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
65 #define BN_MUL_RECURSIVE_SIZE_NORMAL 16
66 #define BN_SQR_RECURSIVE_SIZE_NORMAL BN_MUL_RECURSIVE_SIZE_NORMAL
67
68
bn_mul_normal(BN_ULONG * r,BN_ULONG * a,int na,BN_ULONG * b,int nb)69 static void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
70 int nb) {
71 BN_ULONG *rr;
72
73 if (na < nb) {
74 int itmp;
75 BN_ULONG *ltmp;
76
77 itmp = na;
78 na = nb;
79 nb = itmp;
80 ltmp = a;
81 a = b;
82 b = ltmp;
83 }
84 rr = &(r[na]);
85 if (nb <= 0) {
86 (void)bn_mul_words(r, a, na, 0);
87 return;
88 } else {
89 rr[0] = bn_mul_words(r, a, na, b[0]);
90 }
91
92 for (;;) {
93 if (--nb <= 0) {
94 return;
95 }
96 rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
97 if (--nb <= 0) {
98 return;
99 }
100 rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
101 if (--nb <= 0) {
102 return;
103 }
104 rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
105 if (--nb <= 0) {
106 return;
107 }
108 rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
109 rr += 4;
110 r += 4;
111 b += 4;
112 }
113 }
114
115 #if !defined(OPENSSL_X86) || defined(OPENSSL_NO_ASM)
116 /* Here follows specialised variants of bn_add_words() and bn_sub_words(). They
117 * have the property performing operations on arrays of different sizes. The
118 * sizes of those arrays is expressed through cl, which is the common length (
119 * basicall, min(len(a),len(b)) ), and dl, which is the delta between the two
120 * lengths, calculated as len(a)-len(b). All lengths are the number of
121 * BN_ULONGs... For the operations that require a result array as parameter,
122 * it must have the length cl+abs(dl). These functions should probably end up
123 * in bn_asm.c as soon as there are assembler counterparts for the systems that
124 * use assembler files. */
125
bn_sub_part_words(BN_ULONG * r,const BN_ULONG * a,const BN_ULONG * b,int cl,int dl)126 static BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a,
127 const BN_ULONG *b, int cl, int dl) {
128 BN_ULONG c, t;
129
130 assert(cl >= 0);
131 c = bn_sub_words(r, a, b, cl);
132
133 if (dl == 0) {
134 return c;
135 }
136
137 r += cl;
138 a += cl;
139 b += cl;
140
141 if (dl < 0) {
142 for (;;) {
143 t = b[0];
144 r[0] = (0 - t - c) & BN_MASK2;
145 if (t != 0) {
146 c = 1;
147 }
148 if (++dl >= 0) {
149 break;
150 }
151
152 t = b[1];
153 r[1] = (0 - t - c) & BN_MASK2;
154 if (t != 0) {
155 c = 1;
156 }
157 if (++dl >= 0) {
158 break;
159 }
160
161 t = b[2];
162 r[2] = (0 - t - c) & BN_MASK2;
163 if (t != 0) {
164 c = 1;
165 }
166 if (++dl >= 0) {
167 break;
168 }
169
170 t = b[3];
171 r[3] = (0 - t - c) & BN_MASK2;
172 if (t != 0) {
173 c = 1;
174 }
175 if (++dl >= 0) {
176 break;
177 }
178
179 b += 4;
180 r += 4;
181 }
182 } else {
183 int save_dl = dl;
184 while (c) {
185 t = a[0];
186 r[0] = (t - c) & BN_MASK2;
187 if (t != 0) {
188 c = 0;
189 }
190 if (--dl <= 0) {
191 break;
192 }
193
194 t = a[1];
195 r[1] = (t - c) & BN_MASK2;
196 if (t != 0) {
197 c = 0;
198 }
199 if (--dl <= 0) {
200 break;
201 }
202
203 t = a[2];
204 r[2] = (t - c) & BN_MASK2;
205 if (t != 0) {
206 c = 0;
207 }
208 if (--dl <= 0) {
209 break;
210 }
211
212 t = a[3];
213 r[3] = (t - c) & BN_MASK2;
214 if (t != 0) {
215 c = 0;
216 }
217 if (--dl <= 0) {
218 break;
219 }
220
221 save_dl = dl;
222 a += 4;
223 r += 4;
224 }
225 if (dl > 0) {
226 if (save_dl > dl) {
227 switch (save_dl - dl) {
228 case 1:
229 r[1] = a[1];
230 if (--dl <= 0) {
231 break;
232 }
233 case 2:
234 r[2] = a[2];
235 if (--dl <= 0) {
236 break;
237 }
238 case 3:
239 r[3] = a[3];
240 if (--dl <= 0) {
241 break;
242 }
243 }
244 a += 4;
245 r += 4;
246 }
247 }
248
249 if (dl > 0) {
250 for (;;) {
251 r[0] = a[0];
252 if (--dl <= 0) {
253 break;
254 }
255 r[1] = a[1];
256 if (--dl <= 0) {
257 break;
258 }
259 r[2] = a[2];
260 if (--dl <= 0) {
261 break;
262 }
263 r[3] = a[3];
264 if (--dl <= 0) {
265 break;
266 }
267
268 a += 4;
269 r += 4;
270 }
271 }
272 }
273
274 return c;
275 }
276 #else
277 /* On other platforms the function is defined in asm. */
278 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
279 int cl, int dl);
280 #endif
281
282 /* Karatsuba recursive multiplication algorithm
283 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
284
285 /* r is 2*n2 words in size,
286 * a and b are both n2 words in size.
287 * n2 must be a power of 2.
288 * We multiply and return the result.
289 * t must be 2*n2 words in size
290 * We calculate
291 * a[0]*b[0]
292 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
293 * a[1]*b[1]
294 */
295 /* 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)296 static void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
297 int dna, int dnb, BN_ULONG *t) {
298 int n = n2 / 2, c1, c2;
299 int tna = n + dna, tnb = n + dnb;
300 unsigned int neg, zero;
301 BN_ULONG ln, lo, *p;
302
303 /* Only call bn_mul_comba 8 if n2 == 8 and the
304 * two arrays are complete [steve]
305 */
306 if (n2 == 8 && dna == 0 && dnb == 0) {
307 bn_mul_comba8(r, a, b);
308 return;
309 }
310
311 /* Else do normal multiply */
312 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
313 bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
314 if ((dna + dnb) < 0) {
315 OPENSSL_memset(&r[2 * n2 + dna + dnb], 0,
316 sizeof(BN_ULONG) * -(dna + dnb));
317 }
318 return;
319 }
320
321 /* r=(a[0]-a[1])*(b[1]-b[0]) */
322 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
323 c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
324 zero = neg = 0;
325 switch (c1 * 3 + c2) {
326 case -4:
327 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
328 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
329 break;
330 case -3:
331 zero = 1;
332 break;
333 case -2:
334 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
335 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
336 neg = 1;
337 break;
338 case -1:
339 case 0:
340 case 1:
341 zero = 1;
342 break;
343 case 2:
344 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
345 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
346 neg = 1;
347 break;
348 case 3:
349 zero = 1;
350 break;
351 case 4:
352 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
353 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
354 break;
355 }
356
357 if (n == 4 && dna == 0 && dnb == 0) {
358 /* XXX: bn_mul_comba4 could take extra args to do this well */
359 if (!zero) {
360 bn_mul_comba4(&(t[n2]), t, &(t[n]));
361 } else {
362 OPENSSL_memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
363 }
364
365 bn_mul_comba4(r, a, b);
366 bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
367 } else if (n == 8 && dna == 0 && dnb == 0) {
368 /* XXX: bn_mul_comba8 could take extra args to do this well */
369 if (!zero) {
370 bn_mul_comba8(&(t[n2]), t, &(t[n]));
371 } else {
372 OPENSSL_memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
373 }
374
375 bn_mul_comba8(r, a, b);
376 bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
377 } else {
378 p = &(t[n2 * 2]);
379 if (!zero) {
380 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
381 } else {
382 OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
383 }
384 bn_mul_recursive(r, a, b, n, 0, 0, p);
385 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
386 }
387
388 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
389 * r[10] holds (a[0]*b[0])
390 * r[32] holds (b[1]*b[1]) */
391
392 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
393
394 if (neg) {
395 /* if t[32] is negative */
396 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
397 } else {
398 /* Might have a carry */
399 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
400 }
401
402 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
403 * r[10] holds (a[0]*b[0])
404 * r[32] holds (b[1]*b[1])
405 * c1 holds the carry bits */
406 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
407 if (c1) {
408 p = &(r[n + n2]);
409 lo = *p;
410 ln = (lo + c1) & BN_MASK2;
411 *p = ln;
412
413 /* The overflow will stop before we over write
414 * words we should not overwrite */
415 if (ln < (BN_ULONG)c1) {
416 do {
417 p++;
418 lo = *p;
419 ln = (lo + 1) & BN_MASK2;
420 *p = ln;
421 } while (ln == 0);
422 }
423 }
424 }
425
426 /* n+tn is the word length
427 * t needs to be n*4 is size, as does r */
428 /* 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)429 static void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
430 int tna, int tnb, BN_ULONG *t) {
431 int i, j, n2 = n * 2;
432 int c1, c2, neg;
433 BN_ULONG ln, lo, *p;
434
435 if (n < 8) {
436 bn_mul_normal(r, a, n + tna, b, n + tnb);
437 return;
438 }
439
440 /* r=(a[0]-a[1])*(b[1]-b[0]) */
441 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
442 c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
443 neg = 0;
444 switch (c1 * 3 + c2) {
445 case -4:
446 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
447 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
448 break;
449 case -3:
450 /* break; */
451 case -2:
452 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
453 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
454 neg = 1;
455 break;
456 case -1:
457 case 0:
458 case 1:
459 /* break; */
460 case 2:
461 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
462 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
463 neg = 1;
464 break;
465 case 3:
466 /* break; */
467 case 4:
468 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
469 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
470 break;
471 }
472
473 if (n == 8) {
474 bn_mul_comba8(&(t[n2]), t, &(t[n]));
475 bn_mul_comba8(r, a, b);
476 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
477 OPENSSL_memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
478 } else {
479 p = &(t[n2 * 2]);
480 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
481 bn_mul_recursive(r, a, b, n, 0, 0, p);
482 i = n / 2;
483 /* If there is only a bottom half to the number,
484 * just do it */
485 if (tna > tnb) {
486 j = tna - i;
487 } else {
488 j = tnb - i;
489 }
490
491 if (j == 0) {
492 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p);
493 OPENSSL_memset(&(r[n2 + i * 2]), 0, sizeof(BN_ULONG) * (n2 - i * 2));
494 } else if (j > 0) {
495 /* eg, n == 16, i == 8 and tn == 11 */
496 bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p);
497 OPENSSL_memset(&(r[n2 + tna + tnb]), 0,
498 sizeof(BN_ULONG) * (n2 - tna - tnb));
499 } else {
500 /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
501 OPENSSL_memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
502 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
503 tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
504 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
505 } else {
506 for (;;) {
507 i /= 2;
508 /* these simplified conditions work
509 * exclusively because difference
510 * between tna and tnb is 1 or 0 */
511 if (i < tna || i < tnb) {
512 bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i,
513 tnb - i, p);
514 break;
515 } else if (i == tna || i == tnb) {
516 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i,
517 p);
518 break;
519 }
520 }
521 }
522 }
523 }
524
525 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
526 * r[10] holds (a[0]*b[0])
527 * r[32] holds (b[1]*b[1])
528 */
529
530 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
531
532 if (neg) {
533 /* if t[32] is negative */
534 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
535 } else {
536 /* Might have a carry */
537 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
538 }
539
540 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
541 * r[10] holds (a[0]*b[0])
542 * r[32] holds (b[1]*b[1])
543 * c1 holds the carry bits */
544 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
545 if (c1) {
546 p = &(r[n + n2]);
547 lo = *p;
548 ln = (lo + c1) & BN_MASK2;
549 *p = ln;
550
551 /* The overflow will stop before we over write
552 * words we should not overwrite */
553 if (ln < (BN_ULONG)c1) {
554 do {
555 p++;
556 lo = *p;
557 ln = (lo + 1) & BN_MASK2;
558 *p = ln;
559 } while (ln == 0);
560 }
561 }
562 }
563
BN_mul(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)564 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
565 int ret = 0;
566 int top, al, bl;
567 BIGNUM *rr;
568 int i;
569 BIGNUM *t = NULL;
570 int j = 0, k;
571
572 al = a->top;
573 bl = b->top;
574
575 if ((al == 0) || (bl == 0)) {
576 BN_zero(r);
577 return 1;
578 }
579 top = al + bl;
580
581 BN_CTX_start(ctx);
582 if ((r == a) || (r == b)) {
583 if ((rr = BN_CTX_get(ctx)) == NULL) {
584 goto err;
585 }
586 } else {
587 rr = r;
588 }
589 rr->neg = a->neg ^ b->neg;
590
591 i = al - bl;
592 if (i == 0) {
593 if (al == 8) {
594 if (!bn_wexpand(rr, 16)) {
595 goto err;
596 }
597 rr->top = 16;
598 bn_mul_comba8(rr->d, a->d, b->d);
599 goto end;
600 }
601 }
602
603 static const int kMulNormalSize = 16;
604 if (al >= kMulNormalSize && bl >= kMulNormalSize) {
605 if (i >= -1 && i <= 1) {
606 /* Find out the power of two lower or equal
607 to the longest of the two numbers */
608 if (i >= 0) {
609 j = BN_num_bits_word((BN_ULONG)al);
610 }
611 if (i == -1) {
612 j = BN_num_bits_word((BN_ULONG)bl);
613 }
614 j = 1 << (j - 1);
615 assert(j <= al || j <= bl);
616 k = j + j;
617 t = BN_CTX_get(ctx);
618 if (t == NULL) {
619 goto err;
620 }
621 if (al > j || bl > j) {
622 if (!bn_wexpand(t, k * 4)) {
623 goto err;
624 }
625 if (!bn_wexpand(rr, k * 4)) {
626 goto err;
627 }
628 bn_mul_part_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
629 } else {
630 /* al <= j || bl <= j */
631 if (!bn_wexpand(t, k * 2)) {
632 goto err;
633 }
634 if (!bn_wexpand(rr, k * 2)) {
635 goto err;
636 }
637 bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
638 }
639 rr->top = top;
640 goto end;
641 }
642 }
643
644 if (!bn_wexpand(rr, top)) {
645 goto err;
646 }
647 rr->top = top;
648 bn_mul_normal(rr->d, a->d, al, b->d, bl);
649
650 end:
651 bn_correct_top(rr);
652 if (r != rr && !BN_copy(r, rr)) {
653 goto err;
654 }
655 ret = 1;
656
657 err:
658 BN_CTX_end(ctx);
659 return ret;
660 }
661
662 /* tmp must have 2*n words */
bn_sqr_normal(BN_ULONG * r,const BN_ULONG * a,int n,BN_ULONG * tmp)663 static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp) {
664 int i, j, max;
665 const BN_ULONG *ap;
666 BN_ULONG *rp;
667
668 max = n * 2;
669 ap = a;
670 rp = r;
671 rp[0] = rp[max - 1] = 0;
672 rp++;
673 j = n;
674
675 if (--j > 0) {
676 ap++;
677 rp[j] = bn_mul_words(rp, ap, j, ap[-1]);
678 rp += 2;
679 }
680
681 for (i = n - 2; i > 0; i--) {
682 j--;
683 ap++;
684 rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]);
685 rp += 2;
686 }
687
688 bn_add_words(r, r, r, max);
689
690 /* There will not be a carry */
691
692 bn_sqr_words(tmp, a, n);
693
694 bn_add_words(r, r, tmp, max);
695 }
696
697 /* r is 2*n words in size,
698 * a and b are both n words in size. (There's not actually a 'b' here ...)
699 * n must be a power of 2.
700 * We multiply and return the result.
701 * t must be 2*n words in size
702 * We calculate
703 * a[0]*b[0]
704 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
705 * a[1]*b[1]
706 */
bn_sqr_recursive(BN_ULONG * r,const BN_ULONG * a,int n2,BN_ULONG * t)707 static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t) {
708 int n = n2 / 2;
709 int zero, c1;
710 BN_ULONG ln, lo, *p;
711
712 if (n2 == 4) {
713 bn_sqr_comba4(r, a);
714 return;
715 } else if (n2 == 8) {
716 bn_sqr_comba8(r, a);
717 return;
718 }
719 if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
720 bn_sqr_normal(r, a, n2, t);
721 return;
722 }
723 /* r=(a[0]-a[1])*(a[1]-a[0]) */
724 c1 = bn_cmp_words(a, &(a[n]), n);
725 zero = 0;
726 if (c1 > 0) {
727 bn_sub_words(t, a, &(a[n]), n);
728 } else if (c1 < 0) {
729 bn_sub_words(t, &(a[n]), a, n);
730 } else {
731 zero = 1;
732 }
733
734 /* The result will always be negative unless it is zero */
735 p = &(t[n2 * 2]);
736
737 if (!zero) {
738 bn_sqr_recursive(&(t[n2]), t, n, p);
739 } else {
740 OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
741 }
742 bn_sqr_recursive(r, a, n, p);
743 bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
744
745 /* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
746 * r[10] holds (a[0]*b[0])
747 * r[32] holds (b[1]*b[1]) */
748
749 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
750
751 /* t[32] is negative */
752 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
753
754 /* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
755 * r[10] holds (a[0]*a[0])
756 * r[32] holds (a[1]*a[1])
757 * c1 holds the carry bits */
758 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
759 if (c1) {
760 p = &(r[n + n2]);
761 lo = *p;
762 ln = (lo + c1) & BN_MASK2;
763 *p = ln;
764
765 /* The overflow will stop before we over write
766 * words we should not overwrite */
767 if (ln < (BN_ULONG)c1) {
768 do {
769 p++;
770 lo = *p;
771 ln = (lo + 1) & BN_MASK2;
772 *p = ln;
773 } while (ln == 0);
774 }
775 }
776 }
777
BN_mul_word(BIGNUM * bn,BN_ULONG w)778 int BN_mul_word(BIGNUM *bn, BN_ULONG w) {
779 BN_ULONG ll;
780
781 w &= BN_MASK2;
782 if (!bn->top) {
783 return 1;
784 }
785
786 if (w == 0) {
787 BN_zero(bn);
788 return 1;
789 }
790
791 ll = bn_mul_words(bn->d, bn->d, bn->top, w);
792 if (ll) {
793 if (!bn_wexpand(bn, bn->top + 1)) {
794 return 0;
795 }
796 bn->d[bn->top++] = ll;
797 }
798
799 return 1;
800 }
801
BN_sqr(BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)802 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
803 int max, al;
804 int ret = 0;
805 BIGNUM *tmp, *rr;
806
807 al = a->top;
808 if (al <= 0) {
809 r->top = 0;
810 r->neg = 0;
811 return 1;
812 }
813
814 BN_CTX_start(ctx);
815 rr = (a != r) ? r : BN_CTX_get(ctx);
816 tmp = BN_CTX_get(ctx);
817 if (!rr || !tmp) {
818 goto err;
819 }
820
821 max = 2 * al; /* Non-zero (from above) */
822 if (!bn_wexpand(rr, max)) {
823 goto err;
824 }
825
826 if (al == 4) {
827 bn_sqr_comba4(rr->d, a->d);
828 } else if (al == 8) {
829 bn_sqr_comba8(rr->d, a->d);
830 } else {
831 if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
832 BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
833 bn_sqr_normal(rr->d, a->d, al, t);
834 } else {
835 int j, k;
836
837 j = BN_num_bits_word((BN_ULONG)al);
838 j = 1 << (j - 1);
839 k = j + j;
840 if (al == j) {
841 if (!bn_wexpand(tmp, k * 2)) {
842 goto err;
843 }
844 bn_sqr_recursive(rr->d, a->d, al, tmp->d);
845 } else {
846 if (!bn_wexpand(tmp, max)) {
847 goto err;
848 }
849 bn_sqr_normal(rr->d, a->d, al, tmp->d);
850 }
851 }
852 }
853
854 rr->neg = 0;
855 /* If the most-significant half of the top word of 'a' is zero, then
856 * the square of 'a' will max-1 words. */
857 if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l)) {
858 rr->top = max - 1;
859 } else {
860 rr->top = max;
861 }
862
863 if (rr != r && !BN_copy(r, rr)) {
864 goto err;
865 }
866 ret = 1;
867
868 err:
869 BN_CTX_end(ctx);
870 return ret;
871 }
872