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

Line	Count	Source (jump to first uncovered line)
1		/*
2		* Copyright 2016-2018 The OpenSSL Project Authors. All Rights Reserved.
3		*
4		* Licensed under the OpenSSL license (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		#include <string.h>
11		#include "ec_lcl.h"
12		#include <openssl/sha.h>
13
14		#if defined(X25519_ASM) && (defined(__x86_64) \|\| defined(__x86_64__) \|\| \
15		defined(_M_AMD64) \|\| defined(_M_X64))
16
17		# define BASE_2_64_IMPLEMENTED
18
19		typedef uint64_t fe64[4];
20
21		int x25519_fe64_eligible(void);
22
23		/*
24		* Following subroutines perform corresponding operations modulo
25		* 2^256-38, i.e. double the curve modulus. However, inputs and
26		* outputs are permitted to be partially reduced, i.e. to remain
27		* in [0..2^256) range. It's all tied up in final fe64_tobytes
28		* that performs full reduction modulo 2^255-19.
29		*
30		* There are no reference C implementations for these.
31		*/
32		void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
33		void x25519_fe64_sqr(fe64 h, const fe64 f);
34		void x25519_fe64_mul121666(fe64 h, fe64 f);
35		void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
36		void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
37		void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
38	0	# define fe64_mul x25519_fe64_mul
39	0	# define fe64_sqr x25519_fe64_sqr
40	0	# define fe64_mul121666 x25519_fe64_mul121666
41	0	# define fe64_add x25519_fe64_add
42	0	# define fe64_sub x25519_fe64_sub
43	0	# define fe64_tobytes x25519_fe64_tobytes
44
45		static uint64_t load_8(const uint8_t *in)
46	0	{
47	0	uint64_t result;
48	0
49	0	result = in[0];
50	0	result \|= ((uint64_t)in[1]) << 8;
51	0	result \|= ((uint64_t)in[2]) << 16;
52	0	result \|= ((uint64_t)in[3]) << 24;
53	0	result \|= ((uint64_t)in[4]) << 32;
54	0	result \|= ((uint64_t)in[5]) << 40;
55	0	result \|= ((uint64_t)in[6]) << 48;
56	0	result \|= ((uint64_t)in[7]) << 56;
57	0
58	0	return result;
59	0	}
60
61		static void fe64_frombytes(fe64 h, const uint8_t *s)
62	0	{
63	0	h[0] = load_8(s);
64	0	h[1] = load_8(s + 8);
65	0	h[2] = load_8(s + 16);
66	0	h[3] = load_8(s + 24) & 0x7fffffffffffffff;
67	0	}
68
69		static void fe64_0(fe64 h)
70	0	{
71	0	h[0] = 0;
72	0	h[1] = 0;
73	0	h[2] = 0;
74	0	h[3] = 0;
75	0	}
76
77		static void fe64_1(fe64 h)
78	0	{
79	0	h[0] = 1;
80	0	h[1] = 0;
81	0	h[2] = 0;
82	0	h[3] = 0;
83	0	}
84
85		static void fe64_copy(fe64 h, const fe64 f)
86	0	{
87	0	h[0] = f[0];
88	0	h[1] = f[1];
89	0	h[2] = f[2];
90	0	h[3] = f[3];
91	0	}
92
93		static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
94	0	{
95	0	int i;
96	0	uint64_t mask = 0 - (uint64_t)b;
97	0
98	0	for (i = 0; i < 4; i++) {
99	0	uint64_t x = f[i] ^ g[i];
100	0	x &= mask;
101	0	f[i] ^= x;
102	0	g[i] ^= x;
103	0	}
104	0	}
105
106		static void fe64_invert(fe64 out, const fe64 z)
107	0	{
108	0	fe64 t0;
109	0	fe64 t1;
110	0	fe64 t2;
111	0	fe64 t3;
112	0	int i;
113	0
114	0	/*
115	0	* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
116	0	* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
117	0	*/
118	0
119	0	/* t0 = z ** 2 */
120	0	fe64_sqr(t0, z);
121	0
122	0	/* t1 = t0 (2 2) = z ** 8 */
123	0	fe64_sqr(t1, t0);
124	0	fe64_sqr(t1, t1);
125	0
126	0	/* t1 = z * t1 = z ** 9 */
127	0	fe64_mul(t1, z, t1);
128	0	/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
129	0	fe64_mul(t0, t0, t1);
130	0
131	0	/* t2 = t0 2 = z 22 */
132	0	fe64_sqr(t2, t0);
133	0
134	0	/* t1 = t1 * t2 = z (2 5 - 1) */
135	0	fe64_mul(t1, t1, t2);
136	0
137	0	/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
138	0	fe64_sqr(t2, t1);
139	0	for (i = 1; i < 5; ++i)
140	0	fe64_sqr(t2, t2);
141	0
142	0	/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
143	0	fe64_mul(t1, t2, t1);
144	0
145	0	/* Continuing similarly... */
146	0
147	0	/* t2 = z (2 20 - 1) */
148	0	fe64_sqr(t2, t1);
149	0	for (i = 1; i < 10; ++i)
150	0	fe64_sqr(t2, t2);
151	0
152	0	fe64_mul(t2, t2, t1);
153	0
154	0	/* t2 = z (2 40 - 1) */
155	0	fe64_sqr(t3, t2);
156	0	for (i = 1; i < 20; ++i)
157	0	fe64_sqr(t3, t3);
158	0
159	0	fe64_mul(t2, t3, t2);
160	0
161	0	/* t2 = z (2 10) * (2 ** 40 - 1) */
162	0	for (i = 0; i < 10; ++i)
163	0	fe64_sqr(t2, t2);
164	0
165	0	/* t1 = z (2 50 - 1) */
166	0	fe64_mul(t1, t2, t1);
167	0
168	0	/* t2 = z (2 100 - 1) */
169	0	fe64_sqr(t2, t1);
170	0	for (i = 1; i < 50; ++i)
171	0	fe64_sqr(t2, t2);
172	0
173	0	fe64_mul(t2, t2, t1);
174	0
175	0	/* t2 = z (2 200 - 1) */
176	0	fe64_sqr(t3, t2);
177	0	for (i = 1; i < 100; ++i)
178	0	fe64_sqr(t3, t3);
179	0
180	0	fe64_mul(t2, t3, t2);
181	0
182	0	/* t2 = z ((2 50) * (2 ** 200 - 1) */
183	0	for (i = 0; i < 50; ++i)
184	0	fe64_sqr(t2, t2);
185	0
186	0	/* t1 = z (2 250 - 1) */
187	0	fe64_mul(t1, t2, t1);
188	0
189	0	/* t1 = z ((2 5) * (2 ** 250 - 1)) */
190	0	for (i = 0; i < 5; ++i)
191	0	fe64_sqr(t1, t1);
192	0
193	0	/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
194	0	fe64_mul(out, t1, t0);
195	0	}
196
197		/*
198		* Duplicate of original x25519_scalar_mult_generic, but using
199		* fe64_* subroutines.
200		*/
201		static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
202		const uint8_t point[32])
203	0	{
204	0	fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
205	0	uint8_t e[32];
206	0	unsigned swap = 0;
207	0	int pos;
208	0
209	0	memcpy(e, scalar, 32);
210	0	e[0] &= 0xf8;
211	0	e[31] &= 0x7f;
212	0	e[31] \|= 0x40;
213	0	fe64_frombytes(x1, point);
214	0	fe64_1(x2);
215	0	fe64_0(z2);
216	0	fe64_copy(x3, x1);
217	0	fe64_1(z3);
218	0
219	0	for (pos = 254; pos >= 0; --pos) {
220	0	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
221	0
222	0	swap ^= b;
223	0	fe64_cswap(x2, x3, swap);
224	0	fe64_cswap(z2, z3, swap);
225	0	swap = b;
226	0	fe64_sub(tmp0, x3, z3);
227	0	fe64_sub(tmp1, x2, z2);
228	0	fe64_add(x2, x2, z2);
229	0	fe64_add(z2, x3, z3);
230	0	fe64_mul(z3, x2, tmp0);
231	0	fe64_mul(z2, z2, tmp1);
232	0	fe64_sqr(tmp0, tmp1);
233	0	fe64_sqr(tmp1, x2);
234	0	fe64_add(x3, z3, z2);
235	0	fe64_sub(z2, z3, z2);
236	0	fe64_mul(x2, tmp1, tmp0);
237	0	fe64_sub(tmp1, tmp1, tmp0);
238	0	fe64_sqr(z2, z2);
239	0	fe64_mul121666(z3, tmp1);
240	0	fe64_sqr(x3, x3);
241	0	fe64_add(tmp0, tmp0, z3);
242	0	fe64_mul(z3, x1, z2);
243	0	fe64_mul(z2, tmp1, tmp0);
244	0	}
245	0
246	0	fe64_invert(z2, z2);
247	0	fe64_mul(x2, x2, z2);
248	0	fe64_tobytes(out, x2);
249	0
250	0	OPENSSL_cleanse(e, sizeof(e));
251	0	}
252		#endif
253
254		#if defined(X25519_ASM) \
255		\|\| ( (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16) \
256		&& !defined(__sparc__) \
257		&& !(defined(__ANDROID__) && !defined(__clang__)) )
258		/*
259		* Base 2^51 implementation. It's virtually no different from reference
260		* base 2^25.5 implementation in respect to lax boundary conditions for
261		* intermediate values and even individual limbs. So that whatever you
262		* know about the reference, applies even here...
263		*/
264		# define BASE_2_51_IMPLEMENTED
265
266		typedef uint64_t fe51[5];
267
268		static const uint64_t MASK51 = 0x7ffffffffffff;
269
270		static uint64_t load_7(const uint8_t *in)
271	0	{
272	0	uint64_t result;
273	0
274	0	result = in[0];
275	0	result \|= ((uint64_t)in[1]) << 8;
276	0	result \|= ((uint64_t)in[2]) << 16;
277	0	result \|= ((uint64_t)in[3]) << 24;
278	0	result \|= ((uint64_t)in[4]) << 32;
279	0	result \|= ((uint64_t)in[5]) << 40;
280	0	result \|= ((uint64_t)in[6]) << 48;
281	0
282	0	return result;
283	0	}
284
285		static uint64_t load_6(const uint8_t *in)
286	0	{
287	0	uint64_t result;
288	0
289	0	result = in[0];
290	0	result \|= ((uint64_t)in[1]) << 8;
291	0	result \|= ((uint64_t)in[2]) << 16;
292	0	result \|= ((uint64_t)in[3]) << 24;
293	0	result \|= ((uint64_t)in[4]) << 32;
294	0	result \|= ((uint64_t)in[5]) << 40;
295	0
296	0	return result;
297	0	}
298
299		static void fe51_frombytes(fe51 h, const uint8_t *s)
300	0	{
301	0	uint64_t h0 = load_7(s); /* 56 bits */
302	0	uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
303	0	uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
304	0	uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
305	0	uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
306	0
307	0	h1 \|= h0 >> 51; h0 &= MASK51;
308	0	h2 \|= h1 >> 51; h1 &= MASK51;
309	0	h3 \|= h2 >> 51; h2 &= MASK51;
310	0	h4 \|= h3 >> 51; h3 &= MASK51;
311	0
312	0	h[0] = h0;
313	0	h[1] = h1;
314	0	h[2] = h2;
315	0	h[3] = h3;
316	0	h[4] = h4;
317	0	}
318
319		static void fe51_tobytes(uint8_t *s, const fe51 h)
320	0	{
321	0	uint64_t h0 = h[0];
322	0	uint64_t h1 = h[1];
323	0	uint64_t h2 = h[2];
324	0	uint64_t h3 = h[3];
325	0	uint64_t h4 = h[4];
326	0	uint64_t q;
327	0
328	0	/* compare to modulus */
329	0	q = (h0 + 19) >> 51;
330	0	q = (h1 + q) >> 51;
331	0	q = (h2 + q) >> 51;
332	0	q = (h3 + q) >> 51;
333	0	q = (h4 + q) >> 51;
334	0
335	0	/* full reduce */
336	0	h0 += 19 * q;
337	0	h1 += h0 >> 51; h0 &= MASK51;
338	0	h2 += h1 >> 51; h1 &= MASK51;
339	0	h3 += h2 >> 51; h2 &= MASK51;
340	0	h4 += h3 >> 51; h3 &= MASK51;
341	0	h4 &= MASK51;
342	0
343	0	/* smash */
344	0	s[0] = (uint8_t)(h0 >> 0);
345	0	s[1] = (uint8_t)(h0 >> 8);
346	0	s[2] = (uint8_t)(h0 >> 16);
347	0	s[3] = (uint8_t)(h0 >> 24);
348	0	s[4] = (uint8_t)(h0 >> 32);
349	0	s[5] = (uint8_t)(h0 >> 40);
350	0	s[6] = (uint8_t)((h0 >> 48) \| ((uint32_t)h1 << 3));
351	0	s[7] = (uint8_t)(h1 >> 5);
352	0	s[8] = (uint8_t)(h1 >> 13);
353	0	s[9] = (uint8_t)(h1 >> 21);
354	0	s[10] = (uint8_t)(h1 >> 29);
355	0	s[11] = (uint8_t)(h1 >> 37);
356	0	s[12] = (uint8_t)((h1 >> 45) \| ((uint32_t)h2 << 6));
357	0	s[13] = (uint8_t)(h2 >> 2);
358	0	s[14] = (uint8_t)(h2 >> 10);
359	0	s[15] = (uint8_t)(h2 >> 18);
360	0	s[16] = (uint8_t)(h2 >> 26);
361	0	s[17] = (uint8_t)(h2 >> 34);
362	0	s[18] = (uint8_t)(h2 >> 42);
363	0	s[19] = (uint8_t)((h2 >> 50) \| ((uint32_t)h3 << 1));
364	0	s[20] = (uint8_t)(h3 >> 7);
365	0	s[21] = (uint8_t)(h3 >> 15);
366	0	s[22] = (uint8_t)(h3 >> 23);
367	0	s[23] = (uint8_t)(h3 >> 31);
368	0	s[24] = (uint8_t)(h3 >> 39);
369	0	s[25] = (uint8_t)((h3 >> 47) \| ((uint32_t)h4 << 4));
370	0	s[26] = (uint8_t)(h4 >> 4);
371	0	s[27] = (uint8_t)(h4 >> 12);
372	0	s[28] = (uint8_t)(h4 >> 20);
373	0	s[29] = (uint8_t)(h4 >> 28);
374	0	s[30] = (uint8_t)(h4 >> 36);
375	0	s[31] = (uint8_t)(h4 >> 44);
376	0	}
377
378		# if defined(X25519_ASM)
379		void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
380		void x25519_fe51_sqr(fe51 h, const fe51 f);
381		void x25519_fe51_mul121666(fe51 h, fe51 f);
382	0	# define fe51_mul x25519_fe51_mul
383	0	# define fe51_sq x25519_fe51_sqr
384	0	# define fe51_mul121666 x25519_fe51_mul121666
385		# else
386
387		typedef __uint128_t u128;
388
389		static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
390		{
391		u128 h0, h1, h2, h3, h4;
392		uint64_t f_i, g0, g1, g2, g3, g4;
393
394		f_i = f[0];
395		h0 = (u128)f_i * (g0 = g[0]);
396		h1 = (u128)f_i * (g1 = g[1]);
397		h2 = (u128)f_i * (g2 = g[2]);
398		h3 = (u128)f_i * (g3 = g[3]);
399		h4 = (u128)f_i * (g4 = g[4]);
400
401		f_i = f[1];
402		h0 += (u128)f_i * (g4 *= 19);
403		h1 += (u128)f_i * g0;
404		h2 += (u128)f_i * g1;
405		h3 += (u128)f_i * g2;
406		h4 += (u128)f_i * g3;
407
408		f_i = f[2];
409		h0 += (u128)f_i * (g3 *= 19);
410		h1 += (u128)f_i * g4;
411		h2 += (u128)f_i * g0;
412		h3 += (u128)f_i * g1;
413		h4 += (u128)f_i * g2;
414
415		f_i = f[3];
416		h0 += (u128)f_i * (g2 *= 19);
417		h1 += (u128)f_i * g3;
418		h2 += (u128)f_i * g4;
419		h3 += (u128)f_i * g0;
420		h4 += (u128)f_i * g1;
421
422		f_i = f[4];
423		h0 += (u128)f_i * (g1 *= 19);
424		h1 += (u128)f_i * g2;
425		h2 += (u128)f_i * g3;
426		h3 += (u128)f_i * g4;
427		h4 += (u128)f_i * g0;
428
429		/* partial [lazy] reduction */
430		h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
431		h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
432
433		h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
434		g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
435
436		g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
437		g3 += g2 >> 51; g2 &= MASK51;
438		g1 += g0 >> 51; g0 &= MASK51;
439
440		h[0] = g0;
441		h[1] = g1;
442		h[2] = g2;
443		h[3] = g3;
444		h[4] = g4;
445		}
446
447		static void fe51_sq(fe51 h, const fe51 f)
448		{
449		# if defined(OPENSSL_SMALL_FOOTPRINT)
450		fe51_mul(h, f, f);
451		# else
452		/* dedicated squaring gives 16-25% overall improvement */
453		uint64_t g0 = f[0];
454		uint64_t g1 = f[1];
455		uint64_t g2 = f[2];
456		uint64_t g3 = f[3];
457		uint64_t g4 = f[4];
458		u128 h0, h1, h2, h3, h4;
459
460		h0 = (u128)g0 * g0; g0 *= 2;
461		h1 = (u128)g0 * g1;
462		h2 = (u128)g0 * g2;
463		h3 = (u128)g0 * g3;
464		h4 = (u128)g0 * g4;
465
466		g0 = g4; /* borrow g0 */
467		h3 += (u128)g0 * (g4 *= 19);
468
469		h2 += (u128)g1 * g1; g1 *= 2;
470		h3 += (u128)g1 * g2;
471		h4 += (u128)g1 * g3;
472		h0 += (u128)g1 * g4;
473
474		g0 = g3; /* borrow g0 */
475		h1 += (u128)g0 * (g3 *= 19);
476		h2 += (u128)(g0 * 2) * g4;
477
478		h4 += (u128)g2 * g2; g2 *= 2;
479		h0 += (u128)g2 * g3;
480		h1 += (u128)g2 * g4;
481
482		/* partial [lazy] reduction */
483		h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
484		h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
485
486		h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
487		g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
488
489		g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
490		g3 += g2 >> 51; g2 &= MASK51;
491		g1 += g0 >> 51; g0 &= MASK51;
492
493		h[0] = g0;
494		h[1] = g1;
495		h[2] = g2;
496		h[3] = g3;
497		h[4] = g4;
498		# endif
499		}
500
501		static void fe51_mul121666(fe51 h, fe51 f)
502		{
503		u128 h0 = f[0] * (u128)121666;
504		u128 h1 = f[1] * (u128)121666;
505		u128 h2 = f[2] * (u128)121666;
506		u128 h3 = f[3] * (u128)121666;
507		u128 h4 = f[4] * (u128)121666;
508		uint64_t g0, g1, g2, g3, g4;
509
510		h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
511		h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
512
513		h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
514		g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
515
516		g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
517		g3 += g2 >> 51; g2 &= MASK51;
518		g1 += g0 >> 51; g0 &= MASK51;
519
520		h[0] = g0;
521		h[1] = g1;
522		h[2] = g2;
523		h[3] = g3;
524		h[4] = g4;
525		}
526		# endif
527
528		static void fe51_add(fe51 h, const fe51 f, const fe51 g)
529	0	{
530	0	h[0] = f[0] + g[0];
531	0	h[1] = f[1] + g[1];
532	0	h[2] = f[2] + g[2];
533	0	h[3] = f[3] + g[3];
534	0	h[4] = f[4] + g[4];
535	0	}
536
537		static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
538	0	{
539	0	/*
540	0	* Add 2*modulus to ensure that result remains positive
541	0	* even if subtrahend is partially reduced.
542	0	*/
543	0	h[0] = (f[0] + 0xfffffffffffda) - g[0];
544	0	h[1] = (f[1] + 0xffffffffffffe) - g[1];
545	0	h[2] = (f[2] + 0xffffffffffffe) - g[2];
546	0	h[3] = (f[3] + 0xffffffffffffe) - g[3];
547	0	h[4] = (f[4] + 0xffffffffffffe) - g[4];
548	0	}
549
550		static void fe51_0(fe51 h)
551	0	{
552	0	h[0] = 0;
553	0	h[1] = 0;
554	0	h[2] = 0;
555	0	h[3] = 0;
556	0	h[4] = 0;
557	0	}
558
559		static void fe51_1(fe51 h)
560	0	{
561	0	h[0] = 1;
562	0	h[1] = 0;
563	0	h[2] = 0;
564	0	h[3] = 0;
565	0	h[4] = 0;
566	0	}
567
568		static void fe51_copy(fe51 h, const fe51 f)
569	0	{
570	0	h[0] = f[0];
571	0	h[1] = f[1];
572	0	h[2] = f[2];
573	0	h[3] = f[3];
574	0	h[4] = f[4];
575	0	}
576
577		static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
578	0	{
579	0	int i;
580	0	uint64_t mask = 0 - (uint64_t)b;
581	0
582	0	for (i = 0; i < 5; i++) {
583	0	int64_t x = f[i] ^ g[i];
584	0	x &= mask;
585	0	f[i] ^= x;
586	0	g[i] ^= x;
587	0	}
588	0	}
589
590		static void fe51_invert(fe51 out, const fe51 z)
591	0	{
592	0	fe51 t0;
593	0	fe51 t1;
594	0	fe51 t2;
595	0	fe51 t3;
596	0	int i;
597	0
598	0	/*
599	0	* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
600	0	* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
601	0	*/
602	0
603	0	/* t0 = z ** 2 */
604	0	fe51_sq(t0, z);
605	0
606	0	/* t1 = t0 (2 2) = z ** 8 */
607	0	fe51_sq(t1, t0);
608	0	fe51_sq(t1, t1);
609	0
610	0	/* t1 = z * t1 = z ** 9 */
611	0	fe51_mul(t1, z, t1);
612	0	/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
613	0	fe51_mul(t0, t0, t1);
614	0
615	0	/* t2 = t0 2 = z 22 */
616	0	fe51_sq(t2, t0);
617	0
618	0	/* t1 = t1 * t2 = z (2 5 - 1) */
619	0	fe51_mul(t1, t1, t2);
620	0
621	0	/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
622	0	fe51_sq(t2, t1);
623	0	for (i = 1; i < 5; ++i)
624	0	fe51_sq(t2, t2);
625	0
626	0	/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
627	0	fe51_mul(t1, t2, t1);
628	0
629	0	/* Continuing similarly... */
630	0
631	0	/* t2 = z (2 20 - 1) */
632	0	fe51_sq(t2, t1);
633	0	for (i = 1; i < 10; ++i)
634	0	fe51_sq(t2, t2);
635	0
636	0	fe51_mul(t2, t2, t1);
637	0
638	0	/* t2 = z (2 40 - 1) */
639	0	fe51_sq(t3, t2);
640	0	for (i = 1; i < 20; ++i)
641	0	fe51_sq(t3, t3);
642	0
643	0	fe51_mul(t2, t3, t2);
644	0
645	0	/* t2 = z (2 10) * (2 ** 40 - 1) */
646	0	for (i = 0; i < 10; ++i)
647	0	fe51_sq(t2, t2);
648	0
649	0	/* t1 = z (2 50 - 1) */
650	0	fe51_mul(t1, t2, t1);
651	0
652	0	/* t2 = z (2 100 - 1) */
653	0	fe51_sq(t2, t1);
654	0	for (i = 1; i < 50; ++i)
655	0	fe51_sq(t2, t2);
656	0
657	0	fe51_mul(t2, t2, t1);
658	0
659	0	/* t2 = z (2 200 - 1) */
660	0	fe51_sq(t3, t2);
661	0	for (i = 1; i < 100; ++i)
662	0	fe51_sq(t3, t3);
663	0
664	0	fe51_mul(t2, t3, t2);
665	0
666	0	/* t2 = z ((2 50) * (2 ** 200 - 1) */
667	0	for (i = 0; i < 50; ++i)
668	0	fe51_sq(t2, t2);
669	0
670	0	/* t1 = z (2 250 - 1) */
671	0	fe51_mul(t1, t2, t1);
672	0
673	0	/* t1 = z ((2 5) * (2 ** 250 - 1)) */
674	0	for (i = 0; i < 5; ++i)
675	0	fe51_sq(t1, t1);
676	0
677	0	/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
678	0	fe51_mul(out, t1, t0);
679	0	}
680
681		/*
682		* Duplicate of original x25519_scalar_mult_generic, but using
683		* fe51_* subroutines.
684		*/
685		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
686		const uint8_t point[32])
687	0	{
688	0	fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
689	0	uint8_t e[32];
690	0	unsigned swap = 0;
691	0	int pos;
692	0
693	0	# ifdef BASE_2_64_IMPLEMENTED
694	0	if (x25519_fe64_eligible()) {
695	0	x25519_scalar_mulx(out, scalar, point);
696	0	return;
697	0	}
698	0	# endif
699	0
700	0	memcpy(e, scalar, 32);
701	0	e[0] &= 0xf8;
702	0	e[31] &= 0x7f;
703	0	e[31] \|= 0x40;
704	0	fe51_frombytes(x1, point);
705	0	fe51_1(x2);
706	0	fe51_0(z2);
707	0	fe51_copy(x3, x1);
708	0	fe51_1(z3);
709	0
710	0	for (pos = 254; pos >= 0; --pos) {
711	0	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
712	0
713	0	swap ^= b;
714	0	fe51_cswap(x2, x3, swap);
715	0	fe51_cswap(z2, z3, swap);
716	0	swap = b;
717	0	fe51_sub(tmp0, x3, z3);
718	0	fe51_sub(tmp1, x2, z2);
719	0	fe51_add(x2, x2, z2);
720	0	fe51_add(z2, x3, z3);
721	0	fe51_mul(z3, tmp0, x2);
722	0	fe51_mul(z2, z2, tmp1);
723	0	fe51_sq(tmp0, tmp1);
724	0	fe51_sq(tmp1, x2);
725	0	fe51_add(x3, z3, z2);
726	0	fe51_sub(z2, z3, z2);
727	0	fe51_mul(x2, tmp1, tmp0);
728	0	fe51_sub(tmp1, tmp1, tmp0);
729	0	fe51_sq(z2, z2);
730	0	fe51_mul121666(z3, tmp1);
731	0	fe51_sq(x3, x3);
732	0	fe51_add(tmp0, tmp0, z3);
733	0	fe51_mul(z3, x1, z2);
734	0	fe51_mul(z2, tmp1, tmp0);
735	0	}
736	0
737	0	fe51_invert(z2, z2);
738	0	fe51_mul(x2, x2, z2);
739	0	fe51_tobytes(out, x2);
740	0
741	0	OPENSSL_cleanse(e, sizeof(e));
742	0	}
743		#endif
744
745		/*
746		* Reference base 2^25.5 implementation.
747		*/
748		/*
749		* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
750		* 20141124 (http://bench.cr.yp.to/supercop.html).
751		*
752		* The field functions are shared by Ed25519 and X25519 where possible.
753		*/
754
755		/* fe means field element. Here the field is \Z/(2^255-19). An element t,
756		* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
757		* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
758		* context. */
759		typedef int32_t fe[10];
760
761		static const int64_t kBottom25Bits = 0x1ffffffLL;
762		static const int64_t kBottom26Bits = 0x3ffffffLL;
763		static const int64_t kTop39Bits = 0xfffffffffe000000LL;
764		static const int64_t kTop38Bits = 0xfffffffffc000000LL;
765
766	0	static uint64_t load_3(const uint8_t *in) {
767	0	uint64_t result;
768	0	result = (uint64_t)in[0];
769	0	result \|= ((uint64_t)in[1]) << 8;
770	0	result \|= ((uint64_t)in[2]) << 16;
771	0	return result;
772	0	}
773
774	0	static uint64_t load_4(const uint8_t *in) {
775	0	uint64_t result;
776	0	result = (uint64_t)in[0];
777	0	result \|= ((uint64_t)in[1]) << 8;
778	0	result \|= ((uint64_t)in[2]) << 16;
779	0	result \|= ((uint64_t)in[3]) << 24;
780	0	return result;
781	0	}
782
783	0	static void fe_frombytes(fe h, const uint8_t *s) {
784	0	/* Ignores top bit of h. */
785	0	int64_t h0 = load_4(s);
786	0	int64_t h1 = load_3(s + 4) << 6;
787	0	int64_t h2 = load_3(s + 7) << 5;
788	0	int64_t h3 = load_3(s + 10) << 3;
789	0	int64_t h4 = load_3(s + 13) << 2;
790	0	int64_t h5 = load_4(s + 16);
791	0	int64_t h6 = load_3(s + 20) << 7;
792	0	int64_t h7 = load_3(s + 23) << 5;
793	0	int64_t h8 = load_3(s + 26) << 4;
794	0	int64_t h9 = (load_3(s + 29) & 8388607) << 2;
795	0	int64_t carry0;
796	0	int64_t carry1;
797	0	int64_t carry2;
798	0	int64_t carry3;
799	0	int64_t carry4;
800	0	int64_t carry5;
801	0	int64_t carry6;
802	0	int64_t carry7;
803	0	int64_t carry8;
804	0	int64_t carry9;
805	0
806	0	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
807	0	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
808	0	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
809	0	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
810	0	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
811	0
812	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
813	0	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
814	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
815	0	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
816	0	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
817	0
818	0	h[0] = (int32_t)h0;
819	0	h[1] = (int32_t)h1;
820	0	h[2] = (int32_t)h2;
821	0	h[3] = (int32_t)h3;
822	0	h[4] = (int32_t)h4;
823	0	h[5] = (int32_t)h5;
824	0	h[6] = (int32_t)h6;
825	0	h[7] = (int32_t)h7;
826	0	h[8] = (int32_t)h8;
827	0	h[9] = (int32_t)h9;
828	0	}
829
830		/* Preconditions:
831		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
832		*
833		* Write p=2^255-19; q=floor(h/p).
834		* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
835		*
836		* Proof:
837		* Have \|h\|<=p so \|q\|<=1 so \|19^2 2^(-255) q\|<1/4.
838		* Also have \|h-2^230 h9\|<2^231 so \|19 2^(-255)(h-2^230 h9)\|<1/4.
839		*
840		* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
841		* Then 0<y<1.
842		*
843		* Write r=h-pq.
844		* Have 0<=r<=p-1=2^255-20.
845		* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
846		*
847		* Write x=r+19(2^-255)r+y.
848		* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
849		*
850		* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
851		* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
852	0	static void fe_tobytes(uint8_t *s, const fe h) {
853	0	int32_t h0 = h[0];
854	0	int32_t h1 = h[1];
855	0	int32_t h2 = h[2];
856	0	int32_t h3 = h[3];
857	0	int32_t h4 = h[4];
858	0	int32_t h5 = h[5];
859	0	int32_t h6 = h[6];
860	0	int32_t h7 = h[7];
861	0	int32_t h8 = h[8];
862	0	int32_t h9 = h[9];
863	0	int32_t q;
864	0
865	0	q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
866	0	q = (h0 + q) >> 26;
867	0	q = (h1 + q) >> 25;
868	0	q = (h2 + q) >> 26;
869	0	q = (h3 + q) >> 25;
870	0	q = (h4 + q) >> 26;
871	0	q = (h5 + q) >> 25;
872	0	q = (h6 + q) >> 26;
873	0	q = (h7 + q) >> 25;
874	0	q = (h8 + q) >> 26;
875	0	q = (h9 + q) >> 25;
876	0
877	0	/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
878	0	h0 += 19 * q;
879	0	/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
880	0
881	0	h1 += h0 >> 26; h0 &= kBottom26Bits;
882	0	h2 += h1 >> 25; h1 &= kBottom25Bits;
883	0	h3 += h2 >> 26; h2 &= kBottom26Bits;
884	0	h4 += h3 >> 25; h3 &= kBottom25Bits;
885	0	h5 += h4 >> 26; h4 &= kBottom26Bits;
886	0	h6 += h5 >> 25; h5 &= kBottom25Bits;
887	0	h7 += h6 >> 26; h6 &= kBottom26Bits;
888	0	h8 += h7 >> 25; h7 &= kBottom25Bits;
889	0	h9 += h8 >> 26; h8 &= kBottom26Bits;
890	0	h9 &= kBottom25Bits;
891	0	/* h10 = carry9 */
892	0
893	0	/* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
894	0	* Have h0+...+2^230 h9 between 0 and 2^255-1;
895	0	* evidently 2^255 h10-2^255 q = 0.
896	0	* Goal: Output h0+...+2^230 h9. */
897	0
898	0	s[0] = (uint8_t)(h0 >> 0);
899	0	s[1] = (uint8_t)(h0 >> 8);
900	0	s[2] = (uint8_t)(h0 >> 16);
901	0	s[3] = (uint8_t)((h0 >> 24) \| ((uint32_t)(h1) << 2));
902	0	s[4] = (uint8_t)(h1 >> 6);
903	0	s[5] = (uint8_t)(h1 >> 14);
904	0	s[6] = (uint8_t)((h1 >> 22) \| ((uint32_t)(h2) << 3));
905	0	s[7] = (uint8_t)(h2 >> 5);
906	0	s[8] = (uint8_t)(h2 >> 13);
907	0	s[9] = (uint8_t)((h2 >> 21) \| ((uint32_t)(h3) << 5));
908	0	s[10] = (uint8_t)(h3 >> 3);
909	0	s[11] = (uint8_t)(h3 >> 11);
910	0	s[12] = (uint8_t)((h3 >> 19) \| ((uint32_t)(h4) << 6));
911	0	s[13] = (uint8_t)(h4 >> 2);
912	0	s[14] = (uint8_t)(h4 >> 10);
913	0	s[15] = (uint8_t)(h4 >> 18);
914	0	s[16] = (uint8_t)(h5 >> 0);
915	0	s[17] = (uint8_t)(h5 >> 8);
916	0	s[18] = (uint8_t)(h5 >> 16);
917	0	s[19] = (uint8_t)((h5 >> 24) \| ((uint32_t)(h6) << 1));
918	0	s[20] = (uint8_t)(h6 >> 7);
919	0	s[21] = (uint8_t)(h6 >> 15);
920	0	s[22] = (uint8_t)((h6 >> 23) \| ((uint32_t)(h7) << 3));
921	0	s[23] = (uint8_t)(h7 >> 5);
922	0	s[24] = (uint8_t)(h7 >> 13);
923	0	s[25] = (uint8_t)((h7 >> 21) \| ((uint32_t)(h8) << 4));
924	0	s[26] = (uint8_t)(h8 >> 4);
925	0	s[27] = (uint8_t)(h8 >> 12);
926	0	s[28] = (uint8_t)((h8 >> 20) \| ((uint32_t)(h9) << 6));
927	0	s[29] = (uint8_t)(h9 >> 2);
928	0	s[30] = (uint8_t)(h9 >> 10);
929	0	s[31] = (uint8_t)(h9 >> 18);
930	0	}
931
932		/* h = f */
933	0	static void fe_copy(fe h, const fe f) {
934	0	memmove(h, f, sizeof(int32_t) * 10);
935	0	}
936
937		/* h = 0 */
938	0	static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }
939
940		/* h = 1 */
941	0	static void fe_1(fe h) {
942	0	memset(h, 0, sizeof(int32_t) * 10);
943	0	h[0] = 1;
944	0	}
945
946		/* h = f + g
947		* Can overlap h with f or g.
948		*
949		* Preconditions:
950		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
951		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
952		*
953		* Postconditions:
954		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc. */
955	0	static void fe_add(fe h, const fe f, const fe g) {
956	0	unsigned i;
957	0	for (i = 0; i < 10; i++) {
958	0	h[i] = f[i] + g[i];
959	0	}
960	0	}
961
962		/* h = f - g
963		* Can overlap h with f or g.
964		*
965		* Preconditions:
966		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
967		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
968		*
969		* Postconditions:
970		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc. */
971	0	static void fe_sub(fe h, const fe f, const fe g) {
972	0	unsigned i;
973	0	for (i = 0; i < 10; i++) {
974	0	h[i] = f[i] - g[i];
975	0	}
976	0	}
977
978		/* h = f * g
979		* Can overlap h with f or g.
980		*
981		* Preconditions:
982		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
983		* \|g\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
984		*
985		* Postconditions:
986		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
987		*
988		* Notes on implementation strategy:
989		*
990		* Using schoolbook multiplication.
991		* Karatsuba would save a little in some cost models.
992		*
993		* Most multiplications by 2 and 19 are 32-bit precomputations;
994		* cheaper than 64-bit postcomputations.
995		*
996		* There is one remaining multiplication by 19 in the carry chain;
997		* one *19 precomputation can be merged into this,
998		* but the resulting data flow is considerably less clean.
999		*
1000		* There are 12 carries below.
1001		* 10 of them are 2-way parallelizable and vectorizable.
1002		* Can get away with 11 carries, but then data flow is much deeper.
1003		*
1004		* With tighter constraints on inputs can squeeze carries into int32. */
1005	0	static void fe_mul(fe h, const fe f, const fe g) {
1006	0	int32_t f0 = f[0];
1007	0	int32_t f1 = f[1];
1008	0	int32_t f2 = f[2];
1009	0	int32_t f3 = f[3];
1010	0	int32_t f4 = f[4];
1011	0	int32_t f5 = f[5];
1012	0	int32_t f6 = f[6];
1013	0	int32_t f7 = f[7];
1014	0	int32_t f8 = f[8];
1015	0	int32_t f9 = f[9];
1016	0	int32_t g0 = g[0];
1017	0	int32_t g1 = g[1];
1018	0	int32_t g2 = g[2];
1019	0	int32_t g3 = g[3];
1020	0	int32_t g4 = g[4];
1021	0	int32_t g5 = g[5];
1022	0	int32_t g6 = g[6];
1023	0	int32_t g7 = g[7];
1024	0	int32_t g8 = g[8];
1025	0	int32_t g9 = g[9];
1026	0	int32_t g1_19 = 19 * g1; /* 1.9593752^29 /
1027	0	int32_t g2_19 = 19 * g2; /* 1.9593752^30; still ok /
1028	0	int32_t g3_19 = 19 * g3;
1029	0	int32_t g4_19 = 19 * g4;
1030	0	int32_t g5_19 = 19 * g5;
1031	0	int32_t g6_19 = 19 * g6;
1032	0	int32_t g7_19 = 19 * g7;
1033	0	int32_t g8_19 = 19 * g8;
1034	0	int32_t g9_19 = 19 * g9;
1035	0	int32_t f1_2 = 2 * f1;
1036	0	int32_t f3_2 = 2 * f3;
1037	0	int32_t f5_2 = 2 * f5;
1038	0	int32_t f7_2 = 2 * f7;
1039	0	int32_t f9_2 = 2 * f9;
1040	0	int64_t f0g0 = f0 * (int64_t) g0;
1041	0	int64_t f0g1 = f0 * (int64_t) g1;
1042	0	int64_t f0g2 = f0 * (int64_t) g2;
1043	0	int64_t f0g3 = f0 * (int64_t) g3;
1044	0	int64_t f0g4 = f0 * (int64_t) g4;
1045	0	int64_t f0g5 = f0 * (int64_t) g5;
1046	0	int64_t f0g6 = f0 * (int64_t) g6;
1047	0	int64_t f0g7 = f0 * (int64_t) g7;
1048	0	int64_t f0g8 = f0 * (int64_t) g8;
1049	0	int64_t f0g9 = f0 * (int64_t) g9;
1050	0	int64_t f1g0 = f1 * (int64_t) g0;
1051	0	int64_t f1g1_2 = f1_2 * (int64_t) g1;
1052	0	int64_t f1g2 = f1 * (int64_t) g2;
1053	0	int64_t f1g3_2 = f1_2 * (int64_t) g3;
1054	0	int64_t f1g4 = f1 * (int64_t) g4;
1055	0	int64_t f1g5_2 = f1_2 * (int64_t) g5;
1056	0	int64_t f1g6 = f1 * (int64_t) g6;
1057	0	int64_t f1g7_2 = f1_2 * (int64_t) g7;
1058	0	int64_t f1g8 = f1 * (int64_t) g8;
1059	0	int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
1060	0	int64_t f2g0 = f2 * (int64_t) g0;
1061	0	int64_t f2g1 = f2 * (int64_t) g1;
1062	0	int64_t f2g2 = f2 * (int64_t) g2;
1063	0	int64_t f2g3 = f2 * (int64_t) g3;
1064	0	int64_t f2g4 = f2 * (int64_t) g4;
1065	0	int64_t f2g5 = f2 * (int64_t) g5;
1066	0	int64_t f2g6 = f2 * (int64_t) g6;
1067	0	int64_t f2g7 = f2 * (int64_t) g7;
1068	0	int64_t f2g8_19 = f2 * (int64_t) g8_19;
1069	0	int64_t f2g9_19 = f2 * (int64_t) g9_19;
1070	0	int64_t f3g0 = f3 * (int64_t) g0;
1071	0	int64_t f3g1_2 = f3_2 * (int64_t) g1;
1072	0	int64_t f3g2 = f3 * (int64_t) g2;
1073	0	int64_t f3g3_2 = f3_2 * (int64_t) g3;
1074	0	int64_t f3g4 = f3 * (int64_t) g4;
1075	0	int64_t f3g5_2 = f3_2 * (int64_t) g5;
1076	0	int64_t f3g6 = f3 * (int64_t) g6;
1077	0	int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
1078	0	int64_t f3g8_19 = f3 * (int64_t) g8_19;
1079	0	int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
1080	0	int64_t f4g0 = f4 * (int64_t) g0;
1081	0	int64_t f4g1 = f4 * (int64_t) g1;
1082	0	int64_t f4g2 = f4 * (int64_t) g2;
1083	0	int64_t f4g3 = f4 * (int64_t) g3;
1084	0	int64_t f4g4 = f4 * (int64_t) g4;
1085	0	int64_t f4g5 = f4 * (int64_t) g5;
1086	0	int64_t f4g6_19 = f4 * (int64_t) g6_19;
1087	0	int64_t f4g7_19 = f4 * (int64_t) g7_19;
1088	0	int64_t f4g8_19 = f4 * (int64_t) g8_19;
1089	0	int64_t f4g9_19 = f4 * (int64_t) g9_19;
1090	0	int64_t f5g0 = f5 * (int64_t) g0;
1091	0	int64_t f5g1_2 = f5_2 * (int64_t) g1;
1092	0	int64_t f5g2 = f5 * (int64_t) g2;
1093	0	int64_t f5g3_2 = f5_2 * (int64_t) g3;
1094	0	int64_t f5g4 = f5 * (int64_t) g4;
1095	0	int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
1096	0	int64_t f5g6_19 = f5 * (int64_t) g6_19;
1097	0	int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
1098	0	int64_t f5g8_19 = f5 * (int64_t) g8_19;
1099	0	int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
1100	0	int64_t f6g0 = f6 * (int64_t) g0;
1101	0	int64_t f6g1 = f6 * (int64_t) g1;
1102	0	int64_t f6g2 = f6 * (int64_t) g2;
1103	0	int64_t f6g3 = f6 * (int64_t) g3;
1104	0	int64_t f6g4_19 = f6 * (int64_t) g4_19;
1105	0	int64_t f6g5_19 = f6 * (int64_t) g5_19;
1106	0	int64_t f6g6_19 = f6 * (int64_t) g6_19;
1107	0	int64_t f6g7_19 = f6 * (int64_t) g7_19;
1108	0	int64_t f6g8_19 = f6 * (int64_t) g8_19;
1109	0	int64_t f6g9_19 = f6 * (int64_t) g9_19;
1110	0	int64_t f7g0 = f7 * (int64_t) g0;
1111	0	int64_t f7g1_2 = f7_2 * (int64_t) g1;
1112	0	int64_t f7g2 = f7 * (int64_t) g2;
1113	0	int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
1114	0	int64_t f7g4_19 = f7 * (int64_t) g4_19;
1115	0	int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
1116	0	int64_t f7g6_19 = f7 * (int64_t) g6_19;
1117	0	int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
1118	0	int64_t f7g8_19 = f7 * (int64_t) g8_19;
1119	0	int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
1120	0	int64_t f8g0 = f8 * (int64_t) g0;
1121	0	int64_t f8g1 = f8 * (int64_t) g1;
1122	0	int64_t f8g2_19 = f8 * (int64_t) g2_19;
1123	0	int64_t f8g3_19 = f8 * (int64_t) g3_19;
1124	0	int64_t f8g4_19 = f8 * (int64_t) g4_19;
1125	0	int64_t f8g5_19 = f8 * (int64_t) g5_19;
1126	0	int64_t f8g6_19 = f8 * (int64_t) g6_19;
1127	0	int64_t f8g7_19 = f8 * (int64_t) g7_19;
1128	0	int64_t f8g8_19 = f8 * (int64_t) g8_19;
1129	0	int64_t f8g9_19 = f8 * (int64_t) g9_19;
1130	0	int64_t f9g0 = f9 * (int64_t) g0;
1131	0	int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
1132	0	int64_t f9g2_19 = f9 * (int64_t) g2_19;
1133	0	int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
1134	0	int64_t f9g4_19 = f9 * (int64_t) g4_19;
1135	0	int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
1136	0	int64_t f9g6_19 = f9 * (int64_t) g6_19;
1137	0	int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
1138	0	int64_t f9g8_19 = f9 * (int64_t) g8_19;
1139	0	int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
1140	0	int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
1141	0	int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
1142	0	int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
1143	0	int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
1144	0	int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
1145	0	int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
1146	0	int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
1147	0	int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
1148	0	int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
1149	0	int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
1150	0	int64_t carry0;
1151	0	int64_t carry1;
1152	0	int64_t carry2;
1153	0	int64_t carry3;
1154	0	int64_t carry4;
1155	0	int64_t carry5;
1156	0	int64_t carry6;
1157	0	int64_t carry7;
1158	0	int64_t carry8;
1159	0	int64_t carry9;
1160	0
1161	0	/* \|h0\| <= (1.651.652^52(1+19+19+19+19)+1.651.652^50(38+38+38+38+38))
1162	0	* i.e. \|h0\| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1163	0	* \|h1\| <= (1.651.652^51*(1+1+19+19+19+19+19+19+19+19))
1164	0	* i.e. \|h1\| <= 1.72^59; narrower ranges for h3, h5, h7, h9 /
1165	0
1166	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1167	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1168	0	/* \|h0\| <= 2^25 */
1169	0	/* \|h4\| <= 2^25 */
1170	0	/* \|h1\| <= 1.712^59 /
1171	0	/* \|h5\| <= 1.712^59 /
1172	0
1173	0	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1174	0	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1175	0	/* \|h1\| <= 2^24; from now on fits into int32 */
1176	0	/* \|h5\| <= 2^24; from now on fits into int32 */
1177	0	/* \|h2\| <= 1.412^60 /
1178	0	/* \|h6\| <= 1.412^60 /
1179	0
1180	0	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1181	0	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1182	0	/* \|h2\| <= 2^25; from now on fits into int32 unchanged */
1183	0	/* \|h6\| <= 2^25; from now on fits into int32 unchanged */
1184	0	/* \|h3\| <= 1.712^59 /
1185	0	/* \|h7\| <= 1.712^59 /
1186	0
1187	0	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1188	0	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1189	0	/* \|h3\| <= 2^24; from now on fits into int32 unchanged */
1190	0	/* \|h7\| <= 2^24; from now on fits into int32 unchanged */
1191	0	/* \|h4\| <= 1.722^34 /
1192	0	/* \|h8\| <= 1.412^60 /
1193	0
1194	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1195	0	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1196	0	/* \|h4\| <= 2^25; from now on fits into int32 unchanged */
1197	0	/* \|h8\| <= 2^25; from now on fits into int32 unchanged */
1198	0	/* \|h5\| <= 1.012^24 /
1199	0	/* \|h9\| <= 1.712^59 /
1200	0
1201	0	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1202	0	/* \|h9\| <= 2^24; from now on fits into int32 unchanged */
1203	0	/* \|h0\| <= 1.12^39 /
1204	0
1205	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1206	0	/* \|h0\| <= 2^25; from now on fits into int32 unchanged */
1207	0	/* \|h1\| <= 1.012^24 /
1208	0
1209	0	h[0] = (int32_t)h0;
1210	0	h[1] = (int32_t)h1;
1211	0	h[2] = (int32_t)h2;
1212	0	h[3] = (int32_t)h3;
1213	0	h[4] = (int32_t)h4;
1214	0	h[5] = (int32_t)h5;
1215	0	h[6] = (int32_t)h6;
1216	0	h[7] = (int32_t)h7;
1217	0	h[8] = (int32_t)h8;
1218	0	h[9] = (int32_t)h9;
1219	0	}
1220
1221		/* h = f * f
1222		* Can overlap h with f.
1223		*
1224		* Preconditions:
1225		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1226		*
1227		* Postconditions:
1228		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1229		*
1230		* See fe_mul.c for discussion of implementation strategy. */
1231	0	static void fe_sq(fe h, const fe f) {
1232	0	int32_t f0 = f[0];
1233	0	int32_t f1 = f[1];
1234	0	int32_t f2 = f[2];
1235	0	int32_t f3 = f[3];
1236	0	int32_t f4 = f[4];
1237	0	int32_t f5 = f[5];
1238	0	int32_t f6 = f[6];
1239	0	int32_t f7 = f[7];
1240	0	int32_t f8 = f[8];
1241	0	int32_t f9 = f[9];
1242	0	int32_t f0_2 = 2 * f0;
1243	0	int32_t f1_2 = 2 * f1;
1244	0	int32_t f2_2 = 2 * f2;
1245	0	int32_t f3_2 = 2 * f3;
1246	0	int32_t f4_2 = 2 * f4;
1247	0	int32_t f5_2 = 2 * f5;
1248	0	int32_t f6_2 = 2 * f6;
1249	0	int32_t f7_2 = 2 * f7;
1250	0	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1251	0	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1252	0	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1253	0	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1254	0	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1255	0	int64_t f0f0 = f0 * (int64_t) f0;
1256	0	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1257	0	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1258	0	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1259	0	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1260	0	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1261	0	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1262	0	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1263	0	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1264	0	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1265	0	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1266	0	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1267	0	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1268	0	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1269	0	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1270	0	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1271	0	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1272	0	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1273	0	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1274	0	int64_t f2f2 = f2 * (int64_t) f2;
1275	0	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1276	0	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1277	0	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1278	0	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1279	0	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1280	0	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1281	0	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1282	0	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1283	0	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1284	0	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1285	0	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1286	0	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1287	0	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1288	0	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1289	0	int64_t f4f4 = f4 * (int64_t) f4;
1290	0	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1291	0	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1292	0	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1293	0	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1294	0	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1295	0	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1296	0	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1297	0	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1298	0	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1299	0	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1300	0	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1301	0	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1302	0	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1303	0	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1304	0	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1305	0	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1306	0	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1307	0	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1308	0	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1309	0	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1310	0	int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
1311	0	int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
1312	0	int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
1313	0	int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
1314	0	int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
1315	0	int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
1316	0	int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
1317	0	int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
1318	0	int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
1319	0	int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
1320	0	int64_t carry0;
1321	0	int64_t carry1;
1322	0	int64_t carry2;
1323	0	int64_t carry3;
1324	0	int64_t carry4;
1325	0	int64_t carry5;
1326	0	int64_t carry6;
1327	0	int64_t carry7;
1328	0	int64_t carry8;
1329	0	int64_t carry9;
1330	0
1331	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1332	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1333	0
1334	0	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1335	0	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1336	0
1337	0	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1338	0	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1339	0
1340	0	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1341	0	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1342	0
1343	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1344	0	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1345	0
1346	0	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1347	0
1348	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1349	0
1350	0	h[0] = (int32_t)h0;
1351	0	h[1] = (int32_t)h1;
1352	0	h[2] = (int32_t)h2;
1353	0	h[3] = (int32_t)h3;
1354	0	h[4] = (int32_t)h4;
1355	0	h[5] = (int32_t)h5;
1356	0	h[6] = (int32_t)h6;
1357	0	h[7] = (int32_t)h7;
1358	0	h[8] = (int32_t)h8;
1359	0	h[9] = (int32_t)h9;
1360	0	}
1361
1362	0	static void fe_invert(fe out, const fe z) {
1363	0	fe t0;
1364	0	fe t1;
1365	0	fe t2;
1366	0	fe t3;
1367	0	int i;
1368	0
1369	0	/*
1370	0	* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
1371	0	* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
1372	0	*/
1373	0
1374	0	/* t0 = z ** 2 */
1375	0	fe_sq(t0, z);
1376	0
1377	0	/* t1 = t0 (2 2) = z ** 8 */
1378	0	fe_sq(t1, t0);
1379	0	fe_sq(t1, t1);
1380	0
1381	0	/* t1 = z * t1 = z ** 9 */
1382	0	fe_mul(t1, z, t1);
1383	0	/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1384	0	fe_mul(t0, t0, t1);
1385	0
1386	0	/* t2 = t0 2 = z 22 */
1387	0	fe_sq(t2, t0);
1388	0
1389	0	/* t1 = t1 * t2 = z (2 5 - 1) */
1390	0	fe_mul(t1, t1, t2);
1391	0
1392	0	/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
1393	0	fe_sq(t2, t1);
1394	0	for (i = 1; i < 5; ++i) {
1395	0	fe_sq(t2, t2);
1396	0	}
1397	0
1398	0	/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
1399	0	fe_mul(t1, t2, t1);
1400	0
1401	0	/* Continuing similarly... */
1402	0
1403	0	/* t2 = z (2 20 - 1) */
1404	0	fe_sq(t2, t1);
1405	0	for (i = 1; i < 10; ++i) {
1406	0	fe_sq(t2, t2);
1407	0	}
1408	0	fe_mul(t2, t2, t1);
1409	0
1410	0	/* t2 = z (2 40 - 1) */
1411	0	fe_sq(t3, t2);
1412	0	for (i = 1; i < 20; ++i) {
1413	0	fe_sq(t3, t3);
1414	0	}
1415	0	fe_mul(t2, t3, t2);
1416	0
1417	0	/* t2 = z (2 10) * (2 ** 40 - 1) */
1418	0	for (i = 0; i < 10; ++i) {
1419	0	fe_sq(t2, t2);
1420	0	}
1421	0	/* t1 = z (2 50 - 1) */
1422	0	fe_mul(t1, t2, t1);
1423	0
1424	0	/* t2 = z (2 100 - 1) */
1425	0	fe_sq(t2, t1);
1426	0	for (i = 1; i < 50; ++i) {
1427	0	fe_sq(t2, t2);
1428	0	}
1429	0	fe_mul(t2, t2, t1);
1430	0
1431	0	/* t2 = z (2 200 - 1) */
1432	0	fe_sq(t3, t2);
1433	0	for (i = 1; i < 100; ++i) {
1434	0	fe_sq(t3, t3);
1435	0	}
1436	0	fe_mul(t2, t3, t2);
1437	0
1438	0	/* t2 = z ((2 50) * (2 ** 200 - 1) */
1439	0	fe_sq(t2, t2);
1440	0	for (i = 1; i < 50; ++i) {
1441	0	fe_sq(t2, t2);
1442	0	}
1443	0
1444	0	/* t1 = z (2 250 - 1) */
1445	0	fe_mul(t1, t2, t1);
1446	0
1447	0	/* t1 = z ((2 5) * (2 ** 250 - 1)) */
1448	0	fe_sq(t1, t1);
1449	0	for (i = 1; i < 5; ++i) {
1450	0	fe_sq(t1, t1);
1451	0	}
1452	0
1453	0	/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
1454	0	fe_mul(out, t1, t0);
1455	0	}
1456
1457		/* h = -f
1458		*
1459		* Preconditions:
1460		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1461		*
1462		* Postconditions:
1463		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc. */
1464	0	static void fe_neg(fe h, const fe f) {
1465	0	unsigned i;
1466	0	for (i = 0; i < 10; i++) {
1467	0	h[i] = -f[i];
1468	0	}
1469	0	}
1470
1471		/* Replace (f,g) with (g,g) if b == 1;
1472		* replace (f,g) with (f,g) if b == 0.
1473		*
1474		* Preconditions: b in {0,1}. */
1475	0	static void fe_cmov(fe f, const fe g, unsigned b) {
1476	0	size_t i;
1477	0	b = 0-b;
1478	0	for (i = 0; i < 10; i++) {
1479	0	int32_t x = f[i] ^ g[i];
1480	0	x &= b;
1481	0	f[i] ^= x;
1482	0	}
1483	0	}
1484
1485		/* return 0 if f == 0
1486		* return 1 if f != 0
1487		*
1488		* Preconditions:
1489		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc. */
1490	0	static int fe_isnonzero(const fe f) {
1491	0	uint8_t s[32];
1492	0	static const uint8_t zero[32] = {0};
1493	0	fe_tobytes(s, f);
1494	0
1495	0	return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1496	0	}
1497
1498		/* return 1 if f is in {1,3,5,...,q-2}
1499		* return 0 if f is in {0,2,4,...,q-1}
1500		*
1501		* Preconditions:
1502		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc. */
1503	0	static int fe_isnegative(const fe f) {
1504	0	uint8_t s[32];
1505	0	fe_tobytes(s, f);
1506	0	return s[0] & 1;
1507	0	}
1508
1509		/* h = 2 * f * f
1510		* Can overlap h with f.
1511		*
1512		* Preconditions:
1513		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1514		*
1515		* Postconditions:
1516		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1517		*
1518		* See fe_mul.c for discussion of implementation strategy. */
1519	0	static void fe_sq2(fe h, const fe f) {
1520	0	int32_t f0 = f[0];
1521	0	int32_t f1 = f[1];
1522	0	int32_t f2 = f[2];
1523	0	int32_t f3 = f[3];
1524	0	int32_t f4 = f[4];
1525	0	int32_t f5 = f[5];
1526	0	int32_t f6 = f[6];
1527	0	int32_t f7 = f[7];
1528	0	int32_t f8 = f[8];
1529	0	int32_t f9 = f[9];
1530	0	int32_t f0_2 = 2 * f0;
1531	0	int32_t f1_2 = 2 * f1;
1532	0	int32_t f2_2 = 2 * f2;
1533	0	int32_t f3_2 = 2 * f3;
1534	0	int32_t f4_2 = 2 * f4;
1535	0	int32_t f5_2 = 2 * f5;
1536	0	int32_t f6_2 = 2 * f6;
1537	0	int32_t f7_2 = 2 * f7;
1538	0	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1539	0	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1540	0	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1541	0	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1542	0	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1543	0	int64_t f0f0 = f0 * (int64_t) f0;
1544	0	int64_t f0f1_2 = f0_2 * (int64_t) f1;
1545	0	int64_t f0f2_2 = f0_2 * (int64_t) f2;
1546	0	int64_t f0f3_2 = f0_2 * (int64_t) f3;
1547	0	int64_t f0f4_2 = f0_2 * (int64_t) f4;
1548	0	int64_t f0f5_2 = f0_2 * (int64_t) f5;
1549	0	int64_t f0f6_2 = f0_2 * (int64_t) f6;
1550	0	int64_t f0f7_2 = f0_2 * (int64_t) f7;
1551	0	int64_t f0f8_2 = f0_2 * (int64_t) f8;
1552	0	int64_t f0f9_2 = f0_2 * (int64_t) f9;
1553	0	int64_t f1f1_2 = f1_2 * (int64_t) f1;
1554	0	int64_t f1f2_2 = f1_2 * (int64_t) f2;
1555	0	int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1556	0	int64_t f1f4_2 = f1_2 * (int64_t) f4;
1557	0	int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1558	0	int64_t f1f6_2 = f1_2 * (int64_t) f6;
1559	0	int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1560	0	int64_t f1f8_2 = f1_2 * (int64_t) f8;
1561	0	int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1562	0	int64_t f2f2 = f2 * (int64_t) f2;
1563	0	int64_t f2f3_2 = f2_2 * (int64_t) f3;
1564	0	int64_t f2f4_2 = f2_2 * (int64_t) f4;
1565	0	int64_t f2f5_2 = f2_2 * (int64_t) f5;
1566	0	int64_t f2f6_2 = f2_2 * (int64_t) f6;
1567	0	int64_t f2f7_2 = f2_2 * (int64_t) f7;
1568	0	int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1569	0	int64_t f2f9_38 = f2 * (int64_t) f9_38;
1570	0	int64_t f3f3_2 = f3_2 * (int64_t) f3;
1571	0	int64_t f3f4_2 = f3_2 * (int64_t) f4;
1572	0	int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1573	0	int64_t f3f6_2 = f3_2 * (int64_t) f6;
1574	0	int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1575	0	int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1576	0	int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1577	0	int64_t f4f4 = f4 * (int64_t) f4;
1578	0	int64_t f4f5_2 = f4_2 * (int64_t) f5;
1579	0	int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1580	0	int64_t f4f7_38 = f4 * (int64_t) f7_38;
1581	0	int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1582	0	int64_t f4f9_38 = f4 * (int64_t) f9_38;
1583	0	int64_t f5f5_38 = f5 * (int64_t) f5_38;
1584	0	int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1585	0	int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1586	0	int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1587	0	int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1588	0	int64_t f6f6_19 = f6 * (int64_t) f6_19;
1589	0	int64_t f6f7_38 = f6 * (int64_t) f7_38;
1590	0	int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1591	0	int64_t f6f9_38 = f6 * (int64_t) f9_38;
1592	0	int64_t f7f7_38 = f7 * (int64_t) f7_38;
1593	0	int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1594	0	int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1595	0	int64_t f8f8_19 = f8 * (int64_t) f8_19;
1596	0	int64_t f8f9_38 = f8 * (int64_t) f9_38;
1597	0	int64_t f9f9_38 = f9 * (int64_t) f9_38;
1598	0	int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
1599	0	int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
1600	0	int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
1601	0	int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
1602	0	int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
1603	0	int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
1604	0	int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
1605	0	int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
1606	0	int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
1607	0	int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
1608	0	int64_t carry0;
1609	0	int64_t carry1;
1610	0	int64_t carry2;
1611	0	int64_t carry3;
1612	0	int64_t carry4;
1613	0	int64_t carry5;
1614	0	int64_t carry6;
1615	0	int64_t carry7;
1616	0	int64_t carry8;
1617	0	int64_t carry9;
1618	0
1619	0	h0 += h0;
1620	0	h1 += h1;
1621	0	h2 += h2;
1622	0	h3 += h3;
1623	0	h4 += h4;
1624	0	h5 += h5;
1625	0	h6 += h6;
1626	0	h7 += h7;
1627	0	h8 += h8;
1628	0	h9 += h9;
1629	0
1630	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1631	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1632	0
1633	0	carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1634	0	carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1635	0
1636	0	carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1637	0	carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1638	0
1639	0	carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1640	0	carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1641	0
1642	0	carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1643	0	carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1644	0
1645	0	carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1646	0
1647	0	carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1648	0
1649	0	h[0] = (int32_t)h0;
1650	0	h[1] = (int32_t)h1;
1651	0	h[2] = (int32_t)h2;
1652	0	h[3] = (int32_t)h3;
1653	0	h[4] = (int32_t)h4;
1654	0	h[5] = (int32_t)h5;
1655	0	h[6] = (int32_t)h6;
1656	0	h[7] = (int32_t)h7;
1657	0	h[8] = (int32_t)h8;
1658	0	h[9] = (int32_t)h9;
1659	0	}
1660
1661	0	static void fe_pow22523(fe out, const fe z) {
1662	0	fe t0;
1663	0	fe t1;
1664	0	fe t2;
1665	0	int i;
1666	0
1667	0	fe_sq(t0, z);
1668	0	fe_sq(t1, t0);
1669	0	for (i = 1; i < 2; ++i) {
1670	0	fe_sq(t1, t1);
1671	0	}
1672	0	fe_mul(t1, z, t1);
1673	0	fe_mul(t0, t0, t1);
1674	0	fe_sq(t0, t0);
1675	0	fe_mul(t0, t1, t0);
1676	0	fe_sq(t1, t0);
1677	0	for (i = 1; i < 5; ++i) {
1678	0	fe_sq(t1, t1);
1679	0	}
1680	0	fe_mul(t0, t1, t0);
1681	0	fe_sq(t1, t0);
1682	0	for (i = 1; i < 10; ++i) {
1683	0	fe_sq(t1, t1);
1684	0	}
1685	0	fe_mul(t1, t1, t0);
1686	0	fe_sq(t2, t1);
1687	0	for (i = 1; i < 20; ++i) {
1688	0	fe_sq(t2, t2);
1689	0	}
1690	0	fe_mul(t1, t2, t1);
1691	0	fe_sq(t1, t1);
1692	0	for (i = 1; i < 10; ++i) {
1693	0	fe_sq(t1, t1);
1694	0	}
1695	0	fe_mul(t0, t1, t0);
1696	0	fe_sq(t1, t0);
1697	0	for (i = 1; i < 50; ++i) {
1698	0	fe_sq(t1, t1);
1699	0	}
1700	0	fe_mul(t1, t1, t0);
1701	0	fe_sq(t2, t1);
1702	0	for (i = 1; i < 100; ++i) {
1703	0	fe_sq(t2, t2);
1704	0	}
1705	0	fe_mul(t1, t2, t1);
1706	0	fe_sq(t1, t1);
1707	0	for (i = 1; i < 50; ++i) {
1708	0	fe_sq(t1, t1);
1709	0	}
1710	0	fe_mul(t0, t1, t0);
1711	0	fe_sq(t0, t0);
1712	0	for (i = 1; i < 2; ++i) {
1713	0	fe_sq(t0, t0);
1714	0	}
1715	0	fe_mul(out, t0, z);
1716	0	}
1717
1718		/* ge means group element.
1719
1720		* Here the group is the set of pairs (x,y) of field elements (see fe.h)
1721		* satisfying -x^2 + y^2 = 1 + d x^2y^2
1722		* where d = -121665/121666.
1723		*
1724		* Representations:
1725		* ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1726		* ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1727		* ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1728		* ge_precomp (Duif): (y+x,y-x,2dxy) */
1729
1730		typedef struct {
1731		fe X;
1732		fe Y;
1733		fe Z;
1734		} ge_p2;
1735
1736		typedef struct {
1737		fe X;
1738		fe Y;
1739		fe Z;
1740		fe T;
1741		} ge_p3;
1742
1743		typedef struct {
1744		fe X;
1745		fe Y;
1746		fe Z;
1747		fe T;
1748		} ge_p1p1;
1749
1750		typedef struct {
1751		fe yplusx;
1752		fe yminusx;
1753		fe xy2d;
1754		} ge_precomp;
1755
1756		typedef struct {
1757		fe YplusX;
1758		fe YminusX;
1759		fe Z;
1760		fe T2d;
1761		} ge_cached;
1762
1763	0	static void ge_tobytes(uint8_t s, const ge_p2 h) {
1764	0	fe recip;
1765	0	fe x;
1766	0	fe y;
1767	0
1768	0	fe_invert(recip, h->Z);
1769	0	fe_mul(x, h->X, recip);
1770	0	fe_mul(y, h->Y, recip);
1771	0	fe_tobytes(s, y);
1772	0	s[31] ^= fe_isnegative(x) << 7;
1773	0	}
1774
1775	0	static void ge_p3_tobytes(uint8_t s, const ge_p3 h) {
1776	0	fe recip;
1777	0	fe x;
1778	0	fe y;
1779	0
1780	0	fe_invert(recip, h->Z);
1781	0	fe_mul(x, h->X, recip);
1782	0	fe_mul(y, h->Y, recip);
1783	0	fe_tobytes(s, y);
1784	0	s[31] ^= fe_isnegative(x) << 7;
1785	0	}
1786
1787		static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729,
1788		-8787816, -6275908, -3247719, -18696448, -12055116};
1789
1790		static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472,
1791		-272473, -25146209, -2005654, 326686, 11406482};
1792
1793	0	static int ge_frombytes_vartime(ge_p3 h, const uint8_t s) {
1794	0	fe u;
1795	0	fe v;
1796	0	fe v3;
1797	0	fe vxx;
1798	0	fe check;
1799	0
1800	0	fe_frombytes(h->Y, s);
1801	0	fe_1(h->Z);
1802	0	fe_sq(u, h->Y);
1803	0	fe_mul(v, u, d);
1804	0	fe_sub(u, u, h->Z); /* u = y^2-1 */
1805	0	fe_add(v, v, h->Z); /* v = dy^2+1 */
1806	0
1807	0	fe_sq(v3, v);
1808	0	fe_mul(v3, v3, v); /* v3 = v^3 */
1809	0	fe_sq(h->X, v3);
1810	0	fe_mul(h->X, h->X, v);
1811	0	fe_mul(h->X, h->X, u); /* x = uv^7 */
1812	0
1813	0	fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
1814	0	fe_mul(h->X, h->X, v3);
1815	0	fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
1816	0
1817	0	fe_sq(vxx, h->X);
1818	0	fe_mul(vxx, vxx, v);
1819	0	fe_sub(check, vxx, u); /* vx^2-u */
1820	0	if (fe_isnonzero(check)) {
1821	0	fe_add(check, vxx, u); /* vx^2+u */
1822	0	if (fe_isnonzero(check)) {
1823	0	return -1;
1824	0	}
1825	0	fe_mul(h->X, h->X, sqrtm1);
1826	0	}
1827	0
1828	0	if (fe_isnegative(h->X) != (s[31] >> 7)) {
1829	0	fe_neg(h->X, h->X);
1830	0	}
1831	0
1832	0	fe_mul(h->T, h->X, h->Y);
1833	0	return 0;
1834	0	}
1835
1836	0	static void ge_p2_0(ge_p2 *h) {
1837	0	fe_0(h->X);
1838	0	fe_1(h->Y);
1839	0	fe_1(h->Z);
1840	0	}
1841
1842	0	static void ge_p3_0(ge_p3 *h) {
1843	0	fe_0(h->X);
1844	0	fe_1(h->Y);
1845	0	fe_1(h->Z);
1846	0	fe_0(h->T);
1847	0	}
1848
1849	0	static void ge_precomp_0(ge_precomp *h) {
1850	0	fe_1(h->yplusx);
1851	0	fe_1(h->yminusx);
1852	0	fe_0(h->xy2d);
1853	0	}
1854
1855		/* r = p */
1856	0	static void ge_p3_to_p2(ge_p2 r, const ge_p3 p) {
1857	0	fe_copy(r->X, p->X);
1858	0	fe_copy(r->Y, p->Y);
1859	0	fe_copy(r->Z, p->Z);
1860	0	}
1861
1862		static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458,
1863		15978800, -12551817, -6495438, 29715968, 9444199};
1864
1865		/* r = p */
1866	0	static void ge_p3_to_cached(ge_cached r, const ge_p3 p) {
1867	0	fe_add(r->YplusX, p->Y, p->X);
1868	0	fe_sub(r->YminusX, p->Y, p->X);
1869	0	fe_copy(r->Z, p->Z);
1870	0	fe_mul(r->T2d, p->T, d2);
1871	0	}
1872
1873		/* r = p */
1874	0	static void ge_p1p1_to_p2(ge_p2 r, const ge_p1p1 p) {
1875	0	fe_mul(r->X, p->X, p->T);
1876	0	fe_mul(r->Y, p->Y, p->Z);
1877	0	fe_mul(r->Z, p->Z, p->T);
1878	0	}
1879
1880		/* r = p */
1881	0	static void ge_p1p1_to_p3(ge_p3 r, const ge_p1p1 p) {
1882	0	fe_mul(r->X, p->X, p->T);
1883	0	fe_mul(r->Y, p->Y, p->Z);
1884	0	fe_mul(r->Z, p->Z, p->T);
1885	0	fe_mul(r->T, p->X, p->Y);
1886	0	}
1887
1888		/* r = 2 * p */
1889	0	static void ge_p2_dbl(ge_p1p1 r, const ge_p2 p) {
1890	0	fe t0;
1891	0
1892	0	fe_sq(r->X, p->X);
1893	0	fe_sq(r->Z, p->Y);
1894	0	fe_sq2(r->T, p->Z);
1895	0	fe_add(r->Y, p->X, p->Y);
1896	0	fe_sq(t0, r->Y);
1897	0	fe_add(r->Y, r->Z, r->X);
1898	0	fe_sub(r->Z, r->Z, r->X);
1899	0	fe_sub(r->X, t0, r->Y);
1900	0	fe_sub(r->T, r->T, r->Z);
1901	0	}
1902
1903		/* r = 2 * p */
1904	0	static void ge_p3_dbl(ge_p1p1 r, const ge_p3 p) {
1905	0	ge_p2 q;
1906	0	ge_p3_to_p2(&q, p);
1907	0	ge_p2_dbl(r, &q);
1908	0	}
1909
1910		/* r = p + q */
1911	0	static void ge_madd(ge_p1p1 r, const ge_p3 p, const ge_precomp *q) {
1912	0	fe t0;
1913	0
1914	0	fe_add(r->X, p->Y, p->X);
1915	0	fe_sub(r->Y, p->Y, p->X);
1916	0	fe_mul(r->Z, r->X, q->yplusx);
1917	0	fe_mul(r->Y, r->Y, q->yminusx);
1918	0	fe_mul(r->T, q->xy2d, p->T);
1919	0	fe_add(t0, p->Z, p->Z);
1920	0	fe_sub(r->X, r->Z, r->Y);
1921	0	fe_add(r->Y, r->Z, r->Y);
1922	0	fe_add(r->Z, t0, r->T);
1923	0	fe_sub(r->T, t0, r->T);
1924	0	}
1925
1926		/* r = p - q */
1927	0	static void ge_msub(ge_p1p1 r, const ge_p3 p, const ge_precomp *q) {
1928	0	fe t0;
1929	0
1930	0	fe_add(r->X, p->Y, p->X);
1931	0	fe_sub(r->Y, p->Y, p->X);
1932	0	fe_mul(r->Z, r->X, q->yminusx);
1933	0	fe_mul(r->Y, r->Y, q->yplusx);
1934	0	fe_mul(r->T, q->xy2d, p->T);
1935	0	fe_add(t0, p->Z, p->Z);
1936	0	fe_sub(r->X, r->Z, r->Y);
1937	0	fe_add(r->Y, r->Z, r->Y);
1938	0	fe_sub(r->Z, t0, r->T);
1939	0	fe_add(r->T, t0, r->T);
1940	0	}
1941
1942		/* r = p + q */
1943	0	static void ge_add(ge_p1p1 r, const ge_p3 p, const ge_cached *q) {
1944	0	fe t0;
1945	0
1946	0	fe_add(r->X, p->Y, p->X);
1947	0	fe_sub(r->Y, p->Y, p->X);
1948	0	fe_mul(r->Z, r->X, q->YplusX);
1949	0	fe_mul(r->Y, r->Y, q->YminusX);
1950	0	fe_mul(r->T, q->T2d, p->T);
1951	0	fe_mul(r->X, p->Z, q->Z);
1952	0	fe_add(t0, r->X, r->X);
1953	0	fe_sub(r->X, r->Z, r->Y);
1954	0	fe_add(r->Y, r->Z, r->Y);
1955	0	fe_add(r->Z, t0, r->T);
1956	0	fe_sub(r->T, t0, r->T);
1957	0	}
1958
1959		/* r = p - q */
1960	0	static void ge_sub(ge_p1p1 r, const ge_p3 p, const ge_cached *q) {
1961	0	fe t0;
1962	0
1963	0	fe_add(r->X, p->Y, p->X);
1964	0	fe_sub(r->Y, p->Y, p->X);
1965	0	fe_mul(r->Z, r->X, q->YminusX);
1966	0	fe_mul(r->Y, r->Y, q->YplusX);
1967	0	fe_mul(r->T, q->T2d, p->T);
1968	0	fe_mul(r->X, p->Z, q->Z);
1969	0	fe_add(t0, r->X, r->X);
1970	0	fe_sub(r->X, r->Z, r->Y);
1971	0	fe_add(r->Y, r->Z, r->Y);
1972	0	fe_sub(r->Z, t0, r->T);
1973	0	fe_add(r->T, t0, r->T);
1974	0	}
1975
1976	0	static uint8_t equal(signed char b, signed char c) {
1977	0	uint8_t ub = b;
1978	0	uint8_t uc = c;
1979	0	uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
1980	0	uint32_t y = x; /* 0: yes; 1..255: no */
1981	0	y -= 1; /* 4294967295: yes; 0..254: no */
1982	0	y >>= 31; /* 1: yes; 0: no */
1983	0	return y;
1984	0	}
1985
1986	0	static void cmov(ge_precomp t, const ge_precomp u, uint8_t b) {
1987	0	fe_cmov(t->yplusx, u->yplusx, b);
1988	0	fe_cmov(t->yminusx, u->yminusx, b);
1989	0	fe_cmov(t->xy2d, u->xy2d, b);
1990	0	}
1991
1992		/* k25519Precomp[i][j] = (j+1)256^iB */
1993		static const ge_precomp k25519Precomp[32][8] = {
1994		{
1995		{
1996		{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
1997		27544626, -11754271, -6079156, 2047605},
1998		{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
1999		5043384, 19500929, -15469378},
2000		{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2001		29287919, 11864899, -24514362, -4438546},
2002		},
2003		{
2004		{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2005		-11717903, -3814571, -358445, -10211303},
2006		{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2007		-15616551, 11189268, -26829678, -5319081},
2008		{26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2009		-3128826, -9541118, -15472047, -4166697},
2010		},
2011		{
2012		{15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2013		27787600, -14772189, 28944400, -1550024},
2014		{16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2015		16354577, -11775962, 7689662, 11199574},
2016		{30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2017		7512774, 10017326, -17749093, -9920357},
2018		},
2019		{
2020		{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2021		-28926210, 15006023, 3284568, -6276540},
2022		{23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2023		7464579, 9656445, 13059162, 10374397},
2024		{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2025		-3839045, -641708, -101325},
2026		},
2027		{
2028		{10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2029		32867885, 14515107, -15438304, 10819380},
2030		{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2031		12483688, -12668491, 5581306},
2032		{19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2033		28542350, 13850243, -23678021, -15815942},
2034		},
2035		{
2036		{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2037		-19188627, -15224819, -9818940, -12085777},
2038		{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2039		-15689887, 1762328, 14866737},
2040		{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2041		-28236412, 3959421, 27914454, 4383652},
2042		},
2043		{
2044		{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2045		5230134, -23952439, -15175766},
2046		{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2047		20654025, 16520125, 30598449, 7715701},
2048		{28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2049		-31400660, 1370708, 29794553, -1409300},
2050		},
2051		{
2052		{14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2053		30290735, 10876454, -33154098, 2381726},
2054		{-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2055		-6236617, 3696005, -32300832, 15351955},
2056		{27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2057		-32961401, -2970515, 29551813, 10109425},
2058		},
2059		},
2060		{
2061		{
2062		{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2063		-2378284, -1627556, 10092783, -4764171},
2064		{27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2065		-32508754, 12005538, -17810127, 12803510},
2066		{17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2067		30364213, -9038194, 18016357, 4397660},
2068		},
2069		{
2070		{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2071		-26619106, 14544525, -17477504, 982639},
2072		{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2073		-4120128, -21047696, 9934963},
2074		{5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2075		-14747930, 4559895, -30123922, -10897950},
2076		},
2077		{
2078		{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2079		24191034, 4541697, -13338309, 5500568},
2080		{12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2081		-17430592, 12264343, 10874051, 13524335},
2082		{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2083		5080568, -22528059, 5376628},
2084		},
2085		{
2086		{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2087		-22321305, -9447443, 4535768, 1569007},
2088		{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2089		-30494562, 3044290, 31848280, 12543772},
2090		{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2091		-27377195, -2062731, 7718482, 14474653},
2092		},
2093		{
2094		{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2095		-7236665, 24316168, -5253567},
2096		{13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2097		33040651, -13424532, -20729456, 8321686},
2098		{21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
2099		23845965, -11874838, -9984458, 608372},
2100		},
2101		{
2102		{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
2103		1123968, -6780577, 27229399, 23887},
2104		{-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
2105		12797024, -6440308, -1633405, 16678954},
2106		{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
2107		-1508144, -4795045, -17169265, 4904953},
2108		},
2109		{
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2111		5169211, 16191880, 2128236, -4326833},
2112		{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
2113		-29806336, 916033, -6882542, -2986532},
2114		{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
2115		285431, 2763829, 15736322, 4143876},
2116		},
2117		{
2118		{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
2119		-14594663, 23527084, -16458268},
2120		{33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
2121		-32625340, 4087881, -15188911, -14416214},
2122		{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
2123		4357868, -4774191, -16323038},
2124		},
2125		},
2126		{
2127		{
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2129		23365147, -3949732, 7390890, 2759800},
2130		{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
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2133		9208236, 15886429, 16489664},
2134		},
2135		{
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2138		{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
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2140		{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
2141		-30341101, -7336386, 13847711, 5387222},
2142		},
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2149		11094161, 15689506, 3140038, -16510092},
2150		},
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2157		-15266516, 27000813, -10195553},
2158		},
2159		{
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2161		5336097, 6750977, -14521026},
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2164		{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
2165		-11144307, -2627664, -5990708, -14166033},
2166		},
2167		{
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2169		27884329, 2847284, 2655861, 1738395},
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2172		{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
2173		5821408, 10478196, 8544890},
2174		},
2175		{
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2181		27491595, -4612359, 3179268, -9478891},
2182		},
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2189		28326862, 1721092, -19558642, -3131606},
2190		},
2191		},
2192		{
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2199		2014099, -9050574, -2369172, -5877341},
2200		},
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2208		},
2209		{
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2222		{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
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2224		},
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2240		},
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2255		7283490, -15148073, -19526700, 7734629},
2256		},
2257		},
2258		{
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2266		},
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2270		{8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
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2290		},
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2298		},
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2321		1661597, -12551441, 15271676, -15452665},
2322		},
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2324		{
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2348		},
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2364		},
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2380		},
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2388		},
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2390		{
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2398		},
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2422		},
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2430		},
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2438		},
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2446		},
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2950		},
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2984		{
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2991		22503767, 5561594, -3646624, 3898661},
2992		},
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3000		},
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3048		},
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3050		{
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3082		},
3083		{
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3090		},
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3097		-29171540, 12361135, -18685978, 4578290},
3098		},
3099		{
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3101		-22544529, 14074919, 21964432, 8235257},
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3106		},
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3110		{11423335, -5468059, 32344216, 8962751, 24989809, 9241752,
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3112		{-1409668, 12530728, -6368726, 10847387, 19531186, -14132160,
3113		-11709148, 7791794, -27245943, 4383347},
3114		},
3115		},
3116		{
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3119		-4862407, -4906449, 27193557, 6245191},
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3123		31168030, 13952092, -29571492, -3635906},
3124		},
3125		{
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3128		{-16275802, 14667797, 15906460, 12155291, -22111149, -9039718,
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3130		{-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725,
3131		12376320, 31632953, 190926},
3132		},
3133		{
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3135		-8288749, 4508564, -25341555, -3627528},
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3139		-1800575, -14108036, -24878478, 1541286},
3140		},
3141		{
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3143		-21802117, -3567481, 20456845, -1885033},
3144		{27019610, 12299467, -13658288, -1603234, -12861660, -4861471,
3145		-19540150, -5016058, 29439641, 15138866},
3146		{21536104, -6626420, -32447818, -10690208, -22408077, 5175814,
3147		-5420040, -16361163, 7779328, 109896},
3148		},
3149		{
3150		{30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390,
3151		12180118, 23177719, -554075},
3152		{26572847, 3405927, -31701700, 12890905, -19265668, 5335866,
3153		-6493768, 2378492, 4439158, -13279347},
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3155		14819434, -12731527, -17717757, -5461437},
3156		},
3157		{
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3159		-820954, 2177225, 8550082, -15114165},
3160		{-18473302, 16596775, -381660, 15663611, 22860960, 15585581,
3161		-27844109, -3582739, -23260460, -8428588},
3162		{-32480551, 15707275, -8205912, -5652081, 29464558, 2713815,
3163		-22725137, 15860482, -21902570, 1494193},
3164		},
3165		{
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3168		{-28464899, 1553205, 32536856, -10473729, -24691605, -406174,
3169		-8914625, -2933896, -29903758, 15553883},
3170		{21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572,
3171		14513274, 19375923, -12647961},
3172		},
3173		{
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3175		-6222716, 2862653, 9455043},
3176		{29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124,
3177		-2990080, 15511449, 4789663},
3178		{-20679756, 7004547, 8824831, -9434977, -4045704, -3750736,
3179		-5754762, 108893, 23513200, 16652362},
3180		},
3181		},
3182		{
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3185		-6650416, -12936300, -18319198, 10212860},
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3189		11344424, 864440, -2499677, -16710063},
3190		},
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3197		149635, -15452774, 7159369},
3198		},
3199		{
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3201		8312176, 22477218, -8403385},
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3203		24256460, -4864995, -22548173, 9334109},
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3205		-21413845, 14253545, -22587149, 536906},
3206		},
3207		{
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3213		15693155, -5045064, -13373962},
3214		},
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3218		{10188286, -15770834, -7336361, 13427543, 22223443, 14896287,
3219		30743455, 7116568, -21786507, 5427593},
3220		{696102, 13206899, 27047647, -10632082, 15285305, -9853179,
3221		10798490, -4578720, 19236243, 12477404},
3222		},
3223		{
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3225		-3897669, 11180504, -23169516, 7733644},
3226		{17800790, -14036179, -27000429, -11766671, 23887827, 3149671,
3227		23466177, -10538171, 10322027, 15313801},
3228		{26246234, 11968874, 32263343, -5468728, 6830755, -13323031,
3229		-15794704, -101982, -24449242, 10890804},
3230		},
3231		{
3232		{-31365647, 10271363, -12660625, -6267268, 16690207, -13062544,
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3238		},
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3245		-24884878, -13526194, 5537438, -13914319},
3246		},
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3248		{
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3256		},
3257		{
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3260		{-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656,
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3264		},
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3270		{-21389266, 421932, 26597266, 6860826, 22486084, -6737172,
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3272		},
3273		{
3274		{-20184622, 2338216, 19788685, -9620956, -4001265, -8740893,
3275		-20271184, 4733254, 3727144, -12934448},
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3278		{30069250, -11435332, 30434654, 2958439, 18399564, -976289,
3279		12296869, 9204260, -16432438, 9648165},
3280		},
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3288		},
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3295		-23491134, -11323352, 3059833, -11782870},
3296		},
3297		{
3298		{10141598, 6082907, 17829293, -1947643, 9830092, 13613136,
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3300		{33114168, -15889352, -26525686, -13343397, 33076705, 8716171,
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3303		-16637686, 3891704, 26353178, 693168},
3304		},
3305		{
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3310		{18171223, -11934626, -12500402, 15197122, -11038147, -15230035,
3311		-19172240, -16046376, 8764035, 12309598},
3312		},
3313		},
3314		{
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3320		{-31399660, 11407555, 25755363, 6891399, -3256938, 14872274,
3321		-24849353, 8141295, -10632534, -585479},
3322		},
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3325		-9698672, -11329050, 30944593, 1130208},
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3329		-5908146, -408818, -137719},
3330		},
3331		{
3332		{16091085, -16253926, 18599252, 7340678, 2137637, -1221657,
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3338		},
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3354		},
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3366		{-19288047, 4453152, 15298546, -16178388, 22115043, -15972604,
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3368		{-9558883, -16518835, 33238498, 13506958, 30505848, -1114596,
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3370		},
3371		{
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3376		{12966261, 15550616, -32038948, -1615346, 21025980, -629444,
3377		5642325, 7188737, 18895762, 12629579},
3378		},
3379		},
3380		{
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3389		{
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3396		},
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3404		},
3405		{
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3409		24180793, -12570394, 27679908, -1648928},
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3427		-29595790, 9884936, -9368926, 4745410},
3428		},
3429		{
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3436		},
3437		{
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3443		8601684, -139197, 4242895},
3444		},
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3446		{
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3454		},
3455		{
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3462		},
3463		{
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3467		25947805, 15286587, 30997318, -6703063},
3468		{7392032, 16618386, 23946583, -8039892, -13265164, -1533858,
3469		-14197445, -2321576, 17649998, -250080},
3470		},
3471		{
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3474		{-17558673, 1763594, -33114336, 15908610, -30040870, -12174295,
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3476		{-19889700, -5977008, -24111293, -9688870, 10799743, -16571957,
3477		40450, -4431835, 4862400, 1133},
3478		},
3479		{
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3481		7258061, 311861, -30594991, -7379421},
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3483		16527196, 18278453, 15405622},
3484		{-4381906, 8508652, -19898366, -3674424, -5984453, 15149970,
3485		-13313598, 843523, -21875062, 13626197},
3486		},
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3829		10103221, -18512313, 2424778},
3830		{366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678,
3831		1344109, -3642553, 12412659},
3832		},
3833		{
3834		{-24001791, 7690286, 14929416, -168257, -32210835, -13412986,
3835		24162697, -15326504, -3141501, 11179385},
3836		{18289522, -14724954, 8056945, 16430056, -21729724, 7842514,
3837		-6001441, -1486897, -18684645, -11443503},
3838		{476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959,
3839		13403813, 11052904, 5219329},
3840		},
3841		},
3842		{
3843		{
3844		{20678546, -8375738, -32671898, 8849123, -5009758, 14574752,
3845		31186971, -3973730, 9014762, -8579056},
3846		{-13644050, -10350239, -15962508, 5075808, -1514661, -11534600,
3847		-33102500, 9160280, 8473550, -3256838},
3848		{24900749, 14435722, 17209120, -15292541, -22592275, 9878983,
3849		-7689309, -16335821, -24568481, 11788948},
3850		},
3851		{
3852		{-3118155, -11395194, -13802089, 14797441, 9652448, -6845904,
3853		-20037437, 10410733, -24568470, -1458691},
3854		{-15659161, 16736706, -22467150, 10215878, -9097177, 7563911,
3855		11871841, -12505194, -18513325, 8464118},
3856		{-23400612, 8348507, -14585951, -861714, -3950205, -6373419,
3857		14325289, 8628612, 33313881, -8370517},
3858		},
3859		{
3860		{-20186973, -4967935, 22367356, 5271547, -1097117, -4788838,
3861		-24805667, -10236854, -8940735, -5818269},
3862		{-6948785, -1795212, -32625683, -16021179, 32635414, -7374245,
3863		15989197, -12838188, 28358192, -4253904},
3864		{-23561781, -2799059, -32351682, -1661963, -9147719, 10429267,
3865		-16637684, 4072016, -5351664, 5596589},
3866		},
3867		{
3868		{-28236598, -3390048, 12312896, 6213178, 3117142, 16078565,
3869		29266239, 2557221, 1768301, 15373193},
3870		{-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902,
3871		-4504991, -24660491, 3442910},
3872		{-30210571, 5124043, 14181784, 8197961, 18964734, -11939093,
3873		22597931, 7176455, -18585478, 13365930},
3874		},
3875		{
3876		{-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107,
3877		-8570186, -9689599, -3031667},
3878		{25008904, -10771599, -4305031, -9638010, 16265036, 15721635,
3879		683793, -11823784, 15723479, -15163481},
3880		{-9660625, 12374379, -27006999, -7026148, -7724114, -12314514,
3881		11879682, 5400171, 519526, -1235876},
3882		},
3883		{
3884		{22258397, -16332233, -7869817, 14613016, -22520255, -2950923,
3885		-20353881, 7315967, 16648397, 7605640},
3886		{-8081308, -8464597, -8223311, 9719710, 19259459, -15348212,
3887		23994942, -5281555, -9468848, 4763278},
3888		{-21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
3889		31088447, -7764523, -11356529, 728112},
3890		},
3891		{
3892		{26047220, -11751471, -6900323, -16521798, 24092068, 9158119,
3893		-4273545, -12555558, -29365436, -5498272},
3894		{17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007,
3895		12327945, 10750447, 10014012},
3896		{-10312768, 3936952, 9156313, -8897683, 16498692, -994647,
3897		-27481051, -666732, 3424691, 7540221},
3898		},
3899		{
3900		{30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422,
3901		-16317219, -9244265, 15258046},
3902		{13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
3903		2711395, 1062915, -5136345},
3904		{-19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
3905		-6066489, 12194497, 32960380, 1459310},
3906		},
3907		},
3908		{
3909		{
3910		{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
3911		-6101885, 18638003, -11174937},
3912		{31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
3913		9012486, -7584354, -6643087, -5442636},
3914		{-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
3915		9677543, -32294889, -6456008},
3916		},
3917		{
3918		{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
3919		-7839692, -7852844, -8138429},
3920		{-15236356, -15433509, 7766470, 746860, 26346930, -10221762,
3921		-27333451, 10754588, -9431476, 5203576},
3922		{31834314, 14135496, -770007, 5159118, 20917671, -16768096,
3923		-7467973, -7337524, 31809243, 7347066},
3924		},
3925		{
3926		{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
3927		19797970, -12211255, 15192876, -2087490},
3928		{-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
3929		10609330, 12694420, 33473243, -13382104},
3930		{33184999, 11180355, 15832085, -11385430, -1633671, 225884,
3931		15089336, -11023903, -6135662, 14480053},
3932		},
3933		{
3934		{31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
3935		5496208, 13685227, 27595050, 8737275},
3936		{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
3937		-31008351, -12610604, 26498114, 66511},
3938		{22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
3939		30540766, -4286747, -13327787, -7515095},
3940		},
3941		{
3942		{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
3943		8205540, 13585437, -17127465, 15115439},
3944		{23711543, -672915, 31206561, -8362711, 6164647, -9709987,
3945		-33535882, -1426096, 8236921, 16492939},
3946		{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
3947		19574902, 10071562, 6708380, -6222424},
3948		},
3949		{
3950		{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
3951		9328700, 29955601, -11678310},
3952		{3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
3953		-25892142, -12635595, -9917575, 6216608},
3954		{-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
3955		24822830, -6146567, -26767480, 7525079},
3956		},
3957		{
3958		{-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
3959		-910336, -2782495, -19386633, 11994101},
3960		{21691500, -13624626, -641331, -14367021, 3285881, -3483596,
3961		-25064666, 9718258, -7477437, 13381418},
3962		{18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
3963		23111648, -6375247, 28535282, 15779576},
3964		},
3965		{
3966		{30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
3967		-14068454, 12021730, 9955285, -16303356},
3968		{9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
3969		-18426029, 9924399, 20194861, 13380996},
3970		{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
3971		-1984914, 15707771, 26342023, 10146099},
3972		},
3973		},
3974		{
3975		{
3976		{-26016874, -219943, 21339191, -41388, 19745256, -2878700,
3977		-29637280, 2227040, 21612326, -545728},
3978		{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
3979		25764461, 12243797, -20856566, 11649658},
3980		{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
3981		6114064, 33514190, 2333242},
3982		},
3983		{
3984		{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
3985		-6679750, -12670638, 24350578, -13450001},
3986		{-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
3987		-31536088, -10406836, 8317860, 12352766},
3988		{18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
3989		-23552096, -2287550, 20712163, 6719373},
3990		},
3991		{
3992		{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
3993		-3763210, 26224235, -3297458},
3994		{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
3995		21728352, 9493610, 18620611, -16428628},
3996		{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
3997		-5269471, -9725556, -30701573, -16479657},
3998		},
3999		{
4000		{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
4001		12248509, -5240639, 13735342, 1934062},
4002		{25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
4003		-15136294, -3765346, -21277997, 5473616},
4004		{31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
4005		-7125085, 12469656, 29111212, -5451014},
4006		},
4007		{
4008		{24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
4009		24367466, 6388839, -10295587, 452383},
4010		{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
4011		-24236251, -5915248, 15766062, 8407814},
4012		{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
4013		-8917023, -4388953, -8067909, 2276718},
4014		},
4015		{
4016		{30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
4017		-23827587, 5096219, 22740376, -7303417},
4018		{2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
4019		24051124, 13742383, -15637599, 13295222},
4020		{33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
4021		-17720195, -4612972, -4451357, -14669444},
4022		},
4023		{
4024		{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
4025		-2469266, -4141880, 7770569, 9620597},
4026		{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
4027		-1694323, -33502340, -14767970},
4028		{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
4029		1220118, 30494170, -11440799},
4030		},
4031		{
4032		{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
4033		-26739026, 926050, -1684339, -13333647},
4034		{13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
4035		9021034, 9078865, 3353509, 4033511},
4036		{-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
4037		23161163, 8839127, 27485041, 7356032},
4038		},
4039		},
4040		{
4041		{
4042		{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
4043		2625015, 28431036, -16771834},
4044		{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
4045		-22545972, 14150565, 15970762, 4099461},
4046		{29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
4047		13617293, -9937143, 11465739, 8317062},
4048		},
4049		{
4050		{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
4051		14898637, 3848455, 20969334, -5157516},
4052		{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
4053		-21610826, -3649888, 11177095, 14989547},
4054		{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
4055		13515641, 2581286, -28487508, 9930240},
4056		},
4057		{
4058		{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
4059		18345767, -13403753, 16291481, -5314038},
4060		{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
4061		6957617, 4368891, 9788741},
4062		{16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
4063		-21722536, -8613148, 16250552, -11111103},
4064		},
4065		{
4066		{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
4067		10604807, -30190403, 4782747},
4068		{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
4069		-9981571, 4383045, 22546403, 437323},
4070		{31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
4071		27343084, 2786261, -30633590, -14097016},
4072		},
4073		{
4074		{-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
4075		-19690631, 2355319, -19284671, -6114373},
4076		{15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
4077		18952177, 15496498, -29380133, 11754228},
4078		{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
4079		7141596, 11724556, 22761615, -10134141},
4080		},
4081		{
4082		{16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
4083		-28741185, -12227393, 32851222, 11717399},
4084		{11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
4085		31474879, 3483633, -1193175, -4030831},
4086		{-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4087		33142652, 6546660, -19985279, -3948376},
4088		},
4089		{
4090		{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4091		-8537131, -12833048, -30772034, -15486313},
4092		{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4093		-31135347, -16049879, 10928917, 3011958},
4094		{-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4095		-30831056, -12805180, 18008031, 10258577},
4096		},
4097		{
4098		{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4099		-1853465, 1367120, 25127874, 6671743},
4100		{29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4101		21382910, 11042292, 25838796, 4642684},
4102		{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4103		30468147, -13900640, 18423289, 4177476},
4104		},
4105		},
4106		};
4107
4108	0	static uint8_t negative(signed char b) {
4109	0	uint32_t x = b;
4110	0	x >>= 31; /* 1: yes; 0: no */
4111	0	return x;
4112	0	}
4113
4114	0	static void table_select(ge_precomp *t, int pos, signed char b) {
4115	0	ge_precomp minust;
4116	0	uint8_t bnegative = negative(b);
4117	0	uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4118	0
4119	0	ge_precomp_0(t);
4120	0	cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4121	0	cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4122	0	cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4123	0	cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4124	0	cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4125	0	cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4126	0	cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4127	0	cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4128	0	fe_copy(minust.yplusx, t->yminusx);
4129	0	fe_copy(minust.yminusx, t->yplusx);
4130	0	fe_neg(minust.xy2d, t->xy2d);
4131	0	cmov(t, &minust, bnegative);
4132	0	}
4133
4134		/* h = a * B
4135		* where a = a[0]+256*a[1]+...+256^31 a[31]
4136		* B is the Ed25519 base point (x,4/5) with x positive.
4137		*
4138		* Preconditions:
4139		* a[31] <= 127 */
4140	0	static void ge_scalarmult_base(ge_p3 h, const uint8_t a) {
4141	0	signed char e[64];
4142	0	signed char carry;
4143	0	ge_p1p1 r;
4144	0	ge_p2 s;
4145	0	ge_precomp t;
4146	0	int i;
4147	0
4148	0	for (i = 0; i < 32; ++i) {
4149	0	e[2 * i + 0] = (a[i] >> 0) & 15;
4150	0	e[2 * i + 1] = (a[i] >> 4) & 15;
4151	0	}
4152	0	/* each e[i] is between 0 and 15 */
4153	0	/* e[63] is between 0 and 7 */
4154	0
4155	0	carry = 0;
4156	0	for (i = 0; i < 63; ++i) {
4157	0	e[i] += carry;
4158	0	carry = e[i] + 8;
4159	0	carry >>= 4;
4160	0	e[i] -= carry << 4;
4161	0	}
4162	0	e[63] += carry;
4163	0	/* each e[i] is between -8 and 8 */
4164	0
4165	0	ge_p3_0(h);
4166	0	for (i = 1; i < 64; i += 2) {
4167	0	table_select(&t, i / 2, e[i]);
4168	0	ge_madd(&r, h, &t);
4169	0	ge_p1p1_to_p3(h, &r);
4170	0	}
4171	0
4172	0	ge_p3_dbl(&r, h);
4173	0	ge_p1p1_to_p2(&s, &r);
4174	0	ge_p2_dbl(&r, &s);
4175	0	ge_p1p1_to_p2(&s, &r);
4176	0	ge_p2_dbl(&r, &s);
4177	0	ge_p1p1_to_p2(&s, &r);
4178	0	ge_p2_dbl(&r, &s);
4179	0	ge_p1p1_to_p3(h, &r);
4180	0
4181	0	for (i = 0; i < 64; i += 2) {
4182	0	table_select(&t, i / 2, e[i]);
4183	0	ge_madd(&r, h, &t);
4184	0	ge_p1p1_to_p3(h, &r);
4185	0	}
4186	0
4187	0	OPENSSL_cleanse(e, sizeof(e));
4188	0	}
4189
4190		#if !defined(BASE_2_51_IMPLEMENTED)
4191		/* Replace (f,g) with (g,f) if b == 1;
4192		* replace (f,g) with (f,g) if b == 0.
4193		*
4194		* Preconditions: b in {0,1}. */
4195		static void fe_cswap(fe f, fe g, unsigned int b) {
4196		size_t i;
4197		b = 0-b;
4198		for (i = 0; i < 10; i++) {
4199		int32_t x = f[i] ^ g[i];
4200		x &= b;
4201		f[i] ^= x;
4202		g[i] ^= x;
4203		}
4204		}
4205
4206		/* h = f * 121666
4207		* Can overlap h with f.
4208		*
4209		* Preconditions:
4210		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
4211		*
4212		* Postconditions:
4213		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc. */
4214		static void fe_mul121666(fe h, fe f) {
4215		int32_t f0 = f[0];
4216		int32_t f1 = f[1];
4217		int32_t f2 = f[2];
4218		int32_t f3 = f[3];
4219		int32_t f4 = f[4];
4220		int32_t f5 = f[5];
4221		int32_t f6 = f[6];
4222		int32_t f7 = f[7];
4223		int32_t f8 = f[8];
4224		int32_t f9 = f[9];
4225		int64_t h0 = f0 * (int64_t) 121666;
4226		int64_t h1 = f1 * (int64_t) 121666;
4227		int64_t h2 = f2 * (int64_t) 121666;
4228		int64_t h3 = f3 * (int64_t) 121666;
4229		int64_t h4 = f4 * (int64_t) 121666;
4230		int64_t h5 = f5 * (int64_t) 121666;
4231		int64_t h6 = f6 * (int64_t) 121666;
4232		int64_t h7 = f7 * (int64_t) 121666;
4233		int64_t h8 = f8 * (int64_t) 121666;
4234		int64_t h9 = f9 * (int64_t) 121666;
4235		int64_t carry0;
4236		int64_t carry1;
4237		int64_t carry2;
4238		int64_t carry3;
4239		int64_t carry4;
4240		int64_t carry5;
4241		int64_t carry6;
4242		int64_t carry7;
4243		int64_t carry8;
4244		int64_t carry9;
4245
4246		carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
4247		carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
4248		carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
4249		carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
4250		carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
4251
4252		carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
4253		carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
4254		carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
4255		carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
4256		carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
4257
4258		h[0] = (int32_t)h0;
4259		h[1] = (int32_t)h1;
4260		h[2] = (int32_t)h2;
4261		h[3] = (int32_t)h3;
4262		h[4] = (int32_t)h4;
4263		h[5] = (int32_t)h5;
4264		h[6] = (int32_t)h6;
4265		h[7] = (int32_t)h7;
4266		h[8] = (int32_t)h8;
4267		h[9] = (int32_t)h9;
4268		}
4269
4270		static void x25519_scalar_mult_generic(uint8_t out[32],
4271		const uint8_t scalar[32],
4272		const uint8_t point[32]) {
4273		fe x1, x2, z2, x3, z3, tmp0, tmp1;
4274		uint8_t e[32];
4275		unsigned swap = 0;
4276		int pos;
4277
4278		memcpy(e, scalar, 32);
4279		e[0] &= 248;
4280		e[31] &= 127;
4281		e[31] \|= 64;
4282		fe_frombytes(x1, point);
4283		fe_1(x2);
4284		fe_0(z2);
4285		fe_copy(x3, x1);
4286		fe_1(z3);
4287
4288		for (pos = 254; pos >= 0; --pos) {
4289		unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4290		swap ^= b;
4291		fe_cswap(x2, x3, swap);
4292		fe_cswap(z2, z3, swap);
4293		swap = b;
4294		fe_sub(tmp0, x3, z3);
4295		fe_sub(tmp1, x2, z2);
4296		fe_add(x2, x2, z2);
4297		fe_add(z2, x3, z3);
4298		fe_mul(z3, tmp0, x2);
4299		fe_mul(z2, z2, tmp1);
4300		fe_sq(tmp0, tmp1);
4301		fe_sq(tmp1, x2);
4302		fe_add(x3, z3, z2);
4303		fe_sub(z2, z3, z2);
4304		fe_mul(x2, tmp1, tmp0);
4305		fe_sub(tmp1, tmp1, tmp0);
4306		fe_sq(z2, z2);
4307		fe_mul121666(z3, tmp1);
4308		fe_sq(x3, x3);
4309		fe_add(tmp0, tmp0, z3);
4310		fe_mul(z3, x1, z2);
4311		fe_mul(z2, tmp1, tmp0);
4312		}
4313
4314		fe_invert(z2, z2);
4315		fe_mul(x2, x2, z2);
4316		fe_tobytes(out, x2);
4317
4318		OPENSSL_cleanse(e, sizeof(e));
4319		}
4320
4321		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4322		const uint8_t point[32]) {
4323		x25519_scalar_mult_generic(out, scalar, point);
4324		}
4325		#endif
4326
4327	0	static void slide(signed char r, const uint8_t a) {
4328	0	int i;
4329	0	int b;
4330	0	int k;
4331	0
4332	0	for (i = 0; i < 256; ++i) {
4333	0	r[i] = 1 & (a[i >> 3] >> (i & 7));
4334	0	}
4335	0
4336	0	for (i = 0; i < 256; ++i) {
4337	0	if (r[i]) {
4338	0	for (b = 1; b <= 6 && i + b < 256; ++b) {
4339	0	if (r[i + b]) {
4340	0	if (r[i] + (r[i + b] << b) <= 15) {
4341	0	r[i] += r[i + b] << b;
4342	0	r[i + b] = 0;
4343	0	} else if (r[i] - (r[i + b] << b) >= -15) {
4344	0	r[i] -= r[i + b] << b;
4345	0	for (k = i + b; k < 256; ++k) {
4346	0	if (!r[k]) {
4347	0	r[k] = 1;
4348	0	break;
4349	0	}
4350	0	r[k] = 0;
4351	0	}
4352	0	} else {
4353	0	break;
4354	0	}
4355	0	}
4356	0	}
4357	0	}
4358	0	}
4359	0	}
4360
4361		static const ge_precomp Bi[8] = {
4362		{
4363		{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4364		-11754271, -6079156, 2047605},
4365		{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4366		5043384, 19500929, -15469378},
4367		{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4368		11864899, -24514362, -4438546},
4369		},
4370		{
4371		{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4372		-14772189, 28944400, -1550024},
4373		{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4374		-11775962, 7689662, 11199574},
4375		{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4376		10017326, -17749093, -9920357},
4377		},
4378		{
4379		{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4380		14515107, -15438304, 10819380},
4381		{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4382		12483688, -12668491, 5581306},
4383		{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4384		13850243, -23678021, -15815942},
4385		},
4386		{
4387		{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4388		5230134, -23952439, -15175766},
4389		{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4390		16520125, 30598449, 7715701},
4391		{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4392		1370708, 29794553, -1409300},
4393		},
4394		{
4395		{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4396		-1361450, -13062696, 13821877},
4397		{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4398		-7212327, 18853322, -14220951},
4399		{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4400		-10431137, 2207753, -3209784},
4401		},
4402		{
4403		{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4404		-663000, -31111463, -16132436},
4405		{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4406		15725684, 171356, 6466918},
4407		{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4408		-14088058, -30714912, 16193877},
4409		},
4410		{
4411		{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4412		4729455, -18074513, 9256800},
4413		{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4414		9761698, -19827198, 630305},
4415		{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4416		-15960994, -2449256, -14291300},
4417		},
4418		{
4419		{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4420		15033784, 25105118, -7894876},
4421		{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4422		1573892, -2625887, 2198790, -15804619},
4423		{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4424		-16236442, -32461234, -12290683},
4425		},
4426		};
4427
4428		/* r = a * A + b * B
4429		* where a = a[0]+256*a[1]+...+256^31 a[31].
4430		* and b = b[0]+256*b[1]+...+256^31 b[31].
4431		* B is the Ed25519 base point (x,4/5) with x positive. */
4432		static void ge_double_scalarmult_vartime(ge_p2 r, const uint8_t a,
4433	0	const ge_p3 A, const uint8_t b) {
4434	0	signed char aslide[256];
4435	0	signed char bslide[256];
4436	0	ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4437	0	ge_p1p1 t;
4438	0	ge_p3 u;
4439	0	ge_p3 A2;
4440	0	int i;
4441	0
4442	0	slide(aslide, a);
4443	0	slide(bslide, b);
4444	0
4445	0	ge_p3_to_cached(&Ai[0], A);
4446	0	ge_p3_dbl(&t, A);
4447	0	ge_p1p1_to_p3(&A2, &t);
4448	0	ge_add(&t, &A2, &Ai[0]);
4449	0	ge_p1p1_to_p3(&u, &t);
4450	0	ge_p3_to_cached(&Ai[1], &u);
4451	0	ge_add(&t, &A2, &Ai[1]);
4452	0	ge_p1p1_to_p3(&u, &t);
4453	0	ge_p3_to_cached(&Ai[2], &u);
4454	0	ge_add(&t, &A2, &Ai[2]);
4455	0	ge_p1p1_to_p3(&u, &t);
4456	0	ge_p3_to_cached(&Ai[3], &u);
4457	0	ge_add(&t, &A2, &Ai[3]);
4458	0	ge_p1p1_to_p3(&u, &t);
4459	0	ge_p3_to_cached(&Ai[4], &u);
4460	0	ge_add(&t, &A2, &Ai[4]);
4461	0	ge_p1p1_to_p3(&u, &t);
4462	0	ge_p3_to_cached(&Ai[5], &u);
4463	0	ge_add(&t, &A2, &Ai[5]);
4464	0	ge_p1p1_to_p3(&u, &t);
4465	0	ge_p3_to_cached(&Ai[6], &u);
4466	0	ge_add(&t, &A2, &Ai[6]);
4467	0	ge_p1p1_to_p3(&u, &t);
4468	0	ge_p3_to_cached(&Ai[7], &u);
4469	0
4470	0	ge_p2_0(r);
4471	0
4472	0	for (i = 255; i >= 0; --i) {
4473	0	if (aslide[i] \|\| bslide[i]) {
4474	0	break;
4475	0	}
4476	0	}
4477	0
4478	0	for (; i >= 0; --i) {
4479	0	ge_p2_dbl(&t, r);
4480	0
4481	0	if (aslide[i] > 0) {
4482	0	ge_p1p1_to_p3(&u, &t);
4483	0	ge_add(&t, &u, &Ai[aslide[i] / 2]);
4484	0	} else if (aslide[i] < 0) {
4485	0	ge_p1p1_to_p3(&u, &t);
4486	0	ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4487	0	}
4488	0
4489	0	if (bslide[i] > 0) {
4490	0	ge_p1p1_to_p3(&u, &t);
4491	0	ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4492	0	} else if (bslide[i] < 0) {
4493	0	ge_p1p1_to_p3(&u, &t);
4494	0	ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4495	0	}
4496	0
4497	0	ge_p1p1_to_p2(r, &t);
4498	0	}
4499	0	}
4500
4501		/* The set of scalars is \Z/l
4502		* where l = 2^252 + 27742317777372353535851937790883648493. */
4503
4504		/* Input:
4505		* s[0]+256s[1]+...+256^63s[63] = s
4506		*
4507		* Output:
4508		* s[0]+256s[1]+...+256^31s[31] = s mod l
4509		* where l = 2^252 + 27742317777372353535851937790883648493.
4510		* Overwrites s in place. */
4511	0	static void x25519_sc_reduce(uint8_t *s) {
4512	0	int64_t s0 = 2097151 & load_3(s);
4513	0	int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
4514	0	int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
4515	0	int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
4516	0	int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
4517	0	int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
4518	0	int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
4519	0	int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
4520	0	int64_t s8 = 2097151 & load_3(s + 21);
4521	0	int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
4522	0	int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
4523	0	int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
4524	0	int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
4525	0	int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
4526	0	int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
4527	0	int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
4528	0	int64_t s16 = 2097151 & load_3(s + 42);
4529	0	int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
4530	0	int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
4531	0	int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
4532	0	int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
4533	0	int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
4534	0	int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
4535	0	int64_t s23 = (load_4(s + 60) >> 3);
4536	0	int64_t carry0;
4537	0	int64_t carry1;
4538	0	int64_t carry2;
4539	0	int64_t carry3;
4540	0	int64_t carry4;
4541	0	int64_t carry5;
4542	0	int64_t carry6;
4543	0	int64_t carry7;
4544	0	int64_t carry8;
4545	0	int64_t carry9;
4546	0	int64_t carry10;
4547	0	int64_t carry11;
4548	0	int64_t carry12;
4549	0	int64_t carry13;
4550	0	int64_t carry14;
4551	0	int64_t carry15;
4552	0	int64_t carry16;
4553	0
4554	0	s11 += s23 * 666643;
4555	0	s12 += s23 * 470296;
4556	0	s13 += s23 * 654183;
4557	0	s14 -= s23 * 997805;
4558	0	s15 += s23 * 136657;
4559	0	s16 -= s23 * 683901;
4560	0	s23 = 0;
4561	0
4562	0	s10 += s22 * 666643;
4563	0	s11 += s22 * 470296;
4564	0	s12 += s22 * 654183;
4565	0	s13 -= s22 * 997805;
4566	0	s14 += s22 * 136657;
4567	0	s15 -= s22 * 683901;
4568	0	s22 = 0;
4569	0
4570	0	s9 += s21 * 666643;
4571	0	s10 += s21 * 470296;
4572	0	s11 += s21 * 654183;
4573	0	s12 -= s21 * 997805;
4574	0	s13 += s21 * 136657;
4575	0	s14 -= s21 * 683901;
4576	0	s21 = 0;
4577	0
4578	0	s8 += s20 * 666643;
4579	0	s9 += s20 * 470296;
4580	0	s10 += s20 * 654183;
4581	0	s11 -= s20 * 997805;
4582	0	s12 += s20 * 136657;
4583	0	s13 -= s20 * 683901;
4584	0	s20 = 0;
4585	0
4586	0	s7 += s19 * 666643;
4587	0	s8 += s19 * 470296;
4588	0	s9 += s19 * 654183;
4589	0	s10 -= s19 * 997805;
4590	0	s11 += s19 * 136657;
4591	0	s12 -= s19 * 683901;
4592	0	s19 = 0;
4593	0
4594	0	s6 += s18 * 666643;
4595	0	s7 += s18 * 470296;
4596	0	s8 += s18 * 654183;
4597	0	s9 -= s18 * 997805;
4598	0	s10 += s18 * 136657;
4599	0	s11 -= s18 * 683901;
4600	0	s18 = 0;
4601	0
4602	0	carry6 = (s6 + (1 << 20)) >> 21;
4603	0	s7 += carry6;
4604	0	s6 -= carry6 * (1 << 21);
4605	0	carry8 = (s8 + (1 << 20)) >> 21;
4606	0	s9 += carry8;
4607	0	s8 -= carry8 * (1 << 21);
4608	0	carry10 = (s10 + (1 << 20)) >> 21;
4609	0	s11 += carry10;
4610	0	s10 -= carry10 * (1 << 21);
4611	0	carry12 = (s12 + (1 << 20)) >> 21;
4612	0	s13 += carry12;
4613	0	s12 -= carry12 * (1 << 21);
4614	0	carry14 = (s14 + (1 << 20)) >> 21;
4615	0	s15 += carry14;
4616	0	s14 -= carry14 * (1 << 21);
4617	0	carry16 = (s16 + (1 << 20)) >> 21;
4618	0	s17 += carry16;
4619	0	s16 -= carry16 * (1 << 21);
4620	0
4621	0	carry7 = (s7 + (1 << 20)) >> 21;
4622	0	s8 += carry7;
4623	0	s7 -= carry7 * (1 << 21);
4624	0	carry9 = (s9 + (1 << 20)) >> 21;
4625	0	s10 += carry9;
4626	0	s9 -= carry9 * (1 << 21);
4627	0	carry11 = (s11 + (1 << 20)) >> 21;
4628	0	s12 += carry11;
4629	0	s11 -= carry11 * (1 << 21);
4630	0	carry13 = (s13 + (1 << 20)) >> 21;
4631	0	s14 += carry13;
4632	0	s13 -= carry13 * (1 << 21);
4633	0	carry15 = (s15 + (1 << 20)) >> 21;
4634	0	s16 += carry15;
4635	0	s15 -= carry15 * (1 << 21);
4636	0
4637	0	s5 += s17 * 666643;
4638	0	s6 += s17 * 470296;
4639	0	s7 += s17 * 654183;
4640	0	s8 -= s17 * 997805;
4641	0	s9 += s17 * 136657;
4642	0	s10 -= s17 * 683901;
4643	0	s17 = 0;
4644	0
4645	0	s4 += s16 * 666643;
4646	0	s5 += s16 * 470296;
4647	0	s6 += s16 * 654183;
4648	0	s7 -= s16 * 997805;
4649	0	s8 += s16 * 136657;
4650	0	s9 -= s16 * 683901;
4651	0	s16 = 0;
4652	0
4653	0	s3 += s15 * 666643;
4654	0	s4 += s15 * 470296;
4655	0	s5 += s15 * 654183;
4656	0	s6 -= s15 * 997805;
4657	0	s7 += s15 * 136657;
4658	0	s8 -= s15 * 683901;
4659	0	s15 = 0;
4660	0
4661	0	s2 += s14 * 666643;
4662	0	s3 += s14 * 470296;
4663	0	s4 += s14 * 654183;
4664	0	s5 -= s14 * 997805;
4665	0	s6 += s14 * 136657;
4666	0	s7 -= s14 * 683901;
4667	0	s14 = 0;
4668	0
4669	0	s1 += s13 * 666643;
4670	0	s2 += s13 * 470296;
4671	0	s3 += s13 * 654183;
4672	0	s4 -= s13 * 997805;
4673	0	s5 += s13 * 136657;
4674	0	s6 -= s13 * 683901;
4675	0	s13 = 0;
4676	0
4677	0	s0 += s12 * 666643;
4678	0	s1 += s12 * 470296;
4679	0	s2 += s12 * 654183;
4680	0	s3 -= s12 * 997805;
4681	0	s4 += s12 * 136657;
4682	0	s5 -= s12 * 683901;
4683	0	s12 = 0;
4684	0
4685	0	carry0 = (s0 + (1 << 20)) >> 21;
4686	0	s1 += carry0;
4687	0	s0 -= carry0 * (1 << 21);
4688	0	carry2 = (s2 + (1 << 20)) >> 21;
4689	0	s3 += carry2;
4690	0	s2 -= carry2 * (1 << 21);
4691	0	carry4 = (s4 + (1 << 20)) >> 21;
4692	0	s5 += carry4;
4693	0	s4 -= carry4 * (1 << 21);
4694	0	carry6 = (s6 + (1 << 20)) >> 21;
4695	0	s7 += carry6;
4696	0	s6 -= carry6 * (1 << 21);
4697	0	carry8 = (s8 + (1 << 20)) >> 21;
4698	0	s9 += carry8;
4699	0	s8 -= carry8 * (1 << 21);
4700	0	carry10 = (s10 + (1 << 20)) >> 21;
4701	0	s11 += carry10;
4702	0	s10 -= carry10 * (1 << 21);
4703	0
4704	0	carry1 = (s1 + (1 << 20)) >> 21;
4705	0	s2 += carry1;
4706	0	s1 -= carry1 * (1 << 21);
4707	0	carry3 = (s3 + (1 << 20)) >> 21;
4708	0	s4 += carry3;
4709	0	s3 -= carry3 * (1 << 21);
4710	0	carry5 = (s5 + (1 << 20)) >> 21;
4711	0	s6 += carry5;
4712	0	s5 -= carry5 * (1 << 21);
4713	0	carry7 = (s7 + (1 << 20)) >> 21;
4714	0	s8 += carry7;
4715	0	s7 -= carry7 * (1 << 21);
4716	0	carry9 = (s9 + (1 << 20)) >> 21;
4717	0	s10 += carry9;
4718	0	s9 -= carry9 * (1 << 21);
4719	0	carry11 = (s11 + (1 << 20)) >> 21;
4720	0	s12 += carry11;
4721	0	s11 -= carry11 * (1 << 21);
4722	0
4723	0	s0 += s12 * 666643;
4724	0	s1 += s12 * 470296;
4725	0	s2 += s12 * 654183;
4726	0	s3 -= s12 * 997805;
4727	0	s4 += s12 * 136657;
4728	0	s5 -= s12 * 683901;
4729	0	s12 = 0;
4730	0
4731	0	carry0 = s0 >> 21;
4732	0	s1 += carry0;
4733	0	s0 -= carry0 * (1 << 21);
4734	0	carry1 = s1 >> 21;
4735	0	s2 += carry1;
4736	0	s1 -= carry1 * (1 << 21);
4737	0	carry2 = s2 >> 21;
4738	0	s3 += carry2;
4739	0	s2 -= carry2 * (1 << 21);
4740	0	carry3 = s3 >> 21;
4741	0	s4 += carry3;
4742	0	s3 -= carry3 * (1 << 21);
4743	0	carry4 = s4 >> 21;
4744	0	s5 += carry4;
4745	0	s4 -= carry4 * (1 << 21);
4746	0	carry5 = s5 >> 21;
4747	0	s6 += carry5;
4748	0	s5 -= carry5 * (1 << 21);
4749	0	carry6 = s6 >> 21;
4750	0	s7 += carry6;
4751	0	s6 -= carry6 * (1 << 21);
4752	0	carry7 = s7 >> 21;
4753	0	s8 += carry7;
4754	0	s7 -= carry7 * (1 << 21);
4755	0	carry8 = s8 >> 21;
4756	0	s9 += carry8;
4757	0	s8 -= carry8 * (1 << 21);
4758	0	carry9 = s9 >> 21;
4759	0	s10 += carry9;
4760	0	s9 -= carry9 * (1 << 21);
4761	0	carry10 = s10 >> 21;
4762	0	s11 += carry10;
4763	0	s10 -= carry10 * (1 << 21);
4764	0	carry11 = s11 >> 21;
4765	0	s12 += carry11;
4766	0	s11 -= carry11 * (1 << 21);
4767	0
4768	0	s0 += s12 * 666643;
4769	0	s1 += s12 * 470296;
4770	0	s2 += s12 * 654183;
4771	0	s3 -= s12 * 997805;
4772	0	s4 += s12 * 136657;
4773	0	s5 -= s12 * 683901;
4774	0	s12 = 0;
4775	0
4776	0	carry0 = s0 >> 21;
4777	0	s1 += carry0;
4778	0	s0 -= carry0 * (1 << 21);
4779	0	carry1 = s1 >> 21;
4780	0	s2 += carry1;
4781	0	s1 -= carry1 * (1 << 21);
4782	0	carry2 = s2 >> 21;
4783	0	s3 += carry2;
4784	0	s2 -= carry2 * (1 << 21);
4785	0	carry3 = s3 >> 21;
4786	0	s4 += carry3;
4787	0	s3 -= carry3 * (1 << 21);
4788	0	carry4 = s4 >> 21;
4789	0	s5 += carry4;
4790	0	s4 -= carry4 * (1 << 21);
4791	0	carry5 = s5 >> 21;
4792	0	s6 += carry5;
4793	0	s5 -= carry5 * (1 << 21);
4794	0	carry6 = s6 >> 21;
4795	0	s7 += carry6;
4796	0	s6 -= carry6 * (1 << 21);
4797	0	carry7 = s7 >> 21;
4798	0	s8 += carry7;
4799	0	s7 -= carry7 * (1 << 21);
4800	0	carry8 = s8 >> 21;
4801	0	s9 += carry8;
4802	0	s8 -= carry8 * (1 << 21);
4803	0	carry9 = s9 >> 21;
4804	0	s10 += carry9;
4805	0	s9 -= carry9 * (1 << 21);
4806	0	carry10 = s10 >> 21;
4807	0	s11 += carry10;
4808	0	s10 -= carry10 * (1 << 21);
4809	0
4810	0	s[0] = (uint8_t)(s0 >> 0);
4811	0	s[1] = (uint8_t)(s0 >> 8);
4812	0	s[2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
4813	0	s[3] = (uint8_t)(s1 >> 3);
4814	0	s[4] = (uint8_t)(s1 >> 11);
4815	0	s[5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
4816	0	s[6] = (uint8_t)(s2 >> 6);
4817	0	s[7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
4818	0	s[8] = (uint8_t)(s3 >> 1);
4819	0	s[9] = (uint8_t)(s3 >> 9);
4820	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
4821	0	s[11] = (uint8_t)(s4 >> 4);
4822	0	s[12] = (uint8_t)(s4 >> 12);
4823	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
4824	0	s[14] = (uint8_t)(s5 >> 7);
4825	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
4826	0	s[16] = (uint8_t)(s6 >> 2);
4827	0	s[17] = (uint8_t)(s6 >> 10);
4828	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
4829	0	s[19] = (uint8_t)(s7 >> 5);
4830	0	s[20] = (uint8_t)(s7 >> 13);
4831	0	s[21] = (uint8_t)(s8 >> 0);
4832	0	s[22] = (uint8_t)(s8 >> 8);
4833	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
4834	0	s[24] = (uint8_t)(s9 >> 3);
4835	0	s[25] = (uint8_t)(s9 >> 11);
4836	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
4837	0	s[27] = (uint8_t)(s10 >> 6);
4838	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
4839	0	s[29] = (uint8_t)(s11 >> 1);
4840	0	s[30] = (uint8_t)(s11 >> 9);
4841	0	s[31] = (uint8_t)(s11 >> 17);
4842	0	}
4843
4844		/* Input:
4845		* a[0]+256a[1]+...+256^31a[31] = a
4846		* b[0]+256b[1]+...+256^31b[31] = b
4847		* c[0]+256c[1]+...+256^31c[31] = c
4848		*
4849		* Output:
4850		* s[0]+256s[1]+...+256^31s[31] = (ab+c) mod l
4851		* where l = 2^252 + 27742317777372353535851937790883648493. */
4852		static void sc_muladd(uint8_t s, const uint8_t a, const uint8_t *b,
4853	0	const uint8_t *c) {
4854	0	int64_t a0 = 2097151 & load_3(a);
4855	0	int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
4856	0	int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
4857	0	int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
4858	0	int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
4859	0	int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
4860	0	int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
4861	0	int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
4862	0	int64_t a8 = 2097151 & load_3(a + 21);
4863	0	int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
4864	0	int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
4865	0	int64_t a11 = (load_4(a + 28) >> 7);
4866	0	int64_t b0 = 2097151 & load_3(b);
4867	0	int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
4868	0	int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
4869	0	int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
4870	0	int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
4871	0	int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
4872	0	int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
4873	0	int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
4874	0	int64_t b8 = 2097151 & load_3(b + 21);
4875	0	int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
4876	0	int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
4877	0	int64_t b11 = (load_4(b + 28) >> 7);
4878	0	int64_t c0 = 2097151 & load_3(c);
4879	0	int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
4880	0	int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
4881	0	int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
4882	0	int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
4883	0	int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
4884	0	int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
4885	0	int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
4886	0	int64_t c8 = 2097151 & load_3(c + 21);
4887	0	int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
4888	0	int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
4889	0	int64_t c11 = (load_4(c + 28) >> 7);
4890	0	int64_t s0;
4891	0	int64_t s1;
4892	0	int64_t s2;
4893	0	int64_t s3;
4894	0	int64_t s4;
4895	0	int64_t s5;
4896	0	int64_t s6;
4897	0	int64_t s7;
4898	0	int64_t s8;
4899	0	int64_t s9;
4900	0	int64_t s10;
4901	0	int64_t s11;
4902	0	int64_t s12;
4903	0	int64_t s13;
4904	0	int64_t s14;
4905	0	int64_t s15;
4906	0	int64_t s16;
4907	0	int64_t s17;
4908	0	int64_t s18;
4909	0	int64_t s19;
4910	0	int64_t s20;
4911	0	int64_t s21;
4912	0	int64_t s22;
4913	0	int64_t s23;
4914	0	int64_t carry0;
4915	0	int64_t carry1;
4916	0	int64_t carry2;
4917	0	int64_t carry3;
4918	0	int64_t carry4;
4919	0	int64_t carry5;
4920	0	int64_t carry6;
4921	0	int64_t carry7;
4922	0	int64_t carry8;
4923	0	int64_t carry9;
4924	0	int64_t carry10;
4925	0	int64_t carry11;
4926	0	int64_t carry12;
4927	0	int64_t carry13;
4928	0	int64_t carry14;
4929	0	int64_t carry15;
4930	0	int64_t carry16;
4931	0	int64_t carry17;
4932	0	int64_t carry18;
4933	0	int64_t carry19;
4934	0	int64_t carry20;
4935	0	int64_t carry21;
4936	0	int64_t carry22;
4937	0
4938	0	s0 = c0 + a0 * b0;
4939	0	s1 = c1 + a0 * b1 + a1 * b0;
4940	0	s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
4941	0	s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
4942	0	s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
4943	0	s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
4944	0	s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
4945	0	s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
4946	0	a6 * b1 + a7 * b0;
4947	0	s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
4948	0	a6 * b2 + a7 * b1 + a8 * b0;
4949	0	s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
4950	0	a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
4951	0	s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
4952	0	a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
4953	0	s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
4954	0	a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
4955	0	s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
4956	0	a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
4957	0	s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
4958	0	a9 * b4 + a10 * b3 + a11 * b2;
4959	0	s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
4960	0	a10 * b4 + a11 * b3;
4961	0	s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
4962	0	a11 * b4;
4963	0	s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
4964	0	s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
4965	0	s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
4966	0	s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
4967	0	s20 = a9 * b11 + a10 * b10 + a11 * b9;
4968	0	s21 = a10 * b11 + a11 * b10;
4969	0	s22 = a11 * b11;
4970	0	s23 = 0;
4971	0
4972	0	carry0 = (s0 + (1 << 20)) >> 21;
4973	0	s1 += carry0;
4974	0	s0 -= carry0 * (1 << 21);
4975	0	carry2 = (s2 + (1 << 20)) >> 21;
4976	0	s3 += carry2;
4977	0	s2 -= carry2 * (1 << 21);
4978	0	carry4 = (s4 + (1 << 20)) >> 21;
4979	0	s5 += carry4;
4980	0	s4 -= carry4 * (1 << 21);
4981	0	carry6 = (s6 + (1 << 20)) >> 21;
4982	0	s7 += carry6;
4983	0	s6 -= carry6 * (1 << 21);
4984	0	carry8 = (s8 + (1 << 20)) >> 21;
4985	0	s9 += carry8;
4986	0	s8 -= carry8 * (1 << 21);
4987	0	carry10 = (s10 + (1 << 20)) >> 21;
4988	0	s11 += carry10;
4989	0	s10 -= carry10 * (1 << 21);
4990	0	carry12 = (s12 + (1 << 20)) >> 21;
4991	0	s13 += carry12;
4992	0	s12 -= carry12 * (1 << 21);
4993	0	carry14 = (s14 + (1 << 20)) >> 21;
4994	0	s15 += carry14;
4995	0	s14 -= carry14 * (1 << 21);
4996	0	carry16 = (s16 + (1 << 20)) >> 21;
4997	0	s17 += carry16;
4998	0	s16 -= carry16 * (1 << 21);
4999	0	carry18 = (s18 + (1 << 20)) >> 21;
5000	0	s19 += carry18;
5001	0	s18 -= carry18 * (1 << 21);
5002	0	carry20 = (s20 + (1 << 20)) >> 21;
5003	0	s21 += carry20;
5004	0	s20 -= carry20 * (1 << 21);
5005	0	carry22 = (s22 + (1 << 20)) >> 21;
5006	0	s23 += carry22;
5007	0	s22 -= carry22 * (1 << 21);
5008	0
5009	0	carry1 = (s1 + (1 << 20)) >> 21;
5010	0	s2 += carry1;
5011	0	s1 -= carry1 * (1 << 21);
5012	0	carry3 = (s3 + (1 << 20)) >> 21;
5013	0	s4 += carry3;
5014	0	s3 -= carry3 * (1 << 21);
5015	0	carry5 = (s5 + (1 << 20)) >> 21;
5016	0	s6 += carry5;
5017	0	s5 -= carry5 * (1 << 21);
5018	0	carry7 = (s7 + (1 << 20)) >> 21;
5019	0	s8 += carry7;
5020	0	s7 -= carry7 * (1 << 21);
5021	0	carry9 = (s9 + (1 << 20)) >> 21;
5022	0	s10 += carry9;
5023	0	s9 -= carry9 * (1 << 21);
5024	0	carry11 = (s11 + (1 << 20)) >> 21;
5025	0	s12 += carry11;
5026	0	s11 -= carry11 * (1 << 21);
5027	0	carry13 = (s13 + (1 << 20)) >> 21;
5028	0	s14 += carry13;
5029	0	s13 -= carry13 * (1 << 21);
5030	0	carry15 = (s15 + (1 << 20)) >> 21;
5031	0	s16 += carry15;
5032	0	s15 -= carry15 * (1 << 21);
5033	0	carry17 = (s17 + (1 << 20)) >> 21;
5034	0	s18 += carry17;
5035	0	s17 -= carry17 * (1 << 21);
5036	0	carry19 = (s19 + (1 << 20)) >> 21;
5037	0	s20 += carry19;
5038	0	s19 -= carry19 * (1 << 21);
5039	0	carry21 = (s21 + (1 << 20)) >> 21;
5040	0	s22 += carry21;
5041	0	s21 -= carry21 * (1 << 21);
5042	0
5043	0	s11 += s23 * 666643;
5044	0	s12 += s23 * 470296;
5045	0	s13 += s23 * 654183;
5046	0	s14 -= s23 * 997805;
5047	0	s15 += s23 * 136657;
5048	0	s16 -= s23 * 683901;
5049	0	s23 = 0;
5050	0
5051	0	s10 += s22 * 666643;
5052	0	s11 += s22 * 470296;
5053	0	s12 += s22 * 654183;
5054	0	s13 -= s22 * 997805;
5055	0	s14 += s22 * 136657;
5056	0	s15 -= s22 * 683901;
5057	0	s22 = 0;
5058	0
5059	0	s9 += s21 * 666643;
5060	0	s10 += s21 * 470296;
5061	0	s11 += s21 * 654183;
5062	0	s12 -= s21 * 997805;
5063	0	s13 += s21 * 136657;
5064	0	s14 -= s21 * 683901;
5065	0	s21 = 0;
5066	0
5067	0	s8 += s20 * 666643;
5068	0	s9 += s20 * 470296;
5069	0	s10 += s20 * 654183;
5070	0	s11 -= s20 * 997805;
5071	0	s12 += s20 * 136657;
5072	0	s13 -= s20 * 683901;
5073	0	s20 = 0;
5074	0
5075	0	s7 += s19 * 666643;
5076	0	s8 += s19 * 470296;
5077	0	s9 += s19 * 654183;
5078	0	s10 -= s19 * 997805;
5079	0	s11 += s19 * 136657;
5080	0	s12 -= s19 * 683901;
5081	0	s19 = 0;
5082	0
5083	0	s6 += s18 * 666643;
5084	0	s7 += s18 * 470296;
5085	0	s8 += s18 * 654183;
5086	0	s9 -= s18 * 997805;
5087	0	s10 += s18 * 136657;
5088	0	s11 -= s18 * 683901;
5089	0	s18 = 0;
5090	0
5091	0	carry6 = (s6 + (1 << 20)) >> 21;
5092	0	s7 += carry6;
5093	0	s6 -= carry6 * (1 << 21);
5094	0	carry8 = (s8 + (1 << 20)) >> 21;
5095	0	s9 += carry8;
5096	0	s8 -= carry8 * (1 << 21);
5097	0	carry10 = (s10 + (1 << 20)) >> 21;
5098	0	s11 += carry10;
5099	0	s10 -= carry10 * (1 << 21);
5100	0	carry12 = (s12 + (1 << 20)) >> 21;
5101	0	s13 += carry12;
5102	0	s12 -= carry12 * (1 << 21);
5103	0	carry14 = (s14 + (1 << 20)) >> 21;
5104	0	s15 += carry14;
5105	0	s14 -= carry14 * (1 << 21);
5106	0	carry16 = (s16 + (1 << 20)) >> 21;
5107	0	s17 += carry16;
5108	0	s16 -= carry16 * (1 << 21);
5109	0
5110	0	carry7 = (s7 + (1 << 20)) >> 21;
5111	0	s8 += carry7;
5112	0	s7 -= carry7 * (1 << 21);
5113	0	carry9 = (s9 + (1 << 20)) >> 21;
5114	0	s10 += carry9;
5115	0	s9 -= carry9 * (1 << 21);
5116	0	carry11 = (s11 + (1 << 20)) >> 21;
5117	0	s12 += carry11;
5118	0	s11 -= carry11 * (1 << 21);
5119	0	carry13 = (s13 + (1 << 20)) >> 21;
5120	0	s14 += carry13;
5121	0	s13 -= carry13 * (1 << 21);
5122	0	carry15 = (s15 + (1 << 20)) >> 21;
5123	0	s16 += carry15;
5124	0	s15 -= carry15 * (1 << 21);
5125	0
5126	0	s5 += s17 * 666643;
5127	0	s6 += s17 * 470296;
5128	0	s7 += s17 * 654183;
5129	0	s8 -= s17 * 997805;
5130	0	s9 += s17 * 136657;
5131	0	s10 -= s17 * 683901;
5132	0	s17 = 0;
5133	0
5134	0	s4 += s16 * 666643;
5135	0	s5 += s16 * 470296;
5136	0	s6 += s16 * 654183;
5137	0	s7 -= s16 * 997805;
5138	0	s8 += s16 * 136657;
5139	0	s9 -= s16 * 683901;
5140	0	s16 = 0;
5141	0
5142	0	s3 += s15 * 666643;
5143	0	s4 += s15 * 470296;
5144	0	s5 += s15 * 654183;
5145	0	s6 -= s15 * 997805;
5146	0	s7 += s15 * 136657;
5147	0	s8 -= s15 * 683901;
5148	0	s15 = 0;
5149	0
5150	0	s2 += s14 * 666643;
5151	0	s3 += s14 * 470296;
5152	0	s4 += s14 * 654183;
5153	0	s5 -= s14 * 997805;
5154	0	s6 += s14 * 136657;
5155	0	s7 -= s14 * 683901;
5156	0	s14 = 0;
5157	0
5158	0	s1 += s13 * 666643;
5159	0	s2 += s13 * 470296;
5160	0	s3 += s13 * 654183;
5161	0	s4 -= s13 * 997805;
5162	0	s5 += s13 * 136657;
5163	0	s6 -= s13 * 683901;
5164	0	s13 = 0;
5165	0
5166	0	s0 += s12 * 666643;
5167	0	s1 += s12 * 470296;
5168	0	s2 += s12 * 654183;
5169	0	s3 -= s12 * 997805;
5170	0	s4 += s12 * 136657;
5171	0	s5 -= s12 * 683901;
5172	0	s12 = 0;
5173	0
5174	0	carry0 = (s0 + (1 << 20)) >> 21;
5175	0	s1 += carry0;
5176	0	s0 -= carry0 * (1 << 21);
5177	0	carry2 = (s2 + (1 << 20)) >> 21;
5178	0	s3 += carry2;
5179	0	s2 -= carry2 * (1 << 21);
5180	0	carry4 = (s4 + (1 << 20)) >> 21;
5181	0	s5 += carry4;
5182	0	s4 -= carry4 * (1 << 21);
5183	0	carry6 = (s6 + (1 << 20)) >> 21;
5184	0	s7 += carry6;
5185	0	s6 -= carry6 * (1 << 21);
5186	0	carry8 = (s8 + (1 << 20)) >> 21;
5187	0	s9 += carry8;
5188	0	s8 -= carry8 * (1 << 21);
5189	0	carry10 = (s10 + (1 << 20)) >> 21;
5190	0	s11 += carry10;
5191	0	s10 -= carry10 * (1 << 21);
5192	0
5193	0	carry1 = (s1 + (1 << 20)) >> 21;
5194	0	s2 += carry1;
5195	0	s1 -= carry1 * (1 << 21);
5196	0	carry3 = (s3 + (1 << 20)) >> 21;
5197	0	s4 += carry3;
5198	0	s3 -= carry3 * (1 << 21);
5199	0	carry5 = (s5 + (1 << 20)) >> 21;
5200	0	s6 += carry5;
5201	0	s5 -= carry5 * (1 << 21);
5202	0	carry7 = (s7 + (1 << 20)) >> 21;
5203	0	s8 += carry7;
5204	0	s7 -= carry7 * (1 << 21);
5205	0	carry9 = (s9 + (1 << 20)) >> 21;
5206	0	s10 += carry9;
5207	0	s9 -= carry9 * (1 << 21);
5208	0	carry11 = (s11 + (1 << 20)) >> 21;
5209	0	s12 += carry11;
5210	0	s11 -= carry11 * (1 << 21);
5211	0
5212	0	s0 += s12 * 666643;
5213	0	s1 += s12 * 470296;
5214	0	s2 += s12 * 654183;
5215	0	s3 -= s12 * 997805;
5216	0	s4 += s12 * 136657;
5217	0	s5 -= s12 * 683901;
5218	0	s12 = 0;
5219	0
5220	0	carry0 = s0 >> 21;
5221	0	s1 += carry0;
5222	0	s0 -= carry0 * (1 << 21);
5223	0	carry1 = s1 >> 21;
5224	0	s2 += carry1;
5225	0	s1 -= carry1 * (1 << 21);
5226	0	carry2 = s2 >> 21;
5227	0	s3 += carry2;
5228	0	s2 -= carry2 * (1 << 21);
5229	0	carry3 = s3 >> 21;
5230	0	s4 += carry3;
5231	0	s3 -= carry3 * (1 << 21);
5232	0	carry4 = s4 >> 21;
5233	0	s5 += carry4;
5234	0	s4 -= carry4 * (1 << 21);
5235	0	carry5 = s5 >> 21;
5236	0	s6 += carry5;
5237	0	s5 -= carry5 * (1 << 21);
5238	0	carry6 = s6 >> 21;
5239	0	s7 += carry6;
5240	0	s6 -= carry6 * (1 << 21);
5241	0	carry7 = s7 >> 21;
5242	0	s8 += carry7;
5243	0	s7 -= carry7 * (1 << 21);
5244	0	carry8 = s8 >> 21;
5245	0	s9 += carry8;
5246	0	s8 -= carry8 * (1 << 21);
5247	0	carry9 = s9 >> 21;
5248	0	s10 += carry9;
5249	0	s9 -= carry9 * (1 << 21);
5250	0	carry10 = s10 >> 21;
5251	0	s11 += carry10;
5252	0	s10 -= carry10 * (1 << 21);
5253	0	carry11 = s11 >> 21;
5254	0	s12 += carry11;
5255	0	s11 -= carry11 * (1 << 21);
5256	0
5257	0	s0 += s12 * 666643;
5258	0	s1 += s12 * 470296;
5259	0	s2 += s12 * 654183;
5260	0	s3 -= s12 * 997805;
5261	0	s4 += s12 * 136657;
5262	0	s5 -= s12 * 683901;
5263	0	s12 = 0;
5264	0
5265	0	carry0 = s0 >> 21;
5266	0	s1 += carry0;
5267	0	s0 -= carry0 * (1 << 21);
5268	0	carry1 = s1 >> 21;
5269	0	s2 += carry1;
5270	0	s1 -= carry1 * (1 << 21);
5271	0	carry2 = s2 >> 21;
5272	0	s3 += carry2;
5273	0	s2 -= carry2 * (1 << 21);
5274	0	carry3 = s3 >> 21;
5275	0	s4 += carry3;
5276	0	s3 -= carry3 * (1 << 21);
5277	0	carry4 = s4 >> 21;
5278	0	s5 += carry4;
5279	0	s4 -= carry4 * (1 << 21);
5280	0	carry5 = s5 >> 21;
5281	0	s6 += carry5;
5282	0	s5 -= carry5 * (1 << 21);
5283	0	carry6 = s6 >> 21;
5284	0	s7 += carry6;
5285	0	s6 -= carry6 * (1 << 21);
5286	0	carry7 = s7 >> 21;
5287	0	s8 += carry7;
5288	0	s7 -= carry7 * (1 << 21);
5289	0	carry8 = s8 >> 21;
5290	0	s9 += carry8;
5291	0	s8 -= carry8 * (1 << 21);
5292	0	carry9 = s9 >> 21;
5293	0	s10 += carry9;
5294	0	s9 -= carry9 * (1 << 21);
5295	0	carry10 = s10 >> 21;
5296	0	s11 += carry10;
5297	0	s10 -= carry10 * (1 << 21);
5298	0
5299	0	s[0] = (uint8_t)(s0 >> 0);
5300	0	s[1] = (uint8_t)(s0 >> 8);
5301	0	s[2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5302	0	s[3] = (uint8_t)(s1 >> 3);
5303	0	s[4] = (uint8_t)(s1 >> 11);
5304	0	s[5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5305	0	s[6] = (uint8_t)(s2 >> 6);
5306	0	s[7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5307	0	s[8] = (uint8_t)(s3 >> 1);
5308	0	s[9] = (uint8_t)(s3 >> 9);
5309	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5310	0	s[11] = (uint8_t)(s4 >> 4);
5311	0	s[12] = (uint8_t)(s4 >> 12);
5312	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5313	0	s[14] = (uint8_t)(s5 >> 7);
5314	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5315	0	s[16] = (uint8_t)(s6 >> 2);
5316	0	s[17] = (uint8_t)(s6 >> 10);
5317	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5318	0	s[19] = (uint8_t)(s7 >> 5);
5319	0	s[20] = (uint8_t)(s7 >> 13);
5320	0	s[21] = (uint8_t)(s8 >> 0);
5321	0	s[22] = (uint8_t)(s8 >> 8);
5322	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5323	0	s[24] = (uint8_t)(s9 >> 3);
5324	0	s[25] = (uint8_t)(s9 >> 11);
5325	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5326	0	s[27] = (uint8_t)(s10 >> 6);
5327	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5328	0	s[29] = (uint8_t)(s11 >> 1);
5329	0	s[30] = (uint8_t)(s11 >> 9);
5330	0	s[31] = (uint8_t)(s11 >> 17);
5331	0	}
5332
5333		int ED25519_sign(uint8_t out_sig, const uint8_t message, size_t message_len,
5334	0	const uint8_t public_key[32], const uint8_t private_key[32]) {
5335	0	uint8_t az[SHA512_DIGEST_LENGTH];
5336	0	uint8_t nonce[SHA512_DIGEST_LENGTH];
5337	0	ge_p3 R;
5338	0	uint8_t hram[SHA512_DIGEST_LENGTH];
5339	0	SHA512_CTX hash_ctx;
5340	0
5341	0	SHA512_Init(&hash_ctx);
5342	0	SHA512_Update(&hash_ctx, private_key, 32);
5343	0	SHA512_Final(az, &hash_ctx);
5344	0
5345	0	az[0] &= 248;
5346	0	az[31] &= 63;
5347	0	az[31] \|= 64;
5348	0
5349	0	SHA512_Init(&hash_ctx);
5350	0	SHA512_Update(&hash_ctx, az + 32, 32);
5351	0	SHA512_Update(&hash_ctx, message, message_len);
5352	0	SHA512_Final(nonce, &hash_ctx);
5353	0
5354	0	x25519_sc_reduce(nonce);
5355	0	ge_scalarmult_base(&R, nonce);
5356	0	ge_p3_tobytes(out_sig, &R);
5357	0
5358	0	SHA512_Init(&hash_ctx);
5359	0	SHA512_Update(&hash_ctx, out_sig, 32);
5360	0	SHA512_Update(&hash_ctx, public_key, 32);
5361	0	SHA512_Update(&hash_ctx, message, message_len);
5362	0	SHA512_Final(hram, &hash_ctx);
5363	0
5364	0	x25519_sc_reduce(hram);
5365	0	sc_muladd(out_sig + 32, hram, az, nonce);
5366	0
5367	0	OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx));
5368	0	OPENSSL_cleanse(nonce, sizeof(nonce));
5369	0	OPENSSL_cleanse(az, sizeof(az));
5370	0
5371	0	return 1;
5372	0	}
5373
5374		int ED25519_verify(const uint8_t *message, size_t message_len,
5375	0	const uint8_t signature[64], const uint8_t public_key[32]) {
5376	0	ge_p3 A;
5377	0	uint8_t rcopy[32];
5378	0	uint8_t scopy[32];
5379	0	SHA512_CTX hash_ctx;
5380	0	ge_p2 R;
5381	0	uint8_t rcheck[32];
5382	0	uint8_t h[SHA512_DIGEST_LENGTH];
5383	0
5384	0	if ((signature[63] & 224) != 0 \|\|
5385	0	ge_frombytes_vartime(&A, public_key) != 0) {
5386	0	return 0;
5387	0	}
5388	0
5389	0	fe_neg(A.X, A.X);
5390	0	fe_neg(A.T, A.T);
5391	0
5392	0	memcpy(rcopy, signature, 32);
5393	0	memcpy(scopy, signature + 32, 32);
5394	0
5395	0	SHA512_Init(&hash_ctx);
5396	0	SHA512_Update(&hash_ctx, signature, 32);
5397	0	SHA512_Update(&hash_ctx, public_key, 32);
5398	0	SHA512_Update(&hash_ctx, message, message_len);
5399	0	SHA512_Final(h, &hash_ctx);
5400	0
5401	0	x25519_sc_reduce(h);
5402	0
5403	0	ge_double_scalarmult_vartime(&R, h, &A, scopy);
5404	0
5405	0	ge_tobytes(rcheck, &R);
5406	0
5407	0	return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
5408	0	}
5409
5410		void ED25519_public_from_private(uint8_t out_public_key[32],
5411	0	const uint8_t private_key[32]) {
5412	0	uint8_t az[SHA512_DIGEST_LENGTH];
5413	0	ge_p3 A;
5414	0
5415	0	SHA512(private_key, 32, az);
5416	0
5417	0	az[0] &= 248;
5418	0	az[31] &= 63;
5419	0	az[31] \|= 64;
5420	0
5421	0	ge_scalarmult_base(&A, az);
5422	0	ge_p3_tobytes(out_public_key, &A);
5423	0
5424	0	OPENSSL_cleanse(az, sizeof(az));
5425	0	}
5426
5427		int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5428	0	const uint8_t peer_public_value[32]) {
5429	0	static const uint8_t kZeros[32] = {0};
5430	0	x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5431	0	/* The all-zero output results when the input is a point of small order. */
5432	0	return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5433	0	}
5434
5435		void X25519_public_from_private(uint8_t out_public_value[32],
5436	0	const uint8_t private_key[32]) {
5437	0	uint8_t e[32];
5438	0	ge_p3 A;
5439	0	fe zplusy, zminusy, zminusy_inv;
5440	0
5441	0	memcpy(e, private_key, 32);
5442	0	e[0] &= 248;
5443	0	e[31] &= 127;
5444	0	e[31] \|= 64;
5445	0
5446	0	ge_scalarmult_base(&A, e);
5447	0
5448	0	/* We only need the u-coordinate of the curve25519 point. The map is
5449	0	* u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */
5450	0	fe_add(zplusy, A.Z, A.Y);
5451	0	fe_sub(zminusy, A.Z, A.Y);
5452	0	fe_invert(zminusy_inv, zminusy);
5453	0	fe_mul(zplusy, zplusy, zminusy_inv);
5454	0	fe_tobytes(out_public_value, zplusy);
5455	0
5456	0	OPENSSL_cleanse(e, sizeof(e));
5457	0	}

Coverage Report

Created: 2018-08-29 13:53