xref: /netbsd-src/crypto/external/bsd/openssl/dist/crypto/bn/bn_exp.c (revision b5c47949a45ac972130c38cf13dfd8afb1f09285)
1 /*
2  * Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved.
3  *
4  * Licensed under the OpenSSL license (the "License").  You may not use
5  * this file except in compliance with the License.  You can obtain a copy
6  * in the file LICENSE in the source distribution or at
7  * https://www.openssl.org/source/license.html
8  */
9 
10 #include "internal/cryptlib.h"
11 #include "internal/constant_time.h"
12 #include "bn_local.h"
13 
14 #include <stdlib.h>
15 #ifdef _WIN32
16 # include <malloc.h>
17 # ifndef alloca
18 #  define alloca _alloca
19 # endif
20 #elif defined(__GNUC__)
21 # ifndef __SSP__
22 #  ifndef alloca
23 #   define alloca(s) __builtin_alloca((s))
24 #  endif
25 # else
26 #   undef alloca
27 # endif
28 #elif defined(__sun)
29 # include <alloca.h>
30 #endif
31 
32 #include "rsaz_exp.h"
33 
34 #undef SPARC_T4_MONT
35 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
36 # include "sparc_arch.h"
37 extern unsigned int OPENSSL_sparcv9cap_P[];
38 # define SPARC_T4_MONT
39 #endif
40 
41 /* maximum precomputation table size for *variable* sliding windows */
42 #define TABLE_SIZE      32
43 
44 /* this one works - simple but works */
45 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
46 {
47     int i, bits, ret = 0;
48     BIGNUM *v, *rr;
49 
50     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
51             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) {
52         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
53         BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
54         return 0;
55     }
56 
57     BN_CTX_start(ctx);
58     rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r;
59     v = BN_CTX_get(ctx);
60     if (rr == NULL || v == NULL)
61         goto err;
62 
63     if (BN_copy(v, a) == NULL)
64         goto err;
65     bits = BN_num_bits(p);
66 
67     if (BN_is_odd(p)) {
68         if (BN_copy(rr, a) == NULL)
69             goto err;
70     } else {
71         if (!BN_one(rr))
72             goto err;
73     }
74 
75     for (i = 1; i < bits; i++) {
76         if (!BN_sqr(v, v, ctx))
77             goto err;
78         if (BN_is_bit_set(p, i)) {
79             if (!BN_mul(rr, rr, v, ctx))
80                 goto err;
81         }
82     }
83     if (r != rr && BN_copy(r, rr) == NULL)
84         goto err;
85 
86     ret = 1;
87  err:
88     BN_CTX_end(ctx);
89     bn_check_top(r);
90     return ret;
91 }
92 
93 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
94                BN_CTX *ctx)
95 {
96     int ret;
97 
98     bn_check_top(a);
99     bn_check_top(p);
100     bn_check_top(m);
101 
102     /*-
103      * For even modulus  m = 2^k*m_odd, it might make sense to compute
104      * a^p mod m_odd  and  a^p mod 2^k  separately (with Montgomery
105      * exponentiation for the odd part), using appropriate exponent
106      * reductions, and combine the results using the CRT.
107      *
108      * For now, we use Montgomery only if the modulus is odd; otherwise,
109      * exponentiation using the reciprocal-based quick remaindering
110      * algorithm is used.
111      *
112      * (Timing obtained with expspeed.c [computations  a^p mod m
113      * where  a, p, m  are of the same length: 256, 512, 1024, 2048,
114      * 4096, 8192 bits], compared to the running time of the
115      * standard algorithm:
116      *
117      *   BN_mod_exp_mont   33 .. 40 %  [AMD K6-2, Linux, debug configuration]
118      *                     55 .. 77 %  [UltraSparc processor, but
119      *                                  debug-solaris-sparcv8-gcc conf.]
120      *
121      *   BN_mod_exp_recp   50 .. 70 %  [AMD K6-2, Linux, debug configuration]
122      *                     62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
123      *
124      * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
125      * at 2048 and more bits, but at 512 and 1024 bits, it was
126      * slower even than the standard algorithm!
127      *
128      * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
129      * should be obtained when the new Montgomery reduction code
130      * has been integrated into OpenSSL.)
131      */
132 
133 #define MONT_MUL_MOD
134 #define MONT_EXP_WORD
135 #define RECP_MUL_MOD
136 
137 #ifdef MONT_MUL_MOD
138     if (BN_is_odd(m)) {
139 # ifdef MONT_EXP_WORD
140         if (a->top == 1 && !a->neg
141             && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)
142             && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0)
143             && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) {
144             BN_ULONG A = a->d[0];
145             ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
146         } else
147 # endif
148             ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
149     } else
150 #endif
151 #ifdef RECP_MUL_MOD
152     {
153         ret = BN_mod_exp_recp(r, a, p, m, ctx);
154     }
155 #else
156     {
157         ret = BN_mod_exp_simple(r, a, p, m, ctx);
158     }
159 #endif
160 
161     bn_check_top(r);
162     return ret;
163 }
164 
165 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
166                     const BIGNUM *m, BN_CTX *ctx)
167 {
168     int i, j, bits, ret = 0, wstart, wend, window, wvalue;
169     int start = 1;
170     BIGNUM *aa;
171     /* Table of variables obtained from 'ctx' */
172     BIGNUM *val[TABLE_SIZE];
173     BN_RECP_CTX recp;
174 
175     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
176             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
177             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
178         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
179         BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
180         return 0;
181     }
182 
183     bits = BN_num_bits(p);
184     if (bits == 0) {
185         /* x**0 mod 1, or x**0 mod -1 is still zero. */
186         if (BN_abs_is_word(m, 1)) {
187             ret = 1;
188             BN_zero(r);
189         } else {
190             ret = BN_one(r);
191         }
192         return ret;
193     }
194 
195     BN_CTX_start(ctx);
196     aa = BN_CTX_get(ctx);
197     val[0] = BN_CTX_get(ctx);
198     if (val[0] == NULL)
199         goto err;
200 
201     BN_RECP_CTX_init(&recp);
202     if (m->neg) {
203         /* ignore sign of 'm' */
204         if (!BN_copy(aa, m))
205             goto err;
206         aa->neg = 0;
207         if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
208             goto err;
209     } else {
210         if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
211             goto err;
212     }
213 
214     if (!BN_nnmod(val[0], a, m, ctx))
215         goto err;               /* 1 */
216     if (BN_is_zero(val[0])) {
217         BN_zero(r);
218         ret = 1;
219         goto err;
220     }
221 
222     window = BN_window_bits_for_exponent_size(bits);
223     if (window > 1) {
224         if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
225             goto err;           /* 2 */
226         j = 1 << (window - 1);
227         for (i = 1; i < j; i++) {
228             if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
229                 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
230                 goto err;
231         }
232     }
233 
234     start = 1;                  /* This is used to avoid multiplication etc
235                                  * when there is only the value '1' in the
236                                  * buffer. */
237     wvalue = 0;                 /* The 'value' of the window */
238     wstart = bits - 1;          /* The top bit of the window */
239     wend = 0;                   /* The bottom bit of the window */
240 
241     if (!BN_one(r))
242         goto err;
243 
244     for (;;) {
245         if (BN_is_bit_set(p, wstart) == 0) {
246             if (!start)
247                 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
248                     goto err;
249             if (wstart == 0)
250                 break;
251             wstart--;
252             continue;
253         }
254         /*
255          * We now have wstart on a 'set' bit, we now need to work out how bit
256          * a window to do.  To do this we need to scan forward until the last
257          * set bit before the end of the window
258          */
259         j = wstart;
260         wvalue = 1;
261         wend = 0;
262         for (i = 1; i < window; i++) {
263             if (wstart - i < 0)
264                 break;
265             if (BN_is_bit_set(p, wstart - i)) {
266                 wvalue <<= (i - wend);
267                 wvalue |= 1;
268                 wend = i;
269             }
270         }
271 
272         /* wend is the size of the current window */
273         j = wend + 1;
274         /* add the 'bytes above' */
275         if (!start)
276             for (i = 0; i < j; i++) {
277                 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
278                     goto err;
279             }
280 
281         /* wvalue will be an odd number < 2^window */
282         if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
283             goto err;
284 
285         /* move the 'window' down further */
286         wstart -= wend + 1;
287         wvalue = 0;
288         start = 0;
289         if (wstart < 0)
290             break;
291     }
292     ret = 1;
293  err:
294     BN_CTX_end(ctx);
295     BN_RECP_CTX_free(&recp);
296     bn_check_top(r);
297     return ret;
298 }
299 
300 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
301                     const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
302 {
303     int i, j, bits, ret = 0, wstart, wend, window, wvalue;
304     int start = 1;
305     BIGNUM *d, *r;
306     const BIGNUM *aa;
307     /* Table of variables obtained from 'ctx' */
308     BIGNUM *val[TABLE_SIZE];
309     BN_MONT_CTX *mont = NULL;
310 
311     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
312             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
313             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
314         return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
315     }
316 
317     bn_check_top(a);
318     bn_check_top(p);
319     bn_check_top(m);
320 
321     if (!BN_is_odd(m)) {
322         BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
323         return 0;
324     }
325     bits = BN_num_bits(p);
326     if (bits == 0) {
327         /* x**0 mod 1, or x**0 mod -1 is still zero. */
328         if (BN_abs_is_word(m, 1)) {
329             ret = 1;
330             BN_zero(rr);
331         } else {
332             ret = BN_one(rr);
333         }
334         return ret;
335     }
336 
337     BN_CTX_start(ctx);
338     d = BN_CTX_get(ctx);
339     r = BN_CTX_get(ctx);
340     val[0] = BN_CTX_get(ctx);
341     if (val[0] == NULL)
342         goto err;
343 
344     /*
345      * If this is not done, things will break in the montgomery part
346      */
347 
348     if (in_mont != NULL)
349         mont = in_mont;
350     else {
351         if ((mont = BN_MONT_CTX_new()) == NULL)
352             goto err;
353         if (!BN_MONT_CTX_set(mont, m, ctx))
354             goto err;
355     }
356 
357     if (a->neg || BN_ucmp(a, m) >= 0) {
358         if (!BN_nnmod(val[0], a, m, ctx))
359             goto err;
360         aa = val[0];
361     } else
362         aa = a;
363     if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
364         goto err;               /* 1 */
365 
366     window = BN_window_bits_for_exponent_size(bits);
367     if (window > 1) {
368         if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
369             goto err;           /* 2 */
370         j = 1 << (window - 1);
371         for (i = 1; i < j; i++) {
372             if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
373                 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
374                 goto err;
375         }
376     }
377 
378     start = 1;                  /* This is used to avoid multiplication etc
379                                  * when there is only the value '1' in the
380                                  * buffer. */
381     wvalue = 0;                 /* The 'value' of the window */
382     wstart = bits - 1;          /* The top bit of the window */
383     wend = 0;                   /* The bottom bit of the window */
384 
385 #if 1                           /* by Shay Gueron's suggestion */
386     j = m->top;                 /* borrow j */
387     if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
388         if (bn_wexpand(r, j) == NULL)
389             goto err;
390         /* 2^(top*BN_BITS2) - m */
391         r->d[0] = (0 - m->d[0]) & BN_MASK2;
392         for (i = 1; i < j; i++)
393             r->d[i] = (~m->d[i]) & BN_MASK2;
394         r->top = j;
395         r->flags |= BN_FLG_FIXED_TOP;
396     } else
397 #endif
398     if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx))
399         goto err;
400     for (;;) {
401         if (BN_is_bit_set(p, wstart) == 0) {
402             if (!start) {
403                 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
404                     goto err;
405             }
406             if (wstart == 0)
407                 break;
408             wstart--;
409             continue;
410         }
411         /*
412          * We now have wstart on a 'set' bit, we now need to work out how bit
413          * a window to do.  To do this we need to scan forward until the last
414          * set bit before the end of the window
415          */
416         j = wstart;
417         wvalue = 1;
418         wend = 0;
419         for (i = 1; i < window; i++) {
420             if (wstart - i < 0)
421                 break;
422             if (BN_is_bit_set(p, wstart - i)) {
423                 wvalue <<= (i - wend);
424                 wvalue |= 1;
425                 wend = i;
426             }
427         }
428 
429         /* wend is the size of the current window */
430         j = wend + 1;
431         /* add the 'bytes above' */
432         if (!start)
433             for (i = 0; i < j; i++) {
434                 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
435                     goto err;
436             }
437 
438         /* wvalue will be an odd number < 2^window */
439         if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx))
440             goto err;
441 
442         /* move the 'window' down further */
443         wstart -= wend + 1;
444         wvalue = 0;
445         start = 0;
446         if (wstart < 0)
447             break;
448     }
449     /*
450      * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
451      * removes padding [if any] and makes return value suitable for public
452      * API consumer.
453      */
454 #if defined(SPARC_T4_MONT)
455     if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
456         j = mont->N.top;        /* borrow j */
457         val[0]->d[0] = 1;       /* borrow val[0] */
458         for (i = 1; i < j; i++)
459             val[0]->d[i] = 0;
460         val[0]->top = j;
461         if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
462             goto err;
463     } else
464 #endif
465     if (!BN_from_montgomery(rr, r, mont, ctx))
466         goto err;
467     ret = 1;
468  err:
469     if (in_mont == NULL)
470         BN_MONT_CTX_free(mont);
471     BN_CTX_end(ctx);
472     bn_check_top(rr);
473     return ret;
474 }
475 
476 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
477 {
478     BN_ULONG ret = 0;
479     int wordpos;
480 
481     wordpos = bitpos / BN_BITS2;
482     bitpos %= BN_BITS2;
483     if (wordpos >= 0 && wordpos < a->top) {
484         ret = a->d[wordpos] & BN_MASK2;
485         if (bitpos) {
486             ret >>= bitpos;
487             if (++wordpos < a->top)
488                 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
489         }
490     }
491 
492     return ret & BN_MASK2;
493 }
494 
495 /*
496  * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
497  * layout so that accessing any of these table values shows the same access
498  * pattern as far as cache lines are concerned.  The following functions are
499  * used to transfer a BIGNUM from/to that table.
500  */
501 
502 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
503                                         unsigned char *buf, int idx,
504                                         int window)
505 {
506     int i, j;
507     int width = 1 << window;
508     BN_ULONG *table = (BN_ULONG *)buf;
509 
510     if (top > b->top)
511         top = b->top;           /* this works because 'buf' is explicitly
512                                  * zeroed */
513     for (i = 0, j = idx; i < top; i++, j += width) {
514         table[j] = b->d[i];
515     }
516 
517     return 1;
518 }
519 
520 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
521                                           unsigned char *buf, int idx,
522                                           int window)
523 {
524     int i, j;
525     int width = 1 << window;
526     /*
527      * We declare table 'volatile' in order to discourage compiler
528      * from reordering loads from the table. Concern is that if
529      * reordered in specific manner loads might give away the
530      * information we are trying to conceal. Some would argue that
531      * compiler can reorder them anyway, but it can as well be
532      * argued that doing so would be violation of standard...
533      */
534     volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
535 
536     if (bn_wexpand(b, top) == NULL)
537         return 0;
538 
539     if (window <= 3) {
540         for (i = 0; i < top; i++, table += width) {
541             BN_ULONG acc = 0;
542 
543             for (j = 0; j < width; j++) {
544                 acc |= table[j] &
545                        ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
546             }
547 
548             b->d[i] = acc;
549         }
550     } else {
551         int xstride = 1 << (window - 2);
552         BN_ULONG y0, y1, y2, y3;
553 
554         i = idx >> (window - 2);        /* equivalent of idx / xstride */
555         idx &= xstride - 1;             /* equivalent of idx % xstride */
556 
557         y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
558         y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
559         y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
560         y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
561 
562         for (i = 0; i < top; i++, table += width) {
563             BN_ULONG acc = 0;
564 
565             for (j = 0; j < xstride; j++) {
566                 acc |= ( (table[j + 0 * xstride] & y0) |
567                          (table[j + 1 * xstride] & y1) |
568                          (table[j + 2 * xstride] & y2) |
569                          (table[j + 3 * xstride] & y3) )
570                        & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
571             }
572 
573             b->d[i] = acc;
574         }
575     }
576 
577     b->top = top;
578     b->flags |= BN_FLG_FIXED_TOP;
579     return 1;
580 }
581 
582 /*
583  * Given a pointer value, compute the next address that is a cache line
584  * multiple.
585  */
586 #define MOD_EXP_CTIME_ALIGN(x_) \
587         ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
588 
589 /*
590  * This variant of BN_mod_exp_mont() uses fixed windows and the special
591  * precomputation memory layout to limit data-dependency to a minimum to
592  * protect secret exponents (cf. the hyper-threading timing attacks pointed
593  * out by Colin Percival,
594  * http://www.daemonology.net/hyperthreading-considered-harmful/)
595  */
596 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
597                               const BIGNUM *m, BN_CTX *ctx,
598                               BN_MONT_CTX *in_mont)
599 {
600     int i, bits, ret = 0, window, wvalue, wmask, window0;
601     int top;
602     BN_MONT_CTX *mont = NULL;
603 
604     int numPowers;
605     unsigned char *powerbufFree = NULL;
606     int powerbufLen = 0;
607     unsigned char *powerbuf = NULL;
608     BIGNUM tmp, am;
609 #if defined(SPARC_T4_MONT)
610     unsigned int t4 = 0;
611 #endif
612 
613     bn_check_top(a);
614     bn_check_top(p);
615     bn_check_top(m);
616 
617     if (!BN_is_odd(m)) {
618         BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
619         return 0;
620     }
621 
622     top = m->top;
623 
624     /*
625      * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
626      * whether the top bits are zero.
627      */
628     bits = p->top * BN_BITS2;
629     if (bits == 0) {
630         /* x**0 mod 1, or x**0 mod -1 is still zero. */
631         if (BN_abs_is_word(m, 1)) {
632             ret = 1;
633             BN_zero(rr);
634         } else {
635             ret = BN_one(rr);
636         }
637         return ret;
638     }
639 
640     BN_CTX_start(ctx);
641 
642     /*
643      * Allocate a montgomery context if it was not supplied by the caller. If
644      * this is not done, things will break in the montgomery part.
645      */
646     if (in_mont != NULL)
647         mont = in_mont;
648     else {
649         if ((mont = BN_MONT_CTX_new()) == NULL)
650             goto err;
651         if (!BN_MONT_CTX_set(mont, m, ctx))
652             goto err;
653     }
654 
655     if (a->neg || BN_ucmp(a, m) >= 0) {
656         BIGNUM *reduced = BN_CTX_get(ctx);
657         if (reduced == NULL
658             || !BN_nnmod(reduced, a, m, ctx)) {
659             goto err;
660         }
661         a = reduced;
662     }
663 
664 #ifdef RSAZ_ENABLED
665     /*
666      * If the size of the operands allow it, perform the optimized
667      * RSAZ exponentiation. For further information see
668      * crypto/bn/rsaz_exp.c and accompanying assembly modules.
669      */
670     if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
671         && rsaz_avx2_eligible()) {
672         if (NULL == bn_wexpand(rr, 16))
673             goto err;
674         RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
675                                mont->n0[0]);
676         rr->top = 16;
677         rr->neg = 0;
678         bn_correct_top(rr);
679         ret = 1;
680         goto err;
681     } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
682         if (NULL == bn_wexpand(rr, 8))
683             goto err;
684         RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
685         rr->top = 8;
686         rr->neg = 0;
687         bn_correct_top(rr);
688         ret = 1;
689         goto err;
690     }
691 #endif
692 
693     /* Get the window size to use with size of p. */
694     window = BN_window_bits_for_ctime_exponent_size(bits);
695 #if defined(SPARC_T4_MONT)
696     if (window >= 5 && (top & 15) == 0 && top <= 64 &&
697         (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
698         (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
699         window = 5;
700     else
701 #endif
702 #if defined(OPENSSL_BN_ASM_MONT5)
703     if (window >= 5) {
704         window = 5;             /* ~5% improvement for RSA2048 sign, and even
705                                  * for RSA4096 */
706         /* reserve space for mont->N.d[] copy */
707         powerbufLen += top * sizeof(mont->N.d[0]);
708     }
709 #endif
710     (void)0;
711 
712     /*
713      * Allocate a buffer large enough to hold all of the pre-computed powers
714      * of am, am itself and tmp.
715      */
716     numPowers = 1 << window;
717     powerbufLen += sizeof(m->d[0]) * (top * numPowers +
718                                       ((2 * top) >
719                                        numPowers ? (2 * top) : numPowers));
720 #ifdef alloca
721     if (powerbufLen < 3072)
722         powerbufFree =
723             alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
724     else
725 #endif
726         if ((powerbufFree =
727              OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
728             == NULL)
729         goto err;
730 
731     powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
732     memset(powerbuf, 0, powerbufLen);
733 
734 #ifdef alloca
735     if (powerbufLen < 3072)
736         powerbufFree = NULL;
737 #endif
738 
739     /* lay down tmp and am right after powers table */
740     tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
741     am.d = tmp.d + top;
742     tmp.top = am.top = 0;
743     tmp.dmax = am.dmax = top;
744     tmp.neg = am.neg = 0;
745     tmp.flags = am.flags = BN_FLG_STATIC_DATA;
746 
747     /* prepare a^0 in Montgomery domain */
748 #if 1                           /* by Shay Gueron's suggestion */
749     if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
750         /* 2^(top*BN_BITS2) - m */
751         tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
752         for (i = 1; i < top; i++)
753             tmp.d[i] = (~m->d[i]) & BN_MASK2;
754         tmp.top = top;
755     } else
756 #endif
757     if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
758         goto err;
759 
760     /* prepare a^1 in Montgomery domain */
761     if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
762         goto err;
763 
764 #if defined(SPARC_T4_MONT)
765     if (t4) {
766         typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
767                                        const BN_ULONG *n0, const void *table,
768                                        int power, int bits);
769         int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
770                               const BN_ULONG *n0, const void *table,
771                               int power, int bits);
772         int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
773                                const BN_ULONG *n0, const void *table,
774                                int power, int bits);
775         int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
776                                const BN_ULONG *n0, const void *table,
777                                int power, int bits);
778         int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
779                                const BN_ULONG *n0, const void *table,
780                                int power, int bits);
781         static const bn_pwr5_mont_f pwr5_funcs[4] = {
782             bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
783             bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
784         };
785         bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
786 
787         typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
788                                       const void *bp, const BN_ULONG *np,
789                                       const BN_ULONG *n0);
790         int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
791                              const BN_ULONG *np, const BN_ULONG *n0);
792         int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
793                               const void *bp, const BN_ULONG *np,
794                               const BN_ULONG *n0);
795         int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
796                               const void *bp, const BN_ULONG *np,
797                               const BN_ULONG *n0);
798         int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
799                               const void *bp, const BN_ULONG *np,
800                               const BN_ULONG *n0);
801         static const bn_mul_mont_f mul_funcs[4] = {
802             bn_mul_mont_t4_8, bn_mul_mont_t4_16,
803             bn_mul_mont_t4_24, bn_mul_mont_t4_32
804         };
805         bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
806 
807         void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
808                               const void *bp, const BN_ULONG *np,
809                               const BN_ULONG *n0, int num);
810         void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
811                             const void *bp, const BN_ULONG *np,
812                             const BN_ULONG *n0, int num);
813         void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
814                                     const void *table, const BN_ULONG *np,
815                                     const BN_ULONG *n0, int num, int power);
816         void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
817                                    void *table, size_t power);
818         void bn_gather5_t4(BN_ULONG *out, size_t num,
819                            void *table, size_t power);
820         void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
821 
822         BN_ULONG *np = mont->N.d, *n0 = mont->n0;
823         int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
824                                                 * than 32 */
825 
826         /*
827          * BN_to_montgomery can contaminate words above .top [in
828          * BN_DEBUG[_DEBUG] build]...
829          */
830         for (i = am.top; i < top; i++)
831             am.d[i] = 0;
832         for (i = tmp.top; i < top; i++)
833             tmp.d[i] = 0;
834 
835         bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
836         bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
837         if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
838             !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
839             bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
840         bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
841 
842         for (i = 3; i < 32; i++) {
843             /* Calculate a^i = a^(i-1) * a */
844             if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
845                 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
846                 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
847             bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
848         }
849 
850         /* switch to 64-bit domain */
851         np = alloca(top * sizeof(BN_ULONG));
852         top /= 2;
853         bn_flip_t4(np, mont->N.d, top);
854 
855         /*
856          * The exponent may not have a whole number of fixed-size windows.
857          * To simplify the main loop, the initial window has between 1 and
858          * full-window-size bits such that what remains is always a whole
859          * number of windows
860          */
861         window0 = (bits - 1) % 5 + 1;
862         wmask = (1 << window0) - 1;
863         bits -= window0;
864         wvalue = bn_get_bits(p, bits) & wmask;
865         bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
866 
867         /*
868          * Scan the exponent one window at a time starting from the most
869          * significant bits.
870          */
871         while (bits > 0) {
872             if (bits < stride)
873                 stride = bits;
874             bits -= stride;
875             wvalue = bn_get_bits(p, bits);
876 
877             if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
878                 continue;
879             /* retry once and fall back */
880             if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
881                 continue;
882 
883             bits += stride - 5;
884             wvalue >>= stride - 5;
885             wvalue &= 31;
886             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
887             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
888             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
889             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
890             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
891             bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
892                                    wvalue);
893         }
894 
895         bn_flip_t4(tmp.d, tmp.d, top);
896         top *= 2;
897         /* back to 32-bit domain */
898         tmp.top = top;
899         bn_correct_top(&tmp);
900         OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
901     } else
902 #endif
903 #if defined(OPENSSL_BN_ASM_MONT5)
904     if (window == 5 && top > 1) {
905         /*
906          * This optimization uses ideas from http://eprint.iacr.org/2011/239,
907          * specifically optimization of cache-timing attack countermeasures
908          * and pre-computation optimization.
909          */
910 
911         /*
912          * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
913          * 512-bit RSA is hardly relevant, we omit it to spare size...
914          */
915         void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
916                                  const void *table, const BN_ULONG *np,
917                                  const BN_ULONG *n0, int num, int power);
918         void bn_scatter5(const BN_ULONG *inp, size_t num,
919                          void *table, size_t power);
920         void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
921         void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
922                        const void *table, const BN_ULONG *np,
923                        const BN_ULONG *n0, int num, int power);
924         int bn_get_bits5(const BN_ULONG *ap, int off);
925         int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
926                                const BN_ULONG *not_used, const BN_ULONG *np,
927                                const BN_ULONG *n0, int num);
928 
929         BN_ULONG *n0 = mont->n0, *np;
930 
931         /*
932          * BN_to_montgomery can contaminate words above .top [in
933          * BN_DEBUG[_DEBUG] build]...
934          */
935         for (i = am.top; i < top; i++)
936             am.d[i] = 0;
937         for (i = tmp.top; i < top; i++)
938             tmp.d[i] = 0;
939 
940         /*
941          * copy mont->N.d[] to improve cache locality
942          */
943         for (np = am.d + top, i = 0; i < top; i++)
944             np[i] = mont->N.d[i];
945 
946         bn_scatter5(tmp.d, top, powerbuf, 0);
947         bn_scatter5(am.d, am.top, powerbuf, 1);
948         bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
949         bn_scatter5(tmp.d, top, powerbuf, 2);
950 
951 # if 0
952         for (i = 3; i < 32; i++) {
953             /* Calculate a^i = a^(i-1) * a */
954             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
955             bn_scatter5(tmp.d, top, powerbuf, i);
956         }
957 # else
958         /* same as above, but uses squaring for 1/2 of operations */
959         for (i = 4; i < 32; i *= 2) {
960             bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
961             bn_scatter5(tmp.d, top, powerbuf, i);
962         }
963         for (i = 3; i < 8; i += 2) {
964             int j;
965             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
966             bn_scatter5(tmp.d, top, powerbuf, i);
967             for (j = 2 * i; j < 32; j *= 2) {
968                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
969                 bn_scatter5(tmp.d, top, powerbuf, j);
970             }
971         }
972         for (; i < 16; i += 2) {
973             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
974             bn_scatter5(tmp.d, top, powerbuf, i);
975             bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
976             bn_scatter5(tmp.d, top, powerbuf, 2 * i);
977         }
978         for (; i < 32; i += 2) {
979             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
980             bn_scatter5(tmp.d, top, powerbuf, i);
981         }
982 # endif
983         /*
984          * The exponent may not have a whole number of fixed-size windows.
985          * To simplify the main loop, the initial window has between 1 and
986          * full-window-size bits such that what remains is always a whole
987          * number of windows
988          */
989         window0 = (bits - 1) % 5 + 1;
990         wmask = (1 << window0) - 1;
991         bits -= window0;
992         wvalue = bn_get_bits(p, bits) & wmask;
993         bn_gather5(tmp.d, top, powerbuf, wvalue);
994 
995         /*
996          * Scan the exponent one window at a time starting from the most
997          * significant bits.
998          */
999         if (top & 7) {
1000             while (bits > 0) {
1001                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1002                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1003                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1004                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1005                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1006                 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1007                                     bn_get_bits5(p->d, bits -= 5));
1008             }
1009         } else {
1010             while (bits > 0) {
1011                 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
1012                           bn_get_bits5(p->d, bits -= 5));
1013             }
1014         }
1015 
1016         ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
1017         tmp.top = top;
1018         bn_correct_top(&tmp);
1019         if (ret) {
1020             if (!BN_copy(rr, &tmp))
1021                 ret = 0;
1022             goto err;           /* non-zero ret means it's not error */
1023         }
1024     } else
1025 #endif
1026     {
1027         if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1028             goto err;
1029         if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1030             goto err;
1031 
1032         /*
1033          * If the window size is greater than 1, then calculate
1034          * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1035          * powers could instead be computed as (a^(i/2))^2 to use the slight
1036          * performance advantage of sqr over mul).
1037          */
1038         if (window > 1) {
1039             if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1040                 goto err;
1041             if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1042                                               window))
1043                 goto err;
1044             for (i = 3; i < numPowers; i++) {
1045                 /* Calculate a^i = a^(i-1) * a */
1046                 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1047                     goto err;
1048                 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1049                                                   window))
1050                     goto err;
1051             }
1052         }
1053 
1054         /*
1055          * The exponent may not have a whole number of fixed-size windows.
1056          * To simplify the main loop, the initial window has between 1 and
1057          * full-window-size bits such that what remains is always a whole
1058          * number of windows
1059          */
1060         window0 = (bits - 1) % window + 1;
1061         wmask = (1 << window0) - 1;
1062         bits -= window0;
1063         wvalue = bn_get_bits(p, bits) & wmask;
1064         if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1065                                             window))
1066             goto err;
1067 
1068         wmask = (1 << window) - 1;
1069         /*
1070          * Scan the exponent one window at a time starting from the most
1071          * significant bits.
1072          */
1073         while (bits > 0) {
1074 
1075             /* Square the result window-size times */
1076             for (i = 0; i < window; i++)
1077                 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1078                     goto err;
1079 
1080             /*
1081              * Get a window's worth of bits from the exponent
1082              * This avoids calling BN_is_bit_set for each bit, which
1083              * is not only slower but also makes each bit vulnerable to
1084              * EM (and likely other) side-channel attacks like One&Done
1085              * (for details see "One&Done: A Single-Decryption EM-Based
1086              *  Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1087              *  H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1088              *  M. Prvulovic, in USENIX Security'18)
1089              */
1090             bits -= window;
1091             wvalue = bn_get_bits(p, bits) & wmask;
1092             /*
1093              * Fetch the appropriate pre-computed value from the pre-buf
1094              */
1095             if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1096                                                 window))
1097                 goto err;
1098 
1099             /* Multiply the result into the intermediate result */
1100             if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1101                 goto err;
1102         }
1103     }
1104 
1105     /*
1106      * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1107      * removes padding [if any] and makes return value suitable for public
1108      * API consumer.
1109      */
1110 #if defined(SPARC_T4_MONT)
1111     if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1112         am.d[0] = 1;            /* borrow am */
1113         for (i = 1; i < top; i++)
1114             am.d[i] = 0;
1115         if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1116             goto err;
1117     } else
1118 #endif
1119     if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1120         goto err;
1121     ret = 1;
1122  err:
1123     if (in_mont == NULL)
1124         BN_MONT_CTX_free(mont);
1125     if (powerbuf != NULL) {
1126         OPENSSL_cleanse(powerbuf, powerbufLen);
1127         OPENSSL_free(powerbufFree);
1128     }
1129     BN_CTX_end(ctx);
1130     return ret;
1131 }
1132 
1133 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1134                          const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1135 {
1136     BN_MONT_CTX *mont = NULL;
1137     int b, bits, ret = 0;
1138     int r_is_one;
1139     BN_ULONG w, next_w;
1140     BIGNUM *r, *t;
1141     BIGNUM *swap_tmp;
1142 #define BN_MOD_MUL_WORD(r, w, m) \
1143                 (BN_mul_word(r, (w)) && \
1144                 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/  \
1145                         (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1146     /*
1147      * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1148      * probably more overhead than always using BN_mod (which uses BN_copy if
1149      * a similar test returns true).
1150      */
1151     /*
1152      * We can use BN_mod and do not need BN_nnmod because our accumulator is
1153      * never negative (the result of BN_mod does not depend on the sign of
1154      * the modulus).
1155      */
1156 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1157                 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1158 
1159     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1160             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1161         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1162         BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1163         return 0;
1164     }
1165 
1166     bn_check_top(p);
1167     bn_check_top(m);
1168 
1169     if (!BN_is_odd(m)) {
1170         BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1171         return 0;
1172     }
1173     if (m->top == 1)
1174         a %= m->d[0];           /* make sure that 'a' is reduced */
1175 
1176     bits = BN_num_bits(p);
1177     if (bits == 0) {
1178         /* x**0 mod 1, or x**0 mod -1 is still zero. */
1179         if (BN_abs_is_word(m, 1)) {
1180             ret = 1;
1181             BN_zero(rr);
1182         } else {
1183             ret = BN_one(rr);
1184         }
1185         return ret;
1186     }
1187     if (a == 0) {
1188         BN_zero(rr);
1189         ret = 1;
1190         return ret;
1191     }
1192 
1193     BN_CTX_start(ctx);
1194     r = BN_CTX_get(ctx);
1195     t = BN_CTX_get(ctx);
1196     if (t == NULL)
1197         goto err;
1198 
1199     if (in_mont != NULL)
1200         mont = in_mont;
1201     else {
1202         if ((mont = BN_MONT_CTX_new()) == NULL)
1203             goto err;
1204         if (!BN_MONT_CTX_set(mont, m, ctx))
1205             goto err;
1206     }
1207 
1208     r_is_one = 1;               /* except for Montgomery factor */
1209 
1210     /* bits-1 >= 0 */
1211 
1212     /* The result is accumulated in the product r*w. */
1213     w = a;                      /* bit 'bits-1' of 'p' is always set */
1214     for (b = bits - 2; b >= 0; b--) {
1215         /* First, square r*w. */
1216         next_w = w * w;
1217         if ((next_w / w) != w) { /* overflow */
1218             if (r_is_one) {
1219                 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1220                     goto err;
1221                 r_is_one = 0;
1222             } else {
1223                 if (!BN_MOD_MUL_WORD(r, w, m))
1224                     goto err;
1225             }
1226             next_w = 1;
1227         }
1228         w = next_w;
1229         if (!r_is_one) {
1230             if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1231                 goto err;
1232         }
1233 
1234         /* Second, multiply r*w by 'a' if exponent bit is set. */
1235         if (BN_is_bit_set(p, b)) {
1236             next_w = w * a;
1237             if ((next_w / a) != w) { /* overflow */
1238                 if (r_is_one) {
1239                     if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1240                         goto err;
1241                     r_is_one = 0;
1242                 } else {
1243                     if (!BN_MOD_MUL_WORD(r, w, m))
1244                         goto err;
1245                 }
1246                 next_w = a;
1247             }
1248             w = next_w;
1249         }
1250     }
1251 
1252     /* Finally, set r:=r*w. */
1253     if (w != 1) {
1254         if (r_is_one) {
1255             if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1256                 goto err;
1257             r_is_one = 0;
1258         } else {
1259             if (!BN_MOD_MUL_WORD(r, w, m))
1260                 goto err;
1261         }
1262     }
1263 
1264     if (r_is_one) {             /* can happen only if a == 1 */
1265         if (!BN_one(rr))
1266             goto err;
1267     } else {
1268         if (!BN_from_montgomery(rr, r, mont, ctx))
1269             goto err;
1270     }
1271     ret = 1;
1272  err:
1273     if (in_mont == NULL)
1274         BN_MONT_CTX_free(mont);
1275     BN_CTX_end(ctx);
1276     bn_check_top(rr);
1277     return ret;
1278 }
1279 
1280 /* The old fallback, simple version :-) */
1281 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1282                       const BIGNUM *m, BN_CTX *ctx)
1283 {
1284     int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1285     int start = 1;
1286     BIGNUM *d;
1287     /* Table of variables obtained from 'ctx' */
1288     BIGNUM *val[TABLE_SIZE];
1289 
1290     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1291             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1292             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1293         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1294         BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1295         return 0;
1296     }
1297 
1298     bits = BN_num_bits(p);
1299     if (bits == 0) {
1300         /* x**0 mod 1, or x**0 mod -1 is still zero. */
1301         if (BN_abs_is_word(m, 1)) {
1302             ret = 1;
1303             BN_zero(r);
1304         } else {
1305             ret = BN_one(r);
1306         }
1307         return ret;
1308     }
1309 
1310     BN_CTX_start(ctx);
1311     d = BN_CTX_get(ctx);
1312     val[0] = BN_CTX_get(ctx);
1313     if (val[0] == NULL)
1314         goto err;
1315 
1316     if (!BN_nnmod(val[0], a, m, ctx))
1317         goto err;               /* 1 */
1318     if (BN_is_zero(val[0])) {
1319         BN_zero(r);
1320         ret = 1;
1321         goto err;
1322     }
1323 
1324     window = BN_window_bits_for_exponent_size(bits);
1325     if (window > 1) {
1326         if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1327             goto err;           /* 2 */
1328         j = 1 << (window - 1);
1329         for (i = 1; i < j; i++) {
1330             if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1331                 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1332                 goto err;
1333         }
1334     }
1335 
1336     start = 1;                  /* This is used to avoid multiplication etc
1337                                  * when there is only the value '1' in the
1338                                  * buffer. */
1339     wvalue = 0;                 /* The 'value' of the window */
1340     wstart = bits - 1;          /* The top bit of the window */
1341     wend = 0;                   /* The bottom bit of the window */
1342 
1343     if (!BN_one(r))
1344         goto err;
1345 
1346     for (;;) {
1347         if (BN_is_bit_set(p, wstart) == 0) {
1348             if (!start)
1349                 if (!BN_mod_mul(r, r, r, m, ctx))
1350                     goto err;
1351             if (wstart == 0)
1352                 break;
1353             wstart--;
1354             continue;
1355         }
1356         /*
1357          * We now have wstart on a 'set' bit, we now need to work out how bit
1358          * a window to do.  To do this we need to scan forward until the last
1359          * set bit before the end of the window
1360          */
1361         j = wstart;
1362         wvalue = 1;
1363         wend = 0;
1364         for (i = 1; i < window; i++) {
1365             if (wstart - i < 0)
1366                 break;
1367             if (BN_is_bit_set(p, wstart - i)) {
1368                 wvalue <<= (i - wend);
1369                 wvalue |= 1;
1370                 wend = i;
1371             }
1372         }
1373 
1374         /* wend is the size of the current window */
1375         j = wend + 1;
1376         /* add the 'bytes above' */
1377         if (!start)
1378             for (i = 0; i < j; i++) {
1379                 if (!BN_mod_mul(r, r, r, m, ctx))
1380                     goto err;
1381             }
1382 
1383         /* wvalue will be an odd number < 2^window */
1384         if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1385             goto err;
1386 
1387         /* move the 'window' down further */
1388         wstart -= wend + 1;
1389         wvalue = 0;
1390         start = 0;
1391         if (wstart < 0)
1392             break;
1393     }
1394     ret = 1;
1395  err:
1396     BN_CTX_end(ctx);
1397     bn_check_top(r);
1398     return ret;
1399 }
1400