1 // SPDX-License-Identifier: GPL-2.0 OR MIT
2 /*
3 * Copyright (C) 2015-2016 The fiat-crypto Authors.
4 * Copyright (C) 2018-2020 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 /* fe means field element. Here the field is \Z/(2^255-19). An element t,
14 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
15 * t[3]+2^102 t[4]+...+2^230 t[9].
16 * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc.
17 * Multiplication and carrying produce fe from fe_loose.
18 */
19 typedef struct fe { u32 v[10]; } fe;
20
21 /* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc
22 * Addition and subtraction produce fe_loose from (fe, fe).
23 */
24 typedef struct fe_loose { u32 v[10]; } fe_loose;
25
fe_frombytes_impl(u32 h[10],const u8 * s)26 static __always_inline void fe_frombytes_impl(u32 h[10], const u8 *s)
27 {
28 /* Ignores top bit of s. */
29 u32 a0 = get_unaligned_le32(s);
30 u32 a1 = get_unaligned_le32(s+4);
31 u32 a2 = get_unaligned_le32(s+8);
32 u32 a3 = get_unaligned_le32(s+12);
33 u32 a4 = get_unaligned_le32(s+16);
34 u32 a5 = get_unaligned_le32(s+20);
35 u32 a6 = get_unaligned_le32(s+24);
36 u32 a7 = get_unaligned_le32(s+28);
37 h[0] = a0&((1<<26)-1); /* 26 used, 32-26 left. 26 */
38 h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 = 6+19 = 25 */
39 h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */
40 h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) + 6 = 19+ 6 = 25 */
41 h[4] = (a3>> 6); /* (32- 6) = 26 */
42 h[5] = a4&((1<<25)-1); /* 25 */
43 h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 = 7+19 = 26 */
44 h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */
45 h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) + 6 = 20+ 6 = 26 */
46 h[9] = (a7>> 6)&((1<<25)-1); /* 25 */
47 }
48
fe_frombytes(fe * h,const u8 * s)49 static __always_inline void fe_frombytes(fe *h, const u8 *s)
50 {
51 fe_frombytes_impl(h->v, s);
52 }
53
54 static __always_inline u8 /*bool*/
addcarryx_u25(u8 c,u32 a,u32 b,u32 * low)55 addcarryx_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
56 {
57 /* This function extracts 25 bits of result and 1 bit of carry
58 * (26 total), so a 32-bit intermediate is sufficient.
59 */
60 u32 x = a + b + c;
61 *low = x & ((1 << 25) - 1);
62 return (x >> 25) & 1;
63 }
64
65 static __always_inline u8 /*bool*/
addcarryx_u26(u8 c,u32 a,u32 b,u32 * low)66 addcarryx_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
67 {
68 /* This function extracts 26 bits of result and 1 bit of carry
69 * (27 total), so a 32-bit intermediate is sufficient.
70 */
71 u32 x = a + b + c;
72 *low = x & ((1 << 26) - 1);
73 return (x >> 26) & 1;
74 }
75
76 static __always_inline u8 /*bool*/
subborrow_u25(u8 c,u32 a,u32 b,u32 * low)77 subborrow_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
78 {
79 /* This function extracts 25 bits of result and 1 bit of borrow
80 * (26 total), so a 32-bit intermediate is sufficient.
81 */
82 u32 x = a - b - c;
83 *low = x & ((1 << 25) - 1);
84 return x >> 31;
85 }
86
87 static __always_inline u8 /*bool*/
subborrow_u26(u8 c,u32 a,u32 b,u32 * low)88 subborrow_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low)
89 {
90 /* This function extracts 26 bits of result and 1 bit of borrow
91 *(27 total), so a 32-bit intermediate is sufficient.
92 */
93 u32 x = a - b - c;
94 *low = x & ((1 << 26) - 1);
95 return x >> 31;
96 }
97
cmovznz32(u32 t,u32 z,u32 nz)98 static __always_inline u32 cmovznz32(u32 t, u32 z, u32 nz)
99 {
100 t = -!!t; /* all set if nonzero, 0 if 0 */
101 return (t&nz) | ((~t)&z);
102 }
103
fe_freeze(u32 out[10],const u32 in1[10])104 static __always_inline void fe_freeze(u32 out[10], const u32 in1[10])
105 {
106 { const u32 x17 = in1[9];
107 { const u32 x18 = in1[8];
108 { const u32 x16 = in1[7];
109 { const u32 x14 = in1[6];
110 { const u32 x12 = in1[5];
111 { const u32 x10 = in1[4];
112 { const u32 x8 = in1[3];
113 { const u32 x6 = in1[2];
114 { const u32 x4 = in1[1];
115 { const u32 x2 = in1[0];
116 { u32 x20; u8/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20);
117 { u32 x23; u8/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23);
118 { u32 x26; u8/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26);
119 { u32 x29; u8/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29);
120 { u32 x32; u8/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32);
121 { u32 x35; u8/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35);
122 { u32 x38; u8/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38);
123 { u32 x41; u8/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41);
124 { u32 x44; u8/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44);
125 { u32 x47; u8/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47);
126 { u32 x49 = cmovznz32(x48, 0x0, 0xffffffff);
127 { u32 x50 = (x49 & 0x3ffffed);
128 { u32 x52; u8/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52);
129 { u32 x54 = (x49 & 0x1ffffff);
130 { u32 x56; u8/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56);
131 { u32 x58 = (x49 & 0x3ffffff);
132 { u32 x60; u8/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60);
133 { u32 x62 = (x49 & 0x1ffffff);
134 { u32 x64; u8/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64);
135 { u32 x66 = (x49 & 0x3ffffff);
136 { u32 x68; u8/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68);
137 { u32 x70 = (x49 & 0x1ffffff);
138 { u32 x72; u8/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72);
139 { u32 x74 = (x49 & 0x3ffffff);
140 { u32 x76; u8/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76);
141 { u32 x78 = (x49 & 0x1ffffff);
142 { u32 x80; u8/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80);
143 { u32 x82 = (x49 & 0x3ffffff);
144 { u32 x84; u8/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84);
145 { u32 x86 = (x49 & 0x1ffffff);
146 { u32 x88; addcarryx_u25(x85, x47, x86, &x88);
147 out[0] = x52;
148 out[1] = x56;
149 out[2] = x60;
150 out[3] = x64;
151 out[4] = x68;
152 out[5] = x72;
153 out[6] = x76;
154 out[7] = x80;
155 out[8] = x84;
156 out[9] = x88;
157 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
158 }
159
fe_tobytes(u8 s[32],const fe * f)160 static __always_inline void fe_tobytes(u8 s[32], const fe *f)
161 {
162 u32 h[10];
163 fe_freeze(h, f->v);
164 s[0] = h[0] >> 0;
165 s[1] = h[0] >> 8;
166 s[2] = h[0] >> 16;
167 s[3] = (h[0] >> 24) | (h[1] << 2);
168 s[4] = h[1] >> 6;
169 s[5] = h[1] >> 14;
170 s[6] = (h[1] >> 22) | (h[2] << 3);
171 s[7] = h[2] >> 5;
172 s[8] = h[2] >> 13;
173 s[9] = (h[2] >> 21) | (h[3] << 5);
174 s[10] = h[3] >> 3;
175 s[11] = h[3] >> 11;
176 s[12] = (h[3] >> 19) | (h[4] << 6);
177 s[13] = h[4] >> 2;
178 s[14] = h[4] >> 10;
179 s[15] = h[4] >> 18;
180 s[16] = h[5] >> 0;
181 s[17] = h[5] >> 8;
182 s[18] = h[5] >> 16;
183 s[19] = (h[5] >> 24) | (h[6] << 1);
184 s[20] = h[6] >> 7;
185 s[21] = h[6] >> 15;
186 s[22] = (h[6] >> 23) | (h[7] << 3);
187 s[23] = h[7] >> 5;
188 s[24] = h[7] >> 13;
189 s[25] = (h[7] >> 21) | (h[8] << 4);
190 s[26] = h[8] >> 4;
191 s[27] = h[8] >> 12;
192 s[28] = (h[8] >> 20) | (h[9] << 6);
193 s[29] = h[9] >> 2;
194 s[30] = h[9] >> 10;
195 s[31] = h[9] >> 18;
196 }
197
198 /* h = f */
fe_copy(fe * h,const fe * f)199 static __always_inline void fe_copy(fe *h, const fe *f)
200 {
201 memmove(h, f, sizeof(u32) * 10);
202 }
203
fe_copy_lt(fe_loose * h,const fe * f)204 static __always_inline void fe_copy_lt(fe_loose *h, const fe *f)
205 {
206 memmove(h, f, sizeof(u32) * 10);
207 }
208
209 /* h = 0 */
fe_0(fe * h)210 static __always_inline void fe_0(fe *h)
211 {
212 memset(h, 0, sizeof(u32) * 10);
213 }
214
215 /* h = 1 */
fe_1(fe * h)216 static __always_inline void fe_1(fe *h)
217 {
218 memset(h, 0, sizeof(u32) * 10);
219 h->v[0] = 1;
220 }
221
fe_add_impl(u32 out[10],const u32 in1[10],const u32 in2[10])222 static void fe_add_impl(u32 out[10], const u32 in1[10], const u32 in2[10])
223 {
224 { const u32 x20 = in1[9];
225 { const u32 x21 = in1[8];
226 { const u32 x19 = in1[7];
227 { const u32 x17 = in1[6];
228 { const u32 x15 = in1[5];
229 { const u32 x13 = in1[4];
230 { const u32 x11 = in1[3];
231 { const u32 x9 = in1[2];
232 { const u32 x7 = in1[1];
233 { const u32 x5 = in1[0];
234 { const u32 x38 = in2[9];
235 { const u32 x39 = in2[8];
236 { const u32 x37 = in2[7];
237 { const u32 x35 = in2[6];
238 { const u32 x33 = in2[5];
239 { const u32 x31 = in2[4];
240 { const u32 x29 = in2[3];
241 { const u32 x27 = in2[2];
242 { const u32 x25 = in2[1];
243 { const u32 x23 = in2[0];
244 out[0] = (x5 + x23);
245 out[1] = (x7 + x25);
246 out[2] = (x9 + x27);
247 out[3] = (x11 + x29);
248 out[4] = (x13 + x31);
249 out[5] = (x15 + x33);
250 out[6] = (x17 + x35);
251 out[7] = (x19 + x37);
252 out[8] = (x21 + x39);
253 out[9] = (x20 + x38);
254 }}}}}}}}}}}}}}}}}}}}
255 }
256
257 /* h = f + g
258 * Can overlap h with f or g.
259 */
fe_add(fe_loose * h,const fe * f,const fe * g)260 static __always_inline void fe_add(fe_loose *h, const fe *f, const fe *g)
261 {
262 fe_add_impl(h->v, f->v, g->v);
263 }
264
fe_sub_impl(u32 out[10],const u32 in1[10],const u32 in2[10])265 static void fe_sub_impl(u32 out[10], const u32 in1[10], const u32 in2[10])
266 {
267 { const u32 x20 = in1[9];
268 { const u32 x21 = in1[8];
269 { const u32 x19 = in1[7];
270 { const u32 x17 = in1[6];
271 { const u32 x15 = in1[5];
272 { const u32 x13 = in1[4];
273 { const u32 x11 = in1[3];
274 { const u32 x9 = in1[2];
275 { const u32 x7 = in1[1];
276 { const u32 x5 = in1[0];
277 { const u32 x38 = in2[9];
278 { const u32 x39 = in2[8];
279 { const u32 x37 = in2[7];
280 { const u32 x35 = in2[6];
281 { const u32 x33 = in2[5];
282 { const u32 x31 = in2[4];
283 { const u32 x29 = in2[3];
284 { const u32 x27 = in2[2];
285 { const u32 x25 = in2[1];
286 { const u32 x23 = in2[0];
287 out[0] = ((0x7ffffda + x5) - x23);
288 out[1] = ((0x3fffffe + x7) - x25);
289 out[2] = ((0x7fffffe + x9) - x27);
290 out[3] = ((0x3fffffe + x11) - x29);
291 out[4] = ((0x7fffffe + x13) - x31);
292 out[5] = ((0x3fffffe + x15) - x33);
293 out[6] = ((0x7fffffe + x17) - x35);
294 out[7] = ((0x3fffffe + x19) - x37);
295 out[8] = ((0x7fffffe + x21) - x39);
296 out[9] = ((0x3fffffe + x20) - x38);
297 }}}}}}}}}}}}}}}}}}}}
298 }
299
300 /* h = f - g
301 * Can overlap h with f or g.
302 */
fe_sub(fe_loose * h,const fe * f,const fe * g)303 static __always_inline void fe_sub(fe_loose *h, const fe *f, const fe *g)
304 {
305 fe_sub_impl(h->v, f->v, g->v);
306 }
307
fe_mul_impl(u32 out[10],const u32 in1[10],const u32 in2[10])308 static void fe_mul_impl(u32 out[10], const u32 in1[10], const u32 in2[10])
309 {
310 { const u32 x20 = in1[9];
311 { const u32 x21 = in1[8];
312 { const u32 x19 = in1[7];
313 { const u32 x17 = in1[6];
314 { const u32 x15 = in1[5];
315 { const u32 x13 = in1[4];
316 { const u32 x11 = in1[3];
317 { const u32 x9 = in1[2];
318 { const u32 x7 = in1[1];
319 { const u32 x5 = in1[0];
320 { const u32 x38 = in2[9];
321 { const u32 x39 = in2[8];
322 { const u32 x37 = in2[7];
323 { const u32 x35 = in2[6];
324 { const u32 x33 = in2[5];
325 { const u32 x31 = in2[4];
326 { const u32 x29 = in2[3];
327 { const u32 x27 = in2[2];
328 { const u32 x25 = in2[1];
329 { const u32 x23 = in2[0];
330 { u64 x40 = ((u64)x23 * x5);
331 { u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5));
332 { u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5));
333 { u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5));
334 { u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5));
335 { u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5));
336 { u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5));
337 { 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));
338 { 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));
339 { 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));
340 { 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));
341 { 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));
342 { u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13));
343 { u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13));
344 { u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17));
345 { u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17));
346 { u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19))));
347 { u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21));
348 { u64 x58 = ((u64)(0x2 * x38) * x20);
349 { u64 x59 = (x48 + (x58 << 0x4));
350 { u64 x60 = (x59 + (x58 << 0x1));
351 { u64 x61 = (x60 + x58);
352 { u64 x62 = (x47 + (x57 << 0x4));
353 { u64 x63 = (x62 + (x57 << 0x1));
354 { u64 x64 = (x63 + x57);
355 { u64 x65 = (x46 + (x56 << 0x4));
356 { u64 x66 = (x65 + (x56 << 0x1));
357 { u64 x67 = (x66 + x56);
358 { u64 x68 = (x45 + (x55 << 0x4));
359 { u64 x69 = (x68 + (x55 << 0x1));
360 { u64 x70 = (x69 + x55);
361 { u64 x71 = (x44 + (x54 << 0x4));
362 { u64 x72 = (x71 + (x54 << 0x1));
363 { u64 x73 = (x72 + x54);
364 { u64 x74 = (x43 + (x53 << 0x4));
365 { u64 x75 = (x74 + (x53 << 0x1));
366 { u64 x76 = (x75 + x53);
367 { u64 x77 = (x42 + (x52 << 0x4));
368 { u64 x78 = (x77 + (x52 << 0x1));
369 { u64 x79 = (x78 + x52);
370 { u64 x80 = (x41 + (x51 << 0x4));
371 { u64 x81 = (x80 + (x51 << 0x1));
372 { u64 x82 = (x81 + x51);
373 { u64 x83 = (x40 + (x50 << 0x4));
374 { u64 x84 = (x83 + (x50 << 0x1));
375 { u64 x85 = (x84 + x50);
376 { u64 x86 = (x85 >> 0x1a);
377 { u32 x87 = ((u32)x85 & 0x3ffffff);
378 { u64 x88 = (x86 + x82);
379 { u64 x89 = (x88 >> 0x19);
380 { u32 x90 = ((u32)x88 & 0x1ffffff);
381 { u64 x91 = (x89 + x79);
382 { u64 x92 = (x91 >> 0x1a);
383 { u32 x93 = ((u32)x91 & 0x3ffffff);
384 { u64 x94 = (x92 + x76);
385 { u64 x95 = (x94 >> 0x19);
386 { u32 x96 = ((u32)x94 & 0x1ffffff);
387 { u64 x97 = (x95 + x73);
388 { u64 x98 = (x97 >> 0x1a);
389 { u32 x99 = ((u32)x97 & 0x3ffffff);
390 { u64 x100 = (x98 + x70);
391 { u64 x101 = (x100 >> 0x19);
392 { u32 x102 = ((u32)x100 & 0x1ffffff);
393 { u64 x103 = (x101 + x67);
394 { u64 x104 = (x103 >> 0x1a);
395 { u32 x105 = ((u32)x103 & 0x3ffffff);
396 { u64 x106 = (x104 + x64);
397 { u64 x107 = (x106 >> 0x19);
398 { u32 x108 = ((u32)x106 & 0x1ffffff);
399 { u64 x109 = (x107 + x61);
400 { u64 x110 = (x109 >> 0x1a);
401 { u32 x111 = ((u32)x109 & 0x3ffffff);
402 { u64 x112 = (x110 + x49);
403 { u64 x113 = (x112 >> 0x19);
404 { u32 x114 = ((u32)x112 & 0x1ffffff);
405 { u64 x115 = (x87 + (0x13 * x113));
406 { u32 x116 = (u32) (x115 >> 0x1a);
407 { u32 x117 = ((u32)x115 & 0x3ffffff);
408 { u32 x118 = (x116 + x90);
409 { u32 x119 = (x118 >> 0x19);
410 { u32 x120 = (x118 & 0x1ffffff);
411 out[0] = x117;
412 out[1] = x120;
413 out[2] = (x119 + x93);
414 out[3] = x96;
415 out[4] = x99;
416 out[5] = x102;
417 out[6] = x105;
418 out[7] = x108;
419 out[8] = x111;
420 out[9] = x114;
421 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
422 }
423
fe_mul_ttt(fe * h,const fe * f,const fe * g)424 static __always_inline void fe_mul_ttt(fe *h, const fe *f, const fe *g)
425 {
426 fe_mul_impl(h->v, f->v, g->v);
427 }
428
fe_mul_tlt(fe * h,const fe_loose * f,const fe * g)429 static __always_inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g)
430 {
431 fe_mul_impl(h->v, f->v, g->v);
432 }
433
434 static __always_inline void
fe_mul_tll(fe * h,const fe_loose * f,const fe_loose * g)435 fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g)
436 {
437 fe_mul_impl(h->v, f->v, g->v);
438 }
439
fe_sqr_impl(u32 out[10],const u32 in1[10])440 static void fe_sqr_impl(u32 out[10], const u32 in1[10])
441 {
442 { const u32 x17 = in1[9];
443 { const u32 x18 = in1[8];
444 { const u32 x16 = in1[7];
445 { const u32 x14 = in1[6];
446 { const u32 x12 = in1[5];
447 { const u32 x10 = in1[4];
448 { const u32 x8 = in1[3];
449 { const u32 x6 = in1[2];
450 { const u32 x4 = in1[1];
451 { const u32 x2 = in1[0];
452 { u64 x19 = ((u64)x2 * x2);
453 { u64 x20 = ((u64)(0x2 * x2) * x4);
454 { u64 x21 = (0x2 * (((u64)x4 * x4) + ((u64)x2 * x6)));
455 { u64 x22 = (0x2 * (((u64)x4 * x6) + ((u64)x2 * x8)));
456 { u64 x23 = ((((u64)x6 * x6) + ((u64)(0x4 * x4) * x8)) + ((u64)(0x2 * x2) * x10));
457 { u64 x24 = (0x2 * ((((u64)x6 * x8) + ((u64)x4 * x10)) + ((u64)x2 * x12)));
458 { u64 x25 = (0x2 * (((((u64)x8 * x8) + ((u64)x6 * x10)) + ((u64)x2 * x14)) + ((u64)(0x2 * x4) * x12)));
459 { u64 x26 = (0x2 * (((((u64)x8 * x10) + ((u64)x6 * x12)) + ((u64)x4 * x14)) + ((u64)x2 * x16)));
460 { u64 x27 = (((u64)x10 * x10) + (0x2 * ((((u64)x6 * x14) + ((u64)x2 * x18)) + (0x2 * (((u64)x4 * x16) + ((u64)x8 * x12))))));
461 { u64 x28 = (0x2 * ((((((u64)x10 * x12) + ((u64)x8 * x14)) + ((u64)x6 * x16)) + ((u64)x4 * x18)) + ((u64)x2 * x17)));
462 { u64 x29 = (0x2 * (((((u64)x12 * x12) + ((u64)x10 * x14)) + ((u64)x6 * x18)) + (0x2 * (((u64)x8 * x16) + ((u64)x4 * x17)))));
463 { u64 x30 = (0x2 * (((((u64)x12 * x14) + ((u64)x10 * x16)) + ((u64)x8 * x18)) + ((u64)x6 * x17)));
464 { u64 x31 = (((u64)x14 * x14) + (0x2 * (((u64)x10 * x18) + (0x2 * (((u64)x12 * x16) + ((u64)x8 * x17))))));
465 { u64 x32 = (0x2 * ((((u64)x14 * x16) + ((u64)x12 * x18)) + ((u64)x10 * x17)));
466 { u64 x33 = (0x2 * ((((u64)x16 * x16) + ((u64)x14 * x18)) + ((u64)(0x2 * x12) * x17)));
467 { u64 x34 = (0x2 * (((u64)x16 * x18) + ((u64)x14 * x17)));
468 { u64 x35 = (((u64)x18 * x18) + ((u64)(0x4 * x16) * x17));
469 { u64 x36 = ((u64)(0x2 * x18) * x17);
470 { u64 x37 = ((u64)(0x2 * x17) * x17);
471 { u64 x38 = (x27 + (x37 << 0x4));
472 { u64 x39 = (x38 + (x37 << 0x1));
473 { u64 x40 = (x39 + x37);
474 { u64 x41 = (x26 + (x36 << 0x4));
475 { u64 x42 = (x41 + (x36 << 0x1));
476 { u64 x43 = (x42 + x36);
477 { u64 x44 = (x25 + (x35 << 0x4));
478 { u64 x45 = (x44 + (x35 << 0x1));
479 { u64 x46 = (x45 + x35);
480 { u64 x47 = (x24 + (x34 << 0x4));
481 { u64 x48 = (x47 + (x34 << 0x1));
482 { u64 x49 = (x48 + x34);
483 { u64 x50 = (x23 + (x33 << 0x4));
484 { u64 x51 = (x50 + (x33 << 0x1));
485 { u64 x52 = (x51 + x33);
486 { u64 x53 = (x22 + (x32 << 0x4));
487 { u64 x54 = (x53 + (x32 << 0x1));
488 { u64 x55 = (x54 + x32);
489 { u64 x56 = (x21 + (x31 << 0x4));
490 { u64 x57 = (x56 + (x31 << 0x1));
491 { u64 x58 = (x57 + x31);
492 { u64 x59 = (x20 + (x30 << 0x4));
493 { u64 x60 = (x59 + (x30 << 0x1));
494 { u64 x61 = (x60 + x30);
495 { u64 x62 = (x19 + (x29 << 0x4));
496 { u64 x63 = (x62 + (x29 << 0x1));
497 { u64 x64 = (x63 + x29);
498 { u64 x65 = (x64 >> 0x1a);
499 { u32 x66 = ((u32)x64 & 0x3ffffff);
500 { u64 x67 = (x65 + x61);
501 { u64 x68 = (x67 >> 0x19);
502 { u32 x69 = ((u32)x67 & 0x1ffffff);
503 { u64 x70 = (x68 + x58);
504 { u64 x71 = (x70 >> 0x1a);
505 { u32 x72 = ((u32)x70 & 0x3ffffff);
506 { u64 x73 = (x71 + x55);
507 { u64 x74 = (x73 >> 0x19);
508 { u32 x75 = ((u32)x73 & 0x1ffffff);
509 { u64 x76 = (x74 + x52);
510 { u64 x77 = (x76 >> 0x1a);
511 { u32 x78 = ((u32)x76 & 0x3ffffff);
512 { u64 x79 = (x77 + x49);
513 { u64 x80 = (x79 >> 0x19);
514 { u32 x81 = ((u32)x79 & 0x1ffffff);
515 { u64 x82 = (x80 + x46);
516 { u64 x83 = (x82 >> 0x1a);
517 { u32 x84 = ((u32)x82 & 0x3ffffff);
518 { u64 x85 = (x83 + x43);
519 { u64 x86 = (x85 >> 0x19);
520 { u32 x87 = ((u32)x85 & 0x1ffffff);
521 { u64 x88 = (x86 + x40);
522 { u64 x89 = (x88 >> 0x1a);
523 { u32 x90 = ((u32)x88 & 0x3ffffff);
524 { u64 x91 = (x89 + x28);
525 { u64 x92 = (x91 >> 0x19);
526 { u32 x93 = ((u32)x91 & 0x1ffffff);
527 { u64 x94 = (x66 + (0x13 * x92));
528 { u32 x95 = (u32) (x94 >> 0x1a);
529 { u32 x96 = ((u32)x94 & 0x3ffffff);
530 { u32 x97 = (x95 + x69);
531 { u32 x98 = (x97 >> 0x19);
532 { u32 x99 = (x97 & 0x1ffffff);
533 out[0] = x96;
534 out[1] = x99;
535 out[2] = (x98 + x72);
536 out[3] = x75;
537 out[4] = x78;
538 out[5] = x81;
539 out[6] = x84;
540 out[7] = x87;
541 out[8] = x90;
542 out[9] = x93;
543 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
544 }
545
fe_sq_tl(fe * h,const fe_loose * f)546 static __always_inline void fe_sq_tl(fe *h, const fe_loose *f)
547 {
548 fe_sqr_impl(h->v, f->v);
549 }
550
fe_sq_tt(fe * h,const fe * f)551 static __always_inline void fe_sq_tt(fe *h, const fe *f)
552 {
553 fe_sqr_impl(h->v, f->v);
554 }
555
fe_loose_invert(fe * out,const fe_loose * z)556 static __always_inline void fe_loose_invert(fe *out, const fe_loose *z)
557 {
558 fe t0;
559 fe t1;
560 fe t2;
561 fe t3;
562 int i;
563
564 fe_sq_tl(&t0, z);
565 fe_sq_tt(&t1, &t0);
566 for (i = 1; i < 2; ++i)
567 fe_sq_tt(&t1, &t1);
568 fe_mul_tlt(&t1, z, &t1);
569 fe_mul_ttt(&t0, &t0, &t1);
570 fe_sq_tt(&t2, &t0);
571 fe_mul_ttt(&t1, &t1, &t2);
572 fe_sq_tt(&t2, &t1);
573 for (i = 1; i < 5; ++i)
574 fe_sq_tt(&t2, &t2);
575 fe_mul_ttt(&t1, &t2, &t1);
576 fe_sq_tt(&t2, &t1);
577 for (i = 1; i < 10; ++i)
578 fe_sq_tt(&t2, &t2);
579 fe_mul_ttt(&t2, &t2, &t1);
580 fe_sq_tt(&t3, &t2);
581 for (i = 1; i < 20; ++i)
582 fe_sq_tt(&t3, &t3);
583 fe_mul_ttt(&t2, &t3, &t2);
584 fe_sq_tt(&t2, &t2);
585 for (i = 1; i < 10; ++i)
586 fe_sq_tt(&t2, &t2);
587 fe_mul_ttt(&t1, &t2, &t1);
588 fe_sq_tt(&t2, &t1);
589 for (i = 1; i < 50; ++i)
590 fe_sq_tt(&t2, &t2);
591 fe_mul_ttt(&t2, &t2, &t1);
592 fe_sq_tt(&t3, &t2);
593 for (i = 1; i < 100; ++i)
594 fe_sq_tt(&t3, &t3);
595 fe_mul_ttt(&t2, &t3, &t2);
596 fe_sq_tt(&t2, &t2);
597 for (i = 1; i < 50; ++i)
598 fe_sq_tt(&t2, &t2);
599 fe_mul_ttt(&t1, &t2, &t1);
600 fe_sq_tt(&t1, &t1);
601 for (i = 1; i < 5; ++i)
602 fe_sq_tt(&t1, &t1);
603 fe_mul_ttt(out, &t1, &t0);
604 }
605
fe_invert(fe * out,const fe * z)606 static __always_inline void fe_invert(fe *out, const fe *z)
607 {
608 fe_loose l;
609 fe_copy_lt(&l, z);
610 fe_loose_invert(out, &l);
611 }
612
613 /* Replace (f,g) with (g,f) if b == 1;
614 * replace (f,g) with (f,g) if b == 0.
615 *
616 * Preconditions: b in {0,1}
617 */
fe_cswap(fe * f,fe * g,unsigned int b)618 static __always_inline void fe_cswap(fe *f, fe *g, unsigned int b)
619 {
620 unsigned i;
621 b = 0 - b;
622 for (i = 0; i < 10; i++) {
623 u32 x = f->v[i] ^ g->v[i];
624 x &= b;
625 f->v[i] ^= x;
626 g->v[i] ^= x;
627 }
628 }
629
630 /* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/
fe_mul_121666_impl(u32 out[10],const u32 in1[10])631 static __always_inline void fe_mul_121666_impl(u32 out[10], const u32 in1[10])
632 {
633 { const u32 x20 = in1[9];
634 { const u32 x21 = in1[8];
635 { const u32 x19 = in1[7];
636 { const u32 x17 = in1[6];
637 { const u32 x15 = in1[5];
638 { const u32 x13 = in1[4];
639 { const u32 x11 = in1[3];
640 { const u32 x9 = in1[2];
641 { const u32 x7 = in1[1];
642 { const u32 x5 = in1[0];
643 { const u32 x38 = 0;
644 { const u32 x39 = 0;
645 { const u32 x37 = 0;
646 { const u32 x35 = 0;
647 { const u32 x33 = 0;
648 { const u32 x31 = 0;
649 { const u32 x29 = 0;
650 { const u32 x27 = 0;
651 { const u32 x25 = 0;
652 { const u32 x23 = 121666;
653 { u64 x40 = ((u64)x23 * x5);
654 { u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5));
655 { u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5));
656 { u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5));
657 { u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5));
658 { u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5));
659 { u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5));
660 { 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));
661 { 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));
662 { 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));
663 { 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));
664 { 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));
665 { u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13));
666 { u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13));
667 { u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17));
668 { u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17));
669 { u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19))));
670 { u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21));
671 { u64 x58 = ((u64)(0x2 * x38) * x20);
672 { u64 x59 = (x48 + (x58 << 0x4));
673 { u64 x60 = (x59 + (x58 << 0x1));
674 { u64 x61 = (x60 + x58);
675 { u64 x62 = (x47 + (x57 << 0x4));
676 { u64 x63 = (x62 + (x57 << 0x1));
677 { u64 x64 = (x63 + x57);
678 { u64 x65 = (x46 + (x56 << 0x4));
679 { u64 x66 = (x65 + (x56 << 0x1));
680 { u64 x67 = (x66 + x56);
681 { u64 x68 = (x45 + (x55 << 0x4));
682 { u64 x69 = (x68 + (x55 << 0x1));
683 { u64 x70 = (x69 + x55);
684 { u64 x71 = (x44 + (x54 << 0x4));
685 { u64 x72 = (x71 + (x54 << 0x1));
686 { u64 x73 = (x72 + x54);
687 { u64 x74 = (x43 + (x53 << 0x4));
688 { u64 x75 = (x74 + (x53 << 0x1));
689 { u64 x76 = (x75 + x53);
690 { u64 x77 = (x42 + (x52 << 0x4));
691 { u64 x78 = (x77 + (x52 << 0x1));
692 { u64 x79 = (x78 + x52);
693 { u64 x80 = (x41 + (x51 << 0x4));
694 { u64 x81 = (x80 + (x51 << 0x1));
695 { u64 x82 = (x81 + x51);
696 { u64 x83 = (x40 + (x50 << 0x4));
697 { u64 x84 = (x83 + (x50 << 0x1));
698 { u64 x85 = (x84 + x50);
699 { u64 x86 = (x85 >> 0x1a);
700 { u32 x87 = ((u32)x85 & 0x3ffffff);
701 { u64 x88 = (x86 + x82);
702 { u64 x89 = (x88 >> 0x19);
703 { u32 x90 = ((u32)x88 & 0x1ffffff);
704 { u64 x91 = (x89 + x79);
705 { u64 x92 = (x91 >> 0x1a);
706 { u32 x93 = ((u32)x91 & 0x3ffffff);
707 { u64 x94 = (x92 + x76);
708 { u64 x95 = (x94 >> 0x19);
709 { u32 x96 = ((u32)x94 & 0x1ffffff);
710 { u64 x97 = (x95 + x73);
711 { u64 x98 = (x97 >> 0x1a);
712 { u32 x99 = ((u32)x97 & 0x3ffffff);
713 { u64 x100 = (x98 + x70);
714 { u64 x101 = (x100 >> 0x19);
715 { u32 x102 = ((u32)x100 & 0x1ffffff);
716 { u64 x103 = (x101 + x67);
717 { u64 x104 = (x103 >> 0x1a);
718 { u32 x105 = ((u32)x103 & 0x3ffffff);
719 { u64 x106 = (x104 + x64);
720 { u64 x107 = (x106 >> 0x19);
721 { u32 x108 = ((u32)x106 & 0x1ffffff);
722 { u64 x109 = (x107 + x61);
723 { u64 x110 = (x109 >> 0x1a);
724 { u32 x111 = ((u32)x109 & 0x3ffffff);
725 { u64 x112 = (x110 + x49);
726 { u64 x113 = (x112 >> 0x19);
727 { u32 x114 = ((u32)x112 & 0x1ffffff);
728 { u64 x115 = (x87 + (0x13 * x113));
729 { u32 x116 = (u32) (x115 >> 0x1a);
730 { u32 x117 = ((u32)x115 & 0x3ffffff);
731 { u32 x118 = (x116 + x90);
732 { u32 x119 = (x118 >> 0x19);
733 { u32 x120 = (x118 & 0x1ffffff);
734 out[0] = x117;
735 out[1] = x120;
736 out[2] = (x119 + x93);
737 out[3] = x96;
738 out[4] = x99;
739 out[5] = x102;
740 out[6] = x105;
741 out[7] = x108;
742 out[8] = x111;
743 out[9] = x114;
744 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
745 }
746
fe_mul121666(fe * h,const fe_loose * f)747 static __always_inline void fe_mul121666(fe *h, const fe_loose *f)
748 {
749 fe_mul_121666_impl(h->v, f->v);
750 }
751
curve25519_generic(u8 out[CURVE25519_KEY_SIZE],const u8 scalar[CURVE25519_KEY_SIZE],const u8 point[CURVE25519_KEY_SIZE])752 static void curve25519_generic(u8 out[CURVE25519_KEY_SIZE],
753 const u8 scalar[CURVE25519_KEY_SIZE],
754 const u8 point[CURVE25519_KEY_SIZE])
755 {
756 fe x1, x2, z2, x3, z3;
757 fe_loose x2l, z2l, x3l;
758 unsigned swap = 0;
759 int pos;
760 u8 e[32];
761
762 memcpy(e, scalar, 32);
763 curve25519_clamp_secret(e);
764
765 /* The following implementation was transcribed to Coq and proven to
766 * correspond to unary scalar multiplication in affine coordinates given
767 * that x1 != 0 is the x coordinate of some point on the curve. It was
768 * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives
769 * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was
770 * quantified over the underlying field, so it applies to Curve25519
771 * itself and the quadratic twist of Curve25519. It was not proven in
772 * Coq that prime-field arithmetic correctly simulates extension-field
773 * arithmetic on prime-field values. The decoding of the byte array
774 * representation of e was not considered.
775 *
776 * Specification of Montgomery curves in affine coordinates:
777 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27>
778 *
779 * Proof that these form a group that is isomorphic to a Weierstrass
780 * curve:
781 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35>
782 *
783 * Coq transcription and correctness proof of the loop
784 * (where scalarbits=255):
785 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118>
786 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278>
787 * preconditions: 0 <= e < 2^255 (not necessarily e < order),
788 * fe_invert(0) = 0
789 */
790 fe_frombytes(&x1, point);
791 fe_1(&x2);
792 fe_0(&z2);
793 fe_copy(&x3, &x1);
794 fe_1(&z3);
795
796 for (pos = 254; pos >= 0; --pos) {
797 fe tmp0, tmp1;
798 fe_loose tmp0l, tmp1l;
799 /* loop invariant as of right before the test, for the case
800 * where x1 != 0:
801 * pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3
802 * is nonzero
803 * let r := e >> (pos+1) in the following equalities of
804 * projective points:
805 * to_xz (r*P) === if swap then (x3, z3) else (x2, z2)
806 * to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3)
807 * x1 is the nonzero x coordinate of the nonzero
808 * point (r*P-(r+1)*P)
809 */
810 unsigned b = 1 & (e[pos / 8] >> (pos & 7));
811 swap ^= b;
812 fe_cswap(&x2, &x3, swap);
813 fe_cswap(&z2, &z3, swap);
814 swap = b;
815 /* Coq transcription of ladderstep formula (called from
816 * transcribed loop):
817 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89>
818 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131>
819 * x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217>
820 * x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147>
821 */
822 fe_sub(&tmp0l, &x3, &z3);
823 fe_sub(&tmp1l, &x2, &z2);
824 fe_add(&x2l, &x2, &z2);
825 fe_add(&z2l, &x3, &z3);
826 fe_mul_tll(&z3, &tmp0l, &x2l);
827 fe_mul_tll(&z2, &z2l, &tmp1l);
828 fe_sq_tl(&tmp0, &tmp1l);
829 fe_sq_tl(&tmp1, &x2l);
830 fe_add(&x3l, &z3, &z2);
831 fe_sub(&z2l, &z3, &z2);
832 fe_mul_ttt(&x2, &tmp1, &tmp0);
833 fe_sub(&tmp1l, &tmp1, &tmp0);
834 fe_sq_tl(&z2, &z2l);
835 fe_mul121666(&z3, &tmp1l);
836 fe_sq_tl(&x3, &x3l);
837 fe_add(&tmp0l, &tmp0, &z3);
838 fe_mul_ttt(&z3, &x1, &z2);
839 fe_mul_tll(&z2, &tmp1l, &tmp0l);
840 }
841 /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3)
842 * else (x2, z2)
843 */
844 fe_cswap(&x2, &x3, swap);
845 fe_cswap(&z2, &z3, swap);
846
847 fe_invert(&z2, &z2);
848 fe_mul_ttt(&x2, &x2, &z2);
849 fe_tobytes(out, &x2);
850
851 memzero_explicit(&x1, sizeof(x1));
852 memzero_explicit(&x2, sizeof(x2));
853 memzero_explicit(&z2, sizeof(z2));
854 memzero_explicit(&x3, sizeof(x3));
855 memzero_explicit(&z3, sizeof(z3));
856 memzero_explicit(&x2l, sizeof(x2l));
857 memzero_explicit(&z2l, sizeof(z2l));
858 memzero_explicit(&x3l, sizeof(x3l));
859 memzero_explicit(&e, sizeof(e));
860 }
861