1 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
2 * All rights reserved.
3 *
4 * This package is an SSL implementation written
5 * by Eric Young (eay@cryptsoft.com).
6 * The implementation was written so as to conform with Netscapes SSL.
7 *
8 * This library is free for commercial and non-commercial use as long as
9 * the following conditions are aheared to. The following conditions
10 * apply to all code found in this distribution, be it the RC4, RSA,
11 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
12 * included with this distribution is covered by the same copyright terms
13 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
14 *
15 * Copyright remains Eric Young's, and as such any Copyright notices in
16 * the code are not to be removed.
17 * If this package is used in a product, Eric Young should be given attribution
18 * as the author of the parts of the library used.
19 * This can be in the form of a textual message at program startup or
20 * in documentation (online or textual) provided with the package.
21 *
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
24 * are met:
25 * 1. Redistributions of source code must retain the copyright
26 * notice, this list of conditions and the following disclaimer.
27 * 2. Redistributions in binary form must reproduce the above copyright
28 * notice, this list of conditions and the following disclaimer in the
29 * documentation and/or other materials provided with the distribution.
30 * 3. All advertising materials mentioning features or use of this software
31 * must display the following acknowledgement:
32 * "This product includes cryptographic software written by
33 * Eric Young (eay@cryptsoft.com)"
34 * The word 'cryptographic' can be left out if the rouines from the library
35 * being used are not cryptographic related :-).
36 * 4. If you include any Windows specific code (or a derivative thereof) from
37 * the apps directory (application code) you must include an acknowledgement:
38 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
39 *
40 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
41 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
43 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
44 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
45 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
46 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
48 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
49 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
50 * SUCH DAMAGE.
51 *
52 * The licence and distribution terms for any publically available version or
53 * derivative of this code cannot be changed. i.e. this code cannot simply be
54 * copied and put under another distribution licence
55 * [including the GNU Public Licence.] */
56
57 #include <openssl/bn.h>
58
59 #include <assert.h>
60 #include <string.h>
61
62 #include "internal.h"
63
64
bn_mul_normal(BN_ULONG * r,BN_ULONG * a,int na,BN_ULONG * b,int nb)65 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb) {
66 BN_ULONG *rr;
67
68 if (na < nb) {
69 int itmp;
70 BN_ULONG *ltmp;
71
72 itmp = na;
73 na = nb;
74 nb = itmp;
75 ltmp = a;
76 a = b;
77 b = ltmp;
78 }
79 rr = &(r[na]);
80 if (nb <= 0) {
81 (void)bn_mul_words(r, a, na, 0);
82 return;
83 } else {
84 rr[0] = bn_mul_words(r, a, na, b[0]);
85 }
86
87 for (;;) {
88 if (--nb <= 0) {
89 return;
90 }
91 rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
92 if (--nb <= 0) {
93 return;
94 }
95 rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
96 if (--nb <= 0) {
97 return;
98 }
99 rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
100 if (--nb <= 0) {
101 return;
102 }
103 rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
104 rr += 4;
105 r += 4;
106 b += 4;
107 }
108 }
109
bn_mul_low_normal(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b,int n)110 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n) {
111 bn_mul_words(r, a, n, b[0]);
112
113 for (;;) {
114 if (--n <= 0) {
115 return;
116 }
117 bn_mul_add_words(&(r[1]), a, n, b[1]);
118 if (--n <= 0) {
119 return;
120 }
121 bn_mul_add_words(&(r[2]), a, n, b[2]);
122 if (--n <= 0) {
123 return;
124 }
125 bn_mul_add_words(&(r[3]), a, n, b[3]);
126 if (--n <= 0) {
127 return;
128 }
129 bn_mul_add_words(&(r[4]), a, n, b[4]);
130 r += 4;
131 b += 4;
132 }
133 }
134
135 #if !defined(OPENSSL_X86) || defined(OPENSSL_NO_ASM)
136 /* Here follows specialised variants of bn_add_words() and bn_sub_words(). They
137 * have the property performing operations on arrays of different sizes. The
138 * sizes of those arrays is expressed through cl, which is the common length (
139 * basicall, min(len(a),len(b)) ), and dl, which is the delta between the two
140 * lengths, calculated as len(a)-len(b). All lengths are the number of
141 * BN_ULONGs... For the operations that require a result array as parameter,
142 * it must have the length cl+abs(dl). These functions should probably end up
143 * in bn_asm.c as soon as there are assembler counterparts for the systems that
144 * use assembler files. */
145
bn_sub_part_words(BN_ULONG * r,const BN_ULONG * a,const BN_ULONG * b,int cl,int dl)146 static BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a,
147 const BN_ULONG *b, int cl, int dl) {
148 BN_ULONG c, t;
149
150 assert(cl >= 0);
151 c = bn_sub_words(r, a, b, cl);
152
153 if (dl == 0) {
154 return c;
155 }
156
157 r += cl;
158 a += cl;
159 b += cl;
160
161 if (dl < 0) {
162 for (;;) {
163 t = b[0];
164 r[0] = (0 - t - c) & BN_MASK2;
165 if (t != 0) {
166 c = 1;
167 }
168 if (++dl >= 0) {
169 break;
170 }
171
172 t = b[1];
173 r[1] = (0 - t - c) & BN_MASK2;
174 if (t != 0) {
175 c = 1;
176 }
177 if (++dl >= 0) {
178 break;
179 }
180
181 t = b[2];
182 r[2] = (0 - t - c) & BN_MASK2;
183 if (t != 0) {
184 c = 1;
185 }
186 if (++dl >= 0) {
187 break;
188 }
189
190 t = b[3];
191 r[3] = (0 - t - c) & BN_MASK2;
192 if (t != 0) {
193 c = 1;
194 }
195 if (++dl >= 0) {
196 break;
197 }
198
199 b += 4;
200 r += 4;
201 }
202 } else {
203 int save_dl = dl;
204 while (c) {
205 t = a[0];
206 r[0] = (t - c) & BN_MASK2;
207 if (t != 0) {
208 c = 0;
209 }
210 if (--dl <= 0) {
211 break;
212 }
213
214 t = a[1];
215 r[1] = (t - c) & BN_MASK2;
216 if (t != 0) {
217 c = 0;
218 }
219 if (--dl <= 0) {
220 break;
221 }
222
223 t = a[2];
224 r[2] = (t - c) & BN_MASK2;
225 if (t != 0) {
226 c = 0;
227 }
228 if (--dl <= 0) {
229 break;
230 }
231
232 t = a[3];
233 r[3] = (t - c) & BN_MASK2;
234 if (t != 0) {
235 c = 0;
236 }
237 if (--dl <= 0) {
238 break;
239 }
240
241 save_dl = dl;
242 a += 4;
243 r += 4;
244 }
245 if (dl > 0) {
246 if (save_dl > dl) {
247 switch (save_dl - dl) {
248 case 1:
249 r[1] = a[1];
250 if (--dl <= 0) {
251 break;
252 }
253 case 2:
254 r[2] = a[2];
255 if (--dl <= 0) {
256 break;
257 }
258 case 3:
259 r[3] = a[3];
260 if (--dl <= 0) {
261 break;
262 }
263 }
264 a += 4;
265 r += 4;
266 }
267 }
268
269 if (dl > 0) {
270 for (;;) {
271 r[0] = a[0];
272 if (--dl <= 0) {
273 break;
274 }
275 r[1] = a[1];
276 if (--dl <= 0) {
277 break;
278 }
279 r[2] = a[2];
280 if (--dl <= 0) {
281 break;
282 }
283 r[3] = a[3];
284 if (--dl <= 0) {
285 break;
286 }
287
288 a += 4;
289 r += 4;
290 }
291 }
292 }
293
294 return c;
295 }
296 #else
297 /* On other platforms the function is defined in asm. */
298 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
299 int cl, int dl);
300 #endif
301
302 /* Karatsuba recursive multiplication algorithm
303 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
304
305 /* r is 2*n2 words in size,
306 * a and b are both n2 words in size.
307 * n2 must be a power of 2.
308 * We multiply and return the result.
309 * t must be 2*n2 words in size
310 * We calculate
311 * a[0]*b[0]
312 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
313 * a[1]*b[1]
314 */
315 /* dnX may not be positive, but n2/2+dnX has to be */
bn_mul_recursive(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b,int n2,int dna,int dnb,BN_ULONG * t)316 static void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
317 int dna, int dnb, BN_ULONG *t) {
318 int n = n2 / 2, c1, c2;
319 int tna = n + dna, tnb = n + dnb;
320 unsigned int neg, zero;
321 BN_ULONG ln, lo, *p;
322
323 /* Only call bn_mul_comba 8 if n2 == 8 and the
324 * two arrays are complete [steve]
325 */
326 if (n2 == 8 && dna == 0 && dnb == 0) {
327 bn_mul_comba8(r, a, b);
328 return;
329 }
330
331 /* Else do normal multiply */
332 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
333 bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
334 if ((dna + dnb) < 0) {
335 memset(&r[2 * n2 + dna + dnb], 0, sizeof(BN_ULONG) * -(dna + dnb));
336 }
337 return;
338 }
339
340 /* r=(a[0]-a[1])*(b[1]-b[0]) */
341 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
342 c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
343 zero = neg = 0;
344 switch (c1 * 3 + c2) {
345 case -4:
346 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
347 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
348 break;
349 case -3:
350 zero = 1;
351 break;
352 case -2:
353 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
354 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
355 neg = 1;
356 break;
357 case -1:
358 case 0:
359 case 1:
360 zero = 1;
361 break;
362 case 2:
363 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
364 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
365 neg = 1;
366 break;
367 case 3:
368 zero = 1;
369 break;
370 case 4:
371 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
372 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
373 break;
374 }
375
376 if (n == 4 && dna == 0 && dnb == 0) {
377 /* XXX: bn_mul_comba4 could take extra args to do this well */
378 if (!zero) {
379 bn_mul_comba4(&(t[n2]), t, &(t[n]));
380 } else {
381 memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
382 }
383
384 bn_mul_comba4(r, a, b);
385 bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
386 } else if (n == 8 && dna == 0 && dnb == 0) {
387 /* XXX: bn_mul_comba8 could take extra args to do this well */
388 if (!zero) {
389 bn_mul_comba8(&(t[n2]), t, &(t[n]));
390 } else {
391 memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
392 }
393
394 bn_mul_comba8(r, a, b);
395 bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
396 } else {
397 p = &(t[n2 * 2]);
398 if (!zero) {
399 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
400 } else {
401 memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
402 }
403 bn_mul_recursive(r, a, b, n, 0, 0, p);
404 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
405 }
406
407 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
408 * r[10] holds (a[0]*b[0])
409 * r[32] holds (b[1]*b[1]) */
410
411 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
412
413 if (neg) {
414 /* if t[32] is negative */
415 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
416 } else {
417 /* Might have a carry */
418 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
419 }
420
421 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
422 * r[10] holds (a[0]*b[0])
423 * r[32] holds (b[1]*b[1])
424 * c1 holds the carry bits */
425 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
426 if (c1) {
427 p = &(r[n + n2]);
428 lo = *p;
429 ln = (lo + c1) & BN_MASK2;
430 *p = ln;
431
432 /* The overflow will stop before we over write
433 * words we should not overwrite */
434 if (ln < (BN_ULONG)c1) {
435 do {
436 p++;
437 lo = *p;
438 ln = (lo + 1) & BN_MASK2;
439 *p = ln;
440 } while (ln == 0);
441 }
442 }
443 }
444
445 /* n+tn is the word length
446 * t needs to be n*4 is size, as does r */
447 /* tnX may not be negative but less than n */
bn_mul_part_recursive(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b,int n,int tna,int tnb,BN_ULONG * t)448 static void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
449 int tna, int tnb, BN_ULONG *t) {
450 int i, j, n2 = n * 2;
451 int c1, c2, neg;
452 BN_ULONG ln, lo, *p;
453
454 if (n < 8) {
455 bn_mul_normal(r, a, n + tna, b, n + tnb);
456 return;
457 }
458
459 /* r=(a[0]-a[1])*(b[1]-b[0]) */
460 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
461 c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
462 neg = 0;
463 switch (c1 * 3 + c2) {
464 case -4:
465 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
466 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
467 break;
468 case -3:
469 /* break; */
470 case -2:
471 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
472 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
473 neg = 1;
474 break;
475 case -1:
476 case 0:
477 case 1:
478 /* break; */
479 case 2:
480 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
481 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
482 neg = 1;
483 break;
484 case 3:
485 /* break; */
486 case 4:
487 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
488 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
489 break;
490 }
491
492 if (n == 8) {
493 bn_mul_comba8(&(t[n2]), t, &(t[n]));
494 bn_mul_comba8(r, a, b);
495 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
496 memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
497 } else {
498 p = &(t[n2 * 2]);
499 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
500 bn_mul_recursive(r, a, b, n, 0, 0, p);
501 i = n / 2;
502 /* If there is only a bottom half to the number,
503 * just do it */
504 if (tna > tnb) {
505 j = tna - i;
506 } else {
507 j = tnb - i;
508 }
509
510 if (j == 0) {
511 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p);
512 memset(&(r[n2 + i * 2]), 0, sizeof(BN_ULONG) * (n2 - i * 2));
513 } else if (j > 0) {
514 /* eg, n == 16, i == 8 and tn == 11 */
515 bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p);
516 memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
517 } else {
518 /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
519 memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
520 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
521 tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
522 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
523 } else {
524 for (;;) {
525 i /= 2;
526 /* these simplified conditions work
527 * exclusively because difference
528 * between tna and tnb is 1 or 0 */
529 if (i < tna || i < tnb) {
530 bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i,
531 tnb - i, p);
532 break;
533 } else if (i == tna || i == tnb) {
534 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i,
535 p);
536 break;
537 }
538 }
539 }
540 }
541 }
542
543 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
544 * r[10] holds (a[0]*b[0])
545 * r[32] holds (b[1]*b[1])
546 */
547
548 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
549
550 if (neg) {
551 /* if t[32] is negative */
552 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
553 } else {
554 /* Might have a carry */
555 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
556 }
557
558 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
559 * r[10] holds (a[0]*b[0])
560 * r[32] holds (b[1]*b[1])
561 * c1 holds the carry bits */
562 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
563 if (c1) {
564 p = &(r[n + n2]);
565 lo = *p;
566 ln = (lo + c1) & BN_MASK2;
567 *p = ln;
568
569 /* The overflow will stop before we over write
570 * words we should not overwrite */
571 if (ln < (BN_ULONG)c1) {
572 do {
573 p++;
574 lo = *p;
575 ln = (lo + 1) & BN_MASK2;
576 *p = ln;
577 } while (ln == 0);
578 }
579 }
580 }
581
BN_mul(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)582 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
583 int ret = 0;
584 int top, al, bl;
585 BIGNUM *rr;
586 int i;
587 BIGNUM *t = NULL;
588 int j = 0, k;
589
590 al = a->top;
591 bl = b->top;
592
593 if ((al == 0) || (bl == 0)) {
594 BN_zero(r);
595 return 1;
596 }
597 top = al + bl;
598
599 BN_CTX_start(ctx);
600 if ((r == a) || (r == b)) {
601 if ((rr = BN_CTX_get(ctx)) == NULL) {
602 goto err;
603 }
604 } else {
605 rr = r;
606 }
607 rr->neg = a->neg ^ b->neg;
608
609 i = al - bl;
610 if (i == 0) {
611 if (al == 8) {
612 if (bn_wexpand(rr, 16) == NULL) {
613 goto err;
614 }
615 rr->top = 16;
616 bn_mul_comba8(rr->d, a->d, b->d);
617 goto end;
618 }
619 }
620
621 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
622 if (i >= -1 && i <= 1) {
623 /* Find out the power of two lower or equal
624 to the longest of the two numbers */
625 if (i >= 0) {
626 j = BN_num_bits_word((BN_ULONG)al);
627 }
628 if (i == -1) {
629 j = BN_num_bits_word((BN_ULONG)bl);
630 }
631 j = 1 << (j - 1);
632 assert(j <= al || j <= bl);
633 k = j + j;
634 t = BN_CTX_get(ctx);
635 if (t == NULL) {
636 goto err;
637 }
638 if (al > j || bl > j) {
639 if (bn_wexpand(t, k * 4) == NULL) {
640 goto err;
641 }
642 if (bn_wexpand(rr, k * 4) == NULL) {
643 goto err;
644 }
645 bn_mul_part_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
646 } else {
647 /* al <= j || bl <= j */
648 if (bn_wexpand(t, k * 2) == NULL) {
649 goto err;
650 }
651 if (bn_wexpand(rr, k * 2) == NULL) {
652 goto err;
653 }
654 bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
655 }
656 rr->top = top;
657 goto end;
658 }
659 }
660
661 if (bn_wexpand(rr, top) == NULL) {
662 goto err;
663 }
664 rr->top = top;
665 bn_mul_normal(rr->d, a->d, al, b->d, bl);
666
667 end:
668 bn_correct_top(rr);
669 if (r != rr && !BN_copy(r, rr)) {
670 goto err;
671 }
672 ret = 1;
673
674 err:
675 BN_CTX_end(ctx);
676 return ret;
677 }
678
679 /* tmp must have 2*n words */
bn_sqr_normal(BN_ULONG * r,const BN_ULONG * a,int n,BN_ULONG * tmp)680 static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp) {
681 int i, j, max;
682 const BN_ULONG *ap;
683 BN_ULONG *rp;
684
685 max = n * 2;
686 ap = a;
687 rp = r;
688 rp[0] = rp[max - 1] = 0;
689 rp++;
690 j = n;
691
692 if (--j > 0) {
693 ap++;
694 rp[j] = bn_mul_words(rp, ap, j, ap[-1]);
695 rp += 2;
696 }
697
698 for (i = n - 2; i > 0; i--) {
699 j--;
700 ap++;
701 rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]);
702 rp += 2;
703 }
704
705 bn_add_words(r, r, r, max);
706
707 /* There will not be a carry */
708
709 bn_sqr_words(tmp, a, n);
710
711 bn_add_words(r, r, tmp, max);
712 }
713
714 /* r is 2*n words in size,
715 * a and b are both n words in size. (There's not actually a 'b' here ...)
716 * n must be a power of 2.
717 * We multiply and return the result.
718 * t must be 2*n words in size
719 * We calculate
720 * a[0]*b[0]
721 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
722 * a[1]*b[1]
723 */
bn_sqr_recursive(BN_ULONG * r,const BN_ULONG * a,int n2,BN_ULONG * t)724 static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t) {
725 int n = n2 / 2;
726 int zero, c1;
727 BN_ULONG ln, lo, *p;
728
729 if (n2 == 4) {
730 bn_sqr_comba4(r, a);
731 return;
732 } else if (n2 == 8) {
733 bn_sqr_comba8(r, a);
734 return;
735 }
736 if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
737 bn_sqr_normal(r, a, n2, t);
738 return;
739 }
740 /* r=(a[0]-a[1])*(a[1]-a[0]) */
741 c1 = bn_cmp_words(a, &(a[n]), n);
742 zero = 0;
743 if (c1 > 0) {
744 bn_sub_words(t, a, &(a[n]), n);
745 } else if (c1 < 0) {
746 bn_sub_words(t, &(a[n]), a, n);
747 } else {
748 zero = 1;
749 }
750
751 /* The result will always be negative unless it is zero */
752 p = &(t[n2 * 2]);
753
754 if (!zero) {
755 bn_sqr_recursive(&(t[n2]), t, n, p);
756 } else {
757 memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
758 }
759 bn_sqr_recursive(r, a, n, p);
760 bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
761
762 /* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
763 * r[10] holds (a[0]*b[0])
764 * r[32] holds (b[1]*b[1]) */
765
766 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
767
768 /* t[32] is negative */
769 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
770
771 /* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
772 * r[10] holds (a[0]*a[0])
773 * r[32] holds (a[1]*a[1])
774 * c1 holds the carry bits */
775 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
776 if (c1) {
777 p = &(r[n + n2]);
778 lo = *p;
779 ln = (lo + c1) & BN_MASK2;
780 *p = ln;
781
782 /* The overflow will stop before we over write
783 * words we should not overwrite */
784 if (ln < (BN_ULONG)c1) {
785 do {
786 p++;
787 lo = *p;
788 ln = (lo + 1) & BN_MASK2;
789 *p = ln;
790 } while (ln == 0);
791 }
792 }
793 }
794
BN_mul_word(BIGNUM * bn,BN_ULONG w)795 int BN_mul_word(BIGNUM *bn, BN_ULONG w) {
796 BN_ULONG ll;
797
798 w &= BN_MASK2;
799 if (!bn->top) {
800 return 1;
801 }
802
803 if (w == 0) {
804 BN_zero(bn);
805 return 1;
806 }
807
808 ll = bn_mul_words(bn->d, bn->d, bn->top, w);
809 if (ll) {
810 if (bn_wexpand(bn, bn->top + 1) == NULL) {
811 return 0;
812 }
813 bn->d[bn->top++] = ll;
814 }
815
816 return 1;
817 }
818
BN_sqr(BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)819 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
820 int max, al;
821 int ret = 0;
822 BIGNUM *tmp, *rr;
823
824 al = a->top;
825 if (al <= 0) {
826 r->top = 0;
827 r->neg = 0;
828 return 1;
829 }
830
831 BN_CTX_start(ctx);
832 rr = (a != r) ? r : BN_CTX_get(ctx);
833 tmp = BN_CTX_get(ctx);
834 if (!rr || !tmp) {
835 goto err;
836 }
837
838 max = 2 * al; /* Non-zero (from above) */
839 if (bn_wexpand(rr, max) == NULL) {
840 goto err;
841 }
842
843 if (al == 4) {
844 bn_sqr_comba4(rr->d, a->d);
845 } else if (al == 8) {
846 bn_sqr_comba8(rr->d, a->d);
847 } else {
848 if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
849 BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
850 bn_sqr_normal(rr->d, a->d, al, t);
851 } else {
852 int j, k;
853
854 j = BN_num_bits_word((BN_ULONG)al);
855 j = 1 << (j - 1);
856 k = j + j;
857 if (al == j) {
858 if (bn_wexpand(tmp, k * 2) == NULL) {
859 goto err;
860 }
861 bn_sqr_recursive(rr->d, a->d, al, tmp->d);
862 } else {
863 if (bn_wexpand(tmp, max) == NULL) {
864 goto err;
865 }
866 bn_sqr_normal(rr->d, a->d, al, tmp->d);
867 }
868 }
869 }
870
871 rr->neg = 0;
872 /* If the most-significant half of the top word of 'a' is zero, then
873 * the square of 'a' will max-1 words. */
874 if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l)) {
875 rr->top = max - 1;
876 } else {
877 rr->top = max;
878 }
879
880 if (rr != r && !BN_copy(r, rr)) {
881 goto err;
882 }
883 ret = 1;
884
885 err:
886 BN_CTX_end(ctx);
887 return ret;
888 }
889