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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 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, wvalue;
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) ||
234                 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
235                 goto err;
236         }
237     }
238 
239     start = 1;                  /* This is used to avoid multiplication etc
240                                  * when there is only the value '1' in the
241                                  * buffer. */
242     wvalue = 0;                 /* The 'value' of the window */
243     wstart = bits - 1;          /* The top bit of the window */
244     wend = 0;                   /* The bottom bit of the window */
245 
246     if (!BN_one(r))
247         goto err;
248 
249     for (;;) {
250         if (BN_is_bit_set(p, wstart) == 0) {
251             if (!start)
252                 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
253                     goto err;
254             if (wstart == 0)
255                 break;
256             wstart--;
257             continue;
258         }
259         /*
260          * We now have wstart on a 'set' bit, we now need to work out how bit
261          * a window to do.  To do this we need to scan forward until the last
262          * set bit before the end of the window
263          */
264         wvalue = 1;
265         wend = 0;
266         for (i = 1; i < window; i++) {
267             if (wstart - i < 0)
268                 break;
269             if (BN_is_bit_set(p, wstart - i)) {
270                 wvalue <<= (i - wend);
271                 wvalue |= 1;
272                 wend = i;
273             }
274         }
275 
276         /* wend is the size of the current window */
277         j = wend + 1;
278         /* add the 'bytes above' */
279         if (!start)
280             for (i = 0; i < j; i++) {
281                 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
282                     goto err;
283             }
284 
285         /* wvalue will be an odd number < 2^window */
286         if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
287             goto err;
288 
289         /* move the 'window' down further */
290         wstart -= wend + 1;
291         wvalue = 0;
292         start = 0;
293         if (wstart < 0)
294             break;
295     }
296     ret = 1;
297  err:
298     BN_CTX_end(ctx);
299     BN_RECP_CTX_free(&recp);
300     bn_check_top(r);
301     return ret;
302 }
303 
BN_mod_exp_mont(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)304 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
305                     const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
306 {
307     int i, j, bits, ret = 0, wstart, wend, window, wvalue;
308     int start = 1;
309     BIGNUM *d, *r;
310     const BIGNUM *aa;
311     /* Table of variables obtained from 'ctx' */
312     BIGNUM *val[TABLE_SIZE];
313     BN_MONT_CTX *mont = NULL;
314 
315     bn_check_top(a);
316     bn_check_top(p);
317     bn_check_top(m);
318 
319     if (!BN_is_odd(m)) {
320         ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
321         return 0;
322     }
323 
324     if (m->top <= BN_CONSTTIME_SIZE_LIMIT
325         && (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
326             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
327             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0)) {
328         return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
329     }
330 
331     bits = BN_num_bits(p);
332     if (bits == 0) {
333         /* x**0 mod 1, or x**0 mod -1 is still zero. */
334         if (BN_abs_is_word(m, 1)) {
335             ret = 1;
336             BN_zero(rr);
337         } else {
338             ret = BN_one(rr);
339         }
340         return ret;
341     }
342 
343     BN_CTX_start(ctx);
344     d = BN_CTX_get(ctx);
345     r = BN_CTX_get(ctx);
346     val[0] = BN_CTX_get(ctx);
347     if (val[0] == NULL)
348         goto err;
349 
350     /*
351      * If this is not done, things will break in the montgomery part
352      */
353 
354     if (in_mont != NULL)
355         mont = in_mont;
356     else {
357         if ((mont = BN_MONT_CTX_new()) == NULL)
358             goto err;
359         if (!BN_MONT_CTX_set(mont, m, ctx))
360             goto err;
361     }
362 
363     if (a->neg || BN_ucmp(a, m) >= 0) {
364         if (!BN_nnmod(val[0], a, m, ctx))
365             goto err;
366         aa = val[0];
367     } else
368         aa = a;
369     if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
370         goto err;               /* 1 */
371 
372     window = BN_window_bits_for_exponent_size(bits);
373     if (window > 1) {
374         if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
375             goto err;           /* 2 */
376         j = 1 << (window - 1);
377         for (i = 1; i < j; i++) {
378             if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
379                 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
380                 goto err;
381         }
382     }
383 
384     start = 1;                  /* This is used to avoid multiplication etc
385                                  * when there is only the value '1' in the
386                                  * buffer. */
387     wvalue = 0;                 /* The 'value' of the window */
388     wstart = bits - 1;          /* The top bit of the window */
389     wend = 0;                   /* The bottom bit of the window */
390 
391 #if 1                           /* by Shay Gueron's suggestion */
392     j = m->top;                 /* borrow j */
393     if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
394         if (bn_wexpand(r, j) == NULL)
395             goto err;
396         /* 2^(top*BN_BITS2) - m */
397         r->d[0] = (0 - m->d[0]) & BN_MASK2;
398         for (i = 1; i < j; i++)
399             r->d[i] = (~m->d[i]) & BN_MASK2;
400         r->top = j;
401         r->flags |= BN_FLG_FIXED_TOP;
402     } else
403 #endif
404     if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx))
405         goto err;
406     for (;;) {
407         if (BN_is_bit_set(p, wstart) == 0) {
408             if (!start) {
409                 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
410                     goto err;
411             }
412             if (wstart == 0)
413                 break;
414             wstart--;
415             continue;
416         }
417         /*
418          * We now have wstart on a 'set' bit, we now need to work out how bit
419          * a window to do.  To do this we need to scan forward until the last
420          * set bit before the end of the window
421          */
422         wvalue = 1;
423         wend = 0;
424         for (i = 1; i < window; i++) {
425             if (wstart - i < 0)
426                 break;
427             if (BN_is_bit_set(p, wstart - i)) {
428                 wvalue <<= (i - wend);
429                 wvalue |= 1;
430                 wend = i;
431             }
432         }
433 
434         /* wend is the size of the current window */
435         j = wend + 1;
436         /* add the 'bytes above' */
437         if (!start)
438             for (i = 0; i < j; i++) {
439                 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
440                     goto err;
441             }
442 
443         /* wvalue will be an odd number < 2^window */
444         if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx))
445             goto err;
446 
447         /* move the 'window' down further */
448         wstart -= wend + 1;
449         wvalue = 0;
450         start = 0;
451         if (wstart < 0)
452             break;
453     }
454     /*
455      * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
456      * removes padding [if any] and makes return value suitable for public
457      * API consumer.
458      */
459 #if defined(SPARC_T4_MONT)
460     if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
461         j = mont->N.top;        /* borrow j */
462         val[0]->d[0] = 1;       /* borrow val[0] */
463         for (i = 1; i < j; i++)
464             val[0]->d[i] = 0;
465         val[0]->top = j;
466         if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
467             goto err;
468     } else
469 #endif
470     if (!BN_from_montgomery(rr, r, mont, ctx))
471         goto err;
472     ret = 1;
473  err:
474     if (in_mont == NULL)
475         BN_MONT_CTX_free(mont);
476     BN_CTX_end(ctx);
477     bn_check_top(rr);
478     return ret;
479 }
480 
bn_get_bits(const BIGNUM * a,int bitpos)481 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
482 {
483     BN_ULONG ret = 0;
484     int wordpos;
485 
486     wordpos = bitpos / BN_BITS2;
487     bitpos %= BN_BITS2;
488     if (wordpos >= 0 && wordpos < a->top) {
489         ret = a->d[wordpos] & BN_MASK2;
490         if (bitpos) {
491             ret >>= bitpos;
492             if (++wordpos < a->top)
493                 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
494         }
495     }
496 
497     return ret & BN_MASK2;
498 }
499 
500 /*
501  * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
502  * layout so that accessing any of these table values shows the same access
503  * pattern as far as cache lines are concerned.  The following functions are
504  * used to transfer a BIGNUM from/to that table.
505  */
506 
MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM * b,int top,unsigned char * buf,int idx,int window)507 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
508                                         unsigned char *buf, int idx,
509                                         int window)
510 {
511     int i, j;
512     int width = 1 << window;
513     BN_ULONG *table = (BN_ULONG *)buf;
514 
515     if (top > b->top)
516         top = b->top;           /* this works because 'buf' is explicitly
517                                  * zeroed */
518     for (i = 0, j = idx; i < top; i++, j += width) {
519         table[j] = b->d[i];
520     }
521 
522     return 1;
523 }
524 
MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM * b,int top,unsigned char * buf,int idx,int window)525 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
526                                           unsigned char *buf, int idx,
527                                           int window)
528 {
529     int i, j;
530     int width = 1 << window;
531     /*
532      * We declare table 'volatile' in order to discourage compiler
533      * from reordering loads from the table. Concern is that if
534      * reordered in specific manner loads might give away the
535      * information we are trying to conceal. Some would argue that
536      * compiler can reorder them anyway, but it can as well be
537      * argued that doing so would be violation of standard...
538      */
539     volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
540 
541     if (bn_wexpand(b, top) == NULL)
542         return 0;
543 
544     if (window <= 3) {
545         for (i = 0; i < top; i++, table += width) {
546             BN_ULONG acc = 0;
547 
548             for (j = 0; j < width; j++) {
549                 acc |= table[j] &
550                        ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
551             }
552 
553             b->d[i] = acc;
554         }
555     } else {
556         int xstride = 1 << (window - 2);
557         BN_ULONG y0, y1, y2, y3;
558 
559         i = idx >> (window - 2);        /* equivalent of idx / xstride */
560         idx &= xstride - 1;             /* equivalent of idx % xstride */
561 
562         y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
563         y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
564         y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
565         y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
566 
567         for (i = 0; i < top; i++, table += width) {
568             BN_ULONG acc = 0;
569 
570             for (j = 0; j < xstride; j++) {
571                 acc |= ( (table[j + 0 * xstride] & y0) |
572                          (table[j + 1 * xstride] & y1) |
573                          (table[j + 2 * xstride] & y2) |
574                          (table[j + 3 * xstride] & y3) )
575                        & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
576             }
577 
578             b->d[i] = acc;
579         }
580     }
581 
582     b->top = top;
583     b->flags |= BN_FLG_FIXED_TOP;
584     return 1;
585 }
586 
587 /*
588  * Given a pointer value, compute the next address that is a cache line
589  * multiple.
590  */
591 #define MOD_EXP_CTIME_ALIGN(x_) \
592         ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
593 
594 /*
595  * This variant of BN_mod_exp_mont() uses fixed windows and the special
596  * precomputation memory layout to limit data-dependency to a minimum to
597  * protect secret exponents (cf. the hyper-threading timing attacks pointed
598  * out by Colin Percival,
599  * http://www.daemonology.net/hyperthreading-considered-harmful/)
600  */
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)601 int bn_mod_exp_mont_fixed_top(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
602                               const BIGNUM *m, BN_CTX *ctx,
603                               BN_MONT_CTX *in_mont)
604 {
605     int i, bits, ret = 0, window, wvalue, wmask, window0;
606     int top;
607     BN_MONT_CTX *mont = NULL;
608 
609     int numPowers;
610     unsigned char *powerbufFree = NULL;
611     int powerbufLen = 0;
612     unsigned char *powerbuf = NULL;
613     BIGNUM tmp, am;
614 #if defined(SPARC_T4_MONT)
615     unsigned int t4 = 0;
616 #endif
617 
618     if (!BN_is_odd(m)) {
619         ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
620         return 0;
621     }
622 
623     top = m->top;
624 
625     if (top > BN_CONSTTIME_SIZE_LIMIT) {
626         /* Prevent overflowing the powerbufLen computation below */
627         return BN_mod_exp_mont(rr, a, p, m, ctx, in_mont);
628     }
629 
630     /*
631      * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
632      * whether the top bits are zero.
633      */
634     bits = p->top * BN_BITS2;
635     if (bits == 0) {
636         /* x**0 mod 1, or x**0 mod -1 is still zero. */
637         if (BN_abs_is_word(m, 1)) {
638             ret = 1;
639             BN_zero(rr);
640         } else {
641             ret = BN_one(rr);
642         }
643         return ret;
644     }
645 
646     BN_CTX_start(ctx);
647 
648     /*
649      * Allocate a montgomery context if it was not supplied by the caller. If
650      * this is not done, things will break in the montgomery part.
651      */
652     if (in_mont != NULL)
653         mont = in_mont;
654     else {
655         if ((mont = BN_MONT_CTX_new()) == NULL)
656             goto err;
657         if (!BN_MONT_CTX_set(mont, m, ctx))
658             goto err;
659     }
660 
661     if (a->neg || BN_ucmp(a, m) >= 0) {
662         BIGNUM *reduced = BN_CTX_get(ctx);
663         if (reduced == NULL
664             || !BN_nnmod(reduced, a, m, ctx)) {
665             goto err;
666         }
667         a = reduced;
668     }
669 
670 #ifdef RSAZ_ENABLED
671     /*
672      * If the size of the operands allow it, perform the optimized
673      * RSAZ exponentiation. For further information see
674      * crypto/bn/rsaz_exp.c and accompanying assembly modules.
675      */
676     if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
677         && rsaz_avx2_eligible()) {
678         if (NULL == bn_wexpand(rr, 16))
679             goto err;
680         RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
681                                mont->n0[0]);
682         rr->top = 16;
683         rr->neg = 0;
684         bn_correct_top(rr);
685         ret = 1;
686         goto err;
687     } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
688         if (NULL == bn_wexpand(rr, 8))
689             goto err;
690         RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
691         rr->top = 8;
692         rr->neg = 0;
693         bn_correct_top(rr);
694         ret = 1;
695         goto err;
696     }
697 #endif
698 
699     /* Get the window size to use with size of p. */
700     window = BN_window_bits_for_ctime_exponent_size(bits);
701 #if defined(SPARC_T4_MONT)
702     if (window >= 5 && (top & 15) == 0 && top <= 64 &&
703         (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
704         (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 +
724                                       ((2 * top) >
725                                        numPowers ? (2 * top) : numPowers));
726 #ifdef alloca
727     if (powerbufLen < 3072)
728         powerbufFree =
729             alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
730     else
731 #endif
732         if ((powerbufFree =
733              OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
734             == NULL)
735         goto err;
736 
737     powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
738     memset(powerbuf, 0, powerbufLen);
739 
740 #ifdef alloca
741     if (powerbufLen < 3072)
742         powerbufFree = NULL;
743 #endif
744 
745     /* lay down tmp and am right after powers table */
746     tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
747     am.d = tmp.d + top;
748     tmp.top = am.top = 0;
749     tmp.dmax = am.dmax = top;
750     tmp.neg = am.neg = 0;
751     tmp.flags = am.flags = BN_FLG_STATIC_DATA;
752 
753     /* prepare a^0 in Montgomery domain */
754 #if 1                           /* by Shay Gueron's suggestion */
755     if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
756         /* 2^(top*BN_BITS2) - m */
757         tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
758         for (i = 1; i < top; i++)
759             tmp.d[i] = (~m->d[i]) & BN_MASK2;
760         tmp.top = top;
761     } else
762 #endif
763     if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
764         goto err;
765 
766     /* prepare a^1 in Montgomery domain */
767     if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
768         goto err;
769 
770     if (top > BN_SOFT_LIMIT)
771         goto fallback;
772 
773 #if defined(SPARC_T4_MONT)
774     if (t4) {
775         typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
776                                        const BN_ULONG *n0, const void *table,
777                                        int power, int bits);
778         int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
779                               const BN_ULONG *n0, const void *table,
780                               int power, int bits);
781         int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
782                                const BN_ULONG *n0, const void *table,
783                                int power, int bits);
784         int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
785                                const BN_ULONG *n0, const void *table,
786                                int power, int bits);
787         int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
788                                const BN_ULONG *n0, const void *table,
789                                int power, int bits);
790         static const bn_pwr5_mont_f pwr5_funcs[4] = {
791             bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
792             bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
793         };
794         bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
795 
796         typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
797                                       const void *bp, const BN_ULONG *np,
798                                       const BN_ULONG *n0);
799         int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
800                              const BN_ULONG *np, const BN_ULONG *n0);
801         int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
802                               const void *bp, const BN_ULONG *np,
803                               const BN_ULONG *n0);
804         int bn_mul_mont_t4_24(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_32(BN_ULONG *rp, const BN_ULONG *ap,
808                               const void *bp, const BN_ULONG *np,
809                               const BN_ULONG *n0);
810         static const bn_mul_mont_f mul_funcs[4] = {
811             bn_mul_mont_t4_8, bn_mul_mont_t4_16,
812             bn_mul_mont_t4_24, bn_mul_mont_t4_32
813         };
814         bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
815 
816         void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
817                               const void *bp, const BN_ULONG *np,
818                               const BN_ULONG *n0, int num);
819         void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
820                             const void *bp, const BN_ULONG *np,
821                             const BN_ULONG *n0, int num);
822         void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
823                                     const void *table, const BN_ULONG *np,
824                                     const BN_ULONG *n0, int num, int power);
825         void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
826                                    void *table, size_t power);
827         void bn_gather5_t4(BN_ULONG *out, size_t num,
828                            void *table, size_t power);
829         void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
830 
831         BN_ULONG *np = mont->N.d, *n0 = mont->n0;
832         int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
833                                                 * than 32 */
834 
835         /*
836          * BN_to_montgomery can contaminate words above .top [in
837          * BN_DEBUG build...
838          */
839         for (i = am.top; i < top; i++)
840             am.d[i] = 0;
841         for (i = tmp.top; i < top; i++)
842             tmp.d[i] = 0;
843 
844         bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
845         bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
846         if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
847             !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
848             bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
849         bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
850 
851         for (i = 3; i < 32; i++) {
852             /* Calculate a^i = a^(i-1) * a */
853             if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
854                 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
855                 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
856             bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
857         }
858 
859         /* switch to 64-bit domain */
860         np = alloca(top * sizeof(BN_ULONG));
861         top /= 2;
862         bn_flip_t4(np, mont->N.d, top);
863 
864         /*
865          * The exponent may not have a whole number of fixed-size windows.
866          * To simplify the main loop, the initial window has between 1 and
867          * full-window-size bits such that what remains is always a whole
868          * number of windows
869          */
870         window0 = (bits - 1) % 5 + 1;
871         wmask = (1 << window0) - 1;
872         bits -= window0;
873         wvalue = bn_get_bits(p, bits) & wmask;
874         bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
875 
876         /*
877          * Scan the exponent one window at a time starting from the most
878          * significant bits.
879          */
880         while (bits > 0) {
881             if (bits < stride)
882                 stride = bits;
883             bits -= stride;
884             wvalue = bn_get_bits(p, bits);
885 
886             if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
887                 continue;
888             /* retry once and fall back */
889             if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
890                 continue;
891 
892             bits += stride - 5;
893             wvalue >>= stride - 5;
894             wvalue &= 31;
895             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
896             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
897             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
898             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
899             bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
900             bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
901                                    wvalue);
902         }
903 
904         bn_flip_t4(tmp.d, tmp.d, top);
905         top *= 2;
906         /* back to 32-bit domain */
907         tmp.top = top;
908         bn_correct_top(&tmp);
909         OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
910     } else
911 #endif
912 #if defined(OPENSSL_BN_ASM_MONT5)
913     if (window == 5 && top > 1) {
914         /*
915          * This optimization uses ideas from https://eprint.iacr.org/2011/239,
916          * specifically optimization of cache-timing attack countermeasures,
917          * pre-computation optimization, and Almost Montgomery Multiplication.
918          *
919          * The paper discusses a 4-bit window to optimize 512-bit modular
920          * exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer
921          * important.
922          *
923          * |bn_mul_mont_gather5| and |bn_power5| implement the "almost"
924          * reduction variant, so the values here may not be fully reduced.
925          * They are bounded by R (i.e. they fit in |top| words), not |m|.
926          * Additionally, we pass these "almost" reduced inputs into
927          * |bn_mul_mont|, which implements the normal reduction variant.
928          * Given those inputs, |bn_mul_mont| may not give reduced
929          * output, but it will still produce "almost" reduced output.
930          */
931         void bn_mul_mont_gather5(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         void bn_scatter5(const BN_ULONG *inp, size_t num,
935                          void *table, size_t power);
936         void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
937         void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
938                        const void *table, const BN_ULONG *np,
939                        const BN_ULONG *n0, int num, int power);
940         int bn_get_bits5(const BN_ULONG *ap, int off);
941 
942         BN_ULONG *n0 = mont->n0, *np;
943 
944         /*
945          * BN_to_montgomery can contaminate words above .top [in
946          * BN_DEBUG build...
947          */
948         for (i = am.top; i < top; i++)
949             am.d[i] = 0;
950         for (i = tmp.top; i < top; i++)
951             tmp.d[i] = 0;
952 
953         /*
954          * copy mont->N.d[] to improve cache locality
955          */
956         for (np = am.d + top, i = 0; i < top; i++)
957             np[i] = mont->N.d[i];
958 
959         bn_scatter5(tmp.d, top, powerbuf, 0);
960         bn_scatter5(am.d, am.top, powerbuf, 1);
961         bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
962         bn_scatter5(tmp.d, top, powerbuf, 2);
963 
964 # if 0
965         for (i = 3; i < 32; i++) {
966             /* Calculate a^i = a^(i-1) * a */
967             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
968             bn_scatter5(tmp.d, top, powerbuf, i);
969         }
970 # else
971         /* same as above, but uses squaring for 1/2 of operations */
972         for (i = 4; i < 32; i *= 2) {
973             bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
974             bn_scatter5(tmp.d, top, powerbuf, i);
975         }
976         for (i = 3; i < 8; i += 2) {
977             int j;
978             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
979             bn_scatter5(tmp.d, top, powerbuf, i);
980             for (j = 2 * i; j < 32; j *= 2) {
981                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
982                 bn_scatter5(tmp.d, top, powerbuf, j);
983             }
984         }
985         for (; i < 16; 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             bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
989             bn_scatter5(tmp.d, top, powerbuf, 2 * i);
990         }
991         for (; i < 32; i += 2) {
992             bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
993             bn_scatter5(tmp.d, top, powerbuf, i);
994         }
995 # endif
996         /*
997          * The exponent may not have a whole number of fixed-size windows.
998          * To simplify the main loop, the initial window has between 1 and
999          * full-window-size bits such that what remains is always a whole
1000          * number of windows
1001          */
1002         window0 = (bits - 1) % 5 + 1;
1003         wmask = (1 << window0) - 1;
1004         bits -= window0;
1005         wvalue = bn_get_bits(p, bits) & wmask;
1006         bn_gather5(tmp.d, top, powerbuf, wvalue);
1007 
1008         /*
1009          * Scan the exponent one window at a time starting from the most
1010          * significant bits.
1011          */
1012         if (top & 7) {
1013             while (bits > 0) {
1014                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1015                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1016                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1017                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1018                 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1019                 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1020                                     bn_get_bits5(p->d, bits -= 5));
1021             }
1022         } else {
1023             while (bits > 0) {
1024                 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
1025                           bn_get_bits5(p->d, bits -= 5));
1026             }
1027         }
1028 
1029         tmp.top = top;
1030         /*
1031          * The result is now in |tmp| in Montgomery form, but it may not be
1032          * fully reduced. This is within bounds for |BN_from_montgomery|
1033          * (tmp < R <= m*R) so it will, when converting from Montgomery form,
1034          * produce a fully reduced result.
1035          *
1036          * This differs from Figure 2 of the paper, which uses AMM(h, 1) to
1037          * convert from Montgomery form with unreduced output, followed by an
1038          * extra reduction step. In the paper's terminology, we replace
1039          * steps 9 and 10 with MM(h, 1).
1040          */
1041     } else
1042 #endif
1043     {
1044  fallback:
1045         if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1046             goto err;
1047         if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1048             goto err;
1049 
1050         /*
1051          * If the window size is greater than 1, then calculate
1052          * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1053          * powers could instead be computed as (a^(i/2))^2 to use the slight
1054          * performance advantage of sqr over mul).
1055          */
1056         if (window > 1) {
1057             if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1058                 goto err;
1059             if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1060                                               window))
1061                 goto err;
1062             for (i = 3; i < numPowers; i++) {
1063                 /* Calculate a^i = a^(i-1) * a */
1064                 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1065                     goto err;
1066                 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1067                                                   window))
1068                     goto err;
1069             }
1070         }
1071 
1072         /*
1073          * The exponent may not have a whole number of fixed-size windows.
1074          * To simplify the main loop, the initial window has between 1 and
1075          * full-window-size bits such that what remains is always a whole
1076          * number of windows
1077          */
1078         window0 = (bits - 1) % window + 1;
1079         wmask = (1 << window0) - 1;
1080         bits -= window0;
1081         wvalue = bn_get_bits(p, bits) & wmask;
1082         if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1083                                             window))
1084             goto err;
1085 
1086         wmask = (1 << window) - 1;
1087         /*
1088          * Scan the exponent one window at a time starting from the most
1089          * significant bits.
1090          */
1091         while (bits > 0) {
1092 
1093             /* Square the result window-size times */
1094             for (i = 0; i < window; i++)
1095                 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1096                     goto err;
1097 
1098             /*
1099              * Get a window's worth of bits from the exponent
1100              * This avoids calling BN_is_bit_set for each bit, which
1101              * is not only slower but also makes each bit vulnerable to
1102              * EM (and likely other) side-channel attacks like One&Done
1103              * (for details see "One&Done: A Single-Decryption EM-Based
1104              *  Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1105              *  H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1106              *  M. Prvulovic, in USENIX Security'18)
1107              */
1108             bits -= window;
1109             wvalue = bn_get_bits(p, bits) & wmask;
1110             /*
1111              * Fetch the appropriate pre-computed value from the pre-buf
1112              */
1113             if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1114                                                 window))
1115                 goto err;
1116 
1117             /* Multiply the result into the intermediate result */
1118             if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1119                 goto err;
1120         }
1121     }
1122 
1123     /*
1124      * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1125      * removes padding [if any] and makes return value suitable for public
1126      * API consumer.
1127      */
1128 #if defined(SPARC_T4_MONT)
1129     if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1130         am.d[0] = 1;            /* borrow am */
1131         for (i = 1; i < top; i++)
1132             am.d[i] = 0;
1133         if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1134             goto err;
1135     } else
1136 #endif
1137     if (!bn_from_mont_fixed_top(rr, &tmp, mont, ctx))
1138         goto err;
1139     ret = 1;
1140  err:
1141     if (in_mont == NULL)
1142         BN_MONT_CTX_free(mont);
1143     if (powerbuf != NULL) {
1144         OPENSSL_cleanse(powerbuf, powerbufLen);
1145         OPENSSL_free(powerbufFree);
1146     }
1147     BN_CTX_end(ctx);
1148     return ret;
1149 }
1150 
BN_mod_exp_mont_consttime(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)1151 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
1152                               const BIGNUM *m, BN_CTX *ctx,
1153                               BN_MONT_CTX *in_mont)
1154 {
1155     bn_check_top(a);
1156     bn_check_top(p);
1157     bn_check_top(m);
1158     if (!bn_mod_exp_mont_fixed_top(rr, a, p, m, ctx, in_mont))
1159         return 0;
1160     bn_correct_top(rr);
1161     return 1;
1162 }
1163 
BN_mod_exp_mont_word(BIGNUM * rr,BN_ULONG a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)1164 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1165                          const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1166 {
1167     BN_MONT_CTX *mont = NULL;
1168     int b, bits, ret = 0;
1169     int r_is_one;
1170     BN_ULONG w, next_w;
1171     BIGNUM *r, *t;
1172     BIGNUM *swap_tmp;
1173 #define BN_MOD_MUL_WORD(r, w, m) \
1174                 (BN_mul_word(r, (w)) && \
1175                 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/  \
1176                         (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1177     /*
1178      * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1179      * probably more overhead than always using BN_mod (which uses BN_copy if
1180      * a similar test returns true).
1181      */
1182     /*
1183      * We can use BN_mod and do not need BN_nnmod because our accumulator is
1184      * never negative (the result of BN_mod does not depend on the sign of
1185      * the modulus).
1186      */
1187 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1188                 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1189 
1190     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1191             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1192         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1193         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1194         return 0;
1195     }
1196 
1197     bn_check_top(p);
1198     bn_check_top(m);
1199 
1200     if (!BN_is_odd(m)) {
1201         ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
1202         return 0;
1203     }
1204     if (m->top == 1)
1205         a %= m->d[0];           /* make sure that 'a' is reduced */
1206 
1207     bits = BN_num_bits(p);
1208     if (bits == 0) {
1209         /* x**0 mod 1, or x**0 mod -1 is still zero. */
1210         if (BN_abs_is_word(m, 1)) {
1211             ret = 1;
1212             BN_zero(rr);
1213         } else {
1214             ret = BN_one(rr);
1215         }
1216         return ret;
1217     }
1218     if (a == 0) {
1219         BN_zero(rr);
1220         ret = 1;
1221         return ret;
1222     }
1223 
1224     BN_CTX_start(ctx);
1225     r = BN_CTX_get(ctx);
1226     t = BN_CTX_get(ctx);
1227     if (t == NULL)
1228         goto err;
1229 
1230     if (in_mont != NULL)
1231         mont = in_mont;
1232     else {
1233         if ((mont = BN_MONT_CTX_new()) == NULL)
1234             goto err;
1235         if (!BN_MONT_CTX_set(mont, m, ctx))
1236             goto err;
1237     }
1238 
1239     r_is_one = 1;               /* except for Montgomery factor */
1240 
1241     /* bits-1 >= 0 */
1242 
1243     /* The result is accumulated in the product r*w. */
1244     w = a;                      /* bit 'bits-1' of 'p' is always set */
1245     for (b = bits - 2; b >= 0; b--) {
1246         /* First, square r*w. */
1247         next_w = w * w;
1248         if ((next_w / w) != w) { /* overflow */
1249             if (r_is_one) {
1250                 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1251                     goto err;
1252                 r_is_one = 0;
1253             } else {
1254                 if (!BN_MOD_MUL_WORD(r, w, m))
1255                     goto err;
1256             }
1257             next_w = 1;
1258         }
1259         w = next_w;
1260         if (!r_is_one) {
1261             if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1262                 goto err;
1263         }
1264 
1265         /* Second, multiply r*w by 'a' if exponent bit is set. */
1266         if (BN_is_bit_set(p, b)) {
1267             next_w = w * a;
1268             if ((next_w / a) != w) { /* overflow */
1269                 if (r_is_one) {
1270                     if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1271                         goto err;
1272                     r_is_one = 0;
1273                 } else {
1274                     if (!BN_MOD_MUL_WORD(r, w, m))
1275                         goto err;
1276                 }
1277                 next_w = a;
1278             }
1279             w = next_w;
1280         }
1281     }
1282 
1283     /* Finally, set r:=r*w. */
1284     if (w != 1) {
1285         if (r_is_one) {
1286             if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1287                 goto err;
1288             r_is_one = 0;
1289         } else {
1290             if (!BN_MOD_MUL_WORD(r, w, m))
1291                 goto err;
1292         }
1293     }
1294 
1295     if (r_is_one) {             /* can happen only if a == 1 */
1296         if (!BN_one(rr))
1297             goto err;
1298     } else {
1299         if (!BN_from_montgomery(rr, r, mont, ctx))
1300             goto err;
1301     }
1302     ret = 1;
1303  err:
1304     if (in_mont == NULL)
1305         BN_MONT_CTX_free(mont);
1306     BN_CTX_end(ctx);
1307     bn_check_top(rr);
1308     return ret;
1309 }
1310 
1311 /* The old fallback, simple version :-) */
BN_mod_exp_simple(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)1312 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1313                       const BIGNUM *m, BN_CTX *ctx)
1314 {
1315     int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1316     int start = 1;
1317     BIGNUM *d;
1318     /* Table of variables obtained from 'ctx' */
1319     BIGNUM *val[TABLE_SIZE];
1320 
1321     if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1322             || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1323             || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1324         /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1325         ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1326         return 0;
1327     }
1328 
1329     bits = BN_num_bits(p);
1330     if (bits == 0) {
1331         /* x**0 mod 1, or x**0 mod -1 is still zero. */
1332         if (BN_abs_is_word(m, 1)) {
1333             ret = 1;
1334             BN_zero(r);
1335         } else {
1336             ret = BN_one(r);
1337         }
1338         return ret;
1339     }
1340 
1341     BN_CTX_start(ctx);
1342     d = BN_CTX_get(ctx);
1343     val[0] = BN_CTX_get(ctx);
1344     if (val[0] == NULL)
1345         goto err;
1346 
1347     if (!BN_nnmod(val[0], a, m, ctx))
1348         goto err;               /* 1 */
1349     if (BN_is_zero(val[0])) {
1350         BN_zero(r);
1351         ret = 1;
1352         goto err;
1353     }
1354 
1355     window = BN_window_bits_for_exponent_size(bits);
1356     if (window > 1) {
1357         if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1358             goto err;           /* 2 */
1359         j = 1 << (window - 1);
1360         for (i = 1; i < j; i++) {
1361             if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1362                 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1363                 goto err;
1364         }
1365     }
1366 
1367     start = 1;                  /* This is used to avoid multiplication etc
1368                                  * when there is only the value '1' in the
1369                                  * buffer. */
1370     wvalue = 0;                 /* The 'value' of the window */
1371     wstart = bits - 1;          /* The top bit of the window */
1372     wend = 0;                   /* The bottom bit of the window */
1373 
1374     if (!BN_one(r))
1375         goto err;
1376 
1377     for (;;) {
1378         if (BN_is_bit_set(p, wstart) == 0) {
1379             if (!start)
1380                 if (!BN_mod_mul(r, r, r, m, ctx))
1381                     goto err;
1382             if (wstart == 0)
1383                 break;
1384             wstart--;
1385             continue;
1386         }
1387         /*
1388          * We now have wstart on a 'set' bit, we now need to work out how bit
1389          * a window to do.  To do this we need to scan forward until the last
1390          * set bit before the end of the window
1391          */
1392         wvalue = 1;
1393         wend = 0;
1394         for (i = 1; i < window; i++) {
1395             if (wstart - i < 0)
1396                 break;
1397             if (BN_is_bit_set(p, wstart - i)) {
1398                 wvalue <<= (i - wend);
1399                 wvalue |= 1;
1400                 wend = i;
1401             }
1402         }
1403 
1404         /* wend is the size of the current window */
1405         j = wend + 1;
1406         /* add the 'bytes above' */
1407         if (!start)
1408             for (i = 0; i < j; i++) {
1409                 if (!BN_mod_mul(r, r, r, m, ctx))
1410                     goto err;
1411             }
1412 
1413         /* wvalue will be an odd number < 2^window */
1414         if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1415             goto err;
1416 
1417         /* move the 'window' down further */
1418         wstart -= wend + 1;
1419         wvalue = 0;
1420         start = 0;
1421         if (wstart < 0)
1422             break;
1423     }
1424     ret = 1;
1425  err:
1426     BN_CTX_end(ctx);
1427     bn_check_top(r);
1428     return ret;
1429 }
1430 
1431 /*
1432  * This is a variant of modular exponentiation optimization that does
1433  * parallel 2-primes exponentiation using 256-bit (AVX512VL) AVX512_IFMA ISA
1434  * in 52-bit binary redundant representation.
1435  * If such instructions are not available, or input data size is not supported,
1436  * it falls back to two BN_mod_exp_mont_consttime() calls.
1437  */
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)1438 int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1, const BIGNUM *p1,
1439                                  const BIGNUM *m1, BN_MONT_CTX *in_mont1,
1440                                  BIGNUM *rr2, const BIGNUM *a2, const BIGNUM *p2,
1441                                  const BIGNUM *m2, BN_MONT_CTX *in_mont2,
1442                                  BN_CTX *ctx)
1443 {
1444     int ret = 0;
1445 
1446 #ifdef RSAZ_ENABLED
1447     BN_MONT_CTX *mont1 = NULL;
1448     BN_MONT_CTX *mont2 = NULL;
1449 
1450     if (ossl_rsaz_avx512ifma_eligible() &&
1451         ((a1->top == 16) && (p1->top == 16) && (BN_num_bits(m1) == 1024) &&
1452          (a2->top == 16) && (p2->top == 16) && (BN_num_bits(m2) == 1024))) {
1453 
1454         if (bn_wexpand(rr1, 16) == NULL)
1455             goto err;
1456         if (bn_wexpand(rr2, 16) == NULL)
1457             goto err;
1458 
1459         /*  Ensure that montgomery contexts are initialized */
1460         if (in_mont1 != NULL) {
1461             mont1 = in_mont1;
1462         } else {
1463             if ((mont1 = BN_MONT_CTX_new()) == NULL)
1464                 goto err;
1465             if (!BN_MONT_CTX_set(mont1, m1, ctx))
1466                 goto err;
1467         }
1468         if (in_mont2 != NULL) {
1469             mont2 = in_mont2;
1470         } else {
1471             if ((mont2 = BN_MONT_CTX_new()) == NULL)
1472                 goto err;
1473             if (!BN_MONT_CTX_set(mont2, m2, ctx))
1474                 goto err;
1475         }
1476 
1477         ret = ossl_rsaz_mod_exp_avx512_x2(rr1->d, a1->d, p1->d, m1->d,
1478                                           mont1->RR.d, mont1->n0[0],
1479                                           rr2->d, a2->d, p2->d, m2->d,
1480                                           mont2->RR.d, mont2->n0[0],
1481                                           1024 /* factor bit size */);
1482 
1483         rr1->top = 16;
1484         rr1->neg = 0;
1485         bn_correct_top(rr1);
1486         bn_check_top(rr1);
1487 
1488         rr2->top = 16;
1489         rr2->neg = 0;
1490         bn_correct_top(rr2);
1491         bn_check_top(rr2);
1492 
1493         goto err;
1494     }
1495 #endif
1496 
1497     /* rr1 = a1^p1 mod m1 */
1498     ret = BN_mod_exp_mont_consttime(rr1, a1, p1, m1, ctx, in_mont1);
1499     /* rr2 = a2^p2 mod m2 */
1500     ret &= BN_mod_exp_mont_consttime(rr2, a2, p2, m2, ctx, in_mont2);
1501 
1502 #ifdef RSAZ_ENABLED
1503 err:
1504     if (in_mont2 == NULL)
1505         BN_MONT_CTX_free(mont2);
1506     if (in_mont1 == NULL)
1507         BN_MONT_CTX_free(mont1);
1508 #endif
1509 
1510     return ret;
1511 }
1512