* Sync up to trunk head (r64921).
[reactos.git] / dll / win32 / rsaenh / mpi.c
1 /*
2 * dlls/rsaenh/mpi.c
3 * Multi Precision Integer functions
4 *
5 * Copyright 2004 Michael Jung
6 * Based on public domain code by Tom St Denis (tomstdenis@iahu.ca)
7 *
8 * This library is free software; you can redistribute it and/or
9 * modify it under the terms of the GNU Lesser General Public
10 * License as published by the Free Software Foundation; either
11 * version 2.1 of the License, or (at your option) any later version.
12 *
13 * This library is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
16 * Lesser General Public License for more details.
17 *
18 * You should have received a copy of the GNU Lesser General Public
19 * License along with this library; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
21 */
22
23 /*
24 * This file contains code from the LibTomCrypt cryptographic
25 * library written by Tom St Denis (tomstdenis@iahu.ca). LibTomCrypt
26 * is in the public domain. The code in this file is tailored to
27 * special requirements. Take a look at http://libtomcrypt.org for the
28 * original version.
29 */
30
31 #include <stdarg.h>
32
33 #include <windef.h>
34 #include <winbase.h>
35 #include "tomcrypt.h"
36
37 /* Known optimal configurations
38 CPU /Compiler /MUL CUTOFF/SQR CUTOFF
39 -------------------------------------------------------------
40 Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
41 */
42 static const int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */
43 KARATSUBA_SQR_CUTOFF = 128; /* Min. number of digits before Karatsuba squaring is used. */
44
45
46 /* trim unused digits */
47 static void mp_clamp(mp_int *a);
48
49 /* compare |a| to |b| */
50 static int mp_cmp_mag(const mp_int *a, const mp_int *b);
51
52 /* Counts the number of lsbs which are zero before the first zero bit */
53 static int mp_cnt_lsb(const mp_int *a);
54
55 /* computes a = B**n mod b without division or multiplication useful for
56 * normalizing numbers in a Montgomery system.
57 */
58 static int mp_montgomery_calc_normalization(mp_int *a, const mp_int *b);
59
60 /* computes x/R == x (mod N) via Montgomery Reduction */
61 static int mp_montgomery_reduce(mp_int *a, const mp_int *m, mp_digit mp);
62
63 /* setups the montgomery reduction */
64 static int mp_montgomery_setup(const mp_int *a, mp_digit *mp);
65
66 /* Barrett Reduction, computes a (mod b) with a precomputed value c
67 *
68 * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
69 * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
70 */
71 static int mp_reduce(mp_int *a, const mp_int *b, const mp_int *c);
72
73 /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
74 static int mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d);
75
76 /* determines k value for 2k reduction */
77 static int mp_reduce_2k_setup(const mp_int *a, mp_digit *d);
78
79 /* used to setup the Barrett reduction for a given modulus b */
80 static int mp_reduce_setup(mp_int *a, const mp_int *b);
81
82 /* set to a digit */
83 static void mp_set(mp_int *a, mp_digit b);
84
85 /* b = a*a */
86 static int mp_sqr(const mp_int *a, mp_int *b);
87
88 /* c = a * a (mod b) */
89 static int mp_sqrmod(const mp_int *a, mp_int *b, mp_int *c);
90
91
92 static void bn_reverse(unsigned char *s, int len);
93 static int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
94 static int s_mp_exptmod (const mp_int * G, const mp_int * X, mp_int * P, mp_int * Y);
95 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
96 static int s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs);
97 static int s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs);
98 static int s_mp_sqr(const mp_int *a, mp_int *b);
99 static int s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c);
100 static int mp_exptmod_fast(const mp_int *G, const mp_int *X, mp_int *P, mp_int *Y, int mode);
101 static int mp_invmod_slow (const mp_int * a, mp_int * b, mp_int * c);
102 static int mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c);
103 static int mp_karatsuba_sqr(const mp_int *a, mp_int *b);
104
105 /* grow as required */
106 static int mp_grow (mp_int * a, int size)
107 {
108 int i;
109 mp_digit *tmp;
110
111 /* if the alloc size is smaller alloc more ram */
112 if (a->alloc < size) {
113 /* ensure there are always at least MP_PREC digits extra on top */
114 size += (MP_PREC * 2) - (size % MP_PREC);
115
116 /* reallocate the array a->dp
117 *
118 * We store the return in a temporary variable
119 * in case the operation failed we don't want
120 * to overwrite the dp member of a.
121 */
122 tmp = HeapReAlloc(GetProcessHeap(), 0, a->dp, sizeof (mp_digit) * size);
123 if (tmp == NULL) {
124 /* reallocation failed but "a" is still valid [can be freed] */
125 return MP_MEM;
126 }
127
128 /* reallocation succeeded so set a->dp */
129 a->dp = tmp;
130
131 /* zero excess digits */
132 i = a->alloc;
133 a->alloc = size;
134 for (; i < a->alloc; i++) {
135 a->dp[i] = 0;
136 }
137 }
138 return MP_OKAY;
139 }
140
141 /* b = a/2 */
142 static int mp_div_2(const mp_int * a, mp_int * b)
143 {
144 int x, res, oldused;
145
146 /* copy */
147 if (b->alloc < a->used) {
148 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
149 return res;
150 }
151 }
152
153 oldused = b->used;
154 b->used = a->used;
155 {
156 register mp_digit r, rr, *tmpa, *tmpb;
157
158 /* source alias */
159 tmpa = a->dp + b->used - 1;
160
161 /* dest alias */
162 tmpb = b->dp + b->used - 1;
163
164 /* carry */
165 r = 0;
166 for (x = b->used - 1; x >= 0; x--) {
167 /* get the carry for the next iteration */
168 rr = *tmpa & 1;
169
170 /* shift the current digit, add in carry and store */
171 *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
172
173 /* forward carry to next iteration */
174 r = rr;
175 }
176
177 /* zero excess digits */
178 tmpb = b->dp + b->used;
179 for (x = b->used; x < oldused; x++) {
180 *tmpb++ = 0;
181 }
182 }
183 b->sign = a->sign;
184 mp_clamp (b);
185 return MP_OKAY;
186 }
187
188 /* swap the elements of two integers, for cases where you can't simply swap the
189 * mp_int pointers around
190 */
191 static void
192 mp_exch (mp_int * a, mp_int * b)
193 {
194 mp_int t;
195
196 t = *a;
197 *a = *b;
198 *b = t;
199 }
200
201 /* init a new mp_int */
202 static int mp_init (mp_int * a)
203 {
204 int i;
205
206 /* allocate memory required and clear it */
207 a->dp = HeapAlloc(GetProcessHeap(), 0, sizeof (mp_digit) * MP_PREC);
208 if (a->dp == NULL) {
209 return MP_MEM;
210 }
211
212 /* set the digits to zero */
213 for (i = 0; i < MP_PREC; i++) {
214 a->dp[i] = 0;
215 }
216
217 /* set the used to zero, allocated digits to the default precision
218 * and sign to positive */
219 a->used = 0;
220 a->alloc = MP_PREC;
221 a->sign = MP_ZPOS;
222
223 return MP_OKAY;
224 }
225
226 /* init an mp_init for a given size */
227 static int mp_init_size (mp_int * a, int size)
228 {
229 int x;
230
231 /* pad size so there are always extra digits */
232 size += (MP_PREC * 2) - (size % MP_PREC);
233
234 /* alloc mem */
235 a->dp = HeapAlloc(GetProcessHeap(), 0, sizeof (mp_digit) * size);
236 if (a->dp == NULL) {
237 return MP_MEM;
238 }
239
240 /* set the members */
241 a->used = 0;
242 a->alloc = size;
243 a->sign = MP_ZPOS;
244
245 /* zero the digits */
246 for (x = 0; x < size; x++) {
247 a->dp[x] = 0;
248 }
249
250 return MP_OKAY;
251 }
252
253 /* clear one (frees) */
254 static void
255 mp_clear (mp_int * a)
256 {
257 int i;
258
259 /* only do anything if a hasn't been freed previously */
260 if (a->dp != NULL) {
261 /* first zero the digits */
262 for (i = 0; i < a->used; i++) {
263 a->dp[i] = 0;
264 }
265
266 /* free ram */
267 HeapFree(GetProcessHeap(), 0, a->dp);
268
269 /* reset members to make debugging easier */
270 a->dp = NULL;
271 a->alloc = a->used = 0;
272 a->sign = MP_ZPOS;
273 }
274 }
275
276 /* set to zero */
277 static void
278 mp_zero (mp_int * a)
279 {
280 a->sign = MP_ZPOS;
281 a->used = 0;
282 memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
283 }
284
285 /* b = |a|
286 *
287 * Simple function copies the input and fixes the sign to positive
288 */
289 static int
290 mp_abs (const mp_int * a, mp_int * b)
291 {
292 int res;
293
294 /* copy a to b */
295 if (a != b) {
296 if ((res = mp_copy (a, b)) != MP_OKAY) {
297 return res;
298 }
299 }
300
301 /* force the sign of b to positive */
302 b->sign = MP_ZPOS;
303
304 return MP_OKAY;
305 }
306
307 /* computes the modular inverse via binary extended euclidean algorithm,
308 * that is c = 1/a mod b
309 *
310 * Based on slow invmod except this is optimized for the case where b is
311 * odd as per HAC Note 14.64 on pp. 610
312 */
313 static int
314 fast_mp_invmod (const mp_int * a, mp_int * b, mp_int * c)
315 {
316 mp_int x, y, u, v, B, D;
317 int res, neg;
318
319 /* 2. [modified] b must be odd */
320 if (mp_iseven (b) == 1) {
321 return MP_VAL;
322 }
323
324 /* init all our temps */
325 if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
326 return res;
327 }
328
329 /* x == modulus, y == value to invert */
330 if ((res = mp_copy (b, &x)) != MP_OKAY) {
331 goto __ERR;
332 }
333
334 /* we need y = |a| */
335 if ((res = mp_abs (a, &y)) != MP_OKAY) {
336 goto __ERR;
337 }
338
339 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
340 if ((res = mp_copy (&x, &u)) != MP_OKAY) {
341 goto __ERR;
342 }
343 if ((res = mp_copy (&y, &v)) != MP_OKAY) {
344 goto __ERR;
345 }
346 mp_set (&D, 1);
347
348 top:
349 /* 4. while u is even do */
350 while (mp_iseven (&u) == 1) {
351 /* 4.1 u = u/2 */
352 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
353 goto __ERR;
354 }
355 /* 4.2 if B is odd then */
356 if (mp_isodd (&B) == 1) {
357 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
358 goto __ERR;
359 }
360 }
361 /* B = B/2 */
362 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
363 goto __ERR;
364 }
365 }
366
367 /* 5. while v is even do */
368 while (mp_iseven (&v) == 1) {
369 /* 5.1 v = v/2 */
370 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
371 goto __ERR;
372 }
373 /* 5.2 if D is odd then */
374 if (mp_isodd (&D) == 1) {
375 /* D = (D-x)/2 */
376 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
377 goto __ERR;
378 }
379 }
380 /* D = D/2 */
381 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
382 goto __ERR;
383 }
384 }
385
386 /* 6. if u >= v then */
387 if (mp_cmp (&u, &v) != MP_LT) {
388 /* u = u - v, B = B - D */
389 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
390 goto __ERR;
391 }
392
393 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
394 goto __ERR;
395 }
396 } else {
397 /* v - v - u, D = D - B */
398 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
399 goto __ERR;
400 }
401
402 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
403 goto __ERR;
404 }
405 }
406
407 /* if not zero goto step 4 */
408 if (mp_iszero (&u) == 0) {
409 goto top;
410 }
411
412 /* now a = C, b = D, gcd == g*v */
413
414 /* if v != 1 then there is no inverse */
415 if (mp_cmp_d (&v, 1) != MP_EQ) {
416 res = MP_VAL;
417 goto __ERR;
418 }
419
420 /* b is now the inverse */
421 neg = a->sign;
422 while (D.sign == MP_NEG) {
423 if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
424 goto __ERR;
425 }
426 }
427 mp_exch (&D, c);
428 c->sign = neg;
429 res = MP_OKAY;
430
431 __ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
432 return res;
433 }
434
435 /* computes xR**-1 == x (mod N) via Montgomery Reduction
436 *
437 * This is an optimized implementation of montgomery_reduce
438 * which uses the comba method to quickly calculate the columns of the
439 * reduction.
440 *
441 * Based on Algorithm 14.32 on pp.601 of HAC.
442 */
443 static int
444 fast_mp_montgomery_reduce (mp_int * x, const mp_int * n, mp_digit rho)
445 {
446 int ix, res, olduse;
447 mp_word W[MP_WARRAY];
448
449 /* get old used count */
450 olduse = x->used;
451
452 /* grow a as required */
453 if (x->alloc < n->used + 1) {
454 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
455 return res;
456 }
457 }
458
459 /* first we have to get the digits of the input into
460 * an array of double precision words W[...]
461 */
462 {
463 register mp_word *_W;
464 register mp_digit *tmpx;
465
466 /* alias for the W[] array */
467 _W = W;
468
469 /* alias for the digits of x*/
470 tmpx = x->dp;
471
472 /* copy the digits of a into W[0..a->used-1] */
473 for (ix = 0; ix < x->used; ix++) {
474 *_W++ = *tmpx++;
475 }
476
477 /* zero the high words of W[a->used..m->used*2] */
478 for (; ix < n->used * 2 + 1; ix++) {
479 *_W++ = 0;
480 }
481 }
482
483 /* now we proceed to zero successive digits
484 * from the least significant upwards
485 */
486 for (ix = 0; ix < n->used; ix++) {
487 /* mu = ai * m' mod b
488 *
489 * We avoid a double precision multiplication (which isn't required)
490 * by casting the value down to a mp_digit. Note this requires
491 * that W[ix-1] have the carry cleared (see after the inner loop)
492 */
493 register mp_digit mu;
494 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
495
496 /* a = a + mu * m * b**i
497 *
498 * This is computed in place and on the fly. The multiplication
499 * by b**i is handled by offsetting which columns the results
500 * are added to.
501 *
502 * Note the comba method normally doesn't handle carries in the
503 * inner loop In this case we fix the carry from the previous
504 * column since the Montgomery reduction requires digits of the
505 * result (so far) [see above] to work. This is
506 * handled by fixing up one carry after the inner loop. The
507 * carry fixups are done in order so after these loops the
508 * first m->used words of W[] have the carries fixed
509 */
510 {
511 register int iy;
512 register mp_digit *tmpn;
513 register mp_word *_W;
514
515 /* alias for the digits of the modulus */
516 tmpn = n->dp;
517
518 /* Alias for the columns set by an offset of ix */
519 _W = W + ix;
520
521 /* inner loop */
522 for (iy = 0; iy < n->used; iy++) {
523 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
524 }
525 }
526
527 /* now fix carry for next digit, W[ix+1] */
528 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
529 }
530
531 /* now we have to propagate the carries and
532 * shift the words downward [all those least
533 * significant digits we zeroed].
534 */
535 {
536 register mp_digit *tmpx;
537 register mp_word *_W, *_W1;
538
539 /* nox fix rest of carries */
540
541 /* alias for current word */
542 _W1 = W + ix;
543
544 /* alias for next word, where the carry goes */
545 _W = W + ++ix;
546
547 for (; ix <= n->used * 2 + 1; ix++) {
548 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
549 }
550
551 /* copy out, A = A/b**n
552 *
553 * The result is A/b**n but instead of converting from an
554 * array of mp_word to mp_digit than calling mp_rshd
555 * we just copy them in the right order
556 */
557
558 /* alias for destination word */
559 tmpx = x->dp;
560
561 /* alias for shifted double precision result */
562 _W = W + n->used;
563
564 for (ix = 0; ix < n->used + 1; ix++) {
565 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
566 }
567
568 /* zero oldused digits, if the input a was larger than
569 * m->used+1 we'll have to clear the digits
570 */
571 for (; ix < olduse; ix++) {
572 *tmpx++ = 0;
573 }
574 }
575
576 /* set the max used and clamp */
577 x->used = n->used + 1;
578 mp_clamp (x);
579
580 /* if A >= m then A = A - m */
581 if (mp_cmp_mag (x, n) != MP_LT) {
582 return s_mp_sub (x, n, x);
583 }
584 return MP_OKAY;
585 }
586
587 /* Fast (comba) multiplier
588 *
589 * This is the fast column-array [comba] multiplier. It is
590 * designed to compute the columns of the product first
591 * then handle the carries afterwards. This has the effect
592 * of making the nested loops that compute the columns very
593 * simple and schedulable on super-scalar processors.
594 *
595 * This has been modified to produce a variable number of
596 * digits of output so if say only a half-product is required
597 * you don't have to compute the upper half (a feature
598 * required for fast Barrett reduction).
599 *
600 * Based on Algorithm 14.12 on pp.595 of HAC.
601 *
602 */
603 static int
604 fast_s_mp_mul_digs (const mp_int * a, const mp_int * b, mp_int * c, int digs)
605 {
606 int olduse, res, pa, ix, iz;
607 mp_digit W[MP_WARRAY];
608 register mp_word _W;
609
610 /* grow the destination as required */
611 if (c->alloc < digs) {
612 if ((res = mp_grow (c, digs)) != MP_OKAY) {
613 return res;
614 }
615 }
616
617 /* number of output digits to produce */
618 pa = MIN(digs, a->used + b->used);
619
620 /* clear the carry */
621 _W = 0;
622 for (ix = 0; ix <= pa; ix++) {
623 int tx, ty;
624 int iy;
625 mp_digit *tmpx, *tmpy;
626
627 /* get offsets into the two bignums */
628 ty = MIN(b->used-1, ix);
629 tx = ix - ty;
630
631 /* setup temp aliases */
632 tmpx = a->dp + tx;
633 tmpy = b->dp + ty;
634
635 /* This is the number of times the loop will iterate, essentially it's
636 while (tx++ < a->used && ty-- >= 0) { ... }
637 */
638 iy = MIN(a->used-tx, ty+1);
639
640 /* execute loop */
641 for (iz = 0; iz < iy; ++iz) {
642 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
643 }
644
645 /* store term */
646 W[ix] = ((mp_digit)_W) & MP_MASK;
647
648 /* make next carry */
649 _W = _W >> ((mp_word)DIGIT_BIT);
650 }
651
652 /* setup dest */
653 olduse = c->used;
654 c->used = digs;
655
656 {
657 register mp_digit *tmpc;
658 tmpc = c->dp;
659 for (ix = 0; ix < digs; ix++) {
660 /* now extract the previous digit [below the carry] */
661 *tmpc++ = W[ix];
662 }
663
664 /* clear unused digits [that existed in the old copy of c] */
665 for (; ix < olduse; ix++) {
666 *tmpc++ = 0;
667 }
668 }
669 mp_clamp (c);
670 return MP_OKAY;
671 }
672
673 /* this is a modified version of fast_s_mul_digs that only produces
674 * output digits *above* digs. See the comments for fast_s_mul_digs
675 * to see how it works.
676 *
677 * This is used in the Barrett reduction since for one of the multiplications
678 * only the higher digits were needed. This essentially halves the work.
679 *
680 * Based on Algorithm 14.12 on pp.595 of HAC.
681 */
682 static int
683 fast_s_mp_mul_high_digs (const mp_int * a, const mp_int * b, mp_int * c, int digs)
684 {
685 int olduse, res, pa, ix, iz;
686 mp_digit W[MP_WARRAY];
687 mp_word _W;
688
689 /* grow the destination as required */
690 pa = a->used + b->used;
691 if (c->alloc < pa) {
692 if ((res = mp_grow (c, pa)) != MP_OKAY) {
693 return res;
694 }
695 }
696
697 /* number of output digits to produce */
698 pa = a->used + b->used;
699 _W = 0;
700 for (ix = digs; ix <= pa; ix++) {
701 int tx, ty, iy;
702 mp_digit *tmpx, *tmpy;
703
704 /* get offsets into the two bignums */
705 ty = MIN(b->used-1, ix);
706 tx = ix - ty;
707
708 /* setup temp aliases */
709 tmpx = a->dp + tx;
710 tmpy = b->dp + ty;
711
712 /* This is the number of times the loop will iterate, essentially it's
713 while (tx++ < a->used && ty-- >= 0) { ... }
714 */
715 iy = MIN(a->used-tx, ty+1);
716
717 /* execute loop */
718 for (iz = 0; iz < iy; iz++) {
719 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
720 }
721
722 /* store term */
723 W[ix] = ((mp_digit)_W) & MP_MASK;
724
725 /* make next carry */
726 _W = _W >> ((mp_word)DIGIT_BIT);
727 }
728
729 /* setup dest */
730 olduse = c->used;
731 c->used = pa;
732
733 {
734 register mp_digit *tmpc;
735
736 tmpc = c->dp + digs;
737 for (ix = digs; ix <= pa; ix++) {
738 /* now extract the previous digit [below the carry] */
739 *tmpc++ = W[ix];
740 }
741
742 /* clear unused digits [that existed in the old copy of c] */
743 for (; ix < olduse; ix++) {
744 *tmpc++ = 0;
745 }
746 }
747 mp_clamp (c);
748 return MP_OKAY;
749 }
750
751 /* fast squaring
752 *
753 * This is the comba method where the columns of the product
754 * are computed first then the carries are computed. This
755 * has the effect of making a very simple inner loop that
756 * is executed the most
757 *
758 * W2 represents the outer products and W the inner.
759 *
760 * A further optimizations is made because the inner
761 * products are of the form "A * B * 2". The *2 part does
762 * not need to be computed until the end which is good
763 * because 64-bit shifts are slow!
764 *
765 * Based on Algorithm 14.16 on pp.597 of HAC.
766 *
767 */
768 /* the jist of squaring...
769
770 you do like mult except the offset of the tmpx [one that starts closer to zero]
771 can't equal the offset of tmpy. So basically you set up iy like before then you min it with
772 (ty-tx) so that it never happens. You double all those you add in the inner loop
773
774 After that loop you do the squares and add them in.
775
776 Remove W2 and don't memset W
777
778 */
779
780 static int fast_s_mp_sqr (const mp_int * a, mp_int * b)
781 {
782 int olduse, res, pa, ix, iz;
783 mp_digit W[MP_WARRAY], *tmpx;
784 mp_word W1;
785
786 /* grow the destination as required */
787 pa = a->used + a->used;
788 if (b->alloc < pa) {
789 if ((res = mp_grow (b, pa)) != MP_OKAY) {
790 return res;
791 }
792 }
793
794 /* number of output digits to produce */
795 W1 = 0;
796 for (ix = 0; ix <= pa; ix++) {
797 int tx, ty, iy;
798 mp_word _W;
799 mp_digit *tmpy;
800
801 /* clear counter */
802 _W = 0;
803
804 /* get offsets into the two bignums */
805 ty = MIN(a->used-1, ix);
806 tx = ix - ty;
807
808 /* setup temp aliases */
809 tmpx = a->dp + tx;
810 tmpy = a->dp + ty;
811
812 /* This is the number of times the loop will iterate, essentially it's
813 while (tx++ < a->used && ty-- >= 0) { ... }
814 */
815 iy = MIN(a->used-tx, ty+1);
816
817 /* now for squaring tx can never equal ty
818 * we halve the distance since they approach at a rate of 2x
819 * and we have to round because odd cases need to be executed
820 */
821 iy = MIN(iy, (ty-tx+1)>>1);
822
823 /* execute loop */
824 for (iz = 0; iz < iy; iz++) {
825 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
826 }
827
828 /* double the inner product and add carry */
829 _W = _W + _W + W1;
830
831 /* even columns have the square term in them */
832 if ((ix&1) == 0) {
833 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
834 }
835
836 /* store it */
837 W[ix] = _W;
838
839 /* make next carry */
840 W1 = _W >> ((mp_word)DIGIT_BIT);
841 }
842
843 /* setup dest */
844 olduse = b->used;
845 b->used = a->used+a->used;
846
847 {
848 mp_digit *tmpb;
849 tmpb = b->dp;
850 for (ix = 0; ix < pa; ix++) {
851 *tmpb++ = W[ix] & MP_MASK;
852 }
853
854 /* clear unused digits [that existed in the old copy of c] */
855 for (; ix < olduse; ix++) {
856 *tmpb++ = 0;
857 }
858 }
859 mp_clamp (b);
860 return MP_OKAY;
861 }
862
863 /* computes a = 2**b
864 *
865 * Simple algorithm which zeroes the int, grows it then just sets one bit
866 * as required.
867 */
868 static int
869 mp_2expt (mp_int * a, int b)
870 {
871 int res;
872
873 /* zero a as per default */
874 mp_zero (a);
875
876 /* grow a to accommodate the single bit */
877 if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
878 return res;
879 }
880
881 /* set the used count of where the bit will go */
882 a->used = b / DIGIT_BIT + 1;
883
884 /* put the single bit in its place */
885 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
886
887 return MP_OKAY;
888 }
889
890 /* high level addition (handles signs) */
891 int mp_add (mp_int * a, mp_int * b, mp_int * c)
892 {
893 int sa, sb, res;
894
895 /* get sign of both inputs */
896 sa = a->sign;
897 sb = b->sign;
898
899 /* handle two cases, not four */
900 if (sa == sb) {
901 /* both positive or both negative */
902 /* add their magnitudes, copy the sign */
903 c->sign = sa;
904 res = s_mp_add (a, b, c);
905 } else {
906 /* one positive, the other negative */
907 /* subtract the one with the greater magnitude from */
908 /* the one of the lesser magnitude. The result gets */
909 /* the sign of the one with the greater magnitude. */
910 if (mp_cmp_mag (a, b) == MP_LT) {
911 c->sign = sb;
912 res = s_mp_sub (b, a, c);
913 } else {
914 c->sign = sa;
915 res = s_mp_sub (a, b, c);
916 }
917 }
918 return res;
919 }
920
921
922 /* single digit addition */
923 static int
924 mp_add_d (mp_int * a, mp_digit b, mp_int * c)
925 {
926 int res, ix, oldused;
927 mp_digit *tmpa, *tmpc, mu;
928
929 /* grow c as required */
930 if (c->alloc < a->used + 1) {
931 if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
932 return res;
933 }
934 }
935
936 /* if a is negative and |a| >= b, call c = |a| - b */
937 if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
938 /* temporarily fix sign of a */
939 a->sign = MP_ZPOS;
940
941 /* c = |a| - b */
942 res = mp_sub_d(a, b, c);
943
944 /* fix sign */
945 a->sign = c->sign = MP_NEG;
946
947 return res;
948 }
949
950 /* old number of used digits in c */
951 oldused = c->used;
952
953 /* sign always positive */
954 c->sign = MP_ZPOS;
955
956 /* source alias */
957 tmpa = a->dp;
958
959 /* destination alias */
960 tmpc = c->dp;
961
962 /* if a is positive */
963 if (a->sign == MP_ZPOS) {
964 /* add digit, after this we're propagating
965 * the carry.
966 */
967 *tmpc = *tmpa++ + b;
968 mu = *tmpc >> DIGIT_BIT;
969 *tmpc++ &= MP_MASK;
970
971 /* now handle rest of the digits */
972 for (ix = 1; ix < a->used; ix++) {
973 *tmpc = *tmpa++ + mu;
974 mu = *tmpc >> DIGIT_BIT;
975 *tmpc++ &= MP_MASK;
976 }
977 /* set final carry */
978 ix++;
979 *tmpc++ = mu;
980
981 /* setup size */
982 c->used = a->used + 1;
983 } else {
984 /* a was negative and |a| < b */
985 c->used = 1;
986
987 /* the result is a single digit */
988 if (a->used == 1) {
989 *tmpc++ = b - a->dp[0];
990 } else {
991 *tmpc++ = b;
992 }
993
994 /* setup count so the clearing of oldused
995 * can fall through correctly
996 */
997 ix = 1;
998 }
999
1000 /* now zero to oldused */
1001 while (ix++ < oldused) {
1002 *tmpc++ = 0;
1003 }
1004 mp_clamp(c);
1005
1006 return MP_OKAY;
1007 }
1008
1009 /* trim unused digits
1010 *
1011 * This is used to ensure that leading zero digits are
1012 * trimed and the leading "used" digit will be non-zero
1013 * Typically very fast. Also fixes the sign if there
1014 * are no more leading digits
1015 */
1016 void
1017 mp_clamp (mp_int * a)
1018 {
1019 /* decrease used while the most significant digit is
1020 * zero.
1021 */
1022 while (a->used > 0 && a->dp[a->used - 1] == 0) {
1023 --(a->used);
1024 }
1025
1026 /* reset the sign flag if used == 0 */
1027 if (a->used == 0) {
1028 a->sign = MP_ZPOS;
1029 }
1030 }
1031
1032 void mp_clear_multi(mp_int *mp, ...)
1033 {
1034 mp_int* next_mp = mp;
1035 va_list args;
1036 va_start(args, mp);
1037 while (next_mp != NULL) {
1038 mp_clear(next_mp);
1039 next_mp = va_arg(args, mp_int*);
1040 }
1041 va_end(args);
1042 }
1043
1044 /* compare two ints (signed)*/
1045 int
1046 mp_cmp (const mp_int * a, const mp_int * b)
1047 {
1048 /* compare based on sign */
1049 if (a->sign != b->sign) {
1050 if (a->sign == MP_NEG) {
1051 return MP_LT;
1052 } else {
1053 return MP_GT;
1054 }
1055 }
1056
1057 /* compare digits */
1058 if (a->sign == MP_NEG) {
1059 /* if negative compare opposite direction */
1060 return mp_cmp_mag(b, a);
1061 } else {
1062 return mp_cmp_mag(a, b);
1063 }
1064 }
1065
1066 /* compare a digit */
1067 int mp_cmp_d(const mp_int * a, mp_digit b)
1068 {
1069 /* compare based on sign */
1070 if (a->sign == MP_NEG) {
1071 return MP_LT;
1072 }
1073
1074 /* compare based on magnitude */
1075 if (a->used > 1) {
1076 return MP_GT;
1077 }
1078
1079 /* compare the only digit of a to b */
1080 if (a->dp[0] > b) {
1081 return MP_GT;
1082 } else if (a->dp[0] < b) {
1083 return MP_LT;
1084 } else {
1085 return MP_EQ;
1086 }
1087 }
1088
1089 /* compare maginitude of two ints (unsigned) */
1090 int mp_cmp_mag (const mp_int * a, const mp_int * b)
1091 {
1092 int n;
1093 mp_digit *tmpa, *tmpb;
1094
1095 /* compare based on # of non-zero digits */
1096 if (a->used > b->used) {
1097 return MP_GT;
1098 }
1099
1100 if (a->used < b->used) {
1101 return MP_LT;
1102 }
1103
1104 /* alias for a */
1105 tmpa = a->dp + (a->used - 1);
1106
1107 /* alias for b */
1108 tmpb = b->dp + (a->used - 1);
1109
1110 /* compare based on digits */
1111 for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
1112 if (*tmpa > *tmpb) {
1113 return MP_GT;
1114 }
1115
1116 if (*tmpa < *tmpb) {
1117 return MP_LT;
1118 }
1119 }
1120 return MP_EQ;
1121 }
1122
1123 static const int lnz[16] = {
1124 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
1125 };
1126
1127 /* Counts the number of lsbs which are zero before the first zero bit */
1128 int mp_cnt_lsb(const mp_int *a)
1129 {
1130 int x;
1131 mp_digit q, qq;
1132
1133 /* easy out */
1134 if (mp_iszero(a) == 1) {
1135 return 0;
1136 }
1137
1138 /* scan lower digits until non-zero */
1139 for (x = 0; x < a->used && a->dp[x] == 0; x++);
1140 q = a->dp[x];
1141 x *= DIGIT_BIT;
1142
1143 /* now scan this digit until a 1 is found */
1144 if ((q & 1) == 0) {
1145 do {
1146 qq = q & 15;
1147 x += lnz[qq];
1148 q >>= 4;
1149 } while (qq == 0);
1150 }
1151 return x;
1152 }
1153
1154 /* copy, b = a */
1155 int
1156 mp_copy (const mp_int * a, mp_int * b)
1157 {
1158 int res, n;
1159
1160 /* if dst == src do nothing */
1161 if (a == b) {
1162 return MP_OKAY;
1163 }
1164
1165 /* grow dest */
1166 if (b->alloc < a->used) {
1167 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
1168 return res;
1169 }
1170 }
1171
1172 /* zero b and copy the parameters over */
1173 {
1174 register mp_digit *tmpa, *tmpb;
1175
1176 /* pointer aliases */
1177
1178 /* source */
1179 tmpa = a->dp;
1180
1181 /* destination */
1182 tmpb = b->dp;
1183
1184 /* copy all the digits */
1185 for (n = 0; n < a->used; n++) {
1186 *tmpb++ = *tmpa++;
1187 }
1188
1189 /* clear high digits */
1190 for (; n < b->used; n++) {
1191 *tmpb++ = 0;
1192 }
1193 }
1194
1195 /* copy used count and sign */
1196 b->used = a->used;
1197 b->sign = a->sign;
1198 return MP_OKAY;
1199 }
1200
1201 /* returns the number of bits in an int */
1202 int
1203 mp_count_bits (const mp_int * a)
1204 {
1205 int r;
1206 mp_digit q;
1207
1208 /* shortcut */
1209 if (a->used == 0) {
1210 return 0;
1211 }
1212
1213 /* get number of digits and add that */
1214 r = (a->used - 1) * DIGIT_BIT;
1215
1216 /* take the last digit and count the bits in it */
1217 q = a->dp[a->used - 1];
1218 while (q > 0) {
1219 ++r;
1220 q >>= ((mp_digit) 1);
1221 }
1222 return r;
1223 }
1224
1225 /* calc a value mod 2**b */
1226 static int
1227 mp_mod_2d (const mp_int * a, int b, mp_int * c)
1228 {
1229 int x, res;
1230
1231 /* if b is <= 0 then zero the int */
1232 if (b <= 0) {
1233 mp_zero (c);
1234 return MP_OKAY;
1235 }
1236
1237 /* if the modulus is larger than the value than return */
1238 if (b > a->used * DIGIT_BIT) {
1239 res = mp_copy (a, c);
1240 return res;
1241 }
1242
1243 /* copy */
1244 if ((res = mp_copy (a, c)) != MP_OKAY) {
1245 return res;
1246 }
1247
1248 /* zero digits above the last digit of the modulus */
1249 for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
1250 c->dp[x] = 0;
1251 }
1252 /* clear the digit that is not completely outside/inside the modulus */
1253 c->dp[b / DIGIT_BIT] &= (1 << ((mp_digit)b % DIGIT_BIT)) - 1;
1254 mp_clamp (c);
1255 return MP_OKAY;
1256 }
1257
1258 /* shift right a certain amount of digits */
1259 static void mp_rshd (mp_int * a, int b)
1260 {
1261 int x;
1262
1263 /* if b <= 0 then ignore it */
1264 if (b <= 0) {
1265 return;
1266 }
1267
1268 /* if b > used then simply zero it and return */
1269 if (a->used <= b) {
1270 mp_zero (a);
1271 return;
1272 }
1273
1274 {
1275 register mp_digit *bottom, *top;
1276
1277 /* shift the digits down */
1278
1279 /* bottom */
1280 bottom = a->dp;
1281
1282 /* top [offset into digits] */
1283 top = a->dp + b;
1284
1285 /* this is implemented as a sliding window where
1286 * the window is b-digits long and digits from
1287 * the top of the window are copied to the bottom
1288 *
1289 * e.g.
1290
1291 b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
1292 /\ | ---->
1293 \-------------------/ ---->
1294 */
1295 for (x = 0; x < (a->used - b); x++) {
1296 *bottom++ = *top++;
1297 }
1298
1299 /* zero the top digits */
1300 for (; x < a->used; x++) {
1301 *bottom++ = 0;
1302 }
1303 }
1304
1305 /* remove excess digits */
1306 a->used -= b;
1307 }
1308
1309 /* shift right by a certain bit count (store quotient in c, optional remainder in d) */
1310 static int mp_div_2d (const mp_int * a, int b, mp_int * c, mp_int * d)
1311 {
1312 mp_digit D, r, rr;
1313 int x, res;
1314 mp_int t;
1315
1316
1317 /* if the shift count is <= 0 then we do no work */
1318 if (b <= 0) {
1319 res = mp_copy (a, c);
1320 if (d != NULL) {
1321 mp_zero (d);
1322 }
1323 return res;
1324 }
1325
1326 if ((res = mp_init (&t)) != MP_OKAY) {
1327 return res;
1328 }
1329
1330 /* get the remainder */
1331 if (d != NULL) {
1332 if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
1333 mp_clear (&t);
1334 return res;
1335 }
1336 }
1337
1338 /* copy */
1339 if ((res = mp_copy (a, c)) != MP_OKAY) {
1340 mp_clear (&t);
1341 return res;
1342 }
1343
1344 /* shift by as many digits in the bit count */
1345 if (b >= DIGIT_BIT) {
1346 mp_rshd (c, b / DIGIT_BIT);
1347 }
1348
1349 /* shift any bit count < DIGIT_BIT */
1350 D = (mp_digit) (b % DIGIT_BIT);
1351 if (D != 0) {
1352 register mp_digit *tmpc, mask, shift;
1353
1354 /* mask */
1355 mask = (((mp_digit)1) << D) - 1;
1356
1357 /* shift for lsb */
1358 shift = DIGIT_BIT - D;
1359
1360 /* alias */
1361 tmpc = c->dp + (c->used - 1);
1362
1363 /* carry */
1364 r = 0;
1365 for (x = c->used - 1; x >= 0; x--) {
1366 /* get the lower bits of this word in a temp */
1367 rr = *tmpc & mask;
1368
1369 /* shift the current word and mix in the carry bits from the previous word */
1370 *tmpc = (*tmpc >> D) | (r << shift);
1371 --tmpc;
1372
1373 /* set the carry to the carry bits of the current word found above */
1374 r = rr;
1375 }
1376 }
1377 mp_clamp (c);
1378 if (d != NULL) {
1379 mp_exch (&t, d);
1380 }
1381 mp_clear (&t);
1382 return MP_OKAY;
1383 }
1384
1385 /* shift left a certain amount of digits */
1386 static int mp_lshd (mp_int * a, int b)
1387 {
1388 int x, res;
1389
1390 /* if it's less than zero return */
1391 if (b <= 0) {
1392 return MP_OKAY;
1393 }
1394
1395 /* grow to fit the new digits */
1396 if (a->alloc < a->used + b) {
1397 if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
1398 return res;
1399 }
1400 }
1401
1402 {
1403 register mp_digit *top, *bottom;
1404
1405 /* increment the used by the shift amount then copy upwards */
1406 a->used += b;
1407
1408 /* top */
1409 top = a->dp + a->used - 1;
1410
1411 /* base */
1412 bottom = a->dp + a->used - 1 - b;
1413
1414 /* much like mp_rshd this is implemented using a sliding window
1415 * except the window goes the other way around. Copying from
1416 * the bottom to the top. see bn_mp_rshd.c for more info.
1417 */
1418 for (x = a->used - 1; x >= b; x--) {
1419 *top-- = *bottom--;
1420 }
1421
1422 /* zero the lower digits */
1423 top = a->dp;
1424 for (x = 0; x < b; x++) {
1425 *top++ = 0;
1426 }
1427 }
1428 return MP_OKAY;
1429 }
1430
1431 /* shift left by a certain bit count */
1432 static int mp_mul_2d (const mp_int * a, int b, mp_int * c)
1433 {
1434 mp_digit d;
1435 int res;
1436
1437 /* copy */
1438 if (a != c) {
1439 if ((res = mp_copy (a, c)) != MP_OKAY) {
1440 return res;
1441 }
1442 }
1443
1444 if (c->alloc < c->used + b/DIGIT_BIT + 1) {
1445 if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
1446 return res;
1447 }
1448 }
1449
1450 /* shift by as many digits in the bit count */
1451 if (b >= DIGIT_BIT) {
1452 if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
1453 return res;
1454 }
1455 }
1456
1457 /* shift any bit count < DIGIT_BIT */
1458 d = (mp_digit) (b % DIGIT_BIT);
1459 if (d != 0) {
1460 register mp_digit *tmpc, shift, mask, r, rr;
1461 register int x;
1462
1463 /* bitmask for carries */
1464 mask = (((mp_digit)1) << d) - 1;
1465
1466 /* shift for msbs */
1467 shift = DIGIT_BIT - d;
1468
1469 /* alias */
1470 tmpc = c->dp;
1471
1472 /* carry */
1473 r = 0;
1474 for (x = 0; x < c->used; x++) {
1475 /* get the higher bits of the current word */
1476 rr = (*tmpc >> shift) & mask;
1477
1478 /* shift the current word and OR in the carry */
1479 *tmpc = ((*tmpc << d) | r) & MP_MASK;
1480 ++tmpc;
1481
1482 /* set the carry to the carry bits of the current word */
1483 r = rr;
1484 }
1485
1486 /* set final carry */
1487 if (r != 0) {
1488 c->dp[(c->used)++] = r;
1489 }
1490 }
1491 mp_clamp (c);
1492 return MP_OKAY;
1493 }
1494
1495 /* multiply by a digit */
1496 static int
1497 mp_mul_d (const mp_int * a, mp_digit b, mp_int * c)
1498 {
1499 mp_digit u, *tmpa, *tmpc;
1500 mp_word r;
1501 int ix, res, olduse;
1502
1503 /* make sure c is big enough to hold a*b */
1504 if (c->alloc < a->used + 1) {
1505 if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
1506 return res;
1507 }
1508 }
1509
1510 /* get the original destinations used count */
1511 olduse = c->used;
1512
1513 /* set the sign */
1514 c->sign = a->sign;
1515
1516 /* alias for a->dp [source] */
1517 tmpa = a->dp;
1518
1519 /* alias for c->dp [dest] */
1520 tmpc = c->dp;
1521
1522 /* zero carry */
1523 u = 0;
1524
1525 /* compute columns */
1526 for (ix = 0; ix < a->used; ix++) {
1527 /* compute product and carry sum for this term */
1528 r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
1529
1530 /* mask off higher bits to get a single digit */
1531 *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
1532
1533 /* send carry into next iteration */
1534 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
1535 }
1536
1537 /* store final carry [if any] */
1538 *tmpc++ = u;
1539
1540 /* now zero digits above the top */
1541 while (ix++ < olduse) {
1542 *tmpc++ = 0;
1543 }
1544
1545 /* set used count */
1546 c->used = a->used + 1;
1547 mp_clamp(c);
1548
1549 return MP_OKAY;
1550 }
1551
1552 /* integer signed division.
1553 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
1554 * HAC pp.598 Algorithm 14.20
1555 *
1556 * Note that the description in HAC is horribly
1557 * incomplete. For example, it doesn't consider
1558 * the case where digits are removed from 'x' in
1559 * the inner loop. It also doesn't consider the
1560 * case that y has fewer than three digits, etc..
1561 *
1562 * The overall algorithm is as described as
1563 * 14.20 from HAC but fixed to treat these cases.
1564 */
1565 static int mp_div (const mp_int * a, const mp_int * b, mp_int * c, mp_int * d)
1566 {
1567 mp_int q, x, y, t1, t2;
1568 int res, n, t, i, norm, neg;
1569
1570 /* is divisor zero ? */
1571 if (mp_iszero (b) == 1) {
1572 return MP_VAL;
1573 }
1574
1575 /* if a < b then q=0, r = a */
1576 if (mp_cmp_mag (a, b) == MP_LT) {
1577 if (d != NULL) {
1578 res = mp_copy (a, d);
1579 } else {
1580 res = MP_OKAY;
1581 }
1582 if (c != NULL) {
1583 mp_zero (c);
1584 }
1585 return res;
1586 }
1587
1588 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
1589 return res;
1590 }
1591 q.used = a->used + 2;
1592
1593 if ((res = mp_init (&t1)) != MP_OKAY) {
1594 goto __Q;
1595 }
1596
1597 if ((res = mp_init (&t2)) != MP_OKAY) {
1598 goto __T1;
1599 }
1600
1601 if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
1602 goto __T2;
1603 }
1604
1605 if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
1606 goto __X;
1607 }
1608
1609 /* fix the sign */
1610 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
1611 x.sign = y.sign = MP_ZPOS;
1612
1613 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
1614 norm = mp_count_bits(&y) % DIGIT_BIT;
1615 if (norm < DIGIT_BIT-1) {
1616 norm = (DIGIT_BIT-1) - norm;
1617 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
1618 goto __Y;
1619 }
1620 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
1621 goto __Y;
1622 }
1623 } else {
1624 norm = 0;
1625 }
1626
1627 /* note hac does 0 based, so if used==5 then it's 0,1,2,3,4, e.g. use 4 */
1628 n = x.used - 1;
1629 t = y.used - 1;
1630
1631 /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
1632 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
1633 goto __Y;
1634 }
1635
1636 while (mp_cmp (&x, &y) != MP_LT) {
1637 ++(q.dp[n - t]);
1638 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
1639 goto __Y;
1640 }
1641 }
1642
1643 /* reset y by shifting it back down */
1644 mp_rshd (&y, n - t);
1645
1646 /* step 3. for i from n down to (t + 1) */
1647 for (i = n; i >= (t + 1); i--) {
1648 if (i > x.used) {
1649 continue;
1650 }
1651
1652 /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
1653 * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
1654 if (x.dp[i] == y.dp[t]) {
1655 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
1656 } else {
1657 mp_word tmp;
1658 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
1659 tmp |= ((mp_word) x.dp[i - 1]);
1660 tmp /= ((mp_word) y.dp[t]);
1661 if (tmp > (mp_word) MP_MASK)
1662 tmp = MP_MASK;
1663 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
1664 }
1665
1666 /* while (q{i-t-1} * (yt * b + y{t-1})) >
1667 xi * b**2 + xi-1 * b + xi-2
1668
1669 do q{i-t-1} -= 1;
1670 */
1671 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
1672 do {
1673 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
1674
1675 /* find left hand */
1676 mp_zero (&t1);
1677 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
1678 t1.dp[1] = y.dp[t];
1679 t1.used = 2;
1680 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
1681 goto __Y;
1682 }
1683
1684 /* find right hand */
1685 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
1686 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
1687 t2.dp[2] = x.dp[i];
1688 t2.used = 3;
1689 } while (mp_cmp_mag(&t1, &t2) == MP_GT);
1690
1691 /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
1692 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
1693 goto __Y;
1694 }
1695
1696 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
1697 goto __Y;
1698 }
1699
1700 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
1701 goto __Y;
1702 }
1703
1704 /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
1705 if (x.sign == MP_NEG) {
1706 if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
1707 goto __Y;
1708 }
1709 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
1710 goto __Y;
1711 }
1712 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
1713 goto __Y;
1714 }
1715
1716 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
1717 }
1718 }
1719
1720 /* now q is the quotient and x is the remainder
1721 * [which we have to normalize]
1722 */
1723
1724 /* get sign before writing to c */
1725 x.sign = x.used == 0 ? MP_ZPOS : a->sign;
1726
1727 if (c != NULL) {
1728 mp_clamp (&q);
1729 mp_exch (&q, c);
1730 c->sign = neg;
1731 }
1732
1733 if (d != NULL) {
1734 mp_div_2d (&x, norm, &x, NULL);
1735 mp_exch (&x, d);
1736 }
1737
1738 res = MP_OKAY;
1739
1740 __Y:mp_clear (&y);
1741 __X:mp_clear (&x);
1742 __T2:mp_clear (&t2);
1743 __T1:mp_clear (&t1);
1744 __Q:mp_clear (&q);
1745 return res;
1746 }
1747
1748 static BOOL s_is_power_of_two(mp_digit b, int *p)
1749 {
1750 int x;
1751
1752 for (x = 1; x < DIGIT_BIT; x++) {
1753 if (b == (((mp_digit)1)<<x)) {
1754 *p = x;
1755 return TRUE;
1756 }
1757 }
1758 return FALSE;
1759 }
1760
1761 /* single digit division (based on routine from MPI) */
1762 static int mp_div_d (const mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
1763 {
1764 mp_int q;
1765 mp_word w;
1766 mp_digit t;
1767 int res, ix;
1768
1769 /* cannot divide by zero */
1770 if (b == 0) {
1771 return MP_VAL;
1772 }
1773
1774 /* quick outs */
1775 if (b == 1 || mp_iszero(a) == 1) {
1776 if (d != NULL) {
1777 *d = 0;
1778 }
1779 if (c != NULL) {
1780 return mp_copy(a, c);
1781 }
1782 return MP_OKAY;
1783 }
1784
1785 /* power of two ? */
1786 if (s_is_power_of_two(b, &ix) == 1) {
1787 if (d != NULL) {
1788 *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
1789 }
1790 if (c != NULL) {
1791 return mp_div_2d(a, ix, c, NULL);
1792 }
1793 return MP_OKAY;
1794 }
1795
1796 /* no easy answer [c'est la vie]. Just division */
1797 if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
1798 return res;
1799 }
1800
1801 q.used = a->used;
1802 q.sign = a->sign;
1803 w = 0;
1804 for (ix = a->used - 1; ix >= 0; ix--) {
1805 w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
1806
1807 if (w >= b) {
1808 t = (mp_digit)(w / b);
1809 w -= ((mp_word)t) * ((mp_word)b);
1810 } else {
1811 t = 0;
1812 }
1813 q.dp[ix] = t;
1814 }
1815
1816 if (d != NULL) {
1817 *d = (mp_digit)w;
1818 }
1819
1820 if (c != NULL) {
1821 mp_clamp(&q);
1822 mp_exch(&q, c);
1823 }
1824 mp_clear(&q);
1825
1826 return res;
1827 }
1828
1829 /* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
1830 *
1831 * Based on algorithm from the paper
1832 *
1833 * "Generating Efficient Primes for Discrete Log Cryptosystems"
1834 * Chae Hoon Lim, Pil Loong Lee,
1835 * POSTECH Information Research Laboratories
1836 *
1837 * The modulus must be of a special format [see manual]
1838 *
1839 * Has been modified to use algorithm 7.10 from the LTM book instead
1840 *
1841 * Input x must be in the range 0 <= x <= (n-1)**2
1842 */
1843 static int
1844 mp_dr_reduce (mp_int * x, const mp_int * n, mp_digit k)
1845 {
1846 int err, i, m;
1847 mp_word r;
1848 mp_digit mu, *tmpx1, *tmpx2;
1849
1850 /* m = digits in modulus */
1851 m = n->used;
1852
1853 /* ensure that "x" has at least 2m digits */
1854 if (x->alloc < m + m) {
1855 if ((err = mp_grow (x, m + m)) != MP_OKAY) {
1856 return err;
1857 }
1858 }
1859
1860 /* top of loop, this is where the code resumes if
1861 * another reduction pass is required.
1862 */
1863 top:
1864 /* aliases for digits */
1865 /* alias for lower half of x */
1866 tmpx1 = x->dp;
1867
1868 /* alias for upper half of x, or x/B**m */
1869 tmpx2 = x->dp + m;
1870
1871 /* set carry to zero */
1872 mu = 0;
1873
1874 /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
1875 for (i = 0; i < m; i++) {
1876 r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
1877 *tmpx1++ = (mp_digit)(r & MP_MASK);
1878 mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
1879 }
1880
1881 /* set final carry */
1882 *tmpx1++ = mu;
1883
1884 /* zero words above m */
1885 for (i = m + 1; i < x->used; i++) {
1886 *tmpx1++ = 0;
1887 }
1888
1889 /* clamp, sub and return */
1890 mp_clamp (x);
1891
1892 /* if x >= n then subtract and reduce again
1893 * Each successive "recursion" makes the input smaller and smaller.
1894 */
1895 if (mp_cmp_mag (x, n) != MP_LT) {
1896 s_mp_sub(x, n, x);
1897 goto top;
1898 }
1899 return MP_OKAY;
1900 }
1901
1902 /* sets the value of "d" required for mp_dr_reduce */
1903 static void mp_dr_setup(const mp_int *a, mp_digit *d)
1904 {
1905 /* the casts are required if DIGIT_BIT is one less than
1906 * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
1907 */
1908 *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
1909 ((mp_word)a->dp[0]));
1910 }
1911
1912 /* this is a shell function that calls either the normal or Montgomery
1913 * exptmod functions. Originally the call to the montgomery code was
1914 * embedded in the normal function but that wasted a lot of stack space
1915 * for nothing (since 99% of the time the Montgomery code would be called)
1916 */
1917 int mp_exptmod (const mp_int * G, const mp_int * X, mp_int * P, mp_int * Y)
1918 {
1919 int dr;
1920
1921 /* modulus P must be positive */
1922 if (P->sign == MP_NEG) {
1923 return MP_VAL;
1924 }
1925
1926 /* if exponent X is negative we have to recurse */
1927 if (X->sign == MP_NEG) {
1928 mp_int tmpG, tmpX;
1929 int err;
1930
1931 /* first compute 1/G mod P */
1932 if ((err = mp_init(&tmpG)) != MP_OKAY) {
1933 return err;
1934 }
1935 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
1936 mp_clear(&tmpG);
1937 return err;
1938 }
1939
1940 /* now get |X| */
1941 if ((err = mp_init(&tmpX)) != MP_OKAY) {
1942 mp_clear(&tmpG);
1943 return err;
1944 }
1945 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
1946 mp_clear_multi(&tmpG, &tmpX, NULL);
1947 return err;
1948 }
1949
1950 /* and now compute (1/G)**|X| instead of G**X [X < 0] */
1951 err = mp_exptmod(&tmpG, &tmpX, P, Y);
1952 mp_clear_multi(&tmpG, &tmpX, NULL);
1953 return err;
1954 }
1955
1956 dr = 0;
1957
1958 /* if the modulus is odd or dr != 0 use the fast method */
1959 if (mp_isodd (P) == 1 || dr != 0) {
1960 return mp_exptmod_fast (G, X, P, Y, dr);
1961 } else {
1962 /* otherwise use the generic Barrett reduction technique */
1963 return s_mp_exptmod (G, X, P, Y);
1964 }
1965 }
1966
1967 /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
1968 *
1969 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
1970 * The value of k changes based on the size of the exponent.
1971 *
1972 * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
1973 */
1974
1975 int
1976 mp_exptmod_fast (const mp_int * G, const mp_int * X, mp_int * P, mp_int * Y, int redmode)
1977 {
1978 mp_int M[256], res;
1979 mp_digit buf, mp;
1980 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
1981
1982 /* use a pointer to the reduction algorithm. This allows us to use
1983 * one of many reduction algorithms without modding the guts of
1984 * the code with if statements everywhere.
1985 */
1986 int (*redux)(mp_int*,const mp_int*,mp_digit);
1987
1988 /* find window size */
1989 x = mp_count_bits (X);
1990 if (x <= 7) {
1991 winsize = 2;
1992 } else if (x <= 36) {
1993 winsize = 3;
1994 } else if (x <= 140) {
1995 winsize = 4;
1996 } else if (x <= 450) {
1997 winsize = 5;
1998 } else if (x <= 1303) {
1999 winsize = 6;
2000 } else if (x <= 3529) {
2001 winsize = 7;
2002 } else {
2003 winsize = 8;
2004 }
2005
2006 /* init M array */
2007 /* init first cell */
2008 if ((err = mp_init(&M[1])) != MP_OKAY) {
2009 return err;
2010 }
2011
2012 /* now init the second half of the array */
2013 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
2014 if ((err = mp_init(&M[x])) != MP_OKAY) {
2015 for (y = 1<<(winsize-1); y < x; y++) {
2016 mp_clear (&M[y]);
2017 }
2018 mp_clear(&M[1]);
2019 return err;
2020 }
2021 }
2022
2023 /* determine and setup reduction code */
2024 if (redmode == 0) {
2025 /* now setup montgomery */
2026 if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
2027 goto __M;
2028 }
2029
2030 /* automatically pick the comba one if available (saves quite a few calls/ifs) */
2031 if (((P->used * 2 + 1) < MP_WARRAY) &&
2032 P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2033 redux = fast_mp_montgomery_reduce;
2034 } else {
2035 /* use slower baseline Montgomery method */
2036 redux = mp_montgomery_reduce;
2037 }
2038 } else if (redmode == 1) {
2039 /* setup DR reduction for moduli of the form B**k - b */
2040 mp_dr_setup(P, &mp);
2041 redux = mp_dr_reduce;
2042 } else {
2043 /* setup DR reduction for moduli of the form 2**k - b */
2044 if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
2045 goto __M;
2046 }
2047 redux = mp_reduce_2k;
2048 }
2049
2050 /* setup result */
2051 if ((err = mp_init (&res)) != MP_OKAY) {
2052 goto __M;
2053 }
2054
2055 /* create M table
2056 *
2057
2058 *
2059 * The first half of the table is not computed though accept for M[0] and M[1]
2060 */
2061
2062 if (redmode == 0) {
2063 /* now we need R mod m */
2064 if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
2065 goto __RES;
2066 }
2067
2068 /* now set M[1] to G * R mod m */
2069 if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
2070 goto __RES;
2071 }
2072 } else {
2073 mp_set(&res, 1);
2074 if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
2075 goto __RES;
2076 }
2077 }
2078
2079 /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
2080 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
2081 goto __RES;
2082 }
2083
2084 for (x = 0; x < (winsize - 1); x++) {
2085 if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
2086 goto __RES;
2087 }
2088 if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
2089 goto __RES;
2090 }
2091 }
2092
2093 /* create upper table */
2094 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
2095 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
2096 goto __RES;
2097 }
2098 if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
2099 goto __RES;
2100 }
2101 }
2102
2103 /* set initial mode and bit cnt */
2104 mode = 0;
2105 bitcnt = 1;
2106 buf = 0;
2107 digidx = X->used - 1;
2108 bitcpy = 0;
2109 bitbuf = 0;
2110
2111 for (;;) {
2112 /* grab next digit as required */
2113 if (--bitcnt == 0) {
2114 /* if digidx == -1 we are out of digits so break */
2115 if (digidx == -1) {
2116 break;
2117 }
2118 /* read next digit and reset bitcnt */
2119 buf = X->dp[digidx--];
2120 bitcnt = DIGIT_BIT;
2121 }
2122
2123 /* grab the next msb from the exponent */
2124 y = (buf >> (DIGIT_BIT - 1)) & 1;
2125 buf <<= (mp_digit)1;
2126
2127 /* if the bit is zero and mode == 0 then we ignore it
2128 * These represent the leading zero bits before the first 1 bit
2129 * in the exponent. Technically this opt is not required but it
2130 * does lower the # of trivial squaring/reductions used
2131 */
2132 if (mode == 0 && y == 0) {
2133 continue;
2134 }
2135
2136 /* if the bit is zero and mode == 1 then we square */
2137 if (mode == 1 && y == 0) {
2138 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2139 goto __RES;
2140 }
2141 if ((err = redux (&res, P, mp)) != MP_OKAY) {
2142 goto __RES;
2143 }
2144 continue;
2145 }
2146
2147 /* else we add it to the window */
2148 bitbuf |= (y << (winsize - ++bitcpy));
2149 mode = 2;
2150
2151 if (bitcpy == winsize) {
2152 /* ok window is filled so square as required and multiply */
2153 /* square first */
2154 for (x = 0; x < winsize; x++) {
2155 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2156 goto __RES;
2157 }
2158 if ((err = redux (&res, P, mp)) != MP_OKAY) {
2159 goto __RES;
2160 }
2161 }
2162
2163 /* then multiply */
2164 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
2165 goto __RES;
2166 }
2167 if ((err = redux (&res, P, mp)) != MP_OKAY) {
2168 goto __RES;
2169 }
2170
2171 /* empty window and reset */
2172 bitcpy = 0;
2173 bitbuf = 0;
2174 mode = 1;
2175 }
2176 }
2177
2178 /* if bits remain then square/multiply */
2179 if (mode == 2 && bitcpy > 0) {
2180 /* square then multiply if the bit is set */
2181 for (x = 0; x < bitcpy; x++) {
2182 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2183 goto __RES;
2184 }
2185 if ((err = redux (&res, P, mp)) != MP_OKAY) {
2186 goto __RES;
2187 }
2188
2189 /* get next bit of the window */
2190 bitbuf <<= 1;
2191 if ((bitbuf & (1 << winsize)) != 0) {
2192 /* then multiply */
2193 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
2194 goto __RES;
2195 }
2196 if ((err = redux (&res, P, mp)) != MP_OKAY) {
2197 goto __RES;
2198 }
2199 }
2200 }
2201 }
2202
2203 if (redmode == 0) {
2204 /* fixup result if Montgomery reduction is used
2205 * recall that any value in a Montgomery system is
2206 * actually multiplied by R mod n. So we have
2207 * to reduce one more time to cancel out the factor
2208 * of R.
2209 */
2210 if ((err = redux(&res, P, mp)) != MP_OKAY) {
2211 goto __RES;
2212 }
2213 }
2214
2215 /* swap res with Y */
2216 mp_exch (&res, Y);
2217 err = MP_OKAY;
2218 __RES:mp_clear (&res);
2219 __M:
2220 mp_clear(&M[1]);
2221 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
2222 mp_clear (&M[x]);
2223 }
2224 return err;
2225 }
2226
2227 /* Greatest Common Divisor using the binary method */
2228 int mp_gcd (const mp_int * a, const mp_int * b, mp_int * c)
2229 {
2230 mp_int u, v;
2231 int k, u_lsb, v_lsb, res;
2232
2233 /* either zero than gcd is the largest */
2234 if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
2235 return mp_abs (b, c);
2236 }
2237 if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
2238 return mp_abs (a, c);
2239 }
2240
2241 /* optimized. At this point if a == 0 then
2242 * b must equal zero too
2243 */
2244 if (mp_iszero (a) == 1) {
2245 mp_zero(c);
2246 return MP_OKAY;
2247 }
2248
2249 /* get copies of a and b we can modify */
2250 if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
2251 return res;
2252 }
2253
2254 if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
2255 goto __U;
2256 }
2257
2258 /* must be positive for the remainder of the algorithm */
2259 u.sign = v.sign = MP_ZPOS;
2260
2261 /* B1. Find the common power of two for u and v */
2262 u_lsb = mp_cnt_lsb(&u);
2263 v_lsb = mp_cnt_lsb(&v);
2264 k = MIN(u_lsb, v_lsb);
2265
2266 if (k > 0) {
2267 /* divide the power of two out */
2268 if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
2269 goto __V;
2270 }
2271
2272 if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
2273 goto __V;
2274 }
2275 }
2276
2277 /* divide any remaining factors of two out */
2278 if (u_lsb != k) {
2279 if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
2280 goto __V;
2281 }
2282 }
2283
2284 if (v_lsb != k) {
2285 if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
2286 goto __V;
2287 }
2288 }
2289
2290 while (mp_iszero(&v) == 0) {
2291 /* make sure v is the largest */
2292 if (mp_cmp_mag(&u, &v) == MP_GT) {
2293 /* swap u and v to make sure v is >= u */
2294 mp_exch(&u, &v);
2295 }
2296
2297 /* subtract smallest from largest */
2298 if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
2299 goto __V;
2300 }
2301
2302 /* Divide out all factors of two */
2303 if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
2304 goto __V;
2305 }
2306 }
2307
2308 /* multiply by 2**k which we divided out at the beginning */
2309 if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
2310 goto __V;
2311 }
2312 c->sign = MP_ZPOS;
2313 res = MP_OKAY;
2314 __V:mp_clear (&u);
2315 __U:mp_clear (&v);
2316 return res;
2317 }
2318
2319 /* get the lower 32-bits of an mp_int */
2320 unsigned long mp_get_int(const mp_int * a)
2321 {
2322 int i;
2323 unsigned long res;
2324
2325 if (a->used == 0) {
2326 return 0;
2327 }
2328
2329 /* get number of digits of the lsb we have to read */
2330 i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
2331
2332 /* get most significant digit of result */
2333 res = DIGIT(a,i);
2334
2335 while (--i >= 0) {
2336 res = (res << DIGIT_BIT) | DIGIT(a,i);
2337 }
2338
2339 /* force result to 32-bits always so it is consistent on non 32-bit platforms */
2340 return res & 0xFFFFFFFFUL;
2341 }
2342
2343 /* creates "a" then copies b into it */
2344 int mp_init_copy (mp_int * a, const mp_int * b)
2345 {
2346 int res;
2347
2348 if ((res = mp_init (a)) != MP_OKAY) {
2349 return res;
2350 }
2351 return mp_copy (b, a);
2352 }
2353
2354 int mp_init_multi(mp_int *mp, ...)
2355 {
2356 mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
2357 int n = 0; /* Number of ok inits */
2358 mp_int* cur_arg = mp;
2359 va_list args;
2360
2361 va_start(args, mp); /* init args to next argument from caller */
2362 while (cur_arg != NULL) {
2363 if (mp_init(cur_arg) != MP_OKAY) {
2364 /* Oops - error! Back-track and mp_clear what we already
2365 succeeded in init-ing, then return error.
2366 */
2367 va_list clean_args;
2368
2369 /* end the current list */
2370 va_end(args);
2371
2372 /* now start cleaning up */
2373 cur_arg = mp;
2374 va_start(clean_args, mp);
2375 while (n--) {
2376 mp_clear(cur_arg);
2377 cur_arg = va_arg(clean_args, mp_int*);
2378 }
2379 va_end(clean_args);
2380 res = MP_MEM;
2381 break;
2382 }
2383 n++;
2384 cur_arg = va_arg(args, mp_int*);
2385 }
2386 va_end(args);
2387 return res; /* Assumed ok, if error flagged above. */
2388 }
2389
2390 /* hac 14.61, pp608 */
2391 int mp_invmod (const mp_int * a, mp_int * b, mp_int * c)
2392 {
2393 /* b cannot be negative */
2394 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
2395 return MP_VAL;
2396 }
2397
2398 /* if the modulus is odd we can use a faster routine instead */
2399 if (mp_isodd (b) == 1) {
2400 return fast_mp_invmod (a, b, c);
2401 }
2402
2403 return mp_invmod_slow(a, b, c);
2404 }
2405
2406 /* hac 14.61, pp608 */
2407 int mp_invmod_slow (const mp_int * a, mp_int * b, mp_int * c)
2408 {
2409 mp_int x, y, u, v, A, B, C, D;
2410 int res;
2411
2412 /* b cannot be negative */
2413 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
2414 return MP_VAL;
2415 }
2416
2417 /* init temps */
2418 if ((res = mp_init_multi(&x, &y, &u, &v,
2419 &A, &B, &C, &D, NULL)) != MP_OKAY) {
2420 return res;
2421 }
2422
2423 /* x = a, y = b */
2424 if ((res = mp_copy (a, &x)) != MP_OKAY) {
2425 goto __ERR;
2426 }
2427 if ((res = mp_copy (b, &y)) != MP_OKAY) {
2428 goto __ERR;
2429 }
2430
2431 /* 2. [modified] if x,y are both even then return an error! */
2432 if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
2433 res = MP_VAL;
2434 goto __ERR;
2435 }
2436
2437 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
2438 if ((res = mp_copy (&x, &u)) != MP_OKAY) {
2439 goto __ERR;
2440 }
2441 if ((res = mp_copy (&y, &v)) != MP_OKAY) {
2442 goto __ERR;
2443 }
2444 mp_set (&A, 1);
2445 mp_set (&D, 1);
2446
2447 top:
2448 /* 4. while u is even do */
2449 while (mp_iseven (&u) == 1) {
2450 /* 4.1 u = u/2 */
2451 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
2452 goto __ERR;
2453 }
2454 /* 4.2 if A or B is odd then */
2455 if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
2456 /* A = (A+y)/2, B = (B-x)/2 */
2457 if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
2458 goto __ERR;
2459 }
2460 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
2461 goto __ERR;
2462 }
2463 }
2464 /* A = A/2, B = B/2 */
2465 if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
2466 goto __ERR;
2467 }
2468 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
2469 goto __ERR;
2470 }
2471 }
2472
2473 /* 5. while v is even do */
2474 while (mp_iseven (&v) == 1) {
2475 /* 5.1 v = v/2 */
2476 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
2477 goto __ERR;
2478 }
2479 /* 5.2 if C or D is odd then */
2480 if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
2481 /* C = (C+y)/2, D = (D-x)/2 */
2482 if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
2483 goto __ERR;
2484 }
2485 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
2486 goto __ERR;
2487 }
2488 }
2489 /* C = C/2, D = D/2 */
2490 if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
2491 goto __ERR;
2492 }
2493 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
2494 goto __ERR;
2495 }
2496 }
2497
2498 /* 6. if u >= v then */
2499 if (mp_cmp (&u, &v) != MP_LT) {
2500 /* u = u - v, A = A - C, B = B - D */
2501 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
2502 goto __ERR;
2503 }
2504
2505 if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
2506 goto __ERR;
2507 }
2508
2509 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
2510 goto __ERR;
2511 }
2512 } else {
2513 /* v - v - u, C = C - A, D = D - B */
2514 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
2515 goto __ERR;
2516 }
2517
2518 if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
2519 goto __ERR;
2520 }
2521
2522 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
2523 goto __ERR;
2524 }
2525 }
2526
2527 /* if not zero goto step 4 */
2528 if (mp_iszero (&u) == 0)
2529 goto top;
2530
2531 /* now a = C, b = D, gcd == g*v */
2532
2533 /* if v != 1 then there is no inverse */
2534 if (mp_cmp_d (&v, 1) != MP_EQ) {
2535 res = MP_VAL;
2536 goto __ERR;
2537 }
2538
2539 /* if it's too low */
2540 while (mp_cmp_d(&C, 0) == MP_LT) {
2541 if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
2542 goto __ERR;
2543 }
2544 }
2545
2546 /* too big */
2547 while (mp_cmp_mag(&C, b) != MP_LT) {
2548 if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
2549 goto __ERR;
2550 }
2551 }
2552
2553 /* C is now the inverse */
2554 mp_exch (&C, c);
2555 res = MP_OKAY;
2556 __ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
2557 return res;
2558 }
2559
2560 /* c = |a| * |b| using Karatsuba Multiplication using
2561 * three half size multiplications
2562 *
2563 * Let B represent the radix [e.g. 2**DIGIT_BIT] and
2564 * let n represent half of the number of digits in
2565 * the min(a,b)
2566 *
2567 * a = a1 * B**n + a0
2568 * b = b1 * B**n + b0
2569 *
2570 * Then, a * b =>
2571 a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0
2572 *
2573 * Note that a1b1 and a0b0 are used twice and only need to be
2574 * computed once. So in total three half size (half # of
2575 * digit) multiplications are performed, a0b0, a1b1 and
2576 * (a1-b1)(a0-b0)
2577 *
2578 * Note that a multiplication of half the digits requires
2579 * 1/4th the number of single precision multiplications so in
2580 * total after one call 25% of the single precision multiplications
2581 * are saved. Note also that the call to mp_mul can end up back
2582 * in this function if the a0, a1, b0, or b1 are above the threshold.
2583 * This is known as divide-and-conquer and leads to the famous
2584 * O(N**lg(3)) or O(N**1.584) work which is asymptotically lower than
2585 * the standard O(N**2) that the baseline/comba methods use.
2586 * Generally though the overhead of this method doesn't pay off
2587 * until a certain size (N ~ 80) is reached.
2588 */
2589 int mp_karatsuba_mul (const mp_int * a, const mp_int * b, mp_int * c)
2590 {
2591 mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
2592 int B, err;
2593
2594 /* default the return code to an error */
2595 err = MP_MEM;
2596
2597 /* min # of digits */
2598 B = MIN (a->used, b->used);
2599
2600 /* now divide in two */
2601 B = B >> 1;
2602
2603 /* init copy all the temps */
2604 if (mp_init_size (&x0, B) != MP_OKAY)
2605 goto ERR;
2606 if (mp_init_size (&x1, a->used - B) != MP_OKAY)
2607 goto X0;
2608 if (mp_init_size (&y0, B) != MP_OKAY)
2609 goto X1;
2610 if (mp_init_size (&y1, b->used - B) != MP_OKAY)
2611 goto Y0;
2612
2613 /* init temps */
2614 if (mp_init_size (&t1, B * 2) != MP_OKAY)
2615 goto Y1;
2616 if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
2617 goto T1;
2618 if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
2619 goto X0Y0;
2620
2621 /* now shift the digits */
2622 x0.used = y0.used = B;
2623 x1.used = a->used - B;
2624 y1.used = b->used - B;
2625
2626 {
2627 register int x;
2628 register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
2629
2630 /* we copy the digits directly instead of using higher level functions
2631 * since we also need to shift the digits
2632 */
2633 tmpa = a->dp;
2634 tmpb = b->dp;
2635
2636 tmpx = x0.dp;
2637 tmpy = y0.dp;
2638 for (x = 0; x < B; x++) {
2639 *tmpx++ = *tmpa++;
2640 *tmpy++ = *tmpb++;
2641 }
2642
2643 tmpx = x1.dp;
2644 for (x = B; x < a->used; x++) {
2645 *tmpx++ = *tmpa++;
2646 }
2647
2648 tmpy = y1.dp;
2649 for (x = B; x < b->used; x++) {
2650 *tmpy++ = *tmpb++;
2651 }
2652 }
2653
2654 /* only need to clamp the lower words since by definition the
2655 * upper words x1/y1 must have a known number of digits
2656 */
2657 mp_clamp (&x0);
2658 mp_clamp (&y0);
2659
2660 /* now calc the products x0y0 and x1y1 */
2661 /* after this x0 is no longer required, free temp [x0==t2]! */
2662 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
2663 goto X1Y1; /* x0y0 = x0*y0 */
2664 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
2665 goto X1Y1; /* x1y1 = x1*y1 */
2666
2667 /* now calc x1-x0 and y1-y0 */
2668 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
2669 goto X1Y1; /* t1 = x1 - x0 */
2670 if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
2671 goto X1Y1; /* t2 = y1 - y0 */
2672 if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
2673 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */
2674
2675 /* add x0y0 */
2676 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
2677 goto X1Y1; /* t2 = x0y0 + x1y1 */
2678 if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
2679 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
2680
2681 /* shift by B */
2682 if (mp_lshd (&t1, B) != MP_OKAY)
2683 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
2684 if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
2685 goto X1Y1; /* x1y1 = x1y1 << 2*B */
2686
2687 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
2688 goto X1Y1; /* t1 = x0y0 + t1 */
2689 if (mp_add (&t1, &x1y1, c) != MP_OKAY)
2690 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
2691
2692 /* Algorithm succeeded set the return code to MP_OKAY */
2693 err = MP_OKAY;
2694
2695 X1Y1:mp_clear (&x1y1);
2696 X0Y0:mp_clear (&x0y0);
2697 T1:mp_clear (&t1);
2698 Y1:mp_clear (&y1);
2699 Y0:mp_clear (&y0);
2700 X1:mp_clear (&x1);
2701 X0:mp_clear (&x0);
2702 ERR:
2703 return err;
2704 }
2705
2706 /* Karatsuba squaring, computes b = a*a using three
2707 * half size squarings
2708 *
2709 * See comments of karatsuba_mul for details. It
2710 * is essentially the same algorithm but merely
2711 * tuned to perform recursive squarings.
2712 */
2713 int mp_karatsuba_sqr (const mp_int * a, mp_int * b)
2714 {
2715 mp_int x0, x1, t1, t2, x0x0, x1x1;
2716 int B, err;
2717
2718 err = MP_MEM;
2719
2720 /* min # of digits */
2721 B = a->used;
2722
2723 /* now divide in two */
2724 B = B >> 1;
2725
2726 /* init copy all the temps */
2727 if (mp_init_size (&x0, B) != MP_OKAY)
2728 goto ERR;
2729 if (mp_init_size (&x1, a->used - B) != MP_OKAY)
2730 goto X0;
2731
2732 /* init temps */
2733 if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
2734 goto X1;
2735 if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
2736 goto T1;
2737 if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
2738 goto T2;
2739 if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
2740 goto X0X0;
2741
2742 {
2743 register int x;
2744 register mp_digit *dst, *src;
2745
2746 src = a->dp;
2747
2748 /* now shift the digits */
2749 dst = x0.dp;
2750 for (x = 0; x < B; x++) {
2751 *dst++ = *src++;
2752 }
2753
2754 dst = x1.dp;
2755 for (x = B; x < a->used; x++) {
2756 *dst++ = *src++;
2757 }
2758 }
2759
2760 x0.used = B;
2761 x1.used = a->used - B;
2762
2763 mp_clamp (&x0);
2764
2765 /* now calc the products x0*x0 and x1*x1 */
2766 if (mp_sqr (&x0, &x0x0) != MP_OKAY)
2767 goto X1X1; /* x0x0 = x0*x0 */
2768 if (mp_sqr (&x1, &x1x1) != MP_OKAY)
2769 goto X1X1; /* x1x1 = x1*x1 */
2770
2771 /* now calc (x1-x0)**2 */
2772 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
2773 goto X1X1; /* t1 = x1 - x0 */
2774 if (mp_sqr (&t1, &t1) != MP_OKAY)
2775 goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
2776
2777 /* add x0y0 */
2778 if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
2779 goto X1X1; /* t2 = x0x0 + x1x1 */
2780 if (mp_sub (&t2, &t1, &t1) != MP_OKAY)
2781 goto X1X1; /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */
2782
2783 /* shift by B */
2784 if (mp_lshd (&t1, B) != MP_OKAY)
2785 goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
2786 if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
2787 goto X1X1; /* x1x1 = x1x1 << 2*B */
2788
2789 if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
2790 goto X1X1; /* t1 = x0x0 + t1 */
2791 if (mp_add (&t1, &x1x1, b) != MP_OKAY)
2792 goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
2793
2794 err = MP_OKAY;
2795
2796 X1X1:mp_clear (&x1x1);
2797 X0X0:mp_clear (&x0x0);
2798 T2:mp_clear (&t2);
2799 T1:mp_clear (&t1);
2800 X1:mp_clear (&x1);
2801 X0:mp_clear (&x0);
2802 ERR:
2803 return err;
2804 }
2805
2806 /* computes least common multiple as |a*b|/(a, b) */
2807 int mp_lcm (const mp_int * a, const mp_int * b, mp_int * c)
2808 {
2809 int res;
2810 mp_int t1, t2;
2811
2812
2813 if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
2814 return res;
2815 }
2816
2817 /* t1 = get the GCD of the two inputs */
2818 if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
2819 goto __T;
2820 }
2821
2822 /* divide the smallest by the GCD */
2823 if (mp_cmp_mag(a, b) == MP_LT) {
2824 /* store quotient in t2 so that t2 * b is the LCM */
2825 if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
2826 goto __T;
2827 }
2828 res = mp_mul(b, &t2, c);
2829 } else {
2830 /* store quotient in t2 so that t2 * a is the LCM */
2831 if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
2832 goto __T;
2833 }
2834 res = mp_mul(a, &t2, c);
2835 }
2836
2837 /* fix the sign to positive */
2838 c->sign = MP_ZPOS;
2839
2840 __T:
2841 mp_clear_multi (&t1, &t2, NULL);
2842 return res;
2843 }
2844
2845 /* c = a mod b, 0 <= c < b */
2846 int
2847 mp_mod (const mp_int * a, mp_int * b, mp_int * c)
2848 {
2849 mp_int t;
2850 int res;
2851
2852 if ((res = mp_init (&t)) != MP_OKAY) {
2853 return res;
2854 }
2855
2856 if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
2857 mp_clear (&t);
2858 return res;
2859 }
2860
2861 if (t.sign != b->sign) {
2862 res = mp_add (b, &t, c);
2863 } else {
2864 res = MP_OKAY;
2865 mp_exch (&t, c);
2866 }
2867
2868 mp_clear (&t);
2869 return res;
2870 }
2871
2872 static int
2873 mp_mod_d (const mp_int * a, mp_digit b, mp_digit * c)
2874 {
2875 return mp_div_d(a, b, NULL, c);
2876 }
2877
2878 /* b = a*2 */
2879 static int mp_mul_2(const mp_int * a, mp_int * b)
2880 {
2881 int x, res, oldused;
2882
2883 /* grow to accommodate result */
2884 if (b->alloc < a->used + 1) {
2885 if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
2886 return res;
2887 }
2888 }
2889
2890 oldused = b->used;
2891 b->used = a->used;
2892
2893 {
2894 register mp_digit r, rr, *tmpa, *tmpb;
2895
2896 /* alias for source */
2897 tmpa = a->dp;
2898
2899 /* alias for dest */
2900 tmpb = b->dp;
2901
2902 /* carry */
2903 r = 0;
2904 for (x = 0; x < a->used; x++) {
2905
2906 /* get what will be the *next* carry bit from the
2907 * MSB of the current digit
2908 */
2909 rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
2910
2911 /* now shift up this digit, add in the carry [from the previous] */
2912 *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
2913
2914 /* copy the carry that would be from the source
2915 * digit into the next iteration
2916 */
2917 r = rr;
2918 }
2919
2920 /* new leading digit? */
2921 if (r != 0) {
2922 /* add a MSB which is always 1 at this point */
2923 *tmpb = 1;
2924 ++(b->used);
2925 }
2926
2927 /* now zero any excess digits on the destination
2928 * that we didn't write to
2929 */
2930 tmpb = b->dp + b->used;
2931 for (x = b->used; x < oldused; x++) {
2932 *tmpb++ = 0;
2933 }
2934 }
2935 b->sign = a->sign;
2936 return MP_OKAY;
2937 }
2938
2939 /*
2940 * shifts with subtractions when the result is greater than b.
2941 *
2942 * The method is slightly modified to shift B unconditionally up to just under
2943 * the leading bit of b. This saves a lot of multiple precision shifting.
2944 */
2945 int mp_montgomery_calc_normalization (mp_int * a, const mp_int * b)
2946 {
2947 int x, bits, res;
2948
2949 /* how many bits of last digit does b use */
2950 bits = mp_count_bits (b) % DIGIT_BIT;
2951
2952
2953 if (b->used > 1) {
2954 if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
2955 return res;
2956 }
2957 } else {
2958 mp_set(a, 1);
2959 bits = 1;
2960 }
2961
2962
2963 /* now compute C = A * B mod b */
2964 for (x = bits - 1; x < DIGIT_BIT; x++) {
2965 if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
2966 return res;
2967 }
2968 if (mp_cmp_mag (a, b) != MP_LT) {
2969 if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
2970 return res;
2971 }
2972 }
2973 }
2974
2975 return MP_OKAY;
2976 }
2977
2978 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
2979 int
2980 mp_montgomery_reduce (mp_int * x, const mp_int * n, mp_digit rho)
2981 {
2982 int ix, res, digs;
2983 mp_digit mu;
2984
2985 /* can the fast reduction [comba] method be used?
2986 *
2987 * Note that unlike in mul you're safely allowed *less*
2988 * than the available columns [255 per default] since carries
2989 * are fixed up in the inner loop.
2990 */
2991 digs = n->used * 2 + 1;
2992 if ((digs < MP_WARRAY) &&
2993 n->used <
2994 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2995 return fast_mp_montgomery_reduce (x, n, rho);
2996 }
2997
2998 /* grow the input as required */
2999 if (x->alloc < digs) {
3000 if ((res = mp_grow (x, digs)) != MP_OKAY) {
3001 return res;
3002 }
3003 }
3004 x->used = digs;
3005
3006 for (ix = 0; ix < n->used; ix++) {
3007 /* mu = ai * rho mod b
3008 *
3009 * The value of rho must be precalculated via
3010 * montgomery_setup() such that
3011 * it equals -1/n0 mod b this allows the
3012 * following inner loop to reduce the
3013 * input one digit at a time
3014 */
3015 mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
3016
3017 /* a = a + mu * m * b**i */
3018 {
3019 register int iy;
3020 register mp_digit *tmpn, *tmpx, u;
3021 register mp_word r;
3022
3023 /* alias for digits of the modulus */
3024 tmpn = n->dp;
3025
3026 /* alias for the digits of x [the input] */
3027 tmpx = x->dp + ix;
3028
3029 /* set the carry to zero */
3030 u = 0;
3031
3032 /* Multiply and add in place */
3033 for (iy = 0; iy < n->used; iy++) {
3034 /* compute product and sum */
3035 r = ((mp_word)mu) * ((mp_word)*tmpn++) +
3036 ((mp_word) u) + ((mp_word) * tmpx);
3037
3038 /* get carry */
3039 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
3040
3041 /* fix digit */
3042 *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
3043 }
3044 /* At this point the ix'th digit of x should be zero */
3045
3046
3047 /* propagate carries upwards as required*/
3048 while (u) {
3049 *tmpx += u;
3050 u = *tmpx >> DIGIT_BIT;
3051 *tmpx++ &= MP_MASK;
3052 }
3053 }
3054 }
3055
3056 /* at this point the n.used'th least
3057 * significant digits of x are all zero
3058 * which means we can shift x to the
3059 * right by n.used digits and the
3060 * residue is unchanged.
3061 */
3062
3063 /* x = x/b**n.used */
3064 mp_clamp(x);
3065 mp_rshd (x, n->used);
3066
3067 /* if x >= n then x = x - n */
3068 if (mp_cmp_mag (x, n) != MP_LT) {
3069 return s_mp_sub (x, n, x);
3070 }
3071
3072 return MP_OKAY;
3073 }
3074
3075 /* setups the montgomery reduction stuff */
3076 int
3077 mp_montgomery_setup (const mp_int * n, mp_digit * rho)
3078 {
3079 mp_digit x, b;
3080
3081 /* fast inversion mod 2**k
3082 *
3083 * Based on the fact that
3084 *
3085 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
3086 * => 2*X*A - X*X*A*A = 1
3087 * => 2*(1) - (1) = 1
3088 */
3089 b = n->dp[0];
3090
3091 if ((b & 1) == 0) {
3092 return MP_VAL;
3093 }
3094
3095 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
3096 x *= 2 - b * x; /* here x*a==1 mod 2**8 */
3097 x *= 2 - b * x; /* here x*a==1 mod 2**16 */
3098 x *= 2 - b * x; /* here x*a==1 mod 2**32 */
3099
3100 /* rho = -1/m mod b */
3101 *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
3102
3103 return MP_OKAY;
3104 }
3105
3106 /* high level multiplication (handles sign) */
3107 int mp_mul (const mp_int * a, const mp_int * b, mp_int * c)
3108 {
3109 int res, neg;
3110 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
3111
3112 /* use Karatsuba? */
3113 if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
3114 res = mp_karatsuba_mul (a, b, c);
3115 } else
3116 {
3117 /* can we use the fast multiplier?
3118 *
3119 * The fast multiplier can be used if the output will
3120 * have less than MP_WARRAY digits and the number of
3121 * digits won't affect carry propagation
3122 */
3123 int digs = a->used + b->used + 1;
3124
3125 if ((digs < MP_WARRAY) &&
3126 MIN(a->used, b->used) <=
3127 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
3128 res = fast_s_mp_mul_digs (a, b, c, digs);
3129 } else
3130 res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
3131 }
3132 c->sign = (c->used > 0) ? neg : MP_ZPOS;
3133 return res;
3134 }
3135
3136 /* d = a * b (mod c) */
3137 int
3138 mp_mulmod (const mp_int * a, const mp_int * b, mp_int * c, mp_int * d)
3139 {
3140 int res;
3141 mp_int t;
3142
3143 if ((res = mp_init (&t)) != MP_OKAY) {
3144 return res;
3145 }
3146
3147 if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
3148 mp_clear (&t);
3149 return res;
3150 }
3151 res = mp_mod (&t, c, d);
3152 mp_clear (&t);
3153 return res;
3154 }
3155
3156 /* table of first PRIME_SIZE primes */
3157 static const mp_digit __prime_tab[] = {
3158 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
3159 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
3160 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
3161 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083,
3162 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
3163 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
3164 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
3165 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
3166
3167 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
3168 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
3169 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
3170 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
3171 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
3172 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
3173 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
3174 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
3175
3176 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
3177 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
3178 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
3179 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
3180 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
3181 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
3182 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
3183 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
3184
3185 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
3186 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
3187 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
3188 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
3189 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
3190 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
3191 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
3192 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
3193 };
3194
3195 /* determines if an integers is divisible by one
3196 * of the first PRIME_SIZE primes or not
3197 *
3198 * sets result to 0 if not, 1 if yes
3199 */
3200 static int mp_prime_is_divisible (const mp_int * a, int *result)
3201 {
3202 int err, ix;
3203 mp_digit res;
3204
3205 /* default to not */
3206 *result = MP_NO;
3207
3208 for (ix = 0; ix < PRIME_SIZE; ix++) {
3209 /* what is a mod __prime_tab[ix] */
3210 if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) {
3211 return err;
3212 }
3213
3214 /* is the residue zero? */
3215 if (res == 0) {
3216 *result = MP_YES;
3217 return MP_OKAY;
3218 }
3219 }
3220
3221 return MP_OKAY;
3222 }
3223
3224 /* Miller-Rabin test of "a" to the base of "b" as described in
3225 * HAC pp. 139 Algorithm 4.24
3226 *
3227 * Sets result to 0 if definitely composite or 1 if probably prime.
3228 * Randomly the chance of error is no more than 1/4 and often
3229 * very much lower.
3230 */
3231 static int mp_prime_miller_rabin (mp_int * a, const mp_int * b, int *result)
3232 {
3233 mp_int n1, y, r;
3234 int s, j, err;
3235
3236 /* default */
3237 *result = MP_NO;
3238
3239 /* ensure b > 1 */
3240 if (mp_cmp_d(b, 1) != MP_GT) {
3241 return MP_VAL;
3242 }
3243
3244 /* get n1 = a - 1 */
3245 if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
3246 return err;
3247 }
3248 if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
3249 goto __N1;
3250 }
3251
3252 /* set 2**s * r = n1 */
3253 if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
3254 goto __N1;
3255 }
3256
3257 /* count the number of least significant bits
3258 * which are zero
3259 */
3260 s = mp_cnt_lsb(&r);
3261
3262 /* now divide n - 1 by 2**s */
3263 if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
3264 goto __R;
3265 }
3266
3267 /* compute y = b**r mod a */
3268 if ((err = mp_init (&y)) != MP_OKAY) {
3269 goto __R;
3270 }
3271 if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
3272 goto __Y;
3273 }
3274
3275 /* if y != 1 and y != n1 do */
3276 if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
3277 j = 1;
3278 /* while j <= s-1 and y != n1 */
3279 while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
3280 if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
3281 goto __Y;
3282 }
3283
3284 /* if y == 1 then composite */
3285 if (mp_cmp_d (&y, 1) == MP_EQ) {
3286 goto __Y;
3287 }
3288
3289 ++j;
3290 }
3291
3292 /* if y != n1 then composite */
3293 if (mp_cmp (&y, &n1) != MP_EQ) {
3294 goto __Y;
3295 }
3296 }
3297
3298 /* probably prime now */
3299 *result = MP_YES;
3300 __Y:mp_clear (&y);
3301 __R:mp_clear (&r);
3302 __N1:mp_clear (&n1);
3303 return err;
3304 }
3305
3306 /* performs a variable number of rounds of Miller-Rabin
3307 *
3308 * Probability of error after t rounds is no more than
3309
3310 *
3311 * Sets result to 1 if probably prime, 0 otherwise
3312 */
3313 static int mp_prime_is_prime (mp_int * a, int t, int *result)
3314 {
3315 mp_int b;
3316 int ix, err, res;
3317
3318 /* default to no */
3319 *result = MP_NO;
3320
3321 /* valid value of t? */
3322 if (t <= 0 || t > PRIME_SIZE) {
3323 return MP_VAL;
3324 }
3325
3326 /* is the input equal to one of the primes in the table? */
3327 for (ix = 0; ix < PRIME_SIZE; ix++) {
3328 if (mp_cmp_d(a, __prime_tab[ix]) == MP_EQ) {
3329 *result = 1;
3330 return MP_OKAY;
3331 }
3332 }
3333
3334 /* first perform trial division */
3335 if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
3336 return err;
3337 }
3338
3339 /* return if it was trivially divisible */
3340 if (res == MP_YES) {
3341 return MP_OKAY;
3342 }
3343
3344 /* now perform the miller-rabin rounds */
3345 if ((err = mp_init (&b)) != MP_OKAY) {
3346 return err;
3347 }
3348
3349 for (ix = 0; ix < t; ix++) {
3350 /* set the prime */
3351 mp_set (&b, __prime_tab[ix]);
3352
3353 if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
3354 goto __B;
3355 }
3356
3357 if (res == MP_NO) {
3358 goto __B;
3359 }
3360 }
3361
3362 /* passed the test */
3363 *result = MP_YES;
3364 __B:mp_clear (&b);
3365 return err;
3366 }
3367
3368 static const struct {
3369 int k, t;
3370 } sizes[] = {
3371 { 128, 28 },
3372 { 256, 16 },
3373 { 384, 10 },
3374 { 512, 7 },
3375 { 640, 6 },
3376 { 768, 5 },
3377 { 896, 4 },