xref: /src/crypto/openssl/crypto/bn/bn_exp.c (revision f25b8c9fb4f58cf61adb47d7570abe7caa6d385d)
1 /*
2  * Copyright 1995-2025 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 alloca
22 #define alloca(s) __builtin_alloca((s))
23 #endif
24 #elif defined(__sun)
25 #include <alloca.h>
26 #endif
27 
28 #include "rsaz_exp.h"
29 
30 #undef SPARC_T4_MONT
31 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
32 #include "crypto/sparc_arch.h"
33 #define SPARC_T4_MONT
34 #endif
35 
36 /* maximum precomputation table size for *variable* sliding windows */
37 #define TABLE_SIZE 32
38 
39 /*
40  * Beyond this limit the constant time code is disabled due to
41  * the possible overflow in the computation of powerbufLen in
42  * BN_mod_exp_mont_consttime.
43  * When this limit is exceeded, the computation will be done using
44  * non-constant time code, but it will take very long.
45  */
46 #define BN_CONSTTIME_SIZE_LIMIT (INT_MAX / BN_BYTES / 256)
47 
48 /* this one works - simple but works */
BN_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)49 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
50 {
51     int i, bits, ret = 0;
52     BIGNUM *v, *rr;
53 
54     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
55         || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) {
56         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
57         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
58         return 0;
59     }
60 
61     BN_CTX_start(ctx);
62     rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r;
63     v = BN_CTX_get(ctx);
64     if (rr == NULL || v == NULL)
65         goto err;
66 
67     if (BN_copy(v, a) == NULL)
68         goto err;
69     bits = BN_num_bits(p);
70 
71     if (BN_is_odd(p)) {
72         if (BN_copy(rr, a) == NULL)
73             goto err;
74     } else {
75         if (!BN_one(rr))
76             goto err;
77     }
78 
79     for (i = 1; i < bits; i++) {
80         if (!BN_sqr(v, v, ctx))
81             goto err;
82         if (BN_is_bit_set(p, i)) {
83             if (!BN_mul(rr, rr, v, ctx))
84                 goto err;
85         }
86     }
87     if (r != rr && BN_copy(r, rr) == NULL)
88         goto err;
89 
90     ret = 1;
91 err:
92     BN_CTX_end(ctx);
93     bn_check_top(r);
94     return ret;
95 }
96 
BN_mod_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)97 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
98     BN_CTX *ctx)
99 {
100     int ret;
101 
102     bn_check_top(a);
103     bn_check_top(p);
104     bn_check_top(m);
105 
106     /*-
107      * For even modulus  m = 2^k*m_odd, it might make sense to compute
108      * a^p mod m_odd  and  a^p mod 2^k  separately (with Montgomery
109      * exponentiation for the odd part), using appropriate exponent
110      * reductions, and combine the results using the CRT.
111      *
112      * For now, we use Montgomery only if the modulus is odd; otherwise,
113      * exponentiation using the reciprocal-based quick remaindering
114      * algorithm is used.
115      *
116      * (Timing obtained with expspeed.c [computations  a^p mod m
117      * where  a, p, m  are of the same length: 256, 512, 1024, 2048,
118      * 4096, 8192 bits], compared to the running time of the
119      * standard algorithm:
120      *
121      *   BN_mod_exp_mont   33 .. 40 %  [AMD K6-2, Linux, debug configuration]
122      *                     55 .. 77 %  [UltraSparc processor, but
123      *                                  debug-solaris-sparcv8-gcc conf.]
124      *
125      *   BN_mod_exp_recp   50 .. 70 %  [AMD K6-2, Linux, debug configuration]
126      *                     62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
127      *
128      * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
129      * at 2048 and more bits, but at 512 and 1024 bits, it was
130      * slower even than the standard algorithm!
131      *
132      * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
133      * should be obtained when the new Montgomery reduction code
134      * has been integrated into OpenSSL.)
135      */
136 
137 #define MONT_MUL_MOD
138 #define MONT_EXP_WORD
139 #define RECP_MUL_MOD
140 
141 #ifdef MONT_MUL_MOD
142     if (BN_is_odd(m)) {
143 #ifdef MONT_EXP_WORD
144         if (a->top == 1 && !a->neg
145             && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)
146             && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0)
147             && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) {
148             BN_ULONG A = a->d[0];
149             ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
150         } else
151 #endif
152             ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
153     } else
154 #endif
155 #ifdef RECP_MUL_MOD
156     {
157         ret = BN_mod_exp_recp(r, a, p, m, ctx);
158     }
159 #else
160     {
161         ret = BN_mod_exp_simple(r, a, p, m, ctx);
162     }
163 #endif
164 
165     bn_check_top(r);
166     return ret;
167 }
168 
BN_mod_exp_recp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)169 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
170     const BIGNUM *m, BN_CTX *ctx)
171 {
172     int i, j, bits, ret = 0, wstart, wend, window;
173     int start = 1;
174     BIGNUM *aa;
175     /* Table of variables obtained from 'ctx' */
176     BIGNUM *val[TABLE_SIZE];
177     BN_RECP_CTX recp;
178 
179     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
180         || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
181         || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
182         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
183         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
184         return 0;
185     }
186 
187     bits = BN_num_bits(p);
188     if (bits == 0) {
189         /* x**0 mod 1, or x**0 mod -1 is still zero. */
190         if (BN_abs_is_word(m, 1)) {
191             ret = 1;
192             BN_zero(r);
193         } else {
194             ret = BN_one(r);
195         }
196         return ret;
197     }
198 
199     BN_RECP_CTX_init(&recp);
200 
201     BN_CTX_start(ctx);
202     aa = BN_CTX_get(ctx);
203     val[0] = BN_CTX_get(ctx);
204     if (val[0] == NULL)
205         goto err;
206 
207     if (m->neg) {
208         /* ignore sign of 'm' */
209         if (!BN_copy(aa, m))
210             goto err;
211         aa->neg = 0;
212         if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
213             goto err;
214     } else {
215         if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
216             goto err;
217     }
218 
219     if (!BN_nnmod(val[0], a, m, ctx))
220         goto err; /* 1 */
221     if (BN_is_zero(val[0])) {
222         BN_zero(r);
223         ret = 1;
224         goto err;
225     }
226 
227     window = BN_window_bits_for_exponent_size(bits);
228     if (window > 1) {
229         if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
230             goto err; /* 2 */
231         j = 1 << (window - 1);
232         for (i = 1; i < j; i++) {
233             if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
234                 goto err;
235         }
236     }
237 
238     start = 1; /* This is used to avoid multiplication etc
239                 * when there is only the value '1' in the
240                 * buffer. */
241     wstart = bits - 1; /* The top bit of the window */
242     wend = 0; /* The bottom bit of the window */
243 
244     if (r == p) {
245         BIGNUM *p_dup = BN_CTX_get(ctx);
246 
247         if (p_dup == NULL || BN_copy(p_dup, p) == NULL)
248             goto err;
249         p = p_dup;
250     }
251 
252     if (!BN_one(r))
253         goto err;
254 
255     for (;;) {
256         int wvalue; /* The 'value' of the window */
257 
258         if (BN_is_bit_set(p, wstart) == 0) {
259             if (!start)
260                 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
261                     goto err;
262             if (wstart == 0)
263                 break;
264             wstart--;
265             continue;
266         }
267         /*
268          * We now have wstart on a 'set' bit, we now need to work out how bit
269          * a window to do.  To do this we need to scan forward until the last
270          * set bit before the end of the window
271          */
272         wvalue = 1;
273         wend = 0;
274         for (i = 1; i < window; i++) {
275             if (wstart - i < 0)
276                 break;
277             if (BN_is_bit_set(p, wstart - i)) {
278                 wvalue <<= (i - wend);
279                 wvalue |= 1;
280                 wend = i;
281             }
282         }
283 
284         /* wend is the size of the current window */
285         j = wend + 1;
286         /* add the 'bytes above' */
287         if (!start)
288             for (i = 0; i < j; i++) {
289                 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
290                     goto err;
291             }
292 
293         /* wvalue will be an odd number < 2^window */
294         if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
295             goto err;
296 
297         /* move the 'window' down further */
298         wstart -= wend + 1;
299         start = 0;
300         if (wstart < 0)
301             break;
302     }
303     ret = 1;
304 err:
305     BN_CTX_end(ctx);
306     BN_RECP_CTX_free(&recp);
307     bn_check_top(r);
308     return ret;
309 }
310 
BN_mod_exp_mont(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)311 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
312     const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
313 {
314     int i, j, bits, ret = 0, wstart, wend, window;
315     int start = 1;
316     BIGNUM *d, *r;
317     const BIGNUM *aa;
318     /* Table of variables obtained from 'ctx' */
319     BIGNUM *val[TABLE_SIZE];
320     BN_MONT_CTX *mont = NULL;
321 
322     bn_check_top(a);
323     bn_check_top(p);
324     bn_check_top(m);
325 
326     if (!BN_is_odd(m)) {
327         ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
328         return 0;
329     }
330 
331     if (m->top <= BN_CONSTTIME_SIZE_LIMIT
332         && (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
333             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
334             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0)) {
335         return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
336     }
337 
338     bits = BN_num_bits(p);
339     if (bits == 0) {
340         /* x**0 mod 1, or x**0 mod -1 is still zero. */
341         if (BN_abs_is_word(m, 1)) {
342             ret = 1;
343             BN_zero(rr);
344         } else {
345             ret = BN_one(rr);
346         }
347         return ret;
348     }
349 
350     BN_CTX_start(ctx);
351     d = BN_CTX_get(ctx);
352     r = BN_CTX_get(ctx);
353     val[0] = BN_CTX_get(ctx);
354     if (val[0] == NULL)
355         goto err;
356 
357     /*
358      * If this is not done, things will break in the montgomery part
359      */
360 
361     if (in_mont != NULL)
362         mont = in_mont;
363     else {
364         if ((mont = BN_MONT_CTX_new()) == NULL)
365             goto err;
366         if (!BN_MONT_CTX_set(mont, m, ctx))
367             goto err;
368     }
369 
370     if (a->neg || BN_ucmp(a, m) >= 0) {
371         if (!BN_nnmod(val[0], a, m, ctx))
372             goto err;
373         aa = val[0];
374     } else
375         aa = a;
376     if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
377         goto err; /* 1 */
378 
379     window = BN_window_bits_for_exponent_size(bits);
380     if (window > 1) {
381         if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
382             goto err; /* 2 */
383         j = 1 << (window - 1);
384         for (i = 1; i < j; i++) {
385             if (((val[i] = BN_CTX_get(ctx)) == NULL) || !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
386                 goto err;
387         }
388     }
389 
390     start = 1; /* This is used to avoid multiplication etc
391                 * when there is only the value '1' in the
392                 * buffer. */
393     wstart = bits - 1; /* The top bit of the window */
394     wend = 0; /* The bottom bit of the window */
395 
396 #if 1 /* by Shay Gueron's suggestion */
397     j = m->top; /* borrow j */
398     if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
399         if (bn_wexpand(r, j) == NULL)
400             goto err;
401         /* 2^(top*BN_BITS2) - m */
402         r->d[0] = (0 - m->d[0]) & BN_MASK2;
403         for (i = 1; i < j; i++)
404             r->d[i] = (~m->d[i]) & BN_MASK2;
405         r->top = j;
406         r->flags |= BN_FLG_FIXED_TOP;
407     } else
408 #endif
409         if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx))
410         goto err;
411     for (;;) {
412         int wvalue; /* The 'value' of the window */
413 
414         if (BN_is_bit_set(p, wstart) == 0) {
415             if (!start) {
416                 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
417                     goto err;
418             }
419             if (wstart == 0)
420                 break;
421             wstart--;
422             continue;
423         }
424         /*
425          * We now have wstart on a 'set' bit, we now need to work out how bit
426          * a window to do.  To do this we need to scan forward until the last
427          * set bit before the end of the window
428          */
429         wvalue = 1;
430         wend = 0;
431         for (i = 1; i < window; i++) {
432             if (wstart - i < 0)
433                 break;
434             if (BN_is_bit_set(p, wstart - i)) {
435                 wvalue <<= (i - wend);
436                 wvalue |= 1;
437                 wend = i;
438             }
439         }
440 
441         /* wend is the size of the current window */
442         j = wend + 1;
443         /* add the 'bytes above' */
444         if (!start)
445             for (i = 0; i < j; i++) {
446                 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
447                     goto err;
448             }
449 
450         /* wvalue will be an odd number < 2^window */
451         if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx))
452             goto err;
453 
454         /* move the 'window' down further */
455         wstart -= wend + 1;
456         start = 0;
457         if (wstart < 0)
458             break;
459     }
460     /*
461      * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
462      * removes padding [if any] and makes return value suitable for public
463      * API consumer.
464      */
465 #if defined(SPARC_T4_MONT)
466     if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
467         j = mont->N.top; /* borrow j */
468         val[0]->d[0] = 1; /* borrow val[0] */
469         for (i = 1; i < j; i++)
470             val[0]->d[i] = 0;
471         val[0]->top = j;
472         if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
473             goto err;
474     } else
475 #endif
476         if (!BN_from_montgomery(rr, r, mont, ctx))
477         goto err;
478     ret = 1;
479 err:
480     if (in_mont == NULL)
481         BN_MONT_CTX_free(mont);
482     BN_CTX_end(ctx);
483     bn_check_top(rr);
484     return ret;
485 }
486 
bn_get_bits(const BIGNUM * a,int bitpos)487 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
488 {
489     BN_ULONG ret = 0;
490     int wordpos;
491 
492     wordpos = bitpos / BN_BITS2;
493     bitpos %= BN_BITS2;
494     if (wordpos >= 0 && wordpos < a->top) {
495         ret = a->d[wordpos] & BN_MASK2;
496         if (bitpos) {
497             ret >>= bitpos;
498             if (++wordpos < a->top)
499                 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
500         }
501     }
502 
503     return ret & BN_MASK2;
504 }
505 
506 /*
507  * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
508  * layout so that accessing any of these table values shows the same access
509  * pattern as far as cache lines are concerned.  The following functions are
510  * used to transfer a BIGNUM from/to that table.
511  */
512 
MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM * b,int top,unsigned char * buf,int idx,int window)513 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
514     unsigned char *buf, int idx,
515     int window)
516 {
517     int i, j;
518     int width = 1 << window;
519     BN_ULONG *table = (BN_ULONG *)buf;
520 
521     if (top > b->top)
522         top = b->top; /* this works because 'buf' is explicitly
523                        * zeroed */
524     for (i = 0, j = idx; i < top; i++, j += width) {
525         table[j] = b->d[i];
526     }
527 
528     return 1;
529 }
530 
MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM * b,int top,unsigned char * buf,int idx,int window)531 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
532     unsigned char *buf, int idx,
533     int window)
534 {
535     int i, j;
536     int width = 1 << window;
537     /*
538      * We declare table 'volatile' in order to discourage compiler
539      * from reordering loads from the table. Concern is that if
540      * reordered in specific manner loads might give away the
541      * information we are trying to conceal. Some would argue that
542      * compiler can reorder them anyway, but it can as well be
543      * argued that doing so would be violation of standard...
544      */
545     volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
546 
547     if (bn_wexpand(b, top) == NULL)
548         return 0;
549 
550     if (window <= 3) {
551         for (i = 0; i < top; i++, table += width) {
552             BN_ULONG acc = 0;
553 
554             for (j = 0; j < width; j++) {
555                 acc |= table[j] & ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
556             }
557 
558             b->d[i] = acc;
559         }
560     } else {
561         int xstride = 1 << (window - 2);
562         BN_ULONG y0, y1, y2, y3;
563 
564         i = idx >> (window - 2); /* equivalent of idx / xstride */
565         idx &= xstride - 1; /* equivalent of idx % xstride */
566 
567         y0 = (BN_ULONG)0 - (constant_time_eq_int(i, 0) & 1);
568         y1 = (BN_ULONG)0 - (constant_time_eq_int(i, 1) & 1);
569         y2 = (BN_ULONG)0 - (constant_time_eq_int(i, 2) & 1);
570         y3 = (BN_ULONG)0 - (constant_time_eq_int(i, 3) & 1);
571 
572         for (i = 0; i < top; i++, table += width) {
573             BN_ULONG acc = 0;
574 
575             for (j = 0; j < xstride; j++) {
576                 acc |= ((table[j + 0 * xstride] & y0) | (table[j + 1 * xstride] & y1) | (table[j + 2 * xstride] & y2) | (table[j + 3 * xstride] & y3))
577                     & ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
578             }
579 
580             b->d[i] = acc;
581         }
582     }
583 
584     b->top = top;
585     b->flags |= BN_FLG_FIXED_TOP;
586     return 1;
587 }
588 
589 /*
590  * Given a pointer value, compute the next address that is a cache line
591  * multiple.
592  */
593 #define MOD_EXP_CTIME_ALIGN(x_) \
594     ((unsigned char *)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
595 
596 /*
597  * This variant of BN_mod_exp_mont() uses fixed windows and the special
598  * precomputation memory layout to limit data-dependency to a minimum to
599  * protect secret exponents (cf. the hyper-threading timing attacks pointed
600  * out by Colin Percival,
601  * http://www.daemonology.net/hyperthreading-considered-harmful/)
602  */
bn_mod_exp_mont_fixed_top(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)603 int bn_mod_exp_mont_fixed_top(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
604     const BIGNUM *m, BN_CTX *ctx,
605     BN_MONT_CTX *in_mont)
606 {
607     int i, bits, ret = 0, window, wvalue, wmask, window0;
608     int top;
609     BN_MONT_CTX *mont = NULL;
610 
611     int numPowers;
612     unsigned char *powerbufFree = NULL;
613     int powerbufLen = 0;
614     unsigned char *powerbuf = NULL;
615     BIGNUM tmp, am;
616 #if defined(SPARC_T4_MONT)
617     unsigned int t4 = 0;
618 #endif
619 
620     if (!BN_is_odd(m)) {
621         ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
622         return 0;
623     }
624 
625     top = m->top;
626 
627     if (top > BN_CONSTTIME_SIZE_LIMIT) {
628         /* Prevent overflowing the powerbufLen computation below */
629         return BN_mod_exp_mont(rr, a, p, m, ctx, in_mont);
630     }
631 
632     /*
633      * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
634      * whether the top bits are zero.
635      */
636     bits = p->top * BN_BITS2;
637     if (bits == 0) {
638         /* x**0 mod 1, or x**0 mod -1 is still zero. */
639         if (BN_abs_is_word(m, 1)) {
640             ret = 1;
641             BN_zero(rr);
642         } else {
643             ret = BN_one(rr);
644         }
645         return ret;
646     }
647 
648     BN_CTX_start(ctx);
649 
650     /*
651      * Allocate a montgomery context if it was not supplied by the caller. If
652      * this is not done, things will break in the montgomery part.
653      */
654     if (in_mont != NULL)
655         mont = in_mont;
656     else {
657         if ((mont = BN_MONT_CTX_new()) == NULL)
658             goto err;
659         if (!BN_MONT_CTX_set(mont, m, ctx))
660             goto err;
661     }
662 
663     if (a->neg || BN_ucmp(a, m) >= 0) {
664         BIGNUM *reduced = BN_CTX_get(ctx);
665         if (reduced == NULL
666             || !BN_nnmod(reduced, a, m, ctx)) {
667             goto err;
668         }
669         a = reduced;
670     }
671 
672 #ifdef RSAZ_ENABLED
673     /*
674      * If the size of the operands allow it, perform the optimized
675      * RSAZ exponentiation. For further information see
676      * crypto/bn/rsaz_exp.c and accompanying assembly modules.
677      */
678     if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
679         && rsaz_avx2_eligible()) {
680         if (NULL == bn_wexpand(rr, 16))
681             goto err;
682         RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
683             mont->n0[0]);
684         rr->top = 16;
685         rr->neg = 0;
686         bn_correct_top(rr);
687         ret = 1;
688         goto err;
689     } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
690         if (NULL == bn_wexpand(rr, 8))
691             goto err;
692         RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
693         rr->top = 8;
694         rr->neg = 0;
695         bn_correct_top(rr);
696         ret = 1;
697         goto err;
698     }
699 #endif
700 
701     /* Get the window size to use with size of p. */
702     window = BN_window_bits_for_ctime_exponent_size(bits);
703 #if defined(SPARC_T4_MONT)
704     if (window >= 5 && (top & 15) == 0 && top <= 64 && (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) == (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
705         window = 5;
706     else
707 #endif
708 #if defined(OPENSSL_BN_ASM_MONT5)
709         if (window >= 5 && top <= BN_SOFT_LIMIT) {
710         window = 5; /* ~5% improvement for RSA2048 sign, and even
711                      * for RSA4096 */
712         /* reserve space for mont->N.d[] copy */
713         powerbufLen += top * sizeof(mont->N.d[0]);
714     }
715 #endif
716     (void)0;
717 
718     /*
719      * Allocate a buffer large enough to hold all of the pre-computed powers
720      * of am, am itself and tmp.
721      */
722     numPowers = 1 << window;
723     powerbufLen += sizeof(m->d[0]) * (top * numPowers + ((2 * top) > numPowers ? (2 * top) : numPowers));
724 #ifdef alloca
725     if (powerbufLen < 3072)
726         powerbufFree = alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
727     else
728 #endif
729         if ((powerbufFree = OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
730             == NULL)
731         goto err;
732 
733     powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
734     memset(powerbuf, 0, powerbufLen);
735 
736 #ifdef alloca
737     if (powerbufLen < 3072)
738         powerbufFree = NULL;
739 #endif
740 
741     /* lay down tmp and am right after powers table */
742     tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
743     am.d = tmp.d + top;
744     tmp.top = am.top = 0;
745     tmp.dmax = am.dmax = top;
746     tmp.neg = am.neg = 0;
747     tmp.flags = am.flags = BN_FLG_STATIC_DATA;
748 
749     /* prepare a^0 in Montgomery domain */
750 #if 1 /* by Shay Gueron's suggestion */
751     if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
752         /* 2^(top*BN_BITS2) - m */
753         tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
754         for (i = 1; i < top; i++)
755             tmp.d[i] = (~m->d[i]) & BN_MASK2;
756         tmp.top = top;
757     } else
758 #endif
759         if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
760         goto err;
761 
762     /* prepare a^1 in Montgomery domain */
763     if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
764         goto err;
765 
766     if (top > BN_SOFT_LIMIT)
767         goto fallback;
768 
769 #if defined(SPARC_T4_MONT)
770     if (t4) {
771         typedef int (*bn_pwr5_mont_f)(BN_ULONG *tp, const BN_ULONG *np,
772             const BN_ULONG *n0, const void *table,
773             int power, int bits);
774         int bn_pwr5_mont_t4_8(BN_ULONG * tp, const BN_ULONG *np,
775             const BN_ULONG *n0, const void *table,
776             int power, int bits);
777         int bn_pwr5_mont_t4_16(BN_ULONG * tp, const BN_ULONG *np,
778             const BN_ULONG *n0, const void *table,
779             int power, int bits);
780         int bn_pwr5_mont_t4_24(BN_ULONG * tp, const BN_ULONG *np,
781             const BN_ULONG *n0, const void *table,
782             int power, int bits);
783         int bn_pwr5_mont_t4_32(BN_ULONG * tp, const BN_ULONG *np,
784             const BN_ULONG *n0, const void *table,
785             int power, int bits);
786         static const bn_pwr5_mont_f pwr5_funcs[4] = {
787             bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
788             bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
789         };
790         bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
791 
792         typedef int (*bn_mul_mont_f)(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_8(BN_ULONG * rp, const BN_ULONG *ap, const void *bp,
796             const BN_ULONG *np, const BN_ULONG *n0);
797         int bn_mul_mont_t4_16(BN_ULONG * rp, const BN_ULONG *ap,
798             const void *bp, const BN_ULONG *np,
799             const BN_ULONG *n0);
800         int bn_mul_mont_t4_24(BN_ULONG * rp, const BN_ULONG *ap,
801             const void *bp, const BN_ULONG *np,
802             const BN_ULONG *n0);
803         int bn_mul_mont_t4_32(BN_ULONG * rp, const BN_ULONG *ap,
804             const void *bp, const BN_ULONG *np,
805             const BN_ULONG *n0);
806         static const bn_mul_mont_f mul_funcs[4] = {
807             bn_mul_mont_t4_8, bn_mul_mont_t4_16,
808             bn_mul_mont_t4_24, bn_mul_mont_t4_32
809         };
810         bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
811 
812         void bn_mul_mont_vis3(BN_ULONG * rp, const BN_ULONG *ap,
813             const void *bp, const BN_ULONG *np,
814             const BN_ULONG *n0, int num);
815         void bn_mul_mont_t4(BN_ULONG * rp, const BN_ULONG *ap,
816             const void *bp, const BN_ULONG *np,
817             const BN_ULONG *n0, int num);
818         void bn_mul_mont_gather5_t4(BN_ULONG * rp, const BN_ULONG *ap,
819             const void *table, const BN_ULONG *np,
820             const BN_ULONG *n0, int num, int power);
821         void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
822             void *table, size_t power);
823         void bn_gather5_t4(BN_ULONG * out, size_t num,
824             void *table, size_t power);
825         void bn_flip_t4(BN_ULONG * dst, BN_ULONG * src, size_t num);
826 
827         BN_ULONG *np = mont->N.d, *n0 = mont->n0;
828         int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
829                                                 * than 32 */
830 
831         /*
832          * BN_to_montgomery can contaminate words above .top [in
833          * BN_DEBUG build...
834          */
835         for (i = am.top; i < top; i++)
836             am.d[i] = 0;
837         for (i = tmp.top; i < top; i++)
838             tmp.d[i] = 0;
839 
840         bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
841         bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
842         if (!(*mul_worker)(tmp.d, am.d, am.d, np, n0) && !(*mul_worker)(tmp.d, am.d, am.d, np, n0))
843             bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
844         bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
845 
846         for (i = 3; i < 32; i++) {
847             /* Calculate a^i = a^(i-1) * a */
848             if (!(*mul_worker)(tmp.d, tmp.d, am.d, np, n0) && !(*mul_worker)(tmp.d, tmp.d, am.d, np, n0))
849                 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
850             bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
851         }
852 
853         /* switch to 64-bit domain */
854         np = alloca(top * sizeof(BN_ULONG));
855         top /= 2;
856         bn_flip_t4(np, mont->N.d, top);
857 
858         /*
859          * The exponent may not have a whole number of fixed-size windows.
860          * To simplify the main loop, the initial window has between 1 and
861          * full-window-size bits such that what remains is always a whole
862          * number of windows
863          */
864         window0 = (bits - 1) % 5 + 1;
865         wmask = (1 << window0) - 1;
866         bits -= window0;
867         wvalue = bn_get_bits(p, bits) & wmask;
868         bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
869 
870         /*
871          * Scan the exponent one window at a time starting from the most
872          * significant bits.
873          */
874         while (bits > 0) {
875             if (bits < stride)
876                 stride = bits;
877             bits -= stride;
878             wvalue = bn_get_bits(p, bits);
879 
880             if ((*pwr5_worker)(tmp.d, np, n0, powerbuf, wvalue, stride))
881                 continue;
882             /* retry once and fall back */
883             if ((*pwr5_worker)(tmp.d, np, n0, powerbuf, wvalue, stride))
884                 continue;
885 
886             bits += stride - 5;
887             wvalue >>= stride - 5;
888             wvalue &= 31;
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_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
892             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
893             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
894             bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
895                 wvalue);
896         }
897 
898         bn_flip_t4(tmp.d, tmp.d, top);
899         top *= 2;
900         /* back to 32-bit domain */
901         tmp.top = top;
902         bn_correct_top(&tmp);
903         OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
904     } else
905 #endif
906 #if defined(OPENSSL_BN_ASM_MONT5)
907         if (window == 5 && top > 1) {
908         /*
909          * This optimization uses ideas from https://eprint.iacr.org/2011/239,
910          * specifically optimization of cache-timing attack countermeasures,
911          * pre-computation optimization, and Almost Montgomery Multiplication.
912          *
913          * The paper discusses a 4-bit window to optimize 512-bit modular
914          * exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer
915          * important.
916          *
917          * |bn_mul_mont_gather5| and |bn_power5| implement the "almost"
918          * reduction variant, so the values here may not be fully reduced.
919          * They are bounded by R (i.e. they fit in |top| words), not |m|.
920          * Additionally, we pass these "almost" reduced inputs into
921          * |bn_mul_mont|, which implements the normal reduction variant.
922          * Given those inputs, |bn_mul_mont| may not give reduced
923          * output, but it will still produce "almost" reduced output.
924          */
925         void bn_mul_mont_gather5(BN_ULONG * rp, const BN_ULONG *ap,
926             const void *table, const BN_ULONG *np,
927             const BN_ULONG *n0, int num, int power);
928         void bn_scatter5(const BN_ULONG *inp, size_t num,
929             void *table, size_t power);
930         void bn_gather5(BN_ULONG * out, size_t num, void *table, size_t power);
931         void bn_power5(BN_ULONG * rp, const BN_ULONG *ap,
932             const void *table, const BN_ULONG *np,
933             const BN_ULONG *n0, int num, int power);
934         int bn_get_bits5(const BN_ULONG *ap, int off);
935 
936         BN_ULONG *n0 = mont->n0, *np;
937 
938         /*
939          * BN_to_montgomery can contaminate words above .top [in
940          * BN_DEBUG build...
941          */
942         for (i = am.top; i < top; i++)
943             am.d[i] = 0;
944         for (i = tmp.top; i < top; i++)
945             tmp.d[i] = 0;
946 
947         /*
948          * copy mont->N.d[] to improve cache locality
949          */
950         for (np = am.d + top, i = 0; i < top; i++)
951             np[i] = mont->N.d[i];
952 
953         bn_scatter5(tmp.d, top, powerbuf, 0);
954         bn_scatter5(am.d, am.top, powerbuf, 1);
955         bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
956         bn_scatter5(tmp.d, top, powerbuf, 2);
957 
958 #if 0
959         for (i = 3; i < 32; i++) {
960             /* Calculate a^i = a^(i-1) * a */
961             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
962             bn_scatter5(tmp.d, top, powerbuf, i);
963         }
964 #else
965         /* same as above, but uses squaring for 1/2 of operations */
966         for (i = 4; i < 32; i *= 2) {
967             bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
968             bn_scatter5(tmp.d, top, powerbuf, i);
969         }
970         for (i = 3; i < 8; i += 2) {
971             int j;
972             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
973             bn_scatter5(tmp.d, top, powerbuf, i);
974             for (j = 2 * i; j < 32; j *= 2) {
975                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
976                 bn_scatter5(tmp.d, top, powerbuf, j);
977             }
978         }
979         for (; i < 16; i += 2) {
980             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
981             bn_scatter5(tmp.d, top, powerbuf, i);
982             bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
983             bn_scatter5(tmp.d, top, powerbuf, 2 * i);
984         }
985         for (; i < 32; i += 2) {
986             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
987             bn_scatter5(tmp.d, top, powerbuf, i);
988         }
989 #endif
990         /*
991          * The exponent may not have a whole number of fixed-size windows.
992          * To simplify the main loop, the initial window has between 1 and
993          * full-window-size bits such that what remains is always a whole
994          * number of windows
995          */
996         window0 = (bits - 1) % 5 + 1;
997         wmask = (1 << window0) - 1;
998         bits -= window0;
999         wvalue = bn_get_bits(p, bits) & wmask;
1000         bn_gather5(tmp.d, top, powerbuf, wvalue);
1001 
1002         /*
1003          * Scan the exponent one window at a time starting from the most
1004          * significant bits.
1005          */
1006         if (top & 7) {
1007             while (bits > 0) {
1008                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1009                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1010                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1011                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1012                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1013                 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1014                     bn_get_bits5(p->d, bits -= 5));
1015             }
1016         } else {
1017             while (bits > 0) {
1018                 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
1019                     bn_get_bits5(p->d, bits -= 5));
1020             }
1021         }
1022 
1023         tmp.top = top;
1024         /*
1025          * The result is now in |tmp| in Montgomery form, but it may not be
1026          * fully reduced. This is within bounds for |BN_from_montgomery|
1027          * (tmp < R <= m*R) so it will, when converting from Montgomery form,
1028          * produce a fully reduced result.
1029          *
1030          * This differs from Figure 2 of the paper, which uses AMM(h, 1) to
1031          * convert from Montgomery form with unreduced output, followed by an
1032          * extra reduction step. In the paper's terminology, we replace
1033          * steps 9 and 10 with MM(h, 1).
1034          */
1035     } else
1036 #endif
1037     {
1038     fallback:
1039         if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1040             goto err;
1041         if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1042             goto err;
1043 
1044         /*
1045          * If the window size is greater than 1, then calculate
1046          * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1047          * powers could instead be computed as (a^(i/2))^2 to use the slight
1048          * performance advantage of sqr over mul).
1049          */
1050         if (window > 1) {
1051             if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1052                 goto err;
1053             if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1054                     window))
1055                 goto err;
1056             for (i = 3; i < numPowers; i++) {
1057                 /* Calculate a^i = a^(i-1) * a */
1058                 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1059                     goto err;
1060                 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1061                         window))
1062                     goto err;
1063             }
1064         }
1065 
1066         /*
1067          * The exponent may not have a whole number of fixed-size windows.
1068          * To simplify the main loop, the initial window has between 1 and
1069          * full-window-size bits such that what remains is always a whole
1070          * number of windows
1071          */
1072         window0 = (bits - 1) % window + 1;
1073         wmask = (1 << window0) - 1;
1074         bits -= window0;
1075         wvalue = bn_get_bits(p, bits) & wmask;
1076         if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1077                 window))
1078             goto err;
1079 
1080         wmask = (1 << window) - 1;
1081         /*
1082          * Scan the exponent one window at a time starting from the most
1083          * significant bits.
1084          */
1085         while (bits > 0) {
1086 
1087             /* Square the result window-size times */
1088             for (i = 0; i < window; i++)
1089                 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1090                     goto err;
1091 
1092             /*
1093              * Get a window's worth of bits from the exponent
1094              * This avoids calling BN_is_bit_set for each bit, which
1095              * is not only slower but also makes each bit vulnerable to
1096              * EM (and likely other) side-channel attacks like One&Done
1097              * (for details see "One&Done: A Single-Decryption EM-Based
1098              *  Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1099              *  H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1100              *  M. Prvulovic, in USENIX Security'18)
1101              */
1102             bits -= window;
1103             wvalue = bn_get_bits(p, bits) & wmask;
1104             /*
1105              * Fetch the appropriate pre-computed value from the pre-buf
1106              */
1107             if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1108                     window))
1109                 goto err;
1110 
1111             /* Multiply the result into the intermediate result */
1112             if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1113                 goto err;
1114         }
1115     }
1116 
1117     /*
1118      * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1119      * removes padding [if any] and makes return value suitable for public
1120      * API consumer.
1121      */
1122 #if defined(SPARC_T4_MONT)
1123     if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1124         am.d[0] = 1; /* borrow am */
1125         for (i = 1; i < top; i++)
1126             am.d[i] = 0;
1127         if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1128             goto err;
1129     } else
1130 #endif
1131         if (!bn_from_mont_fixed_top(rr, &tmp, mont, ctx))
1132         goto err;
1133     ret = 1;
1134 err:
1135     if (in_mont == NULL)
1136         BN_MONT_CTX_free(mont);
1137     if (powerbuf != NULL) {
1138         OPENSSL_cleanse(powerbuf, powerbufLen);
1139         OPENSSL_free(powerbufFree);
1140     }
1141     BN_CTX_end(ctx);
1142     return ret;
1143 }
1144 
BN_mod_exp_mont_consttime(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)1145 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
1146     const BIGNUM *m, BN_CTX *ctx,
1147     BN_MONT_CTX *in_mont)
1148 {
1149     bn_check_top(a);
1150     bn_check_top(p);
1151     bn_check_top(m);
1152     if (!bn_mod_exp_mont_fixed_top(rr, a, p, m, ctx, in_mont))
1153         return 0;
1154     bn_correct_top(rr);
1155     return 1;
1156 }
1157 
BN_mod_exp_mont_word(BIGNUM * rr,BN_ULONG a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)1158 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1159     const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1160 {
1161     BN_MONT_CTX *mont = NULL;
1162     int b, bits, ret = 0;
1163     int r_is_one;
1164     BN_ULONG w, next_w;
1165     BIGNUM *r, *t;
1166     BIGNUM *swap_tmp;
1167 #define BN_MOD_MUL_WORD(r, w, m)                            \
1168     (BN_mul_word(r, (w)) && (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1169          (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1170     /*
1171      * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1172      * probably more overhead than always using BN_mod (which uses BN_copy if
1173      * a similar test returns true).
1174      */
1175     /*
1176      * We can use BN_mod and do not need BN_nnmod because our accumulator is
1177      * never negative (the result of BN_mod does not depend on the sign of
1178      * the modulus).
1179      */
1180 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1181     (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1182 
1183     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1184         || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1185         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1186         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1187         return 0;
1188     }
1189 
1190     bn_check_top(p);
1191     bn_check_top(m);
1192 
1193     if (!BN_is_odd(m)) {
1194         ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
1195         return 0;
1196     }
1197     if (m->top == 1)
1198         a %= m->d[0]; /* make sure that 'a' is reduced */
1199 
1200     bits = BN_num_bits(p);
1201     if (bits == 0) {
1202         /* x**0 mod 1, or x**0 mod -1 is still zero. */
1203         if (BN_abs_is_word(m, 1)) {
1204             ret = 1;
1205             BN_zero(rr);
1206         } else {
1207             ret = BN_one(rr);
1208         }
1209         return ret;
1210     }
1211     if (a == 0) {
1212         BN_zero(rr);
1213         ret = 1;
1214         return ret;
1215     }
1216 
1217     BN_CTX_start(ctx);
1218     r = BN_CTX_get(ctx);
1219     t = BN_CTX_get(ctx);
1220     if (t == NULL)
1221         goto err;
1222 
1223     if (in_mont != NULL)
1224         mont = in_mont;
1225     else {
1226         if ((mont = BN_MONT_CTX_new()) == NULL)
1227             goto err;
1228         if (!BN_MONT_CTX_set(mont, m, ctx))
1229             goto err;
1230     }
1231 
1232     r_is_one = 1; /* except for Montgomery factor */
1233 
1234     /* bits-1 >= 0 */
1235 
1236     /* The result is accumulated in the product r*w. */
1237     w = a; /* bit 'bits-1' of 'p' is always set */
1238     for (b = bits - 2; b >= 0; b--) {
1239         /* First, square r*w. */
1240         next_w = w * w;
1241         if ((next_w / w) != w) { /* overflow */
1242             if (r_is_one) {
1243                 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1244                     goto err;
1245                 r_is_one = 0;
1246             } else {
1247                 if (!BN_MOD_MUL_WORD(r, w, m))
1248                     goto err;
1249             }
1250             next_w = 1;
1251         }
1252         w = next_w;
1253         if (!r_is_one) {
1254             if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1255                 goto err;
1256         }
1257 
1258         /* Second, multiply r*w by 'a' if exponent bit is set. */
1259         if (BN_is_bit_set(p, b)) {
1260             next_w = w * a;
1261             if ((next_w / a) != w) { /* overflow */
1262                 if (r_is_one) {
1263                     if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1264                         goto err;
1265                     r_is_one = 0;
1266                 } else {
1267                     if (!BN_MOD_MUL_WORD(r, w, m))
1268                         goto err;
1269                 }
1270                 next_w = a;
1271             }
1272             w = next_w;
1273         }
1274     }
1275 
1276     /* Finally, set r:=r*w. */
1277     if (w != 1) {
1278         if (r_is_one) {
1279             if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1280                 goto err;
1281             r_is_one = 0;
1282         } else {
1283             if (!BN_MOD_MUL_WORD(r, w, m))
1284                 goto err;
1285         }
1286     }
1287 
1288     if (r_is_one) { /* can happen only if a == 1 */
1289         if (!BN_one(rr))
1290             goto err;
1291     } else {
1292         if (!BN_from_montgomery(rr, r, mont, ctx))
1293             goto err;
1294     }
1295     ret = 1;
1296 err:
1297     if (in_mont == NULL)
1298         BN_MONT_CTX_free(mont);
1299     BN_CTX_end(ctx);
1300     bn_check_top(rr);
1301     return ret;
1302 }
1303 
1304 /* The old fallback, simple version :-) */
BN_mod_exp_simple(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)1305 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1306     const BIGNUM *m, BN_CTX *ctx)
1307 {
1308     int i, j, bits, ret = 0, wstart, wend, window;
1309     int start = 1;
1310     BIGNUM *d;
1311     /* Table of variables obtained from 'ctx' */
1312     BIGNUM *val[TABLE_SIZE];
1313 
1314     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1315         || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1316         || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1317         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1318         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1319         return 0;
1320     }
1321 
1322     if (r == m) {
1323         ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
1324         return 0;
1325     }
1326 
1327     bits = BN_num_bits(p);
1328     if (bits == 0) {
1329         /* x**0 mod 1, or x**0 mod -1 is still zero. */
1330         if (BN_abs_is_word(m, 1)) {
1331             ret = 1;
1332             BN_zero(r);
1333         } else {
1334             ret = BN_one(r);
1335         }
1336         return ret;
1337     }
1338 
1339     BN_CTX_start(ctx);
1340     d = BN_CTX_get(ctx);
1341     val[0] = BN_CTX_get(ctx);
1342     if (val[0] == NULL)
1343         goto err;
1344 
1345     if (!BN_nnmod(val[0], a, m, ctx))
1346         goto err; /* 1 */
1347     if (BN_is_zero(val[0])) {
1348         BN_zero(r);
1349         ret = 1;
1350         goto err;
1351     }
1352 
1353     window = BN_window_bits_for_exponent_size(bits);
1354     if (window > 1) {
1355         if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1356             goto err; /* 2 */
1357         j = 1 << (window - 1);
1358         for (i = 1; i < j; i++) {
1359             if (((val[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1360                 goto err;
1361         }
1362     }
1363 
1364     start = 1; /* This is used to avoid multiplication etc
1365                 * when there is only the value '1' in the
1366                 * buffer. */
1367     wstart = bits - 1; /* The top bit of the window */
1368     wend = 0; /* The bottom bit of the window */
1369 
1370     if (r == p) {
1371         BIGNUM *p_dup = BN_CTX_get(ctx);
1372 
1373         if (p_dup == NULL || BN_copy(p_dup, p) == NULL)
1374             goto err;
1375         p = p_dup;
1376     }
1377 
1378     if (!BN_one(r))
1379         goto err;
1380 
1381     for (;;) {
1382         int wvalue; /* The 'value' of the window */
1383 
1384         if (BN_is_bit_set(p, wstart) == 0) {
1385             if (!start)
1386                 if (!BN_mod_mul(r, r, r, m, ctx))
1387                     goto err;
1388             if (wstart == 0)
1389                 break;
1390             wstart--;
1391             continue;
1392         }
1393         /*
1394          * We now have wstart on a 'set' bit, we now need to work out how bit
1395          * a window to do.  To do this we need to scan forward until the last
1396          * set bit before the end of the window
1397          */
1398         wvalue = 1;
1399         wend = 0;
1400         for (i = 1; i < window; i++) {
1401             if (wstart - i < 0)
1402                 break;
1403             if (BN_is_bit_set(p, wstart - i)) {
1404                 wvalue <<= (i - wend);
1405                 wvalue |= 1;
1406                 wend = i;
1407             }
1408         }
1409 
1410         /* wend is the size of the current window */
1411         j = wend + 1;
1412         /* add the 'bytes above' */
1413         if (!start)
1414             for (i = 0; i < j; i++) {
1415                 if (!BN_mod_mul(r, r, r, m, ctx))
1416                     goto err;
1417             }
1418 
1419         /* wvalue will be an odd number < 2^window */
1420         if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1421             goto err;
1422 
1423         /* move the 'window' down further */
1424         wstart -= wend + 1;
1425         start = 0;
1426         if (wstart < 0)
1427             break;
1428     }
1429     ret = 1;
1430 err:
1431     BN_CTX_end(ctx);
1432     bn_check_top(r);
1433     return ret;
1434 }
1435 
1436 /*
1437  * This is a variant of modular exponentiation optimization that does
1438  * parallel 2-primes exponentiation using 256-bit (AVX512VL) AVX512_IFMA ISA
1439  * or AVX_IFMA ISA in 52-bit binary redundant representation.
1440  * If such instructions are not available, or input data size is not supported,
1441  * it falls back to two BN_mod_exp_mont_consttime() calls.
1442  */
BN_mod_exp_mont_consttime_x2(BIGNUM * rr1,const BIGNUM * a1,const BIGNUM * p1,const BIGNUM * m1,BN_MONT_CTX * in_mont1,BIGNUM * rr2,const BIGNUM * a2,const BIGNUM * p2,const BIGNUM * m2,BN_MONT_CTX * in_mont2,BN_CTX * ctx)1443 int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1, const BIGNUM *p1,
1444     const BIGNUM *m1, BN_MONT_CTX *in_mont1,
1445     BIGNUM *rr2, const BIGNUM *a2, const BIGNUM *p2,
1446     const BIGNUM *m2, BN_MONT_CTX *in_mont2,
1447     BN_CTX *ctx)
1448 {
1449     int ret = 0;
1450 
1451 #ifdef RSAZ_ENABLED
1452     BN_MONT_CTX *mont1 = NULL;
1453     BN_MONT_CTX *mont2 = NULL;
1454 
1455     if ((ossl_rsaz_avx512ifma_eligible() || ossl_rsaz_avxifma_eligible()) && (((a1->top == 16) && (p1->top == 16) && (BN_num_bits(m1) == 1024) && (a2->top == 16) && (p2->top == 16) && (BN_num_bits(m2) == 1024)) || ((a1->top == 24) && (p1->top == 24) && (BN_num_bits(m1) == 1536) && (a2->top == 24) && (p2->top == 24) && (BN_num_bits(m2) == 1536)) || ((a1->top == 32) && (p1->top == 32) && (BN_num_bits(m1) == 2048) && (a2->top == 32) && (p2->top == 32) && (BN_num_bits(m2) == 2048)))) {
1456 
1457         int topn = a1->top;
1458         /* Modulus bits of |m1| and |m2| are equal */
1459         int mod_bits = BN_num_bits(m1);
1460 
1461         if (bn_wexpand(rr1, topn) == NULL)
1462             goto err;
1463         if (bn_wexpand(rr2, topn) == NULL)
1464             goto err;
1465 
1466         /*  Ensure that montgomery contexts are initialized */
1467         if (in_mont1 != NULL) {
1468             mont1 = in_mont1;
1469         } else {
1470             if ((mont1 = BN_MONT_CTX_new()) == NULL)
1471                 goto err;
1472             if (!BN_MONT_CTX_set(mont1, m1, ctx))
1473                 goto err;
1474         }
1475         if (in_mont2 != NULL) {
1476             mont2 = in_mont2;
1477         } else {
1478             if ((mont2 = BN_MONT_CTX_new()) == NULL)
1479                 goto err;
1480             if (!BN_MONT_CTX_set(mont2, m2, ctx))
1481                 goto err;
1482         }
1483 
1484         ret = ossl_rsaz_mod_exp_avx512_x2(rr1->d, a1->d, p1->d, m1->d,
1485             mont1->RR.d, mont1->n0[0],
1486             rr2->d, a2->d, p2->d, m2->d,
1487             mont2->RR.d, mont2->n0[0],
1488             mod_bits);
1489 
1490         rr1->top = topn;
1491         rr1->neg = 0;
1492         bn_correct_top(rr1);
1493         bn_check_top(rr1);
1494 
1495         rr2->top = topn;
1496         rr2->neg = 0;
1497         bn_correct_top(rr2);
1498         bn_check_top(rr2);
1499 
1500         goto err;
1501     }
1502 #endif
1503 
1504     /* rr1 = a1^p1 mod m1 */
1505     ret = BN_mod_exp_mont_consttime(rr1, a1, p1, m1, ctx, in_mont1);
1506     /* rr2 = a2^p2 mod m2 */
1507     ret &= BN_mod_exp_mont_consttime(rr2, a2, p2, m2, ctx, in_mont2);
1508 
1509 #ifdef RSAZ_ENABLED
1510 err:
1511     if (in_mont2 == NULL)
1512         BN_MONT_CTX_free(mont2);
1513     if (in_mont1 == NULL)
1514         BN_MONT_CTX_free(mont1);
1515 #endif
1516 
1517     return ret;
1518 }
1519