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>, Sun Microsystems Laboratories
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 #define ECP192_DIGITS ECL_CURVE_DIGITS(192)
54
55 /* Fast modular reduction for p192 = 2^192 - 2^64 - 1. a can be r. Uses
56 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
57 * Implementation of the NIST Elliptic Curves over Prime Fields. */
58 mp_err
ec_GFp_nistp192_mod(const mp_int * a,mp_int * r,const GFMethod * meth)59 ec_GFp_nistp192_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
60 {
61 mp_err res = MP_OKAY;
62 mp_size a_used = MP_USED(a);
63 mp_digit r3;
64 #ifndef MPI_AMD64_ADD
65 mp_digit carry;
66 #endif
67 #ifdef ECL_THIRTY_TWO_BIT
68 mp_digit a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
69 mp_digit r0a, r0b, r1a, r1b, r2a, r2b;
70 #else
71 mp_digit a5 = 0, a4 = 0, a3 = 0;
72 mp_digit r0, r1, r2;
73 #endif
74
75 /* reduction not needed if a is not larger than field size */
76 if (a_used < ECP192_DIGITS) {
77 if (a == r) {
78 return MP_OKAY;
79 }
80 return mp_copy(a, r);
81 }
82
83 /* for polynomials larger than twice the field size, use regular
84 * reduction */
85 if (a_used > ECP192_DIGITS*2) {
86 MP_CHECKOK(mp_mod(a, &meth->irr, r));
87 } else {
88 /* copy out upper words of a */
89
90 #ifdef ECL_THIRTY_TWO_BIT
91
92 /* in all the math below,
93 * nXb is most signifiant, nXa is least significant */
94 switch (a_used) {
95 case 12:
96 a5b = MP_DIGIT(a, 11);
97 /* FALLTHROUGH */
98 case 11:
99 a5a = MP_DIGIT(a, 10);
100 /* FALLTHROUGH */
101 case 10:
102 a4b = MP_DIGIT(a, 9);
103 /* FALLTHROUGH */
104 case 9:
105 a4a = MP_DIGIT(a, 8);
106 /* FALLTHROUGH */
107 case 8:
108 a3b = MP_DIGIT(a, 7);
109 /* FALLTHROUGH */
110 case 7:
111 a3a = MP_DIGIT(a, 6);
112 }
113
114
115 r2b= MP_DIGIT(a, 5);
116 r2a= MP_DIGIT(a, 4);
117 r1b = MP_DIGIT(a, 3);
118 r1a = MP_DIGIT(a, 2);
119 r0b = MP_DIGIT(a, 1);
120 r0a = MP_DIGIT(a, 0);
121
122 /* implement r = (a2,a1,a0)+(a5,a5,a5)+(a4,a4,0)+(0,a3,a3) */
123 MP_ADD_CARRY(r0a, a3a, r0a, 0, carry);
124 MP_ADD_CARRY(r0b, a3b, r0b, carry, carry);
125 MP_ADD_CARRY(r1a, a3a, r1a, carry, carry);
126 MP_ADD_CARRY(r1b, a3b, r1b, carry, carry);
127 MP_ADD_CARRY(r2a, a4a, r2a, carry, carry);
128 MP_ADD_CARRY(r2b, a4b, r2b, carry, carry);
129 r3 = carry; carry = 0;
130 MP_ADD_CARRY(r0a, a5a, r0a, 0, carry);
131 MP_ADD_CARRY(r0b, a5b, r0b, carry, carry);
132 MP_ADD_CARRY(r1a, a5a, r1a, carry, carry);
133 MP_ADD_CARRY(r1b, a5b, r1b, carry, carry);
134 MP_ADD_CARRY(r2a, a5a, r2a, carry, carry);
135 MP_ADD_CARRY(r2b, a5b, r2b, carry, carry);
136 r3 += carry;
137 MP_ADD_CARRY(r1a, a4a, r1a, 0, carry);
138 MP_ADD_CARRY(r1b, a4b, r1b, carry, carry);
139 MP_ADD_CARRY(r2a, 0, r2a, carry, carry);
140 MP_ADD_CARRY(r2b, 0, r2b, carry, carry);
141 r3 += carry;
142
143 /* reduce out the carry */
144 while (r3) {
145 MP_ADD_CARRY(r0a, r3, r0a, 0, carry);
146 MP_ADD_CARRY(r0b, 0, r0b, carry, carry);
147 MP_ADD_CARRY(r1a, r3, r1a, carry, carry);
148 MP_ADD_CARRY(r1b, 0, r1b, carry, carry);
149 MP_ADD_CARRY(r2a, 0, r2a, carry, carry);
150 MP_ADD_CARRY(r2b, 0, r2b, carry, carry);
151 r3 = carry;
152 }
153
154 /* check for final reduction */
155 /*
156 * our field is 0xffffffffffffffff, 0xfffffffffffffffe,
157 * 0xffffffffffffffff. That means we can only be over and need
158 * one more reduction
159 * if r2 == 0xffffffffffffffffff (same as r2+1 == 0)
160 * and
161 * r1 == 0xffffffffffffffffff or
162 * r1 == 0xfffffffffffffffffe and r0 = 0xfffffffffffffffff
163 * In all cases, we subtract the field (or add the 2's
164 * complement value (1,1,0)). (r0, r1, r2)
165 */
166 if (((r2b == 0xffffffff) && (r2a == 0xffffffff)
167 && (r1b == 0xffffffff) ) &&
168 ((r1a == 0xffffffff) ||
169 (r1a == 0xfffffffe) && (r0a == 0xffffffff) &&
170 (r0b == 0xffffffff)) ) {
171 /* do a quick subtract */
172 MP_ADD_CARRY(r0a, 1, r0a, 0, carry);
173 r0b += carry;
174 r1a = r1b = r2a = r2b = 0;
175 }
176
177 /* set the lower words of r */
178 if (a != r) {
179 MP_CHECKOK(s_mp_pad(r, 6));
180 }
181 MP_DIGIT(r, 5) = r2b;
182 MP_DIGIT(r, 4) = r2a;
183 MP_DIGIT(r, 3) = r1b;
184 MP_DIGIT(r, 2) = r1a;
185 MP_DIGIT(r, 1) = r0b;
186 MP_DIGIT(r, 0) = r0a;
187 MP_USED(r) = 6;
188 #else
189 switch (a_used) {
190 case 6:
191 a5 = MP_DIGIT(a, 5);
192 /* FALLTHROUGH */
193 case 5:
194 a4 = MP_DIGIT(a, 4);
195 /* FALLTHROUGH */
196 case 4:
197 a3 = MP_DIGIT(a, 3);
198 }
199
200 r2 = MP_DIGIT(a, 2);
201 r1 = MP_DIGIT(a, 1);
202 r0 = MP_DIGIT(a, 0);
203
204 /* implement r = (a2,a1,a0)+(a5,a5,a5)+(a4,a4,0)+(0,a3,a3) */
205 #ifndef MPI_AMD64_ADD
206 MP_ADD_CARRY(r0, a3, r0, 0, carry);
207 MP_ADD_CARRY(r1, a3, r1, carry, carry);
208 MP_ADD_CARRY(r2, a4, r2, carry, carry);
209 r3 = carry;
210 MP_ADD_CARRY(r0, a5, r0, 0, carry);
211 MP_ADD_CARRY(r1, a5, r1, carry, carry);
212 MP_ADD_CARRY(r2, a5, r2, carry, carry);
213 r3 += carry;
214 MP_ADD_CARRY(r1, a4, r1, 0, carry);
215 MP_ADD_CARRY(r2, 0, r2, carry, carry);
216 r3 += carry;
217
218 #else
219 r2 = MP_DIGIT(a, 2);
220 r1 = MP_DIGIT(a, 1);
221 r0 = MP_DIGIT(a, 0);
222
223 /* set the lower words of r */
224 __asm__ (
225 "xorq %3,%3 \n\t"
226 "addq %4,%0 \n\t"
227 "adcq %4,%1 \n\t"
228 "adcq %5,%2 \n\t"
229 "adcq $0,%3 \n\t"
230 "addq %6,%0 \n\t"
231 "adcq %6,%1 \n\t"
232 "adcq %6,%2 \n\t"
233 "adcq $0,%3 \n\t"
234 "addq %5,%1 \n\t"
235 "adcq $0,%2 \n\t"
236 "adcq $0,%3 \n\t"
237 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(a3),
238 "=r"(a4), "=r"(a5)
239 : "0" (r0), "1" (r1), "2" (r2), "3" (r3),
240 "4" (a3), "5" (a4), "6"(a5)
241 : "%cc" );
242 #endif
243
244 /* reduce out the carry */
245 while (r3) {
246 #ifndef MPI_AMD64_ADD
247 MP_ADD_CARRY(r0, r3, r0, 0, carry);
248 MP_ADD_CARRY(r1, r3, r1, carry, carry);
249 MP_ADD_CARRY(r2, 0, r2, carry, carry);
250 r3 = carry;
251 #else
252 a3=r3;
253 __asm__ (
254 "xorq %3,%3 \n\t"
255 "addq %4,%0 \n\t"
256 "adcq %4,%1 \n\t"
257 "adcq $0,%2 \n\t"
258 "adcq $0,%3 \n\t"
259 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(a3)
260 : "0" (r0), "1" (r1), "2" (r2), "3" (r3), "4"(a3)
261 : "%cc" );
262 #endif
263 }
264
265 /* check for final reduction */
266 /*
267 * our field is 0xffffffffffffffff, 0xfffffffffffffffe,
268 * 0xffffffffffffffff. That means we can only be over and need
269 * one more reduction
270 * if r2 == 0xffffffffffffffffff (same as r2+1 == 0)
271 * and
272 * r1 == 0xffffffffffffffffff or
273 * r1 == 0xfffffffffffffffffe and r0 = 0xfffffffffffffffff
274 * In all cases, we subtract the field (or add the 2's
275 * complement value (1,1,0)). (r0, r1, r2)
276 */
277 if (r3 || ((r2 == MP_DIGIT_MAX) &&
278 ((r1 == MP_DIGIT_MAX) ||
279 ((r1 == (MP_DIGIT_MAX-1)) && (r0 == MP_DIGIT_MAX))))) {
280 /* do a quick subtract */
281 r0++;
282 r1 = r2 = 0;
283 }
284 /* set the lower words of r */
285 if (a != r) {
286 MP_CHECKOK(s_mp_pad(r, 3));
287 }
288 MP_DIGIT(r, 2) = r2;
289 MP_DIGIT(r, 1) = r1;
290 MP_DIGIT(r, 0) = r0;
291 MP_USED(r) = 3;
292 #endif
293 }
294
295 CLEANUP:
296 return res;
297 }
298
299 #ifndef ECL_THIRTY_TWO_BIT
300 /* Compute the sum of 192 bit curves. Do the work in-line since the
301 * number of words are so small, we don't want to overhead of mp function
302 * calls. Uses optimized modular reduction for p192.
303 */
304 mp_err
ec_GFp_nistp192_add(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)305 ec_GFp_nistp192_add(const mp_int *a, const mp_int *b, mp_int *r,
306 const GFMethod *meth)
307 {
308 mp_err res = MP_OKAY;
309 mp_digit a0 = 0, a1 = 0, a2 = 0;
310 mp_digit r0 = 0, r1 = 0, r2 = 0;
311 mp_digit carry;
312
313 switch(MP_USED(a)) {
314 case 3:
315 a2 = MP_DIGIT(a,2);
316 /* FALLTHROUGH */
317 case 2:
318 a1 = MP_DIGIT(a,1);
319 /* FALLTHROUGH */
320 case 1:
321 a0 = MP_DIGIT(a,0);
322 }
323 switch(MP_USED(b)) {
324 case 3:
325 r2 = MP_DIGIT(b,2);
326 /* FALLTHROUGH */
327 case 2:
328 r1 = MP_DIGIT(b,1);
329 /* FALLTHROUGH */
330 case 1:
331 r0 = MP_DIGIT(b,0);
332 }
333
334 #ifndef MPI_AMD64_ADD
335 MP_ADD_CARRY(a0, r0, r0, 0, carry);
336 MP_ADD_CARRY(a1, r1, r1, carry, carry);
337 MP_ADD_CARRY(a2, r2, r2, carry, carry);
338 #else
339 __asm__ (
340 "xorq %3,%3 \n\t"
341 "addq %4,%0 \n\t"
342 "adcq %5,%1 \n\t"
343 "adcq %6,%2 \n\t"
344 "adcq $0,%3 \n\t"
345 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(carry)
346 : "r" (a0), "r" (a1), "r" (a2), "0" (r0),
347 "1" (r1), "2" (r2)
348 : "%cc" );
349 #endif
350
351 /* Do quick 'subract' if we've gone over
352 * (add the 2's complement of the curve field) */
353 if (carry || ((r2 == MP_DIGIT_MAX) &&
354 ((r1 == MP_DIGIT_MAX) ||
355 ((r1 == (MP_DIGIT_MAX-1)) && (r0 == MP_DIGIT_MAX))))) {
356 #ifndef MPI_AMD64_ADD
357 MP_ADD_CARRY(r0, 1, r0, 0, carry);
358 MP_ADD_CARRY(r1, 1, r1, carry, carry);
359 MP_ADD_CARRY(r2, 0, r2, carry, carry);
360 #else
361 __asm__ (
362 "addq $1,%0 \n\t"
363 "adcq $1,%1 \n\t"
364 "adcq $0,%2 \n\t"
365 : "=r"(r0), "=r"(r1), "=r"(r2)
366 : "0" (r0), "1" (r1), "2" (r2)
367 : "%cc" );
368 #endif
369 }
370
371
372 MP_CHECKOK(s_mp_pad(r, 3));
373 MP_DIGIT(r, 2) = r2;
374 MP_DIGIT(r, 1) = r1;
375 MP_DIGIT(r, 0) = r0;
376 MP_SIGN(r) = MP_ZPOS;
377 MP_USED(r) = 3;
378 s_mp_clamp(r);
379
380
381 CLEANUP:
382 return res;
383 }
384
385 /* Compute the diff of 192 bit curves. Do the work in-line since the
386 * number of words are so small, we don't want to overhead of mp function
387 * calls. Uses optimized modular reduction for p192.
388 */
389 mp_err
ec_GFp_nistp192_sub(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)390 ec_GFp_nistp192_sub(const mp_int *a, const mp_int *b, mp_int *r,
391 const GFMethod *meth)
392 {
393 mp_err res = MP_OKAY;
394 mp_digit b0 = 0, b1 = 0, b2 = 0;
395 mp_digit r0 = 0, r1 = 0, r2 = 0;
396 mp_digit borrow;
397
398 switch(MP_USED(a)) {
399 case 3:
400 r2 = MP_DIGIT(a,2);
401 /* FALLTHROUGH */
402 case 2:
403 r1 = MP_DIGIT(a,1);
404 /* FALLTHROUGH */
405 case 1:
406 r0 = MP_DIGIT(a,0);
407 }
408
409 switch(MP_USED(b)) {
410 case 3:
411 b2 = MP_DIGIT(b,2);
412 /* FALLTHROUGH */
413 case 2:
414 b1 = MP_DIGIT(b,1);
415 /* FALLTHROUGH */
416 case 1:
417 b0 = MP_DIGIT(b,0);
418 }
419
420 #ifndef MPI_AMD64_ADD
421 MP_SUB_BORROW(r0, b0, r0, 0, borrow);
422 MP_SUB_BORROW(r1, b1, r1, borrow, borrow);
423 MP_SUB_BORROW(r2, b2, r2, borrow, borrow);
424 #else
425 __asm__ (
426 "xorq %3,%3 \n\t"
427 "subq %4,%0 \n\t"
428 "sbbq %5,%1 \n\t"
429 "sbbq %6,%2 \n\t"
430 "adcq $0,%3 \n\t"
431 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(borrow)
432 : "r" (b0), "r" (b1), "r" (b2), "0" (r0),
433 "1" (r1), "2" (r2)
434 : "%cc" );
435 #endif
436
437 /* Do quick 'add' if we've gone under 0
438 * (subtract the 2's complement of the curve field) */
439 if (borrow) {
440 #ifndef MPI_AMD64_ADD
441 MP_SUB_BORROW(r0, 1, r0, 0, borrow);
442 MP_SUB_BORROW(r1, 1, r1, borrow, borrow);
443 MP_SUB_BORROW(r2, 0, r2, borrow, borrow);
444 #else
445 __asm__ (
446 "subq $1,%0 \n\t"
447 "sbbq $1,%1 \n\t"
448 "sbbq $0,%2 \n\t"
449 : "=r"(r0), "=r"(r1), "=r"(r2)
450 : "0" (r0), "1" (r1), "2" (r2)
451 : "%cc" );
452 #endif
453 }
454
455 MP_CHECKOK(s_mp_pad(r, 3));
456 MP_DIGIT(r, 2) = r2;
457 MP_DIGIT(r, 1) = r1;
458 MP_DIGIT(r, 0) = r0;
459 MP_SIGN(r) = MP_ZPOS;
460 MP_USED(r) = 3;
461 s_mp_clamp(r);
462
463 CLEANUP:
464 return res;
465 }
466
467 #endif
468
469 /* Compute the square of polynomial a, reduce modulo p192. Store the
470 * result in r. r could be a. Uses optimized modular reduction for p192.
471 */
472 mp_err
ec_GFp_nistp192_sqr(const mp_int * a,mp_int * r,const GFMethod * meth)473 ec_GFp_nistp192_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
474 {
475 mp_err res = MP_OKAY;
476
477 MP_CHECKOK(mp_sqr(a, r));
478 MP_CHECKOK(ec_GFp_nistp192_mod(r, r, meth));
479 CLEANUP:
480 return res;
481 }
482
483 /* Compute the product of two polynomials a and b, reduce modulo p192.
484 * Store the result in r. r could be a or b; a could be b. Uses
485 * optimized modular reduction for p192. */
486 mp_err
ec_GFp_nistp192_mul(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)487 ec_GFp_nistp192_mul(const mp_int *a, const mp_int *b, mp_int *r,
488 const GFMethod *meth)
489 {
490 mp_err res = MP_OKAY;
491
492 MP_CHECKOK(mp_mul(a, b, r));
493 MP_CHECKOK(ec_GFp_nistp192_mod(r, r, meth));
494 CLEANUP:
495 return res;
496 }
497
498 /* Divides two field elements. If a is NULL, then returns the inverse of
499 * b. */
500 mp_err
ec_GFp_nistp192_div(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)501 ec_GFp_nistp192_div(const mp_int *a, const mp_int *b, mp_int *r,
502 const GFMethod *meth)
503 {
504 mp_err res = MP_OKAY;
505 mp_int t;
506
507 /* If a is NULL, then return the inverse of b, otherwise return a/b. */
508 if (a == NULL) {
509 return mp_invmod(b, &meth->irr, r);
510 } else {
511 /* MPI doesn't support divmod, so we implement it using invmod and
512 * mulmod. */
513 MP_CHECKOK(mp_init(&t, FLAG(b)));
514 MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
515 MP_CHECKOK(mp_mul(a, &t, r));
516 MP_CHECKOK(ec_GFp_nistp192_mod(r, r, meth));
517 CLEANUP:
518 mp_clear(&t);
519 return res;
520 }
521 }
522
523 /* Wire in fast field arithmetic and precomputation of base point for
524 * named curves. */
525 mp_err
ec_group_set_gfp192(ECGroup * group,ECCurveName name)526 ec_group_set_gfp192(ECGroup *group, ECCurveName name)
527 {
528 if (name == ECCurve_NIST_P192) {
529 group->meth->field_mod = &ec_GFp_nistp192_mod;
530 group->meth->field_mul = &ec_GFp_nistp192_mul;
531 group->meth->field_sqr = &ec_GFp_nistp192_sqr;
532 group->meth->field_div = &ec_GFp_nistp192_div;
533 #ifndef ECL_THIRTY_TWO_BIT
534 group->meth->field_add = &ec_GFp_nistp192_add;
535 group->meth->field_sub = &ec_GFp_nistp192_sub;
536 #endif
537 }
538 return MP_OKAY;
539 }
540