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 <limits.h>
60 #include <openssl/err.h>
61
62 #include "internal.h"
63
64
65 #define asm __asm__
66
67 #if !defined(OPENSSL_NO_ASM)
68 # if defined(__GNUC__) && __GNUC__>=2
69 # if defined(OPENSSL_X86)
70 /*
71 * There were two reasons for implementing this template:
72 * - GNU C generates a call to a function (__udivdi3 to be exact)
73 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
74 * understand why...);
75 * - divl doesn't only calculate quotient, but also leaves
76 * remainder in %edx which we can definitely use here:-)
77 *
78 * <appro@fy.chalmers.se>
79 */
80 #undef div_asm
81 # define div_asm(n0,n1,d0) \
82 ({ asm volatile ( \
83 "divl %4" \
84 : "=a"(q), "=d"(rem) \
85 : "a"(n1), "d"(n0), "g"(d0) \
86 : "cc"); \
87 q; \
88 })
89 # define REMAINDER_IS_ALREADY_CALCULATED
90 # elif defined(OPENSSL_X86_64)
91 /*
92 * Same story here, but it's 128-bit by 64-bit division. Wow!
93 * <appro@fy.chalmers.se>
94 */
95 # undef div_asm
96 # define div_asm(n0,n1,d0) \
97 ({ asm volatile ( \
98 "divq %4" \
99 : "=a"(q), "=d"(rem) \
100 : "a"(n1), "d"(n0), "g"(d0) \
101 : "cc"); \
102 q; \
103 })
104 # define REMAINDER_IS_ALREADY_CALCULATED
105 # endif /* __<cpu> */
106 # endif /* __GNUC__ */
107 #endif /* OPENSSL_NO_ASM */
108
109 /* BN_div computes dv := num / divisor, rounding towards
110 * zero, and sets up rm such that dv*divisor + rm = num holds.
111 * Thus:
112 * dv->neg == num->neg ^ divisor->neg (unless the result is zero)
113 * rm->neg == num->neg (unless the remainder is zero)
114 * If 'dv' or 'rm' is NULL, the respective value is not returned. */
BN_div(BIGNUM * dv,BIGNUM * rm,const BIGNUM * num,const BIGNUM * divisor,BN_CTX * ctx)115 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
116 BN_CTX *ctx) {
117 int norm_shift, i, loop;
118 BIGNUM *tmp, wnum, *snum, *sdiv, *res;
119 BN_ULONG *resp, *wnump;
120 BN_ULONG d0, d1;
121 int num_n, div_n;
122 int no_branch = 0;
123
124 /* Invalid zero-padding would have particularly bad consequences
125 * so don't just rely on bn_check_top() here */
126 if ((num->top > 0 && num->d[num->top - 1] == 0) ||
127 (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
128 OPENSSL_PUT_ERROR(BN, BN_div, BN_R_NOT_INITIALIZED);
129 return 0;
130 }
131
132 if ((num->flags & BN_FLG_CONSTTIME) != 0 ||
133 (divisor->flags & BN_FLG_CONSTTIME) != 0) {
134 no_branch = 1;
135 }
136
137 if (BN_is_zero(divisor)) {
138 OPENSSL_PUT_ERROR(BN, BN_div, BN_R_DIV_BY_ZERO);
139 return 0;
140 }
141
142 if (!no_branch && BN_ucmp(num, divisor) < 0) {
143 if (rm != NULL) {
144 if (BN_copy(rm, num) == NULL) {
145 return 0;
146 }
147 }
148 if (dv != NULL) {
149 BN_zero(dv);
150 }
151 return 1;
152 }
153
154 BN_CTX_start(ctx);
155 tmp = BN_CTX_get(ctx);
156 snum = BN_CTX_get(ctx);
157 sdiv = BN_CTX_get(ctx);
158 if (dv == NULL) {
159 res = BN_CTX_get(ctx);
160 } else {
161 res = dv;
162 }
163 if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL) {
164 goto err;
165 }
166
167 /* First we normalise the numbers */
168 norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
169 if (!(BN_lshift(sdiv, divisor, norm_shift))) {
170 goto err;
171 }
172 sdiv->neg = 0;
173 norm_shift += BN_BITS2;
174 if (!(BN_lshift(snum, num, norm_shift))) {
175 goto err;
176 }
177 snum->neg = 0;
178
179 if (no_branch) {
180 /* Since we don't know whether snum is larger than sdiv,
181 * we pad snum with enough zeroes without changing its
182 * value.
183 */
184 if (snum->top <= sdiv->top + 1) {
185 if (bn_wexpand(snum, sdiv->top + 2) == NULL) {
186 goto err;
187 }
188 for (i = snum->top; i < sdiv->top + 2; i++) {
189 snum->d[i] = 0;
190 }
191 snum->top = sdiv->top + 2;
192 } else {
193 if (bn_wexpand(snum, snum->top + 1) == NULL) {
194 goto err;
195 }
196 snum->d[snum->top] = 0;
197 snum->top++;
198 }
199 }
200
201 div_n = sdiv->top;
202 num_n = snum->top;
203 loop = num_n - div_n;
204 /* Lets setup a 'window' into snum
205 * This is the part that corresponds to the current
206 * 'area' being divided */
207 wnum.neg = 0;
208 wnum.d = &(snum->d[loop]);
209 wnum.top = div_n;
210 /* only needed when BN_ucmp messes up the values between top and max */
211 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
212
213 /* Get the top 2 words of sdiv */
214 /* div_n=sdiv->top; */
215 d0 = sdiv->d[div_n - 1];
216 d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
217
218 /* pointer to the 'top' of snum */
219 wnump = &(snum->d[num_n - 1]);
220
221 /* Setup to 'res' */
222 res->neg = (num->neg ^ divisor->neg);
223 if (!bn_wexpand(res, (loop + 1))) {
224 goto err;
225 }
226 res->top = loop - no_branch;
227 resp = &(res->d[loop - 1]);
228
229 /* space for temp */
230 if (!bn_wexpand(tmp, (div_n + 1))) {
231 goto err;
232 }
233
234 if (!no_branch) {
235 if (BN_ucmp(&wnum, sdiv) >= 0) {
236 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
237 *resp = 1;
238 } else {
239 res->top--;
240 }
241 }
242
243 /* if res->top == 0 then clear the neg value otherwise decrease
244 * the resp pointer */
245 if (res->top == 0) {
246 res->neg = 0;
247 } else {
248 resp--;
249 }
250
251 for (i = 0; i < loop - 1; i++, wnump--, resp--) {
252 BN_ULONG q, l0;
253 /* the first part of the loop uses the top two words of snum and sdiv to
254 * calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv */
255 BN_ULONG n0, n1, rem = 0;
256
257 n0 = wnump[0];
258 n1 = wnump[-1];
259 if (n0 == d0) {
260 q = BN_MASK2;
261 } else {
262 /* n0 < d0 */
263 #ifdef BN_LLONG
264 BN_ULLONG t2;
265
266 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(div_asm)
267 q = (BN_ULONG)(((((BN_ULLONG)n0) << BN_BITS2) | n1) / d0);
268 #else
269 q = div_asm(n0, n1, d0);
270 #endif
271
272 #ifndef REMAINDER_IS_ALREADY_CALCULATED
273 /* rem doesn't have to be BN_ULLONG. The least we know it's less that d0,
274 * isn't it? */
275 rem = (n1 - q * d0) & BN_MASK2;
276 #endif
277
278 t2 = (BN_ULLONG)d1 * q;
279
280 for (;;) {
281 if (t2 <= ((((BN_ULLONG)rem) << BN_BITS2) | wnump[-2]))
282 break;
283 q--;
284 rem += d0;
285 if (rem < d0)
286 break; /* don't let rem overflow */
287 t2 -= d1;
288 }
289 #else /* !BN_LLONG */
290 BN_ULONG t2l, t2h;
291
292 #if defined(div_asm)
293 q = div_asm(n0, n1, d0);
294 #else
295 q = bn_div_words(n0, n1, d0);
296 #endif
297
298 #ifndef REMAINDER_IS_ALREADY_CALCULATED
299 rem = (n1 - q * d0) & BN_MASK2;
300 #endif
301
302 #if defined(BN_UMULT_LOHI)
303 BN_UMULT_LOHI(t2l, t2h, d1, q);
304 #elif defined(BN_UMULT_HIGH)
305 t2l = d1 * q;
306 t2h = BN_UMULT_HIGH(d1, q);
307 #else
308 {
309 BN_ULONG ql, qh;
310 t2l = LBITS(d1);
311 t2h = HBITS(d1);
312 ql = LBITS(q);
313 qh = HBITS(q);
314 mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
315 }
316 #endif
317
318 for (;;) {
319 if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
320 break;
321 q--;
322 rem += d0;
323 if (rem < d0)
324 break; /* don't let rem overflow */
325 if (t2l < d1)
326 t2h--;
327 t2l -= d1;
328 }
329 #endif /* !BN_LLONG */
330 }
331
332 l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
333 tmp->d[div_n] = l0;
334 wnum.d--;
335 /* ingore top values of the bignums just sub the two
336 * BN_ULONG arrays with bn_sub_words */
337 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
338 /* Note: As we have considered only the leading
339 * two BN_ULONGs in the calculation of q, sdiv * q
340 * might be greater than wnum (but then (q-1) * sdiv
341 * is less or equal than wnum)
342 */
343 q--;
344 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) {
345 /* we can't have an overflow here (assuming
346 * that q != 0, but if q == 0 then tmp is
347 * zero anyway) */
348 (*wnump)++;
349 }
350 }
351 /* store part of the result */
352 *resp = q;
353 }
354 bn_correct_top(snum);
355 if (rm != NULL) {
356 /* Keep a copy of the neg flag in num because if rm==num
357 * BN_rshift() will overwrite it.
358 */
359 int neg = num->neg;
360 BN_rshift(rm, snum, norm_shift);
361 if (!BN_is_zero(rm)) {
362 rm->neg = neg;
363 }
364 }
365 if (no_branch) {
366 bn_correct_top(res);
367 }
368 BN_CTX_end(ctx);
369 return 1;
370
371 err:
372 BN_CTX_end(ctx);
373 return 0;
374 }
375
BN_nnmod(BIGNUM * r,const BIGNUM * m,const BIGNUM * d,BN_CTX * ctx)376 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) {
377 if (!(BN_mod(r, m, d, ctx))) {
378 return 0;
379 }
380 if (!r->neg) {
381 return 1;
382 }
383
384 /* now -|d| < r < 0, so we have to set r := r + |d|. */
385 return (d->neg ? BN_sub : BN_add)(r, r, d);
386 }
387
BN_mod_add(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m,BN_CTX * ctx)388 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
389 BN_CTX *ctx) {
390 if (!BN_add(r, a, b)) {
391 return 0;
392 }
393 return BN_nnmod(r, r, m, ctx);
394 }
395
BN_mod_add_quick(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m)396 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
397 const BIGNUM *m) {
398 if (!BN_uadd(r, a, b)) {
399 return 0;
400 }
401 if (BN_ucmp(r, m) >= 0) {
402 return BN_usub(r, r, m);
403 }
404 return 1;
405 }
406
BN_mod_sub(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m,BN_CTX * ctx)407 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
408 BN_CTX *ctx) {
409 if (!BN_sub(r, a, b)) {
410 return 0;
411 }
412 return BN_nnmod(r, r, m, ctx);
413 }
414
415 /* BN_mod_sub variant that may be used if both a and b are non-negative
416 * and less than m */
BN_mod_sub_quick(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m)417 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
418 const BIGNUM *m) {
419 if (!BN_sub(r, a, b)) {
420 return 0;
421 }
422 if (r->neg) {
423 return BN_add(r, r, m);
424 }
425 return 1;
426 }
427
BN_mod_mul(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m,BN_CTX * ctx)428 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
429 BN_CTX *ctx) {
430 BIGNUM *t;
431 int ret = 0;
432
433 BN_CTX_start(ctx);
434 t = BN_CTX_get(ctx);
435 if (t == NULL) {
436 goto err;
437 }
438
439 if (a == b) {
440 if (!BN_sqr(t, a, ctx)) {
441 goto err;
442 }
443 } else {
444 if (!BN_mul(t, a, b, ctx)) {
445 goto err;
446 }
447 }
448
449 if (!BN_nnmod(r, t, m, ctx)) {
450 goto err;
451 }
452
453 ret = 1;
454
455 err:
456 BN_CTX_end(ctx);
457 return ret;
458 }
459
BN_mod_sqr(BIGNUM * r,const BIGNUM * a,const BIGNUM * m,BN_CTX * ctx)460 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
461 if (!BN_sqr(r, a, ctx)) {
462 return 0;
463 }
464
465 /* r->neg == 0, thus we don't need BN_nnmod */
466 return BN_mod(r, r, m, ctx);
467 }
468
BN_mod_lshift(BIGNUM * r,const BIGNUM * a,int n,const BIGNUM * m,BN_CTX * ctx)469 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
470 BN_CTX *ctx) {
471 BIGNUM *abs_m = NULL;
472 int ret;
473
474 if (!BN_nnmod(r, a, m, ctx)) {
475 return 0;
476 }
477
478 if (m->neg) {
479 abs_m = BN_dup(m);
480 if (abs_m == NULL) {
481 return 0;
482 }
483 abs_m->neg = 0;
484 }
485
486 ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
487
488 if (abs_m) {
489 BN_free(abs_m);
490 }
491 return ret;
492 }
493
BN_mod_lshift_quick(BIGNUM * r,const BIGNUM * a,int n,const BIGNUM * m)494 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m) {
495 if (r != a) {
496 if (BN_copy(r, a) == NULL) {
497 return 0;
498 }
499 }
500
501 while (n > 0) {
502 int max_shift;
503
504 /* 0 < r < m */
505 max_shift = BN_num_bits(m) - BN_num_bits(r);
506 /* max_shift >= 0 */
507
508 if (max_shift < 0) {
509 OPENSSL_PUT_ERROR(BN, BN_mod_lshift_quick, BN_R_INPUT_NOT_REDUCED);
510 return 0;
511 }
512
513 if (max_shift > n) {
514 max_shift = n;
515 }
516
517 if (max_shift) {
518 if (!BN_lshift(r, r, max_shift)) {
519 return 0;
520 }
521 n -= max_shift;
522 } else {
523 if (!BN_lshift1(r, r)) {
524 return 0;
525 }
526 --n;
527 }
528
529 /* BN_num_bits(r) <= BN_num_bits(m) */
530 if (BN_cmp(r, m) >= 0) {
531 if (!BN_sub(r, r, m)) {
532 return 0;
533 }
534 }
535 }
536
537 return 1;
538 }
539
BN_mod_lshift1(BIGNUM * r,const BIGNUM * a,const BIGNUM * m,BN_CTX * ctx)540 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
541 if (!BN_lshift1(r, a)) {
542 return 0;
543 }
544
545 return BN_nnmod(r, r, m, ctx);
546 }
547
BN_mod_lshift1_quick(BIGNUM * r,const BIGNUM * a,const BIGNUM * m)548 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m) {
549 if (!BN_lshift1(r, a)) {
550 return 0;
551 }
552 if (BN_cmp(r, m) >= 0) {
553 return BN_sub(r, r, m);
554 }
555
556 return 1;
557 }
558
BN_div_word(BIGNUM * a,BN_ULONG w)559 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w) {
560 BN_ULONG ret = 0;
561 int i, j;
562
563 w &= BN_MASK2;
564
565 if (!w) {
566 /* actually this an error (division by zero) */
567 return (BN_ULONG) - 1;
568 }
569
570 if (a->top == 0) {
571 return 0;
572 }
573
574 /* normalize input (so bn_div_words doesn't complain) */
575 j = BN_BITS2 - BN_num_bits_word(w);
576 w <<= j;
577 if (!BN_lshift(a, a, j)) {
578 return (BN_ULONG) - 1;
579 }
580
581 for (i = a->top - 1; i >= 0; i--) {
582 BN_ULONG l, d;
583
584 l = a->d[i];
585 d = bn_div_words(ret, l, w);
586 ret = (l - ((d * w) & BN_MASK2)) & BN_MASK2;
587 a->d[i] = d;
588 }
589
590 if ((a->top > 0) && (a->d[a->top - 1] == 0)) {
591 a->top--;
592 }
593
594 ret >>= j;
595 return ret;
596 }
597
BN_mod_word(const BIGNUM * a,BN_ULONG w)598 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w) {
599 #ifndef BN_LLONG
600 BN_ULONG ret = 0;
601 #else
602 BN_ULLONG ret = 0;
603 #endif
604 int i;
605
606 if (w == 0) {
607 return (BN_ULONG) -1;
608 }
609
610 w &= BN_MASK2;
611 for (i = a->top - 1; i >= 0; i--) {
612 #ifndef BN_LLONG
613 ret = ((ret << BN_BITS4) | ((a->d[i] >> BN_BITS4) & BN_MASK2l)) % w;
614 ret = ((ret << BN_BITS4) | (a->d[i] & BN_MASK2l)) % w;
615 #else
616 ret = (BN_ULLONG)(((ret << (BN_ULLONG)BN_BITS2) | a->d[i]) % (BN_ULLONG)w);
617 #endif
618 }
619 return (BN_ULONG)ret;
620 }
621