1 // SPDX-License-Identifier: GPL-2.0 OR MIT
2 /*
3 * Copyright (C) 2015-2016 The fiat-crypto Authors.
4 * Copyright (C) 2018-2019 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
5 *
6 * This is a machine-generated formally verified implementation of Curve25519
7 * ECDH from: <https://github.com/mit-plv/fiat-crypto>. Though originally
8 * machine generated, it has been tweaked to be suitable for use in the kernel.
9 * It is optimized for 32-bit machines and machines that cannot work efficiently
10 * with 128-bit integer types.
11 */
12
13 #include <asm/unaligned.h>
14 #include <crypto/curve25519.h>
15 #include <linux/string.h>
16
17 /* fe means field element. Here the field is \Z/(2^255-19). An element t,
18 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
19 * t[3]+2^102 t[4]+...+2^230 t[9].
20 * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc.
21 * Multiplication and carrying produce fe from fe_loose.
22 */
23 typedef struct fe { u32 v[10]; } fe;
24
25 /* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc
26 * Addition and subtraction produce fe_loose from (fe, fe).
27 */
28 typedef struct fe_loose { u32 v[10]; } fe_loose;
29
30 static __always_inline void fe_frombytes_impl(u32 h[10], const u8 *s)
31 {
32 /* Ignores top bit of s. */
33 u32 a0 = get_unaligned_le32(s);
34 u32 a1 = get_unaligned_le32(s+4);
35 u32 a2 = get_unaligned_le32(s+8);
36 u32 a3 = get_unaligned_le32(s+12);
37 u32 a4 = get_unaligned_le32(s+16);
38 u32 a5 = get_unaligned_le32(s+20);
39 u32 a6 = get_unaligned_le32(s+24);
40 u32 a7 = get_unaligned_le32(s+28);
41 h[0] = a0&((1<<26)-1); /* 26 used, 32-26 left. 26 */
42 h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 = 6+19 = 25 */
43 h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */
44 h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) + 6 = 19+ 6 = 25 */
45 h[4] = (a3>> 6); /* (32- 6) = 26 */
46 h[5] = a4&((1<<25)-1); /* 25 */
47 h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 = 7+19 = 26 */
48 h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */
49 h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) + 6 = 20+ 6 = 26 */
50 h[9] = (a7>> 6)&((1<<25)-1); /* 25 */
51 }
52
53 static __always_inline void fe_frombytes(fe *h, const u8 *s)
54 {
55 fe_frombytes_impl(h->v, s);
56 }
57
58 static __always_inline u8 /*bool*/
59 addcarryx_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
60 {
61 /* This function extracts 25 bits of result and 1 bit of carry
62 * (26 total), so a 32-bit intermediate is sufficient.
63 */
64 u32 x = a + b + c;
65 *low = x & ((1 << 25) - 1);
66 return (x >> 25) & 1;
67 }
68
69 static __always_inline u8 /*bool*/
70 addcarryx_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
71 {
72 /* This function extracts 26 bits of result and 1 bit of carry
73 * (27 total), so a 32-bit intermediate is sufficient.
74 */
75 u32 x = a + b + c;
76 *low = x & ((1 << 26) - 1);
77 return (x >> 26) & 1;
78 }
79
80 static __always_inline u8 /*bool*/
81 subborrow_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
82 {
83 /* This function extracts 25 bits of result and 1 bit of borrow
84 * (26 total), so a 32-bit intermediate is sufficient.
85 */
86 u32 x = a - b - c;
87 *low = x & ((1 << 25) - 1);
88 return x >> 31;
89 }
90
91 static __always_inline u8 /*bool*/
92 subborrow_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
93 {
94 /* This function extracts 26 bits of result and 1 bit of borrow
95 *(27 total), so a 32-bit intermediate is sufficient.
96 */
97 u32 x = a - b - c;
98 *low = x & ((1 << 26) - 1);
99 return x >> 31;
100 }
101
102 static __always_inline u32 cmovznz32(u32 t, u32 z, u32 nz)
103 {
104 t = -!!t; /* all set if nonzero, 0 if 0 */
105 return (t&nz) | ((~t)&z);
106 }
107
108 static __always_inline void fe_freeze(u32 out[10], const u32 in1[10])
109 {
110 { const u32 x17 = in1[9];
111 { const u32 x18 = in1[8];
112 { const u32 x16 = in1[7];
113 { const u32 x14 = in1[6];
114 { const u32 x12 = in1[5];
115 { const u32 x10 = in1[4];
116 { const u32 x8 = in1[3];
117 { const u32 x6 = in1[2];
118 { const u32 x4 = in1[1];
119 { const u32 x2 = in1[0];
120 { u32 x20; u8/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20);
121 { u32 x23; u8/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23);
122 { u32 x26; u8/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26);
123 { u32 x29; u8/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29);
124 { u32 x32; u8/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32);
125 { u32 x35; u8/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35);
126 { u32 x38; u8/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38);
127 { u32 x41; u8/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41);
128 { u32 x44; u8/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44);
129 { u32 x47; u8/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47);
130 { u32 x49 = cmovznz32(x48, 0x0, 0xffffffff);
131 { u32 x50 = (x49 & 0x3ffffed);
132 { u32 x52; u8/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52);
133 { u32 x54 = (x49 & 0x1ffffff);
134 { u32 x56; u8/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56);
135 { u32 x58 = (x49 & 0x3ffffff);
136 { u32 x60; u8/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60);
137 { u32 x62 = (x49 & 0x1ffffff);
138 { u32 x64; u8/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64);
139 { u32 x66 = (x49 & 0x3ffffff);
140 { u32 x68; u8/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68);
141 { u32 x70 = (x49 & 0x1ffffff);
142 { u32 x72; u8/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72);
143 { u32 x74 = (x49 & 0x3ffffff);
144 { u32 x76; u8/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76);
145 { u32 x78 = (x49 & 0x1ffffff);
146 { u32 x80; u8/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80);
147 { u32 x82 = (x49 & 0x3ffffff);
148 { u32 x84; u8/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84);
149 { u32 x86 = (x49 & 0x1ffffff);
150 { u32 x88; addcarryx_u25(x85, x47, x86, &x88);
151 out[0] = x52;
152 out[1] = x56;
153 out[2] = x60;
154 out[3] = x64;
155 out[4] = x68;
156 out[5] = x72;
157 out[6] = x76;
158 out[7] = x80;
159 out[8] = x84;
160 out[9] = x88;
161 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
162 }
163
164 static __always_inline void fe_tobytes(u8 s[32], const fe *f)
165 {
166 u32 h[10];
167 fe_freeze(h, f->v);
168 s[0] = h[0] >> 0;
169 s[1] = h[0] >> 8;
170 s[2] = h[0] >> 16;
171 s[3] = (h[0] >> 24) | (h[1] << 2);
172 s[4] = h[1] >> 6;
173 s[5] = h[1] >> 14;
174 s[6] = (h[1] >> 22) | (h[2] << 3);
175 s[7] = h[2] >> 5;
176 s[8] = h[2] >> 13;
177 s[9] = (h[2] >> 21) | (h[3] << 5);
178 s[10] = h[3] >> 3;
179 s[11] = h[3] >> 11;
180 s[12] = (h[3] >> 19) | (h[4] << 6);
181 s[13] = h[4] >> 2;
182 s[14] = h[4] >> 10;
183 s[15] = h[4] >> 18;
184 s[16] = h[5] >> 0;
185 s[17] = h[5] >> 8;
186 s[18] = h[5] >> 16;
187 s[19] = (h[5] >> 24) | (h[6] << 1);
188 s[20] = h[6] >> 7;
189 s[21] = h[6] >> 15;
190 s[22] = (h[6] >> 23) | (h[7] << 3);
191 s[23] = h[7] >> 5;
192 s[24] = h[7] >> 13;
193 s[25] = (h[7] >> 21) | (h[8] << 4);
194 s[26] = h[8] >> 4;
195 s[27] = h[8] >> 12;
196 s[28] = (h[8] >> 20) | (h[9] << 6);
197 s[29] = h[9] >> 2;
198 s[30] = h[9] >> 10;
199 s[31] = h[9] >> 18;
200 }
201
202 /* h = f */
203 static __always_inline void fe_copy(fe *h, const fe *f)
204 {
205 memmove(h, f, sizeof(u32) * 10);
206 }
207
208 static __always_inline void fe_copy_lt(fe_loose *h, const fe *f)
209 {
210 memmove(h, f, sizeof(u32) * 10);
211 }
212
213 /* h = 0 */
214 static __always_inline void fe_0(fe *h)
215 {
216 memset(h, 0, sizeof(u32) * 10);
217 }
218
219 /* h = 1 */
220 static __always_inline void fe_1(fe *h)
221 {
222 memset(h, 0, sizeof(u32) * 10);
223 h->v[0] = 1;
224 }
225
226 static noinline void fe_add_impl(u32 out[10], const u32 in1[10], const u32 in2[10])
227 {
228 { const u32 x20 = in1[9];
229 { const u32 x21 = in1[8];
230 { const u32 x19 = in1[7];
231 { const u32 x17 = in1[6];
232 { const u32 x15 = in1[5];
233 { const u32 x13 = in1[4];
234 { const u32 x11 = in1[3];
235 { const u32 x9 = in1[2];
236 { const u32 x7 = in1[1];
237 { const u32 x5 = in1[0];
238 { const u32 x38 = in2[9];
239 { const u32 x39 = in2[8];
240 { const u32 x37 = in2[7];
241 { const u32 x35 = in2[6];
242 { const u32 x33 = in2[5];
243 { const u32 x31 = in2[4];
244 { const u32 x29 = in2[3];
245 { const u32 x27 = in2[2];
246 { const u32 x25 = in2[1];
247 { const u32 x23 = in2[0];
248 out[0] = (x5 + x23);
249 out[1] = (x7 + x25);
250 out[2] = (x9 + x27);
251 out[3] = (x11 + x29);
252 out[4] = (x13 + x31);
253 out[5] = (x15 + x33);
254 out[6] = (x17 + x35);
255 out[7] = (x19 + x37);
256 out[8] = (x21 + x39);
257 out[9] = (x20 + x38);
258 }}}}}}}}}}}}}}}}}}}}
259 }
260
261 /* h = f + g
262 * Can overlap h with f or g.
263 */
264 static __always_inline void fe_add(fe_loose *h, const fe *f, const fe *g)
265 {
266 fe_add_impl(h->v, f->v, g->v);
267 }
268
269 static noinline void fe_sub_impl(u32 out[10], const u32 in1[10], const u32 in2[10])
270 {
271 { const u32 x20 = in1[9];
272 { const u32 x21 = in1[8];
273 { const u32 x19 = in1[7];
274 { const u32 x17 = in1[6];
275 { const u32 x15 = in1[5];
276 { const u32 x13 = in1[4];
277 { const u32 x11 = in1[3];
278 { const u32 x9 = in1[2];
279 { const u32 x7 = in1[1];
280 { const u32 x5 = in1[0];
281 { const u32 x38 = in2[9];
282 { const u32 x39 = in2[8];
283 { const u32 x37 = in2[7];
284 { const u32 x35 = in2[6];
285 { const u32 x33 = in2[5];
286 { const u32 x31 = in2[4];
287 { const u32 x29 = in2[3];
288 { const u32 x27 = in2[2];
289 { const u32 x25 = in2[1];
290 { const u32 x23 = in2[0];
291 out[0] = ((0x7ffffda + x5) - x23);
292 out[1] = ((0x3fffffe + x7) - x25);
293 out[2] = ((0x7fffffe + x9) - x27);
294 out[3] = ((0x3fffffe + x11) - x29);
295 out[4] = ((0x7fffffe + x13) - x31);
296 out[5] = ((0x3fffffe + x15) - x33);
297 out[6] = ((0x7fffffe + x17) - x35);
298 out[7] = ((0x3fffffe + x19) - x37);
299 out[8] = ((0x7fffffe + x21) - x39);
300 out[9] = ((0x3fffffe + x20) - x38);
301 }}}}}}}}}}}}}}}}}}}}
302 }
303
304 /* h = f - g
305 * Can overlap h with f or g.
306 */
307 static __always_inline void fe_sub(fe_loose *h, const fe *f, const fe *g)
308 {
309 fe_sub_impl(h->v, f->v, g->v);
310 }
311
312 static noinline void fe_mul_impl(u32 out[10], const u32 in1[10], const u32 in2[10])
313 {
314 { const u32 x20 = in1[9];
315 { const u32 x21 = in1[8];
316 { const u32 x19 = in1[7];
317 { const u32 x17 = in1[6];
318 { const u32 x15 = in1[5];
319 { const u32 x13 = in1[4];
320 { const u32 x11 = in1[3];
321 { const u32 x9 = in1[2];
322 { const u32 x7 = in1[1];
323 { const u32 x5 = in1[0];
324 { const u32 x38 = in2[9];
325 { const u32 x39 = in2[8];
326 { const u32 x37 = in2[7];
327 { const u32 x35 = in2[6];
328 { const u32 x33 = in2[5];
329 { const u32 x31 = in2[4];
330 { const u32 x29 = in2[3];
331 { const u32 x27 = in2[2];
332 { const u32 x25 = in2[1];
333 { const u32 x23 = in2[0];
334 { u64 x40 = ((u64)x23 * x5);
335 { u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5));
336 { u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5));
337 { u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5));
338 { u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5));
339 { u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5));
340 { u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5));
341 { u64 x47 = (((((((((u64)x29 * x13) + ((u64)x31 * x11)) + ((u64)x27 * x15)) + ((u64)x33 * x9)) + ((u64)x25 * x17)) + ((u64)x35 * x7)) + ((u64)x23 * x19)) + ((u64)x37 * x5));
342 { u64 x48 = (((((((u64)x31 * x13) + (0x2 * (((((u64)x29 * x15) + ((u64)x33 * x11)) + ((u64)x25 * x19)) + ((u64)x37 * x7)))) + ((u64)x27 * x17)) + ((u64)x35 * x9)) + ((u64)x23 * x21)) + ((u64)x39 * x5));
343 { u64 x49 = (((((((((((u64)x31 * x15) + ((u64)x33 * x13)) + ((u64)x29 * x17)) + ((u64)x35 * x11)) + ((u64)x27 * x19)) + ((u64)x37 * x9)) + ((u64)x25 * x21)) + ((u64)x39 * x7)) + ((u64)x23 * x20)) + ((u64)x38 * x5));
344 { u64 x50 = (((((0x2 * ((((((u64)x33 * x15) + ((u64)x29 * x19)) + ((u64)x37 * x11)) + ((u64)x25 * x20)) + ((u64)x38 * x7))) + ((u64)x31 * x17)) + ((u64)x35 * x13)) + ((u64)x27 * x21)) + ((u64)x39 * x9));
345 { u64 x51 = (((((((((u64)x33 * x17) + ((u64)x35 * x15)) + ((u64)x31 * x19)) + ((u64)x37 * x13)) + ((u64)x29 * x21)) + ((u64)x39 * x11)) + ((u64)x27 * x20)) + ((u64)x38 * x9));
346 { u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13));
347 { u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13));
348 { u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17));
349 { u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17));
350 { u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19))));
351 { u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21));
352 { u64 x58 = ((u64)(0x2 * x38) * x20);
353 { u64 x59 = (x48 + (x58 << 0x4));
354 { u64 x60 = (x59 + (x58 << 0x1));
355 { u64 x61 = (x60 + x58);
356 { u64 x62 = (x47 + (x57 << 0x4));
357 { u64 x63 = (x62 + (x57 << 0x1));
358 { u64 x64 = (x63 + x57);
359 { u64 x65 = (x46 + (x56 << 0x4));
360 { u64 x66 = (x65 + (x56 << 0x1));
361 { u64 x67 = (x66 + x56);
362 { u64 x68 = (x45 + (x55 << 0x4));
363 { u64 x69 = (x68 + (x55 << 0x1));
364 { u64 x70 = (x69 + x55);
365 { u64 x71 = (x44 + (x54 << 0x4));
366 { u64 x72 = (x71 + (x54 << 0x1));
367 { u64 x73 = (x72 + x54);
368 { u64 x74 = (x43 + (x53 << 0x4));
369 { u64 x75 = (x74 + (x53 << 0x1));
370 { u64 x76 = (x75 + x53);
371 { u64 x77 = (x42 + (x52 << 0x4));
372 { u64 x78 = (x77 + (x52 << 0x1));
373 { u64 x79 = (x78 + x52);
374 { u64 x80 = (x41 + (x51 << 0x4));
375 { u64 x81 = (x80 + (x51 << 0x1));
376 { u64 x82 = (x81 + x51);
377 { u64 x83 = (x40 + (x50 << 0x4));
378 { u64 x84 = (x83 + (x50 << 0x1));
379 { u64 x85 = (x84 + x50);
380 { u64 x86 = (x85 >> 0x1a);
381 { u32 x87 = ((u32)x85 & 0x3ffffff);
382 { u64 x88 = (x86 + x82);
383 { u64 x89 = (x88 >> 0x19);
384 { u32 x90 = ((u32)x88 & 0x1ffffff);
385 { u64 x91 = (x89 + x79);
386 { u64 x92 = (x91 >> 0x1a);
387 { u32 x93 = ((u32)x91 & 0x3ffffff);
388 { u64 x94 = (x92 + x76);
389 { u64 x95 = (x94 >> 0x19);
390 { u32 x96 = ((u32)x94 & 0x1ffffff);
391 { u64 x97 = (x95 + x73);
392 { u64 x98 = (x97 >> 0x1a);
393 { u32 x99 = ((u32)x97 & 0x3ffffff);
394 { u64 x100 = (x98 + x70);
395 { u64 x101 = (x100 >> 0x19);
396 { u32 x102 = ((u32)x100 & 0x1ffffff);
397 { u64 x103 = (x101 + x67);
398 { u64 x104 = (x103 >> 0x1a);
399 { u32 x105 = ((u32)x103 & 0x3ffffff);
400 { u64 x106 = (x104 + x64);
401 { u64 x107 = (x106 >> 0x19);
402 { u32 x108 = ((u32)x106 & 0x1ffffff);
403 { u64 x109 = (x107 + x61);
404 { u64 x110 = (x109 >> 0x1a);
405 { u32 x111 = ((u32)x109 & 0x3ffffff);
406 { u64 x112 = (x110 + x49);
407 { u64 x113 = (x112 >> 0x19);
408 { u32 x114 = ((u32)x112 & 0x1ffffff);
409 { u64 x115 = (x87 + (0x13 * x113));
410 { u32 x116 = (u32) (x115 >> 0x1a);
411 { u32 x117 = ((u32)x115 & 0x3ffffff);
412 { u32 x118 = (x116 + x90);
413 { u32 x119 = (x118 >> 0x19);
414 { u32 x120 = (x118 & 0x1ffffff);
415 out[0] = x117;
416 out[1] = x120;
417 out[2] = (x119 + x93);
418 out[3] = x96;
419 out[4] = x99;
420 out[5] = x102;
421 out[6] = x105;
422 out[7] = x108;
423 out[8] = x111;
424 out[9] = x114;
425 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
426 }
427
428 static __always_inline void fe_mul_ttt(fe *h, const fe *f, const fe *g)
429 {
430 fe_mul_impl(h->v, f->v, g->v);
431 }
432
433 static __always_inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g)
434 {
435 fe_mul_impl(h->v, f->v, g->v);
436 }
437
438 static __always_inline void
439 fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g)
440 {
441 fe_mul_impl(h->v, f->v, g->v);
442 }
443
444 static noinline void fe_sqr_impl(u32 out[10], const u32 in1[10])
445 {
446 { const u32 x17 = in1[9];
447 { const u32 x18 = in1[8];
448 { const u32 x16 = in1[7];
449 { const u32 x14 = in1[6];
450 { const u32 x12 = in1[5];
451 { const u32 x10 = in1[4];
452 { const u32 x8 = in1[3];
453 { const u32 x6 = in1[2];
454 { const u32 x4 = in1[1];
455 { const u32 x2 = in1[0];
456 { u64 x19 = ((u64)x2 * x2);
457 { u64 x20 = ((u64)(0x2 * x2) * x4);
458 { u64 x21 = (0x2 * (((u64)x4 * x4) + ((u64)x2 * x6)));
459 { u64 x22 = (0x2 * (((u64)x4 * x6) + ((u64)x2 * x8)));
460 { u64 x23 = ((((u64)x6 * x6) + ((u64)(0x4 * x4) * x8)) + ((u64)(0x2 * x2) * x10));
461 { u64 x24 = (0x2 * ((((u64)x6 * x8) + ((u64)x4 * x10)) + ((u64)x2 * x12)));
462 { u64 x25 = (0x2 * (((((u64)x8 * x8) + ((u64)x6 * x10)) + ((u64)x2 * x14)) + ((u64)(0x2 * x4) * x12)));
463 { u64 x26 = (0x2 * (((((u64)x8 * x10) + ((u64)x6 * x12)) + ((u64)x4 * x14)) + ((u64)x2 * x16)));
464 { u64 x27 = (((u64)x10 * x10) + (0x2 * ((((u64)x6 * x14) + ((u64)x2 * x18)) + (0x2 * (((u64)x4 * x16) + ((u64)x8 * x12))))));
465 { u64 x28 = (0x2 * ((((((u64)x10 * x12) + ((u64)x8 * x14)) + ((u64)x6 * x16)) + ((u64)x4 * x18)) + ((u64)x2 * x17)));
466 { u64 x29 = (0x2 * (((((u64)x12 * x12) + ((u64)x10 * x14)) + ((u64)x6 * x18)) + (0x2 * (((u64)x8 * x16) + ((u64)x4 * x17)))));
467 { u64 x30 = (0x2 * (((((u64)x12 * x14) + ((u64)x10 * x16)) + ((u64)x8 * x18)) + ((u64)x6 * x17)));
468 { u64 x31 = (((u64)x14 * x14) + (0x2 * (((u64)x10 * x18) + (0x2 * (((u64)x12 * x16) + ((u64)x8 * x17))))));
469 { u64 x32 = (0x2 * ((((u64)x14 * x16) + ((u64)x12 * x18)) + ((u64)x10 * x17)));
470 { u64 x33 = (0x2 * ((((u64)x16 * x16) + ((u64)x14 * x18)) + ((u64)(0x2 * x12) * x17)));
471 { u64 x34 = (0x2 * (((u64)x16 * x18) + ((u64)x14 * x17)));
472 { u64 x35 = (((u64)x18 * x18) + ((u64)(0x4 * x16) * x17));
473 { u64 x36 = ((u64)(0x2 * x18) * x17);
474 { u64 x37 = ((u64)(0x2 * x17) * x17);
475 { u64 x38 = (x27 + (x37 << 0x4));
476 { u64 x39 = (x38 + (x37 << 0x1));
477 { u64 x40 = (x39 + x37);
478 { u64 x41 = (x26 + (x36 << 0x4));
479 { u64 x42 = (x41 + (x36 << 0x1));
480 { u64 x43 = (x42 + x36);
481 { u64 x44 = (x25 + (x35 << 0x4));
482 { u64 x45 = (x44 + (x35 << 0x1));
483 { u64 x46 = (x45 + x35);
484 { u64 x47 = (x24 + (x34 << 0x4));
485 { u64 x48 = (x47 + (x34 << 0x1));
486 { u64 x49 = (x48 + x34);
487 { u64 x50 = (x23 + (x33 << 0x4));
488 { u64 x51 = (x50 + (x33 << 0x1));
489 { u64 x52 = (x51 + x33);
490 { u64 x53 = (x22 + (x32 << 0x4));
491 { u64 x54 = (x53 + (x32 << 0x1));
492 { u64 x55 = (x54 + x32);
493 { u64 x56 = (x21 + (x31 << 0x4));
494 { u64 x57 = (x56 + (x31 << 0x1));
495 { u64 x58 = (x57 + x31);
496 { u64 x59 = (x20 + (x30 << 0x4));
497 { u64 x60 = (x59 + (x30 << 0x1));
498 { u64 x61 = (x60 + x30);
499 { u64 x62 = (x19 + (x29 << 0x4));
500 { u64 x63 = (x62 + (x29 << 0x1));
501 { u64 x64 = (x63 + x29);
502 { u64 x65 = (x64 >> 0x1a);
503 { u32 x66 = ((u32)x64 & 0x3ffffff);
504 { u64 x67 = (x65 + x61);
505 { u64 x68 = (x67 >> 0x19);
506 { u32 x69 = ((u32)x67 & 0x1ffffff);
507 { u64 x70 = (x68 + x58);
508 { u64 x71 = (x70 >> 0x1a);
509 { u32 x72 = ((u32)x70 & 0x3ffffff);
510 { u64 x73 = (x71 + x55);
511 { u64 x74 = (x73 >> 0x19);
512 { u32 x75 = ((u32)x73 & 0x1ffffff);
513 { u64 x76 = (x74 + x52);
514 { u64 x77 = (x76 >> 0x1a);
515 { u32 x78 = ((u32)x76 & 0x3ffffff);
516 { u64 x79 = (x77 + x49);
517 { u64 x80 = (x79 >> 0x19);
518 { u32 x81 = ((u32)x79 & 0x1ffffff);
519 { u64 x82 = (x80 + x46);
520 { u64 x83 = (x82 >> 0x1a);
521 { u32 x84 = ((u32)x82 & 0x3ffffff);
522 { u64 x85 = (x83 + x43);
523 { u64 x86 = (x85 >> 0x19);
524 { u32 x87 = ((u32)x85 & 0x1ffffff);
525 { u64 x88 = (x86 + x40);
526 { u64 x89 = (x88 >> 0x1a);
527 { u32 x90 = ((u32)x88 & 0x3ffffff);
528 { u64 x91 = (x89 + x28);
529 { u64 x92 = (x91 >> 0x19);
530 { u32 x93 = ((u32)x91 & 0x1ffffff);
531 { u64 x94 = (x66 + (0x13 * x92));
532 { u32 x95 = (u32) (x94 >> 0x1a);
533 { u32 x96 = ((u32)x94 & 0x3ffffff);
534 { u32 x97 = (x95 + x69);
535 { u32 x98 = (x97 >> 0x19);
536 { u32 x99 = (x97 & 0x1ffffff);
537 out[0] = x96;
538 out[1] = x99;
539 out[2] = (x98 + x72);
540 out[3] = x75;
541 out[4] = x78;
542 out[5] = x81;
543 out[6] = x84;
544 out[7] = x87;
545 out[8] = x90;
546 out[9] = x93;
547 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
548 }
549
550 static __always_inline void fe_sq_tl(fe *h, const fe_loose *f)
551 {
552 fe_sqr_impl(h->v, f->v);
553 }
554
555 static __always_inline void fe_sq_tt(fe *h, const fe *f)
556 {
557 fe_sqr_impl(h->v, f->v);
558 }
559
560 static __always_inline void fe_loose_invert(fe *out, const fe_loose *z)
561 {
562 fe t0;
563 fe t1;
564 fe t2;
565 fe t3;
566 int i;
567
568 fe_sq_tl(&t0, z);
569 fe_sq_tt(&t1, &t0);
570 for (i = 1; i < 2; ++i)
571 fe_sq_tt(&t1, &t1);
572 fe_mul_tlt(&t1, z, &t1);
573 fe_mul_ttt(&t0, &t0, &t1);
574 fe_sq_tt(&t2, &t0);
575 fe_mul_ttt(&t1, &t1, &t2);
576 fe_sq_tt(&t2, &t1);
577 for (i = 1; i < 5; ++i)
578 fe_sq_tt(&t2, &t2);
579 fe_mul_ttt(&t1, &t2, &t1);
580 fe_sq_tt(&t2, &t1);
581 for (i = 1; i < 10; ++i)
582 fe_sq_tt(&t2, &t2);
583 fe_mul_ttt(&t2, &t2, &t1);
584 fe_sq_tt(&t3, &t2);
585 for (i = 1; i < 20; ++i)
586 fe_sq_tt(&t3, &t3);
587 fe_mul_ttt(&t2, &t3, &t2);
588 fe_sq_tt(&t2, &t2);
589 for (i = 1; i < 10; ++i)
590 fe_sq_tt(&t2, &t2);
591 fe_mul_ttt(&t1, &t2, &t1);
592 fe_sq_tt(&t2, &t1);
593 for (i = 1; i < 50; ++i)
594 fe_sq_tt(&t2, &t2);
595 fe_mul_ttt(&t2, &t2, &t1);
596 fe_sq_tt(&t3, &t2);
597 for (i = 1; i < 100; ++i)
598 fe_sq_tt(&t3, &t3);
599 fe_mul_ttt(&t2, &t3, &t2);
600 fe_sq_tt(&t2, &t2);
601 for (i = 1; i < 50; ++i)
602 fe_sq_tt(&t2, &t2);
603 fe_mul_ttt(&t1, &t2, &t1);
604 fe_sq_tt(&t1, &t1);
605 for (i = 1; i < 5; ++i)
606 fe_sq_tt(&t1, &t1);
607 fe_mul_ttt(out, &t1, &t0);
608 }
609
610 static __always_inline void fe_invert(fe *out, const fe *z)
611 {
612 fe_loose l;
613 fe_copy_lt(&l, z);
614 fe_loose_invert(out, &l);
615 }
616
617 /* Replace (f,g) with (g,f) if b == 1;
618 * replace (f,g) with (f,g) if b == 0.
619 *
620 * Preconditions: b in {0,1}
621 */
622 static noinline void fe_cswap(fe *f, fe *g, unsigned int b)
623 {
624 unsigned i;
625 b = 0 - b;
626 for (i = 0; i < 10; i++) {
627 u32 x = f->v[i] ^ g->v[i];
628 x &= b;
629 f->v[i] ^= x;
630 g->v[i] ^= x;
631 }
632 }
633
634 /* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/
635 static __always_inline void fe_mul_121666_impl(u32 out[10], const u32 in1[10])
636 {
637 { const u32 x20 = in1[9];
638 { const u32 x21 = in1[8];
639 { const u32 x19 = in1[7];
640 { const u32 x17 = in1[6];
641 { const u32 x15 = in1[5];
642 { const u32 x13 = in1[4];
643 { const u32 x11 = in1[3];
644 { const u32 x9 = in1[2];
645 { const u32 x7 = in1[1];
646 { const u32 x5 = in1[0];
647 { const u32 x38 = 0;
648 { const u32 x39 = 0;
649 { const u32 x37 = 0;
650 { const u32 x35 = 0;
651 { const u32 x33 = 0;
652 { const u32 x31 = 0;
653 { const u32 x29 = 0;
654 { const u32 x27 = 0;
655 { const u32 x25 = 0;
656 { const u32 x23 = 121666;
657 { u64 x40 = ((u64)x23 * x5);
658 { u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5));
659 { u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5));
660 { u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5));
661 { u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5));
662 { u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5));
663 { u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5));
664 { u64 x47 = (((((((((u64)x29 * x13) + ((u64)x31 * x11)) + ((u64)x27 * x15)) + ((u64)x33 * x9)) + ((u64)x25 * x17)) + ((u64)x35 * x7)) + ((u64)x23 * x19)) + ((u64)x37 * x5));
665 { u64 x48 = (((((((u64)x31 * x13) + (0x2 * (((((u64)x29 * x15) + ((u64)x33 * x11)) + ((u64)x25 * x19)) + ((u64)x37 * x7)))) + ((u64)x27 * x17)) + ((u64)x35 * x9)) + ((u64)x23 * x21)) + ((u64)x39 * x5));
666 { u64 x49 = (((((((((((u64)x31 * x15) + ((u64)x33 * x13)) + ((u64)x29 * x17)) + ((u64)x35 * x11)) + ((u64)x27 * x19)) + ((u64)x37 * x9)) + ((u64)x25 * x21)) + ((u64)x39 * x7)) + ((u64)x23 * x20)) + ((u64)x38 * x5));
667 { u64 x50 = (((((0x2 * ((((((u64)x33 * x15) + ((u64)x29 * x19)) + ((u64)x37 * x11)) + ((u64)x25 * x20)) + ((u64)x38 * x7))) + ((u64)x31 * x17)) + ((u64)x35 * x13)) + ((u64)x27 * x21)) + ((u64)x39 * x9));
668 { u64 x51 = (((((((((u64)x33 * x17) + ((u64)x35 * x15)) + ((u64)x31 * x19)) + ((u64)x37 * x13)) + ((u64)x29 * x21)) + ((u64)x39 * x11)) + ((u64)x27 * x20)) + ((u64)x38 * x9));
669 { u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13));
670 { u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13));
671 { u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17));
672 { u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17));
673 { u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19))));
674 { u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21));
675 { u64 x58 = ((u64)(0x2 * x38) * x20);
676 { u64 x59 = (x48 + (x58 << 0x4));
677 { u64 x60 = (x59 + (x58 << 0x1));
678 { u64 x61 = (x60 + x58);
679 { u64 x62 = (x47 + (x57 << 0x4));
680 { u64 x63 = (x62 + (x57 << 0x1));
681 { u64 x64 = (x63 + x57);
682 { u64 x65 = (x46 + (x56 << 0x4));
683 { u64 x66 = (x65 + (x56 << 0x1));
684 { u64 x67 = (x66 + x56);
685 { u64 x68 = (x45 + (x55 << 0x4));
686 { u64 x69 = (x68 + (x55 << 0x1));
687 { u64 x70 = (x69 + x55);
688 { u64 x71 = (x44 + (x54 << 0x4));
689 { u64 x72 = (x71 + (x54 << 0x1));
690 { u64 x73 = (x72 + x54);
691 { u64 x74 = (x43 + (x53 << 0x4));
692 { u64 x75 = (x74 + (x53 << 0x1));
693 { u64 x76 = (x75 + x53);
694 { u64 x77 = (x42 + (x52 << 0x4));
695 { u64 x78 = (x77 + (x52 << 0x1));
696 { u64 x79 = (x78 + x52);
697 { u64 x80 = (x41 + (x51 << 0x4));
698 { u64 x81 = (x80 + (x51 << 0x1));
699 { u64 x82 = (x81 + x51);
700 { u64 x83 = (x40 + (x50 << 0x4));
701 { u64 x84 = (x83 + (x50 << 0x1));
702 { u64 x85 = (x84 + x50);
703 { u64 x86 = (x85 >> 0x1a);
704 { u32 x87 = ((u32)x85 & 0x3ffffff);
705 { u64 x88 = (x86 + x82);
706 { u64 x89 = (x88 >> 0x19);
707 { u32 x90 = ((u32)x88 & 0x1ffffff);
708 { u64 x91 = (x89 + x79);
709 { u64 x92 = (x91 >> 0x1a);
710 { u32 x93 = ((u32)x91 & 0x3ffffff);
711 { u64 x94 = (x92 + x76);
712 { u64 x95 = (x94 >> 0x19);
713 { u32 x96 = ((u32)x94 & 0x1ffffff);
714 { u64 x97 = (x95 + x73);
715 { u64 x98 = (x97 >> 0x1a);
716 { u32 x99 = ((u32)x97 & 0x3ffffff);
717 { u64 x100 = (x98 + x70);
718 { u64 x101 = (x100 >> 0x19);
719 { u32 x102 = ((u32)x100 & 0x1ffffff);
720 { u64 x103 = (x101 + x67);
721 { u64 x104 = (x103 >> 0x1a);
722 { u32 x105 = ((u32)x103 & 0x3ffffff);
723 { u64 x106 = (x104 + x64);
724 { u64 x107 = (x106 >> 0x19);
725 { u32 x108 = ((u32)x106 & 0x1ffffff);
726 { u64 x109 = (x107 + x61);
727 { u64 x110 = (x109 >> 0x1a);
728 { u32 x111 = ((u32)x109 & 0x3ffffff);
729 { u64 x112 = (x110 + x49);
730 { u64 x113 = (x112 >> 0x19);
731 { u32 x114 = ((u32)x112 & 0x1ffffff);
732 { u64 x115 = (x87 + (0x13 * x113));
733 { u32 x116 = (u32) (x115 >> 0x1a);
734 { u32 x117 = ((u32)x115 & 0x3ffffff);
735 { u32 x118 = (x116 + x90);
736 { u32 x119 = (x118 >> 0x19);
737 { u32 x120 = (x118 & 0x1ffffff);
738 out[0] = x117;
739 out[1] = x120;
740 out[2] = (x119 + x93);
741 out[3] = x96;
742 out[4] = x99;
743 out[5] = x102;
744 out[6] = x105;
745 out[7] = x108;
746 out[8] = x111;
747 out[9] = x114;
748 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
749 }
750
751 static __always_inline void fe_mul121666(fe *h, const fe_loose *f)
752 {
753 fe_mul_121666_impl(h->v, f->v);
754 }
755
756 void curve25519_generic(u8 out[CURVE25519_KEY_SIZE],
757 const u8 scalar[CURVE25519_KEY_SIZE],
758 const u8 point[CURVE25519_KEY_SIZE])
759 {
760 fe x1, x2, z2, x3, z3;
761 fe_loose x2l, z2l, x3l;
762 unsigned swap = 0;
763 int pos;
764 u8 e[32];
765
766 memcpy(e, scalar, 32);
767 curve25519_clamp_secret(e);
768
769 /* The following implementation was transcribed to Coq and proven to
770 * correspond to unary scalar multiplication in affine coordinates given
771 * that x1 != 0 is the x coordinate of some point on the curve. It was
772 * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives
773 * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was
774 * quantified over the underlying field, so it applies to Curve25519
775 * itself and the quadratic twist of Curve25519. It was not proven in
776 * Coq that prime-field arithmetic correctly simulates extension-field
777 * arithmetic on prime-field values. The decoding of the byte array
778 * representation of e was not considered.
779 *
780 * Specification of Montgomery curves in affine coordinates:
781 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27>
782 *
783 * Proof that these form a group that is isomorphic to a Weierstrass
784 * curve:
785 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35>
786 *
787 * Coq transcription and correctness proof of the loop
788 * (where scalarbits=255):
789 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118>
790 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278>
791 * preconditions: 0 <= e < 2^255 (not necessarily e < order),
792 * fe_invert(0) = 0
793 */
794 fe_frombytes(&x1, point);
795 fe_1(&x2);
796 fe_0(&z2);
797 fe_copy(&x3, &x1);
798 fe_1(&z3);
799
800 for (pos = 254; pos >= 0; --pos) {
801 fe tmp0, tmp1;
802 fe_loose tmp0l, tmp1l;
803 /* loop invariant as of right before the test, for the case
804 * where x1 != 0:
805 * pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3
806 * is nonzero
807 * let r := e >> (pos+1) in the following equalities of
808 * projective points:
809 * to_xz (r*P) === if swap then (x3, z3) else (x2, z2)
810 * to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3)
811 * x1 is the nonzero x coordinate of the nonzero
812 * point (r*P-(r+1)*P)
813 */
814 unsigned b = 1 & (e[pos / 8] >> (pos & 7));
815 swap ^= b;
816 fe_cswap(&x2, &x3, swap);
817 fe_cswap(&z2, &z3, swap);
818 swap = b;
819 /* Coq transcription of ladderstep formula (called from
820 * transcribed loop):
821 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89>
822 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131>
823 * x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217>
824 * x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147>
825 */
826 fe_sub(&tmp0l, &x3, &z3);
827 fe_sub(&tmp1l, &x2, &z2);
828 fe_add(&x2l, &x2, &z2);
829 fe_add(&z2l, &x3, &z3);
830 fe_mul_tll(&z3, &tmp0l, &x2l);
831 fe_mul_tll(&z2, &z2l, &tmp1l);
832 fe_sq_tl(&tmp0, &tmp1l);
833 fe_sq_tl(&tmp1, &x2l);
834 fe_add(&x3l, &z3, &z2);
835 fe_sub(&z2l, &z3, &z2);
836 fe_mul_ttt(&x2, &tmp1, &tmp0);
837 fe_sub(&tmp1l, &tmp1, &tmp0);
838 fe_sq_tl(&z2, &z2l);
839 fe_mul121666(&z3, &tmp1l);
840 fe_sq_tl(&x3, &x3l);
841 fe_add(&tmp0l, &tmp0, &z3);
842 fe_mul_ttt(&z3, &x1, &z2);
843 fe_mul_tll(&z2, &tmp1l, &tmp0l);
844 }
845 /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3)
846 * else (x2, z2)
847 */
848 fe_cswap(&x2, &x3, swap);
849 fe_cswap(&z2, &z3, swap);
850
851 fe_invert(&z2, &z2);
852 fe_mul_ttt(&x2, &x2, &z2);
853 fe_tobytes(out, &x2);
854
855 memzero_explicit(&x1, sizeof(x1));
856 memzero_explicit(&x2, sizeof(x2));
857 memzero_explicit(&z2, sizeof(z2));
858 memzero_explicit(&x3, sizeof(x3));
859 memzero_explicit(&z3, sizeof(z3));
860 memzero_explicit(&x2l, sizeof(x2l));
861 memzero_explicit(&z2l, sizeof(z2l));
862 memzero_explicit(&x3l, sizeof(x3l));
863 memzero_explicit(&e, sizeof(e));
864 }
865
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