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1 // Copyright (c) 2013 The Chromium Authors. All rights reserved. | |
2 // Use of this source code is governed by a BSD-style license that can be | |
3 // found in the LICENSE file. | |
4 | |
5 /* | |
6 * curve25519-donna: Curve25519 elliptic curve, public key function | |
7 * | |
8 * http://code.google.com/p/curve25519-donna/ | |
9 * | |
10 * Adam Langley <agl@imperialviolet.org> | |
11 * | |
12 * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to> | |
13 * | |
14 * More information about curve25519 can be found here | |
15 * http://cr.yp.to/ecdh.html | |
16 * | |
17 * djb's sample implementation of curve25519 is written in a special assembly | |
18 * language called qhasm and uses the floating point registers. | |
19 * | |
20 * This is, almost, a clean room reimplementation from the curve25519 paper. It | |
21 * uses many of the tricks described therein. Only the crecip function is taken | |
22 * from the sample implementation. | |
23 */ | |
24 | |
25 #include <string.h> | |
26 #include <stdint.h> | |
27 | |
28 typedef uint8_t u8; | |
29 typedef int32_t s32; | |
30 typedef int64_t limb; | |
31 | |
32 /* Field element representation: | |
33 * | |
34 * Field elements are written as an array of signed, 64-bit limbs, least | |
35 * significant first. The value of the field element is: | |
36 * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ... | |
37 * | |
38 * i.e. the limbs are 26, 25, 26, 25, ... bits wide. | |
39 */ | |
40 | |
41 /* Sum two numbers: output += in */ | |
42 static void fsum(limb *output, const limb *in) { | |
43 unsigned i; | |
44 for (i = 0; i < 10; i += 2) { | |
45 output[0+i] = (output[0+i] + in[0+i]); | |
46 output[1+i] = (output[1+i] + in[1+i]); | |
47 } | |
48 } | |
49 | |
50 /* Find the difference of two numbers: output = in - output | |
51 * (note the order of the arguments!) | |
52 */ | |
53 static void fdifference(limb *output, const limb *in) { | |
54 unsigned i; | |
55 for (i = 0; i < 10; ++i) { | |
56 output[i] = (in[i] - output[i]); | |
57 } | |
58 } | |
59 | |
60 /* Multiply a number my a scalar: output = in * scalar */ | |
61 static void fscalar_product(limb *output, const limb *in, const limb scalar) { | |
62 unsigned i; | |
63 for (i = 0; i < 10; ++i) { | |
64 output[i] = in[i] * scalar; | |
65 } | |
66 } | |
67 | |
68 /* Multiply two numbers: output = in2 * in | |
69 * | |
70 * output must be distinct to both inputs. The inputs are reduced coefficient | |
71 * form, the output is not. | |
72 */ | |
73 static void fproduct(limb *output, const limb *in2, const limb *in) { | |
74 output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]); | |
75 output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) + | |
76 ((limb) ((s32) in2[1])) * ((s32) in[0]); | |
77 output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) + | |
78 ((limb) ((s32) in2[0])) * ((s32) in[2]) + | |
79 ((limb) ((s32) in2[2])) * ((s32) in[0]); | |
80 output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) + | |
81 ((limb) ((s32) in2[2])) * ((s32) in[1]) + | |
82 ((limb) ((s32) in2[0])) * ((s32) in[3]) + | |
83 ((limb) ((s32) in2[3])) * ((s32) in[0]); | |
84 output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) + | |
85 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) + | |
86 ((limb) ((s32) in2[3])) * ((s32) in[1])) + | |
87 ((limb) ((s32) in2[0])) * ((s32) in[4]) + | |
88 ((limb) ((s32) in2[4])) * ((s32) in[0]); | |
89 output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) + | |
90 ((limb) ((s32) in2[3])) * ((s32) in[2]) + | |
91 ((limb) ((s32) in2[1])) * ((s32) in[4]) + | |
92 ((limb) ((s32) in2[4])) * ((s32) in[1]) + | |
93 ((limb) ((s32) in2[0])) * ((s32) in[5]) + | |
94 ((limb) ((s32) in2[5])) * ((s32) in[0]); | |
95 output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) + | |
96 ((limb) ((s32) in2[1])) * ((s32) in[5]) + | |
97 ((limb) ((s32) in2[5])) * ((s32) in[1])) + | |
98 ((limb) ((s32) in2[2])) * ((s32) in[4]) + | |
99 ((limb) ((s32) in2[4])) * ((s32) in[2]) + | |
100 ((limb) ((s32) in2[0])) * ((s32) in[6]) + | |
101 ((limb) ((s32) in2[6])) * ((s32) in[0]); | |
102 output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) + | |
103 ((limb) ((s32) in2[4])) * ((s32) in[3]) + | |
104 ((limb) ((s32) in2[2])) * ((s32) in[5]) + | |
105 ((limb) ((s32) in2[5])) * ((s32) in[2]) + | |
106 ((limb) ((s32) in2[1])) * ((s32) in[6]) + | |
107 ((limb) ((s32) in2[6])) * ((s32) in[1]) + | |
108 ((limb) ((s32) in2[0])) * ((s32) in[7]) + | |
109 ((limb) ((s32) in2[7])) * ((s32) in[0]); | |
110 output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) + | |
111 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) + | |
112 ((limb) ((s32) in2[5])) * ((s32) in[3]) + | |
113 ((limb) ((s32) in2[1])) * ((s32) in[7]) + | |
114 ((limb) ((s32) in2[7])) * ((s32) in[1])) + | |
115 ((limb) ((s32) in2[2])) * ((s32) in[6]) + | |
116 ((limb) ((s32) in2[6])) * ((s32) in[2]) + | |
117 ((limb) ((s32) in2[0])) * ((s32) in[8]) + | |
118 ((limb) ((s32) in2[8])) * ((s32) in[0]); | |
119 output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) + | |
120 ((limb) ((s32) in2[5])) * ((s32) in[4]) + | |
121 ((limb) ((s32) in2[3])) * ((s32) in[6]) + | |
122 ((limb) ((s32) in2[6])) * ((s32) in[3]) + | |
123 ((limb) ((s32) in2[2])) * ((s32) in[7]) + | |
124 ((limb) ((s32) in2[7])) * ((s32) in[2]) + | |
125 ((limb) ((s32) in2[1])) * ((s32) in[8]) + | |
126 ((limb) ((s32) in2[8])) * ((s32) in[1]) + | |
127 ((limb) ((s32) in2[0])) * ((s32) in[9]) + | |
128 ((limb) ((s32) in2[9])) * ((s32) in[0]); | |
129 output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) + | |
130 ((limb) ((s32) in2[3])) * ((s32) in[7]) + | |
131 ((limb) ((s32) in2[7])) * ((s32) in[3]) + | |
132 ((limb) ((s32) in2[1])) * ((s32) in[9]) + | |
133 ((limb) ((s32) in2[9])) * ((s32) in[1])) + | |
134 ((limb) ((s32) in2[4])) * ((s32) in[6]) + | |
135 ((limb) ((s32) in2[6])) * ((s32) in[4]) + | |
136 ((limb) ((s32) in2[2])) * ((s32) in[8]) + | |
137 ((limb) ((s32) in2[8])) * ((s32) in[2]); | |
138 output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) + | |
139 ((limb) ((s32) in2[6])) * ((s32) in[5]) + | |
140 ((limb) ((s32) in2[4])) * ((s32) in[7]) + | |
141 ((limb) ((s32) in2[7])) * ((s32) in[4]) + | |
142 ((limb) ((s32) in2[3])) * ((s32) in[8]) + | |
143 ((limb) ((s32) in2[8])) * ((s32) in[3]) + | |
144 ((limb) ((s32) in2[2])) * ((s32) in[9]) + | |
145 ((limb) ((s32) in2[9])) * ((s32) in[2]); | |
146 output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) + | |
147 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) + | |
148 ((limb) ((s32) in2[7])) * ((s32) in[5]) + | |
149 ((limb) ((s32) in2[3])) * ((s32) in[9]) + | |
150 ((limb) ((s32) in2[9])) * ((s32) in[3])) + | |
151 ((limb) ((s32) in2[4])) * ((s32) in[8]) + | |
152 ((limb) ((s32) in2[8])) * ((s32) in[4]); | |
153 output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) + | |
154 ((limb) ((s32) in2[7])) * ((s32) in[6]) + | |
155 ((limb) ((s32) in2[5])) * ((s32) in[8]) + | |
156 ((limb) ((s32) in2[8])) * ((s32) in[5]) + | |
157 ((limb) ((s32) in2[4])) * ((s32) in[9]) + | |
158 ((limb) ((s32) in2[9])) * ((s32) in[4]); | |
159 output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) + | |
160 ((limb) ((s32) in2[5])) * ((s32) in[9]) + | |
161 ((limb) ((s32) in2[9])) * ((s32) in[5])) + | |
162 ((limb) ((s32) in2[6])) * ((s32) in[8]) + | |
163 ((limb) ((s32) in2[8])) * ((s32) in[6]); | |
164 output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) + | |
165 ((limb) ((s32) in2[8])) * ((s32) in[7]) + | |
166 ((limb) ((s32) in2[6])) * ((s32) in[9]) + | |
167 ((limb) ((s32) in2[9])) * ((s32) in[6]); | |
168 output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) + | |
169 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) + | |
170 ((limb) ((s32) in2[9])) * ((s32) in[7])); | |
171 output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) + | |
172 ((limb) ((s32) in2[9])) * ((s32) in[8]); | |
173 output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]); | |
174 } | |
175 | |
176 /* Reduce a long form to a short form by taking the input mod 2^255 - 19. */ | |
177 static void freduce_degree(limb *output) { | |
178 /* Each of these shifts and adds ends up multiplying the value by 19. */ | |
179 output[8] += output[18] << 4; | |
180 output[8] += output[18] << 1; | |
181 output[8] += output[18]; | |
182 output[7] += output[17] << 4; | |
183 output[7] += output[17] << 1; | |
184 output[7] += output[17]; | |
185 output[6] += output[16] << 4; | |
186 output[6] += output[16] << 1; | |
187 output[6] += output[16]; | |
188 output[5] += output[15] << 4; | |
189 output[5] += output[15] << 1; | |
190 output[5] += output[15]; | |
191 output[4] += output[14] << 4; | |
192 output[4] += output[14] << 1; | |
193 output[4] += output[14]; | |
194 output[3] += output[13] << 4; | |
195 output[3] += output[13] << 1; | |
196 output[3] += output[13]; | |
197 output[2] += output[12] << 4; | |
198 output[2] += output[12] << 1; | |
199 output[2] += output[12]; | |
200 output[1] += output[11] << 4; | |
201 output[1] += output[11] << 1; | |
202 output[1] += output[11]; | |
203 output[0] += output[10] << 4; | |
204 output[0] += output[10] << 1; | |
205 output[0] += output[10]; | |
206 } | |
207 | |
208 /* Reduce all coefficients of the short form input so that |x| < 2^26. | |
209 * | |
210 * On entry: |output[i]| < 2^62 | |
211 */ | |
212 static void freduce_coefficients(limb *output) { | |
213 unsigned i; | |
214 do { | |
215 output[10] = 0; | |
216 | |
217 for (i = 0; i < 10; i += 2) { | |
218 limb over = output[i] / 0x4000000l; | |
219 output[i+1] += over; | |
220 output[i] -= over * 0x4000000l; | |
221 | |
222 over = output[i+1] / 0x2000000; | |
223 output[i+2] += over; | |
224 output[i+1] -= over * 0x2000000; | |
225 } | |
226 output[0] += 19 * output[10]; | |
227 } while (output[10]); | |
228 } | |
229 | |
230 /* A helpful wrapper around fproduct: output = in * in2. | |
231 * | |
232 * output must be distinct to both inputs. The output is reduced degree and | |
233 * reduced coefficient. | |
234 */ | |
235 static void | |
236 fmul(limb *output, const limb *in, const limb *in2) { | |
237 limb t[19]; | |
238 fproduct(t, in, in2); | |
239 freduce_degree(t); | |
240 freduce_coefficients(t); | |
241 memcpy(output, t, sizeof(limb) * 10); | |
242 } | |
243 | |
244 static void fsquare_inner(limb *output, const limb *in) { | |
245 output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]); | |
246 output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]); | |
247 output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) + | |
248 ((limb) ((s32) in[0])) * ((s32) in[2])); | |
249 output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) + | |
250 ((limb) ((s32) in[0])) * ((s32) in[3])); | |
251 output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) + | |
252 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) + | |
253 2 * ((limb) ((s32) in[0])) * ((s32) in[4]); | |
254 output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) + | |
255 ((limb) ((s32) in[1])) * ((s32) in[4]) + | |
256 ((limb) ((s32) in[0])) * ((s32) in[5])); | |
257 output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) + | |
258 ((limb) ((s32) in[2])) * ((s32) in[4]) + | |
259 ((limb) ((s32) in[0])) * ((s32) in[6]) + | |
260 2 * ((limb) ((s32) in[1])) * ((s32) in[5])); | |
261 output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) + | |
262 ((limb) ((s32) in[2])) * ((s32) in[5]) + | |
263 ((limb) ((s32) in[1])) * ((s32) in[6]) + | |
264 ((limb) ((s32) in[0])) * ((s32) in[7])); | |
265 output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) + | |
266 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) + | |
267 ((limb) ((s32) in[0])) * ((s32) in[8]) + | |
268 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) + | |
269 ((limb) ((s32) in[3])) * ((s32) in[5]))); | |
270 output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) + | |
271 ((limb) ((s32) in[3])) * ((s32) in[6]) + | |
272 ((limb) ((s32) in[2])) * ((s32) in[7]) + | |
273 ((limb) ((s32) in[1])) * ((s32) in[8]) + | |
274 ((limb) ((s32) in[0])) * ((s32) in[9])); | |
275 output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) + | |
276 ((limb) ((s32) in[4])) * ((s32) in[6]) + | |
277 ((limb) ((s32) in[2])) * ((s32) in[8]) + | |
278 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) + | |
279 ((limb) ((s32) in[1])) * ((s32) in[9]))); | |
280 output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) + | |
281 ((limb) ((s32) in[4])) * ((s32) in[7]) + | |
282 ((limb) ((s32) in[3])) * ((s32) in[8]) + | |
283 ((limb) ((s32) in[2])) * ((s32) in[9])); | |
284 output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) + | |
285 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) + | |
286 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) + | |
287 ((limb) ((s32) in[3])) * ((s32) in[9]))); | |
288 output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) + | |
289 ((limb) ((s32) in[5])) * ((s32) in[8]) + | |
290 ((limb) ((s32) in[4])) * ((s32) in[9])); | |
291 output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) + | |
292 ((limb) ((s32) in[6])) * ((s32) in[8]) + | |
293 2 * ((limb) ((s32) in[5])) * ((s32) in[9])); | |
294 output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) + | |
295 ((limb) ((s32) in[6])) * ((s32) in[9])); | |
296 output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) + | |
297 4 * ((limb) ((s32) in[7])) * ((s32) in[9]); | |
298 output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]); | |
299 output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]); | |
300 } | |
301 | |
302 static void | |
303 fsquare(limb *output, const limb *in) { | |
304 limb t[19]; | |
305 fsquare_inner(t, in); | |
306 freduce_degree(t); | |
307 freduce_coefficients(t); | |
308 memcpy(output, t, sizeof(limb) * 10); | |
309 } | |
310 | |
311 /* Take a little-endian, 32-byte number and expand it into polynomial form */ | |
312 static void | |
313 fexpand(limb *output, const u8 *input) { | |
314 #define F(n,start,shift,mask) \ | |
315 output[n] = ((((limb) input[start + 0]) | \ | |
316 ((limb) input[start + 1]) << 8 | \ | |
317 ((limb) input[start + 2]) << 16 | \ | |
318 ((limb) input[start + 3]) << 24) >> shift) & mask; | |
319 F(0, 0, 0, 0x3ffffff); | |
320 F(1, 3, 2, 0x1ffffff); | |
321 F(2, 6, 3, 0x3ffffff); | |
322 F(3, 9, 5, 0x1ffffff); | |
323 F(4, 12, 6, 0x3ffffff); | |
324 F(5, 16, 0, 0x1ffffff); | |
325 F(6, 19, 1, 0x3ffffff); | |
326 F(7, 22, 3, 0x1ffffff); | |
327 F(8, 25, 4, 0x3ffffff); | |
328 F(9, 28, 6, 0x1ffffff); | |
329 #undef F | |
330 } | |
331 | |
332 /* Take a fully reduced polynomial form number and contract it into a | |
333 * little-endian, 32-byte array | |
334 */ | |
335 static void | |
336 fcontract(u8 *output, limb *input) { | |
337 int i; | |
338 | |
339 do { | |
340 for (i = 0; i < 9; ++i) { | |
341 if ((i & 1) == 1) { | |
342 while (input[i] < 0) { | |
343 input[i] += 0x2000000; | |
344 input[i + 1]--; | |
345 } | |
346 } else { | |
347 while (input[i] < 0) { | |
348 input[i] += 0x4000000; | |
349 input[i + 1]--; | |
350 } | |
351 } | |
352 } | |
353 while (input[9] < 0) { | |
354 input[9] += 0x2000000; | |
355 input[0] -= 19; | |
356 } | |
357 } while (input[0] < 0); | |
358 | |
359 input[1] <<= 2; | |
360 input[2] <<= 3; | |
361 input[3] <<= 5; | |
362 input[4] <<= 6; | |
363 input[6] <<= 1; | |
364 input[7] <<= 3; | |
365 input[8] <<= 4; | |
366 input[9] <<= 6; | |
367 #define F(i, s) \ | |
368 output[s+0] |= input[i] & 0xff; \ | |
369 output[s+1] = (input[i] >> 8) & 0xff; \ | |
370 output[s+2] = (input[i] >> 16) & 0xff; \ | |
371 output[s+3] = (input[i] >> 24) & 0xff; | |
372 output[0] = 0; | |
373 output[16] = 0; | |
374 F(0,0); | |
375 F(1,3); | |
376 F(2,6); | |
377 F(3,9); | |
378 F(4,12); | |
379 F(5,16); | |
380 F(6,19); | |
381 F(7,22); | |
382 F(8,25); | |
383 F(9,28); | |
384 #undef F | |
385 } | |
386 | |
387 /* Input: Q, Q', Q-Q' | |
388 * Output: 2Q, Q+Q' | |
389 * | |
390 * x2 z3: long form | |
391 * x3 z3: long form | |
392 * x z: short form, destroyed | |
393 * xprime zprime: short form, destroyed | |
394 * qmqp: short form, preserved | |
395 */ | |
396 static void fmonty(limb *x2, limb *z2, /* output 2Q */ | |
397 limb *x3, limb *z3, /* output Q + Q' */ | |
398 limb *x, limb *z, /* input Q */ | |
399 limb *xprime, limb *zprime, /* input Q' */ | |
400 const limb *qmqp /* input Q - Q' */) { | |
401 limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], | |
402 zzprime[19], zzzprime[19], xxxprime[19]; | |
403 | |
404 memcpy(origx, x, 10 * sizeof(limb)); | |
405 fsum(x, z); | |
406 fdifference(z, origx); // does x - z | |
407 | |
408 memcpy(origxprime, xprime, sizeof(limb) * 10); | |
409 fsum(xprime, zprime); | |
410 fdifference(zprime, origxprime); | |
411 fproduct(xxprime, xprime, z); | |
412 fproduct(zzprime, x, zprime); | |
413 freduce_degree(xxprime); | |
414 freduce_coefficients(xxprime); | |
415 freduce_degree(zzprime); | |
416 freduce_coefficients(zzprime); | |
417 memcpy(origxprime, xxprime, sizeof(limb) * 10); | |
418 fsum(xxprime, zzprime); | |
419 fdifference(zzprime, origxprime); | |
420 fsquare(xxxprime, xxprime); | |
421 fsquare(zzzprime, zzprime); | |
422 fproduct(zzprime, zzzprime, qmqp); | |
423 freduce_degree(zzprime); | |
424 freduce_coefficients(zzprime); | |
425 memcpy(x3, xxxprime, sizeof(limb) * 10); | |
426 memcpy(z3, zzprime, sizeof(limb) * 10); | |
427 | |
428 fsquare(xx, x); | |
429 fsquare(zz, z); | |
430 fproduct(x2, xx, zz); | |
431 freduce_degree(x2); | |
432 freduce_coefficients(x2); | |
433 fdifference(zz, xx); // does zz = xx - zz | |
434 memset(zzz + 10, 0, sizeof(limb) * 9); | |
435 fscalar_product(zzz, zz, 121665); | |
436 freduce_degree(zzz); | |
437 freduce_coefficients(zzz); | |
438 fsum(zzz, xx); | |
439 fproduct(z2, zz, zzz); | |
440 freduce_degree(z2); | |
441 freduce_coefficients(z2); | |
442 } | |
443 | |
444 /* Calculates nQ where Q is the x-coordinate of a point on the curve | |
445 * | |
446 * resultx/resultz: the x coordinate of the resulting curve point (short form) | |
447 * n: a little endian, 32-byte number | |
448 * q: a point of the curve (short form) | |
449 */ | |
450 static void | |
451 cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) { | |
452 limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0}; | |
453 limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t; | |
454 limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1}; | |
455 limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h; | |
456 | |
457 unsigned i, j; | |
458 | |
459 memcpy(nqpqx, q, sizeof(limb) * 10); | |
460 | |
461 for (i = 0; i < 32; ++i) { | |
462 u8 byte = n[31 - i]; | |
463 for (j = 0; j < 8; ++j) { | |
464 if (byte & 0x80) { | |
465 fmonty(nqpqx2, nqpqz2, | |
466 nqx2, nqz2, | |
467 nqpqx, nqpqz, | |
468 nqx, nqz, | |
469 q); | |
470 } else { | |
471 fmonty(nqx2, nqz2, | |
472 nqpqx2, nqpqz2, | |
473 nqx, nqz, | |
474 nqpqx, nqpqz, | |
475 q); | |
476 } | |
477 | |
478 t = nqx; | |
479 nqx = nqx2; | |
480 nqx2 = t; | |
481 t = nqz; | |
482 nqz = nqz2; | |
483 nqz2 = t; | |
484 t = nqpqx; | |
485 nqpqx = nqpqx2; | |
486 nqpqx2 = t; | |
487 t = nqpqz; | |
488 nqpqz = nqpqz2; | |
489 nqpqz2 = t; | |
490 | |
491 byte <<= 1; | |
492 } | |
493 } | |
494 | |
495 memcpy(resultx, nqx, sizeof(limb) * 10); | |
496 memcpy(resultz, nqz, sizeof(limb) * 10); | |
497 } | |
498 | |
499 // ----------------------------------------------------------------------------- | |
500 // Shamelessly copied from djb's code | |
501 // ----------------------------------------------------------------------------- | |
502 static void | |
503 crecip(limb *out, const limb *z) { | |
504 limb z2[10]; | |
505 limb z9[10]; | |
506 limb z11[10]; | |
507 limb z2_5_0[10]; | |
508 limb z2_10_0[10]; | |
509 limb z2_20_0[10]; | |
510 limb z2_50_0[10]; | |
511 limb z2_100_0[10]; | |
512 limb t0[10]; | |
513 limb t1[10]; | |
514 int i; | |
515 | |
516 /* 2 */ fsquare(z2,z); | |
517 /* 4 */ fsquare(t1,z2); | |
518 /* 8 */ fsquare(t0,t1); | |
519 /* 9 */ fmul(z9,t0,z); | |
520 /* 11 */ fmul(z11,z9,z2); | |
521 /* 22 */ fsquare(t0,z11); | |
522 /* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9); | |
523 | |
524 /* 2^6 - 2^1 */ fsquare(t0,z2_5_0); | |
525 /* 2^7 - 2^2 */ fsquare(t1,t0); | |
526 /* 2^8 - 2^3 */ fsquare(t0,t1); | |
527 /* 2^9 - 2^4 */ fsquare(t1,t0); | |
528 /* 2^10 - 2^5 */ fsquare(t0,t1); | |
529 /* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0); | |
530 | |
531 /* 2^11 - 2^1 */ fsquare(t0,z2_10_0); | |
532 /* 2^12 - 2^2 */ fsquare(t1,t0); | |
533 /* 2^20 - 2^10 */ | |
534 for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } | |
535 /* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0); | |
536 | |
537 /* 2^21 - 2^1 */ fsquare(t0,z2_20_0); | |
538 /* 2^22 - 2^2 */ fsquare(t1,t0); | |
539 /* 2^40 - 2^20 */ | |
540 for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } | |
541 /* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0); | |
542 | |
543 /* 2^41 - 2^1 */ fsquare(t1,t0); | |
544 /* 2^42 - 2^2 */ fsquare(t0,t1); | |
545 /* 2^50 - 2^10 */ | |
546 for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } | |
547 /* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0); | |
548 | |
549 /* 2^51 - 2^1 */ fsquare(t0,z2_50_0); | |
550 /* 2^52 - 2^2 */ fsquare(t1,t0); | |
551 /* 2^100 - 2^50 */ | |
552 for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } | |
553 /* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0); | |
554 | |
555 /* 2^101 - 2^1 */ fsquare(t1,z2_100_0); | |
556 /* 2^102 - 2^2 */ fsquare(t0,t1); | |
557 /* 2^200 - 2^100 */ | |
558 for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } | |
559 /* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0); | |
560 | |
561 /* 2^201 - 2^1 */ fsquare(t0,t1); | |
562 /* 2^202 - 2^2 */ fsquare(t1,t0); | |
563 /* 2^250 - 2^50 */ | |
564 for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } | |
565 /* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0); | |
566 | |
567 /* 2^251 - 2^1 */ fsquare(t1,t0); | |
568 /* 2^252 - 2^2 */ fsquare(t0,t1); | |
569 /* 2^253 - 2^3 */ fsquare(t1,t0); | |
570 /* 2^254 - 2^4 */ fsquare(t0,t1); | |
571 /* 2^255 - 2^5 */ fsquare(t1,t0); | |
572 /* 2^255 - 21 */ fmul(out,t1,z11); | |
573 } | |
574 | |
575 int | |
576 curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) { | |
577 limb bp[10], x[10], z[10], zmone[10]; | |
578 uint8_t e[32]; | |
579 int i; | |
580 | |
581 for (i = 0; i < 32; ++i) e[i] = secret[i]; | |
582 e[0] &= 248; | |
583 e[31] &= 127; | |
584 e[31] |= 64; | |
585 | |
586 fexpand(bp, basepoint); | |
587 cmult(x, z, e, bp); | |
588 crecip(zmone, z); | |
589 fmul(z, x, zmone); | |
590 fcontract(mypublic, z); | |
591 return 0; | |
592 } | |
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