xref: /netbsd-src/crypto/external/bsd/openssl/dist/crypto/bn/bn_exp.c (revision d16b7486a53dcb8072b60ec6fcb4373a2d0c27b7)
1 /*
2  * Copyright 1995-2023 The OpenSSL Project Authors. All Rights Reserved.
3  *
4  * Licensed under the Apache License 2.0 (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 "crypto/sparc_arch.h"
37 # define SPARC_T4_MONT
38 #endif
39 
40 /* maximum precomputation table size for *variable* sliding windows */
41 #define TABLE_SIZE      32
42 
43 /*
44  * Beyond this limit the constant time code is disabled due to
45  * the possible overflow in the computation of powerbufLen in
46  * BN_mod_exp_mont_consttime.
47  * When this limit is exceeded, the computation will be done using
48  * non-constant time code, but it will take very long.
49  */
50 #define BN_CONSTTIME_SIZE_LIMIT (INT_MAX / BN_BYTES / 256)
51 
52 /* this one works - simple but works */
53 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
54 {
55     int i, bits, ret = 0;
56     BIGNUM *v, *rr;
57 
58     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
59             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) {
60         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
61         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
62         return 0;
63     }
64 
65     BN_CTX_start(ctx);
66     rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r;
67     v = BN_CTX_get(ctx);
68     if (rr == NULL || v == NULL)
69         goto err;
70 
71     if (BN_copy(v, a) == NULL)
72         goto err;
73     bits = BN_num_bits(p);
74 
75     if (BN_is_odd(p)) {
76         if (BN_copy(rr, a) == NULL)
77             goto err;
78     } else {
79         if (!BN_one(rr))
80             goto err;
81     }
82 
83     for (i = 1; i < bits; i++) {
84         if (!BN_sqr(v, v, ctx))
85             goto err;
86         if (BN_is_bit_set(p, i)) {
87             if (!BN_mul(rr, rr, v, ctx))
88                 goto err;
89         }
90     }
91     if (r != rr && BN_copy(r, rr) == NULL)
92         goto err;
93 
94     ret = 1;
95  err:
96     BN_CTX_end(ctx);
97     bn_check_top(r);
98     return ret;
99 }
100 
101 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
102                BN_CTX *ctx)
103 {
104     int ret;
105 
106     bn_check_top(a);
107     bn_check_top(p);
108     bn_check_top(m);
109 
110     /*-
111      * For even modulus  m = 2^k*m_odd, it might make sense to compute
112      * a^p mod m_odd  and  a^p mod 2^k  separately (with Montgomery
113      * exponentiation for the odd part), using appropriate exponent
114      * reductions, and combine the results using the CRT.
115      *
116      * For now, we use Montgomery only if the modulus is odd; otherwise,
117      * exponentiation using the reciprocal-based quick remaindering
118      * algorithm is used.
119      *
120      * (Timing obtained with expspeed.c [computations  a^p mod m
121      * where  a, p, m  are of the same length: 256, 512, 1024, 2048,
122      * 4096, 8192 bits], compared to the running time of the
123      * standard algorithm:
124      *
125      *   BN_mod_exp_mont   33 .. 40 %  [AMD K6-2, Linux, debug configuration]
126      *                     55 .. 77 %  [UltraSparc processor, but
127      *                                  debug-solaris-sparcv8-gcc conf.]
128      *
129      *   BN_mod_exp_recp   50 .. 70 %  [AMD K6-2, Linux, debug configuration]
130      *                     62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
131      *
132      * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
133      * at 2048 and more bits, but at 512 and 1024 bits, it was
134      * slower even than the standard algorithm!
135      *
136      * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
137      * should be obtained when the new Montgomery reduction code
138      * has been integrated into OpenSSL.)
139      */
140 
141 #define MONT_MUL_MOD
142 #define MONT_EXP_WORD
143 #define RECP_MUL_MOD
144 
145 #ifdef MONT_MUL_MOD
146     if (BN_is_odd(m)) {
147 # ifdef MONT_EXP_WORD
148         if (a->top == 1 && !a->neg
149             && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)
150             && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0)
151             && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) {
152             BN_ULONG A = a->d[0];
153             ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
154         } else
155 # endif
156             ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
157     } else
158 #endif
159 #ifdef RECP_MUL_MOD
160     {
161         ret = BN_mod_exp_recp(r, a, p, m, ctx);
162     }
163 #else
164     {
165         ret = BN_mod_exp_simple(r, a, p, m, ctx);
166     }
167 #endif
168 
169     bn_check_top(r);
170     return ret;
171 }
172 
173 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
174                     const BIGNUM *m, BN_CTX *ctx)
175 {
176     int i, j, bits, ret = 0, wstart, wend, window, wvalue;
177     int start = 1;
178     BIGNUM *aa;
179     /* Table of variables obtained from 'ctx' */
180     BIGNUM *val[TABLE_SIZE];
181     BN_RECP_CTX recp;
182 
183     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
184             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
185             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
186         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
187         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
188         return 0;
189     }
190 
191     bits = BN_num_bits(p);
192     if (bits == 0) {
193         /* x**0 mod 1, or x**0 mod -1 is still zero. */
194         if (BN_abs_is_word(m, 1)) {
195             ret = 1;
196             BN_zero(r);
197         } else {
198             ret = BN_one(r);
199         }
200         return ret;
201     }
202 
203     BN_RECP_CTX_init(&recp);
204 
205     BN_CTX_start(ctx);
206     aa = BN_CTX_get(ctx);
207     val[0] = BN_CTX_get(ctx);
208     if (val[0] == NULL)
209         goto err;
210 
211     if (m->neg) {
212         /* ignore sign of 'm' */
213         if (!BN_copy(aa, m))
214             goto err;
215         aa->neg = 0;
216         if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
217             goto err;
218     } else {
219         if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
220             goto err;
221     }
222 
223     if (!BN_nnmod(val[0], a, m, ctx))
224         goto err;               /* 1 */
225     if (BN_is_zero(val[0])) {
226         BN_zero(r);
227         ret = 1;
228         goto err;
229     }
230 
231     window = BN_window_bits_for_exponent_size(bits);
232     if (window > 1) {
233         if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
234             goto err;           /* 2 */
235         j = 1 << (window - 1);
236         for (i = 1; i < j; i++) {
237             if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
238                 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
239                 goto err;
240         }
241     }
242 
243     start = 1;                  /* This is used to avoid multiplication etc
244                                  * when there is only the value '1' in the
245                                  * buffer. */
246     wvalue = 0;                 /* The 'value' of the window */
247     wstart = bits - 1;          /* The top bit of the window */
248     wend = 0;                   /* The bottom bit of the window */
249 
250     if (!BN_one(r))
251         goto err;
252 
253     for (;;) {
254         if (BN_is_bit_set(p, wstart) == 0) {
255             if (!start)
256                 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
257                     goto err;
258             if (wstart == 0)
259                 break;
260             wstart--;
261             continue;
262         }
263         /*
264          * We now have wstart on a 'set' bit, we now need to work out how bit
265          * a window to do.  To do this we need to scan forward until the last
266          * set bit before the end of the window
267          */
268         wvalue = 1;
269         wend = 0;
270         for (i = 1; i < window; i++) {
271             if (wstart - i < 0)
272                 break;
273             if (BN_is_bit_set(p, wstart - i)) {
274                 wvalue <<= (i - wend);
275                 wvalue |= 1;
276                 wend = i;
277             }
278         }
279 
280         /* wend is the size of the current window */
281         j = wend + 1;
282         /* add the 'bytes above' */
283         if (!start)
284             for (i = 0; i < j; i++) {
285                 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
286                     goto err;
287             }
288 
289         /* wvalue will be an odd number < 2^window */
290         if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
291             goto err;
292 
293         /* move the 'window' down further */
294         wstart -= wend + 1;
295         wvalue = 0;
296         start = 0;
297         if (wstart < 0)
298             break;
299     }
300     ret = 1;
301  err:
302     BN_CTX_end(ctx);
303     BN_RECP_CTX_free(&recp);
304     bn_check_top(r);
305     return ret;
306 }
307 
308 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
309                     const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
310 {
311     int i, j, bits, ret = 0, wstart, wend, window, wvalue;
312     int start = 1;
313     BIGNUM *d, *r;
314     const BIGNUM *aa;
315     /* Table of variables obtained from 'ctx' */
316     BIGNUM *val[TABLE_SIZE];
317     BN_MONT_CTX *mont = NULL;
318 
319     bn_check_top(a);
320     bn_check_top(p);
321     bn_check_top(m);
322 
323     if (!BN_is_odd(m)) {
324         ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
325         return 0;
326     }
327 
328     if (m->top <= BN_CONSTTIME_SIZE_LIMIT
329         && (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
330             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
331             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0)) {
332         return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
333     }
334 
335     bits = BN_num_bits(p);
336     if (bits == 0) {
337         /* x**0 mod 1, or x**0 mod -1 is still zero. */
338         if (BN_abs_is_word(m, 1)) {
339             ret = 1;
340             BN_zero(rr);
341         } else {
342             ret = BN_one(rr);
343         }
344         return ret;
345     }
346 
347     BN_CTX_start(ctx);
348     d = BN_CTX_get(ctx);
349     r = BN_CTX_get(ctx);
350     val[0] = BN_CTX_get(ctx);
351     if (val[0] == NULL)
352         goto err;
353 
354     /*
355      * If this is not done, things will break in the montgomery part
356      */
357 
358     if (in_mont != NULL)
359         mont = in_mont;
360     else {
361         if ((mont = BN_MONT_CTX_new()) == NULL)
362             goto err;
363         if (!BN_MONT_CTX_set(mont, m, ctx))
364             goto err;
365     }
366 
367     if (a->neg || BN_ucmp(a, m) >= 0) {
368         if (!BN_nnmod(val[0], a, m, ctx))
369             goto err;
370         aa = val[0];
371     } else
372         aa = a;
373     if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
374         goto err;               /* 1 */
375 
376     window = BN_window_bits_for_exponent_size(bits);
377     if (window > 1) {
378         if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
379             goto err;           /* 2 */
380         j = 1 << (window - 1);
381         for (i = 1; i < j; i++) {
382             if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
383                 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
384                 goto err;
385         }
386     }
387 
388     start = 1;                  /* This is used to avoid multiplication etc
389                                  * when there is only the value '1' in the
390                                  * buffer. */
391     wvalue = 0;                 /* The 'value' of the window */
392     wstart = bits - 1;          /* The top bit of the window */
393     wend = 0;                   /* The bottom bit of the window */
394 
395 #if 1                           /* by Shay Gueron's suggestion */
396     j = m->top;                 /* borrow j */
397     if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
398         if (bn_wexpand(r, j) == NULL)
399             goto err;
400         /* 2^(top*BN_BITS2) - m */
401         r->d[0] = (0 - m->d[0]) & BN_MASK2;
402         for (i = 1; i < j; i++)
403             r->d[i] = (~m->d[i]) & BN_MASK2;
404         r->top = j;
405         r->flags |= BN_FLG_FIXED_TOP;
406     } else
407 #endif
408     if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx))
409         goto err;
410     for (;;) {
411         if (BN_is_bit_set(p, wstart) == 0) {
412             if (!start) {
413                 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
414                     goto err;
415             }
416             if (wstart == 0)
417                 break;
418             wstart--;
419             continue;
420         }
421         /*
422          * We now have wstart on a 'set' bit, we now need to work out how bit
423          * a window to do.  To do this we need to scan forward until the last
424          * set bit before the end of the window
425          */
426         wvalue = 1;
427         wend = 0;
428         for (i = 1; i < window; i++) {
429             if (wstart - i < 0)
430                 break;
431             if (BN_is_bit_set(p, wstart - i)) {
432                 wvalue <<= (i - wend);
433                 wvalue |= 1;
434                 wend = i;
435             }
436         }
437 
438         /* wend is the size of the current window */
439         j = wend + 1;
440         /* add the 'bytes above' */
441         if (!start)
442             for (i = 0; i < j; i++) {
443                 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
444                     goto err;
445             }
446 
447         /* wvalue will be an odd number < 2^window */
448         if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx))
449             goto err;
450 
451         /* move the 'window' down further */
452         wstart -= wend + 1;
453         wvalue = 0;
454         start = 0;
455         if (wstart < 0)
456             break;
457     }
458     /*
459      * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
460      * removes padding [if any] and makes return value suitable for public
461      * API consumer.
462      */
463 #if defined(SPARC_T4_MONT)
464     if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
465         j = mont->N.top;        /* borrow j */
466         val[0]->d[0] = 1;       /* borrow val[0] */
467         for (i = 1; i < j; i++)
468             val[0]->d[i] = 0;
469         val[0]->top = j;
470         if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
471             goto err;
472     } else
473 #endif
474     if (!BN_from_montgomery(rr, r, mont, ctx))
475         goto err;
476     ret = 1;
477  err:
478     if (in_mont == NULL)
479         BN_MONT_CTX_free(mont);
480     BN_CTX_end(ctx);
481     bn_check_top(rr);
482     return ret;
483 }
484 
485 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
486 {
487     BN_ULONG ret = 0;
488     int wordpos;
489 
490     wordpos = bitpos / BN_BITS2;
491     bitpos %= BN_BITS2;
492     if (wordpos >= 0 && wordpos < a->top) {
493         ret = a->d[wordpos] & BN_MASK2;
494         if (bitpos) {
495             ret >>= bitpos;
496             if (++wordpos < a->top)
497                 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
498         }
499     }
500 
501     return ret & BN_MASK2;
502 }
503 
504 /*
505  * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
506  * layout so that accessing any of these table values shows the same access
507  * pattern as far as cache lines are concerned.  The following functions are
508  * used to transfer a BIGNUM from/to that table.
509  */
510 
511 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
512                                         unsigned char *buf, int idx,
513                                         int window)
514 {
515     int i, j;
516     int width = 1 << window;
517     BN_ULONG *table = (BN_ULONG *)buf;
518 
519     if (top > b->top)
520         top = b->top;           /* this works because 'buf' is explicitly
521                                  * zeroed */
522     for (i = 0, j = idx; i < top; i++, j += width) {
523         table[j] = b->d[i];
524     }
525 
526     return 1;
527 }
528 
529 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
530                                           unsigned char *buf, int idx,
531                                           int window)
532 {
533     int i, j;
534     int width = 1 << window;
535     /*
536      * We declare table 'volatile' in order to discourage compiler
537      * from reordering loads from the table. Concern is that if
538      * reordered in specific manner loads might give away the
539      * information we are trying to conceal. Some would argue that
540      * compiler can reorder them anyway, but it can as well be
541      * argued that doing so would be violation of standard...
542      */
543     volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
544 
545     if (bn_wexpand(b, top) == NULL)
546         return 0;
547 
548     if (window <= 3) {
549         for (i = 0; i < top; i++, table += width) {
550             BN_ULONG acc = 0;
551 
552             for (j = 0; j < width; j++) {
553                 acc |= table[j] &
554                        ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
555             }
556 
557             b->d[i] = acc;
558         }
559     } else {
560         int xstride = 1 << (window - 2);
561         BN_ULONG y0, y1, y2, y3;
562 
563         i = idx >> (window - 2);        /* equivalent of idx / xstride */
564         idx &= xstride - 1;             /* equivalent of idx % xstride */
565 
566         y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
567         y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
568         y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
569         y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
570 
571         for (i = 0; i < top; i++, table += width) {
572             BN_ULONG acc = 0;
573 
574             for (j = 0; j < xstride; j++) {
575                 acc |= ( (table[j + 0 * xstride] & y0) |
576                          (table[j + 1 * xstride] & y1) |
577                          (table[j + 2 * xstride] & y2) |
578                          (table[j + 3 * xstride] & y3) )
579                        & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
580             }
581 
582             b->d[i] = acc;
583         }
584     }
585 
586     b->top = top;
587     b->flags |= BN_FLG_FIXED_TOP;
588     return 1;
589 }
590 
591 /*
592  * Given a pointer value, compute the next address that is a cache line
593  * multiple.
594  */
595 #define MOD_EXP_CTIME_ALIGN(x_) \
596         ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
597 
598 /*
599  * This variant of BN_mod_exp_mont() uses fixed windows and the special
600  * precomputation memory layout to limit data-dependency to a minimum to
601  * protect secret exponents (cf. the hyper-threading timing attacks pointed
602  * out by Colin Percival,
603  * http://www.daemonology.net/hyperthreading-considered-harmful/)
604  */
605 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
606                               const BIGNUM *m, BN_CTX *ctx,
607                               BN_MONT_CTX *in_mont)
608 {
609     int i, bits, ret = 0, window, wvalue, wmask, window0;
610     int top;
611     BN_MONT_CTX *mont = NULL;
612 
613     int numPowers;
614     unsigned char *powerbufFree = NULL;
615     int powerbufLen = 0;
616     unsigned char *powerbuf = NULL;
617     BIGNUM tmp, am;
618 #if defined(SPARC_T4_MONT)
619     unsigned int t4 = 0;
620 #endif
621 
622     bn_check_top(a);
623     bn_check_top(p);
624     bn_check_top(m);
625 
626     if (!BN_is_odd(m)) {
627         ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
628         return 0;
629     }
630 
631     top = m->top;
632 
633     if (top > BN_CONSTTIME_SIZE_LIMIT) {
634         /* Prevent overflowing the powerbufLen computation below */
635         return BN_mod_exp_mont(rr, a, p, m, ctx, in_mont);
636     }
637 
638     /*
639      * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
640      * whether the top bits are zero.
641      */
642     bits = p->top * BN_BITS2;
643     if (bits == 0) {
644         /* x**0 mod 1, or x**0 mod -1 is still zero. */
645         if (BN_abs_is_word(m, 1)) {
646             ret = 1;
647             BN_zero(rr);
648         } else {
649             ret = BN_one(rr);
650         }
651         return ret;
652     }
653 
654     BN_CTX_start(ctx);
655 
656     /*
657      * Allocate a montgomery context if it was not supplied by the caller. If
658      * this is not done, things will break in the montgomery part.
659      */
660     if (in_mont != NULL)
661         mont = in_mont;
662     else {
663         if ((mont = BN_MONT_CTX_new()) == NULL)
664             goto err;
665         if (!BN_MONT_CTX_set(mont, m, ctx))
666             goto err;
667     }
668 
669     if (a->neg || BN_ucmp(a, m) >= 0) {
670         BIGNUM *reduced = BN_CTX_get(ctx);
671         if (reduced == NULL
672             || !BN_nnmod(reduced, a, m, ctx)) {
673             goto err;
674         }
675         a = reduced;
676     }
677 
678 #ifdef RSAZ_ENABLED
679     /*
680      * If the size of the operands allow it, perform the optimized
681      * RSAZ exponentiation. For further information see
682      * crypto/bn/rsaz_exp.c and accompanying assembly modules.
683      */
684     if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
685         && rsaz_avx2_eligible()) {
686         if (NULL == bn_wexpand(rr, 16))
687             goto err;
688         RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
689                                mont->n0[0]);
690         rr->top = 16;
691         rr->neg = 0;
692         bn_correct_top(rr);
693         ret = 1;
694         goto err;
695     } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
696         if (NULL == bn_wexpand(rr, 8))
697             goto err;
698         RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
699         rr->top = 8;
700         rr->neg = 0;
701         bn_correct_top(rr);
702         ret = 1;
703         goto err;
704     }
705 #endif
706 
707     /* Get the window size to use with size of p. */
708     window = BN_window_bits_for_ctime_exponent_size(bits);
709 #if defined(SPARC_T4_MONT)
710     if (window >= 5 && (top & 15) == 0 && top <= 64 &&
711         (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
712         (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
713         window = 5;
714     else
715 #endif
716 #if defined(OPENSSL_BN_ASM_MONT5)
717     if (window >= 5 && top <= BN_SOFT_LIMIT) {
718         window = 5;             /* ~5% improvement for RSA2048 sign, and even
719                                  * for RSA4096 */
720         /* reserve space for mont->N.d[] copy */
721         powerbufLen += top * sizeof(mont->N.d[0]);
722     }
723 #endif
724     (void)0;
725 
726     /*
727      * Allocate a buffer large enough to hold all of the pre-computed powers
728      * of am, am itself and tmp.
729      */
730     numPowers = 1 << window;
731     powerbufLen += sizeof(m->d[0]) * (top * numPowers +
732                                       ((2 * top) >
733                                        numPowers ? (2 * top) : numPowers));
734 #ifdef alloca
735     if (powerbufLen < 3072)
736         powerbufFree =
737             alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
738     else
739 #endif
740         if ((powerbufFree =
741              OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
742             == NULL)
743         goto err;
744 
745     powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
746     memset(powerbuf, 0, powerbufLen);
747 
748 #ifdef alloca
749     if (powerbufLen < 3072)
750         powerbufFree = NULL;
751 #endif
752 
753     /* lay down tmp and am right after powers table */
754     tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
755     am.d = tmp.d + top;
756     tmp.top = am.top = 0;
757     tmp.dmax = am.dmax = top;
758     tmp.neg = am.neg = 0;
759     tmp.flags = am.flags = BN_FLG_STATIC_DATA;
760 
761     /* prepare a^0 in Montgomery domain */
762 #if 1                           /* by Shay Gueron's suggestion */
763     if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
764         /* 2^(top*BN_BITS2) - m */
765         tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
766         for (i = 1; i < top; i++)
767             tmp.d[i] = (~m->d[i]) & BN_MASK2;
768         tmp.top = top;
769     } else
770 #endif
771     if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
772         goto err;
773 
774     /* prepare a^1 in Montgomery domain */
775     if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
776         goto err;
777 
778     if (top > BN_SOFT_LIMIT)
779         goto fallback;
780 
781 #if defined(SPARC_T4_MONT)
782     if (t4) {
783         typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
784                                        const BN_ULONG *n0, const void *table,
785                                        int power, int bits);
786         int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
787                               const BN_ULONG *n0, const void *table,
788                               int power, int bits);
789         int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
790                                const BN_ULONG *n0, const void *table,
791                                int power, int bits);
792         int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
793                                const BN_ULONG *n0, const void *table,
794                                int power, int bits);
795         int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
796                                const BN_ULONG *n0, const void *table,
797                                int power, int bits);
798         static const bn_pwr5_mont_f pwr5_funcs[4] = {
799             bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
800             bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
801         };
802         bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
803 
804         typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
805                                       const void *bp, const BN_ULONG *np,
806                                       const BN_ULONG *n0);
807         int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
808                              const BN_ULONG *np, const BN_ULONG *n0);
809         int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
810                               const void *bp, const BN_ULONG *np,
811                               const BN_ULONG *n0);
812         int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
813                               const void *bp, const BN_ULONG *np,
814                               const BN_ULONG *n0);
815         int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
816                               const void *bp, const BN_ULONG *np,
817                               const BN_ULONG *n0);
818         static const bn_mul_mont_f mul_funcs[4] = {
819             bn_mul_mont_t4_8, bn_mul_mont_t4_16,
820             bn_mul_mont_t4_24, bn_mul_mont_t4_32
821         };
822         bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
823 
824         void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
825                               const void *bp, const BN_ULONG *np,
826                               const BN_ULONG *n0, int num);
827         void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
828                             const void *bp, const BN_ULONG *np,
829                             const BN_ULONG *n0, int num);
830         void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
831                                     const void *table, const BN_ULONG *np,
832                                     const BN_ULONG *n0, int num, int power);
833         void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
834                                    void *table, size_t power);
835         void bn_gather5_t4(BN_ULONG *out, size_t num,
836                            void *table, size_t power);
837         void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
838 
839         BN_ULONG *np = mont->N.d, *n0 = mont->n0;
840         int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
841                                                 * than 32 */
842 
843         /*
844          * BN_to_montgomery can contaminate words above .top [in
845          * BN_DEBUG build...
846          */
847         for (i = am.top; i < top; i++)
848             am.d[i] = 0;
849         for (i = tmp.top; i < top; i++)
850             tmp.d[i] = 0;
851 
852         bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
853         bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
854         if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
855             !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
856             bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
857         bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
858 
859         for (i = 3; i < 32; i++) {
860             /* Calculate a^i = a^(i-1) * a */
861             if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
862                 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
863                 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
864             bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
865         }
866 
867         /* switch to 64-bit domain */
868         np = alloca(top * sizeof(BN_ULONG));
869         top /= 2;
870         bn_flip_t4(np, mont->N.d, top);
871 
872         /*
873          * The exponent may not have a whole number of fixed-size windows.
874          * To simplify the main loop, the initial window has between 1 and
875          * full-window-size bits such that what remains is always a whole
876          * number of windows
877          */
878         window0 = (bits - 1) % 5 + 1;
879         wmask = (1 << window0) - 1;
880         bits -= window0;
881         wvalue = bn_get_bits(p, bits) & wmask;
882         bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
883 
884         /*
885          * Scan the exponent one window at a time starting from the most
886          * significant bits.
887          */
888         while (bits > 0) {
889             if (bits < stride)
890                 stride = bits;
891             bits -= stride;
892             wvalue = bn_get_bits(p, bits);
893 
894             if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
895                 continue;
896             /* retry once and fall back */
897             if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
898                 continue;
899 
900             bits += stride - 5;
901             wvalue >>= stride - 5;
902             wvalue &= 31;
903             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
904             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
905             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
906             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
907             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
908             bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
909                                    wvalue);
910         }
911 
912         bn_flip_t4(tmp.d, tmp.d, top);
913         top *= 2;
914         /* back to 32-bit domain */
915         tmp.top = top;
916         bn_correct_top(&tmp);
917         OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
918     } else
919 #endif
920 #if defined(OPENSSL_BN_ASM_MONT5)
921     if (window == 5 && top > 1) {
922         /*
923          * This optimization uses ideas from https://eprint.iacr.org/2011/239,
924          * specifically optimization of cache-timing attack countermeasures,
925          * pre-computation optimization, and Almost Montgomery Multiplication.
926          *
927          * The paper discusses a 4-bit window to optimize 512-bit modular
928          * exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer
929          * important.
930          *
931          * |bn_mul_mont_gather5| and |bn_power5| implement the "almost"
932          * reduction variant, so the values here may not be fully reduced.
933          * They are bounded by R (i.e. they fit in |top| words), not |m|.
934          * Additionally, we pass these "almost" reduced inputs into
935          * |bn_mul_mont|, which implements the normal reduction variant.
936          * Given those inputs, |bn_mul_mont| may not give reduced
937          * output, but it will still produce "almost" reduced output.
938          */
939         void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
940                                  const void *table, const BN_ULONG *np,
941                                  const BN_ULONG *n0, int num, int power);
942         void bn_scatter5(const BN_ULONG *inp, size_t num,
943                          void *table, size_t power);
944         void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
945         void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
946                        const void *table, const BN_ULONG *np,
947                        const BN_ULONG *n0, int num, int power);
948         int bn_get_bits5(const BN_ULONG *ap, int off);
949 
950         BN_ULONG *n0 = mont->n0, *np;
951 
952         /*
953          * BN_to_montgomery can contaminate words above .top [in
954          * BN_DEBUG build...
955          */
956         for (i = am.top; i < top; i++)
957             am.d[i] = 0;
958         for (i = tmp.top; i < top; i++)
959             tmp.d[i] = 0;
960 
961         /*
962          * copy mont->N.d[] to improve cache locality
963          */
964         for (np = am.d + top, i = 0; i < top; i++)
965             np[i] = mont->N.d[i];
966 
967         bn_scatter5(tmp.d, top, powerbuf, 0);
968         bn_scatter5(am.d, am.top, powerbuf, 1);
969         bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
970         bn_scatter5(tmp.d, top, powerbuf, 2);
971 
972 # if 0
973         for (i = 3; i < 32; i++) {
974             /* Calculate a^i = a^(i-1) * a */
975             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
976             bn_scatter5(tmp.d, top, powerbuf, i);
977         }
978 # else
979         /* same as above, but uses squaring for 1/2 of operations */
980         for (i = 4; i < 32; i *= 2) {
981             bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
982             bn_scatter5(tmp.d, top, powerbuf, i);
983         }
984         for (i = 3; i < 8; i += 2) {
985             int j;
986             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
987             bn_scatter5(tmp.d, top, powerbuf, i);
988             for (j = 2 * i; j < 32; j *= 2) {
989                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
990                 bn_scatter5(tmp.d, top, powerbuf, j);
991             }
992         }
993         for (; i < 16; i += 2) {
994             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
995             bn_scatter5(tmp.d, top, powerbuf, i);
996             bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
997             bn_scatter5(tmp.d, top, powerbuf, 2 * i);
998         }
999         for (; i < 32; i += 2) {
1000             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1001             bn_scatter5(tmp.d, top, powerbuf, i);
1002         }
1003 # endif
1004         /*
1005          * The exponent may not have a whole number of fixed-size windows.
1006          * To simplify the main loop, the initial window has between 1 and
1007          * full-window-size bits such that what remains is always a whole
1008          * number of windows
1009          */
1010         window0 = (bits - 1) % 5 + 1;
1011         wmask = (1 << window0) - 1;
1012         bits -= window0;
1013         wvalue = bn_get_bits(p, bits) & wmask;
1014         bn_gather5(tmp.d, top, powerbuf, wvalue);
1015 
1016         /*
1017          * Scan the exponent one window at a time starting from the most
1018          * significant bits.
1019          */
1020         if (top & 7) {
1021             while (bits > 0) {
1022                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1023                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1024                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1025                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1026                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1027                 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1028                                     bn_get_bits5(p->d, bits -= 5));
1029             }
1030         } else {
1031             while (bits > 0) {
1032                 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
1033                           bn_get_bits5(p->d, bits -= 5));
1034             }
1035         }
1036 
1037         tmp.top = top;
1038         /*
1039          * The result is now in |tmp| in Montgomery form, but it may not be
1040          * fully reduced. This is within bounds for |BN_from_montgomery|
1041          * (tmp < R <= m*R) so it will, when converting from Montgomery form,
1042          * produce a fully reduced result.
1043          *
1044          * This differs from Figure 2 of the paper, which uses AMM(h, 1) to
1045          * convert from Montgomery form with unreduced output, followed by an
1046          * extra reduction step. In the paper's terminology, we replace
1047          * steps 9 and 10 with MM(h, 1).
1048          */
1049     } else
1050 #endif
1051     {
1052  fallback:
1053         if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1054             goto err;
1055         if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1056             goto err;
1057 
1058         /*
1059          * If the window size is greater than 1, then calculate
1060          * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1061          * powers could instead be computed as (a^(i/2))^2 to use the slight
1062          * performance advantage of sqr over mul).
1063          */
1064         if (window > 1) {
1065             if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1066                 goto err;
1067             if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1068                                               window))
1069                 goto err;
1070             for (i = 3; i < numPowers; i++) {
1071                 /* Calculate a^i = a^(i-1) * a */
1072                 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1073                     goto err;
1074                 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1075                                                   window))
1076                     goto err;
1077             }
1078         }
1079 
1080         /*
1081          * The exponent may not have a whole number of fixed-size windows.
1082          * To simplify the main loop, the initial window has between 1 and
1083          * full-window-size bits such that what remains is always a whole
1084          * number of windows
1085          */
1086         window0 = (bits - 1) % window + 1;
1087         wmask = (1 << window0) - 1;
1088         bits -= window0;
1089         wvalue = bn_get_bits(p, bits) & wmask;
1090         if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1091                                             window))
1092             goto err;
1093 
1094         wmask = (1 << window) - 1;
1095         /*
1096          * Scan the exponent one window at a time starting from the most
1097          * significant bits.
1098          */
1099         while (bits > 0) {
1100 
1101             /* Square the result window-size times */
1102             for (i = 0; i < window; i++)
1103                 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1104                     goto err;
1105 
1106             /*
1107              * Get a window's worth of bits from the exponent
1108              * This avoids calling BN_is_bit_set for each bit, which
1109              * is not only slower but also makes each bit vulnerable to
1110              * EM (and likely other) side-channel attacks like One&Done
1111              * (for details see "One&Done: A Single-Decryption EM-Based
1112              *  Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1113              *  H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1114              *  M. Prvulovic, in USENIX Security'18)
1115              */
1116             bits -= window;
1117             wvalue = bn_get_bits(p, bits) & wmask;
1118             /*
1119              * Fetch the appropriate pre-computed value from the pre-buf
1120              */
1121             if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1122                                                 window))
1123                 goto err;
1124 
1125             /* Multiply the result into the intermediate result */
1126             if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1127                 goto err;
1128         }
1129     }
1130 
1131     /*
1132      * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1133      * removes padding [if any] and makes return value suitable for public
1134      * API consumer.
1135      */
1136 #if defined(SPARC_T4_MONT)
1137     if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1138         am.d[0] = 1;            /* borrow am */
1139         for (i = 1; i < top; i++)
1140             am.d[i] = 0;
1141         if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1142             goto err;
1143     } else
1144 #endif
1145     if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1146         goto err;
1147     ret = 1;
1148  err:
1149     if (in_mont == NULL)
1150         BN_MONT_CTX_free(mont);
1151     if (powerbuf != NULL) {
1152         OPENSSL_cleanse(powerbuf, powerbufLen);
1153         OPENSSL_free(powerbufFree);
1154     }
1155     BN_CTX_end(ctx);
1156     return ret;
1157 }
1158 
1159 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1160                          const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1161 {
1162     BN_MONT_CTX *mont = NULL;
1163     int b, bits, ret = 0;
1164     int r_is_one;
1165     BN_ULONG w, next_w;
1166     BIGNUM *r, *t;
1167     BIGNUM *swap_tmp;
1168 #define BN_MOD_MUL_WORD(r, w, m) \
1169                 (BN_mul_word(r, (w)) && \
1170                 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/  \
1171                         (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1172     /*
1173      * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1174      * probably more overhead than always using BN_mod (which uses BN_copy if
1175      * a similar test returns true).
1176      */
1177     /*
1178      * We can use BN_mod and do not need BN_nnmod because our accumulator is
1179      * never negative (the result of BN_mod does not depend on the sign of
1180      * the modulus).
1181      */
1182 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1183                 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1184 
1185     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1186             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1187         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1188         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1189         return 0;
1190     }
1191 
1192     bn_check_top(p);
1193     bn_check_top(m);
1194 
1195     if (!BN_is_odd(m)) {
1196         ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
1197         return 0;
1198     }
1199     if (m->top == 1)
1200         a %= m->d[0];           /* make sure that 'a' is reduced */
1201 
1202     bits = BN_num_bits(p);
1203     if (bits == 0) {
1204         /* x**0 mod 1, or x**0 mod -1 is still zero. */
1205         if (BN_abs_is_word(m, 1)) {
1206             ret = 1;
1207             BN_zero(rr);
1208         } else {
1209             ret = BN_one(rr);
1210         }
1211         return ret;
1212     }
1213     if (a == 0) {
1214         BN_zero(rr);
1215         ret = 1;
1216         return ret;
1217     }
1218 
1219     BN_CTX_start(ctx);
1220     r = BN_CTX_get(ctx);
1221     t = BN_CTX_get(ctx);
1222     if (t == NULL)
1223         goto err;
1224 
1225     if (in_mont != NULL)
1226         mont = in_mont;
1227     else {
1228         if ((mont = BN_MONT_CTX_new()) == NULL)
1229             goto err;
1230         if (!BN_MONT_CTX_set(mont, m, ctx))
1231             goto err;
1232     }
1233 
1234     r_is_one = 1;               /* except for Montgomery factor */
1235 
1236     /* bits-1 >= 0 */
1237 
1238     /* The result is accumulated in the product r*w. */
1239     w = a;                      /* bit 'bits-1' of 'p' is always set */
1240     for (b = bits - 2; b >= 0; b--) {
1241         /* First, square r*w. */
1242         next_w = w * w;
1243         if ((next_w / w) != w) { /* overflow */
1244             if (r_is_one) {
1245                 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1246                     goto err;
1247                 r_is_one = 0;
1248             } else {
1249                 if (!BN_MOD_MUL_WORD(r, w, m))
1250                     goto err;
1251             }
1252             next_w = 1;
1253         }
1254         w = next_w;
1255         if (!r_is_one) {
1256             if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1257                 goto err;
1258         }
1259 
1260         /* Second, multiply r*w by 'a' if exponent bit is set. */
1261         if (BN_is_bit_set(p, b)) {
1262             next_w = w * a;
1263             if ((next_w / a) != w) { /* overflow */
1264                 if (r_is_one) {
1265                     if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1266                         goto err;
1267                     r_is_one = 0;
1268                 } else {
1269                     if (!BN_MOD_MUL_WORD(r, w, m))
1270                         goto err;
1271                 }
1272                 next_w = a;
1273             }
1274             w = next_w;
1275         }
1276     }
1277 
1278     /* Finally, set r:=r*w. */
1279     if (w != 1) {
1280         if (r_is_one) {
1281             if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1282                 goto err;
1283             r_is_one = 0;
1284         } else {
1285             if (!BN_MOD_MUL_WORD(r, w, m))
1286                 goto err;
1287         }
1288     }
1289 
1290     if (r_is_one) {             /* can happen only if a == 1 */
1291         if (!BN_one(rr))
1292             goto err;
1293     } else {
1294         if (!BN_from_montgomery(rr, r, mont, ctx))
1295             goto err;
1296     }
1297     ret = 1;
1298  err:
1299     if (in_mont == NULL)
1300         BN_MONT_CTX_free(mont);
1301     BN_CTX_end(ctx);
1302     bn_check_top(rr);
1303     return ret;
1304 }
1305 
1306 /* The old fallback, simple version :-) */
1307 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1308                       const BIGNUM *m, BN_CTX *ctx)
1309 {
1310     int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1311     int start = 1;
1312     BIGNUM *d;
1313     /* Table of variables obtained from 'ctx' */
1314     BIGNUM *val[TABLE_SIZE];
1315 
1316     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1317             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1318             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1319         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1320         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1321         return 0;
1322     }
1323 
1324     bits = BN_num_bits(p);
1325     if (bits == 0) {
1326         /* x**0 mod 1, or x**0 mod -1 is still zero. */
1327         if (BN_abs_is_word(m, 1)) {
1328             ret = 1;
1329             BN_zero(r);
1330         } else {
1331             ret = BN_one(r);
1332         }
1333         return ret;
1334     }
1335 
1336     BN_CTX_start(ctx);
1337     d = BN_CTX_get(ctx);
1338     val[0] = BN_CTX_get(ctx);
1339     if (val[0] == NULL)
1340         goto err;
1341 
1342     if (!BN_nnmod(val[0], a, m, ctx))
1343         goto err;               /* 1 */
1344     if (BN_is_zero(val[0])) {
1345         BN_zero(r);
1346         ret = 1;
1347         goto err;
1348     }
1349 
1350     window = BN_window_bits_for_exponent_size(bits);
1351     if (window > 1) {
1352         if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1353             goto err;           /* 2 */
1354         j = 1 << (window - 1);
1355         for (i = 1; i < j; i++) {
1356             if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1357                 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1358                 goto err;
1359         }
1360     }
1361 
1362     start = 1;                  /* This is used to avoid multiplication etc
1363                                  * when there is only the value '1' in the
1364                                  * buffer. */
1365     wvalue = 0;                 /* The 'value' of the window */
1366     wstart = bits - 1;          /* The top bit of the window */
1367     wend = 0;                   /* The bottom bit of the window */
1368 
1369     if (!BN_one(r))
1370         goto err;
1371 
1372     for (;;) {
1373         if (BN_is_bit_set(p, wstart) == 0) {
1374             if (!start)
1375                 if (!BN_mod_mul(r, r, r, m, ctx))
1376                     goto err;
1377             if (wstart == 0)
1378                 break;
1379             wstart--;
1380             continue;
1381         }
1382         /*
1383          * We now have wstart on a 'set' bit, we now need to work out how bit
1384          * a window to do.  To do this we need to scan forward until the last
1385          * set bit before the end of the window
1386          */
1387         wvalue = 1;
1388         wend = 0;
1389         for (i = 1; i < window; i++) {
1390             if (wstart - i < 0)
1391                 break;
1392             if (BN_is_bit_set(p, wstart - i)) {
1393                 wvalue <<= (i - wend);
1394                 wvalue |= 1;
1395                 wend = i;
1396             }
1397         }
1398 
1399         /* wend is the size of the current window */
1400         j = wend + 1;
1401         /* add the 'bytes above' */
1402         if (!start)
1403             for (i = 0; i < j; i++) {
1404                 if (!BN_mod_mul(r, r, r, m, ctx))
1405                     goto err;
1406             }
1407 
1408         /* wvalue will be an odd number < 2^window */
1409         if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1410             goto err;
1411 
1412         /* move the 'window' down further */
1413         wstart -= wend + 1;
1414         wvalue = 0;
1415         start = 0;
1416         if (wstart < 0)
1417             break;
1418     }
1419     ret = 1;
1420  err:
1421     BN_CTX_end(ctx);
1422     bn_check_top(r);
1423     return ret;
1424 }
1425 
1426 /*
1427  * This is a variant of modular exponentiation optimization that does
1428  * parallel 2-primes exponentiation using 256-bit (AVX512VL) AVX512_IFMA ISA
1429  * in 52-bit binary redundant representation.
1430  * If such instructions are not available, or input data size is not supported,
1431  * it falls back to two BN_mod_exp_mont_consttime() calls.
1432  */
1433 int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1, const BIGNUM *p1,
1434                                  const BIGNUM *m1, BN_MONT_CTX *in_mont1,
1435                                  BIGNUM *rr2, const BIGNUM *a2, const BIGNUM *p2,
1436                                  const BIGNUM *m2, BN_MONT_CTX *in_mont2,
1437                                  BN_CTX *ctx)
1438 {
1439     int ret = 0;
1440 
1441 #ifdef RSAZ_ENABLED
1442     BN_MONT_CTX *mont1 = NULL;
1443     BN_MONT_CTX *mont2 = NULL;
1444 
1445     if (ossl_rsaz_avx512ifma_eligible() &&
1446         ((a1->top == 16) && (p1->top == 16) && (BN_num_bits(m1) == 1024) &&
1447          (a2->top == 16) && (p2->top == 16) && (BN_num_bits(m2) == 1024))) {
1448 
1449         if (bn_wexpand(rr1, 16) == NULL)
1450             goto err;
1451         if (bn_wexpand(rr2, 16) == NULL)
1452             goto err;
1453 
1454         /*  Ensure that montgomery contexts are initialized */
1455         if (in_mont1 != NULL) {
1456             mont1 = in_mont1;
1457         } else {
1458             if ((mont1 = BN_MONT_CTX_new()) == NULL)
1459                 goto err;
1460             if (!BN_MONT_CTX_set(mont1, m1, ctx))
1461                 goto err;
1462         }
1463         if (in_mont2 != NULL) {
1464             mont2 = in_mont2;
1465         } else {
1466             if ((mont2 = BN_MONT_CTX_new()) == NULL)
1467                 goto err;
1468             if (!BN_MONT_CTX_set(mont2, m2, ctx))
1469                 goto err;
1470         }
1471 
1472         ret = ossl_rsaz_mod_exp_avx512_x2(rr1->d, a1->d, p1->d, m1->d,
1473                                           mont1->RR.d, mont1->n0[0],
1474                                           rr2->d, a2->d, p2->d, m2->d,
1475                                           mont2->RR.d, mont2->n0[0],
1476                                           1024 /* factor bit size */);
1477 
1478         rr1->top = 16;
1479         rr1->neg = 0;
1480         bn_correct_top(rr1);
1481         bn_check_top(rr1);
1482 
1483         rr2->top = 16;
1484         rr2->neg = 0;
1485         bn_correct_top(rr2);
1486         bn_check_top(rr2);
1487 
1488         goto err;
1489     }
1490 #endif
1491 
1492     /* rr1 = a1^p1 mod m1 */
1493     ret = BN_mod_exp_mont_consttime(rr1, a1, p1, m1, ctx, in_mont1);
1494     /* rr2 = a2^p2 mod m2 */
1495     ret &= BN_mod_exp_mont_consttime(rr2, a2, p2, m2, ctx, in_mont2);
1496 
1497 #ifdef RSAZ_ENABLED
1498 err:
1499     if (in_mont2 == NULL)
1500         BN_MONT_CTX_free(mont2);
1501     if (in_mont1 == NULL)
1502         BN_MONT_CTX_free(mont1);
1503 #endif
1504 
1505     return ret;
1506 }
1507