1 /* $OpenBSD: curve25519.c,v 1.2 2020/07/22 13:54:30 tobhe Exp $ */
2 /*
3 * Copyright (C) 2018-2020 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
4 * Copyright (C) 2015-2016 The fiat-crypto Authors.
5 *
6 * Permission to use, copy, modify, and distribute this software for any
7 * purpose with or without fee is hereby granted, provided that the above
8 * copyright notice and this permission notice appear in all copies.
9 *
10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17 *
18 * This contains two implementation: a machine-generated formally verified
19 * implementation of Curve25519 ECDH from:
20 * <https://github.com/mit-plv/fiat-crypto>. Though originally machine
21 * generated, it has been tweaked to be suitable for use in the kernel. It is
22 * optimized for 32-bit machines and machines that cannot work efficiently with
23 * 128-bit integer types.
24 */
25
26 #include <sys/types.h>
27 #include <sys/systm.h>
28 #include <crypto/curve25519.h>
29
30 #define __always_inline __inline __attribute__((__always_inline__))
31 static const uint8_t null_point[CURVE25519_KEY_SIZE];
32 static const uint8_t base_point[CURVE25519_KEY_SIZE] = { 9 };
33
curve25519_generate_public(uint8_t pub[CURVE25519_KEY_SIZE],const uint8_t secret[CURVE25519_KEY_SIZE])34 int curve25519_generate_public(uint8_t pub[CURVE25519_KEY_SIZE],
35 const uint8_t secret[CURVE25519_KEY_SIZE])
36 {
37 if (timingsafe_bcmp(secret, null_point, CURVE25519_KEY_SIZE) == 0)
38 return 0;
39 return curve25519(pub, secret, base_point);
40 }
41
get_unaligned_le32(const uint8_t * a)42 static __always_inline uint32_t get_unaligned_le32(const uint8_t *a)
43 {
44 uint32_t l;
45 __builtin_memcpy(&l, a, sizeof(l));
46 return letoh32(l);
47 }
48
49 /* fe means field element. Here the field is \Z/(2^255-19). An element t,
50 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
51 * t[3]+2^102 t[4]+...+2^230 t[9].
52 * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc.
53 * Multiplication and carrying produce fe from fe_loose.
54 */
55 typedef struct fe { uint32_t v[10]; } fe;
56
57 /* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc
58 * Addition and subtraction produce fe_loose from (fe, fe).
59 */
60 typedef struct fe_loose { uint32_t v[10]; } fe_loose;
61
fe_frombytes_impl(uint32_t h[10],const uint8_t * s)62 static __always_inline void fe_frombytes_impl(uint32_t h[10], const uint8_t *s)
63 {
64 /* Ignores top bit of s. */
65 uint32_t a0 = get_unaligned_le32(s);
66 uint32_t a1 = get_unaligned_le32(s+4);
67 uint32_t a2 = get_unaligned_le32(s+8);
68 uint32_t a3 = get_unaligned_le32(s+12);
69 uint32_t a4 = get_unaligned_le32(s+16);
70 uint32_t a5 = get_unaligned_le32(s+20);
71 uint32_t a6 = get_unaligned_le32(s+24);
72 uint32_t a7 = get_unaligned_le32(s+28);
73 h[0] = a0&((1<<26)-1); /* 26 used, 32-26 left. 26 */
74 h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 = 6+19 = 25 */
75 h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */
76 h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) + 6 = 19+ 6 = 25 */
77 h[4] = (a3>> 6); /* (32- 6) = 26 */
78 h[5] = a4&((1<<25)-1); /* 25 */
79 h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 = 7+19 = 26 */
80 h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */
81 h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) + 6 = 20+ 6 = 26 */
82 h[9] = (a7>> 6)&((1<<25)-1); /* 25 */
83 }
84
fe_frombytes(fe * h,const uint8_t * s)85 static __always_inline void fe_frombytes(fe *h, const uint8_t *s)
86 {
87 fe_frombytes_impl(h->v, s);
88 }
89
90 static __always_inline uint8_t /*bool*/
addcarryx_u25(uint8_t c,uint32_t a,uint32_t b,uint32_t * low)91 addcarryx_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
92 {
93 /* This function extracts 25 bits of result and 1 bit of carry
94 * (26 total), so a 32-bit intermediate is sufficient.
95 */
96 uint32_t x = a + b + c;
97 *low = x & ((1 << 25) - 1);
98 return (x >> 25) & 1;
99 }
100
101 static __always_inline uint8_t /*bool*/
addcarryx_u26(uint8_t c,uint32_t a,uint32_t b,uint32_t * low)102 addcarryx_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
103 {
104 /* This function extracts 26 bits of result and 1 bit of carry
105 * (27 total), so a 32-bit intermediate is sufficient.
106 */
107 uint32_t x = a + b + c;
108 *low = x & ((1 << 26) - 1);
109 return (x >> 26) & 1;
110 }
111
112 static __always_inline uint8_t /*bool*/
subborrow_u25(uint8_t c,uint32_t a,uint32_t b,uint32_t * low)113 subborrow_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
114 {
115 /* This function extracts 25 bits of result and 1 bit of borrow
116 * (26 total), so a 32-bit intermediate is sufficient.
117 */
118 uint32_t x = a - b - c;
119 *low = x & ((1 << 25) - 1);
120 return x >> 31;
121 }
122
123 static __always_inline uint8_t /*bool*/
subborrow_u26(uint8_t c,uint32_t a,uint32_t b,uint32_t * low)124 subborrow_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
125 {
126 /* This function extracts 26 bits of result and 1 bit of borrow
127 *(27 total), so a 32-bit intermediate is sufficient.
128 */
129 uint32_t x = a - b - c;
130 *low = x & ((1 << 26) - 1);
131 return x >> 31;
132 }
133
cmovznz32(uint32_t t,uint32_t z,uint32_t nz)134 static __always_inline uint32_t cmovznz32(uint32_t t, uint32_t z, uint32_t nz)
135 {
136 t = -!!t; /* all set if nonzero, 0 if 0 */
137 return (t&nz) | ((~t)&z);
138 }
139
fe_freeze(uint32_t out[10],const uint32_t in1[10])140 static __always_inline void fe_freeze(uint32_t out[10], const uint32_t in1[10])
141 {
142 const uint32_t x17 = in1[9];
143 const uint32_t x18 = in1[8];
144 const uint32_t x16 = in1[7];
145 const uint32_t x14 = in1[6];
146 const uint32_t x12 = in1[5];
147 const uint32_t x10 = in1[4];
148 const uint32_t x8 = in1[3];
149 const uint32_t x6 = in1[2];
150 const uint32_t x4 = in1[1];
151 const uint32_t x2 = in1[0];
152 uint32_t x20; uint8_t/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20);
153 uint32_t x23; uint8_t/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23);
154 uint32_t x26; uint8_t/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26);
155 uint32_t x29; uint8_t/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29);
156 uint32_t x32; uint8_t/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32);
157 uint32_t x35; uint8_t/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35);
158 uint32_t x38; uint8_t/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38);
159 uint32_t x41; uint8_t/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41);
160 uint32_t x44; uint8_t/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44);
161 uint32_t x47; uint8_t/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47);
162 uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff);
163 uint32_t x50 = (x49 & 0x3ffffed);
164 uint32_t x52; uint8_t/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52);
165 uint32_t x54 = (x49 & 0x1ffffff);
166 uint32_t x56; uint8_t/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56);
167 uint32_t x58 = (x49 & 0x3ffffff);
168 uint32_t x60; uint8_t/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60);
169 uint32_t x62 = (x49 & 0x1ffffff);
170 uint32_t x64; uint8_t/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64);
171 uint32_t x66 = (x49 & 0x3ffffff);
172 uint32_t x68; uint8_t/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68);
173 uint32_t x70 = (x49 & 0x1ffffff);
174 uint32_t x72; uint8_t/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72);
175 uint32_t x74 = (x49 & 0x3ffffff);
176 uint32_t x76; uint8_t/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76);
177 uint32_t x78 = (x49 & 0x1ffffff);
178 uint32_t x80; uint8_t/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80);
179 uint32_t x82 = (x49 & 0x3ffffff);
180 uint32_t x84; uint8_t/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84);
181 uint32_t x86 = (x49 & 0x1ffffff);
182 uint32_t x88; addcarryx_u25(x85, x47, x86, &x88);
183 out[0] = x52;
184 out[1] = x56;
185 out[2] = x60;
186 out[3] = x64;
187 out[4] = x68;
188 out[5] = x72;
189 out[6] = x76;
190 out[7] = x80;
191 out[8] = x84;
192 out[9] = x88;
193 }
194
fe_tobytes(uint8_t s[32],const fe * f)195 static __always_inline void fe_tobytes(uint8_t s[32], const fe *f)
196 {
197 uint32_t h[10];
198 fe_freeze(h, f->v);
199 s[0] = h[0] >> 0;
200 s[1] = h[0] >> 8;
201 s[2] = h[0] >> 16;
202 s[3] = (h[0] >> 24) | (h[1] << 2);
203 s[4] = h[1] >> 6;
204 s[5] = h[1] >> 14;
205 s[6] = (h[1] >> 22) | (h[2] << 3);
206 s[7] = h[2] >> 5;
207 s[8] = h[2] >> 13;
208 s[9] = (h[2] >> 21) | (h[3] << 5);
209 s[10] = h[3] >> 3;
210 s[11] = h[3] >> 11;
211 s[12] = (h[3] >> 19) | (h[4] << 6);
212 s[13] = h[4] >> 2;
213 s[14] = h[4] >> 10;
214 s[15] = h[4] >> 18;
215 s[16] = h[5] >> 0;
216 s[17] = h[5] >> 8;
217 s[18] = h[5] >> 16;
218 s[19] = (h[5] >> 24) | (h[6] << 1);
219 s[20] = h[6] >> 7;
220 s[21] = h[6] >> 15;
221 s[22] = (h[6] >> 23) | (h[7] << 3);
222 s[23] = h[7] >> 5;
223 s[24] = h[7] >> 13;
224 s[25] = (h[7] >> 21) | (h[8] << 4);
225 s[26] = h[8] >> 4;
226 s[27] = h[8] >> 12;
227 s[28] = (h[8] >> 20) | (h[9] << 6);
228 s[29] = h[9] >> 2;
229 s[30] = h[9] >> 10;
230 s[31] = h[9] >> 18;
231 }
232
233 /* h = f */
fe_copy(fe * h,const fe * f)234 static __always_inline void fe_copy(fe *h, const fe *f)
235 {
236 memmove(h, f, sizeof(uint32_t) * 10);
237 }
238
fe_copy_lt(fe_loose * h,const fe * f)239 static __always_inline void fe_copy_lt(fe_loose *h, const fe *f)
240 {
241 memmove(h, f, sizeof(uint32_t) * 10);
242 }
243
244 /* h = 0 */
fe_0(fe * h)245 static __always_inline void fe_0(fe *h)
246 {
247 memset(h, 0, sizeof(uint32_t) * 10);
248 }
249
250 /* h = 1 */
fe_1(fe * h)251 static __always_inline void fe_1(fe *h)
252 {
253 memset(h, 0, sizeof(uint32_t) * 10);
254 h->v[0] = 1;
255 }
256
fe_add_impl(uint32_t out[10],const uint32_t in1[10],const uint32_t in2[10])257 static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10])
258 {
259 const uint32_t x20 = in1[9];
260 const uint32_t x21 = in1[8];
261 const uint32_t x19 = in1[7];
262 const uint32_t x17 = in1[6];
263 const uint32_t x15 = in1[5];
264 const uint32_t x13 = in1[4];
265 const uint32_t x11 = in1[3];
266 const uint32_t x9 = in1[2];
267 const uint32_t x7 = in1[1];
268 const uint32_t x5 = in1[0];
269 const uint32_t x38 = in2[9];
270 const uint32_t x39 = in2[8];
271 const uint32_t x37 = in2[7];
272 const uint32_t x35 = in2[6];
273 const uint32_t x33 = in2[5];
274 const uint32_t x31 = in2[4];
275 const uint32_t x29 = in2[3];
276 const uint32_t x27 = in2[2];
277 const uint32_t x25 = in2[1];
278 const uint32_t x23 = in2[0];
279 out[0] = (x5 + x23);
280 out[1] = (x7 + x25);
281 out[2] = (x9 + x27);
282 out[3] = (x11 + x29);
283 out[4] = (x13 + x31);
284 out[5] = (x15 + x33);
285 out[6] = (x17 + x35);
286 out[7] = (x19 + x37);
287 out[8] = (x21 + x39);
288 out[9] = (x20 + x38);
289 }
290
291 /* h = f + g
292 * Can overlap h with f or g.
293 */
fe_add(fe_loose * h,const fe * f,const fe * g)294 static __always_inline void fe_add(fe_loose *h, const fe *f, const fe *g)
295 {
296 fe_add_impl(h->v, f->v, g->v);
297 }
298
fe_sub_impl(uint32_t out[10],const uint32_t in1[10],const uint32_t in2[10])299 static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10])
300 {
301 const uint32_t x20 = in1[9];
302 const uint32_t x21 = in1[8];
303 const uint32_t x19 = in1[7];
304 const uint32_t x17 = in1[6];
305 const uint32_t x15 = in1[5];
306 const uint32_t x13 = in1[4];
307 const uint32_t x11 = in1[3];
308 const uint32_t x9 = in1[2];
309 const uint32_t x7 = in1[1];
310 const uint32_t x5 = in1[0];
311 const uint32_t x38 = in2[9];
312 const uint32_t x39 = in2[8];
313 const uint32_t x37 = in2[7];
314 const uint32_t x35 = in2[6];
315 const uint32_t x33 = in2[5];
316 const uint32_t x31 = in2[4];
317 const uint32_t x29 = in2[3];
318 const uint32_t x27 = in2[2];
319 const uint32_t x25 = in2[1];
320 const uint32_t x23 = in2[0];
321 out[0] = ((0x7ffffda + x5) - x23);
322 out[1] = ((0x3fffffe + x7) - x25);
323 out[2] = ((0x7fffffe + x9) - x27);
324 out[3] = ((0x3fffffe + x11) - x29);
325 out[4] = ((0x7fffffe + x13) - x31);
326 out[5] = ((0x3fffffe + x15) - x33);
327 out[6] = ((0x7fffffe + x17) - x35);
328 out[7] = ((0x3fffffe + x19) - x37);
329 out[8] = ((0x7fffffe + x21) - x39);
330 out[9] = ((0x3fffffe + x20) - x38);
331 }
332
333 /* h = f - g
334 * Can overlap h with f or g.
335 */
fe_sub(fe_loose * h,const fe * f,const fe * g)336 static __always_inline void fe_sub(fe_loose *h, const fe *f, const fe *g)
337 {
338 fe_sub_impl(h->v, f->v, g->v);
339 }
340
fe_mul_impl(uint32_t out[10],const uint32_t in1[10],const uint32_t in2[10])341 static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10])
342 {
343 const uint32_t x20 = in1[9];
344 const uint32_t x21 = in1[8];
345 const uint32_t x19 = in1[7];
346 const uint32_t x17 = in1[6];
347 const uint32_t x15 = in1[5];
348 const uint32_t x13 = in1[4];
349 const uint32_t x11 = in1[3];
350 const uint32_t x9 = in1[2];
351 const uint32_t x7 = in1[1];
352 const uint32_t x5 = in1[0];
353 const uint32_t x38 = in2[9];
354 const uint32_t x39 = in2[8];
355 const uint32_t x37 = in2[7];
356 const uint32_t x35 = in2[6];
357 const uint32_t x33 = in2[5];
358 const uint32_t x31 = in2[4];
359 const uint32_t x29 = in2[3];
360 const uint32_t x27 = in2[2];
361 const uint32_t x25 = in2[1];
362 const uint32_t x23 = in2[0];
363 uint64_t x40 = ((uint64_t)x23 * x5);
364 uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
365 uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
366 uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
367 uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
368 uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
369 uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
370 uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
371 uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
372 uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
373 uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
374 uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
375 uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
376 uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
377 uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
378 uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
379 uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
380 uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
381 uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
382 uint64_t x59 = (x48 + (x58 << 0x4));
383 uint64_t x60 = (x59 + (x58 << 0x1));
384 uint64_t x61 = (x60 + x58);
385 uint64_t x62 = (x47 + (x57 << 0x4));
386 uint64_t x63 = (x62 + (x57 << 0x1));
387 uint64_t x64 = (x63 + x57);
388 uint64_t x65 = (x46 + (x56 << 0x4));
389 uint64_t x66 = (x65 + (x56 << 0x1));
390 uint64_t x67 = (x66 + x56);
391 uint64_t x68 = (x45 + (x55 << 0x4));
392 uint64_t x69 = (x68 + (x55 << 0x1));
393 uint64_t x70 = (x69 + x55);
394 uint64_t x71 = (x44 + (x54 << 0x4));
395 uint64_t x72 = (x71 + (x54 << 0x1));
396 uint64_t x73 = (x72 + x54);
397 uint64_t x74 = (x43 + (x53 << 0x4));
398 uint64_t x75 = (x74 + (x53 << 0x1));
399 uint64_t x76 = (x75 + x53);
400 uint64_t x77 = (x42 + (x52 << 0x4));
401 uint64_t x78 = (x77 + (x52 << 0x1));
402 uint64_t x79 = (x78 + x52);
403 uint64_t x80 = (x41 + (x51 << 0x4));
404 uint64_t x81 = (x80 + (x51 << 0x1));
405 uint64_t x82 = (x81 + x51);
406 uint64_t x83 = (x40 + (x50 << 0x4));
407 uint64_t x84 = (x83 + (x50 << 0x1));
408 uint64_t x85 = (x84 + x50);
409 uint64_t x86 = (x85 >> 0x1a);
410 uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
411 uint64_t x88 = (x86 + x82);
412 uint64_t x89 = (x88 >> 0x19);
413 uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
414 uint64_t x91 = (x89 + x79);
415 uint64_t x92 = (x91 >> 0x1a);
416 uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
417 uint64_t x94 = (x92 + x76);
418 uint64_t x95 = (x94 >> 0x19);
419 uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
420 uint64_t x97 = (x95 + x73);
421 uint64_t x98 = (x97 >> 0x1a);
422 uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
423 uint64_t x100 = (x98 + x70);
424 uint64_t x101 = (x100 >> 0x19);
425 uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
426 uint64_t x103 = (x101 + x67);
427 uint64_t x104 = (x103 >> 0x1a);
428 uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
429 uint64_t x106 = (x104 + x64);
430 uint64_t x107 = (x106 >> 0x19);
431 uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
432 uint64_t x109 = (x107 + x61);
433 uint64_t x110 = (x109 >> 0x1a);
434 uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
435 uint64_t x112 = (x110 + x49);
436 uint64_t x113 = (x112 >> 0x19);
437 uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
438 uint64_t x115 = (x87 + (0x13 * x113));
439 uint32_t x116 = (uint32_t) (x115 >> 0x1a);
440 uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
441 uint32_t x118 = (x116 + x90);
442 uint32_t x119 = (x118 >> 0x19);
443 uint32_t x120 = (x118 & 0x1ffffff);
444 out[0] = x117;
445 out[1] = x120;
446 out[2] = (x119 + x93);
447 out[3] = x96;
448 out[4] = x99;
449 out[5] = x102;
450 out[6] = x105;
451 out[7] = x108;
452 out[8] = x111;
453 out[9] = x114;
454 }
455
fe_mul_ttt(fe * h,const fe * f,const fe * g)456 static __always_inline void fe_mul_ttt(fe *h, const fe *f, const fe *g)
457 {
458 fe_mul_impl(h->v, f->v, g->v);
459 }
460
fe_mul_tlt(fe * h,const fe_loose * f,const fe * g)461 static __always_inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g)
462 {
463 fe_mul_impl(h->v, f->v, g->v);
464 }
465
466 static __always_inline void
fe_mul_tll(fe * h,const fe_loose * f,const fe_loose * g)467 fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g)
468 {
469 fe_mul_impl(h->v, f->v, g->v);
470 }
471
fe_sqr_impl(uint32_t out[10],const uint32_t in1[10])472 static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10])
473 {
474 const uint32_t x17 = in1[9];
475 const uint32_t x18 = in1[8];
476 const uint32_t x16 = in1[7];
477 const uint32_t x14 = in1[6];
478 const uint32_t x12 = in1[5];
479 const uint32_t x10 = in1[4];
480 const uint32_t x8 = in1[3];
481 const uint32_t x6 = in1[2];
482 const uint32_t x4 = in1[1];
483 const uint32_t x2 = in1[0];
484 uint64_t x19 = ((uint64_t)x2 * x2);
485 uint64_t x20 = ((uint64_t)(0x2 * x2) * x4);
486 uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6)));
487 uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8)));
488 uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10));
489 uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12)));
490 uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12)));
491 uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16)));
492 uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12))))));
493 uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17)));
494 uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17)))));
495 uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17)));
496 uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17))))));
497 uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17)));
498 uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17)));
499 uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17)));
500 uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17));
501 uint64_t x36 = ((uint64_t)(0x2 * x18) * x17);
502 uint64_t x37 = ((uint64_t)(0x2 * x17) * x17);
503 uint64_t x38 = (x27 + (x37 << 0x4));
504 uint64_t x39 = (x38 + (x37 << 0x1));
505 uint64_t x40 = (x39 + x37);
506 uint64_t x41 = (x26 + (x36 << 0x4));
507 uint64_t x42 = (x41 + (x36 << 0x1));
508 uint64_t x43 = (x42 + x36);
509 uint64_t x44 = (x25 + (x35 << 0x4));
510 uint64_t x45 = (x44 + (x35 << 0x1));
511 uint64_t x46 = (x45 + x35);
512 uint64_t x47 = (x24 + (x34 << 0x4));
513 uint64_t x48 = (x47 + (x34 << 0x1));
514 uint64_t x49 = (x48 + x34);
515 uint64_t x50 = (x23 + (x33 << 0x4));
516 uint64_t x51 = (x50 + (x33 << 0x1));
517 uint64_t x52 = (x51 + x33);
518 uint64_t x53 = (x22 + (x32 << 0x4));
519 uint64_t x54 = (x53 + (x32 << 0x1));
520 uint64_t x55 = (x54 + x32);
521 uint64_t x56 = (x21 + (x31 << 0x4));
522 uint64_t x57 = (x56 + (x31 << 0x1));
523 uint64_t x58 = (x57 + x31);
524 uint64_t x59 = (x20 + (x30 << 0x4));
525 uint64_t x60 = (x59 + (x30 << 0x1));
526 uint64_t x61 = (x60 + x30);
527 uint64_t x62 = (x19 + (x29 << 0x4));
528 uint64_t x63 = (x62 + (x29 << 0x1));
529 uint64_t x64 = (x63 + x29);
530 uint64_t x65 = (x64 >> 0x1a);
531 uint32_t x66 = ((uint32_t)x64 & 0x3ffffff);
532 uint64_t x67 = (x65 + x61);
533 uint64_t x68 = (x67 >> 0x19);
534 uint32_t x69 = ((uint32_t)x67 & 0x1ffffff);
535 uint64_t x70 = (x68 + x58);
536 uint64_t x71 = (x70 >> 0x1a);
537 uint32_t x72 = ((uint32_t)x70 & 0x3ffffff);
538 uint64_t x73 = (x71 + x55);
539 uint64_t x74 = (x73 >> 0x19);
540 uint32_t x75 = ((uint32_t)x73 & 0x1ffffff);
541 uint64_t x76 = (x74 + x52);
542 uint64_t x77 = (x76 >> 0x1a);
543 uint32_t x78 = ((uint32_t)x76 & 0x3ffffff);
544 uint64_t x79 = (x77 + x49);
545 uint64_t x80 = (x79 >> 0x19);
546 uint32_t x81 = ((uint32_t)x79 & 0x1ffffff);
547 uint64_t x82 = (x80 + x46);
548 uint64_t x83 = (x82 >> 0x1a);
549 uint32_t x84 = ((uint32_t)x82 & 0x3ffffff);
550 uint64_t x85 = (x83 + x43);
551 uint64_t x86 = (x85 >> 0x19);
552 uint32_t x87 = ((uint32_t)x85 & 0x1ffffff);
553 uint64_t x88 = (x86 + x40);
554 uint64_t x89 = (x88 >> 0x1a);
555 uint32_t x90 = ((uint32_t)x88 & 0x3ffffff);
556 uint64_t x91 = (x89 + x28);
557 uint64_t x92 = (x91 >> 0x19);
558 uint32_t x93 = ((uint32_t)x91 & 0x1ffffff);
559 uint64_t x94 = (x66 + (0x13 * x92));
560 uint32_t x95 = (uint32_t) (x94 >> 0x1a);
561 uint32_t x96 = ((uint32_t)x94 & 0x3ffffff);
562 uint32_t x97 = (x95 + x69);
563 uint32_t x98 = (x97 >> 0x19);
564 uint32_t x99 = (x97 & 0x1ffffff);
565 out[0] = x96;
566 out[1] = x99;
567 out[2] = (x98 + x72);
568 out[3] = x75;
569 out[4] = x78;
570 out[5] = x81;
571 out[6] = x84;
572 out[7] = x87;
573 out[8] = x90;
574 out[9] = x93;
575 }
576
fe_sq_tl(fe * h,const fe_loose * f)577 static __always_inline void fe_sq_tl(fe *h, const fe_loose *f)
578 {
579 fe_sqr_impl(h->v, f->v);
580 }
581
fe_sq_tt(fe * h,const fe * f)582 static __always_inline void fe_sq_tt(fe *h, const fe *f)
583 {
584 fe_sqr_impl(h->v, f->v);
585 }
586
fe_loose_invert(fe * out,const fe_loose * z)587 static __always_inline void fe_loose_invert(fe *out, const fe_loose *z)
588 {
589 fe t0;
590 fe t1;
591 fe t2;
592 fe t3;
593 int i;
594
595 fe_sq_tl(&t0, z);
596 fe_sq_tt(&t1, &t0);
597 for (i = 1; i < 2; ++i)
598 fe_sq_tt(&t1, &t1);
599 fe_mul_tlt(&t1, z, &t1);
600 fe_mul_ttt(&t0, &t0, &t1);
601 fe_sq_tt(&t2, &t0);
602 fe_mul_ttt(&t1, &t1, &t2);
603 fe_sq_tt(&t2, &t1);
604 for (i = 1; i < 5; ++i)
605 fe_sq_tt(&t2, &t2);
606 fe_mul_ttt(&t1, &t2, &t1);
607 fe_sq_tt(&t2, &t1);
608 for (i = 1; i < 10; ++i)
609 fe_sq_tt(&t2, &t2);
610 fe_mul_ttt(&t2, &t2, &t1);
611 fe_sq_tt(&t3, &t2);
612 for (i = 1; i < 20; ++i)
613 fe_sq_tt(&t3, &t3);
614 fe_mul_ttt(&t2, &t3, &t2);
615 fe_sq_tt(&t2, &t2);
616 for (i = 1; i < 10; ++i)
617 fe_sq_tt(&t2, &t2);
618 fe_mul_ttt(&t1, &t2, &t1);
619 fe_sq_tt(&t2, &t1);
620 for (i = 1; i < 50; ++i)
621 fe_sq_tt(&t2, &t2);
622 fe_mul_ttt(&t2, &t2, &t1);
623 fe_sq_tt(&t3, &t2);
624 for (i = 1; i < 100; ++i)
625 fe_sq_tt(&t3, &t3);
626 fe_mul_ttt(&t2, &t3, &t2);
627 fe_sq_tt(&t2, &t2);
628 for (i = 1; i < 50; ++i)
629 fe_sq_tt(&t2, &t2);
630 fe_mul_ttt(&t1, &t2, &t1);
631 fe_sq_tt(&t1, &t1);
632 for (i = 1; i < 5; ++i)
633 fe_sq_tt(&t1, &t1);
634 fe_mul_ttt(out, &t1, &t0);
635 }
636
fe_invert(fe * out,const fe * z)637 static __always_inline void fe_invert(fe *out, const fe *z)
638 {
639 fe_loose l;
640 fe_copy_lt(&l, z);
641 fe_loose_invert(out, &l);
642 }
643
644 /* Replace (f,g) with (g,f) if b == 1;
645 * replace (f,g) with (f,g) if b == 0.
646 *
647 * Preconditions: b in {0,1}
648 */
fe_cswap(fe * f,fe * g,unsigned int b)649 static __always_inline void fe_cswap(fe *f, fe *g, unsigned int b)
650 {
651 unsigned i;
652 b = 0 - b;
653 for (i = 0; i < 10; i++) {
654 uint32_t x = f->v[i] ^ g->v[i];
655 x &= b;
656 f->v[i] ^= x;
657 g->v[i] ^= x;
658 }
659 }
660
661 /* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/
fe_mul_121666_impl(uint32_t out[10],const uint32_t in1[10])662 static __always_inline void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10])
663 {
664 const uint32_t x20 = in1[9];
665 const uint32_t x21 = in1[8];
666 const uint32_t x19 = in1[7];
667 const uint32_t x17 = in1[6];
668 const uint32_t x15 = in1[5];
669 const uint32_t x13 = in1[4];
670 const uint32_t x11 = in1[3];
671 const uint32_t x9 = in1[2];
672 const uint32_t x7 = in1[1];
673 const uint32_t x5 = in1[0];
674 const uint32_t x38 = 0;
675 const uint32_t x39 = 0;
676 const uint32_t x37 = 0;
677 const uint32_t x35 = 0;
678 const uint32_t x33 = 0;
679 const uint32_t x31 = 0;
680 const uint32_t x29 = 0;
681 const uint32_t x27 = 0;
682 const uint32_t x25 = 0;
683 const uint32_t x23 = 121666;
684 uint64_t x40 = ((uint64_t)x23 * x5);
685 uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
686 uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
687 uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
688 uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
689 uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
690 uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
691 uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
692 uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
693 uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
694 uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
695 uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
696 uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
697 uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
698 uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
699 uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
700 uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
701 uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
702 uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
703 uint64_t x59 = (x48 + (x58 << 0x4));
704 uint64_t x60 = (x59 + (x58 << 0x1));
705 uint64_t x61 = (x60 + x58);
706 uint64_t x62 = (x47 + (x57 << 0x4));
707 uint64_t x63 = (x62 + (x57 << 0x1));
708 uint64_t x64 = (x63 + x57);
709 uint64_t x65 = (x46 + (x56 << 0x4));
710 uint64_t x66 = (x65 + (x56 << 0x1));
711 uint64_t x67 = (x66 + x56);
712 uint64_t x68 = (x45 + (x55 << 0x4));
713 uint64_t x69 = (x68 + (x55 << 0x1));
714 uint64_t x70 = (x69 + x55);
715 uint64_t x71 = (x44 + (x54 << 0x4));
716 uint64_t x72 = (x71 + (x54 << 0x1));
717 uint64_t x73 = (x72 + x54);
718 uint64_t x74 = (x43 + (x53 << 0x4));
719 uint64_t x75 = (x74 + (x53 << 0x1));
720 uint64_t x76 = (x75 + x53);
721 uint64_t x77 = (x42 + (x52 << 0x4));
722 uint64_t x78 = (x77 + (x52 << 0x1));
723 uint64_t x79 = (x78 + x52);
724 uint64_t x80 = (x41 + (x51 << 0x4));
725 uint64_t x81 = (x80 + (x51 << 0x1));
726 uint64_t x82 = (x81 + x51);
727 uint64_t x83 = (x40 + (x50 << 0x4));
728 uint64_t x84 = (x83 + (x50 << 0x1));
729 uint64_t x85 = (x84 + x50);
730 uint64_t x86 = (x85 >> 0x1a);
731 uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
732 uint64_t x88 = (x86 + x82);
733 uint64_t x89 = (x88 >> 0x19);
734 uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
735 uint64_t x91 = (x89 + x79);
736 uint64_t x92 = (x91 >> 0x1a);
737 uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
738 uint64_t x94 = (x92 + x76);
739 uint64_t x95 = (x94 >> 0x19);
740 uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
741 uint64_t x97 = (x95 + x73);
742 uint64_t x98 = (x97 >> 0x1a);
743 uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
744 uint64_t x100 = (x98 + x70);
745 uint64_t x101 = (x100 >> 0x19);
746 uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
747 uint64_t x103 = (x101 + x67);
748 uint64_t x104 = (x103 >> 0x1a);
749 uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
750 uint64_t x106 = (x104 + x64);
751 uint64_t x107 = (x106 >> 0x19);
752 uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
753 uint64_t x109 = (x107 + x61);
754 uint64_t x110 = (x109 >> 0x1a);
755 uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
756 uint64_t x112 = (x110 + x49);
757 uint64_t x113 = (x112 >> 0x19);
758 uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
759 uint64_t x115 = (x87 + (0x13 * x113));
760 uint32_t x116 = (uint32_t) (x115 >> 0x1a);
761 uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
762 uint32_t x118 = (x116 + x90);
763 uint32_t x119 = (x118 >> 0x19);
764 uint32_t x120 = (x118 & 0x1ffffff);
765 out[0] = x117;
766 out[1] = x120;
767 out[2] = (x119 + x93);
768 out[3] = x96;
769 out[4] = x99;
770 out[5] = x102;
771 out[6] = x105;
772 out[7] = x108;
773 out[8] = x111;
774 out[9] = x114;
775 }
776
fe_mul121666(fe * h,const fe_loose * f)777 static __always_inline void fe_mul121666(fe *h, const fe_loose *f)
778 {
779 fe_mul_121666_impl(h->v, f->v);
780 }
781
curve25519(uint8_t out[CURVE25519_KEY_SIZE],const uint8_t scalar[CURVE25519_KEY_SIZE],const uint8_t point[CURVE25519_KEY_SIZE])782 int curve25519(uint8_t out[CURVE25519_KEY_SIZE],
783 const uint8_t scalar[CURVE25519_KEY_SIZE],
784 const uint8_t point[CURVE25519_KEY_SIZE])
785 {
786 fe x1, x2, z2, x3, z3;
787 fe_loose x2l, z2l, x3l;
788 unsigned swap = 0;
789 int pos;
790 uint8_t e[32];
791
792 memcpy(e, scalar, 32);
793 curve25519_clamp_secret(e);
794
795 /* The following implementation was transcribed to Coq and proven to
796 * correspond to unary scalar multiplication in affine coordinates given
797 * that x1 != 0 is the x coordinate of some point on the curve. It was
798 * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives
799 * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was
800 * quantified over the underlying field, so it applies to Curve25519
801 * itself and the quadratic twist of Curve25519. It was not proven in
802 * Coq that prime-field arithmetic correctly simulates extension-field
803 * arithmetic on prime-field values. The decoding of the byte array
804 * representation of e was not considered.
805 *
806 * Specification of Montgomery curves in affine coordinates:
807 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27>
808 *
809 * Proof that these form a group that is isomorphic to a Weierstrass
810 * curve:
811 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35>
812 *
813 * Coq transcription and correctness proof of the loop
814 * (where scalarbits=255):
815 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118>
816 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278>
817 * preconditions: 0 <= e < 2^255 (not necessarily e < order),
818 * fe_invert(0) = 0
819 */
820 fe_frombytes(&x1, point);
821 fe_1(&x2);
822 fe_0(&z2);
823 fe_copy(&x3, &x1);
824 fe_1(&z3);
825
826 for (pos = 254; pos >= 0; --pos) {
827 fe tmp0, tmp1;
828 fe_loose tmp0l, tmp1l;
829 /* loop invariant as of right before the test, for the case
830 * where x1 != 0:
831 * pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3
832 * is nonzero
833 * let r := e >> (pos+1) in the following equalities of
834 * projective points:
835 * to_xz (r*P) === if swap then (x3, z3) else (x2, z2)
836 * to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3)
837 * x1 is the nonzero x coordinate of the nonzero
838 * point (r*P-(r+1)*P)
839 */
840 unsigned b = 1 & (e[pos / 8] >> (pos & 7));
841 swap ^= b;
842 fe_cswap(&x2, &x3, swap);
843 fe_cswap(&z2, &z3, swap);
844 swap = b;
845 /* Coq transcription of ladderstep formula (called from
846 * transcribed loop):
847 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89>
848 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131>
849 * x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217>
850 * x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147>
851 */
852 fe_sub(&tmp0l, &x3, &z3);
853 fe_sub(&tmp1l, &x2, &z2);
854 fe_add(&x2l, &x2, &z2);
855 fe_add(&z2l, &x3, &z3);
856 fe_mul_tll(&z3, &tmp0l, &x2l);
857 fe_mul_tll(&z2, &z2l, &tmp1l);
858 fe_sq_tl(&tmp0, &tmp1l);
859 fe_sq_tl(&tmp1, &x2l);
860 fe_add(&x3l, &z3, &z2);
861 fe_sub(&z2l, &z3, &z2);
862 fe_mul_ttt(&x2, &tmp1, &tmp0);
863 fe_sub(&tmp1l, &tmp1, &tmp0);
864 fe_sq_tl(&z2, &z2l);
865 fe_mul121666(&z3, &tmp1l);
866 fe_sq_tl(&x3, &x3l);
867 fe_add(&tmp0l, &tmp0, &z3);
868 fe_mul_ttt(&z3, &x1, &z2);
869 fe_mul_tll(&z2, &tmp1l, &tmp0l);
870 }
871 /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3)
872 * else (x2, z2)
873 */
874 fe_cswap(&x2, &x3, swap);
875 fe_cswap(&z2, &z3, swap);
876
877 fe_invert(&z2, &z2);
878 fe_mul_ttt(&x2, &x2, &z2);
879 fe_tobytes(out, &x2);
880
881 explicit_bzero(&x1, sizeof(x1));
882 explicit_bzero(&x2, sizeof(x2));
883 explicit_bzero(&z2, sizeof(z2));
884 explicit_bzero(&x3, sizeof(x3));
885 explicit_bzero(&z3, sizeof(z3));
886 explicit_bzero(&x2l, sizeof(x2l));
887 explicit_bzero(&z2l, sizeof(z2l));
888 explicit_bzero(&x3l, sizeof(x3l));
889 explicit_bzero(&e, sizeof(e));
890 return timingsafe_bcmp(out, null_point, CURVE25519_KEY_SIZE);
891 }
892