] = (int32_t)h8;
845	0	h[9] = (int32_t)h9;
846	0	}
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	0	{
874	0	int32_t h0 = h[0];
875	0	int32_t h1 = h[1];
876	0	int32_t h2 = h[2];
877	0	int32_t h3 = h[3];
878	0	int32_t h4 = h[4];
879	0	int32_t h5 = h[5];
880	0	int32_t h6 = h[6];
881	0	int32_t h7 = h[7];
882	0	int32_t h8 = h[8];
883	0	int32_t h9 = h[9];
884	0	int32_t q;
885
886	0	q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
887	0	q = (h0 + q) >> 26;
888	0	q = (h1 + q) >> 25;
889	0	q = (h2 + q) >> 26;
890	0	q = (h3 + q) >> 25;
891	0	q = (h4 + q) >> 26;
892	0	q = (h5 + q) >> 25;
893	0	q = (h6 + q) >> 26;
894	0	q = (h7 + q) >> 25;
895	0	q = (h8 + q) >> 26;
896	0	q = (h9 + q) >> 25;
897
898		/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
899	0	h0 += 19 * q;
900		/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
901
902	0	h1 += h0 >> 26; h0 &= kBottom26Bits;
903	0	h2 += h1 >> 25; h1 &= kBottom25Bits;
904	0	h3 += h2 >> 26; h2 &= kBottom26Bits;
905	0	h4 += h3 >> 25; h3 &= kBottom25Bits;
906	0	h5 += h4 >> 26; h4 &= kBottom26Bits;
907	0	h6 += h5 >> 25; h5 &= kBottom25Bits;
908	0	h7 += h6 >> 26; h6 &= kBottom26Bits;
909	0	h8 += h7 >> 25; h7 &= kBottom25Bits;
910	0	h9 += h8 >> 26; h8 &= kBottom26Bits;
911	0	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	0	s[ 0] = (uint8_t) (h0 >> 0);
921	0	s[ 1] = (uint8_t) (h0 >> 8);
922	0	s[ 2] = (uint8_t) (h0 >> 16);
923	0	s[ 3] = (uint8_t)((h0 >> 24) \| ((uint32_t)(h1) << 2));
924	0	s[ 4] = (uint8_t) (h1 >> 6);
925	0	s[ 5] = (uint8_t) (h1 >> 14);
926	0	s[ 6] = (uint8_t)((h1 >> 22) \| ((uint32_t)(h2) << 3));
927	0	s[ 7] = (uint8_t) (h2 >> 5);
928	0	s[ 8] = (uint8_t) (h2 >> 13);
929	0	s[ 9] = (uint8_t)((h2 >> 21) \| ((uint32_t)(h3) << 5));
930	0	s[10] = (uint8_t) (h3 >> 3);
931	0	s[11] = (uint8_t) (h3 >> 11);
932	0	s[12] = (uint8_t)((h3 >> 19) \| ((uint32_t)(h4) << 6));
933	0	s[13] = (uint8_t) (h4 >> 2);
934	0	s[14] = (uint8_t) (h4 >> 10);
935	0	s[15] = (uint8_t) (h4 >> 18);
936	0	s[16] = (uint8_t) (h5 >> 0);
937	0	s[17] = (uint8_t) (h5 >> 8);
938	0	s[18] = (uint8_t) (h5 >> 16);
939	0	s[19] = (uint8_t)((h5 >> 24) \| ((uint32_t)(h6) << 1));
940	0	s[20] = (uint8_t) (h6 >> 7);
941	0	s[21] = (uint8_t) (h6 >> 15);
942	0	s[22] = (uint8_t)((h6 >> 23) \| ((uint32_t)(h7) << 3));
943	0	s[23] = (uint8_t) (h7 >> 5);
944	0	s[24] = (uint8_t) (h7 >> 13);
945	0	s[25] = (uint8_t)((h7 >> 21) \| ((uint32_t)(h8) << 4));
946	0	s[26] = (uint8_t) (h8 >> 4);
947	0	s[27] = (uint8_t) (h8 >> 12);
948	0	s[28] = (uint8_t)((h8 >> 20) \| ((uint32_t)(h9) << 6));
949	0	s[29] = (uint8_t) (h9 >> 2);
950	0	s[30] = (uint8_t) (h9 >> 10);
951	0	s[31] = (uint8_t) (h9 >> 18);
952	0	}
953
954		/* h = f */
955		static void fe_copy(fe h, const fe f)
956	0	{
957	0	memmove(h, f, sizeof(int32_t) * 10);
958	0	}
959
960		/* h = 0 */
961		static void fe_0(fe h)
962	0	{
963	0	memset(h, 0, sizeof(int32_t) * 10);
964	0	}
965
966		/* h = 1 */
967		static void fe_1(fe h)
968	0	{
969	0	memset(h, 0, sizeof(int32_t) * 10);
970	0	h[0] = 1;
971	0	}
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	0	{
987	0	unsigned i;
988
989	0	for (i = 0; i < 10; i++) {
990	0	h[i] = f[i] + g[i];
991	0	}
992	0	}
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	0	{
1008	0	unsigned i;
1009
1010	0	for (i = 0; i < 10; i++) {
1011	0	h[i] = f[i] - g[i];
1012	0	}
1013	0	}
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	0	{
1047	0	int32_t f0 = f[0];
1048	0	int32_t f1 = f[1];
1049	0	int32_t f2 = f[2];
1050	0	int32_t f3 = f[3];
1051	0	int32_t f4 = f[4];
1052	0	int32_t f5 = f[5];
1053	0	int32_t f6 = f[6];
1054	0	int32_t f7 = f[7];
1055	0	int32_t f8 = f[8];
1056	0	int32_t f9 = f[9];
1057	0	int32_t g0 = g[0];
1058	0	int32_t g1 = g[1];
1059	0	int32_t g2 = g[2];
1060	0	int32_t g3 = g[3];
1061	0	int32_t g4 = g[4];
1062	0	int32_t g5 = g[5];
1063	0	int32_t g6 = g[6];
1064	0	int32_t g7 = g[7];
1065	0	int32_t g8 = g[8];
1066	0	int32_t g9 = g[9];
1067	0	int32_t g1_19 = 19 * g1; /* 1.9593752^29 /
1068	0	int32_t g2_19 = 19 * g2; /* 1.9593752^30; still ok /
1069	0	int32_t g3_19 = 19 * g3;
1070	0	int32_t g4_19 = 19 * g4;
1071	0	int32_t g5_19 = 19 * g5;
1072	0	int32_t g6_19 = 19 * g6;
1073	0	int32_t g7_19 = 19 * g7;
1074	0	int32_t g8_19 = 19 * g8;
1075	0	int32_t g9_19 = 19 * g9;
1076	0	int32_t f1_2 = 2 * f1;
1077	0	int32_t f3_2 = 2 * f3;
1078	0	int32_t f5_2 = 2 * f5;
1079	0	int32_t f7_2 = 2 * f7;
1080	0	int32_t f9_2 = 2 * f9;
1081	0	int64_t f0g0 = f0 * (int64_t) g0;
1082	0	int64_t f0g1 = f0 * (int64_t) g1;
1083	0	int64_t f0g2 = f0 * (int64_t) g2;
1084	0	int64_t f0g3 = f0 * (int64_t) g3;
1085	0	int64_t f0g4 = f0 * (int64_t) g4;
1086	0	int64_t f0g5 = f0 * (int64_t) g5;
1087	0	int64_t f0g6 = f0 * (int64_t) g6;
1088	0	int64_t f0g7 = f0 * (int64_t) g7;
1089	0	int64_t f0g8 = f0 * (int64_t) g8;
1090	0	int64_t f0g9 = f0 * (int64_t) g9;
1091	0	int64_t f1g0 = f1 * (int64_t) g0;
1092	0	int64_t f1g1_2 = f1_2 * (int64_t) g1;
1093	0	int64_t f1g2 = f1 * (int64_t) g2;
1094	0	int64_t f1g3_2 = f1_2 * (int64_t) g3;
1095	0	int64_t f1g4 = f1 * (int64_t) g4;
1096	0	int64_t f1g5_2 = f1_2 * (int64_t) g5;
1097	0	int64_t f1g6 = f1 * (int64_t) g6;
1098	0	int64_t f1g7_2 = f1_2 * (int64_t) g7;
1099	0	int64_t f1g8 = f1 * (int64_t) g8;
1100	0	int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
1101	0	int64_t f2g0 = f2 * (int64_t) g0;
1102	0	int64_t f2g1 = f2 * (int64_t) g1;
1103	0	int64_t f2g2 = f2 * (int64_t) g2;
1104	0	int64_t f2g3 = f2 * (int64_t) g3;
1105	0	int64_t f2g4 = f2 * (int64_t) g4;
1106	0	int64_t f2g5 = f2 * (int64_t) g5;
1107	0	int64_t f2g6 = f2 * (int64_t) g6;
1108	0	int64_t f2g7 = f2 * (int64_t) g7;
1109	0	int64_t f2g8_19 = f2 * (int64_t) g8_19;
1110	0	int64_t f2g9_19 = f2 * (int64_t) g9_19;
1111	0	int64_t f3g0 = f3 * (int64_t) g0;
1112	0	int64_t f3g1_2 = f3_2 * (int64_t) g1;
1113	0	int64_t f3g2 = f3 * (int64_t) g2;
1114	0	int64_t f3g3_2 = f3_2 * (int64_t) g3;
1115	0	int64_t f3g4 = f3 * (int64_t) g4;
1116	0	int64_t f3g5_2 = f3_2 * (int64_t) g5;
1117	0	int64_t f3g6 = f3 * (int64_t) g6;
1118	0	int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
1119	0	int64_t f3g8_19 = f3 * (int64_t) g8_19;
1120	0	int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
1121	0	int64_t f4g0 = f4 * (int64_t) g0;
1122	0	int64_t f4g1 = f4 * (int64_t) g1;
1123	0	int64_t f4g2 = f4 * (int64_t) g2;
1124	0	int64_t f4g3 = f4 * (int64_t) g3;
1125	0	int64_t f4g4 = f4 * (int64_t) g4;
1126	0	int64_t f4g5 = f4 * (int64_t) g5;
1127	0	int64_t f4g6_19 = f4 * (int64_t) g6_19;
1128	0	int64_t f4g7_19 = f4 * (int64_t) g7_19;
1129	0	int64_t f4g8_19 = f4 * (int64_t) g8_19;
1130	0	int64_t f4g9_19 = f4 * (int64_t) g9_19;
1131	0	int64_t f5g0 = f5 * (int64_t) g0;
1132	0	int64_t f5g1_2 = f5_2 * (int64_t) g1;
1133	0	int64_t f5g2 = f5 * (int64_t) g2;
1134	0	int64_t f5g3_2 = f5_2 * (int64_t) g3;
1135	0	int64_t f5g4 = f5 * (int64_t) g4;
1136	0	int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
1137	0	int64_t f5g6_19 = f5 * (int64_t) g6_19;
1138	0	int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
1139	0	int64_t f5g8_19 = f5 * (int64_t) g8_19;
1140	0	int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
1141	0	int64_t f6g0 = f6 * (int64_t) g0;
1142	0	int64_t f6g1 = f6 * (int64_t) g1;
1143	0	int64_t f6g2 = f6 * (int64_t) g2;
1144	0	int64_t f6g3 = f6 * (int64_t) g3;
1145	0	int64_t f6g4_19 = f6 * (int64_t) g4_19;
1146	0	int64_t f6g5_19 = f6 * (int64_t) g5_19;
1147	0	int64_t f6g6_19 = f6 * (int64_t) g6_19;
1148	0	int64_t f6g7_19 = f6 * (int64_t) g7_19;
1149	0	int64_t f6g8_19 = f6 * (int64_t) g8_19;
1150	0	int64_t f6g9_19 = f6 * (int64_t) g9_19;
1151	0	int64_t f7g0 = f7 * (int64_t) g0;
1152	0	int64_t f7g1_2 = f7_2 * (int64_t) g1;
1153	0	int64_t f7g2 = f7 * (int64_t) g2;
1154	0	int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
1155	0	int64_t f7g4_19 = f7 * (int64_t) g4_19;
1156	0	int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
1157	0	int64_t f7g6_19 = f7 * (int64_t) g6_19;
1158	0	int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
1159	0	int64_t f7g8_19 = f7 * (int64_t) g8_19;
1160	0	int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
1161	0	int64_t f8g0 = f8 * (int64_t) g0;
1162	0	int64_t f8g1 = f8 * (int64_t) g1;
1163	0	int64_t f8g2_19 = f8 * (int64_t) g2_19;
1164	0	int64_t f8g3_19 = f8 * (int64_t) g3_19;
1165	0	int64_t f8g4_19 = f8 * (int64_t) g4_19;
1166	0	int64_t f8g5_19 = f8 * (int64_t) g5_19;
1167	0	int64_t f8g6_19 = f8 * (int64_t) g6_19;
1168	0	int64_t f8g7_19 = f8 * (int64_t) g7_19;
1169	0	int64_t f8g8_19 = f8 * (int64_t) g8_19;
1170	0	int64_t f8g9_19 = f8 * (int64_t) g9_19;
1171	0	int64_t f9g0 = f9 * (int64_t) g0;
1172	0	int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
1173	0	int64_t f9g2_19 = f9 * (int64_t) g2_19;
1174	0	int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
1175	0	int64_t f9g4_19 = f9 * (int64_t) g4_19;
1176	0	int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
1177	0	int64_t f9g6_19 = f9 * (int64_t) g6_19;
1178	0	int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
1179	0	int64_t f9g8_19 = f9 * (int64_t) g8_19;
1180	0	int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
1181	0	int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1182	0	int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1183	0	int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1184	0	int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1185	0	int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1186	0	int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1187	0	int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
1188	0	int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
1189	0	int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
1190	0	int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ;
1191	0	int64_t carry0;
1192	0	int64_t carry1;
1193	0	int64_t carry2;
1194	0	int64_t carry3;
1195	0	int64_t carry4;
1196	0	int64_t carry5;
1197	0	int64_t carry6;
1198	0	int64_t carry7;
1199	0	int64_t carry8;
1200	0	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	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1208	0	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	0	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1215	0	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	0	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1222	0	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	0	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1229	0	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	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1236	0	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	0	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	0	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	0	h[0] = (int32_t)h0;
1251	0	h[1] = (int32_t)h1;
1252	0	h[2] = (int32_t)h2;
1253	0	h[3] = (int32_t)h3;
1254	0	h[4] = (int32_t)h4;
1255	0	h[5] = (int32_t)h5;
1256	0	h[6] = (int32_t)h6;
1257	0	h[7] = (int32_t)h7;
1258	0	h[8] = (int32_t)h8;
1259	0	h[9] = (int32_t)h9;
1260	0	}
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	0	{
1277	0	int32_t f0 = f[0];
1278	0	int32_t f1 = f[1];
1279	0	int32_t f2 = f[2];
1280	0	int32_t f3 = f[3];
1281	0	int32_t f4 = f[4];
1282	0	int32_t f5 = f[5];
1283	0	int32_t f6 = f[6];
1284	0	int32_t f7 = f[7];
1285	0	int32_t f8 = f[8];
1286	0	int32_t f9 = f[9];
1287	0	int32_t f0_2 = 2 * f0;
1288	0	int32_t f1_2 = 2 * f1;
1289	0	int32_t f2_2 = 2 * f2;
1290	0	int32_t f3_2 = 2 * f3;
1291	0	int32_t f4_2 = 2 * f4;
1292	0	int32_t f5_2 = 2 * f5;
1293	0	int32_t f6_2 = 2 * f6;
1294	0	int32_t f7_2 = 2 * f7;
1295	0	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1296	0	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1297	0	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1298	0	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1299	0	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1300	0	int64_t f0f0 = f0 * (int64_t) f0;
1301	0	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1302	0	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1303	0	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1304	0	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1305	0	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1306	0	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1307	0	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1308	0	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1309	0	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1310	0	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1311	0	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1312	0	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1313	0	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1314	0	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1315	0	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1316	0	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1317	0	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1318	0	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1319	0	int64_t f2f2 = f2 * (int64_t) f2;
1320	0	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1321	0	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1322	0	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1323	0	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1324	0	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1325	0	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1326	0	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1327	0	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1328	0	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1329	0	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1330	0	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1331	0	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1332	0	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1333	0	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1334	0	int64_t f4f4 = f4 * (int64_t) f4;
1335	0	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1336	0	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1337	0	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1338	0	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1339	0	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1340	0	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1341	0	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1342	0	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1343	0	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1344	0	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1345	0	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1346	0	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1347	0	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1348	0	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1349	0	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1350	0	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1351	0	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1352	0	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1353	0	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1354	0	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1355	0	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1356	0	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1357	0	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1358	0	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1359	0	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1360	0	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1361	0	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1362	0	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1363	0	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1364	0	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1365	0	int64_t carry0;
1366	0	int64_t carry1;
1367	0	int64_t carry2;
1368	0	int64_t carry3;
1369	0	int64_t carry4;
1370	0	int64_t carry5;
1371	0	int64_t carry6;
1372	0	int64_t carry7;
1373	0	int64_t carry8;
1374	0	int64_t carry9;
1375
1376	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1377	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1378
1379	0	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1380	0	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1381
1382	0	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1383	0	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1384
1385	0	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1386	0	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1387
1388	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1389	0	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1390
1391	0	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1392
1393	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1394
1395	0	h[0] = (int32_t)h0;
1396	0	h[1] = (int32_t)h1;
1397	0	h[2] = (int32_t)h2;
1398	0	h[3] = (int32_t)h3;
1399	0	h[4] = (int32_t)h4;
1400	0	h[5] = (int32_t)h5;
1401	0	h[6] = (int32_t)h6;
1402	0	h[7] = (int32_t)h7;
1403	0	h[8] = (int32_t)h8;
1404	0	h[9] = (int32_t)h9;
1405	0	}
1406
1407		static void fe_invert(fe out, const fe z)
1408	0	{
1409	0	fe t0;
1410	0	fe t1;
1411	0	fe t2;
1412	0	fe t3;
1413	0	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	0	fe_sq(t0, z);
1422
1423		/* t1 = t0 (2 2) = z ** 8 */
1424	0	fe_sq(t1, t0);
1425	0	fe_sq(t1, t1);
1426
1427		/* t1 = z * t1 = z ** 9 */
1428	0	fe_mul(t1, z, t1);
1429		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1430	0	fe_mul(t0, t0, t1);
1431
1432		/* t2 = t0 2 = z 22 */
1433	0	fe_sq(t2, t0);
1434
1435		/* t1 = t1 * t2 = z (2 5 - 1) */
1436	0	fe_mul(t1, t1, t2);
1437
1438		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
1439	0	fe_sq(t2, t1);
1440	0	for (i = 1; i < 5; ++i) {
1441	0	fe_sq(t2, t2);
1442	0	}
1443
1444		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
1445	0	fe_mul(t1, t2, t1);
1446
1447		/* Continuing similarly... */
1448
1449		/* t2 = z (2 20 - 1) */
1450	0	fe_sq(t2, t1);
1451	0	for (i = 1; i < 10; ++i) {
1452	0	fe_sq(t2, t2);
1453	0	}
1454	0	fe_mul(t2, t2, t1);
1455
1456		/* t2 = z (2 40 - 1) */
1457	0	fe_sq(t3, t2);
1458	0	for (i = 1; i < 20; ++i) {
1459	0	fe_sq(t3, t3);
1460	0	}
1461	0	fe_mul(t2, t3, t2);
1462
1463		/* t2 = z (2 10) * (2 ** 40 - 1) */
1464	0	for (i = 0; i < 10; ++i) {
1465	0	fe_sq(t2, t2);
1466	0	}
1467		/* t1 = z (2 50 - 1) */
1468	0	fe_mul(t1, t2, t1);
1469
1470		/* t2 = z (2 100 - 1) */
1471	0	fe_sq(t2, t1);
1472	0	for (i = 1; i < 50; ++i) {
1473	0	fe_sq(t2, t2);
1474	0	}
1475	0	fe_mul(t2, t2, t1);
1476
1477		/* t2 = z (2 200 - 1) */
1478	0	fe_sq(t3, t2);
1479	0	for (i = 1; i < 100; ++i) {
1480	0	fe_sq(t3, t3);
1481	0	}
1482	0	fe_mul(t2, t3, t2);
1483
1484		/* t2 = z ((2 50) * (2 ** 200 - 1) */
1485	0	fe_sq(t2, t2);
1486	0	for (i = 1; i < 50; ++i) {
1487	0	fe_sq(t2, t2);
1488	0	}
1489
1490		/* t1 = z (2 250 - 1) */
1491	0	fe_mul(t1, t2, t1);
1492
1493		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
1494	0	fe_sq(t1, t1);
1495	0	for (i = 1; i < 5; ++i) {
1496	0	fe_sq(t1, t1);
1497	0	}
1498
1499		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
1500	0	fe_mul(out, t1, t0);
1501	0	}
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	0	{
1514	0	unsigned i;
1515
1516	0	for (i = 0; i < 10; i++) {
1517	0	h[i] = -f[i];
1518	0	}
1519	0	}
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	0	{
1529	0	size_t i;
1530
1531	0	b = 0-b;
1532	0	for (i = 0; i < 10; i++) {
1533	0	int32_t x = f[i] ^ g[i];
1534	0	x &= b;
1535	0	f[i] ^= x;
1536	0	}
1537	0	}
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	0	{
1548	0	uint8_t s[32];
1549	0	static const uint8_t zero[32] = {0};
1550
1551	0	fe_tobytes(s, f);
1552
1553	0	return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1554	0	}
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	0	{
1565	0	uint8_t s[32];
1566
1567	0	fe_tobytes(s, f);
1568	0	return s[0] & 1;
1569	0	}
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	0	{
1586	0	int32_t f0 = f[0];
1587	0	int32_t f1 = f[1];
1588	0	int32_t f2 = f[2];
1589	0	int32_t f3 = f[3];
1590	0	int32_t f4 = f[4];
1591	0	int32_t f5 = f[5];
1592	0	int32_t f6 = f[6];
1593	0	int32_t f7 = f[7];
1594	0	int32_t f8 = f[8];
1595	0	int32_t f9 = f[9];
1596	0	int32_t f0_2 = 2 * f0;
1597	0	int32_t f1_2 = 2 * f1;
1598	0	int32_t f2_2 = 2 * f2;
1599	0	int32_t f3_2 = 2 * f3;
1600	0	int32_t f4_2 = 2 * f4;
1601	0	int32_t f5_2 = 2 * f5;
1602	0	int32_t f6_2 = 2 * f6;
1603	0	int32_t f7_2 = 2 * f7;
1604	0	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1605	0	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1606	0	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1607	0	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1608	0	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1609	0	int64_t f0f0 = f0 * (int64_t) f0;
1610	0	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1611	0	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1612	0	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1613	0	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1614	0	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1615	0	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1616	0	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1617	0	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1618	0	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1619	0	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1620	0	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1621	0	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1622	0	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1623	0	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1624	0	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1625	0	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1626	0	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1627	0	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1628	0	int64_t f2f2 = f2 * (int64_t) f2;
1629	0	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1630	0	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1631	0	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1632	0	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1633	0	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1634	0	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1635	0	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1636	0	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1637	0	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1638	0	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1639	0	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1640	0	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1641	0	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1642	0	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1643	0	int64_t f4f4 = f4 * (int64_t) f4;
1644	0	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1645	0	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1646	0	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1647	0	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1648	0	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1649	0	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1650	0	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1651	0	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1652	0	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1653	0	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1654	0	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1655	0	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1656	0	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1657	0	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1658	0	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1659	0	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1660	0	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1661	0	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1662	0	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1663	0	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1664	0	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1665	0	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1666	0	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1667	0	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1668	0	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1669	0	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1670	0	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1671	0	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1672	0	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1673	0	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1674	0	int64_t carry0;
1675	0	int64_t carry1;
1676	0	int64_t carry2;
1677	0	int64_t carry3;
1678	0	int64_t carry4;
1679	0	int64_t carry5;
1680	0	int64_t carry6;
1681	0	int64_t carry7;
1682	0	int64_t carry8;
1683	0	int64_t carry9;
1684
1685	0	h0 += h0;
1686	0	h1 += h1;
1687	0	h2 += h2;
1688	0	h3 += h3;
1689	0	h4 += h4;
1690	0	h5 += h5;
1691	0	h6 += h6;
1692	0	h7 += h7;
1693	0	h8 += h8;
1694	0	h9 += h9;
1695
1696	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1697	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1698
1699	0	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1700	0	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1701
1702	0	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1703	0	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1704
1705	0	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1706	0	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1707
1708	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1709	0	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1710
1711	0	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1712
1713	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1714
1715	0	h[0] = (int32_t)h0;
1716	0	h[1] = (int32_t)h1;
1717	0	h[2] = (int32_t)h2;
1718	0	h[3] = (int32_t)h3;
1719	0	h[4] = (int32_t)h4;
1720	0	h[5] = (int32_t)h5;
1721	0	h[6] = (int32_t)h6;
1722	0	h[7] = (int32_t)h7;
1723	0	h[8] = (int32_t)h8;
1724	0	h[9] = (int32_t)h9;
1725	0	}
1726
1727		static void fe_pow22523(fe out, const fe z)
1728	0	{
1729	0	fe t0;
1730	0	fe t1;
1731	0	fe t2;
1732	0	int i;
1733
1734	0	fe_sq(t0, z);
1735	0	fe_sq(t1, t0);
1736	0	for (i = 1; i < 2; ++i) {
1737	0	fe_sq(t1, t1);
1738	0	}
1739	0	fe_mul(t1, z, t1);
1740	0	fe_mul(t0, t0, t1);
1741	0	fe_sq(t0, t0);
1742	0	fe_mul(t0, t1, t0);
1743	0	fe_sq(t1, t0);
1744	0	for (i = 1; i < 5; ++i) {
1745	0	fe_sq(t1, t1);
1746	0	}
1747	0	fe_mul(t0, t1, t0);
1748	0	fe_sq(t1, t0);
1749	0	for (i = 1; i < 10; ++i) {
1750	0	fe_sq(t1, t1);
1751	0	}
1752	0	fe_mul(t1, t1, t0);
1753	0	fe_sq(t2, t1);
1754	0	for (i = 1; i < 20; ++i) {
1755	0	fe_sq(t2, t2);
1756	0	}
1757	0	fe_mul(t1, t2, t1);
1758	0	fe_sq(t1, t1);
1759	0	for (i = 1; i < 10; ++i) {
1760	0	fe_sq(t1, t1);
1761	0	}
1762	0	fe_mul(t0, t1, t0);
1763	0	fe_sq(t1, t0);
1764	0	for (i = 1; i < 50; ++i) {
1765	0	fe_sq(t1, t1);
1766	0	}
1767	0	fe_mul(t1, t1, t0);
1768	0	fe_sq(t2, t1);
1769	0	for (i = 1; i < 100; ++i) {
1770	0	fe_sq(t2, t2);
1771	0	}
1772	0	fe_mul(t1, t2, t1);
1773	0	fe_sq(t1, t1);
1774	0	for (i = 1; i < 50; ++i) {
1775	0	fe_sq(t1, t1);
1776	0	}
1777	0	fe_mul(t0, t1, t0);
1778	0	fe_sq(t0, t0);
1779	0	for (i = 1; i < 2; ++i) {
1780	0	fe_sq(t0, t0);
1781	0	}
1782	0	fe_mul(out, t0, z);
1783	0	}
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	0	{
1833	0	fe recip;
1834	0	fe x;
1835	0	fe y;
1836
1837	0	fe_invert(recip, h->Z);
1838	0	fe_mul(x, h->X, recip);
1839	0	fe_mul(y, h->Y, recip);
1840	0	fe_tobytes(s, y);
1841	0	s[31] ^= fe_isnegative(x) << 7;
1842	0	}
1843
1844		static void ge_p3_tobytes(uint8_t s, const ge_p3 h)
1845	0	{
1846	0	fe recip;
1847	0	fe x;
1848	0	fe y;
1849
1850	0	fe_invert(recip, h->Z);
1851	0	fe_mul(x, h->X, recip);
1852	0	fe_mul(y, h->Y, recip);
1853	0	fe_tobytes(s, y);
1854	0	s[31] ^= fe_isnegative(x) << 7;
1855	0	}
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	0	{
1869	0	fe u;
1870	0	fe v;
1871	0	fe w;
1872	0	fe vxx;
1873	0	fe check;
1874
1875	0	fe_frombytes(h->Y, s);
1876	0	fe_1(h->Z);
1877	0	fe_sq(u, h->Y);
1878	0	fe_mul(v, u, d);
1879	0	fe_sub(u, u, h->Z); /* u = y^2-1 */
1880	0	fe_add(v, v, h->Z); /* v = dy^2+1 */
1881
1882	0	fe_mul(w, u, v); /* w = uv /
1883
1884	0	fe_pow22523(h->X, w); /* x = w^((q-5)/8) */
1885	0	fe_mul(h->X, h->X, u); /* x = u * w^((q-5)/8) */
1886
1887	0	fe_sq(vxx, h->X);
1888	0	fe_mul(vxx, vxx, v);
1889	0	fe_sub(check, vxx, u); /* vx^2-u */
1890	0	if (fe_isnonzero(check)) {
1891	0	fe_add(check, vxx, u); /* vx^2+u */
1892	0	if (fe_isnonzero(check)) {
1893	0	return -1;
1894	0	}
1895	0	fe_mul(h->X, h->X, sqrtm1);
1896	0	}
1897
1898	0	if (fe_isnegative(h->X) != (s[31] >> 7)) {
1899	0	fe_neg(h->X, h->X);
1900	0	}
1901
1902	0	fe_mul(h->T, h->X, h->Y);
1903	0	return 0;
1904	0	}
1905
1906		static void ge_p2_0(ge_p2 *h)
1907	0	{
1908	0	fe_0(h->X);
1909	0	fe_1(h->Y);
1910	0	fe_1(h->Z);
1911	0	}
1912
1913		static void ge_p3_0(ge_p3 *h)
1914	0	{
1915	0	fe_0(h->X);
1916	0	fe_1(h->Y);
1917	0	fe_1(h->Z);
1918	0	fe_0(h->T);
1919	0	}
1920
1921		static void ge_precomp_0(ge_precomp *h)
1922	0	{
1923	0	fe_1(h->yplusx);
1924	0	fe_1(h->yminusx);
1925	0	fe_0(h->xy2d);
1926	0	}
1927
1928		/* r = p */
1929		static void ge_p3_to_p2(ge_p2 r, const ge_p3 p)
1930	0	{
1931	0	fe_copy(r->X, p->X);
1932	0	fe_copy(r->Y, p->Y);
1933	0	fe_copy(r->Z, p->Z);
1934	0	}
1935
1936		static const fe d2 = {
1937		-21827239, -5839606, -30745221, 13898782, 229458,
1938		15978800, -12551817, -6495438, 29715968, 9444199
1939		};
1940
1941		/* r = p */
1942		static void ge_p3_to_cached(ge_cached r, const ge_p3 p)
1943	0	{
1944	0	fe_add(r->YplusX, p->Y, p->X);
1945	0	fe_sub(r->YminusX, p->Y, p->X);
1946	0	fe_copy(r->Z, p->Z);
1947	0	fe_mul(r->T2d, p->T, d2);
1948	0	}
1949
1950		/* r = p */
1951		static void ge_p1p1_to_p2(ge_p2 r, const ge_p1p1 p)
1952	0	{
1953	0	fe_mul(r->X, p->X, p->T);
1954	0	fe_mul(r->Y, p->Y, p->Z);
1955	0	fe_mul(r->Z, p->Z, p->T);
1956	0	}
1957
1958		/* r = p */
1959		static void ge_p1p1_to_p3(ge_p3 r, const ge_p1p1 p)
1960	0	{
1961	0	fe_mul(r->X, p->X, p->T);
1962	0	fe_mul(r->Y, p->Y, p->Z);
1963	0	fe_mul(r->Z, p->Z, p->T);
1964	0	fe_mul(r->T, p->X, p->Y);
1965	0	}
1966
1967		/* r = 2 * p */
1968		static void ge_p2_dbl(ge_p1p1 r, const ge_p2 p)
1969	0	{
1970	0	fe t0;
1971
1972	0	fe_sq(r->X, p->X);
1973	0	fe_sq(r->Z, p->Y);
1974	0	fe_sq2(r->T, p->Z);
1975	0	fe_add(r->Y, p->X, p->Y);
1976	0	fe_sq(t0, r->Y);
1977	0	fe_add(r->Y, r->Z, r->X);
1978	0	fe_sub(r->Z, r->Z, r->X);
1979	0	fe_sub(r->X, t0, r->Y);
1980	0	fe_sub(r->T, r->T, r->Z);
1981	0	}
1982
1983		/* r = 2 * p */
1984		static void ge_p3_dbl(ge_p1p1 r, const ge_p3 p)
1985	0	{
1986	0	ge_p2 q;
1987	0	ge_p3_to_p2(&q, p);
1988	0	ge_p2_dbl(r, &q);
1989	0	}
1990
1991		/* r = p + q */
1992		static void ge_madd(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
1993	0	{
1994	0	fe t0;
1995
1996	0	fe_add(r->X, p->Y, p->X);
1997	0	fe_sub(r->Y, p->Y, p->X);
1998	0	fe_mul(r->Z, r->X, q->yplusx);
1999	0	fe_mul(r->Y, r->Y, q->yminusx);
2000	0	fe_mul(r->T, q->xy2d, p->T);
2001	0	fe_add(t0, p->Z, p->Z);
2002	0	fe_sub(r->X, r->Z, r->Y);
2003	0	fe_add(r->Y, r->Z, r->Y);
2004	0	fe_add(r->Z, t0, r->T);
2005	0	fe_sub(r->T, t0, r->T);
2006	0	}
2007
2008		/* r = p - q */
2009		static void ge_msub(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2010	0	{
2011	0	fe t0;
2012
2013	0	fe_add(r->X, p->Y, p->X);
2014	0	fe_sub(r->Y, p->Y, p->X);
2015	0	fe_mul(r->Z, r->X, q->yminusx);
2016	0	fe_mul(r->Y, r->Y, q->yplusx);
2017	0	fe_mul(r->T, q->xy2d, p->T);
2018	0	fe_add(t0, p->Z, p->Z);
2019	0	fe_sub(r->X, r->Z, r->Y);
2020	0	fe_add(r->Y, r->Z, r->Y);
2021	0	fe_sub(r->Z, t0, r->T);
2022	0	fe_add(r->T, t0, r->T);
2023	0	}
2024
2025		/* r = p + q */
2026		static void ge_add(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2027	0	{
2028	0	fe t0;
2029
2030	0	fe_add(r->X, p->Y, p->X);
2031	0	fe_sub(r->Y, p->Y, p->X);
2032	0	fe_mul(r->Z, r->X, q->YplusX);
2033	0	fe_mul(r->Y, r->Y, q->YminusX);
2034	0	fe_mul(r->T, q->T2d, p->T);
2035	0	fe_mul(r->X, p->Z, q->Z);
2036	0	fe_add(t0, r->X, r->X);
2037	0	fe_sub(r->X, r->Z, r->Y);
2038	0	fe_add(r->Y, r->Z, r->Y);
2039	0	fe_add(r->Z, t0, r->T);
2040	0	fe_sub(r->T, t0, r->T);
2041	0	}
2042
2043		/* r = p - q */
2044		static void ge_sub(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2045	0	{
2046	0	fe t0;
2047
2048	0	fe_add(r->X, p->Y, p->X);
2049	0	fe_sub(r->Y, p->Y, p->X);
2050	0	fe_mul(r->Z, r->X, q->YminusX);
2051	0	fe_mul(r->Y, r->Y, q->YplusX);
2052	0	fe_mul(r->T, q->T2d, p->T);
2053	0	fe_mul(r->X, p->Z, q->Z);
2054	0	fe_add(t0, r->X, r->X);
2055	0	fe_sub(r->X, r->Z, r->Y);
2056	0	fe_add(r->Y, r->Z, r->Y);
2057	0	fe_sub(r->Z, t0, r->T);
2058	0	fe_add(r->T, t0, r->T);
2059	0	}
2060
2061		static uint8_t equal(signed char b, signed char c)
2062	0	{
2063	0	uint8_t ub = b;
2064	0	uint8_t uc = c;
2065	0	uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2066	0	uint32_t y = x; /* 0: yes; 1..255: no */
2067	0	y -= 1; /* 4294967295: yes; 0..254: no */
2068	0	y >>= 31; /* 1: yes; 0: no */
2069	0	return y;
2070	0	}
2071
2072		static void cmov(ge_precomp t, const ge_precomp u, uint8_t b)
2073	0	{
2074	0	fe_cmov(t->yplusx, u->yplusx, b);
2075	0	fe_cmov(t->yminusx, u->yminusx, b);
2076	0	fe_cmov(t->xy2d, u->xy2d, b);
2077	0	}
2078
2079		/* k25519Precomp[i][j] = (j+1)256^iB */
2080		static const ge_precomp k25519Precomp[32][8] = {
2081		{
2082		{
2083		{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2084		27544626, -11754271, -6079156, 2047605},
2085		{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2086		5043384, 19500929, -15469378},
2087		{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2088		29287919, 11864899, -24514362, -4438546},
2089		},
2090		{
2091		{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2092		-11717903, -3814571, -358445, -10211303},
2093		{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2094		-15616551, 11189268, -26829678, -5319081},
2095		{26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2096		-3128826, -9541118, -15472047, -4166697},
2097		},
2098		{
2099		{15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2100		27787600, -14772189, 28944400, -1550024},
2101		{16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2102		16354577, -11775962, 7689662, 11199574},
2103		{30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2104		7512774, 10017326, -17749093, -9920357},
2105		},
2106		{
2107		{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2108		-28926210, 15006023, 3284568, -6276540},
2109		{23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2110		7464579, 9656445, 13059162, 10374397},
2111		{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2112		-3839045, -641708, -101325},
2113		},
2114		{
2115		{10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2116		32867885, 14515107, -15438304, 10819380},
2117		{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2118		12483688, -12668491, 5581306},
2119		{19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2120		28542350, 13850243, -23678021, -15815942},
2121		},
2122		{
2123		{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2124		-19188627, -15224819, -9818940, -12085777},
2125		{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2126		-15689887, 1762328, 14866737},
2127		{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2128		-28236412, 3959421, 27914454, 4383652},
2129		},
2130		{
2131		{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2132		5230134, -23952439, -15175766},
2133		{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2134		20654025, 16520125, 30598449, 7715701},
2135		{28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2136		-31400660, 1370708, 29794553, -1409300},
2137		},
2138		{
2139		{14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2140		30290735, 10876454, -33154098, 2381726},
2141		{-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2142		-6236617, 3696005, -32300832, 15351955},
2143		{27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2144		-32961401, -2970515, 29551813, 10109425},
2145		},
2146		},
2147		{
2148		{
2149		{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2150		-2378284, -1627556, 10092783, -4764171},
2151		{27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2152		-32508754, 12005538, -17810127, 12803510},
2153		{17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2154		30364213, -9038194, 18016357, 4397660},
2155		},
2156		{
2157		{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2158		-26619106, 14544525, -17477504, 982639},
2159		{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2160		-4120128, -21047696, 9934963},
2161		{5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2162		-14747930, 4559895, -30123922, -10897950},
2163		},
2164		{
2165		{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2166		24191034, 4541697, -13338309, 5500568},
2167		{12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2168		-17430592, 12264343, 10874051, 13524335},
2169		{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2170		5080568, -22528059, 5376628},
2171		},
2172		{
2173		{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2174		-22321305, -9447443, 4535768, 1569007},
2175		{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2176		-30494562, 3044290, 31848280, 12543772},
2177		{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2178		-27377195, -2062731, 7718482, 14474653},
2179		},
2180		{
2181		{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2182		-7236665, 24316168, -5253567},
2183		{13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2184		33040651, -13424532, -20729456, 8321686},
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2939		{
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2995		},
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3005		{
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3028		-102766, 1876699, 30801119, 2164795},
3029		},
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3069		},
3070		},
3071		{
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3095		},
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3103		},
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3111		},
3112		{
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3118		-1683975, 9177853, -27493162, 15431203},
3119		},
3120		{
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3126		-6492290, 13352335, -10977084},
3127		},
3128		{
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3130		-29783850, -7752482, -13215537, -319204},
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3135		},
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3137		{
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3141		{-12730809, 10311867, 1510375, 10778093, -2119455, -9145702,
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3169		},
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3172		-6567787, 26333140, 14267664},
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3176		1541940, 4757911, -26491501, -16408940},
3177		},
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3185		},
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3193		},
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3197		{11423335, -5468059, 32344216, 8962751, 24989809, 9241752,
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3199		{-1409668, 12530728, -6368726, 10847387, 19531186, -14132160,
3200		-11709148, 7791794, -27245943, 4383347},
3201		},
3202		},
3203		{
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3206		-4862407, -4906449, 27193557, 6245191},
3207		{-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898,
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3210		31168030, 13952092, -29571492, -3635906},
3211		},
3212		{
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3215		{-16275802, 14667797, 15906460, 12155291, -22111149, -9039718,
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3217		{-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725,
3218		12376320, 31632953, 190926},
3219		},
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3908		2825960, -4897045, -23971776, -11267415},
3909		{-15924766, -5229880, -17443532, 6410664, 3622847, 10243618,
3910		20615400, 12405433, -23753030, -8436416},
3911		},
3912		{
3913		{-7091295, 12556208, -20191352, 9025187, -17072479, 4333801,
3914		4378436, 2432030, 23097949, -566018},
3915		{4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264,
3916		10103221, -18512313, 2424778},
3917		{366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678,
3918		1344109, -3642553, 12412659},
3919		},
3920		{
3921		{-24001791, 7690286, 14929416, -168257, -32210835, -13412986,
3922		24162697, -15326504, -3141501, 11179385},
3923		{18289522, -14724954, 8056945, 16430056, -21729724, 7842514,
3924		-6001441, -1486897, -18684645, -11443503},
3925		{476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959,
3926		13403813, 11052904, 5219329},
3927		},
3928		},
3929		{
3930		{
3931		{20678546, -8375738, -32671898, 8849123, -5009758, 14574752,
3932		31186971, -3973730, 9014762, -8579056},
3933		{-13644050, -10350239, -15962508, 5075808, -1514661, -11534600,
3934		-33102500, 9160280, 8473550, -3256838},
3935		{24900749, 14435722, 17209120, -15292541, -22592275, 9878983,
3936		-7689309, -16335821, -24568481, 11788948},
3937		},
3938		{
3939		{-3118155, -11395194, -13802089, 14797441, 9652448, -6845904,
3940		-20037437, 10410733, -24568470, -1458691},
3941		{-15659161, 16736706, -22467150, 10215878, -9097177, 7563911,
3942		11871841, -12505194, -18513325, 8464118},
3943		{-23400612, 8348507, -14585951, -861714, -3950205, -6373419,
3944		14325289, 8628612, 33313881, -8370517},
3945		},
3946		{
3947		{-20186973, -4967935, 22367356, 5271547, -1097117, -4788838,
3948		-24805667, -10236854, -8940735, -5818269},
3949		{-6948785, -1795212, -32625683, -16021179, 32635414, -7374245,
3950		15989197, -12838188, 28358192, -4253904},
3951		{-23561781, -2799059, -32351682, -1661963, -9147719, 10429267,
3952		-16637684, 4072016, -5351664, 5596589},
3953		},
3954		{
3955		{-28236598, -3390048, 12312896, 6213178, 3117142, 16078565,
3956		29266239, 2557221, 1768301, 15373193},
3957		{-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902,
3958		-4504991, -24660491, 3442910},
3959		{-30210571, 5124043, 14181784, 8197961, 18964734, -11939093,
3960		22597931, 7176455, -18585478, 13365930},
3961		},
3962		{
3963		{-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107,
3964		-8570186, -9689599, -3031667},
3965		{25008904, -10771599, -4305031, -9638010, 16265036, 15721635,
3966		683793, -11823784, 15723479, -15163481},
3967		{-9660625, 12374379, -27006999, -7026148, -7724114, -12314514,
3968		11879682, 5400171, 519526, -1235876},
3969		},
3970		{
3971		{22258397, -16332233, -7869817, 14613016, -22520255, -2950923,
3972		-20353881, 7315967, 16648397, 7605640},
3973		{-8081308, -8464597, -8223311, 9719710, 19259459, -15348212,
3974		23994942, -5281555, -9468848, 4763278},
3975		{-21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
3976		31088447, -7764523, -11356529, 728112},
3977		},
3978		{
3979		{26047220, -11751471, -6900323, -16521798, 24092068, 9158119,
3980		-4273545, -12555558, -29365436, -5498272},
3981		{17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007,
3982		12327945, 10750447, 10014012},
3983		{-10312768, 3936952, 9156313, -8897683, 16498692, -994647,
3984		-27481051, -666732, 3424691, 7540221},
3985		},
3986		{
3987		{30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422,
3988		-16317219, -9244265, 15258046},
3989		{13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
3990		2711395, 1062915, -5136345},
3991		{-19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
3992		-6066489, 12194497, 32960380, 1459310},
3993		},
3994		},
3995		{
3996		{
3997		{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
3998		-6101885, 18638003, -11174937},
3999		{31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
4000		9012486, -7584354, -6643087, -5442636},
4001		{-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
4002		9677543, -32294889, -6456008},
4003		},
4004		{
4005		{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
4006		-7839692, -7852844, -8138429},
4007		{-15236356, -15433509, 7766470, 746860, 26346930, -10221762,
4008		-27333451, 10754588, -9431476, 5203576},
4009		{31834314, 14135496, -770007, 5159118, 20917671, -16768096,
4010		-7467973, -7337524, 31809243, 7347066},
4011		},
4012		{
4013		{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
4014		19797970, -12211255, 15192876, -2087490},
4015		{-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
4016		10609330, 12694420, 33473243, -13382104},
4017		{33184999, 11180355, 15832085, -11385430, -1633671, 225884,
4018		15089336, -11023903, -6135662, 14480053},
4019		},
4020		{
4021		{31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
4022		5496208, 13685227, 27595050, 8737275},
4023		{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
4024		-31008351, -12610604, 26498114, 66511},
4025		{22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
4026		30540766, -4286747, -13327787, -7515095},
4027		},
4028		{
4029		{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
4030		8205540, 13585437, -17127465, 15115439},
4031		{23711543, -672915, 31206561, -8362711, 6164647, -9709987,
4032		-33535882, -1426096, 8236921, 16492939},
4033		{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
4034		19574902, 10071562, 6708380, -6222424},
4035		},
4036		{
4037		{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
4038		9328700, 29955601, -11678310},
4039		{3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
4040		-25892142, -12635595, -9917575, 6216608},
4041		{-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
4042		24822830, -6146567, -26767480, 7525079},
4043		},
4044		{
4045		{-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
4046		-910336, -2782495, -19386633, 11994101},
4047		{21691500, -13624626, -641331, -14367021, 3285881, -3483596,
4048		-25064666, 9718258, -7477437, 13381418},
4049		{18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
4050		23111648, -6375247, 28535282, 15779576},
4051		},
4052		{
4053		{30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
4054		-14068454, 12021730, 9955285, -16303356},
4055		{9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
4056		-18426029, 9924399, 20194861, 13380996},
4057		{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
4058		-1984914, 15707771, 26342023, 10146099},
4059		},
4060		},
4061		{
4062		{
4063		{-26016874, -219943, 21339191, -41388, 19745256, -2878700,
4064		-29637280, 2227040, 21612326, -545728},
4065		{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
4066		25764461, 12243797, -20856566, 11649658},
4067		{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
4068		6114064, 33514190, 2333242},
4069		},
4070		{
4071		{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
4072		-6679750, -12670638, 24350578, -13450001},
4073		{-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
4074		-31536088, -10406836, 8317860, 12352766},
4075		{18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
4076		-23552096, -2287550, 20712163, 6719373},
4077		},
4078		{
4079		{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
4080		-3763210, 26224235, -3297458},
4081		{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
4082		21728352, 9493610, 18620611, -16428628},
4083		{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
4084		-5269471, -9725556, -30701573, -16479657},
4085		},
4086		{
4087		{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
4088		12248509, -5240639, 13735342, 1934062},
4089		{25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
4090		-15136294, -3765346, -21277997, 5473616},
4091		{31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
4092		-7125085, 12469656, 29111212, -5451014},
4093		},
4094		{
4095		{24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
4096		24367466, 6388839, -10295587, 452383},
4097		{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
4098		-24236251, -5915248, 15766062, 8407814},
4099		{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
4100		-8917023, -4388953, -8067909, 2276718},
4101		},
4102		{
4103		{30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
4104		-23827587, 5096219, 22740376, -7303417},
4105		{2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
4106		24051124, 13742383, -15637599, 13295222},
4107		{33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
4108		-17720195, -4612972, -4451357, -14669444},
4109		},
4110		{
4111		{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
4112		-2469266, -4141880, 7770569, 9620597},
4113		{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
4114		-1694323, -33502340, -14767970},
4115		{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
4116		1220118, 30494170, -11440799},
4117		},
4118		{
4119		{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
4120		-26739026, 926050, -1684339, -13333647},
4121		{13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
4122		9021034, 9078865, 3353509, 4033511},
4123		{-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
4124		23161163, 8839127, 27485041, 7356032},
4125		},
4126		},
4127		{
4128		{
4129		{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
4130		2625015, 28431036, -16771834},
4131		{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
4132		-22545972, 14150565, 15970762, 4099461},
4133		{29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
4134		13617293, -9937143, 11465739, 8317062},
4135		},
4136		{
4137		{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
4138		14898637, 3848455, 20969334, -5157516},
4139		{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
4140		-21610826, -3649888, 11177095, 14989547},
4141		{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
4142		13515641, 2581286, -28487508, 9930240},
4143		},
4144		{
4145		{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
4146		18345767, -13403753, 16291481, -5314038},
4147		{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
4148		6957617, 4368891, 9788741},
4149		{16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
4150		-21722536, -8613148, 16250552, -11111103},
4151		},
4152		{
4153		{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
4154		10604807, -30190403, 4782747},
4155		{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
4156		-9981571, 4383045, 22546403, 437323},
4157		{31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
4158		27343084, 2786261, -30633590, -14097016},
4159		},
4160		{
4161		{-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
4162		-19690631, 2355319, -19284671, -6114373},
4163		{15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
4164		18952177, 15496498, -29380133, 11754228},
4165		{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
4166		7141596, 11724556, 22761615, -10134141},
4167		},
4168		{
4169		{16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
4170		-28741185, -12227393, 32851222, 11717399},
4171		{11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
4172		31474879, 3483633, -1193175, -4030831},
4173		{-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4174		33142652, 6546660, -19985279, -3948376},
4175		},
4176		{
4177		{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4178		-8537131, -12833048, -30772034, -15486313},
4179		{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4180		-31135347, -16049879, 10928917, 3011958},
4181		{-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4182		-30831056, -12805180, 18008031, 10258577},
4183		},
4184		{
4185		{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4186		-1853465, 1367120, 25127874, 6671743},
4187		{29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4188		21382910, 11042292, 25838796, 4642684},
4189		{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4190		30468147, -13900640, 18423289, 4177476},
4191		},
4192		},
4193		};
4194
4195		static uint8_t negative(signed char b)
4196	0	{
4197	0	uint32_t x = b;
4198
4199	0	x >>= 31; /* 1: yes; 0: no */
4200	0	return x;
4201	0	}
4202
4203		static void table_select(ge_precomp *t, int pos, signed char b)
4204	0	{
4205	0	ge_precomp minust;
4206	0	uint8_t bnegative = negative(b);
4207	0	uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4208
4209	0	ge_precomp_0(t);
4210	0	cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4211	0	cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4212	0	cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4213	0	cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4214	0	cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4215	0	cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4216	0	cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4217	0	cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4218	0	fe_copy(minust.yplusx, t->yminusx);
4219	0	fe_copy(minust.yminusx, t->yplusx);
4220	0	fe_neg(minust.xy2d, t->xy2d);
4221	0	cmov(t, &minust, bnegative);
4222	0	}
4223
4224		/*
4225		* h = a * B
4226		*
4227		* where a = a[0]+256*a[1]+...+256^31 a[31]
4228		* B is the Ed25519 base point (x,4/5) with x positive.
4229		*
4230		* Preconditions:
4231		* a[31] <= 127
4232		*/
4233		static void ge_scalarmult_base(ge_p3 h, const uint8_t a)
4234	0	{
4235	0	signed char e[64];
4236	0	signed char carry;
4237	0	ge_p1p1 r;
4238	0	ge_p2 s;
4239	0	ge_precomp t;
4240	0	int i;
4241
4242	0	for (i = 0; i < 32; ++i) {
4243	0	e[2 * i + 0] = (a[i] >> 0) & 15;
4244	0	e[2 * i + 1] = (a[i] >> 4) & 15;
4245	0	}
4246		/* each e[i] is between 0 and 15 */
4247		/* e[63] is between 0 and 7 */
4248
4249	0	carry = 0;
4250	0	for (i = 0; i < 63; ++i) {
4251	0	e[i] += carry;
4252	0	carry = e[i] + 8;
4253	0	carry >>= 4;
4254	0	e[i] -= carry << 4;
4255	0	}
4256	0	e[63] += carry;
4257		/* each e[i] is between -8 and 8 */
4258
4259	0	ge_p3_0(h);
4260	0	for (i = 1; i < 64; i += 2) {
4261	0	table_select(&t, i / 2, e[i]);
4262	0	ge_madd(&r, h, &t);
4263	0	ge_p1p1_to_p3(h, &r);
4264	0	}
4265
4266	0	ge_p3_dbl(&r, h);
4267	0	ge_p1p1_to_p2(&s, &r);
4268	0	ge_p2_dbl(&r, &s);
4269	0	ge_p1p1_to_p2(&s, &r);
4270	0	ge_p2_dbl(&r, &s);
4271	0	ge_p1p1_to_p2(&s, &r);
4272	0	ge_p2_dbl(&r, &s);
4273	0	ge_p1p1_to_p3(h, &r);
4274
4275	0	for (i = 0; i < 64; i += 2) {
4276	0	table_select(&t, i / 2, e[i]);
4277	0	ge_madd(&r, h, &t);
4278	0	ge_p1p1_to_p3(h, &r);
4279	0	}
4280
4281	0	OPENSSL_cleanse(e, sizeof(e));
4282	0	}
4283
4284		#if !defined(BASE_2_51_IMPLEMENTED)
4285		/*
4286		* Replace (f,g) with (g,f) if b == 1;
4287		* replace (f,g) with (f,g) if b == 0.
4288		*
4289		* Preconditions: b in {0,1}.
4290		*/
4291		static void fe_cswap(fe f, fe g, unsigned int b)
4292		{
4293		size_t i;
4294
4295		b = 0-b;
4296		for (i = 0; i < 10; i++) {
4297		int32_t x = f[i] ^ g[i];
4298		x &= b;
4299		f[i] ^= x;
4300		g[i] ^= x;
4301		}
4302		}
4303
4304		/*
4305		* h = f * 121666
4306		*
4307		* Can overlap h with f.
4308		*
4309		* Preconditions:
4310		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
4311		*
4312		* Postconditions:
4313		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
4314		*/
4315		static void fe_mul121666(fe h, fe f)
4316		{
4317		int32_t f0 = f[0];
4318		int32_t f1 = f[1];
4319		int32_t f2 = f[2];
4320		int32_t f3 = f[3];
4321		int32_t f4 = f[4];
4322		int32_t f5 = f[5];
4323		int32_t f6 = f[6];
4324		int32_t f7 = f[7];
4325		int32_t f8 = f[8];
4326		int32_t f9 = f[9];
4327		int64_t h0 = f0 * (int64_t) 121666;
4328		int64_t h1 = f1 * (int64_t) 121666;
4329		int64_t h2 = f2 * (int64_t) 121666;
4330		int64_t h3 = f3 * (int64_t) 121666;
4331		int64_t h4 = f4 * (int64_t) 121666;
4332		int64_t h5 = f5 * (int64_t) 121666;
4333		int64_t h6 = f6 * (int64_t) 121666;
4334		int64_t h7 = f7 * (int64_t) 121666;
4335		int64_t h8 = f8 * (int64_t) 121666;
4336		int64_t h9 = f9 * (int64_t) 121666;
4337		int64_t carry0;
4338		int64_t carry1;
4339		int64_t carry2;
4340		int64_t carry3;
4341		int64_t carry4;
4342		int64_t carry5;
4343		int64_t carry6;
4344		int64_t carry7;
4345		int64_t carry8;
4346		int64_t carry9;
4347
4348		carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
4349		carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
4350		carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
4351		carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
4352		carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
4353
4354		carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
4355		carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
4356		carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
4357		carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
4358		carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
4359
4360		h[0] = (int32_t)h0;
4361		h[1] = (int32_t)h1;
4362		h[2] = (int32_t)h2;
4363		h[3] = (int32_t)h3;
4364		h[4] = (int32_t)h4;
4365		h[5] = (int32_t)h5;
4366		h[6] = (int32_t)h6;
4367		h[7] = (int32_t)h7;
4368		h[8] = (int32_t)h8;
4369		h[9] = (int32_t)h9;
4370		}
4371
4372		static void x25519_scalar_mult_generic(uint8_t out[32],
4373		const uint8_t scalar[32],
4374		const uint8_t point[32]) {
4375		fe x1, x2, z2, x3, z3, tmp0, tmp1;
4376		uint8_t e[32];
4377		unsigned swap = 0;
4378		int pos;
4379
4380		memcpy(e, scalar, 32);
4381		e[0] &= 248;
4382		e[31] &= 127;
4383		e[31] \|= 64;
4384		fe_frombytes(x1, point);
4385		fe_1(x2);
4386		fe_0(z2);
4387		fe_copy(x3, x1);
4388		fe_1(z3);
4389
4390		for (pos = 254; pos >= 0; --pos) {
4391		unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4392		swap ^= b;
4393		fe_cswap(x2, x3, swap);
4394		fe_cswap(z2, z3, swap);
4395		swap = b;
4396		fe_sub(tmp0, x3, z3);
4397		fe_sub(tmp1, x2, z2);
4398		fe_add(x2, x2, z2);
4399		fe_add(z2, x3, z3);
4400		fe_mul(z3, tmp0, x2);
4401		fe_mul(z2, z2, tmp1);
4402		fe_sq(tmp0, tmp1);
4403		fe_sq(tmp1, x2);
4404		fe_add(x3, z3, z2);
4405		fe_sub(z2, z3, z2);
4406		fe_mul(x2, tmp1, tmp0);
4407		fe_sub(tmp1, tmp1, tmp0);
4408		fe_sq(z2, z2);
4409		fe_mul121666(z3, tmp1);
4410		fe_sq(x3, x3);
4411		fe_add(tmp0, tmp0, z3);
4412		fe_mul(z3, x1, z2);
4413		fe_mul(z2, tmp1, tmp0);
4414		}
4415
4416		fe_invert(z2, z2);
4417		fe_mul(x2, x2, z2);
4418		fe_tobytes(out, x2);
4419
4420		OPENSSL_cleanse(e, sizeof(e));
4421		}
4422
4423		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4424		const uint8_t point[32]) {
4425		x25519_scalar_mult_generic(out, scalar, point);
4426		}
4427		#endif
4428
4429		static void slide(signed char r, const uint8_t a)
4430	0	{
4431	0	int i;
4432	0	int b;
4433	0	int k;
4434
4435	0	for (i = 0; i < 256; ++i) {
4436	0	r[i] = 1 & (a[i >> 3] >> (i & 7));
4437	0	}
4438
4439	0	for (i = 0; i < 256; ++i) {
4440	0	if (r[i]) {
4441	0	for (b = 1; b <= 6 && i + b < 256; ++b) {
4442	0	if (r[i + b]) {
4443	0	if (r[i] + (r[i + b] << b) <= 15) {
4444	0	r[i] += r[i + b] << b;
4445	0	r[i + b] = 0;
4446	0	} else if (r[i] - (r[i + b] << b) >= -15) {
4447	0	r[i] -= r[i + b] << b;
4448	0	for (k = i + b; k < 256; ++k) {
4449	0	if (!r[k]) {
4450	0	r[k] = 1;
4451	0	break;
4452	0	}
4453	0	r[k] = 0;
4454	0	}
4455	0	} else {
4456	0	break;
4457	0	}
4458	0	}
4459	0	}
4460	0	}
4461	0	}
4462	0	}
4463
4464		static const ge_precomp Bi[8] = {
4465		{
4466		{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4467		-11754271, -6079156, 2047605},
4468		{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4469		5043384, 19500929, -15469378},
4470		{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4471		11864899, -24514362, -4438546},
4472		},
4473		{
4474		{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4475		-14772189, 28944400, -1550024},
4476		{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4477		-11775962, 7689662, 11199574},
4478		{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4479		10017326, -17749093, -9920357},
4480		},
4481		{
4482		{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4483		14515107, -15438304, 10819380},
4484		{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4485		12483688, -12668491, 5581306},
4486		{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4487		13850243, -23678021, -15815942},
4488		},
4489		{
4490		{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4491		5230134, -23952439, -15175766},
4492		{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4493		16520125, 30598449, 7715701},
4494		{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4495		1370708, 29794553, -1409300},
4496		},
4497		{
4498		{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4499		-1361450, -13062696, 13821877},
4500		{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4501		-7212327, 18853322, -14220951},
4502		{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4503		-10431137, 2207753, -3209784},
4504		},
4505		{
4506		{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4507		-663000, -31111463, -16132436},
4508		{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4509		15725684, 171356, 6466918},
4510		{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4511		-14088058, -30714912, 16193877},
4512		},
4513		{
4514		{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4515		4729455, -18074513, 9256800},
4516		{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4517		9761698, -19827198, 630305},
4518		{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4519		-15960994, -2449256, -14291300},
4520		},
4521		{
4522		{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4523		15033784, 25105118, -7894876},
4524		{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4525		1573892, -2625887, 2198790, -15804619},
4526		{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4527		-16236442, -32461234, -12290683},
4528		},
4529		};
4530
4531		/*
4532		* r = a * A + b * B
4533		*
4534		* where a = a[0]+256*a[1]+...+256^31 a[31].
4535		* and b = b[0]+256*b[1]+...+256^31 b[31].
4536		* B is the Ed25519 base point (x,4/5) with x positive.
4537		*/
4538		static void ge_double_scalarmult_vartime(ge_p2 r, const uint8_t a,
4539		const ge_p3 A, const uint8_t b)
4540	0	{
4541	0	signed char aslide[256];
4542	0	signed char bslide[256];
4543	0	ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4544	0	ge_p1p1 t;
4545	0	ge_p3 u;
4546	0	ge_p3 A2;
4547	0	int i;
4548
4549	0	slide(aslide, a);
4550	0	slide(bslide, b);
4551
4552	0	ge_p3_to_cached(&Ai[0], A);
4553	0	ge_p3_dbl(&t, A);
4554	0	ge_p1p1_to_p3(&A2, &t);
4555	0	ge_add(&t, &A2, &Ai[0]);
4556	0	ge_p1p1_to_p3(&u, &t);
4557	0	ge_p3_to_cached(&Ai[1], &u);
4558	0	ge_add(&t, &A2, &Ai[1]);
4559	0	ge_p1p1_to_p3(&u, &t);
4560	0	ge_p3_to_cached(&Ai[2], &u);
4561	0	ge_add(&t, &A2, &Ai[2]);
4562	0	ge_p1p1_to_p3(&u, &t);
4563	0	ge_p3_to_cached(&Ai[3], &u);
4564	0	ge_add(&t, &A2, &Ai[3]);
4565	0	ge_p1p1_to_p3(&u, &t);
4566	0	ge_p3_to_cached(&Ai[4], &u);
4567	0	ge_add(&t, &A2, &Ai[4]);
4568	0	ge_p1p1_to_p3(&u, &t);
4569	0	ge_p3_to_cached(&Ai[5], &u);
4570	0	ge_add(&t, &A2, &Ai[5]);
4571	0	ge_p1p1_to_p3(&u, &t);
4572	0	ge_p3_to_cached(&Ai[6], &u);
4573	0	ge_add(&t, &A2, &Ai[6]);
4574	0	ge_p1p1_to_p3(&u, &t);
4575	0	ge_p3_to_cached(&Ai[7], &u);
4576
4577	0	ge_p2_0(r);
4578
4579	0	for (i = 255; i >= 0; --i) {
4580	0	if (aslide[i] \|\| bslide[i]) {
4581	0	break;
4582	0	}
4583	0	}
4584
4585	0	for (; i >= 0; --i) {
4586	0	ge_p2_dbl(&t, r);
4587
4588	0	if (aslide[i] > 0) {
4589	0	ge_p1p1_to_p3(&u, &t);
4590	0	ge_add(&t, &u, &Ai[aslide[i] / 2]);
4591	0	} else if (aslide[i] < 0) {
4592	0	ge_p1p1_to_p3(&u, &t);
4593	0	ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4594	0	}
4595
4596	0	if (bslide[i] > 0) {
4597	0	ge_p1p1_to_p3(&u, &t);
4598	0	ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4599	0	} else if (bslide[i] < 0) {
4600	0	ge_p1p1_to_p3(&u, &t);
4601	0	ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4602	0	}
4603
4604	0	ge_p1p1_to_p2(r, &t);
4605	0	}
4606	0	}
4607
4608		/*
4609		* The set of scalars is \Z/l
4610		* where l = 2^252 + 27742317777372353535851937790883648493.
4611		*
4612		* Input:
4613		* s[0]+256s[1]+...+256^63s[63] = s
4614		*
4615		* Output:
4616		* s[0]+256s[1]+...+256^31s[31] = s mod l
4617		* where l = 2^252 + 27742317777372353535851937790883648493.
4618		* Overwrites s in place.
4619		*/
4620		static void x25519_sc_reduce(uint8_t *s)
4621	0	{
4622	0	int64_t s0 = kBottom21Bits & load_3(s);
4623	0	int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
4624	0	int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
4625	0	int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
4626	0	int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
4627	0	int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
4628	0	int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
4629	0	int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
4630	0	int64_t s8 = kBottom21Bits & load_3(s + 21);
4631	0	int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
4632	0	int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4633	0	int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4634	0	int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4635	0	int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4636	0	int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4637	0	int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4638	0	int64_t s16 = kBottom21Bits & load_3(s + 42);
4639	0	int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4640	0	int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4641	0	int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4642	0	int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4643	0	int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4644	0	int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4645	0	int64_t s23 = (load_4(s + 60) >> 3);
4646	0	int64_t carry0;
4647	0	int64_t carry1;
4648	0	int64_t carry2;
4649	0	int64_t carry3;
4650	0	int64_t carry4;
4651	0	int64_t carry5;
4652	0	int64_t carry6;
4653	0	int64_t carry7;
4654	0	int64_t carry8;
4655	0	int64_t carry9;
4656	0	int64_t carry10;
4657	0	int64_t carry11;
4658	0	int64_t carry12;
4659	0	int64_t carry13;
4660	0	int64_t carry14;
4661	0	int64_t carry15;
4662	0	int64_t carry16;
4663
4664	0	s11 += s23 * 666643;
4665	0	s12 += s23 * 470296;
4666	0	s13 += s23 * 654183;
4667	0	s14 -= s23 * 997805;
4668	0	s15 += s23 * 136657;
4669	0	s16 -= s23 * 683901;
4670	0	s23 = 0;
4671
4672	0	s10 += s22 * 666643;
4673	0	s11 += s22 * 470296;
4674	0	s12 += s22 * 654183;
4675	0	s13 -= s22 * 997805;
4676	0	s14 += s22 * 136657;
4677	0	s15 -= s22 * 683901;
4678	0	s22 = 0;
4679
4680	0	s9 += s21 * 666643;
4681	0	s10 += s21 * 470296;
4682	0	s11 += s21 * 654183;
4683	0	s12 -= s21 * 997805;
4684	0	s13 += s21 * 136657;
4685	0	s14 -= s21 * 683901;
4686	0	s21 = 0;
4687
4688	0	s8 += s20 * 666643;
4689	0	s9 += s20 * 470296;
4690	0	s10 += s20 * 654183;
4691	0	s11 -= s20 * 997805;
4692	0	s12 += s20 * 136657;
4693	0	s13 -= s20 * 683901;
4694	0	s20 = 0;
4695
4696	0	s7 += s19 * 666643;
4697	0	s8 += s19 * 470296;
4698	0	s9 += s19 * 654183;
4699	0	s10 -= s19 * 997805;
4700	0	s11 += s19 * 136657;
4701	0	s12 -= s19 * 683901;
4702	0	s19 = 0;
4703
4704	0	s6 += s18 * 666643;
4705	0	s7 += s18 * 470296;
4706	0	s8 += s18 * 654183;
4707	0	s9 -= s18 * 997805;
4708	0	s10 += s18 * 136657;
4709	0	s11 -= s18 * 683901;
4710	0	s18 = 0;
4711
4712	0	carry6 = (s6 + (1 << 20)) >> 21;
4713	0	s7 += carry6;
4714	0	s6 -= carry6 * (1 << 21);
4715	0	carry8 = (s8 + (1 << 20)) >> 21;
4716	0	s9 += carry8;
4717	0	s8 -= carry8 * (1 << 21);
4718	0	carry10 = (s10 + (1 << 20)) >> 21;
4719	0	s11 += carry10;
4720	0	s10 -= carry10 * (1 << 21);
4721	0	carry12 = (s12 + (1 << 20)) >> 21;
4722	0	s13 += carry12;
4723	0	s12 -= carry12 * (1 << 21);
4724	0	carry14 = (s14 + (1 << 20)) >> 21;
4725	0	s15 += carry14;
4726	0	s14 -= carry14 * (1 << 21);
4727	0	carry16 = (s16 + (1 << 20)) >> 21;
4728	0	s17 += carry16;
4729	0	s16 -= carry16 * (1 << 21);
4730
4731	0	carry7 = (s7 + (1 << 20)) >> 21;
4732	0	s8 += carry7;
4733	0	s7 -= carry7 * (1 << 21);
4734	0	carry9 = (s9 + (1 << 20)) >> 21;
4735	0	s10 += carry9;
4736	0	s9 -= carry9 * (1 << 21);
4737	0	carry11 = (s11 + (1 << 20)) >> 21;
4738	0	s12 += carry11;
4739	0	s11 -= carry11 * (1 << 21);
4740	0	carry13 = (s13 + (1 << 20)) >> 21;
4741	0	s14 += carry13;
4742	0	s13 -= carry13 * (1 << 21);
4743	0	carry15 = (s15 + (1 << 20)) >> 21;
4744	0	s16 += carry15;
4745	0	s15 -= carry15 * (1 << 21);
4746
4747	0	s5 += s17 * 666643;
4748	0	s6 += s17 * 470296;
4749	0	s7 += s17 * 654183;
4750	0	s8 -= s17 * 997805;
4751	0	s9 += s17 * 136657;
4752	0	s10 -= s17 * 683901;
4753	0	s17 = 0;
4754
4755	0	s4 += s16 * 666643;
4756	0	s5 += s16 * 470296;
4757	0	s6 += s16 * 654183;
4758	0	s7 -= s16 * 997805;
4759	0	s8 += s16 * 136657;
4760	0	s9 -= s16 * 683901;
4761	0	s16 = 0;
4762
4763	0	s3 += s15 * 666643;
4764	0	s4 += s15 * 470296;
4765	0	s5 += s15 * 654183;
4766	0	s6 -= s15 * 997805;
4767	0	s7 += s15 * 136657;
4768	0	s8 -= s15 * 683901;
4769	0	s15 = 0;
4770
4771	0	s2 += s14 * 666643;
4772	0	s3 += s14 * 470296;
4773	0	s4 += s14 * 654183;
4774	0	s5 -= s14 * 997805;
4775	0	s6 += s14 * 136657;
4776	0	s7 -= s14 * 683901;
4777	0	s14 = 0;
4778
4779	0	s1 += s13 * 666643;
4780	0	s2 += s13 * 470296;
4781	0	s3 += s13 * 654183;
4782	0	s4 -= s13 * 997805;
4783	0	s5 += s13 * 136657;
4784	0	s6 -= s13 * 683901;
4785	0	s13 = 0;
4786
4787	0	s0 += s12 * 666643;
4788	0	s1 += s12 * 470296;
4789	0	s2 += s12 * 654183;
4790	0	s3 -= s12 * 997805;
4791	0	s4 += s12 * 136657;
4792	0	s5 -= s12 * 683901;
4793	0	s12 = 0;
4794
4795	0	carry0 = (s0 + (1 << 20)) >> 21;
4796	0	s1 += carry0;
4797	0	s0 -= carry0 * (1 << 21);
4798	0	carry2 = (s2 + (1 << 20)) >> 21;
4799	0	s3 += carry2;
4800	0	s2 -= carry2 * (1 << 21);
4801	0	carry4 = (s4 + (1 << 20)) >> 21;
4802	0	s5 += carry4;
4803	0	s4 -= carry4 * (1 << 21);
4804	0	carry6 = (s6 + (1 << 20)) >> 21;
4805	0	s7 += carry6;
4806	0	s6 -= carry6 * (1 << 21);
4807	0	carry8 = (s8 + (1 << 20)) >> 21;
4808	0	s9 += carry8;
4809	0	s8 -= carry8 * (1 << 21);
4810	0	carry10 = (s10 + (1 << 20)) >> 21;
4811	0	s11 += carry10;
4812	0	s10 -= carry10 * (1 << 21);
4813
4814	0	carry1 = (s1 + (1 << 20)) >> 21;
4815	0	s2 += carry1;
4816	0	s1 -= carry1 * (1 << 21);
4817	0	carry3 = (s3 + (1 << 20)) >> 21;
4818	0	s4 += carry3;
4819	0	s3 -= carry3 * (1 << 21);
4820	0	carry5 = (s5 + (1 << 20)) >> 21;
4821	0	s6 += carry5;
4822	0	s5 -= carry5 * (1 << 21);
4823	0	carry7 = (s7 + (1 << 20)) >> 21;
4824	0	s8 += carry7;
4825	0	s7 -= carry7 * (1 << 21);
4826	0	carry9 = (s9 + (1 << 20)) >> 21;
4827	0	s10 += carry9;
4828	0	s9 -= carry9 * (1 << 21);
4829	0	carry11 = (s11 + (1 << 20)) >> 21;
4830	0	s12 += carry11;
4831	0	s11 -= carry11 * (1 << 21);
4832
4833	0	s0 += s12 * 666643;
4834	0	s1 += s12 * 470296;
4835	0	s2 += s12 * 654183;
4836	0	s3 -= s12 * 997805;
4837	0	s4 += s12 * 136657;
4838	0	s5 -= s12 * 683901;
4839	0	s12 = 0;
4840
4841	0	carry0 = s0 >> 21;
4842	0	s1 += carry0;
4843	0	s0 -= carry0 * (1 << 21);
4844	0	carry1 = s1 >> 21;
4845	0	s2 += carry1;
4846	0	s1 -= carry1 * (1 << 21);
4847	0	carry2 = s2 >> 21;
4848	0	s3 += carry2;
4849	0	s2 -= carry2 * (1 << 21);
4850	0	carry3 = s3 >> 21;
4851	0	s4 += carry3;
4852	0	s3 -= carry3 * (1 << 21);
4853	0	carry4 = s4 >> 21;
4854	0	s5 += carry4;
4855	0	s4 -= carry4 * (1 << 21);
4856	0	carry5 = s5 >> 21;
4857	0	s6 += carry5;
4858	0	s5 -= carry5 * (1 << 21);
4859	0	carry6 = s6 >> 21;
4860	0	s7 += carry6;
4861	0	s6 -= carry6 * (1 << 21);
4862	0	carry7 = s7 >> 21;
4863	0	s8 += carry7;
4864	0	s7 -= carry7 * (1 << 21);
4865	0	carry8 = s8 >> 21;
4866	0	s9 += carry8;
4867	0	s8 -= carry8 * (1 << 21);
4868	0	carry9 = s9 >> 21;
4869	0	s10 += carry9;
4870	0	s9 -= carry9 * (1 << 21);
4871	0	carry10 = s10 >> 21;
4872	0	s11 += carry10;
4873	0	s10 -= carry10 * (1 << 21);
4874	0	carry11 = s11 >> 21;
4875	0	s12 += carry11;
4876	0	s11 -= carry11 * (1 << 21);
4877
4878	0	s0 += s12 * 666643;
4879	0	s1 += s12 * 470296;
4880	0	s2 += s12 * 654183;
4881	0	s3 -= s12 * 997805;
4882	0	s4 += s12 * 136657;
4883	0	s5 -= s12 * 683901;
4884	0	s12 = 0;
4885
4886	0	carry0 = s0 >> 21;
4887	0	s1 += carry0;
4888	0	s0 -= carry0 * (1 << 21);
4889	0	carry1 = s1 >> 21;
4890	0	s2 += carry1;
4891	0	s1 -= carry1 * (1 << 21);
4892	0	carry2 = s2 >> 21;
4893	0	s3 += carry2;
4894	0	s2 -= carry2 * (1 << 21);
4895	0	carry3 = s3 >> 21;
4896	0	s4 += carry3;
4897	0	s3 -= carry3 * (1 << 21);
4898	0	carry4 = s4 >> 21;
4899	0	s5 += carry4;
4900	0	s4 -= carry4 * (1 << 21);
4901	0	carry5 = s5 >> 21;
4902	0	s6 += carry5;
4903	0	s5 -= carry5 * (1 << 21);
4904	0	carry6 = s6 >> 21;
4905	0	s7 += carry6;
4906	0	s6 -= carry6 * (1 << 21);
4907	0	carry7 = s7 >> 21;
4908	0	s8 += carry7;
4909	0	s7 -= carry7 * (1 << 21);
4910	0	carry8 = s8 >> 21;
4911	0	s9 += carry8;
4912	0	s8 -= carry8 * (1 << 21);
4913	0	carry9 = s9 >> 21;
4914	0	s10 += carry9;
4915	0	s9 -= carry9 * (1 << 21);
4916	0	carry10 = s10 >> 21;
4917	0	s11 += carry10;
4918	0	s10 -= carry10 * (1 << 21);
4919
4920	0	s[ 0] = (uint8_t) (s0 >> 0);
4921	0	s[ 1] = (uint8_t) (s0 >> 8);
4922	0	s[ 2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
4923	0	s[ 3] = (uint8_t) (s1 >> 3);
4924	0	s[ 4] = (uint8_t) (s1 >> 11);
4925	0	s[ 5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
4926	0	s[ 6] = (uint8_t) (s2 >> 6);
4927	0	s[ 7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
4928	0	s[ 8] = (uint8_t) (s3 >> 1);
4929	0	s[ 9] = (uint8_t) (s3 >> 9);
4930	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
4931	0	s[11] = (uint8_t) (s4 >> 4);
4932	0	s[12] = (uint8_t) (s4 >> 12);
4933	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
4934	0	s[14] = (uint8_t) (s5 >> 7);
4935	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
4936	0	s[16] = (uint8_t) (s6 >> 2);
4937	0	s[17] = (uint8_t) (s6 >> 10);
4938	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
4939	0	s[19] = (uint8_t) (s7 >> 5);
4940	0	s[20] = (uint8_t) (s7 >> 13);
4941	0	s[21] = (uint8_t) (s8 >> 0);
4942	0	s[22] = (uint8_t) (s8 >> 8);
4943	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
4944	0	s[24] = (uint8_t) (s9 >> 3);
4945	0	s[25] = (uint8_t) (s9 >> 11);
4946	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
4947	0	s[27] = (uint8_t) (s10 >> 6);
4948	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
4949	0	s[29] = (uint8_t) (s11 >> 1);
4950	0	s[30] = (uint8_t) (s11 >> 9);
4951	0	s[31] = (uint8_t) (s11 >> 17);
4952	0	}
4953
4954		/*
4955		* Input:
4956		* a[0]+256a[1]+...+256^31a[31] = a
4957		* b[0]+256b[1]+...+256^31b[31] = b
4958		* c[0]+256c[1]+...+256^31c[31] = c
4959		*
4960		* Output:
4961		* s[0]+256s[1]+...+256^31s[31] = (ab+c) mod l
4962		* where l = 2^252 + 27742317777372353535851937790883648493.
4963		*/
4964		static void sc_muladd(uint8_t s, const uint8_t a, const uint8_t *b,
4965		const uint8_t *c)
4966	0	{
4967	0	int64_t a0 = kBottom21Bits & load_3(a);
4968	0	int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
4969	0	int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
4970	0	int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
4971	0	int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
4972	0	int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
4973	0	int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
4974	0	int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
4975	0	int64_t a8 = kBottom21Bits & load_3(a + 21);
4976	0	int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
4977	0	int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
4978	0	int64_t a11 = (load_4(a + 28) >> 7);
4979	0	int64_t b0 = kBottom21Bits & load_3(b);
4980	0	int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
4981	0	int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
4982	0	int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
4983	0	int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
4984	0	int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
4985	0	int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
4986	0	int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
4987	0	int64_t b8 = kBottom21Bits & load_3(b + 21);
4988	0	int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
4989	0	int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
4990	0	int64_t b11 = (load_4(b + 28) >> 7);
4991	0	int64_t c0 = kBottom21Bits & load_3(c);
4992	0	int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
4993	0	int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
4994	0	int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
4995	0	int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
4996	0	int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
4997	0	int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
4998	0	int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
4999	0	int64_t c8 = kBottom21Bits & load_3(c + 21);
5000	0	int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
5001	0	int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
5002	0	int64_t c11 = (load_4(c + 28) >> 7);
5003	0	int64_t s0;
5004	0	int64_t s1;
5005	0	int64_t s2;
5006	0	int64_t s3;
5007	0	int64_t s4;
5008	0	int64_t s5;
5009	0	int64_t s6;
5010	0	int64_t s7;
5011	0	int64_t s8;
5012	0	int64_t s9;
5013	0	int64_t s10;
5014	0	int64_t s11;
5015	0	int64_t s12;
5016	0	int64_t s13;
5017	0	int64_t s14;
5018	0	int64_t s15;
5019	0	int64_t s16;
5020	0	int64_t s17;
5021	0	int64_t s18;
5022	0	int64_t s19;
5023	0	int64_t s20;
5024	0	int64_t s21;
5025	0	int64_t s22;
5026	0	int64_t s23;
5027	0	int64_t carry0;
5028	0	int64_t carry1;
5029	0	int64_t carry2;
5030	0	int64_t carry3;
5031	0	int64_t carry4;
5032	0	int64_t carry5;
5033	0	int64_t carry6;
5034	0	int64_t carry7;
5035	0	int64_t carry8;
5036	0	int64_t carry9;
5037	0	int64_t carry10;
5038	0	int64_t carry11;
5039	0	int64_t carry12;
5040	0	int64_t carry13;
5041	0	int64_t carry14;
5042	0	int64_t carry15;
5043	0	int64_t carry16;
5044	0	int64_t carry17;
5045	0	int64_t carry18;
5046	0	int64_t carry19;
5047	0	int64_t carry20;
5048	0	int64_t carry21;
5049	0	int64_t carry22;
5050
5051	0	s0 = c0 + a0 * b0;
5052	0	s1 = c1 + a0 * b1 + a1 * b0;
5053	0	s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
5054	0	s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
5055	0	s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
5056	0	s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
5057	0	s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
5058	0	s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
5059	0	s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
5060	0	s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
5061	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;
5062	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;
5063	0	s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
5064	0	s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
5065	0	s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
5066	0	s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
5067	0	s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
5068	0	s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
5069	0	s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
5070	0	s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
5071	0	s20 = a9 * b11 + a10 * b10 + a11 * b9;
5072	0	s21 = a10 * b11 + a11 * b10;
5073	0	s22 = a11 * b11;
5074	0	s23 = 0;
5075
5076	0	carry0 = (s0 + (1 << 20)) >> 21;
5077	0	s1 += carry0;
5078	0	s0 -= carry0 * (1 << 21);
5079	0	carry2 = (s2 + (1 << 20)) >> 21;
5080	0	s3 += carry2;
5081	0	s2 -= carry2 * (1 << 21);
5082	0	carry4 = (s4 + (1 << 20)) >> 21;
5083	0	s5 += carry4;
5084	0	s4 -= carry4 * (1 << 21);
5085	0	carry6 = (s6 + (1 << 20)) >> 21;
5086	0	s7 += carry6;
5087	0	s6 -= carry6 * (1 << 21);
5088	0	carry8 = (s8 + (1 << 20)) >> 21;
5089	0	s9 += carry8;
5090	0	s8 -= carry8 * (1 << 21);
5091	0	carry10 = (s10 + (1 << 20)) >> 21;
5092	0	s11 += carry10;
5093	0	s10 -= carry10 * (1 << 21);
5094	0	carry12 = (s12 + (1 << 20)) >> 21;
5095	0	s13 += carry12;
5096	0	s12 -= carry12 * (1 << 21);
5097	0	carry14 = (s14 + (1 << 20)) >> 21;
5098	0	s15 += carry14;
5099	0	s14 -= carry14 * (1 << 21);
5100	0	carry16 = (s16 + (1 << 20)) >> 21;
5101	0	s17 += carry16;
5102	0	s16 -= carry16 * (1 << 21);
5103	0	carry18 = (s18 + (1 << 20)) >> 21;
5104	0	s19 += carry18;
5105	0	s18 -= carry18 * (1 << 21);
5106	0	carry20 = (s20 + (1 << 20)) >> 21;
5107	0	s21 += carry20;
5108	0	s20 -= carry20 * (1 << 21);
5109	0	carry22 = (s22 + (1 << 20)) >> 21;
5110	0	s23 += carry22;
5111	0	s22 -= carry22 * (1 << 21);
5112
5113	0	carry1 = (s1 + (1 << 20)) >> 21;
5114	0	s2 += carry1;
5115	0	s1 -= carry1 * (1 << 21);
5116	0	carry3 = (s3 + (1 << 20)) >> 21;
5117	0	s4 += carry3;
5118	0	s3 -= carry3 * (1 << 21);
5119	0	carry5 = (s5 + (1 << 20)) >> 21;
5120	0	s6 += carry5;
5121	0	s5 -= carry5 * (1 << 21);
5122	0	carry7 = (s7 + (1 << 20)) >> 21;
5123	0	s8 += carry7;
5124	0	s7 -= carry7 * (1 << 21);
5125	0	carry9 = (s9 + (1 << 20)) >> 21;
5126	0	s10 += carry9;
5127	0	s9 -= carry9 * (1 << 21);
5128	0	carry11 = (s11 + (1 << 20)) >> 21;
5129	0	s12 += carry11;
5130	0	s11 -= carry11 * (1 << 21);
5131	0	carry13 = (s13 + (1 << 20)) >> 21;
5132	0	s14 += carry13;
5133	0	s13 -= carry13 * (1 << 21);
5134	0	carry15 = (s15 + (1 << 20)) >> 21;
5135	0	s16 += carry15;
5136	0	s15 -= carry15 * (1 << 21);
5137	0	carry17 = (s17 + (1 << 20)) >> 21;
5138	0	s18 += carry17;
5139	0	s17 -= carry17 * (1 << 21);
5140	0	carry19 = (s19 + (1 << 20)) >> 21;
5141	0	s20 += carry19;
5142	0	s19 -= carry19 * (1 << 21);
5143	0	carry21 = (s21 + (1 << 20)) >> 21;
5144	0	s22 += carry21;
5145	0	s21 -= carry21 * (1 << 21);
5146
5147	0	s11 += s23 * 666643;
5148	0	s12 += s23 * 470296;
5149	0	s13 += s23 * 654183;
5150	0	s14 -= s23 * 997805;
5151	0	s15 += s23 * 136657;
5152	0	s16 -= s23 * 683901;
5153	0	s23 = 0;
5154
5155	0	s10 += s22 * 666643;
5156	0	s11 += s22 * 470296;
5157	0	s12 += s22 * 654183;
5158	0	s13 -= s22 * 997805;
5159	0	s14 += s22 * 136657;
5160	0	s15 -= s22 * 683901;
5161	0	s22 = 0;
5162
5163	0	s9 += s21 * 666643;
5164	0	s10 += s21 * 470296;
5165	0	s11 += s21 * 654183;
5166	0	s12 -= s21 * 997805;
5167	0	s13 += s21 * 136657;
5168	0	s14 -= s21 * 683901;
5169	0	s21 = 0;
5170
5171	0	s8 += s20 * 666643;
5172	0	s9 += s20 * 470296;
5173	0	s10 += s20 * 654183;
5174	0	s11 -= s20 * 997805;
5175	0	s12 += s20 * 136657;
5176	0	s13 -= s20 * 683901;
5177	0	s20 = 0;
5178
5179	0	s7 += s19 * 666643;
5180	0	s8 += s19 * 470296;
5181	0	s9 += s19 * 654183;
5182	0	s10 -= s19 * 997805;
5183	0	s11 += s19 * 136657;
5184	0	s12 -= s19 * 683901;
5185	0	s19 = 0;
5186
5187	0	s6 += s18 * 666643;
5188	0	s7 += s18 * 470296;
5189	0	s8 += s18 * 654183;
5190	0	s9 -= s18 * 997805;
5191	0	s10 += s18 * 136657;
5192	0	s11 -= s18 * 683901;
5193	0	s18 = 0;
5194
5195	0	carry6 = (s6 + (1 << 20)) >> 21;
5196	0	s7 += carry6;
5197	0	s6 -= carry6 * (1 << 21);
5198	0	carry8 = (s8 + (1 << 20)) >> 21;
5199	0	s9 += carry8;
5200	0	s8 -= carry8 * (1 << 21);
5201	0	carry10 = (s10 + (1 << 20)) >> 21;
5202	0	s11 += carry10;
5203	0	s10 -= carry10 * (1 << 21);
5204	0	carry12 = (s12 + (1 << 20)) >> 21;
5205	0	s13 += carry12;
5206	0	s12 -= carry12 * (1 << 21);
5207	0	carry14 = (s14 + (1 << 20)) >> 21;
5208	0	s15 += carry14;
5209	0	s14 -= carry14 * (1 << 21);
5210	0	carry16 = (s16 + (1 << 20)) >> 21;
5211	0	s17 += carry16;
5212	0	s16 -= carry16 * (1 << 21);
5213
5214	0	carry7 = (s7 + (1 << 20)) >> 21;
5215	0	s8 += carry7;
5216	0	s7 -= carry7 * (1 << 21);
5217	0	carry9 = (s9 + (1 << 20)) >> 21;
5218	0	s10 += carry9;
5219	0	s9 -= carry9 * (1 << 21);
5220	0	carry11 = (s11 + (1 << 20)) >> 21;
5221	0	s12 += carry11;
5222	0	s11 -= carry11 * (1 << 21);
5223	0	carry13 = (s13 + (1 << 20)) >> 21;
5224	0	s14 += carry13;
5225	0	s13 -= carry13 * (1 << 21);
5226	0	carry15 = (s15 + (1 << 20)) >> 21;
5227	0	s16 += carry15;
5228	0	s15 -= carry15 * (1 << 21);
5229
5230	0	s5 += s17 * 666643;
5231	0	s6 += s17 * 470296;
5232	0	s7 += s17 * 654183;
5233	0	s8 -= s17 * 997805;
5234	0	s9 += s17 * 136657;
5235	0	s10 -= s17 * 683901;
5236	0	s17 = 0;
5237
5238	0	s4 += s16 * 666643;
5239	0	s5 += s16 * 470296;
5240	0	s6 += s16 * 654183;
5241	0	s7 -= s16 * 997805;
5242	0	s8 += s16 * 136657;
5243	0	s9 -= s16 * 683901;
5244	0	s16 = 0;
5245
5246	0	s3 += s15 * 666643;
5247	0	s4 += s15 * 470296;
5248	0	s5 += s15 * 654183;
5249	0	s6 -= s15 * 997805;
5250	0	s7 += s15 * 136657;
5251	0	s8 -= s15 * 683901;
5252	0	s15 = 0;
5253
5254	0	s2 += s14 * 666643;
5255	0	s3 += s14 * 470296;
5256	0	s4 += s14 * 654183;
5257	0	s5 -= s14 * 997805;
5258	0	s6 += s14 * 136657;
5259	0	s7 -= s14 * 683901;
5260	0	s14 = 0;
5261
5262	0	s1 += s13 * 666643;
5263	0	s2 += s13 * 470296;
5264	0	s3 += s13 * 654183;
5265	0	s4 -= s13 * 997805;
5266	0	s5 += s13 * 136657;
5267	0	s6 -= s13 * 683901;
5268	0	s13 = 0;
5269
5270	0	s0 += s12 * 666643;
5271	0	s1 += s12 * 470296;
5272	0	s2 += s12 * 654183;
5273	0	s3 -= s12 * 997805;
5274	0	s4 += s12 * 136657;
5275	0	s5 -= s12 * 683901;
5276	0	s12 = 0;
5277
5278	0	carry0 = (s0 + (1 << 20)) >> 21;
5279	0	s1 += carry0;
5280	0	s0 -= carry0 * (1 << 21);
5281	0	carry2 = (s2 + (1 << 20)) >> 21;
5282	0	s3 += carry2;
5283	0	s2 -= carry2 * (1 << 21);
5284	0	carry4 = (s4 + (1 << 20)) >> 21;
5285	0	s5 += carry4;
5286	0	s4 -= carry4 * (1 << 21);
5287	0	carry6 = (s6 + (1 << 20)) >> 21;
5288	0	s7 += carry6;
5289	0	s6 -= carry6 * (1 << 21);
5290	0	carry8 = (s8 + (1 << 20)) >> 21;
5291	0	s9 += carry8;
5292	0	s8 -= carry8 * (1 << 21);
5293	0	carry10 = (s10 + (1 << 20)) >> 21;
5294	0	s11 += carry10;
5295	0	s10 -= carry10 * (1 << 21);
5296
5297	0	carry1 = (s1 + (1 << 20)) >> 21;
5298	0	s2 += carry1;
5299	0	s1 -= carry1 * (1 << 21);
5300	0	carry3 = (s3 + (1 << 20)) >> 21;
5301	0	s4 += carry3;
5302	0	s3 -= carry3 * (1 << 21);
5303	0	carry5 = (s5 + (1 << 20)) >> 21;
5304	0	s6 += carry5;
5305	0	s5 -= carry5 * (1 << 21);
5306	0	carry7 = (s7 + (1 << 20)) >> 21;
5307	0	s8 += carry7;
5308	0	s7 -= carry7 * (1 << 21);
5309	0	carry9 = (s9 + (1 << 20)) >> 21;
5310	0	s10 += carry9;
5311	0	s9 -= carry9 * (1 << 21);
5312	0	carry11 = (s11 + (1 << 20)) >> 21;
5313	0	s12 += carry11;
5314	0	s11 -= carry11 * (1 << 21);
5315
5316	0	s0 += s12 * 666643;
5317	0	s1 += s12 * 470296;
5318	0	s2 += s12 * 654183;
5319	0	s3 -= s12 * 997805;
5320	0	s4 += s12 * 136657;
5321	0	s5 -= s12 * 683901;
5322	0	s12 = 0;
5323
5324	0	carry0 = s0 >> 21;
5325	0	s1 += carry0;
5326	0	s0 -= carry0 * (1 << 21);
5327	0	carry1 = s1 >> 21;
5328	0	s2 += carry1;
5329	0	s1 -= carry1 * (1 << 21);
5330	0	carry2 = s2 >> 21;
5331	0	s3 += carry2;
5332	0	s2 -= carry2 * (1 << 21);
5333	0	carry3 = s3 >> 21;
5334	0	s4 += carry3;
5335	0	s3 -= carry3 * (1 << 21);
5336	0	carry4 = s4 >> 21;
5337	0	s5 += carry4;
5338	0	s4 -= carry4 * (1 << 21);
5339	0	carry5 = s5 >> 21;
5340	0	s6 += carry5;
5341	0	s5 -= carry5 * (1 << 21);
5342	0	carry6 = s6 >> 21;
5343	0	s7 += carry6;
5344	0	s6 -= carry6 * (1 << 21);
5345	0	carry7 = s7 >> 21;
5346	0	s8 += carry7;
5347	0	s7 -= carry7 * (1 << 21);
5348	0	carry8 = s8 >> 21;
5349	0	s9 += carry8;
5350	0	s8 -= carry8 * (1 << 21);
5351	0	carry9 = s9 >> 21;
5352	0	s10 += carry9;
5353	0	s9 -= carry9 * (1 << 21);
5354	0	carry10 = s10 >> 21;
5355	0	s11 += carry10;
5356	0	s10 -= carry10 * (1 << 21);
5357	0	carry11 = s11 >> 21;
5358	0	s12 += carry11;
5359	0	s11 -= carry11 * (1 << 21);
5360
5361	0	s0 += s12 * 666643;
5362	0	s1 += s12 * 470296;
5363	0	s2 += s12 * 654183;
5364	0	s3 -= s12 * 997805;
5365	0	s4 += s12 * 136657;
5366	0	s5 -= s12 * 683901;
5367	0	s12 = 0;
5368
5369	0	carry0 = s0 >> 21;
5370	0	s1 += carry0;
5371	0	s0 -= carry0 * (1 << 21);
5372	0	carry1 = s1 >> 21;
5373	0	s2 += carry1;
5374	0	s1 -= carry1 * (1 << 21);
5375	0	carry2 = s2 >> 21;
5376	0	s3 += carry2;
5377	0	s2 -= carry2 * (1 << 21);
5378	0	carry3 = s3 >> 21;
5379	0	s4 += carry3;
5380	0	s3 -= carry3 * (1 << 21);
5381	0	carry4 = s4 >> 21;
5382	0	s5 += carry4;
5383	0	s4 -= carry4 * (1 << 21);
5384	0	carry5 = s5 >> 21;
5385	0	s6 += carry5;
5386	0	s5 -= carry5 * (1 << 21);
5387	0	carry6 = s6 >> 21;
5388	0	s7 += carry6;
5389	0	s6 -= carry6 * (1 << 21);
5390	0	carry7 = s7 >> 21;
5391	0	s8 += carry7;
5392	0	s7 -= carry7 * (1 << 21);
5393	0	carry8 = s8 >> 21;
5394	0	s9 += carry8;
5395	0	s8 -= carry8 * (1 << 21);
5396	0	carry9 = s9 >> 21;
5397	0	s10 += carry9;
5398	0	s9 -= carry9 * (1 << 21);
5399	0	carry10 = s10 >> 21;
5400	0	s11 += carry10;
5401	0	s10 -= carry10 * (1 << 21);
5402
5403	0	s[ 0] = (uint8_t) (s0 >> 0);
5404	0	s[ 1] = (uint8_t) (s0 >> 8);
5405	0	s[ 2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5406	0	s[ 3] = (uint8_t) (s1 >> 3);
5407	0	s[ 4] = (uint8_t) (s1 >> 11);
5408	0	s[ 5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5409	0	s[ 6] = (uint8_t) (s2 >> 6);
5410	0	s[ 7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5411	0	s[ 8] = (uint8_t) (s3 >> 1);
5412	0	s[ 9] = (uint8_t) (s3 >> 9);
5413	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5414	0	s[11] = (uint8_t) (s4 >> 4);
5415	0	s[12] = (uint8_t) (s4 >> 12);
5416	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5417	0	s[14] = (uint8_t) (s5 >> 7);
5418	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5419	0	s[16] = (uint8_t) (s6 >> 2);
5420	0	s[17] = (uint8_t) (s6 >> 10);
5421	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5422	0	s[19] = (uint8_t) (s7 >> 5);
5423	0	s[20] = (uint8_t) (s7 >> 13);
5424	0	s[21] = (uint8_t) (s8 >> 0);
5425	0	s[22] = (uint8_t) (s8 >> 8);
5426	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5427	0	s[24] = (uint8_t) (s9 >> 3);
5428	0	s[25] = (uint8_t) (s9 >> 11);
5429	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5430	0	s[27] = (uint8_t) (s10 >> 6);
5431	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5432	0	s[29] = (uint8_t) (s11 >> 1);
5433	0	s[30] = (uint8_t) (s11 >> 9);
5434	0	s[31] = (uint8_t) (s11 >> 17);
5435	0	}
5436
5437		static int hash_init_with_dom(EVP_MD_CTX *hash_ctx,
5438		EVP_MD *sha512,
5439		const uint8_t dom2flag,
5440		const uint8_t phflag,
5441		const uint8_t *context,
5442		const size_t context_len)
5443	0	{
5444		/* ASCII: "SigEd25519 no Ed25519 collisions", in hex for EBCDIC compatibility */
5445	0	const char dom_s[] =
5446	0	"\x53\x69\x67\x45\x64\x32\x35\x35\x31\x39\x20\x6e"
5447	0	"\x6f\x20\x45\x64\x32\x35\x35\x31\x39\x20\x63\x6f"
5448	0	"\x6c\x6c\x69\x73\x69\x6f\x6e\x73";
5449	0	uint8_t dom[2];
5450
5451	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL))
5452	0	return 0;
5453
5454		/* return early if dom2flag is not set */
5455	0	if (!dom2flag)
5456	0	return 1;
5457
5458	0	if (context_len > UINT8_MAX)
5459	0	return 0;
5460
5461	0	dom[0] = (uint8_t)(phflag >= 1 ? 1 : 0);
5462	0	dom[1] = (uint8_t)context_len;
5463
5464	0	if (!EVP_DigestUpdate(hash_ctx, dom_s, sizeof(dom_s)-1)
5465	0	\|\| !EVP_DigestUpdate(hash_ctx, dom, sizeof(dom))
5466	0	\|\| !EVP_DigestUpdate(hash_ctx, context, context_len)) {
5467	0	return 0;
5468	0	}
5469
5470	0	return 1;
5471	0	}
5472
5473		int
5474		ossl_ed25519_sign(uint8_t out_sig, const uint8_t tbs, size_t tbs_len,
5475		const uint8_t public_key[32], const uint8_t private_key[32],
5476		const uint8_t dom2flag, const uint8_t phflag, const uint8_t csflag,
5477		const uint8_t *context, size_t context_len,
5478		OSSL_LIB_CTX libctx, const char propq)
5479	0	{
5480	0	uint8_t az[SHA512_DIGEST_LENGTH];
5481	0	uint8_t nonce[SHA512_DIGEST_LENGTH];
5482	0	ge_p3 R;
5483	0	uint8_t hram[SHA512_DIGEST_LENGTH];
5484	0	EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5485	0	EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
5486	0	unsigned int sz;
5487	0	int res = 0;
5488
5489	0	if (context == NULL)
5490	0	context_len = 0;
5491
5492		/* if csflag is set, then a non-empty context-string is required */
5493	0	if (csflag && context_len == 0)
5494	0	goto err;
5495
5496		/* if dom2flag is not set, then an empty context-string is required */
5497	0	if (!dom2flag && context_len > 0)
5498	0	goto err;
5499
5500	0	if (sha512 == NULL \|\| hash_ctx == NULL)
5501	0	goto err;
5502
5503	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5504	0	\|\| !EVP_DigestUpdate(hash_ctx, private_key, 32)
5505	0	\|\| !EVP_DigestFinal_ex(hash_ctx, az, &sz))
5506	0	goto err;
5507
5508	0	az[0] &= 248;
5509	0	az[31] &= 63;
5510	0	az[31] \|= 64;
5511
5512	0	if (!hash_init_with_dom(hash_ctx, sha512, dom2flag, phflag, context, context_len)
5513	0	\|\| !EVP_DigestUpdate(hash_ctx, az + 32, 32)
5514	0	\|\| !EVP_DigestUpdate(hash_ctx, tbs, tbs_len)
5515	0	\|\| !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
5516	0	goto err;
5517
5518	0	x25519_sc_reduce(nonce);
5519	0	ge_scalarmult_base(&R, nonce);
5520	0	ge_p3_tobytes(out_sig, &R);
5521
5522	0	if (!hash_init_with_dom(hash_ctx, sha512, dom2flag, phflag, context, context_len)
5523	0	\|\| !EVP_DigestUpdate(hash_ctx, out_sig, 32)
5524	0	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5525	0	\|\| !EVP_DigestUpdate(hash_ctx, tbs, tbs_len)
5526	0	\|\| !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
5527	0	goto err;
5528
5529	0	x25519_sc_reduce(hram);
5530	0	sc_muladd(out_sig + 32, hram, az, nonce);
5531
5532	0	res = 1;
5533	0	err:
5534	0	OPENSSL_cleanse(nonce, sizeof(nonce));
5535	0	OPENSSL_cleanse(az, sizeof(az));
5536	0	EVP_MD_free(sha512);
5537	0	EVP_MD_CTX_free(hash_ctx);
5538	0	return res;
5539	0	}
5540
5541		/*
5542		* This function should not be necessary since ossl_ed25519_verify() already
5543		* does this check internally.
5544		* For some reason the FIPS ACVP requires a EDDSA KeyVer test.
5545		*/
5546		int
5547		ossl_ed25519_pubkey_verify(const uint8_t *pub, size_t pub_len)
5548	0	{
5549	0	ge_p3 A;
5550
5551	0	if (pub_len != ED25519_KEYLEN)
5552	0	return 0;
5553	0	return (ge_frombytes_vartime(&A, pub) == 0);
5554	0	}
5555
5556		static const char allzeroes[15];
5557
5558		int
5559		ossl_ed25519_verify(const uint8_t *tbs, size_t tbs_len,
5560		const uint8_t signature[64], const uint8_t public_key[32],
5561		const uint8_t dom2flag, const uint8_t phflag, const uint8_t csflag,
5562		const uint8_t *context, size_t context_len,
5563		OSSL_LIB_CTX libctx, const char propq)
5564	0	{
5565	0	int i;
5566	0	ge_p3 A;
5567	0	const uint8_t r, s;
5568	0	EVP_MD *sha512;
5569	0	EVP_MD_CTX *hash_ctx = NULL;
5570	0	unsigned int sz;
5571	0	int res = 0;
5572	0	ge_p2 R;
5573	0	uint8_t rcheck[32];
5574	0	uint8_t h[SHA512_DIGEST_LENGTH];
5575		/* 27742317777372353535851937790883648493 in little endian format */
5576	0	const uint8_t l_low[16] = {
5577	0	0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5578	0	0xDE, 0xF9, 0xDE, 0x14
5579	0	};
5580
5581	0	if (context == NULL)
5582	0	context_len = 0;
5583
5584		/* if csflag is set, then a non-empty context-string is required */
5585	0	if (csflag && context_len == 0)
5586	0	return 0;
5587
5588		/* if dom2flag is not set, then an empty context-string is required */
5589	0	if (!dom2flag && context_len > 0)
5590	0	return 0;
5591
5592	0	r = signature;
5593	0	s = signature + 32;
5594
5595		/*
5596		* Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5597		*
5598		* If not the signature is publicly invalid. Since it's public we can do the
5599		* check in variable time.
5600		*
5601		* First check the most significant byte
5602		*/
5603	0	if (s[31] > 0x10)
5604	0	return 0;
5605	0	if (s[31] == 0x10) {
5606		/*
5607		* Most significant byte indicates a value close to 2^252 so check the
5608		* rest
5609		*/
5610	0	if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5611	0	return 0;
5612	0	for (i = 15; i >= 0; i--) {
5613	0	if (s[i] < l_low[i])
5614	0	break;
5615	0	if (s[i] > l_low[i])
5616	0	return 0;
5617	0	}
5618	0	if (i < 0)
5619	0	return 0;
5620	0	}
5621
5622	0	if (ge_frombytes_vartime(&A, public_key) != 0) {
5623	0	return 0;
5624	0	}
5625
5626	0	fe_neg(A.X, A.X);
5627	0	fe_neg(A.T, A.T);
5628
5629	0	sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5630	0	if (sha512 == NULL)
5631	0	return 0;
5632	0	hash_ctx = EVP_MD_CTX_new();
5633	0	if (hash_ctx == NULL)
5634	0	goto err;
5635
5636	0	if (!hash_init_with_dom(hash_ctx, sha512, dom2flag, phflag, context, context_len)
5637	0	\|\| !EVP_DigestUpdate(hash_ctx, r, 32)
5638	0	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5639	0	\|\| !EVP_DigestUpdate(hash_ctx, tbs, tbs_len)
5640	0	\|\| !EVP_DigestFinal_ex(hash_ctx, h, &sz))
5641	0	goto err;
5642
5643	0	x25519_sc_reduce(h);
5644
5645	0	ge_double_scalarmult_vartime(&R, h, &A, s);
5646
5647	0	ge_tobytes(rcheck, &R);
5648
5649	0	res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5650
5651		/* note that we have used the strict verification equation here.
5652		* we checked that ENC( [h](-A) + [s]B ) == r
5653		* B is the base point.
5654		*
5655		* the less strict verification equation uses the curve cofactor:
5656		* [h8](-A) + [s8]B == [8]R
5657		*/
5658	0	err:
5659	0	EVP_MD_free(sha512);
5660	0	EVP_MD_CTX_free(hash_ctx);
5661	0	return res;
5662	0	}
5663
5664		int
5665		ossl_ed25519_public_from_private(OSSL_LIB_CTX *ctx, uint8_t out_public_key[32],
5666		const uint8_t private_key[32],
5667		const char *propq)
5668	0	{
5669	0	uint8_t az[SHA512_DIGEST_LENGTH];
5670	0	ge_p3 A;
5671	0	int r;
5672	0	EVP_MD *sha512 = NULL;
5673
5674	0	sha512 = EVP_MD_fetch(ctx, SN_sha512, propq);
5675	0	if (sha512 == NULL)
5676	0	return 0;
5677	0	r = EVP_Digest(private_key, 32, az, NULL, sha512, NULL);
5678	0	EVP_MD_free(sha512);
5679	0	if (!r) {
5680	0	OPENSSL_cleanse(az, sizeof(az));
5681	0	return 0;
5682	0	}
5683
5684	0	az[0] &= 248;
5685	0	az[31] &= 63;
5686	0	az[31] \|= 64;
5687
5688	0	ge_scalarmult_base(&A, az);
5689	0	ge_p3_tobytes(out_public_key, &A);
5690
5691	0	OPENSSL_cleanse(az, sizeof(az));
5692	0	return 1;
5693	0	}
5694
5695		int
5696		ossl_x25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5697		const uint8_t peer_public_value[32])
5698	0	{
5699	0	static const uint8_t kZeros[32] = {0};
5700	0	x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5701		/* The all-zero output results when the input is a point of small order. */
5702	0	return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5703	0	}
5704
5705		void
5706		ossl_x25519_public_from_private(uint8_t out_public_value[32],
5707		const uint8_t private_key[32])
5708	0	{
5709	0	uint8_t e[32];
5710	0	ge_p3 A;
5711	0	fe zplusy, zminusy, zminusy_inv;
5712
5713	0	memcpy(e, private_key, 32);
5714	0	e[0] &= 248;
5715	0	e[31] &= 127;
5716	0	e[31] \|= 64;
5717
5718	0	ge_scalarmult_base(&A, e);
5719
5720		/*
5721		* We only need the u-coordinate of the curve25519 point.
5722		* The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5723		* u=(Z+Y)/(Z-Y).
5724		*/
5725	0	fe_add(zplusy, A.Z, A.Y);
5726	0	fe_sub(zminusy, A.Z, A.Y);
5727	0	fe_invert(zminusy_inv, zminusy);
5728	0	fe_mul(zplusy, zplusy, zminusy_inv);
5729	0	fe_tobytes(out_public_value, zplusy);
5730
5731	0	OPENSSL_cleanse(e, sizeof(e));
5732	0	}

Coverage Report

Created: 2025-06-22 06:56