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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 | ||
660bb8e1 | 226 | static noinline void fe_add_impl(u32 out[10], const u32 in1[10], const u32 in2[10]) |
0ed42a6f JD |
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 | ||
660bb8e1 | 269 | static noinline void fe_sub_impl(u32 out[10], const u32 in1[10], const u32 in2[10]) |
0ed42a6f JD |
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 | ||
660bb8e1 | 312 | static noinline void fe_mul_impl(u32 out[10], const u32 in1[10], const u32 in2[10]) |
0ed42a6f JD |
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 | ||
660bb8e1 | 444 | static noinline void fe_sqr_impl(u32 out[10], const u32 in1[10]) |
0ed42a6f JD |
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 | */ | |
660bb8e1 | 622 | static noinline void fe_cswap(fe *f, fe *g, unsigned int b) |
0ed42a6f JD |
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 | } |