1 /*
2 * ***** BEGIN LICENSE BLOCK *****
3 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
4 *
5 * The contents of this file are subject to the Mozilla Public License Version
6 * 1.1 (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 * http://www.mozilla.org/MPL/
9 *
10 * Software distributed under the License is distributed on an "AS IS" basis,
11 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
12 * for the specific language governing rights and limitations under the
13 * License.
14 *
15 * The Original Code is the elliptic curve math library for prime field curves.
16 *
17 * The Initial Developer of the Original Code is
18 * Sun Microsystems, Inc.
19 * Portions created by the Initial Developer are Copyright (C) 2003
20 * the Initial Developer. All Rights Reserved.
21 *
22 * Contributor(s):
23 * Douglas Stebila <douglas@stebila.ca>
24 *
25 * Alternatively, the contents of this file may be used under the terms of
26 * either the GNU General Public License Version 2 or later (the "GPL"), or
27 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
28 * in which case the provisions of the GPL or the LGPL are applicable instead
29 * of those above. If you wish to allow use of your version of this file only
30 * under the terms of either the GPL or the LGPL, and not to allow others to
31 * use your version of this file under the terms of the MPL, indicate your
32 * decision by deleting the provisions above and replace them with the notice
33 * and other provisions required by the GPL or the LGPL. If you do not delete
34 * the provisions above, a recipient may use your version of this file under
35 * the terms of any one of the MPL, the GPL or the LGPL.
36 *
37 * ***** END LICENSE BLOCK ***** */
38 /*
39 * Copyright 2007 Sun Microsystems, Inc. All rights reserved.
40 * Use is subject to license terms.
41 *
42 * Sun elects to use this software under the MPL license.
43 */
44
45 #include "ecp.h"
46 #include "mpi.h"
47 #include "mplogic.h"
48 #include "mpi-priv.h"
49 #ifndef _KERNEL
50 #include <stdlib.h>
51 #endif
52
53 /* Fast modular reduction for p256 = 2^256 - 2^224 + 2^192+ 2^96 - 1. a can be r.
54 * Uses algorithm 2.29 from Hankerson, Menezes, Vanstone. Guide to
55 * Elliptic Curve Cryptography. */
56 mp_err
ec_GFp_nistp256_mod(const mp_int * a,mp_int * r,const GFMethod * meth)57 ec_GFp_nistp256_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
58 {
59 mp_err res = MP_OKAY;
60 mp_size a_used = MP_USED(a);
61 int a_bits = mpl_significant_bits(a);
62 mp_digit carry;
63
64 #ifdef ECL_THIRTY_TWO_BIT
65 mp_digit a8=0, a9=0, a10=0, a11=0, a12=0, a13=0, a14=0, a15=0;
66 mp_digit r0, r1, r2, r3, r4, r5, r6, r7;
67 int r8; /* must be a signed value ! */
68 #else
69 mp_digit a4=0, a5=0, a6=0, a7=0;
70 mp_digit a4h, a4l, a5h, a5l, a6h, a6l, a7h, a7l;
71 mp_digit r0, r1, r2, r3;
72 int r4; /* must be a signed value ! */
73 #endif
74 /* for polynomials larger than twice the field size
75 * use regular reduction */
76 if (a_bits < 256) {
77 if (a == r) return MP_OKAY;
78 return mp_copy(a,r);
79 }
80 if (a_bits > 512) {
81 MP_CHECKOK(mp_mod(a, &meth->irr, r));
82 } else {
83
84 #ifdef ECL_THIRTY_TWO_BIT
85 switch (a_used) {
86 case 16:
87 a15 = MP_DIGIT(a,15);
88 /* FALLTHROUGH */
89 case 15:
90 a14 = MP_DIGIT(a,14);
91 /* FALLTHROUGH */
92 case 14:
93 a13 = MP_DIGIT(a,13);
94 /* FALLTHROUGH */
95 case 13:
96 a12 = MP_DIGIT(a,12);
97 /* FALLTHROUGH */
98 case 12:
99 a11 = MP_DIGIT(a,11);
100 /* FALLTHROUGH */
101 case 11:
102 a10 = MP_DIGIT(a,10);
103 /* FALLTHROUGH */
104 case 10:
105 a9 = MP_DIGIT(a,9);
106 /* FALLTHROUGH */
107 case 9:
108 a8 = MP_DIGIT(a,8);
109 }
110
111 r0 = MP_DIGIT(a,0);
112 r1 = MP_DIGIT(a,1);
113 r2 = MP_DIGIT(a,2);
114 r3 = MP_DIGIT(a,3);
115 r4 = MP_DIGIT(a,4);
116 r5 = MP_DIGIT(a,5);
117 r6 = MP_DIGIT(a,6);
118 r7 = MP_DIGIT(a,7);
119
120 /* sum 1 */
121 MP_ADD_CARRY(r3, a11, r3, 0, carry);
122 MP_ADD_CARRY(r4, a12, r4, carry, carry);
123 MP_ADD_CARRY(r5, a13, r5, carry, carry);
124 MP_ADD_CARRY(r6, a14, r6, carry, carry);
125 MP_ADD_CARRY(r7, a15, r7, carry, carry);
126 r8 = carry;
127 MP_ADD_CARRY(r3, a11, r3, 0, carry);
128 MP_ADD_CARRY(r4, a12, r4, carry, carry);
129 MP_ADD_CARRY(r5, a13, r5, carry, carry);
130 MP_ADD_CARRY(r6, a14, r6, carry, carry);
131 MP_ADD_CARRY(r7, a15, r7, carry, carry);
132 r8 += carry;
133 /* sum 2 */
134 MP_ADD_CARRY(r3, a12, r3, 0, carry);
135 MP_ADD_CARRY(r4, a13, r4, carry, carry);
136 MP_ADD_CARRY(r5, a14, r5, carry, carry);
137 MP_ADD_CARRY(r6, a15, r6, carry, carry);
138 MP_ADD_CARRY(r7, 0, r7, carry, carry);
139 r8 += carry;
140 /* combine last bottom of sum 3 with second sum 2 */
141 MP_ADD_CARRY(r0, a8, r0, 0, carry);
142 MP_ADD_CARRY(r1, a9, r1, carry, carry);
143 MP_ADD_CARRY(r2, a10, r2, carry, carry);
144 MP_ADD_CARRY(r3, a12, r3, carry, carry);
145 MP_ADD_CARRY(r4, a13, r4, carry, carry);
146 MP_ADD_CARRY(r5, a14, r5, carry, carry);
147 MP_ADD_CARRY(r6, a15, r6, carry, carry);
148 MP_ADD_CARRY(r7, a15, r7, carry, carry); /* from sum 3 */
149 r8 += carry;
150 /* sum 3 (rest of it)*/
151 MP_ADD_CARRY(r6, a14, r6, 0, carry);
152 MP_ADD_CARRY(r7, 0, r7, carry, carry);
153 r8 += carry;
154 /* sum 4 (rest of it)*/
155 MP_ADD_CARRY(r0, a9, r0, 0, carry);
156 MP_ADD_CARRY(r1, a10, r1, carry, carry);
157 MP_ADD_CARRY(r2, a11, r2, carry, carry);
158 MP_ADD_CARRY(r3, a13, r3, carry, carry);
159 MP_ADD_CARRY(r4, a14, r4, carry, carry);
160 MP_ADD_CARRY(r5, a15, r5, carry, carry);
161 MP_ADD_CARRY(r6, a13, r6, carry, carry);
162 MP_ADD_CARRY(r7, a8, r7, carry, carry);
163 r8 += carry;
164 /* diff 5 */
165 MP_SUB_BORROW(r0, a11, r0, 0, carry);
166 MP_SUB_BORROW(r1, a12, r1, carry, carry);
167 MP_SUB_BORROW(r2, a13, r2, carry, carry);
168 MP_SUB_BORROW(r3, 0, r3, carry, carry);
169 MP_SUB_BORROW(r4, 0, r4, carry, carry);
170 MP_SUB_BORROW(r5, 0, r5, carry, carry);
171 MP_SUB_BORROW(r6, a8, r6, carry, carry);
172 MP_SUB_BORROW(r7, a10, r7, carry, carry);
173 r8 -= carry;
174 /* diff 6 */
175 MP_SUB_BORROW(r0, a12, r0, 0, carry);
176 MP_SUB_BORROW(r1, a13, r1, carry, carry);
177 MP_SUB_BORROW(r2, a14, r2, carry, carry);
178 MP_SUB_BORROW(r3, a15, r3, carry, carry);
179 MP_SUB_BORROW(r4, 0, r4, carry, carry);
180 MP_SUB_BORROW(r5, 0, r5, carry, carry);
181 MP_SUB_BORROW(r6, a9, r6, carry, carry);
182 MP_SUB_BORROW(r7, a11, r7, carry, carry);
183 r8 -= carry;
184 /* diff 7 */
185 MP_SUB_BORROW(r0, a13, r0, 0, carry);
186 MP_SUB_BORROW(r1, a14, r1, carry, carry);
187 MP_SUB_BORROW(r2, a15, r2, carry, carry);
188 MP_SUB_BORROW(r3, a8, r3, carry, carry);
189 MP_SUB_BORROW(r4, a9, r4, carry, carry);
190 MP_SUB_BORROW(r5, a10, r5, carry, carry);
191 MP_SUB_BORROW(r6, 0, r6, carry, carry);
192 MP_SUB_BORROW(r7, a12, r7, carry, carry);
193 r8 -= carry;
194 /* diff 8 */
195 MP_SUB_BORROW(r0, a14, r0, 0, carry);
196 MP_SUB_BORROW(r1, a15, r1, carry, carry);
197 MP_SUB_BORROW(r2, 0, r2, carry, carry);
198 MP_SUB_BORROW(r3, a9, r3, carry, carry);
199 MP_SUB_BORROW(r4, a10, r4, carry, carry);
200 MP_SUB_BORROW(r5, a11, r5, carry, carry);
201 MP_SUB_BORROW(r6, 0, r6, carry, carry);
202 MP_SUB_BORROW(r7, a13, r7, carry, carry);
203 r8 -= carry;
204
205 /* reduce the overflows */
206 while (r8 > 0) {
207 mp_digit r8_d = r8;
208 MP_ADD_CARRY(r0, r8_d, r0, 0, carry);
209 MP_ADD_CARRY(r1, 0, r1, carry, carry);
210 MP_ADD_CARRY(r2, 0, r2, carry, carry);
211 MP_ADD_CARRY(r3, -r8_d, r3, carry, carry);
212 MP_ADD_CARRY(r4, MP_DIGIT_MAX, r4, carry, carry);
213 MP_ADD_CARRY(r5, MP_DIGIT_MAX, r5, carry, carry);
214 MP_ADD_CARRY(r6, -(r8_d+1), r6, carry, carry);
215 MP_ADD_CARRY(r7, (r8_d-1), r7, carry, carry);
216 r8 = carry;
217 }
218
219 /* reduce the underflows */
220 while (r8 < 0) {
221 mp_digit r8_d = -r8;
222 MP_SUB_BORROW(r0, r8_d, r0, 0, carry);
223 MP_SUB_BORROW(r1, 0, r1, carry, carry);
224 MP_SUB_BORROW(r2, 0, r2, carry, carry);
225 MP_SUB_BORROW(r3, -r8_d, r3, carry, carry);
226 MP_SUB_BORROW(r4, MP_DIGIT_MAX, r4, carry, carry);
227 MP_SUB_BORROW(r5, MP_DIGIT_MAX, r5, carry, carry);
228 MP_SUB_BORROW(r6, -(r8_d+1), r6, carry, carry);
229 MP_SUB_BORROW(r7, (r8_d-1), r7, carry, carry);
230 r8 = -carry;
231 }
232 if (a != r) {
233 MP_CHECKOK(s_mp_pad(r,8));
234 }
235 MP_SIGN(r) = MP_ZPOS;
236 MP_USED(r) = 8;
237
238 MP_DIGIT(r,7) = r7;
239 MP_DIGIT(r,6) = r6;
240 MP_DIGIT(r,5) = r5;
241 MP_DIGIT(r,4) = r4;
242 MP_DIGIT(r,3) = r3;
243 MP_DIGIT(r,2) = r2;
244 MP_DIGIT(r,1) = r1;
245 MP_DIGIT(r,0) = r0;
246
247 /* final reduction if necessary */
248 if ((r7 == MP_DIGIT_MAX) &&
249 ((r6 > 1) || ((r6 == 1) &&
250 (r5 || r4 || r3 ||
251 ((r2 == MP_DIGIT_MAX) && (r1 == MP_DIGIT_MAX)
252 && (r0 == MP_DIGIT_MAX)))))) {
253 MP_CHECKOK(mp_sub(r, &meth->irr, r));
254 }
255 #ifdef notdef
256
257
258 /* smooth the negatives */
259 while (MP_SIGN(r) != MP_ZPOS) {
260 MP_CHECKOK(mp_add(r, &meth->irr, r));
261 }
262 while (MP_USED(r) > 8) {
263 MP_CHECKOK(mp_sub(r, &meth->irr, r));
264 }
265
266 /* final reduction if necessary */
267 if (MP_DIGIT(r,7) >= MP_DIGIT(&meth->irr,7)) {
268 if (mp_cmp(r,&meth->irr) != MP_LT) {
269 MP_CHECKOK(mp_sub(r, &meth->irr, r));
270 }
271 }
272 #endif
273 s_mp_clamp(r);
274 #else
275 switch (a_used) {
276 case 8:
277 a7 = MP_DIGIT(a,7);
278 /* FALLTHROUGH */
279 case 7:
280 a6 = MP_DIGIT(a,6);
281 /* FALLTHROUGH */
282 case 6:
283 a5 = MP_DIGIT(a,5);
284 /* FALLTHROUGH */
285 case 5:
286 a4 = MP_DIGIT(a,4);
287 }
288 a7l = a7 << 32;
289 a7h = a7 >> 32;
290 a6l = a6 << 32;
291 a6h = a6 >> 32;
292 a5l = a5 << 32;
293 a5h = a5 >> 32;
294 a4l = a4 << 32;
295 a4h = a4 >> 32;
296 r3 = MP_DIGIT(a,3);
297 r2 = MP_DIGIT(a,2);
298 r1 = MP_DIGIT(a,1);
299 r0 = MP_DIGIT(a,0);
300
301 /* sum 1 */
302 MP_ADD_CARRY(r1, a5h << 32, r1, 0, carry);
303 MP_ADD_CARRY(r2, a6, r2, carry, carry);
304 MP_ADD_CARRY(r3, a7, r3, carry, carry);
305 r4 = carry;
306 MP_ADD_CARRY(r1, a5h << 32, r1, 0, carry);
307 MP_ADD_CARRY(r2, a6, r2, carry, carry);
308 MP_ADD_CARRY(r3, a7, r3, carry, carry);
309 r4 += carry;
310 /* sum 2 */
311 MP_ADD_CARRY(r1, a6l, r1, 0, carry);
312 MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
313 MP_ADD_CARRY(r3, a7h, r3, carry, carry);
314 r4 += carry;
315 MP_ADD_CARRY(r1, a6l, r1, 0, carry);
316 MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
317 MP_ADD_CARRY(r3, a7h, r3, carry, carry);
318 r4 += carry;
319
320 /* sum 3 */
321 MP_ADD_CARRY(r0, a4, r0, 0, carry);
322 MP_ADD_CARRY(r1, a5l >> 32, r1, carry, carry);
323 MP_ADD_CARRY(r2, 0, r2, carry, carry);
324 MP_ADD_CARRY(r3, a7, r3, carry, carry);
325 r4 += carry;
326 /* sum 4 */
327 MP_ADD_CARRY(r0, a4h | a5l, r0, 0, carry);
328 MP_ADD_CARRY(r1, a5h|(a6h<<32), r1, carry, carry);
329 MP_ADD_CARRY(r2, a7, r2, carry, carry);
330 MP_ADD_CARRY(r3, a6h | a4l, r3, carry, carry);
331 r4 += carry;
332 /* diff 5 */
333 MP_SUB_BORROW(r0, a5h | a6l, r0, 0, carry);
334 MP_SUB_BORROW(r1, a6h, r1, carry, carry);
335 MP_SUB_BORROW(r2, 0, r2, carry, carry);
336 MP_SUB_BORROW(r3, (a4l>>32)|a5l,r3, carry, carry);
337 r4 -= carry;
338 /* diff 6 */
339 MP_SUB_BORROW(r0, a6, r0, 0, carry);
340 MP_SUB_BORROW(r1, a7, r1, carry, carry);
341 MP_SUB_BORROW(r2, 0, r2, carry, carry);
342 MP_SUB_BORROW(r3, a4h|(a5h<<32),r3, carry, carry);
343 r4 -= carry;
344 /* diff 7 */
345 MP_SUB_BORROW(r0, a6h|a7l, r0, 0, carry);
346 MP_SUB_BORROW(r1, a7h|a4l, r1, carry, carry);
347 MP_SUB_BORROW(r2, a4h|a5l, r2, carry, carry);
348 MP_SUB_BORROW(r3, a6l, r3, carry, carry);
349 r4 -= carry;
350 /* diff 8 */
351 MP_SUB_BORROW(r0, a7, r0, 0, carry);
352 MP_SUB_BORROW(r1, a4h<<32, r1, carry, carry);
353 MP_SUB_BORROW(r2, a5, r2, carry, carry);
354 MP_SUB_BORROW(r3, a6h<<32, r3, carry, carry);
355 r4 -= carry;
356
357 /* reduce the overflows */
358 while (r4 > 0) {
359 mp_digit r4_long = r4;
360 mp_digit r4l = (r4_long << 32);
361 MP_ADD_CARRY(r0, r4_long, r0, 0, carry);
362 MP_ADD_CARRY(r1, -r4l, r1, carry, carry);
363 MP_ADD_CARRY(r2, MP_DIGIT_MAX, r2, carry, carry);
364 MP_ADD_CARRY(r3, r4l-r4_long-1,r3, carry, carry);
365 r4 = carry;
366 }
367
368 /* reduce the underflows */
369 while (r4 < 0) {
370 mp_digit r4_long = -r4;
371 mp_digit r4l = (r4_long << 32);
372 MP_SUB_BORROW(r0, r4_long, r0, 0, carry);
373 MP_SUB_BORROW(r1, -r4l, r1, carry, carry);
374 MP_SUB_BORROW(r2, MP_DIGIT_MAX, r2, carry, carry);
375 MP_SUB_BORROW(r3, r4l-r4_long-1,r3, carry, carry);
376 r4 = -carry;
377 }
378
379 if (a != r) {
380 MP_CHECKOK(s_mp_pad(r,4));
381 }
382 MP_SIGN(r) = MP_ZPOS;
383 MP_USED(r) = 4;
384
385 MP_DIGIT(r,3) = r3;
386 MP_DIGIT(r,2) = r2;
387 MP_DIGIT(r,1) = r1;
388 MP_DIGIT(r,0) = r0;
389
390 /* final reduction if necessary */
391 if ((r3 > 0xFFFFFFFF00000001ULL) ||
392 ((r3 == 0xFFFFFFFF00000001ULL) &&
393 (r2 || (r1 >> 32)||
394 (r1 == 0xFFFFFFFFULL && r0 == MP_DIGIT_MAX)))) {
395 /* very rare, just use mp_sub */
396 MP_CHECKOK(mp_sub(r, &meth->irr, r));
397 }
398
399 s_mp_clamp(r);
400 #endif
401 }
402
403 CLEANUP:
404 return res;
405 }
406
407 /* Compute the square of polynomial a, reduce modulo p256. Store the
408 * result in r. r could be a. Uses optimized modular reduction for p256.
409 */
410 mp_err
ec_GFp_nistp256_sqr(const mp_int * a,mp_int * r,const GFMethod * meth)411 ec_GFp_nistp256_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
412 {
413 mp_err res = MP_OKAY;
414
415 MP_CHECKOK(mp_sqr(a, r));
416 MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth));
417 CLEANUP:
418 return res;
419 }
420
421 /* Compute the product of two polynomials a and b, reduce modulo p256.
422 * Store the result in r. r could be a or b; a could be b. Uses
423 * optimized modular reduction for p256. */
424 mp_err
ec_GFp_nistp256_mul(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)425 ec_GFp_nistp256_mul(const mp_int *a, const mp_int *b, mp_int *r,
426 const GFMethod *meth)
427 {
428 mp_err res = MP_OKAY;
429
430 MP_CHECKOK(mp_mul(a, b, r));
431 MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth));
432 CLEANUP:
433 return res;
434 }
435
436 /* Wire in fast field arithmetic and precomputation of base point for
437 * named curves. */
438 mp_err
ec_group_set_gfp256(ECGroup * group,ECCurveName name)439 ec_group_set_gfp256(ECGroup *group, ECCurveName name)
440 {
441 if (name == ECCurve_NIST_P256) {
442 group->meth->field_mod = &ec_GFp_nistp256_mod;
443 group->meth->field_mul = &ec_GFp_nistp256_mul;
444 group->meth->field_sqr = &ec_GFp_nistp256_sqr;
445 }
446 return MP_OKAY;
447 }
448