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(p: s); |
34 | u32 a1 = get_unaligned_le32(p: s+4); |
35 | u32 a2 = get_unaligned_le32(p: s+8); |
36 | u32 a3 = get_unaligned_le32(p: s+12); |
37 | u32 a4 = get_unaligned_le32(p: s+16); |
38 | u32 a5 = get_unaligned_le32(p: s+20); |
39 | u32 a6 = get_unaligned_le32(p: s+24); |
40 | u32 a7 = get_unaligned_le32(p: 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: 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(c: 0x0, a: x2, b: 0x3ffffed, low: &x20); |
121 | { u32 x23; u8/*bool*/ x24 = subborrow_u25(c: x21, a: x4, b: 0x1ffffff, low: &x23); |
122 | { u32 x26; u8/*bool*/ x27 = subborrow_u26(c: x24, a: x6, b: 0x3ffffff, low: &x26); |
123 | { u32 x29; u8/*bool*/ x30 = subborrow_u25(c: x27, a: x8, b: 0x1ffffff, low: &x29); |
124 | { u32 x32; u8/*bool*/ x33 = subborrow_u26(c: x30, a: x10, b: 0x3ffffff, low: &x32); |
125 | { u32 x35; u8/*bool*/ x36 = subborrow_u25(c: x33, a: x12, b: 0x1ffffff, low: &x35); |
126 | { u32 x38; u8/*bool*/ x39 = subborrow_u26(c: x36, a: x14, b: 0x3ffffff, low: &x38); |
127 | { u32 x41; u8/*bool*/ x42 = subborrow_u25(c: x39, a: x16, b: 0x1ffffff, low: &x41); |
128 | { u32 x44; u8/*bool*/ x45 = subborrow_u26(c: x42, a: x18, b: 0x3ffffff, low: &x44); |
129 | { u32 x47; u8/*bool*/ x48 = subborrow_u25(c: x45, a: x17, b: 0x1ffffff, low: &x47); |
130 | { u32 x49 = cmovznz32(t: x48, z: 0x0, nz: 0xffffffff); |
131 | { u32 x50 = (x49 & 0x3ffffed); |
132 | { u32 x52; u8/*bool*/ x53 = addcarryx_u26(c: 0x0, a: x20, b: x50, low: &x52); |
133 | { u32 x54 = (x49 & 0x1ffffff); |
134 | { u32 x56; u8/*bool*/ x57 = addcarryx_u25(c: x53, a: x23, b: x54, low: &x56); |
135 | { u32 x58 = (x49 & 0x3ffffff); |
136 | { u32 x60; u8/*bool*/ x61 = addcarryx_u26(c: x57, a: x26, b: x58, low: &x60); |
137 | { u32 x62 = (x49 & 0x1ffffff); |
138 | { u32 x64; u8/*bool*/ x65 = addcarryx_u25(c: x61, a: x29, b: x62, low: &x64); |
139 | { u32 x66 = (x49 & 0x3ffffff); |
140 | { u32 x68; u8/*bool*/ x69 = addcarryx_u26(c: x65, a: x32, b: x66, low: &x68); |
141 | { u32 x70 = (x49 & 0x1ffffff); |
142 | { u32 x72; u8/*bool*/ x73 = addcarryx_u25(c: x69, a: x35, b: x70, low: &x72); |
143 | { u32 x74 = (x49 & 0x3ffffff); |
144 | { u32 x76; u8/*bool*/ x77 = addcarryx_u26(c: x73, a: x38, b: x74, low: &x76); |
145 | { u32 x78 = (x49 & 0x1ffffff); |
146 | { u32 x80; u8/*bool*/ x81 = addcarryx_u25(c: x77, a: x41, b: x78, low: &x80); |
147 | { u32 x82 = (x49 & 0x3ffffff); |
148 | { u32 x84; u8/*bool*/ x85 = addcarryx_u26(c: x81, a: x44, b: x82, low: &x84); |
149 | { u32 x86 = (x49 & 0x1ffffff); |
150 | { u32 x88; addcarryx_u25(c: x85, a: x47, b: x86, low: &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(out: h, in1: 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(out: h->v, in1: f->v, in2: 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(out: h->v, in1: f->v, in2: 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(out: h->v, in1: f->v, in2: 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(out: h->v, in1: f->v, in2: 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(out: h->v, in1: f->v, in2: 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(out: h->v, in1: f->v); |
553 | } |
554 | |
555 | static __always_inline void fe_sq_tt(fe *h, const fe *f) |
556 | { |
557 | fe_sqr_impl(out: h->v, in1: 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(h: &t0, f: z); |
569 | fe_sq_tt(h: &t1, f: &t0); |
570 | for (i = 1; i < 2; ++i) |
571 | fe_sq_tt(h: &t1, f: &t1); |
572 | fe_mul_tlt(h: &t1, f: z, g: &t1); |
573 | fe_mul_ttt(h: &t0, f: &t0, g: &t1); |
574 | fe_sq_tt(h: &t2, f: &t0); |
575 | fe_mul_ttt(h: &t1, f: &t1, g: &t2); |
576 | fe_sq_tt(h: &t2, f: &t1); |
577 | for (i = 1; i < 5; ++i) |
578 | fe_sq_tt(h: &t2, f: &t2); |
579 | fe_mul_ttt(h: &t1, f: &t2, g: &t1); |
580 | fe_sq_tt(h: &t2, f: &t1); |
581 | for (i = 1; i < 10; ++i) |
582 | fe_sq_tt(h: &t2, f: &t2); |
583 | fe_mul_ttt(h: &t2, f: &t2, g: &t1); |
584 | fe_sq_tt(h: &t3, f: &t2); |
585 | for (i = 1; i < 20; ++i) |
586 | fe_sq_tt(h: &t3, f: &t3); |
587 | fe_mul_ttt(h: &t2, f: &t3, g: &t2); |
588 | fe_sq_tt(h: &t2, f: &t2); |
589 | for (i = 1; i < 10; ++i) |
590 | fe_sq_tt(h: &t2, f: &t2); |
591 | fe_mul_ttt(h: &t1, f: &t2, g: &t1); |
592 | fe_sq_tt(h: &t2, f: &t1); |
593 | for (i = 1; i < 50; ++i) |
594 | fe_sq_tt(h: &t2, f: &t2); |
595 | fe_mul_ttt(h: &t2, f: &t2, g: &t1); |
596 | fe_sq_tt(h: &t3, f: &t2); |
597 | for (i = 1; i < 100; ++i) |
598 | fe_sq_tt(h: &t3, f: &t3); |
599 | fe_mul_ttt(h: &t2, f: &t3, g: &t2); |
600 | fe_sq_tt(h: &t2, f: &t2); |
601 | for (i = 1; i < 50; ++i) |
602 | fe_sq_tt(h: &t2, f: &t2); |
603 | fe_mul_ttt(h: &t1, f: &t2, g: &t1); |
604 | fe_sq_tt(h: &t1, f: &t1); |
605 | for (i = 1; i < 5; ++i) |
606 | fe_sq_tt(h: &t1, f: &t1); |
607 | fe_mul_ttt(h: out, f: &t1, g: &t0); |
608 | } |
609 | |
610 | static __always_inline void fe_invert(fe *out, const fe *z) |
611 | { |
612 | fe_loose l; |
613 | fe_copy_lt(h: &l, f: z); |
614 | fe_loose_invert(out, z: &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(out: h->v, in1: 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(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(h: &x1, s: point); |
795 | fe_1(h: &x2); |
796 | fe_0(h: &z2); |
797 | fe_copy(h: &x3, f: &x1); |
798 | fe_1(h: &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(f: &x2, g: &x3, b: swap); |
817 | fe_cswap(f: &z2, g: &z3, b: 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(h: &tmp0l, f: &x3, g: &z3); |
827 | fe_sub(h: &tmp1l, f: &x2, g: &z2); |
828 | fe_add(h: &x2l, f: &x2, g: &z2); |
829 | fe_add(h: &z2l, f: &x3, g: &z3); |
830 | fe_mul_tll(h: &z3, f: &tmp0l, g: &x2l); |
831 | fe_mul_tll(h: &z2, f: &z2l, g: &tmp1l); |
832 | fe_sq_tl(h: &tmp0, f: &tmp1l); |
833 | fe_sq_tl(h: &tmp1, f: &x2l); |
834 | fe_add(h: &x3l, f: &z3, g: &z2); |
835 | fe_sub(h: &z2l, f: &z3, g: &z2); |
836 | fe_mul_ttt(h: &x2, f: &tmp1, g: &tmp0); |
837 | fe_sub(h: &tmp1l, f: &tmp1, g: &tmp0); |
838 | fe_sq_tl(h: &z2, f: &z2l); |
839 | fe_mul121666(h: &z3, f: &tmp1l); |
840 | fe_sq_tl(h: &x3, f: &x3l); |
841 | fe_add(h: &tmp0l, f: &tmp0, g: &z3); |
842 | fe_mul_ttt(h: &z3, f: &x1, g: &z2); |
843 | fe_mul_tll(h: &z2, f: &tmp1l, g: &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(f: &x2, g: &x3, b: swap); |
849 | fe_cswap(f: &z2, g: &z3, b: swap); |
850 | |
851 | fe_invert(out: &z2, z: &z2); |
852 | fe_mul_ttt(h: &x2, f: &x2, g: &z2); |
853 | fe_tobytes(s: out, f: &x2); |
854 | |
855 | memzero_explicit(s: &x1, count: sizeof(x1)); |
856 | memzero_explicit(s: &x2, count: sizeof(x2)); |
857 | memzero_explicit(s: &z2, count: sizeof(z2)); |
858 | memzero_explicit(s: &x3, count: sizeof(x3)); |
859 | memzero_explicit(s: &z3, count: sizeof(z3)); |
860 | memzero_explicit(s: &x2l, count: sizeof(x2l)); |
861 | memzero_explicit(s: &z2l, count: sizeof(z2l)); |
862 | memzero_explicit(s: &x3l, count: sizeof(x3l)); |
863 | memzero_explicit(s: &e, count: sizeof(e)); |
864 | } |
865 | |