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 #pragma ident "%Z%%M% %I% %E% SMI"
46
47 #include "ecp.h"
48 #include "mpi.h"
49 #include "mplogic.h"
50 #include "mpi-priv.h"
51 #ifndef _KERNEL
52 #include <stdlib.h>
53 #endif
54
55 #define ECP192_DIGITS ECL_CURVE_DIGITS(192)
56
57 /* Fast modular reduction for p192 = 2^192 - 2^64 - 1. a can be r. Uses
58 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
59 * Implementation of the NIST Elliptic Curves over Prime Fields. */
60 mp_err
ec_GFp_nistp192_mod(const mp_int * a,mp_int * r,const GFMethod * meth)61 ec_GFp_nistp192_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
62 {
63 mp_err res = MP_OKAY;
64 mp_size a_used = MP_USED(a);
65 mp_digit r3;
66 #ifndef MPI_AMD64_ADD
67 mp_digit carry;
68 #endif
69 #ifdef ECL_THIRTY_TWO_BIT
70 mp_digit a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
71 mp_digit r0a, r0b, r1a, r1b, r2a, r2b;
72 #else
73 mp_digit a5 = 0, a4 = 0, a3 = 0;
74 mp_digit r0, r1, r2;
75 #endif
76
77 /* reduction not needed if a is not larger than field size */
78 if (a_used < ECP192_DIGITS) {
79 if (a == r) {
80 return MP_OKAY;
81 }
82 return mp_copy(a, r);
83 }
84
85 /* for polynomials larger than twice the field size, use regular
86 * reduction */
87 if (a_used > ECP192_DIGITS*2) {
88 MP_CHECKOK(mp_mod(a, &meth->irr, r));
89 } else {
90 /* copy out upper words of a */
91
92 #ifdef ECL_THIRTY_TWO_BIT
93
94 /* in all the math below,
95 * nXb is most signifiant, nXa is least significant */
96 switch (a_used) {
97 case 12:
98 a5b = MP_DIGIT(a, 11);
99 case 11:
100 a5a = MP_DIGIT(a, 10);
101 case 10:
102 a4b = MP_DIGIT(a, 9);
103 case 9:
104 a4a = MP_DIGIT(a, 8);
105 case 8:
106 a3b = MP_DIGIT(a, 7);
107 case 7:
108 a3a = MP_DIGIT(a, 6);
109 }
110
111
112 r2b= MP_DIGIT(a, 5);
113 r2a= MP_DIGIT(a, 4);
114 r1b = MP_DIGIT(a, 3);
115 r1a = MP_DIGIT(a, 2);
116 r0b = MP_DIGIT(a, 1);
117 r0a = MP_DIGIT(a, 0);
118
119 /* implement r = (a2,a1,a0)+(a5,a5,a5)+(a4,a4,0)+(0,a3,a3) */
120 MP_ADD_CARRY(r0a, a3a, r0a, 0, carry);
121 MP_ADD_CARRY(r0b, a3b, r0b, carry, carry);
122 MP_ADD_CARRY(r1a, a3a, r1a, carry, carry);
123 MP_ADD_CARRY(r1b, a3b, r1b, carry, carry);
124 MP_ADD_CARRY(r2a, a4a, r2a, carry, carry);
125 MP_ADD_CARRY(r2b, a4b, r2b, carry, carry);
126 r3 = carry; carry = 0;
127 MP_ADD_CARRY(r0a, a5a, r0a, 0, carry);
128 MP_ADD_CARRY(r0b, a5b, r0b, carry, carry);
129 MP_ADD_CARRY(r1a, a5a, r1a, carry, carry);
130 MP_ADD_CARRY(r1b, a5b, r1b, carry, carry);
131 MP_ADD_CARRY(r2a, a5a, r2a, carry, carry);
132 MP_ADD_CARRY(r2b, a5b, r2b, carry, carry);
133 r3 += carry;
134 MP_ADD_CARRY(r1a, a4a, r1a, 0, carry);
135 MP_ADD_CARRY(r1b, a4b, r1b, carry, carry);
136 MP_ADD_CARRY(r2a, 0, r2a, carry, carry);
137 MP_ADD_CARRY(r2b, 0, r2b, carry, carry);
138 r3 += carry;
139
140 /* reduce out the carry */
141 while (r3) {
142 MP_ADD_CARRY(r0a, r3, r0a, 0, carry);
143 MP_ADD_CARRY(r0b, 0, r0b, carry, carry);
144 MP_ADD_CARRY(r1a, r3, r1a, carry, carry);
145 MP_ADD_CARRY(r1b, 0, r1b, carry, carry);
146 MP_ADD_CARRY(r2a, 0, r2a, carry, carry);
147 MP_ADD_CARRY(r2b, 0, r2b, carry, carry);
148 r3 = carry;
149 }
150
151 /* check for final reduction */
152 /*
153 * our field is 0xffffffffffffffff, 0xfffffffffffffffe,
154 * 0xffffffffffffffff. That means we can only be over and need
155 * one more reduction
156 * if r2 == 0xffffffffffffffffff (same as r2+1 == 0)
157 * and
158 * r1 == 0xffffffffffffffffff or
159 * r1 == 0xfffffffffffffffffe and r0 = 0xfffffffffffffffff
160 * In all cases, we subtract the field (or add the 2's
161 * complement value (1,1,0)). (r0, r1, r2)
162 */
163 if (((r2b == 0xffffffff) && (r2a == 0xffffffff)
164 && (r1b == 0xffffffff) ) &&
165 ((r1a == 0xffffffff) ||
166 (r1a == 0xfffffffe) && (r0a == 0xffffffff) &&
167 (r0b == 0xffffffff)) ) {
168 /* do a quick subtract */
169 MP_ADD_CARRY(r0a, 1, r0a, 0, carry);
170 r0b += carry;
171 r1a = r1b = r2a = r2b = 0;
172 }
173
174 /* set the lower words of r */
175 if (a != r) {
176 MP_CHECKOK(s_mp_pad(r, 6));
177 }
178 MP_DIGIT(r, 5) = r2b;
179 MP_DIGIT(r, 4) = r2a;
180 MP_DIGIT(r, 3) = r1b;
181 MP_DIGIT(r, 2) = r1a;
182 MP_DIGIT(r, 1) = r0b;
183 MP_DIGIT(r, 0) = r0a;
184 MP_USED(r) = 6;
185 #else
186 switch (a_used) {
187 case 6:
188 a5 = MP_DIGIT(a, 5);
189 case 5:
190 a4 = MP_DIGIT(a, 4);
191 case 4:
192 a3 = MP_DIGIT(a, 3);
193 }
194
195 r2 = MP_DIGIT(a, 2);
196 r1 = MP_DIGIT(a, 1);
197 r0 = MP_DIGIT(a, 0);
198
199 /* implement r = (a2,a1,a0)+(a5,a5,a5)+(a4,a4,0)+(0,a3,a3) */
200 #ifndef MPI_AMD64_ADD
201 MP_ADD_CARRY(r0, a3, r0, 0, carry);
202 MP_ADD_CARRY(r1, a3, r1, carry, carry);
203 MP_ADD_CARRY(r2, a4, r2, carry, carry);
204 r3 = carry;
205 MP_ADD_CARRY(r0, a5, r0, 0, carry);
206 MP_ADD_CARRY(r1, a5, r1, carry, carry);
207 MP_ADD_CARRY(r2, a5, r2, carry, carry);
208 r3 += carry;
209 MP_ADD_CARRY(r1, a4, r1, 0, carry);
210 MP_ADD_CARRY(r2, 0, r2, carry, carry);
211 r3 += carry;
212
213 #else
214 r2 = MP_DIGIT(a, 2);
215 r1 = MP_DIGIT(a, 1);
216 r0 = MP_DIGIT(a, 0);
217
218 /* set the lower words of r */
219 __asm__ (
220 "xorq %3,%3 \n\t"
221 "addq %4,%0 \n\t"
222 "adcq %4,%1 \n\t"
223 "adcq %5,%2 \n\t"
224 "adcq $0,%3 \n\t"
225 "addq %6,%0 \n\t"
226 "adcq %6,%1 \n\t"
227 "adcq %6,%2 \n\t"
228 "adcq $0,%3 \n\t"
229 "addq %5,%1 \n\t"
230 "adcq $0,%2 \n\t"
231 "adcq $0,%3 \n\t"
232 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(a3),
233 "=r"(a4), "=r"(a5)
234 : "0" (r0), "1" (r1), "2" (r2), "3" (r3),
235 "4" (a3), "5" (a4), "6"(a5)
236 : "%cc" );
237 #endif
238
239 /* reduce out the carry */
240 while (r3) {
241 #ifndef MPI_AMD64_ADD
242 MP_ADD_CARRY(r0, r3, r0, 0, carry);
243 MP_ADD_CARRY(r1, r3, r1, carry, carry);
244 MP_ADD_CARRY(r2, 0, r2, carry, carry);
245 r3 = carry;
246 #else
247 a3=r3;
248 __asm__ (
249 "xorq %3,%3 \n\t"
250 "addq %4,%0 \n\t"
251 "adcq %4,%1 \n\t"
252 "adcq $0,%2 \n\t"
253 "adcq $0,%3 \n\t"
254 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(a3)
255 : "0" (r0), "1" (r1), "2" (r2), "3" (r3), "4"(a3)
256 : "%cc" );
257 #endif
258 }
259
260 /* check for final reduction */
261 /*
262 * our field is 0xffffffffffffffff, 0xfffffffffffffffe,
263 * 0xffffffffffffffff. That means we can only be over and need
264 * one more reduction
265 * if r2 == 0xffffffffffffffffff (same as r2+1 == 0)
266 * and
267 * r1 == 0xffffffffffffffffff or
268 * r1 == 0xfffffffffffffffffe and r0 = 0xfffffffffffffffff
269 * In all cases, we subtract the field (or add the 2's
270 * complement value (1,1,0)). (r0, r1, r2)
271 */
272 if (r3 || ((r2 == MP_DIGIT_MAX) &&
273 ((r1 == MP_DIGIT_MAX) ||
274 ((r1 == (MP_DIGIT_MAX-1)) && (r0 == MP_DIGIT_MAX))))) {
275 /* do a quick subtract */
276 r0++;
277 r1 = r2 = 0;
278 }
279 /* set the lower words of r */
280 if (a != r) {
281 MP_CHECKOK(s_mp_pad(r, 3));
282 }
283 MP_DIGIT(r, 2) = r2;
284 MP_DIGIT(r, 1) = r1;
285 MP_DIGIT(r, 0) = r0;
286 MP_USED(r) = 3;
287 #endif
288 }
289
290 CLEANUP:
291 return res;
292 }
293
294 #ifndef ECL_THIRTY_TWO_BIT
295 /* Compute the sum of 192 bit curves. Do the work in-line since the
296 * number of words are so small, we don't want to overhead of mp function
297 * calls. Uses optimized modular reduction for p192.
298 */
299 mp_err
ec_GFp_nistp192_add(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)300 ec_GFp_nistp192_add(const mp_int *a, const mp_int *b, mp_int *r,
301 const GFMethod *meth)
302 {
303 mp_err res = MP_OKAY;
304 mp_digit a0 = 0, a1 = 0, a2 = 0;
305 mp_digit r0 = 0, r1 = 0, r2 = 0;
306 mp_digit carry;
307
308 switch(MP_USED(a)) {
309 case 3:
310 a2 = MP_DIGIT(a,2);
311 case 2:
312 a1 = MP_DIGIT(a,1);
313 case 1:
314 a0 = MP_DIGIT(a,0);
315 }
316 switch(MP_USED(b)) {
317 case 3:
318 r2 = MP_DIGIT(b,2);
319 case 2:
320 r1 = MP_DIGIT(b,1);
321 case 1:
322 r0 = MP_DIGIT(b,0);
323 }
324
325 #ifndef MPI_AMD64_ADD
326 MP_ADD_CARRY(a0, r0, r0, 0, carry);
327 MP_ADD_CARRY(a1, r1, r1, carry, carry);
328 MP_ADD_CARRY(a2, r2, r2, carry, carry);
329 #else
330 __asm__ (
331 "xorq %3,%3 \n\t"
332 "addq %4,%0 \n\t"
333 "adcq %5,%1 \n\t"
334 "adcq %6,%2 \n\t"
335 "adcq $0,%3 \n\t"
336 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(carry)
337 : "r" (a0), "r" (a1), "r" (a2), "0" (r0),
338 "1" (r1), "2" (r2)
339 : "%cc" );
340 #endif
341
342 /* Do quick 'subract' if we've gone over
343 * (add the 2's complement of the curve field) */
344 if (carry || ((r2 == MP_DIGIT_MAX) &&
345 ((r1 == MP_DIGIT_MAX) ||
346 ((r1 == (MP_DIGIT_MAX-1)) && (r0 == MP_DIGIT_MAX))))) {
347 #ifndef MPI_AMD64_ADD
348 MP_ADD_CARRY(r0, 1, r0, 0, carry);
349 MP_ADD_CARRY(r1, 1, r1, carry, carry);
350 MP_ADD_CARRY(r2, 0, r2, carry, carry);
351 #else
352 __asm__ (
353 "addq $1,%0 \n\t"
354 "adcq $1,%1 \n\t"
355 "adcq $0,%2 \n\t"
356 : "=r"(r0), "=r"(r1), "=r"(r2)
357 : "0" (r0), "1" (r1), "2" (r2)
358 : "%cc" );
359 #endif
360 }
361
362
363 MP_CHECKOK(s_mp_pad(r, 3));
364 MP_DIGIT(r, 2) = r2;
365 MP_DIGIT(r, 1) = r1;
366 MP_DIGIT(r, 0) = r0;
367 MP_SIGN(r) = MP_ZPOS;
368 MP_USED(r) = 3;
369 s_mp_clamp(r);
370
371
372 CLEANUP:
373 return res;
374 }
375
376 /* Compute the diff of 192 bit curves. Do the work in-line since the
377 * number of words are so small, we don't want to overhead of mp function
378 * calls. Uses optimized modular reduction for p192.
379 */
380 mp_err
ec_GFp_nistp192_sub(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)381 ec_GFp_nistp192_sub(const mp_int *a, const mp_int *b, mp_int *r,
382 const GFMethod *meth)
383 {
384 mp_err res = MP_OKAY;
385 mp_digit b0 = 0, b1 = 0, b2 = 0;
386 mp_digit r0 = 0, r1 = 0, r2 = 0;
387 mp_digit borrow;
388
389 switch(MP_USED(a)) {
390 case 3:
391 r2 = MP_DIGIT(a,2);
392 case 2:
393 r1 = MP_DIGIT(a,1);
394 case 1:
395 r0 = MP_DIGIT(a,0);
396 }
397
398 switch(MP_USED(b)) {
399 case 3:
400 b2 = MP_DIGIT(b,2);
401 case 2:
402 b1 = MP_DIGIT(b,1);
403 case 1:
404 b0 = MP_DIGIT(b,0);
405 }
406
407 #ifndef MPI_AMD64_ADD
408 MP_SUB_BORROW(r0, b0, r0, 0, borrow);
409 MP_SUB_BORROW(r1, b1, r1, borrow, borrow);
410 MP_SUB_BORROW(r2, b2, r2, borrow, borrow);
411 #else
412 __asm__ (
413 "xorq %3,%3 \n\t"
414 "subq %4,%0 \n\t"
415 "sbbq %5,%1 \n\t"
416 "sbbq %6,%2 \n\t"
417 "adcq $0,%3 \n\t"
418 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(borrow)
419 : "r" (b0), "r" (b1), "r" (b2), "0" (r0),
420 "1" (r1), "2" (r2)
421 : "%cc" );
422 #endif
423
424 /* Do quick 'add' if we've gone under 0
425 * (subtract the 2's complement of the curve field) */
426 if (borrow) {
427 #ifndef MPI_AMD64_ADD
428 MP_SUB_BORROW(r0, 1, r0, 0, borrow);
429 MP_SUB_BORROW(r1, 1, r1, borrow, borrow);
430 MP_SUB_BORROW(r2, 0, r2, borrow, borrow);
431 #else
432 __asm__ (
433 "subq $1,%0 \n\t"
434 "sbbq $1,%1 \n\t"
435 "sbbq $0,%2 \n\t"
436 : "=r"(r0), "=r"(r1), "=r"(r2)
437 : "0" (r0), "1" (r1), "2" (r2)
438 : "%cc" );
439 #endif
440 }
441
442 MP_CHECKOK(s_mp_pad(r, 3));
443 MP_DIGIT(r, 2) = r2;
444 MP_DIGIT(r, 1) = r1;
445 MP_DIGIT(r, 0) = r0;
446 MP_SIGN(r) = MP_ZPOS;
447 MP_USED(r) = 3;
448 s_mp_clamp(r);
449
450 CLEANUP:
451 return res;
452 }
453
454 #endif
455
456 /* Compute the square of polynomial a, reduce modulo p192. Store the
457 * result in r. r could be a. Uses optimized modular reduction for p192.
458 */
459 mp_err
ec_GFp_nistp192_sqr(const mp_int * a,mp_int * r,const GFMethod * meth)460 ec_GFp_nistp192_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
461 {
462 mp_err res = MP_OKAY;
463
464 MP_CHECKOK(mp_sqr(a, r));
465 MP_CHECKOK(ec_GFp_nistp192_mod(r, r, meth));
466 CLEANUP:
467 return res;
468 }
469
470 /* Compute the product of two polynomials a and b, reduce modulo p192.
471 * Store the result in r. r could be a or b; a could be b. Uses
472 * optimized modular reduction for p192. */
473 mp_err
ec_GFp_nistp192_mul(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)474 ec_GFp_nistp192_mul(const mp_int *a, const mp_int *b, mp_int *r,
475 const GFMethod *meth)
476 {
477 mp_err res = MP_OKAY;
478
479 MP_CHECKOK(mp_mul(a, b, r));
480 MP_CHECKOK(ec_GFp_nistp192_mod(r, r, meth));
481 CLEANUP:
482 return res;
483 }
484
485 /* Divides two field elements. If a is NULL, then returns the inverse of
486 * b. */
487 mp_err
ec_GFp_nistp192_div(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)488 ec_GFp_nistp192_div(const mp_int *a, const mp_int *b, mp_int *r,
489 const GFMethod *meth)
490 {
491 mp_err res = MP_OKAY;
492 mp_int t;
493
494 /* If a is NULL, then return the inverse of b, otherwise return a/b. */
495 if (a == NULL) {
496 return mp_invmod(b, &meth->irr, r);
497 } else {
498 /* MPI doesn't support divmod, so we implement it using invmod and
499 * mulmod. */
500 MP_CHECKOK(mp_init(&t, FLAG(b)));
501 MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
502 MP_CHECKOK(mp_mul(a, &t, r));
503 MP_CHECKOK(ec_GFp_nistp192_mod(r, r, meth));
504 CLEANUP:
505 mp_clear(&t);
506 return res;
507 }
508 }
509
510 /* Wire in fast field arithmetic and precomputation of base point for
511 * named curves. */
512 mp_err
ec_group_set_gfp192(ECGroup * group,ECCurveName name)513 ec_group_set_gfp192(ECGroup *group, ECCurveName name)
514 {
515 if (name == ECCurve_NIST_P192) {
516 group->meth->field_mod = &ec_GFp_nistp192_mod;
517 group->meth->field_mul = &ec_GFp_nistp192_mul;
518 group->meth->field_sqr = &ec_GFp_nistp192_sqr;
519 group->meth->field_div = &ec_GFp_nistp192_div;
520 #ifndef ECL_THIRTY_TWO_BIT
521 group->meth->field_add = &ec_GFp_nistp192_add;
522 group->meth->field_sub = &ec_GFp_nistp192_sub;
523 #endif
524 }
525 return MP_OKAY;
526 }
527