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1 /* This Source Code Form is subject to the terms of the Mozilla Public | |
2 * License, v. 2.0. If a copy of the MPL was not distributed with this | |
3 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ | |
4 | |
5 #include "ecp.h" | |
6 #include "mpi.h" | |
7 #include "mplogic.h" | |
8 #include "mpi-priv.h" | |
9 | |
10 /* Fast modular reduction for p256 = 2^256 - 2^224 + 2^192+ 2^96 - 1. a can be
r. | |
11 * Uses algorithm 2.29 from Hankerson, Menezes, Vanstone. Guide to | |
12 * Elliptic Curve Cryptography. */ | |
13 static mp_err | |
14 ec_GFp_nistp256_mod(const mp_int *a, mp_int *r, const GFMethod *meth) | |
15 { | |
16 mp_err res = MP_OKAY; | |
17 mp_size a_used = MP_USED(a); | |
18 int a_bits = mpl_significant_bits(a); | |
19 mp_digit carry; | |
20 | |
21 #ifdef ECL_THIRTY_TWO_BIT | |
22 mp_digit a8=0, a9=0, a10=0, a11=0, a12=0, a13=0, a14=0, a15=0; | |
23 mp_digit r0, r1, r2, r3, r4, r5, r6, r7; | |
24 int r8; /* must be a signed value ! */ | |
25 #else | |
26 mp_digit a4=0, a5=0, a6=0, a7=0; | |
27 mp_digit a4h, a4l, a5h, a5l, a6h, a6l, a7h, a7l; | |
28 mp_digit r0, r1, r2, r3; | |
29 int r4; /* must be a signed value ! */ | |
30 #endif | |
31 /* for polynomials larger than twice the field size | |
32 * use regular reduction */ | |
33 if (a_bits < 256) { | |
34 if (a == r) return MP_OKAY; | |
35 return mp_copy(a,r); | |
36 } | |
37 if (a_bits > 512) { | |
38 MP_CHECKOK(mp_mod(a, &meth->irr, r)); | |
39 } else { | |
40 | |
41 #ifdef ECL_THIRTY_TWO_BIT | |
42 switch (a_used) { | |
43 case 16: | |
44 a15 = MP_DIGIT(a,15); | |
45 case 15: | |
46 a14 = MP_DIGIT(a,14); | |
47 case 14: | |
48 a13 = MP_DIGIT(a,13); | |
49 case 13: | |
50 a12 = MP_DIGIT(a,12); | |
51 case 12: | |
52 a11 = MP_DIGIT(a,11); | |
53 case 11: | |
54 a10 = MP_DIGIT(a,10); | |
55 case 10: | |
56 a9 = MP_DIGIT(a,9); | |
57 case 9: | |
58 a8 = MP_DIGIT(a,8); | |
59 } | |
60 | |
61 r0 = MP_DIGIT(a,0); | |
62 r1 = MP_DIGIT(a,1); | |
63 r2 = MP_DIGIT(a,2); | |
64 r3 = MP_DIGIT(a,3); | |
65 r4 = MP_DIGIT(a,4); | |
66 r5 = MP_DIGIT(a,5); | |
67 r6 = MP_DIGIT(a,6); | |
68 r7 = MP_DIGIT(a,7); | |
69 | |
70 /* sum 1 */ | |
71 carry = 0; | |
72 MP_ADD_CARRY(r3, a11, r3, carry); | |
73 MP_ADD_CARRY(r4, a12, r4, carry); | |
74 MP_ADD_CARRY(r5, a13, r5, carry); | |
75 MP_ADD_CARRY(r6, a14, r6, carry); | |
76 MP_ADD_CARRY(r7, a15, r7, carry); | |
77 r8 = carry; carry = 0; | |
78 MP_ADD_CARRY(r3, a11, r3, carry); | |
79 MP_ADD_CARRY(r4, a12, r4, carry); | |
80 MP_ADD_CARRY(r5, a13, r5, carry); | |
81 MP_ADD_CARRY(r6, a14, r6, carry); | |
82 MP_ADD_CARRY(r7, a15, r7, carry); | |
83 r8 += carry; carry = 0; | |
84 /* sum 2 */ | |
85 MP_ADD_CARRY(r3, a12, r3, carry); | |
86 MP_ADD_CARRY(r4, a13, r4, carry); | |
87 MP_ADD_CARRY(r5, a14, r5, carry); | |
88 MP_ADD_CARRY(r6, a15, r6, carry); | |
89 MP_ADD_CARRY(r7, 0, r7, carry); | |
90 r8 += carry; carry = 0; | |
91 /* combine last bottom of sum 3 with second sum 2 */ | |
92 MP_ADD_CARRY(r0, a8, r0, carry); | |
93 MP_ADD_CARRY(r1, a9, r1, carry); | |
94 MP_ADD_CARRY(r2, a10, r2, carry); | |
95 MP_ADD_CARRY(r3, a12, r3, carry); | |
96 MP_ADD_CARRY(r4, a13, r4, carry); | |
97 MP_ADD_CARRY(r5, a14, r5, carry); | |
98 MP_ADD_CARRY(r6, a15, r6, carry); | |
99 MP_ADD_CARRY(r7, a15, r7, carry); /* from sum 3 */ | |
100 r8 += carry; carry = 0; | |
101 /* sum 3 (rest of it)*/ | |
102 MP_ADD_CARRY(r6, a14, r6, carry); | |
103 MP_ADD_CARRY(r7, 0, r7, carry); | |
104 r8 += carry; carry = 0; | |
105 /* sum 4 (rest of it)*/ | |
106 MP_ADD_CARRY(r0, a9, r0, carry); | |
107 MP_ADD_CARRY(r1, a10, r1, carry); | |
108 MP_ADD_CARRY(r2, a11, r2, carry); | |
109 MP_ADD_CARRY(r3, a13, r3, carry); | |
110 MP_ADD_CARRY(r4, a14, r4, carry); | |
111 MP_ADD_CARRY(r5, a15, r5, carry); | |
112 MP_ADD_CARRY(r6, a13, r6, carry); | |
113 MP_ADD_CARRY(r7, a8, r7, carry); | |
114 r8 += carry; carry = 0; | |
115 /* diff 5 */ | |
116 MP_SUB_BORROW(r0, a11, r0, carry); | |
117 MP_SUB_BORROW(r1, a12, r1, carry); | |
118 MP_SUB_BORROW(r2, a13, r2, carry); | |
119 MP_SUB_BORROW(r3, 0, r3, carry); | |
120 MP_SUB_BORROW(r4, 0, r4, carry); | |
121 MP_SUB_BORROW(r5, 0, r5, carry); | |
122 MP_SUB_BORROW(r6, a8, r6, carry); | |
123 MP_SUB_BORROW(r7, a10, r7, carry); | |
124 r8 -= carry; carry = 0; | |
125 /* diff 6 */ | |
126 MP_SUB_BORROW(r0, a12, r0, carry); | |
127 MP_SUB_BORROW(r1, a13, r1, carry); | |
128 MP_SUB_BORROW(r2, a14, r2, carry); | |
129 MP_SUB_BORROW(r3, a15, r3, carry); | |
130 MP_SUB_BORROW(r4, 0, r4, carry); | |
131 MP_SUB_BORROW(r5, 0, r5, carry); | |
132 MP_SUB_BORROW(r6, a9, r6, carry); | |
133 MP_SUB_BORROW(r7, a11, r7, carry); | |
134 r8 -= carry; carry = 0; | |
135 /* diff 7 */ | |
136 MP_SUB_BORROW(r0, a13, r0, carry); | |
137 MP_SUB_BORROW(r1, a14, r1, carry); | |
138 MP_SUB_BORROW(r2, a15, r2, carry); | |
139 MP_SUB_BORROW(r3, a8, r3, carry); | |
140 MP_SUB_BORROW(r4, a9, r4, carry); | |
141 MP_SUB_BORROW(r5, a10, r5, carry); | |
142 MP_SUB_BORROW(r6, 0, r6, carry); | |
143 MP_SUB_BORROW(r7, a12, r7, carry); | |
144 r8 -= carry; carry = 0; | |
145 /* diff 8 */ | |
146 MP_SUB_BORROW(r0, a14, r0, carry); | |
147 MP_SUB_BORROW(r1, a15, r1, carry); | |
148 MP_SUB_BORROW(r2, 0, r2, carry); | |
149 MP_SUB_BORROW(r3, a9, r3, carry); | |
150 MP_SUB_BORROW(r4, a10, r4, carry); | |
151 MP_SUB_BORROW(r5, a11, r5, carry); | |
152 MP_SUB_BORROW(r6, 0, r6, carry); | |
153 MP_SUB_BORROW(r7, a13, r7, carry); | |
154 r8 -= carry; | |
155 | |
156 /* reduce the overflows */ | |
157 while (r8 > 0) { | |
158 mp_digit r8_d = r8; carry = 0; | |
159 carry = 0; | |
160 MP_ADD_CARRY(r0, r8_d, r0, carry); | |
161 MP_ADD_CARRY(r1, 0, r1, carry); | |
162 MP_ADD_CARRY(r2, 0, r2, carry); | |
163 MP_ADD_CARRY(r3, 0-r8_d, r3, carry); | |
164 MP_ADD_CARRY(r4, MP_DIGIT_MAX, r4, carry); | |
165 MP_ADD_CARRY(r5, MP_DIGIT_MAX, r5, carry); | |
166 MP_ADD_CARRY(r6, 0-(r8_d+1), r6, carry); | |
167 MP_ADD_CARRY(r7, (r8_d-1), r7, carry); | |
168 r8 = carry; | |
169 } | |
170 | |
171 /* reduce the underflows */ | |
172 while (r8 < 0) { | |
173 mp_digit r8_d = -r8; | |
174 carry = 0; | |
175 MP_SUB_BORROW(r0, r8_d, r0, carry); | |
176 MP_SUB_BORROW(r1, 0, r1, carry); | |
177 MP_SUB_BORROW(r2, 0, r2, carry); | |
178 MP_SUB_BORROW(r3, 0-r8_d, r3, carry); | |
179 MP_SUB_BORROW(r4, MP_DIGIT_MAX, r4, carry); | |
180 MP_SUB_BORROW(r5, MP_DIGIT_MAX, r5, carry); | |
181 MP_SUB_BORROW(r6, 0-(r8_d+1), r6, carry); | |
182 MP_SUB_BORROW(r7, (r8_d-1), r7, carry); | |
183 r8 = 0-carry; | |
184 } | |
185 if (a != r) { | |
186 MP_CHECKOK(s_mp_pad(r,8)); | |
187 } | |
188 MP_SIGN(r) = MP_ZPOS; | |
189 MP_USED(r) = 8; | |
190 | |
191 MP_DIGIT(r,7) = r7; | |
192 MP_DIGIT(r,6) = r6; | |
193 MP_DIGIT(r,5) = r5; | |
194 MP_DIGIT(r,4) = r4; | |
195 MP_DIGIT(r,3) = r3; | |
196 MP_DIGIT(r,2) = r2; | |
197 MP_DIGIT(r,1) = r1; | |
198 MP_DIGIT(r,0) = r0; | |
199 | |
200 /* final reduction if necessary */ | |
201 if ((r7 == MP_DIGIT_MAX) && | |
202 ((r6 > 1) || ((r6 == 1) && | |
203 (r5 || r4 || r3 || | |
204 ((r2 == MP_DIGIT_MAX) && (r1 == MP_DIGIT_MAX) | |
205 && (r0 == MP_DIGIT_MAX)))))) { | |
206 MP_CHECKOK(mp_sub(r, &meth->irr, r)); | |
207 } | |
208 | |
209 s_mp_clamp(r); | |
210 #else | |
211 switch (a_used) { | |
212 case 8: | |
213 a7 = MP_DIGIT(a,7); | |
214 case 7: | |
215 a6 = MP_DIGIT(a,6); | |
216 case 6: | |
217 a5 = MP_DIGIT(a,5); | |
218 case 5: | |
219 a4 = MP_DIGIT(a,4); | |
220 } | |
221 a7l = a7 << 32; | |
222 a7h = a7 >> 32; | |
223 a6l = a6 << 32; | |
224 a6h = a6 >> 32; | |
225 a5l = a5 << 32; | |
226 a5h = a5 >> 32; | |
227 a4l = a4 << 32; | |
228 a4h = a4 >> 32; | |
229 r3 = MP_DIGIT(a,3); | |
230 r2 = MP_DIGIT(a,2); | |
231 r1 = MP_DIGIT(a,1); | |
232 r0 = MP_DIGIT(a,0); | |
233 | |
234 /* sum 1 */ | |
235 carry = 0; | |
236 carry = 0; | |
237 MP_ADD_CARRY(r1, a5h << 32, r1, carry); | |
238 MP_ADD_CARRY(r2, a6, r2, carry); | |
239 MP_ADD_CARRY(r3, a7, r3, carry); | |
240 r4 = carry; carry = 0; | |
241 carry = 0; | |
242 MP_ADD_CARRY(r1, a5h << 32, r1, carry); | |
243 MP_ADD_CARRY(r2, a6, r2, carry); | |
244 MP_ADD_CARRY(r3, a7, r3, carry); | |
245 r4 += carry; carry = 0; | |
246 /* sum 2 */ | |
247 carry = 0; | |
248 MP_ADD_CARRY(r1, a6l, r1, carry); | |
249 MP_ADD_CARRY(r2, a6h | a7l, r2, carry); | |
250 MP_ADD_CARRY(r3, a7h, r3, carry); | |
251 r4 += carry; carry = 0; | |
252 carry = 0; | |
253 MP_ADD_CARRY(r1, a6l, r1, carry); | |
254 MP_ADD_CARRY(r2, a6h | a7l, r2, carry); | |
255 MP_ADD_CARRY(r3, a7h, r3, carry); | |
256 r4 += carry; carry = 0; | |
257 | |
258 /* sum 3 */ | |
259 carry = 0; | |
260 MP_ADD_CARRY(r0, a4, r0, carry); | |
261 MP_ADD_CARRY(r1, a5l >> 32, r1, carry); | |
262 MP_ADD_CARRY(r2, 0, r2, carry); | |
263 MP_ADD_CARRY(r3, a7, r3, carry); | |
264 r4 += carry; carry = 0; | |
265 /* sum 4 */ | |
266 carry = 0; | |
267 MP_ADD_CARRY(r0, a4h | a5l, r0, carry); | |
268 MP_ADD_CARRY(r1, a5h|(a6h<<32), r1, carry); | |
269 MP_ADD_CARRY(r2, a7, r2, carry); | |
270 MP_ADD_CARRY(r3, a6h | a4l, r3, carry); | |
271 r4 += carry; | |
272 /* diff 5 */ | |
273 carry = 0; | |
274 MP_SUB_BORROW(r0, a5h | a6l, r0, carry); | |
275 MP_SUB_BORROW(r1, a6h, r1, carry); | |
276 MP_SUB_BORROW(r2, 0, r2, carry); | |
277 MP_SUB_BORROW(r3, (a4l>>32)|a5l,r3, carry); | |
278 r4 -= carry; | |
279 /* diff 6 */ | |
280 carry = 0; | |
281 MP_SUB_BORROW(r0, a6, r0, carry); | |
282 MP_SUB_BORROW(r1, a7, r1, carry); | |
283 MP_SUB_BORROW(r2, 0, r2, carry); | |
284 MP_SUB_BORROW(r3, a4h|(a5h<<32),r3, carry); | |
285 r4 -= carry; | |
286 /* diff 7 */ | |
287 carry = 0; | |
288 MP_SUB_BORROW(r0, a6h|a7l, r0, carry); | |
289 MP_SUB_BORROW(r1, a7h|a4l, r1, carry); | |
290 MP_SUB_BORROW(r2, a4h|a5l, r2, carry); | |
291 MP_SUB_BORROW(r3, a6l, r3, carry); | |
292 r4 -= carry; | |
293 /* diff 8 */ | |
294 carry = 0; | |
295 MP_SUB_BORROW(r0, a7, r0, carry); | |
296 MP_SUB_BORROW(r1, a4h<<32, r1, carry); | |
297 MP_SUB_BORROW(r2, a5, r2, carry); | |
298 MP_SUB_BORROW(r3, a6h<<32, r3, carry); | |
299 r4 -= carry; | |
300 | |
301 /* reduce the overflows */ | |
302 while (r4 > 0) { | |
303 mp_digit r4_long = r4; | |
304 mp_digit r4l = (r4_long << 32); | |
305 carry = 0; | |
306 carry = 0; | |
307 MP_ADD_CARRY(r0, r4_long, r0, carry); | |
308 MP_ADD_CARRY(r1, 0-r4l, r1, carry); | |
309 MP_ADD_CARRY(r2, MP_DIGIT_MAX, r2, carry); | |
310 MP_ADD_CARRY(r3, r4l-r4_long-1,r3, carry); | |
311 r4 = carry; | |
312 } | |
313 | |
314 /* reduce the underflows */ | |
315 while (r4 < 0) { | |
316 mp_digit r4_long = -r4; | |
317 mp_digit r4l = (r4_long << 32); | |
318 carry = 0; | |
319 MP_SUB_BORROW(r0, r4_long, r0, carry); | |
320 MP_SUB_BORROW(r1, 0-r4l, r1, carry); | |
321 MP_SUB_BORROW(r2, MP_DIGIT_MAX, r2, carry); | |
322 MP_SUB_BORROW(r3, r4l-r4_long-1,r3, carry); | |
323 r4 = 0-carry; | |
324 } | |
325 | |
326 if (a != r) { | |
327 MP_CHECKOK(s_mp_pad(r,4)); | |
328 } | |
329 MP_SIGN(r) = MP_ZPOS; | |
330 MP_USED(r) = 4; | |
331 | |
332 MP_DIGIT(r,3) = r3; | |
333 MP_DIGIT(r,2) = r2; | |
334 MP_DIGIT(r,1) = r1; | |
335 MP_DIGIT(r,0) = r0; | |
336 | |
337 /* final reduction if necessary */ | |
338 if ((r3 > 0xFFFFFFFF00000001ULL) || | |
339 ((r3 == 0xFFFFFFFF00000001ULL) && | |
340 (r2 || (r1 >> 32)|| | |
341 (r1 == 0xFFFFFFFFULL && r0 == MP_DIGIT_MAX)))) { | |
342 /* very rare, just use mp_sub */ | |
343 MP_CHECKOK(mp_sub(r, &meth->irr, r)); | |
344 } | |
345 | |
346 s_mp_clamp(r); | |
347 #endif | |
348 } | |
349 | |
350 CLEANUP: | |
351 return res; | |
352 } | |
353 | |
354 /* Compute the square of polynomial a, reduce modulo p256. Store the | |
355 * result in r. r could be a. Uses optimized modular reduction for p256. | |
356 */ | |
357 static mp_err | |
358 ec_GFp_nistp256_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) | |
359 { | |
360 mp_err res = MP_OKAY; | |
361 | |
362 MP_CHECKOK(mp_sqr(a, r)); | |
363 MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth)); | |
364 CLEANUP: | |
365 return res; | |
366 } | |
367 | |
368 /* Compute the product of two polynomials a and b, reduce modulo p256. | |
369 * Store the result in r. r could be a or b; a could be b. Uses | |
370 * optimized modular reduction for p256. */ | |
371 static mp_err | |
372 ec_GFp_nistp256_mul(const mp_int *a, const mp_int *b, mp_int *r, | |
373 const GFMethod *meth) | |
374 { | |
375 mp_err res = MP_OKAY; | |
376 | |
377 MP_CHECKOK(mp_mul(a, b, r)); | |
378 MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth)); | |
379 CLEANUP: | |
380 return res; | |
381 } | |
382 | |
383 /* Wire in fast field arithmetic and precomputation of base point for | |
384 * named curves. */ | |
385 mp_err | |
386 ec_group_set_gfp256(ECGroup *group, ECCurveName name) | |
387 { | |
388 if (name == ECCurve_NIST_P256) { | |
389 group->meth->field_mod = &ec_GFp_nistp256_mod; | |
390 group->meth->field_mul = &ec_GFp_nistp256_mul; | |
391 group->meth->field_sqr = &ec_GFp_nistp256_sqr; | |
392 } | |
393 return MP_OKAY; | |
394 } | |
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