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

Line	Count	Source
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__) \|\| defined(_M_AMD64) \|\| defined(_M_X64))
25
26		#define BASE_2_64_IMPLEMENTED
27
28		typedef uint64_t fe64[4];
29
30		int x25519_fe64_eligible(void);
31
32		/*
33		* Following subroutines perform corresponding operations modulo
34		* 2^256-38, i.e. double the curve modulus. However, inputs and
35		* outputs are permitted to be partially reduced, i.e. to remain
36		* in [0..2^256) range. It's all tied up in final fe64_tobytes
37		* that performs full reduction modulo 2^255-19.
38		*
39		* There are no reference C implementations for these.
40		*/
41		void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
42		void x25519_fe64_sqr(fe64 h, const fe64 f);
43		void x25519_fe64_mul121666(fe64 h, fe64 f);
44		void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
45		void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
46		void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
47		#define fe64_mul x25519_fe64_mul
48		#define fe64_sqr x25519_fe64_sqr
49		#define fe64_mul121666 x25519_fe64_mul121666
50		#define fe64_add x25519_fe64_add
51		#define fe64_sub x25519_fe64_sub
52		#define fe64_tobytes x25519_fe64_tobytes
53
54		static uint64_t load_8(const uint8_t *in)
55		{
56		uint64_t result;
57
58		result = in[0];
59		result \|= ((uint64_t)in[1]) << 8;
60		result \|= ((uint64_t)in[2]) << 16;
61		result \|= ((uint64_t)in[3]) << 24;
62		result \|= ((uint64_t)in[4]) << 32;
63		result \|= ((uint64_t)in[5]) << 40;
64		result \|= ((uint64_t)in[6]) << 48;
65		result \|= ((uint64_t)in[7]) << 56;
66
67		return result;
68		}
69
70		static void fe64_frombytes(fe64 h, const uint8_t *s)
71		{
72		h[0] = load_8(s);
73		h[1] = load_8(s + 8);
74		h[2] = load_8(s + 16);
75		h[3] = load_8(s + 24) & 0x7fffffffffffffff;
76		}
77
78		static void fe64_0(fe64 h)
79		{
80		h[0] = 0;
81		h[1] = 0;
82		h[2] = 0;
83		h[3] = 0;
84		}
85
86		static void fe64_1(fe64 h)
87		{
88		h[0] = 1;
89		h[1] = 0;
90		h[2] = 0;
91		h[3] = 0;
92		}
93
94		static void fe64_copy(fe64 h, const fe64 f)
95		{
96		h[0] = f[0];
97		h[1] = f[1];
98		h[2] = f[2];
99		h[3] = f[3];
100		}
101
102		static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
103		{
104		int i;
105		uint64_t mask = 0 - (uint64_t)b;
106
107		for (i = 0; i < 4; i++) {
108		uint64_t x = f[i] ^ g[i];
109		x &= mask;
110		f[i] ^= x;
111		g[i] ^= x;
112		}
113		}
114
115		static void fe64_invert(fe64 out, const fe64 z)
116		{
117		fe64 t0;
118		fe64 t1;
119		fe64 t2;
120		fe64 t3;
121		int i;
122
123		/*
124		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
125		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
126		*/
127
128		/* t0 = z ** 2 */
129		fe64_sqr(t0, z);
130
131		/* t1 = t0 (2 2) = z ** 8 */
132		fe64_sqr(t1, t0);
133		fe64_sqr(t1, t1);
134
135		/* t1 = z * t1 = z ** 9 */
136		fe64_mul(t1, z, t1);
137		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
138		fe64_mul(t0, t0, t1);
139
140		/* t2 = t0 2 = z 22 */
141		fe64_sqr(t2, t0);
142
143		/* t1 = t1 * t2 = z (2 5 - 1) */
144		fe64_mul(t1, t1, t2);
145
146		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
147		fe64_sqr(t2, t1);
148		for (i = 1; i < 5; ++i)
149		fe64_sqr(t2, t2);
150
151		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
152		fe64_mul(t1, t2, t1);
153
154		/* Continuing similarly... */
155
156		/* t2 = z (2 20 - 1) */
157		fe64_sqr(t2, t1);
158		for (i = 1; i < 10; ++i)
159		fe64_sqr(t2, t2);
160
161		fe64_mul(t2, t2, t1);
162
163		/* t2 = z (2 40 - 1) */
164		fe64_sqr(t3, t2);
165		for (i = 1; i < 20; ++i)
166		fe64_sqr(t3, t3);
167
168		fe64_mul(t2, t3, t2);
169
170		/* t2 = z (2 10) * (2 ** 40 - 1) */
171		for (i = 0; i < 10; ++i)
172		fe64_sqr(t2, t2);
173
174		/* t1 = z (2 50 - 1) */
175		fe64_mul(t1, t2, t1);
176
177		/* t2 = z (2 100 - 1) */
178		fe64_sqr(t2, t1);
179		for (i = 1; i < 50; ++i)
180		fe64_sqr(t2, t2);
181
182		fe64_mul(t2, t2, t1);
183
184		/* t2 = z (2 200 - 1) */
185		fe64_sqr(t3, t2);
186		for (i = 1; i < 100; ++i)
187		fe64_sqr(t3, t3);
188
189		fe64_mul(t2, t3, t2);
190
191		/* t2 = z ((2 50) * (2 ** 200 - 1) */
192		for (i = 0; i < 50; ++i)
193		fe64_sqr(t2, t2);
194
195		/* t1 = z (2 250 - 1) */
196		fe64_mul(t1, t2, t1);
197
198		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
199		for (i = 0; i < 5; ++i)
200		fe64_sqr(t1, t1);
201
202		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
203		fe64_mul(out, t1, t0);
204		}
205
206		/*
207		* Duplicate of original x25519_scalar_mult_generic, but using
208		* fe64_* subroutines.
209		*/
210		static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
211		const uint8_t point[32])
212		{
213		fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
214		uint8_t e[32];
215		unsigned swap = 0;
216		int pos;
217
218		memcpy(e, scalar, 32);
219		e[0] &= 0xf8;
220		e[31] &= 0x7f;
221		e[31] \|= 0x40;
222		fe64_frombytes(x1, point);
223		fe64_1(x2);
224		fe64_0(z2);
225		fe64_copy(x3, x1);
226		fe64_1(z3);
227
228		for (pos = 254; pos >= 0; --pos) {
229		unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
230
231		swap ^= b;
232		fe64_cswap(x2, x3, swap);
233		fe64_cswap(z2, z3, swap);
234		swap = b;
235		fe64_sub(tmp0, x3, z3);
236		fe64_sub(tmp1, x2, z2);
237		fe64_add(x2, x2, z2);
238		fe64_add(z2, x3, z3);
239		fe64_mul(z3, x2, tmp0);
240		fe64_mul(z2, z2, tmp1);
241		fe64_sqr(tmp0, tmp1);
242		fe64_sqr(tmp1, x2);
243		fe64_add(x3, z3, z2);
244		fe64_sub(z2, z3, z2);
245		fe64_mul(x2, tmp1, tmp0);
246		fe64_sub(tmp1, tmp1, tmp0);
247		fe64_sqr(z2, z2);
248		fe64_mul121666(z3, tmp1);
249		fe64_sqr(x3, x3);
250		fe64_add(tmp0, tmp0, z3);
251		fe64_mul(z3, x1, z2);
252		fe64_mul(z2, tmp1, tmp0);
253		}
254
255		fe64_invert(z2, z2);
256		fe64_mul(x2, x2, z2);
257		fe64_tobytes(out, x2);
258
259		OPENSSL_cleanse(e, sizeof(e));
260		}
261		#endif
262
263		#if defined(X25519_ASM) \
264		\|\| (defined(INT128_MAX) \
265		&& !defined(__sparc__) \
266		&& (!defined(__SIZEOF_LONG__) \|\| (__SIZEOF_LONG__ == 8)) \
267		&& !(defined(__ANDROID__) && !defined(__clang__)))
268		/*
269		* Base 2^51 implementation. It's virtually no different from reference
270		* base 2^25.5 implementation in respect to lax boundary conditions for
271		* intermediate values and even individual limbs. So that whatever you
272		* know about the reference, applies even here...
273		*/
274		#define BASE_2_51_IMPLEMENTED
275
276		typedef uint64_t fe51[5];
277
278		static const uint64_t MASK51 = 0x7ffffffffffff;
279
280		static uint64_t load_7(const uint8_t *in)
281	0	{
282	0	uint64_t result;
283
284	0	result = in[0];
285	0	result \|= ((uint64_t)in[1]) << 8;
286	0	result \|= ((uint64_t)in[2]) << 16;
287	0	result \|= ((uint64_t)in[3]) << 24;
288	0	result \|= ((uint64_t)in[4]) << 32;
289	0	result \|= ((uint64_t)in[5]) << 40;
290	0	result \|= ((uint64_t)in[6]) << 48;
291
292	0	return result;
293	0	}
294
295		static uint64_t load_6(const uint8_t *in)
296	0	{
297	0	uint64_t result;
298
299	0	result = in[0];
300	0	result \|= ((uint64_t)in[1]) << 8;
301	0	result \|= ((uint64_t)in[2]) << 16;
302	0	result \|= ((uint64_t)in[3]) << 24;
303	0	result \|= ((uint64_t)in[4]) << 32;
304	0	result \|= ((uint64_t)in[5]) << 40;
305
306	0	return result;
307	0	}
308
309		static void fe51_frombytes(fe51 h, const uint8_t *s)
310	0	{
311	0	uint64_t h0 = load_7(s); /* 56 bits */
312	0	uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
313	0	uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
314	0	uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
315	0	uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
316
317	0	h1 \|= h0 >> 51;
318	0	h0 &= MASK51;
319	0	h2 \|= h1 >> 51;
320	0	h1 &= MASK51;
321	0	h3 \|= h2 >> 51;
322	0	h2 &= MASK51;
323	0	h4 \|= h3 >> 51;
324	0	h3 &= MASK51;
325
326	0	h[0] = h0;
327	0	h[1] = h1;
328	0	h[2] = h2;
329	0	h[3] = h3;
330	0	h[4] = h4;
331	0	}
332
333		static void fe51_tobytes(uint8_t *s, const fe51 h)
334	0	{
335	0	uint64_t h0 = h[0];
336	0	uint64_t h1 = h[1];
337	0	uint64_t h2 = h[2];
338	0	uint64_t h3 = h[3];
339	0	uint64_t h4 = h[4];
340	0	uint64_t q;
341
342		/* compare to modulus */
343	0	q = (h0 + 19) >> 51;
344	0	q = (h1 + q) >> 51;
345	0	q = (h2 + q) >> 51;
346	0	q = (h3 + q) >> 51;
347	0	q = (h4 + q) >> 51;
348
349		/* full reduce */
350	0	h0 += 19 * q;
351	0	h1 += h0 >> 51;
352	0	h0 &= MASK51;
353	0	h2 += h1 >> 51;
354	0	h1 &= MASK51;
355	0	h3 += h2 >> 51;
356	0	h2 &= MASK51;
357	0	h4 += h3 >> 51;
358	0	h3 &= MASK51;
359	0	h4 &= MASK51;
360
361		/* smash */
362	0	s[0] = (uint8_t)(h0 >> 0);
363	0	s[1] = (uint8_t)(h0 >> 8);
364	0	s[2] = (uint8_t)(h0 >> 16);
365	0	s[3] = (uint8_t)(h0 >> 24);
366	0	s[4] = (uint8_t)(h0 >> 32);
367	0	s[5] = (uint8_t)(h0 >> 40);
368	0	s[6] = (uint8_t)((h0 >> 48) \| ((uint32_t)h1 << 3));
369	0	s[7] = (uint8_t)(h1 >> 5);
370	0	s[8] = (uint8_t)(h1 >> 13);
371	0	s[9] = (uint8_t)(h1 >> 21);
372	0	s[10] = (uint8_t)(h1 >> 29);
373	0	s[11] = (uint8_t)(h1 >> 37);
374	0	s[12] = (uint8_t)((h1 >> 45) \| ((uint32_t)h2 << 6));
375	0	s[13] = (uint8_t)(h2 >> 2);
376	0	s[14] = (uint8_t)(h2 >> 10);
377	0	s[15] = (uint8_t)(h2 >> 18);
378	0	s[16] = (uint8_t)(h2 >> 26);
379	0	s[17] = (uint8_t)(h2 >> 34);
380	0	s[18] = (uint8_t)(h2 >> 42);
381	0	s[19] = (uint8_t)((h2 >> 50) \| ((uint32_t)h3 << 1));
382	0	s[20] = (uint8_t)(h3 >> 7);
383	0	s[21] = (uint8_t)(h3 >> 15);
384	0	s[22] = (uint8_t)(h3 >> 23);
385	0	s[23] = (uint8_t)(h3 >> 31);
386	0	s[24] = (uint8_t)(h3 >> 39);
387	0	s[25] = (uint8_t)((h3 >> 47) \| ((uint32_t)h4 << 4));
388	0	s[26] = (uint8_t)(h4 >> 4);
389	0	s[27] = (uint8_t)(h4 >> 12);
390	0	s[28] = (uint8_t)(h4 >> 20);
391	0	s[29] = (uint8_t)(h4 >> 28);
392	0	s[30] = (uint8_t)(h4 >> 36);
393	0	s[31] = (uint8_t)(h4 >> 44);
394	0	}
395
396		#if defined(X25519_ASM)
397		void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
398		void x25519_fe51_sqr(fe51 h, const fe51 f);
399		void x25519_fe51_mul121666(fe51 h, fe51 f);
400		#define fe51_mul x25519_fe51_mul
401		#define fe51_sq x25519_fe51_sqr
402		#define fe51_mul121666 x25519_fe51_mul121666
403		#else
404
405		typedef uint128_t u128;
406
407		static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
408	0	{
409	0	u128 h0, h1, h2, h3, h4;
410	0	uint64_t f_i, g0, g1, g2, g3, g4;
411
412	0	f_i = f[0];
413	0	h0 = (u128)f_i * (g0 = g[0]);
414	0	h1 = (u128)f_i * (g1 = g[1]);
415	0	h2 = (u128)f_i * (g2 = g[2]);
416	0	h3 = (u128)f_i * (g3 = g[3]);
417	0	h4 = (u128)f_i * (g4 = g[4]);
418
419	0	f_i = f[1];
420	0	h0 += (u128)f_i * (g4 *= 19);
421	0	h1 += (u128)f_i * g0;
422	0	h2 += (u128)f_i * g1;
423	0	h3 += (u128)f_i * g2;
424	0	h4 += (u128)f_i * g3;
425
426	0	f_i = f[2];
427	0	h0 += (u128)f_i * (g3 *= 19);
428	0	h1 += (u128)f_i * g4;
429	0	h2 += (u128)f_i * g0;
430	0	h3 += (u128)f_i * g1;
431	0	h4 += (u128)f_i * g2;
432
433	0	f_i = f[3];
434	0	h0 += (u128)f_i * (g2 *= 19);
435	0	h1 += (u128)f_i * g3;
436	0	h2 += (u128)f_i * g4;
437	0	h3 += (u128)f_i * g0;
438	0	h4 += (u128)f_i * g1;
439
440	0	f_i = f[4];
441	0	h0 += (u128)f_i * (g1 *= 19);
442	0	h1 += (u128)f_i * g2;
443	0	h2 += (u128)f_i * g3;
444	0	h3 += (u128)f_i * g4;
445	0	h4 += (u128)f_i * g0;
446
447		/* partial [lazy] reduction */
448	0	h3 += (uint64_t)(h2 >> 51);
449	0	g2 = (uint64_t)h2 & MASK51;
450	0	h1 += (uint64_t)(h0 >> 51);
451	0	g0 = (uint64_t)h0 & MASK51;
452
453	0	h4 += (uint64_t)(h3 >> 51);
454	0	g3 = (uint64_t)h3 & MASK51;
455	0	g2 += (uint64_t)(h1 >> 51);
456	0	g1 = (uint64_t)h1 & MASK51;
457
458	0	g0 += (uint64_t)(h4 >> 51) * 19;
459	0	g4 = (uint64_t)h4 & MASK51;
460	0	g3 += g2 >> 51;
461	0	g2 &= MASK51;
462	0	g1 += g0 >> 51;
463	0	g0 &= MASK51;
464
465	0	h[0] = g0;
466	0	h[1] = g1;
467	0	h[2] = g2;
468	0	h[3] = g3;
469	0	h[4] = g4;
470	0	}
471
472		static void fe51_sq(fe51 h, const fe51 f)
473	0	{
474		#if defined(OPENSSL_SMALL_FOOTPRINT)
475		fe51_mul(h, f, f);
476		#else
477		/* dedicated squaring gives 16-25% overall improvement */
478	0	uint64_t g0 = f[0];
479	0	uint64_t g1 = f[1];
480	0	uint64_t g2 = f[2];
481	0	uint64_t g3 = f[3];
482	0	uint64_t g4 = f[4];
483	0	u128 h0, h1, h2, h3, h4;
484
485	0	h0 = (u128)g0 * g0;
486	0	g0 *= 2;
487	0	h1 = (u128)g0 * g1;
488	0	h2 = (u128)g0 * g2;
489	0	h3 = (u128)g0 * g3;
490	0	h4 = (u128)g0 * g4;
491
492	0	g0 = g4; /* borrow g0 */
493	0	h3 += (u128)g0 * (g4 *= 19);
494
495	0	h2 += (u128)g1 * g1;
496	0	g1 *= 2;
497	0	h3 += (u128)g1 * g2;
498	0	h4 += (u128)g1 * g3;
499	0	h0 += (u128)g1 * g4;
500
501	0	g0 = g3; /* borrow g0 */
502	0	h1 += (u128)g0 * (g3 *= 19);
503	0	h2 += (u128)(g0 * 2) * g4;
504
505	0	h4 += (u128)g2 * g2;
506	0	g2 *= 2;
507	0	h0 += (u128)g2 * g3;
508	0	h1 += (u128)g2 * g4;
509
510		/* partial [lazy] reduction */
511	0	h3 += (uint64_t)(h2 >> 51);
512	0	g2 = (uint64_t)h2 & MASK51;
513	0	h1 += (uint64_t)(h0 >> 51);
514	0	g0 = (uint64_t)h0 & MASK51;
515
516	0	h4 += (uint64_t)(h3 >> 51);
517	0	g3 = (uint64_t)h3 & MASK51;
518	0	g2 += (uint64_t)(h1 >> 51);
519	0	g1 = (uint64_t)h1 & MASK51;
520
521	0	g0 += (uint64_t)(h4 >> 51) * 19;
522	0	g4 = (uint64_t)h4 & MASK51;
523	0	g3 += g2 >> 51;
524	0	g2 &= MASK51;
525	0	g1 += g0 >> 51;
526	0	g0 &= MASK51;
527
528	0	h[0] = g0;
529	0	h[1] = g1;
530	0	h[2] = g2;
531	0	h[3] = g3;
532	0	h[4] = g4;
533	0	#endif
534	0	}
535
536		static void fe51_mul121666(fe51 h, fe51 f)
537	0	{
538	0	u128 h0 = f[0] * (u128)121666;
539	0	u128 h1 = f[1] * (u128)121666;
540	0	u128 h2 = f[2] * (u128)121666;
541	0	u128 h3 = f[3] * (u128)121666;
542	0	u128 h4 = f[4] * (u128)121666;
543	0	uint64_t g0, g1, g2, g3, g4;
544
545	0	h3 += (uint64_t)(h2 >> 51);
546	0	g2 = (uint64_t)h2 & MASK51;
547	0	h1 += (uint64_t)(h0 >> 51);
548	0	g0 = (uint64_t)h0 & MASK51;
549
550	0	h4 += (uint64_t)(h3 >> 51);
551	0	g3 = (uint64_t)h3 & MASK51;
552	0	g2 += (uint64_t)(h1 >> 51);
553	0	g1 = (uint64_t)h1 & MASK51;
554
555	0	g0 += (uint64_t)(h4 >> 51) * 19;
556	0	g4 = (uint64_t)h4 & MASK51;
557	0	g3 += g2 >> 51;
558	0	g2 &= MASK51;
559	0	g1 += g0 >> 51;
560	0	g0 &= MASK51;
561
562	0	h[0] = g0;
563	0	h[1] = g1;
564	0	h[2] = g2;
565	0	h[3] = g3;
566	0	h[4] = g4;
567	0	}
568		#endif
569
570		static void fe51_add(fe51 h, const fe51 f, const fe51 g)
571	0	{
572	0	h[0] = f[0] + g[0];
573	0	h[1] = f[1] + g[1];
574	0	h[2] = f[2] + g[2];
575	0	h[3] = f[3] + g[3];
576	0	h[4] = f[4] + g[4];
577	0	}
578
579		static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
580	0	{
581		/*
582		* Add 2*modulus to ensure that result remains positive
583		* even if subtrahend is partially reduced.
584		*/
585	0	h[0] = (f[0] + 0xfffffffffffda) - g[0];
586	0	h[1] = (f[1] + 0xffffffffffffe) - g[1];
587	0	h[2] = (f[2] + 0xffffffffffffe) - g[2];
588	0	h[3] = (f[3] + 0xffffffffffffe) - g[3];
589	0	h[4] = (f[4] + 0xffffffffffffe) - g[4];
590	0	}
591
592		static void fe51_0(fe51 h)
593	0	{
594	0	h[0] = 0;
595	0	h[1] = 0;
596	0	h[2] = 0;
597	0	h[3] = 0;
598	0	h[4] = 0;
599	0	}
600
601		static void fe51_1(fe51 h)
602	0	{
603	0	h[0] = 1;
604	0	h[1] = 0;
605	0	h[2] = 0;
606	0	h[3] = 0;
607	0	h[4] = 0;
608	0	}
609
610		static void fe51_copy(fe51 h, const fe51 f)
611	0	{
612	0	h[0] = f[0];
613	0	h[1] = f[1];
614	0	h[2] = f[2];
615	0	h[3] = f[3];
616	0	h[4] = f[4];
617	0	}
618
619		static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
620	0	{
621	0	int i;
622	0	uint64_t mask = 0 - (uint64_t)b;
623
624	0	for (i = 0; i < 5; i++) {
625	0	int64_t x = f[i] ^ g[i];
626	0	x &= mask;
627	0	f[i] ^= x;
628	0	g[i] ^= x;
629	0	}
630	0	}
631
632		static void fe51_invert(fe51 out, const fe51 z)
633	0	{
634	0	fe51 t0;
635	0	fe51 t1;
636	0	fe51 t2;
637	0	fe51 t3;
638	0	int i;
639
640		/*
641		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
642		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
643		*/
644
645		/* t0 = z ** 2 */
646	0	fe51_sq(t0, z);
647
648		/* t1 = t0 (2 2) = z ** 8 */
649	0	fe51_sq(t1, t0);
650	0	fe51_sq(t1, t1);
651
652		/* t1 = z * t1 = z ** 9 */
653	0	fe51_mul(t1, z, t1);
654		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
655	0	fe51_mul(t0, t0, t1);
656
657		/* t2 = t0 2 = z 22 */
658	0	fe51_sq(t2, t0);
659
660		/* t1 = t1 * t2 = z (2 5 - 1) */
661	0	fe51_mul(t1, t1, t2);
662
663		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
664	0	fe51_sq(t2, t1);
665	0	for (i = 1; i < 5; ++i)
666	0	fe51_sq(t2, t2);
667
668		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
669	0	fe51_mul(t1, t2, t1);
670
671		/* Continuing similarly... */
672
673		/* t2 = z (2 20 - 1) */
674	0	fe51_sq(t2, t1);
675	0	for (i = 1; i < 10; ++i)
676	0	fe51_sq(t2, t2);
677
678	0	fe51_mul(t2, t2, t1);
679
680		/* t2 = z (2 40 - 1) */
681	0	fe51_sq(t3, t2);
682	0	for (i = 1; i < 20; ++i)
683	0	fe51_sq(t3, t3);
684
685	0	fe51_mul(t2, t3, t2);
686
687		/* t2 = z (2 10) * (2 ** 40 - 1) */
688	0	for (i = 0; i < 10; ++i)
689	0	fe51_sq(t2, t2);
690
691		/* t1 = z (2 50 - 1) */
692	0	fe51_mul(t1, t2, t1);
693
694		/* t2 = z (2 100 - 1) */
695	0	fe51_sq(t2, t1);
696	0	for (i = 1; i < 50; ++i)
697	0	fe51_sq(t2, t2);
698
699	0	fe51_mul(t2, t2, t1);
700
701		/* t2 = z (2 200 - 1) */
702	0	fe51_sq(t3, t2);
703	0	for (i = 1; i < 100; ++i)
704	0	fe51_sq(t3, t3);
705
706	0	fe51_mul(t2, t3, t2);
707
708		/* t2 = z ((2 50) * (2 ** 200 - 1) */
709	0	for (i = 0; i < 50; ++i)
710	0	fe51_sq(t2, t2);
711
712		/* t1 = z (2 250 - 1) */
713	0	fe51_mul(t1, t2, t1);
714
715		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
716	0	for (i = 0; i < 5; ++i)
717	0	fe51_sq(t1, t1);
718
719		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
720	0	fe51_mul(out, t1, t0);
721	0	}
722
723		/*
724		* Duplicate of original x25519_scalar_mult_generic, but using
725		* fe51_* subroutines.
726		*/
727		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
728		const uint8_t point[32])
729	0	{
730	0	fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
731	0	uint8_t e[32];
732	0	unsigned swap = 0;
733	0	int pos;
734
735		#ifdef BASE_2_64_IMPLEMENTED
736		if (x25519_fe64_eligible()) {
737		x25519_scalar_mulx(out, scalar, point);
738		return;
739		}
740		#endif
741
742	0	memcpy(e, scalar, 32);
743	0	e[0] &= 0xf8;
744	0	e[31] &= 0x7f;
745	0	e[31] \|= 0x40;
746	0	fe51_frombytes(x1, point);
747	0	fe51_1(x2);
748	0	fe51_0(z2);
749	0	fe51_copy(x3, x1);
750	0	fe51_1(z3);
751
752	0	for (pos = 254; pos >= 0; --pos) {
753	0	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
754
755	0	swap ^= b;
756	0	fe51_cswap(x2, x3, swap);
757	0	fe51_cswap(z2, z3, swap);
758	0	swap = b;
759	0	fe51_sub(tmp0, x3, z3);
760	0	fe51_sub(tmp1, x2, z2);
761	0	fe51_add(x2, x2, z2);
762	0	fe51_add(z2, x3, z3);
763	0	fe51_mul(z3, tmp0, x2);
764	0	fe51_mul(z2, z2, tmp1);
765	0	fe51_sq(tmp0, tmp1);
766	0	fe51_sq(tmp1, x2);
767	0	fe51_add(x3, z3, z2);
768	0	fe51_sub(z2, z3, z2);
769	0	fe51_mul(x2, tmp1, tmp0);
770	0	fe51_sub(tmp1, tmp1, tmp0);
771	0	fe51_sq(z2, z2);
772	0	fe51_mul121666(z3, tmp1);
773	0	fe51_sq(x3, x3);
774	0	fe51_add(tmp0, tmp0, z3);
775	0	fe51_mul(z3, x1, z2);
776	0	fe51_mul(z2, tmp1, tmp0);
777	0	}
778
779	0	fe51_invert(z2, z2);
780	0	fe51_mul(x2, x2, z2);
781	0	fe51_tobytes(out, x2);
782
783	0	OPENSSL_cleanse(e, sizeof(e));
784	0	}
785		#endif
786
787		/*
788		* Reference base 2^25.5 implementation.
789		*
790		* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
791		* 20141124 (http://bench.cr.yp.to/supercop.html).
792		*
793		* The field functions are shared by Ed25519 and X25519 where possible.
794		*/
795
796		/*
797		* fe means field element. Here the field is \Z/(2^255-19). An element t,
798		* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
799		* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
800		* context.
801		*/
802		typedef int32_t fe[10];
803
804		static const int64_t kBottom21Bits = 0x1fffffLL;
805		static const int64_t kBottom25Bits = 0x1ffffffLL;
806		static const int64_t kBottom26Bits = 0x3ffffffLL;
807		static const int64_t kTop39Bits = 0xfffffffffe000000LL;
808		static const int64_t kTop38Bits = 0xfffffffffc000000LL;
809
810		static uint64_t load_3(const uint8_t *in)
811	0	{
812	0	uint64_t result;
813
814	0	result = ((uint64_t)in[0]);
815	0	result \|= ((uint64_t)in[1]) << 8;
816	0	result \|= ((uint64_t)in[2]) << 16;
817	0	return result;
818	0	}
819
820		static uint64_t load_4(const uint8_t *in)
821	0	{
822	0	uint64_t result;
823
824	0	result = ((uint64_t)in[0]);
825	0	result \|= ((uint64_t)in[1]) << 8;
826	0	result \|= ((uint64_t)in[2]) << 16;
827	0	result \|= ((uint64_t)in[3]) << 24;
828	0	return result;
829	0	}
830
831		static void fe_frombytes(fe h, const uint8_t *s)
832	0	{
833		/* Ignores top bit of h. */
834	0	int64_t h0 = load_4(s);
835	0	int64_t h1 = load_3(s + 4) << 6;
836	0	int64_t h2 = load_3(s + 7) << 5;
837	0	int64_t h3 = load_3(s + 10) << 3;
838	0	int64_t h4 = load_3(s + 13) << 2;
839	0	int64_t h5 = load_4(s + 16);
840	0	int64_t h6 = load_3(s + 20) << 7;
841	0	int64_t h7 = load_3(s + 23) << 5;
842	0	int64_t h8 = load_3(s + 26) << 4;
843	0	int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
844	0	int64_t carry0;
845	0	int64_t carry1;
846	0	int64_t carry2;
847	0	int64_t carry3;
848	0	int64_t carry4;
849	0	int64_t carry5;
850	0	int64_t carry6;
851	0	int64_t carry7;
852	0	int64_t carry8;
853	0	int64_t carry9;
854
855	0	carry9 = h9 + (1 << 24);
856	0	h0 += (carry9 >> 25) * 19;
857	0	h9 -= carry9 & kTop39Bits;
858	0	carry1 = h1 + (1 << 24);
859	0	h2 += carry1 >> 25;
860	0	h1 -= carry1 & kTop39Bits;
861	0	carry3 = h3 + (1 << 24);
862	0	h4 += carry3 >> 25;
863	0	h3 -= carry3 & kTop39Bits;
864	0	carry5 = h5 + (1 << 24);
865	0	h6 += carry5 >> 25;
866	0	h5 -= carry5 & kTop39Bits;
867	0	carry7 = h7 + (1 << 24);
868	0	h8 += carry7 >> 25;
869	0	h7 -= carry7 & kTop39Bits;
870
871	0	carry0 = h0 + (1 << 25);
872	0	h1 += carry0 >> 26;
873	0	h0 -= carry0 & kTop38Bits;
874	0	carry2 = h2 + (1 << 25);
875	0	h3 += carry2 >> 26;
876	0	h2 -= carry2 & kTop38Bits;
877	0	carry4 = h4 + (1 << 25);
878	0	h5 += carry4 >> 26;
879	0	h4 -= carry4 & kTop38Bits;
880	0	carry6 = h6 + (1 << 25);
881	0	h7 += carry6 >> 26;
882	0	h6 -= carry6 & kTop38Bits;
883	0	carry8 = h8 + (1 << 25);
884	0	h9 += carry8 >> 26;
885	0	h8 -= carry8 & kTop38Bits;
886
887	0	h[0] = (int32_t)h0;
888	0	h[1] = (int32_t)h1;
889	0	h[2] = (int32_t)h2;
890	0	h[3] = (int32_t)h3;
891	0	h[4] = (int32_t)h4;
892	0	h[5] = (int32_t)h5;
893	0	h[6] = (int32_t)h6;
894	0	h[7] = (int32_t)h7;
895	0	h[8] = (int32_t)h8;
896	0	h[9] = (int32_t)h9;
897	0	}
898
899		/*
900		* Preconditions:
901		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
902		*
903		* Write p=2^255-19; q=floor(h/p).
904		* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
905		*
906		* Proof:
907		* Have \|h\|<=p so \|q\|<=1 so \|19^2 2^(-255) q\|<1/4.
908		* Also have \|h-2^230 h9\|<2^231 so \|19 2^(-255)(h-2^230 h9)\|<1/4.
909		*
910		* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
911		* Then 0<y<1.
912		*
913		* Write r=h-pq.
914		* Have 0<=r<=p-1=2^255-20.
915		* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
916		*
917		* Write x=r+19(2^-255)r+y.
918		* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
919		*
920		* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
921		* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
922		*/
923		static void fe_tobytes(uint8_t *s, const fe h)
924	0	{
925	0	int32_t h0 = h[0];
926	0	int32_t h1 = h[1];
927	0	int32_t h2 = h[2];
928	0	int32_t h3 = h[3];
929	0	int32_t h4 = h[4];
930	0	int32_t h5 = h[5];
931	0	int32_t h6 = h[6];
932	0	int32_t h7 = h[7];
933	0	int32_t h8 = h[8];
934	0	int32_t h9 = h[9];
935	0	int32_t q;
936
937	0	q = (19 * h9 + (((int32_t)1) << 24)) >> 25;
938	0	q = (h0 + q) >> 26;
939	0	q = (h1 + q) >> 25;
940	0	q = (h2 + q) >> 26;
941	0	q = (h3 + q) >> 25;
942	0	q = (h4 + q) >> 26;
943	0	q = (h5 + q) >> 25;
944	0	q = (h6 + q) >> 26;
945	0	q = (h7 + q) >> 25;
946	0	q = (h8 + q) >> 26;
947	0	q = (h9 + q) >> 25;
948
949		/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
950	0	h0 += 19 * q;
951		/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
952
953	0	h1 += h0 >> 26;
954	0	h0 &= kBottom26Bits;
955	0	h2 += h1 >> 25;
956	0	h1 &= kBottom25Bits;
957	0	h3 += h2 >> 26;
958	0	h2 &= kBottom26Bits;
959	0	h4 += h3 >> 25;
960	0	h3 &= kBottom25Bits;
961	0	h5 += h4 >> 26;
962	0	h4 &= kBottom26Bits;
963	0	h6 += h5 >> 25;
964	0	h5 &= kBottom25Bits;
965	0	h7 += h6 >> 26;
966	0	h6 &= kBottom26Bits;
967	0	h8 += h7 >> 25;
968	0	h7 &= kBottom25Bits;
969	0	h9 += h8 >> 26;
970	0	h8 &= kBottom26Bits;
971	0	h9 &= kBottom25Bits;
972		/* h10 = carry9 */
973
974		/*
975		* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
976		* Have h0+...+2^230 h9 between 0 and 2^255-1;
977		* evidently 2^255 h10-2^255 q = 0.
978		* Goal: Output h0+...+2^230 h9.
979		*/
980	0	s[0] = (uint8_t)(h0 >> 0);
981	0	s[1] = (uint8_t)(h0 >> 8);
982	0	s[2] = (uint8_t)(h0 >> 16);
983	0	s[3] = (uint8_t)((h0 >> 24) \| ((uint32_t)(h1) << 2));
984	0	s[4] = (uint8_t)(h1 >> 6);
985	0	s[5] = (uint8_t)(h1 >> 14);
986	0	s[6] = (uint8_t)((h1 >> 22) \| ((uint32_t)(h2) << 3));
987	0	s[7] = (uint8_t)(h2 >> 5);
988	0	s[8] = (uint8_t)(h2 >> 13);
989	0	s[9] = (uint8_t)((h2 >> 21) \| ((uint32_t)(h3) << 5));
990	0	s[10] = (uint8_t)(h3 >> 3);
991	0	s[11] = (uint8_t)(h3 >> 11);
992	0	s[12] = (uint8_t)((h3 >> 19) \| ((uint32_t)(h4) << 6));
993	0	s[13] = (uint8_t)(h4 >> 2);
994	0	s[14] = (uint8_t)(h4 >> 10);
995	0	s[15] = (uint8_t)(h4 >> 18);
996	0	s[16] = (uint8_t)(h5 >> 0);
997	0	s[17] = (uint8_t)(h5 >> 8);
998	0	s[18] = (uint8_t)(h5 >> 16);
999	0	s[19] = (uint8_t)((h5 >> 24) \| ((uint32_t)(h6) << 1));
1000	0	s[20] = (uint8_t)(h6 >> 7);
1001	0	s[21] = (uint8_t)(h6 >> 15);
1002	0	s[22] = (uint8_t)((h6 >> 23) \| ((uint32_t)(h7) << 3));
1003	0	s[23] = (uint8_t)(h7 >> 5);
1004	0	s[24] = (uint8_t)(h7 >> 13);
1005	0	s[25] = (uint8_t)((h7 >> 21) \| ((uint32_t)(h8) << 4));
1006	0	s[26] = (uint8_t)(h8 >> 4);
1007	0	s[27] = (uint8_t)(h8 >> 12);
1008	0	s[28] = (uint8_t)((h8 >> 20) \| ((uint32_t)(h9) << 6));
1009	0	s[29] = (uint8_t)(h9 >> 2);
1010	0	s[30] = (uint8_t)(h9 >> 10);
1011	0	s[31] = (uint8_t)(h9 >> 18);
1012	0	}
1013
1014		/* h = f */
1015		static void fe_copy(fe h, const fe f)
1016	0	{
1017	0	memmove(h, f, sizeof(int32_t) * 10);
1018	0	}
1019
1020		/* h = 0 */
1021		static void fe_0(fe h)
1022	0	{
1023	0	memset(h, 0, sizeof(int32_t) * 10);
1024	0	}
1025
1026		/* h = 1 */
1027		static void fe_1(fe h)
1028	0	{
1029	0	memset(h, 0, sizeof(int32_t) * 10);
1030	0	h[0] = 1;
1031	0	}
1032
1033		/*
1034		* h = f + g
1035		*
1036		* Can overlap h with f or g.
1037		*
1038		* Preconditions:
1039		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1040		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1041		*
1042		* Postconditions:
1043		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1044		*/
1045		static void fe_add(fe h, const fe f, const fe g)
1046	0	{
1047	0	unsigned i;
1048
1049	0	for (i = 0; i < 10; i++) {
1050	0	h[i] = f[i] + g[i];
1051	0	}
1052	0	}
1053
1054		/*
1055		* h = f - g
1056		*
1057		* Can overlap h with f or g.
1058		*
1059		* Preconditions:
1060		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1061		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1062		*
1063		* Postconditions:
1064		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1065		*/
1066		static void fe_sub(fe h, const fe f, const fe g)
1067	0	{
1068	0	unsigned i;
1069
1070	0	for (i = 0; i < 10; i++) {
1071	0	h[i] = f[i] - g[i];
1072	0	}
1073	0	}
1074
1075		/*
1076		* h = f * g
1077		*
1078		* Can overlap h with f or g.
1079		*
1080		* Preconditions:
1081		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1082		* \|g\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1083		*
1084		* Postconditions:
1085		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1086		*
1087		* Notes on implementation strategy:
1088		*
1089		* Using schoolbook multiplication.
1090		* Karatsuba would save a little in some cost models.
1091		*
1092		* Most multiplications by 2 and 19 are 32-bit precomputations;
1093		* cheaper than 64-bit postcomputations.
1094		*
1095		* There is one remaining multiplication by 19 in the carry chain;
1096		* one *19 precomputation can be merged into this,
1097		* but the resulting data flow is considerably less clean.
1098		*
1099		* There are 12 carries below.
1100		* 10 of them are 2-way parallelizable and vectorizable.
1101		* Can get away with 11 carries, but then data flow is much deeper.
1102		*
1103		* With tighter constraints on inputs can squeeze carries into int32.
1104		*/
1105		static void fe_mul(fe h, const fe f, const fe g)
1106	0	{
1107	0	int32_t f0 = f[0];
1108	0	int32_t f1 = f[1];
1109	0	int32_t f2 = f[2];
1110	0	int32_t f3 = f[3];
1111	0	int32_t f4 = f[4];
1112	0	int32_t f5 = f[5];
1113	0	int32_t f6 = f[6];
1114	0	int32_t f7 = f[7];
1115	0	int32_t f8 = f[8];
1116	0	int32_t f9 = f[9];
1117	0	int32_t g0 = g[0];
1118	0	int32_t g1 = g[1];
1119	0	int32_t g2 = g[2];
1120	0	int32_t g3 = g[3];
1121	0	int32_t g4 = g[4];
1122	0	int32_t g5 = g[5];
1123	0	int32_t g6 = g[6];
1124	0	int32_t g7 = g[7];
1125	0	int32_t g8 = g[8];
1126	0	int32_t g9 = g[9];
1127	0	int32_t g1_19 = 19 * g1; /* 1.9593752^29 /
1128	0	int32_t g2_19 = 19 * g2; /* 1.9593752^30; still ok /
1129	0	int32_t g3_19 = 19 * g3;
1130	0	int32_t g4_19 = 19 * g4;
1131	0	int32_t g5_19 = 19 * g5;
1132	0	int32_t g6_19 = 19 * g6;
1133	0	int32_t g7_19 = 19 * g7;
1134	0	int32_t g8_19 = 19 * g8;
1135	0	int32_t g9_19 = 19 * g9;
1136	0	int32_t f1_2 = 2 * f1;
1137	0	int32_t f3_2 = 2 * f3;
1138	0	int32_t f5_2 = 2 * f5;
1139	0	int32_t f7_2 = 2 * f7;
1140	0	int32_t f9_2 = 2 * f9;
1141	0	int64_t f0g0 = f0 * (int64_t)g0;
1142	0	int64_t f0g1 = f0 * (int64_t)g1;
1143	0	int64_t f0g2 = f0 * (int64_t)g2;
1144	0	int64_t f0g3 = f0 * (int64_t)g3;
1145	0	int64_t f0g4 = f0 * (int64_t)g4;
1146	0	int64_t f0g5 = f0 * (int64_t)g5;
1147	0	int64_t f0g6 = f0 * (int64_t)g6;
1148	0	int64_t f0g7 = f0 * (int64_t)g7;
1149	0	int64_t f0g8 = f0 * (int64_t)g8;
1150	0	int64_t f0g9 = f0 * (int64_t)g9;
1151	0	int64_t f1g0 = f1 * (int64_t)g0;
1152	0	int64_t f1g1_2 = f1_2 * (int64_t)g1;
1153	0	int64_t f1g2 = f1 * (int64_t)g2;
1154	0	int64_t f1g3_2 = f1_2 * (int64_t)g3;
1155	0	int64_t f1g4 = f1 * (int64_t)g4;
1156	0	int64_t f1g5_2 = f1_2 * (int64_t)g5;
1157	0	int64_t f1g6 = f1 * (int64_t)g6;
1158	0	int64_t f1g7_2 = f1_2 * (int64_t)g7;
1159	0	int64_t f1g8 = f1 * (int64_t)g8;
1160	0	int64_t f1g9_38 = f1_2 * (int64_t)g9_19;
1161	0	int64_t f2g0 = f2 * (int64_t)g0;
1162	0	int64_t f2g1 = f2 * (int64_t)g1;
1163	0	int64_t f2g2 = f2 * (int64_t)g2;
1164	0	int64_t f2g3 = f2 * (int64_t)g3;
1165	0	int64_t f2g4 = f2 * (int64_t)g4;
1166	0	int64_t f2g5 = f2 * (int64_t)g5;
1167	0	int64_t f2g6 = f2 * (int64_t)g6;
1168	0	int64_t f2g7 = f2 * (int64_t)g7;
1169	0	int64_t f2g8_19 = f2 * (int64_t)g8_19;
1170	0	int64_t f2g9_19 = f2 * (int64_t)g9_19;
1171	0	int64_t f3g0 = f3 * (int64_t)g0;
1172	0	int64_t f3g1_2 = f3_2 * (int64_t)g1;
1173	0	int64_t f3g2 = f3 * (int64_t)g2;
1174	0	int64_t f3g3_2 = f3_2 * (int64_t)g3;
1175	0	int64_t f3g4 = f3 * (int64_t)g4;
1176	0	int64_t f3g5_2 = f3_2 * (int64_t)g5;
1177	0	int64_t f3g6 = f3 * (int64_t)g6;
1178	0	int64_t f3g7_38 = f3_2 * (int64_t)g7_19;
1179	0	int64_t f3g8_19 = f3 * (int64_t)g8_19;
1180	0	int64_t f3g9_38 = f3_2 * (int64_t)g9_19;
1181	0	int64_t f4g0 = f4 * (int64_t)g0;
1182	0	int64_t f4g1 = f4 * (int64_t)g1;
1183	0	int64_t f4g2 = f4 * (int64_t)g2;
1184	0	int64_t f4g3 = f4 * (int64_t)g3;
1185	0	int64_t f4g4 = f4 * (int64_t)g4;
1186	0	int64_t f4g5 = f4 * (int64_t)g5;
1187	0	int64_t f4g6_19 = f4 * (int64_t)g6_19;
1188	0	int64_t f4g7_19 = f4 * (int64_t)g7_19;
1189	0	int64_t f4g8_19 = f4 * (int64_t)g8_19;
1190	0	int64_t f4g9_19 = f4 * (int64_t)g9_19;
1191	0	int64_t f5g0 = f5 * (int64_t)g0;
1192	0	int64_t f5g1_2 = f5_2 * (int64_t)g1;
1193	0	int64_t f5g2 = f5 * (int64_t)g2;
1194	0	int64_t f5g3_2 = f5_2 * (int64_t)g3;
1195	0	int64_t f5g4 = f5 * (int64_t)g4;
1196	0	int64_t f5g5_38 = f5_2 * (int64_t)g5_19;
1197	0	int64_t f5g6_19 = f5 * (int64_t)g6_19;
1198	0	int64_t f5g7_38 = f5_2 * (int64_t)g7_19;
1199	0	int64_t f5g8_19 = f5 * (int64_t)g8_19;
1200	0	int64_t f5g9_38 = f5_2 * (int64_t)g9_19;
1201	0	int64_t f6g0 = f6 * (int64_t)g0;
1202	0	int64_t f6g1 = f6 * (int64_t)g1;
1203	0	int64_t f6g2 = f6 * (int64_t)g2;
1204	0	int64_t f6g3 = f6 * (int64_t)g3;
1205	0	int64_t f6g4_19 = f6 * (int64_t)g4_19;
1206	0	int64_t f6g5_19 = f6 * (int64_t)g5_19;
1207	0	int64_t f6g6_19 = f6 * (int64_t)g6_19;
1208	0	int64_t f6g7_19 = f6 * (int64_t)g7_19;
1209	0	int64_t f6g8_19 = f6 * (int64_t)g8_19;
1210	0	int64_t f6g9_19 = f6 * (int64_t)g9_19;
1211	0	int64_t f7g0 = f7 * (int64_t)g0;
1212	0	int64_t f7g1_2 = f7_2 * (int64_t)g1;
1213	0	int64_t f7g2 = f7 * (int64_t)g2;
1214	0	int64_t f7g3_38 = f7_2 * (int64_t)g3_19;
1215	0	int64_t f7g4_19 = f7 * (int64_t)g4_19;
1216	0	int64_t f7g5_38 = f7_2 * (int64_t)g5_19;
1217	0	int64_t f7g6_19 = f7 * (int64_t)g6_19;
1218	0	int64_t f7g7_38 = f7_2 * (int64_t)g7_19;
1219	0	int64_t f7g8_19 = f7 * (int64_t)g8_19;
1220	0	int64_t f7g9_38 = f7_2 * (int64_t)g9_19;
1221	0	int64_t f8g0 = f8 * (int64_t)g0;
1222	0	int64_t f8g1 = f8 * (int64_t)g1;
1223	0	int64_t f8g2_19 = f8 * (int64_t)g2_19;
1224	0	int64_t f8g3_19 = f8 * (int64_t)g3_19;
1225	0	int64_t f8g4_19 = f8 * (int64_t)g4_19;
1226	0	int64_t f8g5_19 = f8 * (int64_t)g5_19;
1227	0	int64_t f8g6_19 = f8 * (int64_t)g6_19;
1228	0	int64_t f8g7_19 = f8 * (int64_t)g7_19;
1229	0	int64_t f8g8_19 = f8 * (int64_t)g8_19;
1230	0	int64_t f8g9_19 = f8 * (int64_t)g9_19;
1231	0	int64_t f9g0 = f9 * (int64_t)g0;
1232	0	int64_t f9g1_38 = f9_2 * (int64_t)g1_19;
1233	0	int64_t f9g2_19 = f9 * (int64_t)g2_19;
1234	0	int64_t f9g3_38 = f9_2 * (int64_t)g3_19;
1235	0	int64_t f9g4_19 = f9 * (int64_t)g4_19;
1236	0	int64_t f9g5_38 = f9_2 * (int64_t)g5_19;
1237	0	int64_t f9g6_19 = f9 * (int64_t)g6_19;
1238	0	int64_t f9g7_38 = f9_2 * (int64_t)g7_19;
1239	0	int64_t f9g8_19 = f9 * (int64_t)g8_19;
1240	0	int64_t f9g9_38 = f9_2 * (int64_t)g9_19;
1241	0	int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1242	0	int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1243	0	int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1244	0	int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1245	0	int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1246	0	int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1247	0	int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
1248	0	int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
1249	0	int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
1250	0	int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
1251	0	int64_t carry0;
1252	0	int64_t carry1;
1253	0	int64_t carry2;
1254	0	int64_t carry3;
1255	0	int64_t carry4;
1256	0	int64_t carry5;
1257	0	int64_t carry6;
1258	0	int64_t carry7;
1259	0	int64_t carry8;
1260	0	int64_t carry9;
1261
1262		/* \|h0\| <= (1.651.652^52(1+19+19+19+19)+1.651.652^50(38+38+38+38+38))
1263		* i.e. \|h0\| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1264		* \|h1\| <= (1.651.652^51*(1+1+19+19+19+19+19+19+19+19))
1265		* i.e. \|h1\| <= 1.72^59; narrower ranges for h3, h5, h7, h9 /
1266
1267	0	carry0 = h0 + (1 << 25);
1268	0	h1 += carry0 >> 26;
1269	0	h0 -= carry0 & kTop38Bits;
1270	0	carry4 = h4 + (1 << 25);
1271	0	h5 += carry4 >> 26;
1272	0	h4 -= carry4 & kTop38Bits;
1273		/* \|h0\| <= 2^25 */
1274		/* \|h4\| <= 2^25 */
1275		/* \|h1\| <= 1.712^59 /
1276		/* \|h5\| <= 1.712^59 /
1277
1278	0	carry1 = h1 + (1 << 24);
1279	0	h2 += carry1 >> 25;
1280	0	h1 -= carry1 & kTop39Bits;
1281	0	carry5 = h5 + (1 << 24);
1282	0	h6 += carry5 >> 25;
1283	0	h5 -= carry5 & kTop39Bits;
1284		/* \|h1\| <= 2^24; from now on fits into int32 */
1285		/* \|h5\| <= 2^24; from now on fits into int32 */
1286		/* \|h2\| <= 1.412^60 /
1287		/* \|h6\| <= 1.412^60 /
1288
1289	0	carry2 = h2 + (1 << 25);
1290	0	h3 += carry2 >> 26;
1291	0	h2 -= carry2 & kTop38Bits;
1292	0	carry6 = h6 + (1 << 25);
1293	0	h7 += carry6 >> 26;
1294	0	h6 -= carry6 & kTop38Bits;
1295		/* \|h2\| <= 2^25; from now on fits into int32 unchanged */
1296		/* \|h6\| <= 2^25; from now on fits into int32 unchanged */
1297		/* \|h3\| <= 1.712^59 /
1298		/* \|h7\| <= 1.712^59 /
1299
1300	0	carry3 = h3 + (1 << 24);
1301	0	h4 += carry3 >> 25;
1302	0	h3 -= carry3 & kTop39Bits;
1303	0	carry7 = h7 + (1 << 24);
1304	0	h8 += carry7 >> 25;
1305	0	h7 -= carry7 & kTop39Bits;
1306		/* \|h3\| <= 2^24; from now on fits into int32 unchanged */
1307		/* \|h7\| <= 2^24; from now on fits into int32 unchanged */
1308		/* \|h4\| <= 1.722^34 /
1309		/* \|h8\| <= 1.412^60 /
1310
1311	0	carry4 = h4 + (1 << 25);
1312	0	h5 += carry4 >> 26;
1313	0	h4 -= carry4 & kTop38Bits;
1314	0	carry8 = h8 + (1 << 25);
1315	0	h9 += carry8 >> 26;
1316	0	h8 -= carry8 & kTop38Bits;
1317		/* \|h4\| <= 2^25; from now on fits into int32 unchanged */
1318		/* \|h8\| <= 2^25; from now on fits into int32 unchanged */
1319		/* \|h5\| <= 1.012^24 /
1320		/* \|h9\| <= 1.712^59 /
1321
1322	0	carry9 = h9 + (1 << 24);
1323	0	h0 += (carry9 >> 25) * 19;
1324	0	h9 -= carry9 & kTop39Bits;
1325		/* \|h9\| <= 2^24; from now on fits into int32 unchanged */
1326		/* \|h0\| <= 1.12^39 /
1327
1328	0	carry0 = h0 + (1 << 25);
1329	0	h1 += carry0 >> 26;
1330	0	h0 -= carry0 & kTop38Bits;
1331		/* \|h0\| <= 2^25; from now on fits into int32 unchanged */
1332		/* \|h1\| <= 1.012^24 /
1333
1334	0	h[0] = (int32_t)h0;
1335	0	h[1] = (int32_t)h1;
1336	0	h[2] = (int32_t)h2;
1337	0	h[3] = (int32_t)h3;
1338	0	h[4] = (int32_t)h4;
1339	0	h[5] = (int32_t)h5;
1340	0	h[6] = (int32_t)h6;
1341	0	h[7] = (int32_t)h7;
1342	0	h[8] = (int32_t)h8;
1343	0	h[9] = (int32_t)h9;
1344	0	}
1345
1346		/*
1347		* h = f * f
1348		*
1349		* Can overlap h with f.
1350		*
1351		* Preconditions:
1352		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1353		*
1354		* Postconditions:
1355		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1356		*
1357		* See fe_mul.c for discussion of implementation strategy.
1358		*/
1359		static void fe_sq(fe h, const fe f)
1360	0	{
1361	0	int32_t f0 = f[0];
1362	0	int32_t f1 = f[1];
1363	0	int32_t f2 = f[2];
1364	0	int32_t f3 = f[3];
1365	0	int32_t f4 = f[4];
1366	0	int32_t f5 = f[5];
1367	0	int32_t f6 = f[6];
1368	0	int32_t f7 = f[7];
1369	0	int32_t f8 = f[8];
1370	0	int32_t f9 = f[9];
1371	0	int32_t f0_2 = 2 * f0;
1372	0	int32_t f1_2 = 2 * f1;
1373	0	int32_t f2_2 = 2 * f2;
1374	0	int32_t f3_2 = 2 * f3;
1375	0	int32_t f4_2 = 2 * f4;
1376	0	int32_t f5_2 = 2 * f5;
1377	0	int32_t f6_2 = 2 * f6;
1378	0	int32_t f7_2 = 2 * f7;
1379	0	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1380	0	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1381	0	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1382	0	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1383	0	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1384	0	int64_t f0f0 = f0 * (int64_t)f0;
1385	0	int64_t f0f1_2 = f0_2 * (int64_t)f1;
1386	0	int64_t f0f2_2 = f0_2 * (int64_t)f2;
1387	0	int64_t f0f3_2 = f0_2 * (int64_t)f3;
1388	0	int64_t f0f4_2 = f0_2 * (int64_t)f4;
1389	0	int64_t f0f5_2 = f0_2 * (int64_t)f5;
1390	0	int64_t f0f6_2 = f0_2 * (int64_t)f6;
1391	0	int64_t f0f7_2 = f0_2 * (int64_t)f7;
1392	0	int64_t f0f8_2 = f0_2 * (int64_t)f8;
1393	0	int64_t f0f9_2 = f0_2 * (int64_t)f9;
1394	0	int64_t f1f1_2 = f1_2 * (int64_t)f1;
1395	0	int64_t f1f2_2 = f1_2 * (int64_t)f2;
1396	0	int64_t f1f3_4 = f1_2 * (int64_t)f3_2;
1397	0	int64_t f1f4_2 = f1_2 * (int64_t)f4;
1398	0	int64_t f1f5_4 = f1_2 * (int64_t)f5_2;
1399	0	int64_t f1f6_2 = f1_2 * (int64_t)f6;
1400	0	int64_t f1f7_4 = f1_2 * (int64_t)f7_2;
1401	0	int64_t f1f8_2 = f1_2 * (int64_t)f8;
1402	0	int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
1403	0	int64_t f2f2 = f2 * (int64_t)f2;
1404	0	int64_t f2f3_2 = f2_2 * (int64_t)f3;
1405	0	int64_t f2f4_2 = f2_2 * (int64_t)f4;
1406	0	int64_t f2f5_2 = f2_2 * (int64_t)f5;
1407	0	int64_t f2f6_2 = f2_2 * (int64_t)f6;
1408	0	int64_t f2f7_2 = f2_2 * (int64_t)f7;
1409	0	int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
1410	0	int64_t f2f9_38 = f2 * (int64_t)f9_38;
1411	0	int64_t f3f3_2 = f3_2 * (int64_t)f3;
1412	0	int64_t f3f4_2 = f3_2 * (int64_t)f4;
1413	0	int64_t f3f5_4 = f3_2 * (int64_t)f5_2;
1414	0	int64_t f3f6_2 = f3_2 * (int64_t)f6;
1415	0	int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
1416	0	int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
1417	0	int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
1418	0	int64_t f4f4 = f4 * (int64_t)f4;
1419	0	int64_t f4f5_2 = f4_2 * (int64_t)f5;
1420	0	int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
1421	0	int64_t f4f7_38 = f4 * (int64_t)f7_38;
1422	0	int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
1423	0	int64_t f4f9_38 = f4 * (int64_t)f9_38;
1424	0	int64_t f5f5_38 = f5 * (int64_t)f5_38;
1425	0	int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
1426	0	int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
1427	0	int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
1428	0	int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
1429	0	int64_t f6f6_19 = f6 * (int64_t)f6_19;
1430	0	int64_t f6f7_38 = f6 * (int64_t)f7_38;
1431	0	int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
1432	0	int64_t f6f9_38 = f6 * (int64_t)f9_38;
1433	0	int64_t f7f7_38 = f7 * (int64_t)f7_38;
1434	0	int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
1435	0	int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
1436	0	int64_t f8f8_19 = f8 * (int64_t)f8_19;
1437	0	int64_t f8f9_38 = f8 * (int64_t)f9_38;
1438	0	int64_t f9f9_38 = f9 * (int64_t)f9_38;
1439	0	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1440	0	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1441	0	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1442	0	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1443	0	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1444	0	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1445	0	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1446	0	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1447	0	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1448	0	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1449	0	int64_t carry0;
1450	0	int64_t carry1;
1451	0	int64_t carry2;
1452	0	int64_t carry3;
1453	0	int64_t carry4;
1454	0	int64_t carry5;
1455	0	int64_t carry6;
1456	0	int64_t carry7;
1457	0	int64_t carry8;
1458	0	int64_t carry9;
1459
1460	0	carry0 = h0 + (1 << 25);
1461	0	h1 += carry0 >> 26;
1462	0	h0 -= carry0 & kTop38Bits;
1463	0	carry4 = h4 + (1 << 25);
1464	0	h5 += carry4 >> 26;
1465	0	h4 -= carry4 & kTop38Bits;
1466
1467	0	carry1 = h1 + (1 << 24);
1468	0	h2 += carry1 >> 25;
1469	0	h1 -= carry1 & kTop39Bits;
1470	0	carry5 = h5 + (1 << 24);
1471	0	h6 += carry5 >> 25;
1472	0	h5 -= carry5 & kTop39Bits;
1473
1474	0	carry2 = h2 + (1 << 25);
1475	0	h3 += carry2 >> 26;
1476	0	h2 -= carry2 & kTop38Bits;
1477	0	carry6 = h6 + (1 << 25);
1478	0	h7 += carry6 >> 26;
1479	0	h6 -= carry6 & kTop38Bits;
1480
1481	0	carry3 = h3 + (1 << 24);
1482	0	h4 += carry3 >> 25;
1483	0	h3 -= carry3 & kTop39Bits;
1484	0	carry7 = h7 + (1 << 24);
1485	0	h8 += carry7 >> 25;
1486	0	h7 -= carry7 & kTop39Bits;
1487
1488	0	carry4 = h4 + (1 << 25);
1489	0	h5 += carry4 >> 26;
1490	0	h4 -= carry4 & kTop38Bits;
1491	0	carry8 = h8 + (1 << 25);
1492	0	h9 += carry8 >> 26;
1493	0	h8 -= carry8 & kTop38Bits;
1494
1495	0	carry9 = h9 + (1 << 24);
1496	0	h0 += (carry9 >> 25) * 19;
1497	0	h9 -= carry9 & kTop39Bits;
1498
1499	0	carry0 = h0 + (1 << 25);
1500	0	h1 += carry0 >> 26;
1501	0	h0 -= carry0 & kTop38Bits;
1502
1503	0	h[0] = (int32_t)h0;
1504	0	h[1] = (int32_t)h1;
1505	0	h[2] = (int32_t)h2;
1506	0	h[3] = (int32_t)h3;
1507	0	h[4] = (int32_t)h4;
1508	0	h[5] = (int32_t)h5;
1509	0	h[6] = (int32_t)h6;
1510	0	h[7] = (int32_t)h7;
1511	0	h[8] = (int32_t)h8;
1512	0	h[9] = (int32_t)h9;
1513	0	}
1514
1515		static void fe_invert(fe out, const fe z)
1516	0	{
1517	0	fe t0;
1518	0	fe t1;
1519	0	fe t2;
1520	0	fe t3;
1521	0	int i;
1522
1523		/*
1524		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
1525		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
1526		*/
1527
1528		/* t0 = z ** 2 */
1529	0	fe_sq(t0, z);
1530
1531		/* t1 = t0 (2 2) = z ** 8 */
1532	0	fe_sq(t1, t0);
1533	0	fe_sq(t1, t1);
1534
1535		/* t1 = z * t1 = z ** 9 */
1536	0	fe_mul(t1, z, t1);
1537		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1538	0	fe_mul(t0, t0, t1);
1539
1540		/* t2 = t0 2 = z 22 */
1541	0	fe_sq(t2, t0);
1542
1543		/* t1 = t1 * t2 = z (2 5 - 1) */
1544	0	fe_mul(t1, t1, t2);
1545
1546		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
1547	0	fe_sq(t2, t1);
1548	0	for (i = 1; i < 5; ++i) {
1549	0	fe_sq(t2, t2);
1550	0	}
1551
1552		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
1553	0	fe_mul(t1, t2, t1);
1554
1555		/* Continuing similarly... */
1556
1557		/* t2 = z (2 20 - 1) */
1558	0	fe_sq(t2, t1);
1559	0	for (i = 1; i < 10; ++i) {
1560	0	fe_sq(t2, t2);
1561	0	}
1562	0	fe_mul(t2, t2, t1);
1563
1564		/* t2 = z (2 40 - 1) */
1565	0	fe_sq(t3, t2);
1566	0	for (i = 1; i < 20; ++i) {
1567	0	fe_sq(t3, t3);
1568	0	}
1569	0	fe_mul(t2, t3, t2);
1570
1571		/* t2 = z (2 10) * (2 ** 40 - 1) */
1572	0	for (i = 0; i < 10; ++i) {
1573	0	fe_sq(t2, t2);
1574	0	}
1575		/* t1 = z (2 50 - 1) */
1576	0	fe_mul(t1, t2, t1);
1577
1578		/* t2 = z (2 100 - 1) */
1579	0	fe_sq(t2, t1);
1580	0	for (i = 1; i < 50; ++i) {
1581	0	fe_sq(t2, t2);
1582	0	}
1583	0	fe_mul(t2, t2, t1);
1584
1585		/* t2 = z (2 200 - 1) */
1586	0	fe_sq(t3, t2);
1587	0	for (i = 1; i < 100; ++i) {
1588	0	fe_sq(t3, t3);
1589	0	}
1590	0	fe_mul(t2, t3, t2);
1591
1592		/* t2 = z ((2 50) * (2 ** 200 - 1) */
1593	0	fe_sq(t2, t2);
1594	0	for (i = 1; i < 50; ++i) {
1595	0	fe_sq(t2, t2);
1596	0	}
1597
1598		/* t1 = z (2 250 - 1) */
1599	0	fe_mul(t1, t2, t1);
1600
1601		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
1602	0	fe_sq(t1, t1);
1603	0	for (i = 1; i < 5; ++i) {
1604	0	fe_sq(t1, t1);
1605	0	}
1606
1607		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
1608	0	fe_mul(out, t1, t0);
1609	0	}
1610
1611		/*
1612		* h = -f
1613		*
1614		* Preconditions:
1615		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1616		*
1617		* Postconditions:
1618		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1619		*/
1620		static void fe_neg(fe h, const fe f)
1621	0	{
1622	0	unsigned i;
1623
1624	0	for (i = 0; i < 10; i++) {
1625	0	h[i] = -f[i];
1626	0	}
1627	0	}
1628
1629		/*
1630		* Replace (f,g) with (g,g) if b == 1;
1631		* replace (f,g) with (f,g) if b == 0.
1632		*
1633		* Preconditions: b in {0,1}.
1634		*/
1635		static void fe_cmov(fe f, const fe g, unsigned b)
1636	0	{
1637	0	size_t i;
1638
1639	0	b = 0 - b;
1640	0	for (i = 0; i < 10; i++) {
1641	0	int32_t x = f[i] ^ g[i];
1642	0	x &= b;
1643	0	f[i] ^= x;
1644	0	}
1645	0	}
1646
1647		/*
1648		* return 0 if f == 0
1649		* return 1 if f != 0
1650		*
1651		* Preconditions:
1652		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1653		*/
1654		static int fe_isnonzero(const fe f)
1655	0	{
1656	0	uint8_t s[32];
1657	0	static const uint8_t zero[32] = { 0 };
1658
1659	0	fe_tobytes(s, f);
1660
1661	0	return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1662	0	}
1663
1664		/*
1665		* return 1 if f is in {1,3,5,...,q-2}
1666		* return 0 if f is in {0,2,4,...,q-1}
1667		*
1668		* Preconditions:
1669		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1670		*/
1671		static int fe_isnegative(const fe f)
1672	0	{
1673	0	uint8_t s[32];
1674
1675	0	fe_tobytes(s, f);
1676	0	return s[0] & 1;
1677	0	}
1678
1679		/*
1680		* h = 2 * f * f
1681		*
1682		* Can overlap h with f.
1683		*
1684		* Preconditions:
1685		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1686		*
1687		* Postconditions:
1688		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1689		*
1690		* See fe_mul.c for discussion of implementation strategy.
1691		*/
1692		static void fe_sq2(fe h, const fe f)
1693	0	{
1694	0	int32_t f0 = f[0];
1695	0	int32_t f1 = f[1];
1696	0	int32_t f2 = f[2];
1697	0	int32_t f3 = f[3];
1698	0	int32_t f4 = f[4];
1699	0	int32_t f5 = f[5];
1700	0	int32_t f6 = f[6];
1701	0	int32_t f7 = f[7];
1702	0	int32_t f8 = f[8];
1703	0	int32_t f9 = f[9];
1704	0	int32_t f0_2 = 2 * f0;
1705	0	int32_t f1_2 = 2 * f1;
1706	0	int32_t f2_2 = 2 * f2;
1707	0	int32_t f3_2 = 2 * f3;
1708	0	int32_t f4_2 = 2 * f4;
1709	0	int32_t f5_2 = 2 * f5;
1710	0	int32_t f6_2 = 2 * f6;
1711	0	int32_t f7_2 = 2 * f7;
1712	0	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1713	0	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1714	0	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1715	0	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1716	0	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1717	0	int64_t f0f0 = f0 * (int64_t)f0;
1718	0	int64_t f0f1_2 = f0_2 * (int64_t)f1;
1719	0	int64_t f0f2_2 = f0_2 * (int64_t)f2;
1720	0	int64_t f0f3_2 = f0_2 * (int64_t)f3;
1721	0	int64_t f0f4_2 = f0_2 * (int64_t)f4;
1722	0	int64_t f0f5_2 = f0_2 * (int64_t)f5;
1723	0	int64_t f0f6_2 = f0_2 * (int64_t)f6;
1724	0	int64_t f0f7_2 = f0_2 * (int64_t)f7;
1725	0	int64_t f0f8_2 = f0_2 * (int64_t)f8;
1726	0	int64_t f0f9_2 = f0_2 * (int64_t)f9;
1727	0	int64_t f1f1_2 = f1_2 * (int64_t)f1;
1728	0	int64_t f1f2_2 = f1_2 * (int64_t)f2;
1729	0	int64_t f1f3_4 = f1_2 * (int64_t)f3_2;
1730	0	int64_t f1f4_2 = f1_2 * (int64_t)f4;
1731	0	int64_t f1f5_4 = f1_2 * (int64_t)f5_2;
1732	0	int64_t f1f6_2 = f1_2 * (int64_t)f6;
1733	0	int64_t f1f7_4 = f1_2 * (int64_t)f7_2;
1734	0	int64_t f1f8_2 = f1_2 * (int64_t)f8;
1735	0	int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
1736	0	int64_t f2f2 = f2 * (int64_t)f2;
1737	0	int64_t f2f3_2 = f2_2 * (int64_t)f3;
1738	0	int64_t f2f4_2 = f2_2 * (int64_t)f4;
1739	0	int64_t f2f5_2 = f2_2 * (int64_t)f5;
1740	0	int64_t f2f6_2 = f2_2 * (int64_t)f6;
1741	0	int64_t f2f7_2 = f2_2 * (int64_t)f7;
1742	0	int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
1743	0	int64_t f2f9_38 = f2 * (int64_t)f9_38;
1744	0	int64_t f3f3_2 = f3_2 * (int64_t)f3;
1745	0	int64_t f3f4_2 = f3_2 * (int64_t)f4;
1746	0	int64_t f3f5_4 = f3_2 * (int64_t)f5_2;
1747	0	int64_t f3f6_2 = f3_2 * (int64_t)f6;
1748	0	int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
1749	0	int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
1750	0	int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
1751	0	int64_t f4f4 = f4 * (int64_t)f4;
1752	0	int64_t f4f5_2 = f4_2 * (int64_t)f5;
1753	0	int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
1754	0	int64_t f4f7_38 = f4 * (int64_t)f7_38;
1755	0	int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
1756	0	int64_t f4f9_38 = f4 * (int64_t)f9_38;
1757	0	int64_t f5f5_38 = f5 * (int64_t)f5_38;
1758	0	int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
1759	0	int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
1760	0	int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
1761	0	int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
1762	0	int64_t f6f6_19 = f6 * (int64_t)f6_19;
1763	0	int64_t f6f7_38 = f6 * (int64_t)f7_38;
1764	0	int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
1765	0	int64_t f6f9_38 = f6 * (int64_t)f9_38;
1766	0	int64_t f7f7_38 = f7 * (int64_t)f7_38;
1767	0	int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
1768	0	int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
1769	0	int64_t f8f8_19 = f8 * (int64_t)f8_19;
1770	0	int64_t f8f9_38 = f8 * (int64_t)f9_38;
1771	0	int64_t f9f9_38 = f9 * (int64_t)f9_38;
1772	0	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1773	0	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1774	0	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1775	0	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1776	0	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1777	0	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1778	0	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1779	0	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1780	0	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1781	0	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1782	0	int64_t carry0;
1783	0	int64_t carry1;
1784	0	int64_t carry2;
1785	0	int64_t carry3;
1786	0	int64_t carry4;
1787	0	int64_t carry5;
1788	0	int64_t carry6;
1789	0	int64_t carry7;
1790	0	int64_t carry8;
1791	0	int64_t carry9;
1792
1793	0	h0 += h0;
1794	0	h1 += h1;
1795	0	h2 += h2;
1796	0	h3 += h3;
1797	0	h4 += h4;
1798	0	h5 += h5;
1799	0	h6 += h6;
1800	0	h7 += h7;
1801	0	h8 += h8;
1802	0	h9 += h9;
1803
1804	0	carry0 = h0 + (1 << 25);
1805	0	h1 += carry0 >> 26;
1806	0	h0 -= carry0 & kTop38Bits;
1807	0	carry4 = h4 + (1 << 25);
1808	0	h5 += carry4 >> 26;
1809	0	h4 -= carry4 & kTop38Bits;
1810
1811	0	carry1 = h1 + (1 << 24);
1812	0	h2 += carry1 >> 25;
1813	0	h1 -= carry1 & kTop39Bits;
1814	0	carry5 = h5 + (1 << 24);
1815	0	h6 += carry5 >> 25;
1816	0	h5 -= carry5 & kTop39Bits;
1817
1818	0	carry2 = h2 + (1 << 25);
1819	0	h3 += carry2 >> 26;
1820	0	h2 -= carry2 & kTop38Bits;
1821	0	carry6 = h6 + (1 << 25);
1822	0	h7 += carry6 >> 26;
1823	0	h6 -= carry6 & kTop38Bits;
1824
1825	0	carry3 = h3 + (1 << 24);
1826	0	h4 += carry3 >> 25;
1827	0	h3 -= carry3 & kTop39Bits;
1828	0	carry7 = h7 + (1 << 24);
1829	0	h8 += carry7 >> 25;
1830	0	h7 -= carry7 & kTop39Bits;
1831
1832	0	carry4 = h4 + (1 << 25);
1833	0	h5 += carry4 >> 26;
1834	0	h4 -= carry4 & kTop38Bits;
1835	0	carry8 = h8 + (1 << 25);
1836	0	h9 += carry8 >> 26;
1837	0	h8 -= carry8 & kTop38Bits;
1838
1839	0	carry9 = h9 + (1 << 24);
1840	0	h0 += (carry9 >> 25) * 19;
1841	0	h9 -= carry9 & kTop39Bits;
1842
1843	0	carry0 = h0 + (1 << 25);
1844	0	h1 += carry0 >> 26;
1845	0	h0 -= carry0 & kTop38Bits;
1846
1847	0	h[0] = (int32_t)h0;
1848	0	h[1] = (int32_t)h1;
1849	0	h[2] = (int32_t)h2;
1850	0	h[3] = (int32_t)h3;
1851	0	h[4] = (int32_t)h4;
1852	0	h[5] = (int32_t)h5;
1853	0	h[6] = (int32_t)h6;
1854	0	h[7] = (int32_t)h7;
1855	0	h[8] = (int32_t)h8;
1856	0	h[9] = (int32_t)h9;
1857	0	}
1858
1859		static void fe_pow22523(fe out, const fe z)
1860	0	{
1861	0	fe t0;
1862	0	fe t1;
1863	0	fe t2;
1864	0	int i;
1865
1866	0	fe_sq(t0, z);
1867	0	fe_sq(t1, t0);
1868	0	for (i = 1; i < 2; ++i) {
1869	0	fe_sq(t1, t1);
1870	0	}
1871	0	fe_mul(t1, z, t1);
1872	0	fe_mul(t0, t0, t1);
1873	0	fe_sq(t0, t0);
1874	0	fe_mul(t0, t1, t0);
1875	0	fe_sq(t1, t0);
1876	0	for (i = 1; i < 5; ++i) {
1877	0	fe_sq(t1, t1);
1878	0	}
1879	0	fe_mul(t0, t1, t0);
1880	0	fe_sq(t1, t0);
1881	0	for (i = 1; i < 10; ++i) {
1882	0	fe_sq(t1, t1);
1883	0	}
1884	0	fe_mul(t1, t1, t0);
1885	0	fe_sq(t2, t1);
1886	0	for (i = 1; i < 20; ++i) {
1887	0	fe_sq(t2, t2);
1888	0	}
1889	0	fe_mul(t1, t2, t1);
1890	0	fe_sq(t1, t1);
1891	0	for (i = 1; i < 10; ++i) {
1892	0	fe_sq(t1, t1);
1893	0	}
1894	0	fe_mul(t0, t1, t0);
1895	0	fe_sq(t1, t0);
1896	0	for (i = 1; i < 50; ++i) {
1897	0	fe_sq(t1, t1);
1898	0	}
1899	0	fe_mul(t1, t1, t0);
1900	0	fe_sq(t2, t1);
1901	0	for (i = 1; i < 100; ++i) {
1902	0	fe_sq(t2, t2);
1903	0	}
1904	0	fe_mul(t1, t2, t1);
1905	0	fe_sq(t1, t1);
1906	0	for (i = 1; i < 50; ++i) {
1907	0	fe_sq(t1, t1);
1908	0	}
1909	0	fe_mul(t0, t1, t0);
1910	0	fe_sq(t0, t0);
1911	0	for (i = 1; i < 2; ++i) {
1912	0	fe_sq(t0, t0);
1913	0	}
1914	0	fe_mul(out, t0, z);
1915	0	}
1916
1917		/*
1918		* ge means group element.
1919		*
1920		* Here the group is the set of pairs (x,y) of field elements (see fe.h)
1921		* satisfying -x^2 + y^2 = 1 + d x^2y^2
1922		* where d = -121665/121666.
1923		*
1924		* Representations:
1925		* ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1926		* ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1927		* ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1928		* ge_precomp (Duif): (y+x,y-x,2dxy)
1929		*/
1930		typedef struct {
1931		fe X;
1932		fe Y;
1933		fe Z;
1934		} ge_p2;
1935
1936		typedef struct {
1937		fe X;
1938		fe Y;
1939		fe Z;
1940		fe T;
1941		} ge_p3;
1942
1943		typedef struct {
1944		fe X;
1945		fe Y;
1946		fe Z;
1947		fe T;
1948		} ge_p1p1;
1949
1950		typedef struct {
1951		fe yplusx;
1952		fe yminusx;
1953		fe xy2d;
1954		} ge_precomp;
1955
1956		typedef struct {
1957		fe YplusX;
1958		fe YminusX;
1959		fe Z;
1960		fe T2d;
1961		} ge_cached;
1962
1963		static void ge_tobytes(uint8_t s, const ge_p2 h)
1964	0	{
1965	0	fe recip;
1966	0	fe x;
1967	0	fe y;
1968
1969	0	fe_invert(recip, h->Z);
1970	0	fe_mul(x, h->X, recip);
1971	0	fe_mul(y, h->Y, recip);
1972	0	fe_tobytes(s, y);
1973	0	s[31] ^= fe_isnegative(x) << 7;
1974	0	}
1975
1976		static void ge_p3_tobytes(uint8_t s, const ge_p3 h)
1977	0	{
1978	0	fe recip;
1979	0	fe x;
1980	0	fe y;
1981
1982	0	fe_invert(recip, h->Z);
1983	0	fe_mul(x, h->X, recip);
1984	0	fe_mul(y, h->Y, recip);
1985	0	fe_tobytes(s, y);
1986	0	s[31] ^= fe_isnegative(x) << 7;
1987	0	}
1988
1989		static const fe d = {
1990		-10913610, 13857413, -15372611, 6949391, 114729,
1991		-8787816, -6275908, -3247719, -18696448, -12055116
1992		};
1993
1994		static const fe sqrtm1 = {
1995		-32595792, -7943725, 9377950, 3500415, 12389472,
1996		-272473, -25146209, -2005654, 326686, 11406482
1997		};
1998
1999		static int ge_frombytes_vartime(ge_p3 h, const uint8_t s)
2000	0	{
2001	0	fe u;
2002	0	fe v;
2003	0	fe w;
2004	0	fe vxx;
2005	0	fe check;
2006
2007	0	fe_frombytes(h->Y, s);
2008	0	fe_1(h->Z);
2009	0	fe_sq(u, h->Y);
2010	0	fe_mul(v, u, d);
2011	0	fe_sub(u, u, h->Z); /* u = y^2-1 */
2012	0	fe_add(v, v, h->Z); /* v = dy^2+1 */
2013
2014	0	fe_mul(w, u, v); /* w = uv /
2015
2016	0	fe_pow22523(h->X, w); /* x = w^((q-5)/8) */
2017	0	fe_mul(h->X, h->X, u); /* x = u * w^((q-5)/8) */
2018
2019	0	fe_sq(vxx, h->X);
2020	0	fe_mul(vxx, vxx, v);
2021	0	fe_sub(check, vxx, u); /* vx^2-u */
2022	0	if (fe_isnonzero(check)) {
2023	0	fe_add(check, vxx, u); /* vx^2+u */
2024	0	if (fe_isnonzero(check)) {
2025	0	return -1;
2026	0	}
2027	0	fe_mul(h->X, h->X, sqrtm1);
2028	0	}
2029
2030	0	if (fe_isnegative(h->X) != (s[31] >> 7)) {
2031	0	fe_neg(h->X, h->X);
2032	0	}
2033
2034	0	fe_mul(h->T, h->X, h->Y);
2035	0	return 0;
2036	0	}
2037
2038		static void ge_p2_0(ge_p2 *h)
2039	0	{
2040	0	fe_0(h->X);
2041	0	fe_1(h->Y);
2042	0	fe_1(h->Z);
2043	0	}
2044
2045		static void ge_p3_0(ge_p3 *h)
2046	0	{
2047	0	fe_0(h->X);
2048	0	fe_1(h->Y);
2049	0	fe_1(h->Z);
2050	0	fe_0(h->T);
2051	0	}
2052
2053		static void ge_precomp_0(ge_precomp *h)
2054	0	{
2055	0	fe_1(h->yplusx);
2056	0	fe_1(h->yminusx);
2057	0	fe_0(h->xy2d);
2058	0	}
2059
2060		/* r = p */
2061		static void ge_p3_to_p2(ge_p2 r, const ge_p3 p)
2062	0	{
2063	0	fe_copy(r->X, p->X);
2064	0	fe_copy(r->Y, p->Y);
2065	0	fe_copy(r->Z, p->Z);
2066	0	}
2067
2068		static const fe d2 = {
2069		-21827239, -5839606, -30745221, 13898782, 229458,
2070		15978800, -12551817, -6495438, 29715968, 9444199
2071		};
2072
2073		/* r = p */
2074		static void ge_p3_to_cached(ge_cached r, const ge_p3 p)
2075	0	{
2076	0	fe_add(r->YplusX, p->Y, p->X);
2077	0	fe_sub(r->YminusX, p->Y, p->X);
2078	0	fe_copy(r->Z, p->Z);
2079	0	fe_mul(r->T2d, p->T, d2);
2080	0	}
2081
2082		/* r = p */
2083		static void ge_p1p1_to_p2(ge_p2 r, const ge_p1p1 p)
2084	0	{
2085	0	fe_mul(r->X, p->X, p->T);
2086	0	fe_mul(r->Y, p->Y, p->Z);
2087	0	fe_mul(r->Z, p->Z, p->T);
2088	0	}
2089
2090		/* r = p */
2091		static void ge_p1p1_to_p3(ge_p3 r, const ge_p1p1 p)
2092	0	{
2093	0	fe_mul(r->X, p->X, p->T);
2094	0	fe_mul(r->Y, p->Y, p->Z);
2095	0	fe_mul(r->Z, p->Z, p->T);
2096	0	fe_mul(r->T, p->X, p->Y);
2097	0	}
2098
2099		/* r = 2 * p */
2100		static void ge_p2_dbl(ge_p1p1 r, const ge_p2 p)
2101	0	{
2102	0	fe t0;
2103
2104	0	fe_sq(r->X, p->X);
2105	0	fe_sq(r->Z, p->Y);
2106	0	fe_sq2(r->T, p->Z);
2107	0	fe_add(r->Y, p->X, p->Y);
2108	0	fe_sq(t0, r->Y);
2109	0	fe_add(r->Y, r->Z, r->X);
2110	0	fe_sub(r->Z, r->Z, r->X);
2111	0	fe_sub(r->X, t0, r->Y);
2112	0	fe_sub(r->T, r->T, r->Z);
2113	0	}
2114
2115		/* r = 2 * p */
2116		static void ge_p3_dbl(ge_p1p1 r, const ge_p3 p)
2117	0	{
2118	0	ge_p2 q;
2119	0	ge_p3_to_p2(&q, p);
2120	0	ge_p2_dbl(r, &q);
2121	0	}
2122
2123		/* r = p + q */
2124		static void ge_madd(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2125	0	{
2126	0	fe t0;
2127
2128	0	fe_add(r->X, p->Y, p->X);
2129	0	fe_sub(r->Y, p->Y, p->X);
2130	0	fe_mul(r->Z, r->X, q->yplusx);
2131	0	fe_mul(r->Y, r->Y, q->yminusx);
2132	0	fe_mul(r->T, q->xy2d, p->T);
2133	0	fe_add(t0, p->Z, p->Z);
2134	0	fe_sub(r->X, r->Z, r->Y);
2135	0	fe_add(r->Y, r->Z, r->Y);
2136	0	fe_add(r->Z, t0, r->T);
2137	0	fe_sub(r->T, t0, r->T);
2138	0	}
2139
2140		/* r = p - q */
2141		static void ge_msub(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2142	0	{
2143	0	fe t0;
2144
2145	0	fe_add(r->X, p->Y, p->X);
2146	0	fe_sub(r->Y, p->Y, p->X);
2147	0	fe_mul(r->Z, r->X, q->yminusx);
2148	0	fe_mul(r->Y, r->Y, q->yplusx);
2149	0	fe_mul(r->T, q->xy2d, p->T);
2150	0	fe_add(t0, p->Z, p->Z);
2151	0	fe_sub(r->X, r->Z, r->Y);
2152	0	fe_add(r->Y, r->Z, r->Y);
2153	0	fe_sub(r->Z, t0, r->T);
2154	0	fe_add(r->T, t0, r->T);
2155	0	}
2156
2157		/* r = p + q */
2158		static void ge_add(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2159	0	{
2160	0	fe t0;
2161
2162	0	fe_add(r->X, p->Y, p->X);
2163	0	fe_sub(r->Y, p->Y, p->X);
2164	0	fe_mul(r->Z, r->X, q->YplusX);
2165	0	fe_mul(r->Y, r->Y, q->YminusX);
2166	0	fe_mul(r->T, q->T2d, p->T);
2167	0	fe_mul(r->X, p->Z, q->Z);
2168	0	fe_add(t0, r->X, r->X);
2169	0	fe_sub(r->X, r->Z, r->Y);
2170	0	fe_add(r->Y, r->Z, r->Y);
2171	0	fe_add(r->Z, t0, r->T);
2172	0	fe_sub(r->T, t0, r->T);
2173	0	}
2174
2175		/* r = p - q */
2176		static void ge_sub(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2177	0	{
2178	0	fe t0;
2179
2180	0	fe_add(r->X, p->Y, p->X);
2181	0	fe_sub(r->Y, p->Y, p->X);
2182	0	fe_mul(r->Z, r->X, q->YminusX);
2183	0	fe_mul(r->Y, r->Y, q->YplusX);
2184	0	fe_mul(r->T, q->T2d, p->T);
2185	0	fe_mul(r->X, p->Z, q->Z);
2186	0	fe_add(t0, r->X, r->X);
2187	0	fe_sub(r->X, r->Z, r->Y);
2188	0	fe_add(r->Y, r->Z, r->Y);
2189	0	fe_sub(r->Z, t0, r->T);
2190	0	fe_add(r->T, t0, r->T);
2191	0	}
2192
2193		static uint8_t equal(signed char b, signed char c)
2194	0	{
2195	0	uint8_t ub = b;
2196	0	uint8_t uc = c;
2197	0	uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2198	0	uint32_t y = x; /* 0: yes; 1..255: no */
2199	0	y -= 1; /* 4294967295: yes; 0..254: no */
2200	0	y >>= 31; /* 1: yes; 0: no */
2201	0	return y;
2202	0	}
2203
2204		static void cmov(ge_precomp t, const ge_precomp u, uint8_t b)
2205	0	{
2206	0	fe_cmov(t->yplusx, u->yplusx, b);
2207	0	fe_cmov(t->yminusx, u->yminusx, b);
2208	0	fe_cmov(t->xy2d, u->xy2d, b);
2209	0	}
2210
2211		/* k25519Precomp[i][j] = (j+1)256^iB */
2212		static const ge_precomp k25519Precomp[32][8] = {
2213		{
2214		{
2215		{ 25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2216		27544626, -11754271, -6079156, 2047605 },
2217		{ -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2218		5043384, 19500929, -15469378 },
2219		{ -8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2220		29287919, 11864899, -24514362, -4438546 },
2221		},
2222		{
2223		{ -12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2224		-11717903, -3814571, -358445, -10211303 },
2225		{ -21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2226		-15616551, 11189268, -26829678, -5319081 },
2227		{ 26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2228		-3128826, -9541118, -15472047, -4166697 },
2229		},
2230		{
2231		{ 15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2232		27787600, -14772189, 28944400, -1550024 },
2233		{ 16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2234		16354577, -11775962, 7689662, 11199574 },
2235		{ 30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2236		7512774, 10017326, -17749093, -9920357 },
2237		},
2238		{
2239		{ -17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2240		-28926210, 15006023, 3284568, -6276540 },
2241		{ 23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2242		7464579, 9656445, 13059162, 10374397 },
2243		{ 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2244		-3839045, -641708, -101325 },
2245		},
2246		{
2247		{ 10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2248		32867885, 14515107, -15438304, 10819380 },
2249		{ 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2250		12483688, -12668491, 5581306 },
2251		{ 19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2252		28542350, 13850243, -23678021, -15815942 },
2253		},
2254		{
2255		{ -15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2256		-19188627, -15224819, -9818940, -12085777 },
2257		{ -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2258		-15689887, 1762328, 14866737 },
2259		{ -18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2260		-28236412, 3959421, 27914454, 4383652 },
2261		},
2262		{
2263		{ 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2264		5230134, -23952439, -15175766 },
2265		{ -30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2266		20654025, 16520125, 30598449, 7715701 },
2267		{ 28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2268		-31400660, 1370708, 29794553, -1409300 },
2269		},
2270		{
2271		{ 14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2272		30290735, 10876454, -33154098, 2381726 },
2273		{ -7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2274		-6236617, 3696005, -32300832, 15351955 },
2275		{ 27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2276		-32961401, -2970515, 29551813, 10109425 },
2277		},
2278		},
2279		{
2280		{
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3989		{ -1731589, -15155870, -3262930, 16143082, 19294135, 13385325,
3990		14741514, -9103726, 7903886, 2348101 },
3991		{ 24536016, -16515207, 12715592, -3862155, 1511293, 10047386,
3992		-3842346, -7129159, -28377538, 10048127 },
3993		},
3994		},
3995		{
3996		{
3997		{ -12622226, -6204820, 30718825, 2591312, -10617028, 12192840,
3998		18873298, -7297090, -32297756, 15221632 },
3999		{ -26478122, -11103864, 11546244, -1852483, 9180880, 7656409,
4000		-21343950, 2095755, 29769758, 6593415 },
4001		{ -31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345,
4002		-6118678, 30958054, 8292160 },
4003		},
4004		{
4005		{ 31429822, -13959116, 29173532, 15632448, 12174511, -2760094,
4006		32808831, 3977186, 26143136, -3148876 },
4007		{ 22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633,
4008		-1674433, -3758243, -2304625 },
4009		{ -15491917, 8012313, -2514730, -12702462, -23965846, -10254029,
4010		-1612713, -1535569, -16664475, 8194478 },
4011		},
4012		{
4013		{ 27338066, -7507420, -7414224, 10140405, -19026427, -6589889,
4014		27277191, 8855376, 28572286, 3005164 },
4015		{ 26287124, 4821776, 25476601, -4145903, -3764513, -15788984,
4016		-18008582, 1182479, -26094821, -13079595 },
4017		{ -7171154, 3178080, 23970071, 6201893, -17195577, -4489192,
4018		-21876275, -13982627, 32208683, -1198248 },
4019		},
4020		{
4021		{ -16657702, 2817643, -10286362, 14811298, 6024667, 13349505,
4022		-27315504, -10497842, -27672585, -11539858 },
4023		{ 15941029, -9405932, -21367050, 8062055, 31876073, -238629,
4024		-15278393, -1444429, 15397331, -4130193 },
4025		{ 8934485, -13485467, -23286397, -13423241, -32446090, 14047986,
4026		31170398, -1441021, -27505566, 15087184 },
4027		},
4028		{
4029		{ -18357243, -2156491, 24524913, -16677868, 15520427, -6360776,
4030		-15502406, 11461896, 16788528, -5868942 },
4031		{ -1947386, 16013773, 21750665, 3714552, -17401782, -16055433,
4032		-3770287, -10323320, 31322514, -11615635 },
4033		{ 21426655, -5650218, -13648287, -5347537, -28812189, -4920970,
4034		-18275391, -14621414, 13040862, -12112948 },
4035		},
4036		{
4037		{ 11293895, 12478086, -27136401, 15083750, -29307421, 14748872,
4038		14555558, -13417103, 1613711, 4896935 },
4039		{ -25894883, 15323294, -8489791, -8057900, 25967126, -13425460,
4040		2825960, -4897045, -23971776, -11267415 },
4041		{ -15924766, -5229880, -17443532, 6410664, 3622847, 10243618,
4042		20615400, 12405433, -23753030, -8436416 },
4043		},
4044		{
4045		{ -7091295, 12556208, -20191352, 9025187, -17072479, 4333801,
4046		4378436, 2432030, 23097949, -566018 },
4047		{ 4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264,
4048		10103221, -18512313, 2424778 },
4049		{ 366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678,
4050		1344109, -3642553, 12412659 },
4051		},
4052		{
4053		{ -24001791, 7690286, 14929416, -168257, -32210835, -13412986,
4054		24162697, -15326504, -3141501, 11179385 },
4055		{ 18289522, -14724954, 8056945, 16430056, -21729724, 7842514,
4056		-6001441, -1486897, -18684645, -11443503 },
4057		{ 476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959,
4058		13403813, 11052904, 5219329 },
4059		},
4060		},
4061		{
4062		{
4063		{ 20678546, -8375738, -32671898, 8849123, -5009758, 14574752,
4064		31186971, -3973730, 9014762, -8579056 },
4065		{ -13644050, -10350239, -15962508, 5075808, -1514661, -11534600,
4066		-33102500, 9160280, 8473550, -3256838 },
4067		{ 24900749, 14435722, 17209120, -15292541, -22592275, 9878983,
4068		-7689309, -16335821, -24568481, 11788948 },
4069		},
4070		{
4071		{ -3118155, -11395194, -13802089, 14797441, 9652448, -6845904,
4072		-20037437, 10410733, -24568470, -1458691 },
4073		{ -15659161, 16736706, -22467150, 10215878, -9097177, 7563911,
4074		11871841, -12505194, -18513325, 8464118 },
4075		{ -23400612, 8348507, -14585951, -861714, -3950205, -6373419,
4076		14325289, 8628612, 33313881, -8370517 },
4077		},
4078		{
4079		{ -20186973, -4967935, 22367356, 5271547, -1097117, -4788838,
4080		-24805667, -10236854, -8940735, -5818269 },
4081		{ -6948785, -1795212, -32625683, -16021179, 32635414, -7374245,
4082		15989197, -12838188, 28358192, -4253904 },
4083		{ -23561781, -2799059, -32351682, -1661963, -9147719, 10429267,
4084		-16637684, 4072016, -5351664, 5596589 },
4085		},
4086		{
4087		{ -28236598, -3390048, 12312896, 6213178, 3117142, 16078565,
4088		29266239, 2557221, 1768301, 15373193 },
4089		{ -7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902,
4090		-4504991, -24660491, 3442910 },
4091		{ -30210571, 5124043, 14181784, 8197961, 18964734, -11939093,
4092		22597931, 7176455, -18585478, 13365930 },
4093		},
4094		{
4095		{ -7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107,
4096		-8570186, -9689599, -3031667 },
4097		{ 25008904, -10771599, -4305031, -9638010, 16265036, 15721635,
4098		683793, -11823784, 15723479, -15163481 },
4099		{ -9660625, 12374379, -27006999, -7026148, -7724114, -12314514,
4100		11879682, 5400171, 519526, -1235876 },
4101		},
4102		{
4103		{ 22258397, -16332233, -7869817, 14613016, -22520255, -2950923,
4104		-20353881, 7315967, 16648397, 7605640 },
4105		{ -8081308, -8464597, -8223311, 9719710, 19259459, -15348212,
4106		23994942, -5281555, -9468848, 4763278 },
4107		{ -21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
4108		31088447, -7764523, -11356529, 728112 },
4109		},
4110		{
4111		{ 26047220, -11751471, -6900323, -16521798, 24092068, 9158119,
4112		-4273545, -12555558, -29365436, -5498272 },
4113		{ 17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007,
4114		12327945, 10750447, 10014012 },
4115		{ -10312768, 3936952, 9156313, -8897683, 16498692, -994647,
4116		-27481051, -666732, 3424691, 7540221 },
4117		},
4118		{
4119		{ 30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422,
4120		-16317219, -9244265, 15258046 },
4121		{ 13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
4122		2711395, 1062915, -5136345 },
4123		{ -19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
4124		-6066489, 12194497, 32960380, 1459310 },
4125		},
4126		},
4127		{
4128		{
4129		{ 19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
4130		-6101885, 18638003, -11174937 },
4131		{ 31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
4132		9012486, -7584354, -6643087, -5442636 },
4133		{ -9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
4134		9677543, -32294889, -6456008 },
4135		},
4136		{
4137		{ -2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
4138		-7839692, -7852844, -8138429 },
4139		{ -15236356, -15433509, 7766470, 746860, 26346930, -10221762,
4140		-27333451, 10754588, -9431476, 5203576 },
4141		{ 31834314, 14135496, -770007, 5159118, 20917671, -16768096,
4142		-7467973, -7337524, 31809243, 7347066 },
4143		},
4144		{
4145		{ -9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
4146		19797970, -12211255, 15192876, -2087490 },
4147		{ -12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
4148		10609330, 12694420, 33473243, -13382104 },
4149		{ 33184999, 11180355, 15832085, -11385430, -1633671, 225884,
4150		15089336, -11023903, -6135662, 14480053 },
4151		},
4152		{
4153		{ 31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
4154		5496208, 13685227, 27595050, 8737275 },
4155		{ -20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
4156		-31008351, -12610604, 26498114, 66511 },
4157		{ 22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
4158		30540766, -4286747, -13327787, -7515095 },
4159		},
4160		{
4161		{ -28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
4162		8205540, 13585437, -17127465, 15115439 },
4163		{ 23711543, -672915, 31206561, -8362711, 6164647, -9709987,
4164		-33535882, -1426096, 8236921, 16492939 },
4165		{ -23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
4166		19574902, 10071562, 6708380, -6222424 },
4167		},
4168		{
4169		{ 2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
4170		9328700, 29955601, -11678310 },
4171		{ 3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
4172		-25892142, -12635595, -9917575, 6216608 },
4173		{ -32615849, 338663, -25195611, 2510422, -29213566, -13820213,
4174		24822830, -6146567, -26767480, 7525079 },
4175		},
4176		{
4177		{ -23066649, -13985623, 16133487, -7896178, -3389565, 778788,
4178		-910336, -2782495, -19386633, 11994101 },
4179		{ 21691500, -13624626, -641331, -14367021, 3285881, -3483596,
4180		-25064666, 9718258, -7477437, 13381418 },
4181		{ 18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
4182		23111648, -6375247, 28535282, 15779576 },
4183		},
4184		{
4185		{ 30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
4186		-14068454, 12021730, 9955285, -16303356 },
4187		{ 9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
4188		-18426029, 9924399, 20194861, 13380996 },
4189		{ -26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
4190		-1984914, 15707771, 26342023, 10146099 },
4191		},
4192		},
4193		{
4194		{
4195		{ -26016874, -219943, 21339191, -41388, 19745256, -2878700,
4196		-29637280, 2227040, 21612326, -545728 },
4197		{ -13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
4198		25764461, 12243797, -20856566, 11649658 },
4199		{ -10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
4200		6114064, 33514190, 2333242 },
4201		},
4202		{
4203		{ -21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
4204		-6679750, -12670638, 24350578, -13450001 },
4205		{ -4116307, -11271533, -23886186, 4843615, -30088339, 690623,
4206		-31536088, -10406836, 8317860, 12352766 },
4207		{ 18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
4208		-23552096, -2287550, 20712163, 6719373 },
4209		},
4210		{
4211		{ 26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
4212		-3763210, 26224235, -3297458 },
4213		{ -17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
4214		21728352, 9493610, 18620611, -16428628 },
4215		{ -13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
4216		-5269471, -9725556, -30701573, -16479657 },
4217		},
4218		{
4219		{ -23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
4220		12248509, -5240639, 13735342, 1934062 },
4221		{ 25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
4222		-15136294, -3765346, -21277997, 5473616 },
4223		{ 31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
4224		-7125085, 12469656, 29111212, -5451014 },
4225		},
4226		{
4227		{ 24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
4228		24367466, 6388839, -10295587, 452383 },
4229		{ -25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
4230		-24236251, -5915248, 15766062, 8407814 },
4231		{ -20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
4232		-8917023, -4388953, -8067909, 2276718 },
4233		},
4234		{
4235		{ 30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
4236		-23827587, 5096219, 22740376, -7303417 },
4237		{ 2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
4238		24051124, 13742383, -15637599, 13295222 },
4239		{ 33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
4240		-17720195, -4612972, -4451357, -14669444 },
4241		},
4242		{
4243		{ -20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
4244		-2469266, -4141880, 7770569, 9620597 },
4245		{ 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
4246		-1694323, -33502340, -14767970 },
4247		{ 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
4248		1220118, 30494170, -11440799 },
4249		},
4250		{
4251		{ -5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
4252		-26739026, 926050, -1684339, -13333647 },
4253		{ 13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
4254		9021034, 9078865, 3353509, 4033511 },
4255		{ -29663431, -15113610, 32259991, -344482, 24295849, -12912123,
4256		23161163, 8839127, 27485041, 7356032 },
4257		},
4258		},
4259		{
4260		{
4261		{ 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
4262		2625015, 28431036, -16771834 },
4263		{ -23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
4264		-22545972, 14150565, 15970762, 4099461 },
4265		{ 29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
4266		13617293, -9937143, 11465739, 8317062 },
4267		},
4268		{
4269		{ -25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
4270		14898637, 3848455, 20969334, -5157516 },
4271		{ -20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
4272		-21610826, -3649888, 11177095, 14989547 },
4273		{ -24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
4274		13515641, 2581286, -28487508, 9930240 },
4275		},
4276		{
4277		{ -17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
4278		18345767, -13403753, 16291481, -5314038 },
4279		{ -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
4280		6957617, 4368891, 9788741 },
4281		{ 16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
4282		-21722536, -8613148, 16250552, -11111103 },
4283		},
4284		{
4285		{ -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
4286		10604807, -30190403, 4782747 },
4287		{ -1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
4288		-9981571, 4383045, 22546403, 437323 },
4289		{ 31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
4290		27343084, 2786261, -30633590, -14097016 },
4291		},
4292		{
4293		{ -14467279, -683715, -33374107, 7448552, 19294360, 14334329,
4294		-19690631, 2355319, -19284671, -6114373 },
4295		{ 15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
4296		18952177, 15496498, -29380133, 11754228 },
4297		{ -2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
4298		7141596, 11724556, 22761615, -10134141 },
4299		},
4300		{
4301		{ 16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
4302		-28741185, -12227393, 32851222, 11717399 },
4303		{ 11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
4304		31474879, 3483633, -1193175, -4030831 },
4305		{ -185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4306		33142652, 6546660, -19985279, -3948376 },
4307		},
4308		{
4309		{ -32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4310		-8537131, -12833048, -30772034, -15486313 },
4311		{ -18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4312		-31135347, -16049879, 10928917, 3011958 },
4313		{ -6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4314		-30831056, -12805180, 18008031, 10258577 },
4315		},
4316		{
4317		{ -22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4318		-1853465, 1367120, 25127874, 6671743 },
4319		{ 29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4320		21382910, 11042292, 25838796, 4642684 },
4321		{ -20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4322		30468147, -13900640, 18423289, 4177476 },
4323		},
4324		},
4325		};
4326
4327		static uint8_t negative(signed char b)
4328	0	{
4329	0	uint32_t x = b;
4330
4331	0	x >>= 31; /* 1: yes; 0: no */
4332	0	return x;
4333	0	}
4334
4335		static void table_select(ge_precomp *t, int pos, signed char b)
4336	0	{
4337	0	ge_precomp minust;
4338	0	uint8_t bnegative = negative(b);
4339	0	uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4340
4341	0	ge_precomp_0(t);
4342	0	cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4343	0	cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4344	0	cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4345	0	cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4346	0	cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4347	0	cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4348	0	cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4349	0	cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4350	0	fe_copy(minust.yplusx, t->yminusx);
4351	0	fe_copy(minust.yminusx, t->yplusx);
4352	0	fe_neg(minust.xy2d, t->xy2d);
4353	0	cmov(t, &minust, bnegative);
4354	0	}
4355
4356		/*
4357		* h = a * B
4358		*
4359		* where a = a[0]+256*a[1]+...+256^31 a[31]
4360		* B is the Ed25519 base point (x,4/5) with x positive.
4361		*
4362		* Preconditions:
4363		* a[31] <= 127
4364		*/
4365		static void ge_scalarmult_base(ge_p3 h, const uint8_t a)
4366	0	{
4367	0	signed char e[64];
4368	0	signed char carry;
4369	0	ge_p1p1 r;
4370	0	ge_p2 s;
4371	0	ge_precomp t;
4372	0	int i;
4373
4374	0	for (i = 0; i < 32; ++i) {
4375	0	e[2 * i + 0] = (a[i] >> 0) & 15;
4376	0	e[2 * i + 1] = (a[i] >> 4) & 15;
4377	0	}
4378		/* each e[i] is between 0 and 15 */
4379		/* e[63] is between 0 and 7 */
4380
4381	0	carry = 0;
4382	0	for (i = 0; i < 63; ++i) {
4383	0	e[i] += carry;
4384	0	carry = e[i] + 8;
4385	0	carry >>= 4;
4386	0	e[i] -= carry << 4;
4387	0	}
4388	0	e[63] += carry;
4389		/* each e[i] is between -8 and 8 */
4390
4391	0	ge_p3_0(h);
4392	0	for (i = 1; i < 64; i += 2) {
4393	0	table_select(&t, i / 2, e[i]);
4394	0	ge_madd(&r, h, &t);
4395	0	ge_p1p1_to_p3(h, &r);
4396	0	}
4397
4398	0	ge_p3_dbl(&r, h);
4399	0	ge_p1p1_to_p2(&s, &r);
4400	0	ge_p2_dbl(&r, &s);
4401	0	ge_p1p1_to_p2(&s, &r);
4402	0	ge_p2_dbl(&r, &s);
4403	0	ge_p1p1_to_p2(&s, &r);
4404	0	ge_p2_dbl(&r, &s);
4405	0	ge_p1p1_to_p3(h, &r);
4406
4407	0	for (i = 0; i < 64; i += 2) {
4408	0	table_select(&t, i / 2, e[i]);
4409	0	ge_madd(&r, h, &t);
4410	0	ge_p1p1_to_p3(h, &r);
4411	0	}
4412
4413	0	OPENSSL_cleanse(e, sizeof(e));
4414	0	}
4415
4416		#if !defined(BASE_2_51_IMPLEMENTED)
4417		/*
4418		* Replace (f,g) with (g,f) if b == 1;
4419		* replace (f,g) with (f,g) if b == 0.
4420		*
4421		* Preconditions: b in {0,1}.
4422		*/
4423		static void fe_cswap(fe f, fe g, unsigned int b)
4424		{
4425		size_t i;
4426
4427		b = 0 - b;
4428		for (i = 0; i < 10; i++) {
4429		int32_t x = f[i] ^ g[i];
4430		x &= b;
4431		f[i] ^= x;
4432		g[i] ^= x;
4433		}
4434		}
4435
4436		/*
4437		* h = f * 121666
4438		*
4439		* Can overlap h with f.
4440		*
4441		* Preconditions:
4442		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
4443		*
4444		* Postconditions:
4445		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
4446		*/
4447		static void fe_mul121666(fe h, fe f)
4448		{
4449		int32_t f0 = f[0];
4450		int32_t f1 = f[1];
4451		int32_t f2 = f[2];
4452		int32_t f3 = f[3];
4453		int32_t f4 = f[4];
4454		int32_t f5 = f[5];
4455		int32_t f6 = f[6];
4456		int32_t f7 = f[7];
4457		int32_t f8 = f[8];
4458		int32_t f9 = f[9];
4459		int64_t h0 = f0 * (int64_t)121666;
4460		int64_t h1 = f1 * (int64_t)121666;
4461		int64_t h2 = f2 * (int64_t)121666;
4462		int64_t h3 = f3 * (int64_t)121666;
4463		int64_t h4 = f4 * (int64_t)121666;
4464		int64_t h5 = f5 * (int64_t)121666;
4465		int64_t h6 = f6 * (int64_t)121666;
4466		int64_t h7 = f7 * (int64_t)121666;
4467		int64_t h8 = f8 * (int64_t)121666;
4468		int64_t h9 = f9 * (int64_t)121666;
4469		int64_t carry0;
4470		int64_t carry1;
4471		int64_t carry2;
4472		int64_t carry3;
4473		int64_t carry4;
4474		int64_t carry5;
4475		int64_t carry6;
4476		int64_t carry7;
4477		int64_t carry8;
4478		int64_t carry9;
4479
4480		carry9 = h9 + (1 << 24);
4481		h0 += (carry9 >> 25) * 19;
4482		h9 -= carry9 & kTop39Bits;
4483		carry1 = h1 + (1 << 24);
4484		h2 += carry1 >> 25;
4485		h1 -= carry1 & kTop39Bits;
4486		carry3 = h3 + (1 << 24);
4487		h4 += carry3 >> 25;
4488		h3 -= carry3 & kTop39Bits;
4489		carry5 = h5 + (1 << 24);
4490		h6 += carry5 >> 25;
4491		h5 -= carry5 & kTop39Bits;
4492		carry7 = h7 + (1 << 24);
4493		h8 += carry7 >> 25;
4494		h7 -= carry7 & kTop39Bits;
4495
4496		carry0 = h0 + (1 << 25);
4497		h1 += carry0 >> 26;
4498		h0 -= carry0 & kTop38Bits;
4499		carry2 = h2 + (1 << 25);
4500		h3 += carry2 >> 26;
4501		h2 -= carry2 & kTop38Bits;
4502		carry4 = h4 + (1 << 25);
4503		h5 += carry4 >> 26;
4504		h4 -= carry4 & kTop38Bits;
4505		carry6 = h6 + (1 << 25);
4506		h7 += carry6 >> 26;
4507		h6 -= carry6 & kTop38Bits;
4508		carry8 = h8 + (1 << 25);
4509		h9 += carry8 >> 26;
4510		h8 -= carry8 & kTop38Bits;
4511
4512		h[0] = (int32_t)h0;
4513		h[1] = (int32_t)h1;
4514		h[2] = (int32_t)h2;
4515		h[3] = (int32_t)h3;
4516		h[4] = (int32_t)h4;
4517		h[5] = (int32_t)h5;
4518		h[6] = (int32_t)h6;
4519		h[7] = (int32_t)h7;
4520		h[8] = (int32_t)h8;
4521		h[9] = (int32_t)h9;
4522		}
4523
4524		static void x25519_scalar_mult_generic(uint8_t out[32],
4525		const uint8_t scalar[32],
4526		const uint8_t point[32])
4527		{
4528		fe x1, x2, z2, x3, z3, tmp0, tmp1;
4529		uint8_t e[32];
4530		unsigned swap = 0;
4531		int pos;
4532
4533		memcpy(e, scalar, 32);
4534		e[0] &= 248;
4535		e[31] &= 127;
4536		e[31] \|= 64;
4537		fe_frombytes(x1, point);
4538		fe_1(x2);
4539		fe_0(z2);
4540		fe_copy(x3, x1);
4541		fe_1(z3);
4542
4543		for (pos = 254; pos >= 0; --pos) {
4544		unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4545		swap ^= b;
4546		fe_cswap(x2, x3, swap);
4547		fe_cswap(z2, z3, swap);
4548		swap = b;
4549		fe_sub(tmp0, x3, z3);
4550		fe_sub(tmp1, x2, z2);
4551		fe_add(x2, x2, z2);
4552		fe_add(z2, x3, z3);
4553		fe_mul(z3, tmp0, x2);
4554		fe_mul(z2, z2, tmp1);
4555		fe_sq(tmp0, tmp1);
4556		fe_sq(tmp1, x2);
4557		fe_add(x3, z3, z2);
4558		fe_sub(z2, z3, z2);
4559		fe_mul(x2, tmp1, tmp0);
4560		fe_sub(tmp1, tmp1, tmp0);
4561		fe_sq(z2, z2);
4562		fe_mul121666(z3, tmp1);
4563		fe_sq(x3, x3);
4564		fe_add(tmp0, tmp0, z3);
4565		fe_mul(z3, x1, z2);
4566		fe_mul(z2, tmp1, tmp0);
4567		}
4568
4569		fe_invert(z2, z2);
4570		fe_mul(x2, x2, z2);
4571		fe_tobytes(out, x2);
4572
4573		OPENSSL_cleanse(e, sizeof(e));
4574		}
4575
4576		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4577		const uint8_t point[32])
4578		{
4579		x25519_scalar_mult_generic(out, scalar, point);
4580		}
4581		#endif
4582
4583		static void slide(signed char r, const uint8_t a)
4584	0	{
4585	0	int i;
4586	0	int b;
4587	0	int k;
4588
4589	0	for (i = 0; i < 256; ++i) {
4590	0	r[i] = 1 & (a[i >> 3] >> (i & 7));
4591	0	}
4592
4593	0	for (i = 0; i < 256; ++i) {
4594	0	if (r[i]) {
4595	0	for (b = 1; b <= 6 && i + b < 256; ++b) {
4596	0	if (r[i + b]) {
4597	0	if (r[i] + (r[i + b] << b) <= 15) {
4598	0	r[i] += r[i + b] << b;
4599	0	r[i + b] = 0;
4600	0	} else if (r[i] - (r[i + b] << b) >= -15) {
4601	0	r[i] -= r[i + b] << b;
4602	0	for (k = i + b; k < 256; ++k) {
4603	0	if (!r[k]) {
4604	0	r[k] = 1;
4605	0	break;
4606	0	}
4607	0	r[k] = 0;
4608	0	}
4609	0	} else {
4610	0	break;
4611	0	}
4612	0	}
4613	0	}
4614	0	}
4615	0	}
4616	0	}
4617
4618		static const ge_precomp Bi[8] = {
4619		{
4620		{ 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4621		-11754271, -6079156, 2047605 },
4622		{ -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4623		5043384, 19500929, -15469378 },
4624		{ -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4625		11864899, -24514362, -4438546 },
4626		},
4627		{
4628		{ 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4629		-14772189, 28944400, -1550024 },
4630		{ 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4631		-11775962, 7689662, 11199574 },
4632		{ 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4633		10017326, -17749093, -9920357 },
4634		},
4635		{
4636		{ 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4637		14515107, -15438304, 10819380 },
4638		{ 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4639		12483688, -12668491, 5581306 },
4640		{ 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4641		13850243, -23678021, -15815942 },
4642		},
4643		{
4644		{ 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4645		5230134, -23952439, -15175766 },
4646		{ -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4647		16520125, 30598449, 7715701 },
4648		{ 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4649		1370708, 29794553, -1409300 },
4650		},
4651		{
4652		{ -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4653		-1361450, -13062696, 13821877 },
4654		{ -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4655		-7212327, 18853322, -14220951 },
4656		{ 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4657		-10431137, 2207753, -3209784 },
4658		},
4659		{
4660		{ -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4661		-663000, -31111463, -16132436 },
4662		{ 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4663		15725684, 171356, 6466918 },
4664		{ 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4665		-14088058, -30714912, 16193877 },
4666		},
4667		{
4668		{ -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4669		4729455, -18074513, 9256800 },
4670		{ -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4671		9761698, -19827198, 630305 },
4672		{ -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4673		-15960994, -2449256, -14291300 },
4674		},
4675		{
4676		{ -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4677		15033784, 25105118, -7894876 },
4678		{ -24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4679		1573892, -2625887, 2198790, -15804619 },
4680		{ -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4681		-16236442, -32461234, -12290683 },
4682		},
4683		};
4684
4685		/*
4686		* r = a * A + b * B
4687		*
4688		* where a = a[0]+256*a[1]+...+256^31 a[31].
4689		* and b = b[0]+256*b[1]+...+256^31 b[31].
4690		* B is the Ed25519 base point (x,4/5) with x positive.
4691		*/
4692		static void ge_double_scalarmult_vartime(ge_p2 r, const uint8_t a,
4693		const ge_p3 A, const uint8_t b)
4694	0	{
4695	0	signed char aslide[256];
4696	0	signed char bslide[256];
4697	0	ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4698	0	ge_p1p1 t;
4699	0	ge_p3 u;
4700	0	ge_p3 A2;
4701	0	int i;
4702
4703	0	slide(aslide, a);
4704	0	slide(bslide, b);
4705
4706	0	ge_p3_to_cached(&Ai[0], A);
4707	0	ge_p3_dbl(&t, A);
4708	0	ge_p1p1_to_p3(&A2, &t);
4709	0	ge_add(&t, &A2, &Ai[0]);
4710	0	ge_p1p1_to_p3(&u, &t);
4711	0	ge_p3_to_cached(&Ai[1], &u);
4712	0	ge_add(&t, &A2, &Ai[1]);
4713	0	ge_p1p1_to_p3(&u, &t);
4714	0	ge_p3_to_cached(&Ai[2], &u);
4715	0	ge_add(&t, &A2, &Ai[2]);
4716	0	ge_p1p1_to_p3(&u, &t);
4717	0	ge_p3_to_cached(&Ai[3], &u);
4718	0	ge_add(&t, &A2, &Ai[3]);
4719	0	ge_p1p1_to_p3(&u, &t);
4720	0	ge_p3_to_cached(&Ai[4], &u);
4721	0	ge_add(&t, &A2, &Ai[4]);
4722	0	ge_p1p1_to_p3(&u, &t);
4723	0	ge_p3_to_cached(&Ai[5], &u);
4724	0	ge_add(&t, &A2, &Ai[5]);
4725	0	ge_p1p1_to_p3(&u, &t);
4726	0	ge_p3_to_cached(&Ai[6], &u);
4727	0	ge_add(&t, &A2, &Ai[6]);
4728	0	ge_p1p1_to_p3(&u, &t);
4729	0	ge_p3_to_cached(&Ai[7], &u);
4730
4731	0	ge_p2_0(r);
4732
4733	0	for (i = 255; i >= 0; --i) {
4734	0	if (aslide[i] \|\| bslide[i]) {
4735	0	break;
4736	0	}
4737	0	}
4738
4739	0	for (; i >= 0; --i) {
4740	0	ge_p2_dbl(&t, r);
4741
4742	0	if (aslide[i] > 0) {
4743	0	ge_p1p1_to_p3(&u, &t);
4744	0	ge_add(&t, &u, &Ai[aslide[i] / 2]);
4745	0	} else if (aslide[i] < 0) {
4746	0	ge_p1p1_to_p3(&u, &t);
4747	0	ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4748	0	}
4749
4750	0	if (bslide[i] > 0) {
4751	0	ge_p1p1_to_p3(&u, &t);
4752	0	ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4753	0	} else if (bslide[i] < 0) {
4754	0	ge_p1p1_to_p3(&u, &t);
4755	0	ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4756	0	}
4757
4758	0	ge_p1p1_to_p2(r, &t);
4759	0	}
4760	0	}
4761
4762		/*
4763		* The set of scalars is \Z/l
4764		* where l = 2^252 + 27742317777372353535851937790883648493.
4765		*
4766		* Input:
4767		* s[0]+256s[1]+...+256^63s[63] = s
4768		*
4769		* Output:
4770		* s[0]+256s[1]+...+256^31s[31] = s mod l
4771		* where l = 2^252 + 27742317777372353535851937790883648493.
4772		* Overwrites s in place.
4773		*/
4774		static void x25519_sc_reduce(uint8_t *s)
4775	0	{
4776	0	int64_t s0 = kBottom21Bits & load_3(s);
4777	0	int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
4778	0	int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
4779	0	int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
4780	0	int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
4781	0	int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
4782	0	int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
4783	0	int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
4784	0	int64_t s8 = kBottom21Bits & load_3(s + 21);
4785	0	int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
4786	0	int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4787	0	int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4788	0	int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4789	0	int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4790	0	int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4791	0	int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4792	0	int64_t s16 = kBottom21Bits & load_3(s + 42);
4793	0	int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4794	0	int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4795	0	int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4796	0	int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4797	0	int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4798	0	int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4799	0	int64_t s23 = (load_4(s + 60) >> 3);
4800	0	int64_t carry0;
4801	0	int64_t carry1;
4802	0	int64_t carry2;
4803	0	int64_t carry3;
4804	0	int64_t carry4;
4805	0	int64_t carry5;
4806	0	int64_t carry6;
4807	0	int64_t carry7;
4808	0	int64_t carry8;
4809	0	int64_t carry9;
4810	0	int64_t carry10;
4811	0	int64_t carry11;
4812	0	int64_t carry12;
4813	0	int64_t carry13;
4814	0	int64_t carry14;
4815	0	int64_t carry15;
4816	0	int64_t carry16;
4817
4818	0	s11 += s23 * 666643;
4819	0	s12 += s23 * 470296;
4820	0	s13 += s23 * 654183;
4821	0	s14 -= s23 * 997805;
4822	0	s15 += s23 * 136657;
4823	0	s16 -= s23 * 683901;
4824	0	s23 = 0;
4825
4826	0	s10 += s22 * 666643;
4827	0	s11 += s22 * 470296;
4828	0	s12 += s22 * 654183;
4829	0	s13 -= s22 * 997805;
4830	0	s14 += s22 * 136657;
4831	0	s15 -= s22 * 683901;
4832	0	s22 = 0;
4833
4834	0	s9 += s21 * 666643;
4835	0	s10 += s21 * 470296;
4836	0	s11 += s21 * 654183;
4837	0	s12 -= s21 * 997805;
4838	0	s13 += s21 * 136657;
4839	0	s14 -= s21 * 683901;
4840	0	s21 = 0;
4841
4842	0	s8 += s20 * 666643;
4843	0	s9 += s20 * 470296;
4844	0	s10 += s20 * 654183;
4845	0	s11 -= s20 * 997805;
4846	0	s12 += s20 * 136657;
4847	0	s13 -= s20 * 683901;
4848	0	s20 = 0;
4849
4850	0	s7 += s19 * 666643;
4851	0	s8 += s19 * 470296;
4852	0	s9 += s19 * 654183;
4853	0	s10 -= s19 * 997805;
4854	0	s11 += s19 * 136657;
4855	0	s12 -= s19 * 683901;
4856	0	s19 = 0;
4857
4858	0	s6 += s18 * 666643;
4859	0	s7 += s18 * 470296;
4860	0	s8 += s18 * 654183;
4861	0	s9 -= s18 * 997805;
4862	0	s10 += s18 * 136657;
4863	0	s11 -= s18 * 683901;
4864	0	s18 = 0;
4865
4866	0	carry6 = (s6 + (1 << 20)) >> 21;
4867	0	s7 += carry6;
4868	0	s6 -= carry6 * (1 << 21);
4869	0	carry8 = (s8 + (1 << 20)) >> 21;
4870	0	s9 += carry8;
4871	0	s8 -= carry8 * (1 << 21);
4872	0	carry10 = (s10 + (1 << 20)) >> 21;
4873	0	s11 += carry10;
4874	0	s10 -= carry10 * (1 << 21);
4875	0	carry12 = (s12 + (1 << 20)) >> 21;
4876	0	s13 += carry12;
4877	0	s12 -= carry12 * (1 << 21);
4878	0	carry14 = (s14 + (1 << 20)) >> 21;
4879	0	s15 += carry14;
4880	0	s14 -= carry14 * (1 << 21);
4881	0	carry16 = (s16 + (1 << 20)) >> 21;
4882	0	s17 += carry16;
4883	0	s16 -= carry16 * (1 << 21);
4884
4885	0	carry7 = (s7 + (1 << 20)) >> 21;
4886	0	s8 += carry7;
4887	0	s7 -= carry7 * (1 << 21);
4888	0	carry9 = (s9 + (1 << 20)) >> 21;
4889	0	s10 += carry9;
4890	0	s9 -= carry9 * (1 << 21);
4891	0	carry11 = (s11 + (1 << 20)) >> 21;
4892	0	s12 += carry11;
4893	0	s11 -= carry11 * (1 << 21);
4894	0	carry13 = (s13 + (1 << 20)) >> 21;
4895	0	s14 += carry13;
4896	0	s13 -= carry13 * (1 << 21);
4897	0	carry15 = (s15 + (1 << 20)) >> 21;
4898	0	s16 += carry15;
4899	0	s15 -= carry15 * (1 << 21);
4900
4901	0	s5 += s17 * 666643;
4902	0	s6 += s17 * 470296;
4903	0	s7 += s17 * 654183;
4904	0	s8 -= s17 * 997805;
4905	0	s9 += s17 * 136657;
4906	0	s10 -= s17 * 683901;
4907	0	s17 = 0;
4908
4909	0	s4 += s16 * 666643;
4910	0	s5 += s16 * 470296;
4911	0	s6 += s16 * 654183;
4912	0	s7 -= s16 * 997805;
4913	0	s8 += s16 * 136657;
4914	0	s9 -= s16 * 683901;
4915	0	s16 = 0;
4916
4917	0	s3 += s15 * 666643;
4918	0	s4 += s15 * 470296;
4919	0	s5 += s15 * 654183;
4920	0	s6 -= s15 * 997805;
4921	0	s7 += s15 * 136657;
4922	0	s8 -= s15 * 683901;
4923	0	s15 = 0;
4924
4925	0	s2 += s14 * 666643;
4926	0	s3 += s14 * 470296;
4927	0	s4 += s14 * 654183;
4928	0	s5 -= s14 * 997805;
4929	0	s6 += s14 * 136657;
4930	0	s7 -= s14 * 683901;
4931	0	s14 = 0;
4932
4933	0	s1 += s13 * 666643;
4934	0	s2 += s13 * 470296;
4935	0	s3 += s13 * 654183;
4936	0	s4 -= s13 * 997805;
4937	0	s5 += s13 * 136657;
4938	0	s6 -= s13 * 683901;
4939	0	s13 = 0;
4940
4941	0	s0 += s12 * 666643;
4942	0	s1 += s12 * 470296;
4943	0	s2 += s12 * 654183;
4944	0	s3 -= s12 * 997805;
4945	0	s4 += s12 * 136657;
4946	0	s5 -= s12 * 683901;
4947	0	s12 = 0;
4948
4949	0	carry0 = (s0 + (1 << 20)) >> 21;
4950	0	s1 += carry0;
4951	0	s0 -= carry0 * (1 << 21);
4952	0	carry2 = (s2 + (1 << 20)) >> 21;
4953	0	s3 += carry2;
4954	0	s2 -= carry2 * (1 << 21);
4955	0	carry4 = (s4 + (1 << 20)) >> 21;
4956	0	s5 += carry4;
4957	0	s4 -= carry4 * (1 << 21);
4958	0	carry6 = (s6 + (1 << 20)) >> 21;
4959	0	s7 += carry6;
4960	0	s6 -= carry6 * (1 << 21);
4961	0	carry8 = (s8 + (1 << 20)) >> 21;
4962	0	s9 += carry8;
4963	0	s8 -= carry8 * (1 << 21);
4964	0	carry10 = (s10 + (1 << 20)) >> 21;
4965	0	s11 += carry10;
4966	0	s10 -= carry10 * (1 << 21);
4967
4968	0	carry1 = (s1 + (1 << 20)) >> 21;
4969	0	s2 += carry1;
4970	0	s1 -= carry1 * (1 << 21);
4971	0	carry3 = (s3 + (1 << 20)) >> 21;
4972	0	s4 += carry3;
4973	0	s3 -= carry3 * (1 << 21);
4974	0	carry5 = (s5 + (1 << 20)) >> 21;
4975	0	s6 += carry5;
4976	0	s5 -= carry5 * (1 << 21);
4977	0	carry7 = (s7 + (1 << 20)) >> 21;
4978	0	s8 += carry7;
4979	0	s7 -= carry7 * (1 << 21);
4980	0	carry9 = (s9 + (1 << 20)) >> 21;
4981	0	s10 += carry9;
4982	0	s9 -= carry9 * (1 << 21);
4983	0	carry11 = (s11 + (1 << 20)) >> 21;
4984	0	s12 += carry11;
4985	0	s11 -= carry11 * (1 << 21);
4986
4987	0	s0 += s12 * 666643;
4988	0	s1 += s12 * 470296;
4989	0	s2 += s12 * 654183;
4990	0	s3 -= s12 * 997805;
4991	0	s4 += s12 * 136657;
4992	0	s5 -= s12 * 683901;
4993	0	s12 = 0;
4994
4995	0	carry0 = s0 >> 21;
4996	0	s1 += carry0;
4997	0	s0 -= carry0 * (1 << 21);
4998	0	carry1 = s1 >> 21;
4999	0	s2 += carry1;
5000	0	s1 -= carry1 * (1 << 21);
5001	0	carry2 = s2 >> 21;
5002	0	s3 += carry2;
5003	0	s2 -= carry2 * (1 << 21);
5004	0	carry3 = s3 >> 21;
5005	0	s4 += carry3;
5006	0	s3 -= carry3 * (1 << 21);
5007	0	carry4 = s4 >> 21;
5008	0	s5 += carry4;
5009	0	s4 -= carry4 * (1 << 21);
5010	0	carry5 = s5 >> 21;
5011	0	s6 += carry5;
5012	0	s5 -= carry5 * (1 << 21);
5013	0	carry6 = s6 >> 21;
5014	0	s7 += carry6;
5015	0	s6 -= carry6 * (1 << 21);
5016	0	carry7 = s7 >> 21;
5017	0	s8 += carry7;
5018	0	s7 -= carry7 * (1 << 21);
5019	0	carry8 = s8 >> 21;
5020	0	s9 += carry8;
5021	0	s8 -= carry8 * (1 << 21);
5022	0	carry9 = s9 >> 21;
5023	0	s10 += carry9;
5024	0	s9 -= carry9 * (1 << 21);
5025	0	carry10 = s10 >> 21;
5026	0	s11 += carry10;
5027	0	s10 -= carry10 * (1 << 21);
5028	0	carry11 = s11 >> 21;
5029	0	s12 += carry11;
5030	0	s11 -= carry11 * (1 << 21);
5031
5032	0	s0 += s12 * 666643;
5033	0	s1 += s12 * 470296;
5034	0	s2 += s12 * 654183;
5035	0	s3 -= s12 * 997805;
5036	0	s4 += s12 * 136657;
5037	0	s5 -= s12 * 683901;
5038	0	s12 = 0;
5039
5040	0	carry0 = s0 >> 21;
5041	0	s1 += carry0;
5042	0	s0 -= carry0 * (1 << 21);
5043	0	carry1 = s1 >> 21;
5044	0	s2 += carry1;
5045	0	s1 -= carry1 * (1 << 21);
5046	0	carry2 = s2 >> 21;
5047	0	s3 += carry2;
5048	0	s2 -= carry2 * (1 << 21);
5049	0	carry3 = s3 >> 21;
5050	0	s4 += carry3;
5051	0	s3 -= carry3 * (1 << 21);
5052	0	carry4 = s4 >> 21;
5053	0	s5 += carry4;
5054	0	s4 -= carry4 * (1 << 21);
5055	0	carry5 = s5 >> 21;
5056	0	s6 += carry5;
5057	0	s5 -= carry5 * (1 << 21);
5058	0	carry6 = s6 >> 21;
5059	0	s7 += carry6;
5060	0	s6 -= carry6 * (1 << 21);
5061	0	carry7 = s7 >> 21;
5062	0	s8 += carry7;
5063	0	s7 -= carry7 * (1 << 21);
5064	0	carry8 = s8 >> 21;
5065	0	s9 += carry8;
5066	0	s8 -= carry8 * (1 << 21);
5067	0	carry9 = s9 >> 21;
5068	0	s10 += carry9;
5069	0	s9 -= carry9 * (1 << 21);
5070	0	carry10 = s10 >> 21;
5071	0	s11 += carry10;
5072	0	s10 -= carry10 * (1 << 21);
5073
5074	0	s[0] = (uint8_t)(s0 >> 0);
5075	0	s[1] = (uint8_t)(s0 >> 8);
5076	0	s[2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5077	0	s[3] = (uint8_t)(s1 >> 3);
5078	0	s[4] = (uint8_t)(s1 >> 11);
5079	0	s[5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5080	0	s[6] = (uint8_t)(s2 >> 6);
5081	0	s[7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5082	0	s[8] = (uint8_t)(s3 >> 1);
5083	0	s[9] = (uint8_t)(s3 >> 9);
5084	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5085	0	s[11] = (uint8_t)(s4 >> 4);
5086	0	s[12] = (uint8_t)(s4 >> 12);
5087	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5088	0	s[14] = (uint8_t)(s5 >> 7);
5089	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5090	0	s[16] = (uint8_t)(s6 >> 2);
5091	0	s[17] = (uint8_t)(s6 >> 10);
5092	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5093	0	s[19] = (uint8_t)(s7 >> 5);
5094	0	s[20] = (uint8_t)(s7 >> 13);
5095	0	s[21] = (uint8_t)(s8 >> 0);
5096	0	s[22] = (uint8_t)(s8 >> 8);
5097	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5098	0	s[24] = (uint8_t)(s9 >> 3);
5099	0	s[25] = (uint8_t)(s9 >> 11);
5100	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5101	0	s[27] = (uint8_t)(s10 >> 6);
5102	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5103	0	s[29] = (uint8_t)(s11 >> 1);
5104	0	s[30] = (uint8_t)(s11 >> 9);
5105	0	s[31] = (uint8_t)(s11 >> 17);
5106	0	}
5107
5108		/*
5109		* Input:
5110		* a[0]+256a[1]+...+256^31a[31] = a
5111		* b[0]+256b[1]+...+256^31b[31] = b
5112		* c[0]+256c[1]+...+256^31c[31] = c
5113		*
5114		* Output:
5115		* s[0]+256s[1]+...+256^31s[31] = (ab+c) mod l
5116		* where l = 2^252 + 27742317777372353535851937790883648493.
5117		*/
5118		static void sc_muladd(uint8_t s, const uint8_t a, const uint8_t *b,
5119		const uint8_t *c)
5120	0	{
5121	0	int64_t a0 = kBottom21Bits & load_3(a);
5122	0	int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
5123	0	int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
5124	0	int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
5125	0	int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
5126	0	int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
5127	0	int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
5128	0	int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
5129	0	int64_t a8 = kBottom21Bits & load_3(a + 21);
5130	0	int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
5131	0	int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
5132	0	int64_t a11 = (load_4(a + 28) >> 7);
5133	0	int64_t b0 = kBottom21Bits & load_3(b);
5134	0	int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
5135	0	int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
5136	0	int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
5137	0	int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
5138	0	int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
5139	0	int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
5140	0	int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
5141	0	int64_t b8 = kBottom21Bits & load_3(b + 21);
5142	0	int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
5143	0	int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
5144	0	int64_t b11 = (load_4(b + 28) >> 7);
5145	0	int64_t c0 = kBottom21Bits & load_3(c);
5146	0	int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
5147	0	int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
5148	0	int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
5149	0	int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
5150	0	int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
5151	0	int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
5152	0	int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
5153	0	int64_t c8 = kBottom21Bits & load_3(c + 21);
5154	0	int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
5155	0	int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
5156	0	int64_t c11 = (load_4(c + 28) >> 7);
5157	0	int64_t s0;
5158	0	int64_t s1;
5159	0	int64_t s2;
5160	0	int64_t s3;
5161	0	int64_t s4;
5162	0	int64_t s5;
5163	0	int64_t s6;
5164	0	int64_t s7;
5165	0	int64_t s8;
5166	0	int64_t s9;
5167	0	int64_t s10;
5168	0	int64_t s11;
5169	0	int64_t s12;
5170	0	int64_t s13;
5171	0	int64_t s14;
5172	0	int64_t s15;
5173	0	int64_t s16;
5174	0	int64_t s17;
5175	0	int64_t s18;
5176	0	int64_t s19;
5177	0	int64_t s20;
5178	0	int64_t s21;
5179	0	int64_t s22;
5180	0	int64_t s23;
5181	0	int64_t carry0;
5182	0	int64_t carry1;
5183	0	int64_t carry2;
5184	0	int64_t carry3;
5185	0	int64_t carry4;
5186	0	int64_t carry5;
5187	0	int64_t carry6;
5188	0	int64_t carry7;
5189	0	int64_t carry8;
5190	0	int64_t carry9;
5191	0	int64_t carry10;
5192	0	int64_t carry11;
5193	0	int64_t carry12;
5194	0	int64_t carry13;
5195	0	int64_t carry14;
5196	0	int64_t carry15;
5197	0	int64_t carry16;
5198	0	int64_t carry17;
5199	0	int64_t carry18;
5200	0	int64_t carry19;
5201	0	int64_t carry20;
5202	0	int64_t carry21;
5203	0	int64_t carry22;
5204
5205	0	s0 = c0 + a0 * b0;
5206	0	s1 = c1 + a0 * b1 + a1 * b0;
5207	0	s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
5208	0	s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
5209	0	s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
5210	0	s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
5211	0	s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
5212	0	s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
5213	0	s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
5214	0	s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
5215	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;
5216	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;
5217	0	s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
5218	0	s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
5219	0	s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
5220	0	s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
5221	0	s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
5222	0	s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
5223	0	s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
5224	0	s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
5225	0	s20 = a9 * b11 + a10 * b10 + a11 * b9;
5226	0	s21 = a10 * b11 + a11 * b10;
5227	0	s22 = a11 * b11;
5228	0	s23 = 0;
5229
5230	0	carry0 = (s0 + (1 << 20)) >> 21;
5231	0	s1 += carry0;
5232	0	s0 -= carry0 * (1 << 21);
5233	0	carry2 = (s2 + (1 << 20)) >> 21;
5234	0	s3 += carry2;
5235	0	s2 -= carry2 * (1 << 21);
5236	0	carry4 = (s4 + (1 << 20)) >> 21;
5237	0	s5 += carry4;
5238	0	s4 -= carry4 * (1 << 21);
5239	0	carry6 = (s6 + (1 << 20)) >> 21;
5240	0	s7 += carry6;
5241	0	s6 -= carry6 * (1 << 21);
5242	0	carry8 = (s8 + (1 << 20)) >> 21;
5243	0	s9 += carry8;
5244	0	s8 -= carry8 * (1 << 21);
5245	0	carry10 = (s10 + (1 << 20)) >> 21;
5246	0	s11 += carry10;
5247	0	s10 -= carry10 * (1 << 21);
5248	0	carry12 = (s12 + (1 << 20)) >> 21;
5249	0	s13 += carry12;
5250	0	s12 -= carry12 * (1 << 21);
5251	0	carry14 = (s14 + (1 << 20)) >> 21;
5252	0	s15 += carry14;
5253	0	s14 -= carry14 * (1 << 21);
5254	0	carry16 = (s16 + (1 << 20)) >> 21;
5255	0	s17 += carry16;
5256	0	s16 -= carry16 * (1 << 21);
5257	0	carry18 = (s18 + (1 << 20)) >> 21;
5258	0	s19 += carry18;
5259	0	s18 -= carry18 * (1 << 21);
5260	0	carry20 = (s20 + (1 << 20)) >> 21;
5261	0	s21 += carry20;
5262	0	s20 -= carry20 * (1 << 21);
5263	0	carry22 = (s22 + (1 << 20)) >> 21;
5264	0	s23 += carry22;
5265	0	s22 -= carry22 * (1 << 21);
5266
5267	0	carry1 = (s1 + (1 << 20)) >> 21;
5268	0	s2 += carry1;
5269	0	s1 -= carry1 * (1 << 21);
5270	0	carry3 = (s3 + (1 << 20)) >> 21;
5271	0	s4 += carry3;
5272	0	s3 -= carry3 * (1 << 21);
5273	0	carry5 = (s5 + (1 << 20)) >> 21;
5274	0	s6 += carry5;
5275	0	s5 -= carry5 * (1 << 21);
5276	0	carry7 = (s7 + (1 << 20)) >> 21;
5277	0	s8 += carry7;
5278	0	s7 -= carry7 * (1 << 21);
5279	0	carry9 = (s9 + (1 << 20)) >> 21;
5280	0	s10 += carry9;
5281	0	s9 -= carry9 * (1 << 21);
5282	0	carry11 = (s11 + (1 << 20)) >> 21;
5283	0	s12 += carry11;
5284	0	s11 -= carry11 * (1 << 21);
5285	0	carry13 = (s13 + (1 << 20)) >> 21;
5286	0	s14 += carry13;
5287	0	s13 -= carry13 * (1 << 21);
5288	0	carry15 = (s15 + (1 << 20)) >> 21;
5289	0	s16 += carry15;
5290	0	s15 -= carry15 * (1 << 21);
5291	0	carry17 = (s17 + (1 << 20)) >> 21;
5292	0	s18 += carry17;
5293	0	s17 -= carry17 * (1 << 21);
5294	0	carry19 = (s19 + (1 << 20)) >> 21;
5295	0	s20 += carry19;
5296	0	s19 -= carry19 * (1 << 21);
5297	0	carry21 = (s21 + (1 << 20)) >> 21;
5298	0	s22 += carry21;
5299	0	s21 -= carry21 * (1 << 21);
5300
5301	0	s11 += s23 * 666643;
5302	0	s12 += s23 * 470296;
5303	0	s13 += s23 * 654183;
5304	0	s14 -= s23 * 997805;
5305	0	s15 += s23 * 136657;
5306	0	s16 -= s23 * 683901;
5307	0	s23 = 0;
5308
5309	0	s10 += s22 * 666643;
5310	0	s11 += s22 * 470296;
5311	0	s12 += s22 * 654183;
5312	0	s13 -= s22 * 997805;
5313	0	s14 += s22 * 136657;
5314	0	s15 -= s22 * 683901;
5315	0	s22 = 0;
5316
5317	0	s9 += s21 * 666643;
5318	0	s10 += s21 * 470296;
5319	0	s11 += s21 * 654183;
5320	0	s12 -= s21 * 997805;
5321	0	s13 += s21 * 136657;
5322	0	s14 -= s21 * 683901;
5323	0	s21 = 0;
5324
5325	0	s8 += s20 * 666643;
5326	0	s9 += s20 * 470296;
5327	0	s10 += s20 * 654183;
5328	0	s11 -= s20 * 997805;
5329	0	s12 += s20 * 136657;
5330	0	s13 -= s20 * 683901;
5331	0	s20 = 0;
5332
5333	0	s7 += s19 * 666643;
5334	0	s8 += s19 * 470296;
5335	0	s9 += s19 * 654183;
5336	0	s10 -= s19 * 997805;
5337	0	s11 += s19 * 136657;
5338	0	s12 -= s19 * 683901;
5339	0	s19 = 0;
5340
5341	0	s6 += s18 * 666643;
5342	0	s7 += s18 * 470296;
5343	0	s8 += s18 * 654183;
5344	0	s9 -= s18 * 997805;
5345	0	s10 += s18 * 136657;
5346	0	s11 -= s18 * 683901;
5347	0	s18 = 0;
5348
5349	0	carry6 = (s6 + (1 << 20)) >> 21;
5350	0	s7 += carry6;
5351	0	s6 -= carry6 * (1 << 21);
5352	0	carry8 = (s8 + (1 << 20)) >> 21;
5353	0	s9 += carry8;
5354	0	s8 -= carry8 * (1 << 21);
5355	0	carry10 = (s10 + (1 << 20)) >> 21;
5356	0	s11 += carry10;
5357	0	s10 -= carry10 * (1 << 21);
5358	0	carry12 = (s12 + (1 << 20)) >> 21;
5359	0	s13 += carry12;
5360	0	s12 -= carry12 * (1 << 21);
5361	0	carry14 = (s14 + (1 << 20)) >> 21;
5362	0	s15 += carry14;
5363	0	s14 -= carry14 * (1 << 21);
5364	0	carry16 = (s16 + (1 << 20)) >> 21;
5365	0	s17 += carry16;
5366	0	s16 -= carry16 * (1 << 21);
5367
5368	0	carry7 = (s7 + (1 << 20)) >> 21;
5369	0	s8 += carry7;
5370	0	s7 -= carry7 * (1 << 21);
5371	0	carry9 = (s9 + (1 << 20)) >> 21;
5372	0	s10 += carry9;
5373	0	s9 -= carry9 * (1 << 21);
5374	0	carry11 = (s11 + (1 << 20)) >> 21;
5375	0	s12 += carry11;
5376	0	s11 -= carry11 * (1 << 21);
5377	0	carry13 = (s13 + (1 << 20)) >> 21;
5378	0	s14 += carry13;
5379	0	s13 -= carry13 * (1 << 21);
5380	0	carry15 = (s15 + (1 << 20)) >> 21;
5381	0	s16 += carry15;
5382	0	s15 -= carry15 * (1 << 21);
5383
5384	0	s5 += s17 * 666643;
5385	0	s6 += s17 * 470296;
5386	0	s7 += s17 * 654183;
5387	0	s8 -= s17 * 997805;
5388	0	s9 += s17 * 136657;
5389	0	s10 -= s17 * 683901;
5390	0	s17 = 0;
5391
5392	0	s4 += s16 * 666643;
5393	0	s5 += s16 * 470296;
5394	0	s6 += s16 * 654183;
5395	0	s7 -= s16 * 997805;
5396	0	s8 += s16 * 136657;
5397	0	s9 -= s16 * 683901;
5398	0	s16 = 0;
5399
5400	0	s3 += s15 * 666643;
5401	0	s4 += s15 * 470296;
5402	0	s5 += s15 * 654183;
5403	0	s6 -= s15 * 997805;
5404	0	s7 += s15 * 136657;
5405	0	s8 -= s15 * 683901;
5406	0	s15 = 0;
5407
5408	0	s2 += s14 * 666643;
5409	0	s3 += s14 * 470296;
5410	0	s4 += s14 * 654183;
5411	0	s5 -= s14 * 997805;
5412	0	s6 += s14 * 136657;
5413	0	s7 -= s14 * 683901;
5414	0	s14 = 0;
5415
5416	0	s1 += s13 * 666643;
5417	0	s2 += s13 * 470296;
5418	0	s3 += s13 * 654183;
5419	0	s4 -= s13 * 997805;
5420	0	s5 += s13 * 136657;
5421	0	s6 -= s13 * 683901;
5422	0	s13 = 0;
5423
5424	0	s0 += s12 * 666643;
5425	0	s1 += s12 * 470296;
5426	0	s2 += s12 * 654183;
5427	0	s3 -= s12 * 997805;
5428	0	s4 += s12 * 136657;
5429	0	s5 -= s12 * 683901;
5430	0	s12 = 0;
5431
5432	0	carry0 = (s0 + (1 << 20)) >> 21;
5433	0	s1 += carry0;
5434	0	s0 -= carry0 * (1 << 21);
5435	0	carry2 = (s2 + (1 << 20)) >> 21;
5436	0	s3 += carry2;
5437	0	s2 -= carry2 * (1 << 21);
5438	0	carry4 = (s4 + (1 << 20)) >> 21;
5439	0	s5 += carry4;
5440	0	s4 -= carry4 * (1 << 21);
5441	0	carry6 = (s6 + (1 << 20)) >> 21;
5442	0	s7 += carry6;
5443	0	s6 -= carry6 * (1 << 21);
5444	0	carry8 = (s8 + (1 << 20)) >> 21;
5445	0	s9 += carry8;
5446	0	s8 -= carry8 * (1 << 21);
5447	0	carry10 = (s10 + (1 << 20)) >> 21;
5448	0	s11 += carry10;
5449	0	s10 -= carry10 * (1 << 21);
5450
5451	0	carry1 = (s1 + (1 << 20)) >> 21;
5452	0	s2 += carry1;
5453	0	s1 -= carry1 * (1 << 21);
5454	0	carry3 = (s3 + (1 << 20)) >> 21;
5455	0	s4 += carry3;
5456	0	s3 -= carry3 * (1 << 21);
5457	0	carry5 = (s5 + (1 << 20)) >> 21;
5458	0	s6 += carry5;
5459	0	s5 -= carry5 * (1 << 21);
5460	0	carry7 = (s7 + (1 << 20)) >> 21;
5461	0	s8 += carry7;
5462	0	s7 -= carry7 * (1 << 21);
5463	0	carry9 = (s9 + (1 << 20)) >> 21;
5464	0	s10 += carry9;
5465	0	s9 -= carry9 * (1 << 21);
5466	0	carry11 = (s11 + (1 << 20)) >> 21;
5467	0	s12 += carry11;
5468	0	s11 -= carry11 * (1 << 21);
5469
5470	0	s0 += s12 * 666643;
5471	0	s1 += s12 * 470296;
5472	0	s2 += s12 * 654183;
5473	0	s3 -= s12 * 997805;
5474	0	s4 += s12 * 136657;
5475	0	s5 -= s12 * 683901;
5476	0	s12 = 0;
5477
5478	0	carry0 = s0 >> 21;
5479	0	s1 += carry0;
5480	0	s0 -= carry0 * (1 << 21);
5481	0	carry1 = s1 >> 21;
5482	0	s2 += carry1;
5483	0	s1 -= carry1 * (1 << 21);
5484	0	carry2 = s2 >> 21;
5485	0	s3 += carry2;
5486	0	s2 -= carry2 * (1 << 21);
5487	0	carry3 = s3 >> 21;
5488	0	s4 += carry3;
5489	0	s3 -= carry3 * (1 << 21);
5490	0	carry4 = s4 >> 21;
5491	0	s5 += carry4;
5492	0	s4 -= carry4 * (1 << 21);
5493	0	carry5 = s5 >> 21;
5494	0	s6 += carry5;
5495	0	s5 -= carry5 * (1 << 21);
5496	0	carry6 = s6 >> 21;
5497	0	s7 += carry6;
5498	0	s6 -= carry6 * (1 << 21);
5499	0	carry7 = s7 >> 21;
5500	0	s8 += carry7;
5501	0	s7 -= carry7 * (1 << 21);
5502	0	carry8 = s8 >> 21;
5503	0	s9 += carry8;
5504	0	s8 -= carry8 * (1 << 21);
5505	0	carry9 = s9 >> 21;
5506	0	s10 += carry9;
5507	0	s9 -= carry9 * (1 << 21);
5508	0	carry10 = s10 >> 21;
5509	0	s11 += carry10;
5510	0	s10 -= carry10 * (1 << 21);
5511	0	carry11 = s11 >> 21;
5512	0	s12 += carry11;
5513	0	s11 -= carry11 * (1 << 21);
5514
5515	0	s0 += s12 * 666643;
5516	0	s1 += s12 * 470296;
5517	0	s2 += s12 * 654183;
5518	0	s3 -= s12 * 997805;
5519	0	s4 += s12 * 136657;
5520	0	s5 -= s12 * 683901;
5521	0	s12 = 0;
5522
5523	0	carry0 = s0 >> 21;
5524	0	s1 += carry0;
5525	0	s0 -= carry0 * (1 << 21);
5526	0	carry1 = s1 >> 21;
5527	0	s2 += carry1;
5528	0	s1 -= carry1 * (1 << 21);
5529	0	carry2 = s2 >> 21;
5530	0	s3 += carry2;
5531	0	s2 -= carry2 * (1 << 21);
5532	0	carry3 = s3 >> 21;
5533	0	s4 += carry3;
5534	0	s3 -= carry3 * (1 << 21);
5535	0	carry4 = s4 >> 21;
5536	0	s5 += carry4;
5537	0	s4 -= carry4 * (1 << 21);
5538	0	carry5 = s5 >> 21;
5539	0	s6 += carry5;
5540	0	s5 -= carry5 * (1 << 21);
5541	0	carry6 = s6 >> 21;
5542	0	s7 += carry6;
5543	0	s6 -= carry6 * (1 << 21);
5544	0	carry7 = s7 >> 21;
5545	0	s8 += carry7;
5546	0	s7 -= carry7 * (1 << 21);
5547	0	carry8 = s8 >> 21;
5548	0	s9 += carry8;
5549	0	s8 -= carry8 * (1 << 21);
5550	0	carry9 = s9 >> 21;
5551	0	s10 += carry9;
5552	0	s9 -= carry9 * (1 << 21);
5553	0	carry10 = s10 >> 21;
5554	0	s11 += carry10;
5555	0	s10 -= carry10 * (1 << 21);
5556
5557	0	s[0] = (uint8_t)(s0 >> 0);
5558	0	s[1] = (uint8_t)(s0 >> 8);
5559	0	s[2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5560	0	s[3] = (uint8_t)(s1 >> 3);
5561	0	s[4] = (uint8_t)(s1 >> 11);
5562	0	s[5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5563	0	s[6] = (uint8_t)(s2 >> 6);
5564	0	s[7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5565	0	s[8] = (uint8_t)(s3 >> 1);
5566	0	s[9] = (uint8_t)(s3 >> 9);
5567	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5568	0	s[11] = (uint8_t)(s4 >> 4);
5569	0	s[12] = (uint8_t)(s4 >> 12);
5570	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5571	0	s[14] = (uint8_t)(s5 >> 7);
5572	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5573	0	s[16] = (uint8_t)(s6 >> 2);
5574	0	s[17] = (uint8_t)(s6 >> 10);
5575	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5576	0	s[19] = (uint8_t)(s7 >> 5);
5577	0	s[20] = (uint8_t)(s7 >> 13);
5578	0	s[21] = (uint8_t)(s8 >> 0);
5579	0	s[22] = (uint8_t)(s8 >> 8);
5580	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5581	0	s[24] = (uint8_t)(s9 >> 3);
5582	0	s[25] = (uint8_t)(s9 >> 11);
5583	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5584	0	s[27] = (uint8_t)(s10 >> 6);
5585	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5586	0	s[29] = (uint8_t)(s11 >> 1);
5587	0	s[30] = (uint8_t)(s11 >> 9);
5588	0	s[31] = (uint8_t)(s11 >> 17);
5589	0	}
5590
5591		static int hash_init_with_dom(EVP_MD_CTX *hash_ctx,
5592		EVP_MD *sha512,
5593		const uint8_t dom2flag,
5594		const uint8_t phflag,
5595		const uint8_t *context,
5596		const size_t context_len)
5597	0	{
5598		/* ASCII: "SigEd25519 no Ed25519 collisions", in hex for EBCDIC compatibility */
5599	0	const char dom_s[] = "\x53\x69\x67\x45\x64\x32\x35\x35\x31\x39\x20\x6e"
5600	0	"\x6f\x20\x45\x64\x32\x35\x35\x31\x39\x20\x63\x6f"
5601	0	"\x6c\x6c\x69\x73\x69\x6f\x6e\x73";
5602	0	uint8_t dom[2];
5603
5604	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL))
5605	0	return 0;
5606
5607		/* return early if dom2flag is not set */
5608	0	if (!dom2flag)
5609	0	return 1;
5610
5611	0	if (context_len > UINT8_MAX)
5612	0	return 0;
5613
5614	0	dom[0] = (uint8_t)(phflag >= 1 ? 1 : 0);
5615	0	dom[1] = (uint8_t)context_len;
5616
5617	0	if (!EVP_DigestUpdate(hash_ctx, dom_s, sizeof(dom_s) - 1)
5618	0	\|\| !EVP_DigestUpdate(hash_ctx, dom, sizeof(dom))
5619	0	\|\| !EVP_DigestUpdate(hash_ctx, context, context_len)) {
5620	0	return 0;
5621	0	}
5622
5623	0	return 1;
5624	0	}
5625
5626		int ossl_ed25519_sign(uint8_t out_sig, const uint8_t tbs, size_t tbs_len,
5627		const uint8_t public_key[32], const uint8_t private_key[32],
5628		const uint8_t dom2flag, const uint8_t phflag, const uint8_t csflag,
5629		const uint8_t *context, size_t context_len,
5630		OSSL_LIB_CTX libctx, const char propq)
5631	0	{
5632	0	uint8_t az[SHA512_DIGEST_LENGTH];
5633	0	uint8_t nonce[SHA512_DIGEST_LENGTH];
5634	0	ge_p3 R;
5635	0	uint8_t hram[SHA512_DIGEST_LENGTH];
5636	0	EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5637	0	EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
5638	0	unsigned int sz;
5639	0	int res = 0;
5640
5641	0	if (context == NULL)
5642	0	context_len = 0;
5643
5644		/* if csflag is set, then a non-empty context-string is required */
5645	0	if (csflag && context_len == 0)
5646	0	goto err;
5647
5648		/* if dom2flag is not set, then an empty context-string is required */
5649	0	if (!dom2flag && context_len > 0)
5650	0	goto err;
5651
5652	0	if (sha512 == NULL \|\| hash_ctx == NULL)
5653	0	goto err;
5654
5655	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5656	0	\|\| !EVP_DigestUpdate(hash_ctx, private_key, 32)
5657	0	\|\| !EVP_DigestFinal_ex(hash_ctx, az, &sz))
5658	0	goto err;
5659
5660	0	az[0] &= 248;
5661	0	az[31] &= 63;
5662	0	az[31] \|= 64;
5663
5664	0	if (!hash_init_with_dom(hash_ctx, sha512, dom2flag, phflag, context, context_len)
5665	0	\|\| !EVP_DigestUpdate(hash_ctx, az + 32, 32)
5666	0	\|\| !EVP_DigestUpdate(hash_ctx, tbs, tbs_len)
5667	0	\|\| !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
5668	0	goto err;
5669
5670	0	x25519_sc_reduce(nonce);
5671	0	ge_scalarmult_base(&R, nonce);
5672	0	ge_p3_tobytes(out_sig, &R);
5673
5674	0	if (!hash_init_with_dom(hash_ctx, sha512, dom2flag, phflag, context, context_len)
5675	0	\|\| !EVP_DigestUpdate(hash_ctx, out_sig, 32)
5676	0	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5677	0	\|\| !EVP_DigestUpdate(hash_ctx, tbs, tbs_len)
5678	0	\|\| !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
5679	0	goto err;
5680
5681	0	x25519_sc_reduce(hram);
5682	0	sc_muladd(out_sig + 32, hram, az, nonce);
5683
5684	0	res = 1;
5685	0	err:
5686	0	OPENSSL_cleanse(nonce, sizeof(nonce));
5687	0	OPENSSL_cleanse(az, sizeof(az));
5688	0	EVP_MD_free(sha512);
5689	0	EVP_MD_CTX_free(hash_ctx);
5690	0	return res;
5691	0	}
5692
5693		/*
5694		* This function should not be necessary since ossl_ed25519_verify() already
5695		* does this check internally.
5696		* For some reason the FIPS ACVP requires a EDDSA KeyVer test.
5697		*/
5698		int ossl_ed25519_pubkey_verify(const uint8_t *pub, size_t pub_len)
5699	0	{
5700	0	ge_p3 A;
5701
5702	0	if (pub_len != ED25519_KEYLEN)
5703	0	return 0;
5704	0	return (ge_frombytes_vartime(&A, pub) == 0);
5705	0	}
5706
5707		static const char allzeroes[15];
5708
5709		int ossl_ed25519_verify(const uint8_t *tbs, size_t tbs_len,
5710		const uint8_t signature[64], const uint8_t public_key[32],
5711		const uint8_t dom2flag, const uint8_t phflag, const uint8_t csflag,
5712		const uint8_t *context, size_t context_len,
5713		OSSL_LIB_CTX libctx, const char propq)
5714	0	{
5715	0	int i;
5716	0	ge_p3 A;
5717	0	const uint8_t r, s;
5718	0	EVP_MD *sha512;
5719	0	EVP_MD_CTX *hash_ctx = NULL;
5720	0	unsigned int sz;
5721	0	int res = 0;
5722	0	ge_p2 R;
5723	0	uint8_t rcheck[32];
5724	0	uint8_t h[SHA512_DIGEST_LENGTH];
5725		/* 27742317777372353535851937790883648493 in little endian format */
5726	0	const uint8_t l_low[16] = {
5727	0	0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5728	0	0xDE, 0xF9, 0xDE, 0x14
5729	0	};
5730
5731	0	if (context == NULL)
5732	0	context_len = 0;
5733
5734		/* if csflag is set, then a non-empty context-string is required */
5735	0	if (csflag && context_len == 0)
5736	0	return 0;
5737
5738		/* if dom2flag is not set, then an empty context-string is required */
5739	0	if (!dom2flag && context_len > 0)
5740	0	return 0;
5741
5742	0	r = signature;
5743	0	s = signature + 32;
5744
5745		/*
5746		* Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5747		*
5748		* If not the signature is publicly invalid. Since it's public we can do the
5749		* check in variable time.
5750		*
5751		* First check the most significant byte
5752		*/
5753	0	if (s[31] > 0x10)
5754	0	return 0;
5755	0	if (s[31] == 0x10) {
5756		/*
5757		* Most significant byte indicates a value close to 2^252 so check the
5758		* rest
5759		*/
5760	0	if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5761	0	return 0;
5762	0	for (i = 15; i >= 0; i--) {
5763	0	if (s[i] < l_low[i])
5764	0	break;
5765	0	if (s[i] > l_low[i])
5766	0	return 0;
5767	0	}
5768	0	if (i < 0)
5769	0	return 0;
5770	0	}
5771
5772	0	if (ge_frombytes_vartime(&A, public_key) != 0) {
5773	0	return 0;
5774	0	}
5775
5776	0	fe_neg(A.X, A.X);
5777	0	fe_neg(A.T, A.T);
5778
5779	0	sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5780	0	if (sha512 == NULL)
5781	0	return 0;
5782	0	hash_ctx = EVP_MD_CTX_new();
5783	0	if (hash_ctx == NULL)
5784	0	goto err;
5785
5786	0	if (!hash_init_with_dom(hash_ctx, sha512, dom2flag, phflag, context, context_len)
5787	0	\|\| !EVP_DigestUpdate(hash_ctx, r, 32)
5788	0	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5789	0	\|\| !EVP_DigestUpdate(hash_ctx, tbs, tbs_len)
5790	0	\|\| !EVP_DigestFinal_ex(hash_ctx, h, &sz))
5791	0	goto err;
5792
5793	0	x25519_sc_reduce(h);
5794
5795	0	ge_double_scalarmult_vartime(&R, h, &A, s);
5796
5797	0	ge_tobytes(rcheck, &R);
5798
5799	0	res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5800
5801		/* note that we have used the strict verification equation here.
5802		* we checked that ENC( [h](-A) + [s]B ) == r
5803		* B is the base point.
5804		*
5805		* the less strict verification equation uses the curve cofactor:
5806		* [h8](-A) + [s8]B == [8]R
5807		*/
5808	0	err:
5809	0	EVP_MD_free(sha512);
5810	0	EVP_MD_CTX_free(hash_ctx);
5811	0	return res;
5812	0	}
5813
5814		int ossl_ed25519_public_from_private(OSSL_LIB_CTX *ctx, uint8_t out_public_key[32],
5815		const uint8_t private_key[32],
5816		const char *propq)
5817	0	{
5818	0	uint8_t az[SHA512_DIGEST_LENGTH];
5819	0	ge_p3 A;
5820	0	int r;
5821	0	EVP_MD *sha512 = NULL;
5822
5823	0	sha512 = EVP_MD_fetch(ctx, SN_sha512, propq);
5824	0	if (sha512 == NULL)
5825	0	return 0;
5826	0	r = EVP_Digest(private_key, 32, az, NULL, sha512, NULL);
5827	0	EVP_MD_free(sha512);
5828	0	if (!r) {
5829	0	OPENSSL_cleanse(az, sizeof(az));
5830	0	return 0;
5831	0	}
5832
5833	0	az[0] &= 248;
5834	0	az[31] &= 63;
5835	0	az[31] \|= 64;
5836
5837	0	ge_scalarmult_base(&A, az);
5838	0	ge_p3_tobytes(out_public_key, &A);
5839
5840	0	OPENSSL_cleanse(az, sizeof(az));
5841	0	return 1;
5842	0	}
5843
5844		int ossl_x25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5845		const uint8_t peer_public_value[32])
5846	0	{
5847	0	static const uint8_t kZeros[32] = { 0 };
5848	0	x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5849		/* The all-zero output results when the input is a point of small order. */
5850	0	return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5851	0	}
5852
5853		void ossl_x25519_public_from_private(uint8_t out_public_value[32],
5854		const uint8_t private_key[32])
5855	0	{
5856	0	uint8_t e[32];
5857	0	ge_p3 A;
5858	0	fe zplusy, zminusy, zminusy_inv;
5859
5860	0	memcpy(e, private_key, 32);
5861	0	e[0] &= 248;
5862	0	e[31] &= 127;
5863	0	e[31] \|= 64;
5864
5865	0	ge_scalarmult_base(&A, e);
5866
5867		/*
5868		* We only need the u-coordinate of the curve25519 point.
5869		* The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5870		* u=(Z+Y)/(Z-Y).
5871		*/
5872	0	fe_add(zplusy, A.Z, A.Y);
5873	0	fe_sub(zminusy, A.Z, A.Y);
5874	0	fe_invert(zminusy_inv, zminusy);
5875	0	fe_mul(zplusy, zplusy, zminusy_inv);
5876	0	fe_tobytes(out_public_value, zplusy);
5877
5878	0	OPENSSL_cleanse(e, sizeof(e));
5879	0	}

Coverage Report

Created: 2025-12-10 06:24