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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 /* ====================================================================
58  * Copyright (c) 1998-2005 The OpenSSL Project.  All rights reserved.
59  *
60  * Redistribution and use in source and binary forms, with or without
61  * modification, are permitted provided that the following conditions
62  * are met:
63  *
64  * 1. Redistributions of source code must retain the above copyright
65  *    notice, this list of conditions and the following disclaimer.
66  *
67  * 2. Redistributions in binary form must reproduce the above copyright
68  *    notice, this list of conditions and the following disclaimer in
69  *    the documentation and/or other materials provided with the
70  *    distribution.
71  *
72  * 3. All advertising materials mentioning features or use of this
73  *    software must display the following acknowledgment:
74  *    "This product includes software developed by the OpenSSL Project
75  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
76  *
77  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
78  *    endorse or promote products derived from this software without
79  *    prior written permission. For written permission, please contact
80  *    openssl-core@openssl.org.
81  *
82  * 5. Products derived from this software may not be called "OpenSSL"
83  *    nor may "OpenSSL" appear in their names without prior written
84  *    permission of the OpenSSL Project.
85  *
86  * 6. Redistributions of any form whatsoever must retain the following
87  *    acknowledgment:
88  *    "This product includes software developed by the OpenSSL Project
89  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
90  *
91  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
92  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
93  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
94  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
95  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
96  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
97  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
98  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
99  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
100  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
101  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
102  * OF THE POSSIBILITY OF SUCH DAMAGE.
103  * ====================================================================
104  *
105  * This product includes cryptographic software written by Eric Young
106  * (eay@cryptsoft.com).  This product includes software written by Tim
107  * Hudson (tjh@cryptsoft.com). */
108 
109 #include <openssl/bn.h>
110 
111 #include <assert.h>
112 #include <string.h>
113 
114 #include <openssl/cpu.h>
115 #include <openssl/err.h>
116 #include <openssl/mem.h>
117 
118 #include "internal.h"
119 
120 
121 #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64)
122 #define OPENSSL_BN_ASM_MONT5
123 #define RSAZ_ENABLED
124 
125 #include "rsaz_exp.h"
126 
127 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, const void *table,
128                          const BN_ULONG *np, const BN_ULONG *n0, int num,
129                          int power);
130 void bn_scatter5(const BN_ULONG *inp, size_t num, void *table, size_t power);
131 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
132 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, const void *table,
133                const BN_ULONG *np, const BN_ULONG *n0, int num, int power);
134 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
135                        const BN_ULONG *not_used, const BN_ULONG *np,
136                        const BN_ULONG *n0, int num);
137 #endif
138 
BN_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)139 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) {
140   int i, bits, ret = 0;
141   BIGNUM *v, *rr;
142 
143   BN_CTX_start(ctx);
144   if (r == a || r == p) {
145     rr = BN_CTX_get(ctx);
146   } else {
147     rr = r;
148   }
149 
150   v = BN_CTX_get(ctx);
151   if (rr == NULL || v == NULL) {
152     goto err;
153   }
154 
155   if (BN_copy(v, a) == NULL) {
156     goto err;
157   }
158   bits = BN_num_bits(p);
159 
160   if (BN_is_odd(p)) {
161     if (BN_copy(rr, a) == NULL) {
162       goto err;
163     }
164   } else {
165     if (!BN_one(rr)) {
166       goto err;
167     }
168   }
169 
170   for (i = 1; i < bits; i++) {
171     if (!BN_sqr(v, v, ctx)) {
172       goto err;
173     }
174     if (BN_is_bit_set(p, i)) {
175       if (!BN_mul(rr, rr, v, ctx)) {
176         goto err;
177       }
178     }
179   }
180 
181   if (r != rr && !BN_copy(r, rr)) {
182     goto err;
183   }
184   ret = 1;
185 
186 err:
187   BN_CTX_end(ctx);
188   return ret;
189 }
190 
191 typedef struct bn_recp_ctx_st {
192   BIGNUM N;   // the divisor
193   BIGNUM Nr;  // the reciprocal
194   int num_bits;
195   int shift;
196   int flags;
197 } BN_RECP_CTX;
198 
BN_RECP_CTX_init(BN_RECP_CTX * recp)199 static void BN_RECP_CTX_init(BN_RECP_CTX *recp) {
200   BN_init(&recp->N);
201   BN_init(&recp->Nr);
202   recp->num_bits = 0;
203   recp->shift = 0;
204   recp->flags = 0;
205 }
206 
BN_RECP_CTX_free(BN_RECP_CTX * recp)207 static void BN_RECP_CTX_free(BN_RECP_CTX *recp) {
208   if (recp == NULL) {
209     return;
210   }
211 
212   BN_free(&recp->N);
213   BN_free(&recp->Nr);
214 }
215 
BN_RECP_CTX_set(BN_RECP_CTX * recp,const BIGNUM * d,BN_CTX * ctx)216 static int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx) {
217   if (!BN_copy(&(recp->N), d)) {
218     return 0;
219   }
220   BN_zero(&recp->Nr);
221   recp->num_bits = BN_num_bits(d);
222   recp->shift = 0;
223 
224   return 1;
225 }
226 
227 // len is the expected size of the result We actually calculate with an extra
228 // word of precision, so we can do faster division if the remainder is not
229 // required.
230 // r := 2^len / m
BN_reciprocal(BIGNUM * r,const BIGNUM * m,int len,BN_CTX * ctx)231 static int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx) {
232   int ret = -1;
233   BIGNUM *t;
234 
235   BN_CTX_start(ctx);
236   t = BN_CTX_get(ctx);
237   if (t == NULL) {
238     goto err;
239   }
240 
241   if (!BN_set_bit(t, len)) {
242     goto err;
243   }
244 
245   if (!BN_div(r, NULL, t, m, ctx)) {
246     goto err;
247   }
248 
249   ret = len;
250 
251 err:
252   BN_CTX_end(ctx);
253   return ret;
254 }
255 
BN_div_recp(BIGNUM * dv,BIGNUM * rem,const BIGNUM * m,BN_RECP_CTX * recp,BN_CTX * ctx)256 static int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
257                        BN_RECP_CTX *recp, BN_CTX *ctx) {
258   int i, j, ret = 0;
259   BIGNUM *a, *b, *d, *r;
260 
261   BN_CTX_start(ctx);
262   a = BN_CTX_get(ctx);
263   b = BN_CTX_get(ctx);
264   if (dv != NULL) {
265     d = dv;
266   } else {
267     d = BN_CTX_get(ctx);
268   }
269 
270   if (rem != NULL) {
271     r = rem;
272   } else {
273     r = BN_CTX_get(ctx);
274   }
275 
276   if (a == NULL || b == NULL || d == NULL || r == NULL) {
277     goto err;
278   }
279 
280   if (BN_ucmp(m, &recp->N) < 0) {
281     BN_zero(d);
282     if (!BN_copy(r, m)) {
283       goto err;
284     }
285     BN_CTX_end(ctx);
286     return 1;
287   }
288 
289   // We want the remainder
290   // Given input of ABCDEF / ab
291   // we need multiply ABCDEF by 3 digests of the reciprocal of ab
292 
293   // i := max(BN_num_bits(m), 2*BN_num_bits(N))
294   i = BN_num_bits(m);
295   j = recp->num_bits << 1;
296   if (j > i) {
297     i = j;
298   }
299 
300   // Nr := round(2^i / N)
301   if (i != recp->shift) {
302     recp->shift =
303         BN_reciprocal(&(recp->Nr), &(recp->N), i,
304                       ctx);  // BN_reciprocal returns i, or -1 for an error
305   }
306 
307   if (recp->shift == -1) {
308     goto err;
309   }
310 
311   // d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i -
312   // BN_num_bits(N)))|
313   //    = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i -
314   // BN_num_bits(N)))|
315   //   <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
316   //    = |m/N|
317   if (!BN_rshift(a, m, recp->num_bits)) {
318     goto err;
319   }
320   if (!BN_mul(b, a, &(recp->Nr), ctx)) {
321     goto err;
322   }
323   if (!BN_rshift(d, b, i - recp->num_bits)) {
324     goto err;
325   }
326   d->neg = 0;
327 
328   if (!BN_mul(b, &(recp->N), d, ctx)) {
329     goto err;
330   }
331   if (!BN_usub(r, m, b)) {
332     goto err;
333   }
334   r->neg = 0;
335 
336   j = 0;
337   while (BN_ucmp(r, &(recp->N)) >= 0) {
338     if (j++ > 2) {
339       OPENSSL_PUT_ERROR(BN, BN_R_BAD_RECIPROCAL);
340       goto err;
341     }
342     if (!BN_usub(r, r, &(recp->N))) {
343       goto err;
344     }
345     if (!BN_add_word(d, 1)) {
346       goto err;
347     }
348   }
349 
350   r->neg = BN_is_zero(r) ? 0 : m->neg;
351   d->neg = m->neg ^ recp->N.neg;
352   ret = 1;
353 
354 err:
355   BN_CTX_end(ctx);
356   return ret;
357 }
358 
BN_mod_mul_reciprocal(BIGNUM * r,const BIGNUM * x,const BIGNUM * y,BN_RECP_CTX * recp,BN_CTX * ctx)359 static int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
360                                  BN_RECP_CTX *recp, BN_CTX *ctx) {
361   int ret = 0;
362   BIGNUM *a;
363   const BIGNUM *ca;
364 
365   BN_CTX_start(ctx);
366   a = BN_CTX_get(ctx);
367   if (a == NULL) {
368     goto err;
369   }
370 
371   if (y != NULL) {
372     if (x == y) {
373       if (!BN_sqr(a, x, ctx)) {
374         goto err;
375       }
376     } else {
377       if (!BN_mul(a, x, y, ctx)) {
378         goto err;
379       }
380     }
381     ca = a;
382   } else {
383     ca = x;  // Just do the mod
384   }
385 
386   ret = BN_div_recp(NULL, r, ca, recp, ctx);
387 
388 err:
389   BN_CTX_end(ctx);
390   return ret;
391 }
392 
393 // BN_window_bits_for_exponent_size returns sliding window size for mod_exp with
394 // a |b| bit exponent.
395 //
396 // For window size 'w' (w >= 2) and a random 'b' bits exponent, the number of
397 // multiplications is a constant plus on average
398 //
399 //    2^(w-1) + (b-w)/(w+1);
400 //
401 // here 2^(w-1)  is for precomputing the table (we actually need entries only
402 // for windows that have the lowest bit set), and (b-w)/(w+1)  is an
403 // approximation for the expected number of w-bit windows, not counting the
404 // first one.
405 //
406 // Thus we should use
407 //
408 //    w >= 6  if        b > 671
409 //     w = 5  if  671 > b > 239
410 //     w = 4  if  239 > b >  79
411 //     w = 3  if   79 > b >  23
412 //    w <= 2  if   23 > b
413 //
414 // (with draws in between).  Very small exponents are often selected
415 // with low Hamming weight, so we use  w = 1  for b <= 23.
BN_window_bits_for_exponent_size(int b)416 static int BN_window_bits_for_exponent_size(int b) {
417   if (b > 671) {
418     return 6;
419   }
420   if (b > 239) {
421     return 5;
422   }
423   if (b > 79) {
424     return 4;
425   }
426   if (b > 23) {
427     return 3;
428   }
429   return 1;
430 }
431 
432 // TABLE_SIZE is the maximum precomputation table size for *variable* sliding
433 // windows. This must be 2^(max_window - 1), where max_window is the largest
434 // value returned from |BN_window_bits_for_exponent_size|.
435 #define TABLE_SIZE 32
436 
437 // TABLE_BITS_SMALL is the smallest value returned from
438 // |BN_window_bits_for_exponent_size| when |b| is at most |BN_BITS2| *
439 // |BN_SMALL_MAX_WORDS| words.
440 #define TABLE_BITS_SMALL 5
441 
442 // TABLE_SIZE_SMALL is the same as |TABLE_SIZE|, but when |b| is at most
443 // |BN_BITS2| * |BN_SMALL_MAX_WORDS|.
444 #define TABLE_SIZE_SMALL (1 << (TABLE_BITS_SMALL - 1))
445 
mod_exp_recp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)446 static int mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
447                         const BIGNUM *m, BN_CTX *ctx) {
448   int i, j, bits, ret = 0, wstart, window;
449   int start = 1;
450   BIGNUM *aa;
451   // Table of variables obtained from 'ctx'
452   BIGNUM *val[TABLE_SIZE];
453   BN_RECP_CTX recp;
454 
455   bits = BN_num_bits(p);
456 
457   if (bits == 0) {
458     // x**0 mod 1 is still zero.
459     if (BN_is_one(m)) {
460       BN_zero(r);
461       return 1;
462     }
463     return BN_one(r);
464   }
465 
466   BN_CTX_start(ctx);
467   aa = BN_CTX_get(ctx);
468   val[0] = BN_CTX_get(ctx);
469   if (!aa || !val[0]) {
470     goto err;
471   }
472 
473   BN_RECP_CTX_init(&recp);
474   if (m->neg) {
475     // ignore sign of 'm'
476     if (!BN_copy(aa, m)) {
477       goto err;
478     }
479     aa->neg = 0;
480     if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) {
481       goto err;
482     }
483   } else {
484     if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) {
485       goto err;
486     }
487   }
488 
489   if (!BN_nnmod(val[0], a, m, ctx)) {
490     goto err;  // 1
491   }
492   if (BN_is_zero(val[0])) {
493     BN_zero(r);
494     ret = 1;
495     goto err;
496   }
497 
498   window = BN_window_bits_for_exponent_size(bits);
499   if (window > 1) {
500     if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) {
501       goto err;  // 2
502     }
503     j = 1 << (window - 1);
504     for (i = 1; i < j; i++) {
505       if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
506           !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) {
507         goto err;
508       }
509     }
510   }
511 
512   start = 1;  // This is used to avoid multiplication etc
513               // when there is only the value '1' in the
514               // buffer.
515   wstart = bits - 1;  // The top bit of the window
516 
517   if (!BN_one(r)) {
518     goto err;
519   }
520 
521   for (;;) {
522     int wvalue;  // The 'value' of the window
523     int wend;  // The bottom bit of the window
524 
525     if (!BN_is_bit_set(p, wstart)) {
526       if (!start) {
527         if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) {
528           goto err;
529         }
530       }
531       if (wstart == 0) {
532         break;
533       }
534       wstart--;
535       continue;
536     }
537 
538     // We now have wstart on a 'set' bit, we now need to work out
539     // how bit a window to do.  To do this we need to scan
540     // forward until the last set bit before the end of the
541     // window
542     wvalue = 1;
543     wend = 0;
544     for (i = 1; i < window; i++) {
545       if (wstart - i < 0) {
546         break;
547       }
548       if (BN_is_bit_set(p, wstart - i)) {
549         wvalue <<= (i - wend);
550         wvalue |= 1;
551         wend = i;
552       }
553     }
554 
555     // wend is the size of the current window
556     j = wend + 1;
557     // add the 'bytes above'
558     if (!start) {
559       for (i = 0; i < j; i++) {
560         if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) {
561           goto err;
562         }
563       }
564     }
565 
566     // wvalue will be an odd number < 2^window
567     if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) {
568       goto err;
569     }
570 
571     // move the 'window' down further
572     wstart -= wend + 1;
573     start = 0;
574     if (wstart < 0) {
575       break;
576     }
577   }
578   ret = 1;
579 
580 err:
581   BN_CTX_end(ctx);
582   BN_RECP_CTX_free(&recp);
583   return ret;
584 }
585 
BN_mod_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)586 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
587                BN_CTX *ctx) {
588   if (BN_is_odd(m)) {
589     return BN_mod_exp_mont(r, a, p, m, ctx, NULL);
590   }
591 
592   return mod_exp_recp(r, a, p, m, ctx);
593 }
594 
BN_mod_exp_mont(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,const BN_MONT_CTX * mont)595 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
596                     const BIGNUM *m, BN_CTX *ctx, const BN_MONT_CTX *mont) {
597   if (!BN_is_odd(m)) {
598     OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
599     return 0;
600   }
601   int bits = BN_num_bits(p);
602   if (bits == 0) {
603     // x**0 mod 1 is still zero.
604     if (BN_is_one(m)) {
605       BN_zero(rr);
606       return 1;
607     }
608     return BN_one(rr);
609   }
610 
611   int ret = 0;
612   BIGNUM *val[TABLE_SIZE];
613   BN_MONT_CTX *new_mont = NULL;
614 
615   BN_CTX_start(ctx);
616   BIGNUM *d = BN_CTX_get(ctx);
617   BIGNUM *r = BN_CTX_get(ctx);
618   val[0] = BN_CTX_get(ctx);
619   if (!d || !r || !val[0]) {
620     goto err;
621   }
622 
623   // Allocate a montgomery context if it was not supplied by the caller.
624   if (mont == NULL) {
625     new_mont = BN_MONT_CTX_new_for_modulus(m, ctx);
626     if (new_mont == NULL) {
627       goto err;
628     }
629     mont = new_mont;
630   }
631 
632   const BIGNUM *aa;
633   if (a->neg || BN_ucmp(a, m) >= 0) {
634     if (!BN_nnmod(val[0], a, m, ctx)) {
635       goto err;
636     }
637     aa = val[0];
638   } else {
639     aa = a;
640   }
641 
642   if (BN_is_zero(aa)) {
643     BN_zero(rr);
644     ret = 1;
645     goto err;
646   }
647 
648   // We exponentiate by looking at sliding windows of the exponent and
649   // precomputing powers of |aa|. Windows may be shifted so they always end on a
650   // set bit, so only precompute odd powers. We compute val[i] = aa^(2*i + 1)
651   // for i = 0 to 2^(window-1), all in Montgomery form.
652   int window = BN_window_bits_for_exponent_size(bits);
653   if (!BN_to_montgomery(val[0], aa, mont, ctx)) {
654     goto err;
655   }
656   if (window > 1) {
657     if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx)) {
658       goto err;
659     }
660     for (int i = 1; i < 1 << (window - 1); i++) {
661       val[i] = BN_CTX_get(ctx);
662       if (val[i] == NULL ||
663           !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx)) {
664         goto err;
665       }
666     }
667   }
668 
669   if (!bn_one_to_montgomery(r, mont, ctx)) {
670     goto err;
671   }
672 
673   int r_is_one = 1;
674   int wstart = bits - 1;  // The top bit of the window.
675   for (;;) {
676     if (!BN_is_bit_set(p, wstart)) {
677       if (!r_is_one && !BN_mod_mul_montgomery(r, r, r, mont, ctx)) {
678         goto err;
679       }
680       if (wstart == 0) {
681         break;
682       }
683       wstart--;
684       continue;
685     }
686 
687     // We now have wstart on a set bit. Find the largest window we can use.
688     int wvalue = 1;
689     int wsize = 0;
690     for (int i = 1; i < window && i <= wstart; i++) {
691       if (BN_is_bit_set(p, wstart - i)) {
692         wvalue <<= (i - wsize);
693         wvalue |= 1;
694         wsize = i;
695       }
696     }
697 
698     // Shift |r| to the end of the window.
699     if (!r_is_one) {
700       for (int i = 0; i < wsize + 1; i++) {
701         if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) {
702           goto err;
703         }
704       }
705     }
706 
707     assert(wvalue & 1);
708     assert(wvalue < (1 << window));
709     if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx)) {
710       goto err;
711     }
712 
713     r_is_one = 0;
714     if (wstart == wsize) {
715       break;
716     }
717     wstart -= wsize + 1;
718   }
719 
720   if (!BN_from_montgomery(rr, r, mont, ctx)) {
721     goto err;
722   }
723   ret = 1;
724 
725 err:
726   BN_MONT_CTX_free(new_mont);
727   BN_CTX_end(ctx);
728   return ret;
729 }
730 
bn_mod_exp_mont_small(BN_ULONG * r,size_t num_r,const BN_ULONG * a,size_t num_a,const BN_ULONG * p,size_t num_p,const BN_MONT_CTX * mont)731 int bn_mod_exp_mont_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
732                           size_t num_a, const BN_ULONG *p, size_t num_p,
733                           const BN_MONT_CTX *mont) {
734   size_t num_n = mont->N.top;
735   if (num_n != num_a || num_n != num_r || num_n > BN_SMALL_MAX_WORDS) {
736     OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
737     return 0;
738   }
739   if (!BN_is_odd(&mont->N)) {
740     OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
741     return 0;
742   }
743   unsigned bits = 0;
744   if (num_p != 0) {
745     bits = BN_num_bits_word(p[num_p - 1]) + (num_p - 1) * BN_BITS2;
746   }
747   if (bits == 0) {
748     OPENSSL_memset(r, 0, num_r * sizeof(BN_ULONG));
749     if (!BN_is_one(&mont->N)) {
750       r[0] = 1;
751     }
752     return 1;
753   }
754 
755   // We exponentiate by looking at sliding windows of the exponent and
756   // precomputing powers of |a|. Windows may be shifted so they always end on a
757   // set bit, so only precompute odd powers. We compute val[i] = a^(2*i + 1) for
758   // i = 0 to 2^(window-1), all in Montgomery form.
759   unsigned window = BN_window_bits_for_exponent_size(bits);
760   if (window > TABLE_BITS_SMALL) {
761     window = TABLE_BITS_SMALL;  // Tolerate excessively large |p|.
762   }
763   int ret = 0;
764   BN_ULONG val[TABLE_SIZE_SMALL][BN_SMALL_MAX_WORDS];
765   OPENSSL_memcpy(val[0], a, num_n * sizeof(BN_ULONG));
766   if (window > 1) {
767     BN_ULONG d[BN_SMALL_MAX_WORDS];
768     if (!bn_mod_mul_montgomery_small(d, num_n, val[0], num_n, val[0], num_n,
769                                      mont)) {
770       goto err;
771     }
772     for (unsigned i = 1; i < 1u << (window - 1); i++) {
773       if (!bn_mod_mul_montgomery_small(val[i], num_n, val[i - 1], num_n, d,
774                                        num_n, mont)) {
775         goto err;
776       }
777     }
778   }
779 
780   if (!bn_one_to_montgomery_small(r, num_r, mont)) {
781     goto err;
782   }
783 
784   int r_is_one = 1;
785   unsigned wstart = bits - 1;  // The top bit of the window.
786   for (;;) {
787     if (!bn_is_bit_set_words(p, num_p, wstart)) {
788       if (!r_is_one &&
789           !bn_mod_mul_montgomery_small(r, num_r, r, num_r, r, num_r, mont)) {
790         goto err;
791       }
792       if (wstart == 0) {
793         break;
794       }
795       wstart--;
796       continue;
797     }
798 
799     // We now have wstart on a set bit. Find the largest window we can use.
800     unsigned wvalue = 1;
801     unsigned wsize = 0;
802     for (unsigned i = 1; i < window && i <= wstart; i++) {
803       if (bn_is_bit_set_words(p, num_p, wstart - i)) {
804         wvalue <<= (i - wsize);
805         wvalue |= 1;
806         wsize = i;
807       }
808     }
809 
810     // Shift |r| to the end of the window.
811     if (!r_is_one) {
812       for (unsigned i = 0; i < wsize + 1; i++) {
813         if (!bn_mod_mul_montgomery_small(r, num_r, r, num_r, r, num_r, mont)) {
814           goto err;
815         }
816       }
817     }
818 
819     assert(wvalue & 1);
820     assert(wvalue < (1u << window));
821     if (!bn_mod_mul_montgomery_small(r, num_r, r, num_r, val[wvalue >> 1],
822                                      num_n, mont)) {
823       goto err;
824     }
825 
826     r_is_one = 0;
827     if (wstart == wsize) {
828       break;
829     }
830     wstart -= wsize + 1;
831   }
832 
833   ret = 1;
834 
835 err:
836   OPENSSL_cleanse(val, sizeof(val));
837   return ret;
838 }
839 
bn_mod_inverse_prime_mont_small(BN_ULONG * r,size_t num_r,const BN_ULONG * a,size_t num_a,const BN_MONT_CTX * mont)840 int bn_mod_inverse_prime_mont_small(BN_ULONG *r, size_t num_r,
841                                     const BN_ULONG *a, size_t num_a,
842                                     const BN_MONT_CTX *mont) {
843   const BN_ULONG *p = mont->N.d;
844   size_t num_p = mont->N.top;
845   if (num_p > BN_SMALL_MAX_WORDS || num_p == 0) {
846     OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
847     return 0;
848   }
849 
850   // Per Fermat's Little Theorem, a^-1 = a^(p-2) (mod p) for p prime.
851   BN_ULONG p_minus_two[BN_SMALL_MAX_WORDS];
852   OPENSSL_memcpy(p_minus_two, p, num_p * sizeof(BN_ULONG));
853   if (p_minus_two[0] >= 2) {
854     p_minus_two[0] -= 2;
855   } else {
856     p_minus_two[0] -= 2;
857     for (size_t i = 1; i < num_p; i++) {
858       if (p_minus_two[i]-- != 0) {
859         break;
860       }
861     }
862   }
863 
864   return bn_mod_exp_mont_small(r, num_r, a, num_a, p_minus_two, num_p, mont);
865 }
866 
867 
868 // |BN_mod_exp_mont_consttime| stores the precomputed powers in a specific
869 // layout so that accessing any of these table values shows the same access
870 // pattern as far as cache lines are concerned. The following functions are
871 // used to transfer a BIGNUM from/to that table.
872 
copy_to_prebuf(const BIGNUM * b,int top,unsigned char * buf,int idx,int window)873 static void copy_to_prebuf(const BIGNUM *b, int top, unsigned char *buf,
874                            int idx, int window) {
875   int i, j;
876   const int width = 1 << window;
877   BN_ULONG *table = (BN_ULONG *) buf;
878 
879   if (top > b->top) {
880     top = b->top;  // this works because 'buf' is explicitly zeroed
881   }
882 
883   for (i = 0, j = idx; i < top; i++, j += width)  {
884     table[j] = b->d[i];
885   }
886 }
887 
copy_from_prebuf(BIGNUM * b,int top,unsigned char * buf,int idx,int window)888 static int copy_from_prebuf(BIGNUM *b, int top, unsigned char *buf, int idx,
889                             int window) {
890   int i, j;
891   const int width = 1 << window;
892   volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
893 
894   if (!bn_wexpand(b, top)) {
895     return 0;
896   }
897 
898   if (window <= 3) {
899     for (i = 0; i < top; i++, table += width) {
900       BN_ULONG acc = 0;
901 
902       for (j = 0; j < width; j++) {
903         acc |= table[j] & ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
904       }
905 
906       b->d[i] = acc;
907     }
908   } else {
909     int xstride = 1 << (window - 2);
910     BN_ULONG y0, y1, y2, y3;
911 
912     i = idx >> (window - 2);  // equivalent of idx / xstride
913     idx &= xstride - 1;       // equivalent of idx % xstride
914 
915     y0 = (BN_ULONG)0 - (constant_time_eq_int(i, 0) & 1);
916     y1 = (BN_ULONG)0 - (constant_time_eq_int(i, 1) & 1);
917     y2 = (BN_ULONG)0 - (constant_time_eq_int(i, 2) & 1);
918     y3 = (BN_ULONG)0 - (constant_time_eq_int(i, 3) & 1);
919 
920     for (i = 0; i < top; i++, table += width) {
921       BN_ULONG acc = 0;
922 
923       for (j = 0; j < xstride; j++) {
924         acc |= ((table[j + 0 * xstride] & y0) | (table[j + 1 * xstride] & y1) |
925                 (table[j + 2 * xstride] & y2) | (table[j + 3 * xstride] & y3)) &
926                ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
927       }
928 
929       b->d[i] = acc;
930     }
931   }
932 
933   b->top = top;
934   bn_correct_top(b);
935   return 1;
936 }
937 
938 // BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
939 // line width of the target processor is at least the following value.
940 #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH (64)
941 #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK \
942   (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
943 
944 // Window sizes optimized for fixed window size modular exponentiation
945 // algorithm (BN_mod_exp_mont_consttime).
946 //
947 // To achieve the security goals of BN_mode_exp_mont_consttime, the maximum
948 // size of the window must not exceed
949 // log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
950 //
951 // Window size thresholds are defined for cache line sizes of 32 and 64, cache
952 // line sizes where log_2(32)=5 and log_2(64)=6 respectively. A window size of
953 // 7 should only be used on processors that have a 128 byte or greater cache
954 // line size.
955 #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
956 
957 #define BN_window_bits_for_ctime_exponent_size(b) \
958   ((b) > 937 ? 6 : (b) > 306 ? 5 : (b) > 89 ? 4 : (b) > 22 ? 3 : 1)
959 #define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
960 
961 #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
962 
963 #define BN_window_bits_for_ctime_exponent_size(b) \
964   ((b) > 306 ? 5 : (b) > 89 ? 4 : (b) > 22 ? 3 : 1)
965 #define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
966 
967 #endif
968 
969 // Given a pointer value, compute the next address that is a cache line
970 // multiple.
971 #define MOD_EXP_CTIME_ALIGN(x_)          \
972   ((unsigned char *)(x_) +               \
973    (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - \
974     (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
975 
976 // This variant of BN_mod_exp_mont() uses fixed windows and the special
977 // precomputation memory layout to limit data-dependency to a minimum
978 // to protect secret exponents (cf. the hyper-threading timing attacks
979 // pointed out by Colin Percival,
980 // http://www.daemonology.net/hyperthreading-considered-harmful/)
BN_mod_exp_mont_consttime(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,const BN_MONT_CTX * mont)981 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
982                               const BIGNUM *m, BN_CTX *ctx,
983                               const BN_MONT_CTX *mont) {
984   int i, ret = 0, window, wvalue;
985   int top;
986   BN_MONT_CTX *new_mont = NULL;
987 
988   int numPowers;
989   unsigned char *powerbufFree = NULL;
990   int powerbufLen = 0;
991   unsigned char *powerbuf = NULL;
992   BIGNUM tmp, am;
993   BIGNUM *new_a = NULL;
994 
995   if (!BN_is_odd(m)) {
996     OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
997     return 0;
998   }
999 
1000   top = m->top;
1001 
1002   // Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
1003   // whether the top bits are zero.
1004   int max_bits = p->top * BN_BITS2;
1005   int bits = max_bits;
1006   if (bits == 0) {
1007     // x**0 mod 1 is still zero.
1008     if (BN_is_one(m)) {
1009       BN_zero(rr);
1010       return 1;
1011     }
1012     return BN_one(rr);
1013   }
1014 
1015   // Allocate a montgomery context if it was not supplied by the caller.
1016   if (mont == NULL) {
1017     new_mont = BN_MONT_CTX_new_for_modulus(m, ctx);
1018     if (new_mont == NULL) {
1019       goto err;
1020     }
1021     mont = new_mont;
1022   }
1023 
1024   if (a->neg || BN_ucmp(a, m) >= 0) {
1025     new_a = BN_new();
1026     if (new_a == NULL ||
1027         !BN_nnmod(new_a, a, m, ctx)) {
1028       goto err;
1029     }
1030     a = new_a;
1031   }
1032 
1033 #ifdef RSAZ_ENABLED
1034   // If the size of the operands allow it, perform the optimized
1035   // RSAZ exponentiation. For further information see
1036   // crypto/bn/rsaz_exp.c and accompanying assembly modules.
1037   if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024) &&
1038       rsaz_avx2_eligible()) {
1039     if (!bn_wexpand(rr, 16)) {
1040       goto err;
1041     }
1042     RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, mont->n0[0]);
1043     rr->top = 16;
1044     rr->neg = 0;
1045     bn_correct_top(rr);
1046     ret = 1;
1047     goto err;
1048   }
1049 #endif
1050 
1051   // Get the window size to use with size of p.
1052   window = BN_window_bits_for_ctime_exponent_size(bits);
1053 #if defined(OPENSSL_BN_ASM_MONT5)
1054   if (window >= 5) {
1055     window = 5;  // ~5% improvement for RSA2048 sign, and even for RSA4096
1056     // reserve space for mont->N.d[] copy
1057     powerbufLen += top * sizeof(mont->N.d[0]);
1058   }
1059 #endif
1060 
1061   // Allocate a buffer large enough to hold all of the pre-computed
1062   // powers of am, am itself and tmp.
1063   numPowers = 1 << window;
1064   powerbufLen +=
1065       sizeof(m->d[0]) *
1066       (top * numPowers + ((2 * top) > numPowers ? (2 * top) : numPowers));
1067 #ifdef alloca
1068   if (powerbufLen < 3072) {
1069     powerbufFree = alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
1070   } else
1071 #endif
1072   {
1073     if ((powerbufFree = OPENSSL_malloc(
1074             powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL) {
1075       goto err;
1076     }
1077   }
1078 
1079   powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
1080   OPENSSL_memset(powerbuf, 0, powerbufLen);
1081 
1082 #ifdef alloca
1083   if (powerbufLen < 3072) {
1084     powerbufFree = NULL;
1085   }
1086 #endif
1087 
1088   // lay down tmp and am right after powers table
1089   tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
1090   am.d = tmp.d + top;
1091   tmp.top = am.top = 0;
1092   tmp.dmax = am.dmax = top;
1093   tmp.neg = am.neg = 0;
1094   tmp.flags = am.flags = BN_FLG_STATIC_DATA;
1095 
1096   if (!bn_one_to_montgomery(&tmp, mont, ctx)) {
1097     goto err;
1098   }
1099 
1100   // prepare a^1 in Montgomery domain
1101   assert(!a->neg);
1102   assert(BN_ucmp(a, m) < 0);
1103   if (!BN_to_montgomery(&am, a, mont, ctx)) {
1104     goto err;
1105   }
1106 
1107 #if defined(OPENSSL_BN_ASM_MONT5)
1108   // This optimization uses ideas from http://eprint.iacr.org/2011/239,
1109   // specifically optimization of cache-timing attack countermeasures
1110   // and pre-computation optimization.
1111 
1112   // Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
1113   // 512-bit RSA is hardly relevant, we omit it to spare size...
1114   if (window == 5 && top > 1) {
1115     const BN_ULONG *n0 = mont->n0;
1116     BN_ULONG *np;
1117 
1118     // BN_to_montgomery can contaminate words above .top
1119     // [in BN_DEBUG[_DEBUG] build]...
1120     for (i = am.top; i < top; i++) {
1121       am.d[i] = 0;
1122     }
1123     for (i = tmp.top; i < top; i++) {
1124       tmp.d[i] = 0;
1125     }
1126 
1127     // copy mont->N.d[] to improve cache locality
1128     for (np = am.d + top, i = 0; i < top; i++) {
1129       np[i] = mont->N.d[i];
1130     }
1131 
1132     bn_scatter5(tmp.d, top, powerbuf, 0);
1133     bn_scatter5(am.d, am.top, powerbuf, 1);
1134     bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
1135     bn_scatter5(tmp.d, top, powerbuf, 2);
1136 
1137     // same as above, but uses squaring for 1/2 of operations
1138     for (i = 4; i < 32; i *= 2) {
1139       bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1140       bn_scatter5(tmp.d, top, powerbuf, i);
1141     }
1142     for (i = 3; i < 8; i += 2) {
1143       int j;
1144       bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1145       bn_scatter5(tmp.d, top, powerbuf, i);
1146       for (j = 2 * i; j < 32; j *= 2) {
1147         bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1148         bn_scatter5(tmp.d, top, powerbuf, j);
1149       }
1150     }
1151     for (; i < 16; i += 2) {
1152       bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1153       bn_scatter5(tmp.d, top, powerbuf, i);
1154       bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1155       bn_scatter5(tmp.d, top, powerbuf, 2 * i);
1156     }
1157     for (; i < 32; i += 2) {
1158       bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1159       bn_scatter5(tmp.d, top, powerbuf, i);
1160     }
1161 
1162     bits--;
1163     for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) {
1164       wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1165     }
1166     bn_gather5(tmp.d, top, powerbuf, wvalue);
1167 
1168     // At this point |bits| is 4 mod 5 and at least -1. (|bits| is the first bit
1169     // that has not been read yet.)
1170     assert(bits >= -1 && (bits == -1 || bits % 5 == 4));
1171 
1172     // Scan the exponent one window at a time starting from the most
1173     // significant bits.
1174     if (top & 7) {
1175       while (bits >= 0) {
1176         for (wvalue = 0, i = 0; i < 5; i++, bits--) {
1177           wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1178         }
1179 
1180         bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1181         bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1182         bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1183         bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1184         bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1185         bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
1186       }
1187     } else {
1188       const uint8_t *p_bytes = (const uint8_t *)p->d;
1189       assert(bits < max_bits);
1190       // |p = 0| has been handled as a special case, so |max_bits| is at least
1191       // one word.
1192       assert(max_bits >= 64);
1193 
1194       // If the first bit to be read lands in the last byte, unroll the first
1195       // iteration to avoid reading past the bounds of |p->d|. (After the first
1196       // iteration, we are guaranteed to be past the last byte.) Note |bits|
1197       // here is the top bit, inclusive.
1198       if (bits - 4 >= max_bits - 8) {
1199         // Read five bits from |bits-4| through |bits|, inclusive.
1200         wvalue = p_bytes[p->top * BN_BYTES - 1];
1201         wvalue >>= (bits - 4) & 7;
1202         wvalue &= 0x1f;
1203         bits -= 5;
1204         bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
1205       }
1206       while (bits >= 0) {
1207         // Read five bits from |bits-4| through |bits|, inclusive.
1208         int first_bit = bits - 4;
1209         uint16_t val;
1210         OPENSSL_memcpy(&val, p_bytes + (first_bit >> 3), sizeof(val));
1211         val >>= first_bit & 7;
1212         val &= 0x1f;
1213         bits -= 5;
1214         bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, val);
1215       }
1216     }
1217 
1218     ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
1219     tmp.top = top;
1220     bn_correct_top(&tmp);
1221     if (ret) {
1222       if (!BN_copy(rr, &tmp)) {
1223         ret = 0;
1224       }
1225       goto err;  // non-zero ret means it's not error
1226     }
1227   } else
1228 #endif
1229   {
1230     copy_to_prebuf(&tmp, top, powerbuf, 0, window);
1231     copy_to_prebuf(&am, top, powerbuf, 1, window);
1232 
1233     // If the window size is greater than 1, then calculate
1234     // val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
1235     // (even powers could instead be computed as (a^(i/2))^2
1236     // to use the slight performance advantage of sqr over mul).
1237     if (window > 1) {
1238       if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx)) {
1239         goto err;
1240       }
1241 
1242       copy_to_prebuf(&tmp, top, powerbuf, 2, window);
1243 
1244       for (i = 3; i < numPowers; i++) {
1245         // Calculate a^i = a^(i-1) * a
1246         if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx)) {
1247           goto err;
1248         }
1249 
1250         copy_to_prebuf(&tmp, top, powerbuf, i, window);
1251       }
1252     }
1253 
1254     bits--;
1255     for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) {
1256       wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1257     }
1258     if (!copy_from_prebuf(&tmp, top, powerbuf, wvalue, window)) {
1259       goto err;
1260     }
1261 
1262     // Scan the exponent one window at a time starting from the most
1263     // significant bits.
1264     while (bits >= 0) {
1265       wvalue = 0;  // The 'value' of the window
1266 
1267       // Scan the window, squaring the result as we go
1268       for (i = 0; i < window; i++, bits--) {
1269         if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx)) {
1270           goto err;
1271         }
1272         wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1273       }
1274 
1275       // Fetch the appropriate pre-computed value from the pre-buf
1276       if (!copy_from_prebuf(&am, top, powerbuf, wvalue, window)) {
1277         goto err;
1278       }
1279 
1280       // Multiply the result into the intermediate result
1281       if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx)) {
1282         goto err;
1283       }
1284     }
1285   }
1286 
1287   // Convert the final result from montgomery to standard format
1288   if (!BN_from_montgomery(rr, &tmp, mont, ctx)) {
1289     goto err;
1290   }
1291   ret = 1;
1292 
1293 err:
1294   BN_MONT_CTX_free(new_mont);
1295   BN_clear_free(new_a);
1296   OPENSSL_free(powerbufFree);
1297   return (ret);
1298 }
1299 
BN_mod_exp_mont_word(BIGNUM * rr,BN_ULONG a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,const BN_MONT_CTX * mont)1300 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1301                          const BIGNUM *m, BN_CTX *ctx,
1302                          const BN_MONT_CTX *mont) {
1303   BIGNUM a_bignum;
1304   BN_init(&a_bignum);
1305 
1306   int ret = 0;
1307 
1308   if (!BN_set_word(&a_bignum, a)) {
1309     OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
1310     goto err;
1311   }
1312 
1313   ret = BN_mod_exp_mont(rr, &a_bignum, p, m, ctx, mont);
1314 
1315 err:
1316   BN_free(&a_bignum);
1317 
1318   return ret;
1319 }
1320 
1321 #define TABLE_SIZE 32
1322 
BN_mod_exp2_mont(BIGNUM * rr,const BIGNUM * a1,const BIGNUM * p1,const BIGNUM * a2,const BIGNUM * p2,const BIGNUM * m,BN_CTX * ctx,const BN_MONT_CTX * mont)1323 int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
1324                      const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
1325                      BN_CTX *ctx, const BN_MONT_CTX *mont) {
1326   BIGNUM tmp;
1327   BN_init(&tmp);
1328 
1329   int ret = 0;
1330   BN_MONT_CTX *new_mont = NULL;
1331 
1332   // Allocate a montgomery context if it was not supplied by the caller.
1333   if (mont == NULL) {
1334     new_mont = BN_MONT_CTX_new_for_modulus(m, ctx);
1335     if (new_mont == NULL) {
1336       goto err;
1337     }
1338     mont = new_mont;
1339   }
1340 
1341   // BN_mod_mul_montgomery removes one Montgomery factor, so passing one
1342   // Montgomery-encoded and one non-Montgomery-encoded value gives a
1343   // non-Montgomery-encoded result.
1344   if (!BN_mod_exp_mont(rr, a1, p1, m, ctx, mont) ||
1345       !BN_mod_exp_mont(&tmp, a2, p2, m, ctx, mont) ||
1346       !BN_to_montgomery(rr, rr, mont, ctx) ||
1347       !BN_mod_mul_montgomery(rr, rr, &tmp, mont, ctx)) {
1348     goto err;
1349   }
1350 
1351   ret = 1;
1352 
1353 err:
1354   BN_MONT_CTX_free(new_mont);
1355   BN_free(&tmp);
1356 
1357   return ret;
1358 }
1359