1 /* crypto/bn/bn_exp.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
58 /* ====================================================================
59 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
112 #define OPENSSL_FIPSAPI
114 #include "cryptlib.h"
121 # define alloca _alloca
123 #elif defined(__GNUC__)
125 # define alloca(s) __builtin_alloca((s))
129 /* maximum precomputation table size for *variable* sliding windows */
130 #define TABLE_SIZE 32
132 /* this one works - simple but works */
133 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
138 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
140 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
141 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
146 if ((r == a) || (r == p))
147 rr = BN_CTX_get(ctx);
151 if (rr == NULL || v == NULL) goto err;
153 if (BN_copy(v,a) == NULL) goto err;
157 { if (BN_copy(rr,a) == NULL) goto err; }
158 else { if (!BN_one(rr)) goto err; }
160 for (i=1; i<bits; i++)
162 if (!BN_sqr(v,v,ctx)) goto err;
163 if (BN_is_bit_set(p,i))
165 if (!BN_mul(rr,rr,v,ctx)) goto err;
170 if (r != rr) BN_copy(r,rr);
177 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
186 /* For even modulus m = 2^k*m_odd, it might make sense to compute
187 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
188 * exponentiation for the odd part), using appropriate exponent
189 * reductions, and combine the results using the CRT.
191 * For now, we use Montgomery only if the modulus is odd; otherwise,
192 * exponentiation using the reciprocal-based quick remaindering
195 * (Timing obtained with expspeed.c [computations a^p mod m
196 * where a, p, m are of the same length: 256, 512, 1024, 2048,
197 * 4096, 8192 bits], compared to the running time of the
198 * standard algorithm:
200 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
201 * 55 .. 77 % [UltraSparc processor, but
202 * debug-solaris-sparcv8-gcc conf.]
204 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
205 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
207 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
208 * at 2048 and more bits, but at 512 and 1024 bits, it was
209 * slower even than the standard algorithm!
211 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
212 * should be obtained when the new Montgomery reduction code
213 * has been integrated into OpenSSL.)
217 #define MONT_EXP_WORD
221 /* I have finally been able to take out this pre-condition of
222 * the top bit being set. It was caused by an error in BN_div
223 * with negatives. There was also another problem when for a^b%m
224 * a >= m. eay 07-May-97 */
225 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
229 # ifdef MONT_EXP_WORD
230 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
232 BN_ULONG A = a->d[0];
233 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
237 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
242 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
244 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
252 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
253 const BIGNUM *m, BN_CTX *ctx)
255 int i,j,bits,ret=0,wstart,wend,window,wvalue;
258 /* Table of variables obtained from 'ctx' */
259 BIGNUM *val[TABLE_SIZE];
262 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
264 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
265 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
278 aa = BN_CTX_get(ctx);
279 val[0] = BN_CTX_get(ctx);
280 if(!aa || !val[0]) goto err;
282 BN_RECP_CTX_init(&recp);
285 /* ignore sign of 'm' */
286 if (!BN_copy(aa, m)) goto err;
288 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
292 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
295 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
296 if (BN_is_zero(val[0]))
303 window = BN_window_bits_for_exponent_size(bits);
306 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
311 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
312 !BN_mod_mul_reciprocal(val[i],val[i-1],
318 start=1; /* This is used to avoid multiplication etc
319 * when there is only the value '1' in the
321 wvalue=0; /* The 'value' of the window */
322 wstart=bits-1; /* The top bit of the window */
323 wend=0; /* The bottom bit of the window */
325 if (!BN_one(r)) goto err;
329 if (BN_is_bit_set(p,wstart) == 0)
332 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
334 if (wstart == 0) break;
338 /* We now have wstart on a 'set' bit, we now need to work out
339 * how bit a window to do. To do this we need to scan
340 * forward until the last set bit before the end of the
345 for (i=1; i<window; i++)
347 if (wstart-i < 0) break;
348 if (BN_is_bit_set(p,wstart-i))
356 /* wend is the size of the current window */
358 /* add the 'bytes above' */
362 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
366 /* wvalue will be an odd number < 2^window */
367 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
370 /* move the 'window' down further */
374 if (wstart < 0) break;
379 BN_RECP_CTX_free(&recp);
385 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
386 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
388 int i,j,bits,ret=0,wstart,wend,window,wvalue;
392 /* Table of variables obtained from 'ctx' */
393 BIGNUM *val[TABLE_SIZE];
394 BN_MONT_CTX *mont=NULL;
396 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
398 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
407 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
420 val[0] = BN_CTX_get(ctx);
421 if (!d || !r || !val[0]) goto err;
423 /* If this is not done, things will break in the montgomery
430 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
431 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
434 if (a->neg || BN_ucmp(a,m) >= 0)
436 if (!BN_nnmod(val[0],a,m,ctx))
448 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
450 window = BN_window_bits_for_exponent_size(bits);
453 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
457 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
458 !BN_mod_mul_montgomery(val[i],val[i-1],
464 start=1; /* This is used to avoid multiplication etc
465 * when there is only the value '1' in the
467 wvalue=0; /* The 'value' of the window */
468 wstart=bits-1; /* The top bit of the window */
469 wend=0; /* The bottom bit of the window */
471 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
474 if (BN_is_bit_set(p,wstart) == 0)
478 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
481 if (wstart == 0) break;
485 /* We now have wstart on a 'set' bit, we now need to work out
486 * how bit a window to do. To do this we need to scan
487 * forward until the last set bit before the end of the
492 for (i=1; i<window; i++)
494 if (wstart-i < 0) break;
495 if (BN_is_bit_set(p,wstart-i))
503 /* wend is the size of the current window */
505 /* add the 'bytes above' */
509 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
513 /* wvalue will be an odd number < 2^window */
514 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
517 /* move the 'window' down further */
521 if (wstart < 0) break;
523 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
526 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
533 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
534 * so that accessing any of these table values shows the same access pattern as far
535 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
536 * from/to that table. */
538 static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
542 if (bn_wexpand(b, top) == NULL)
549 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
551 buf[j] = ((unsigned char*)b->d)[i];
558 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
562 if (bn_wexpand(b, top) == NULL)
565 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
567 ((unsigned char*)b->d)[i] = buf[j];
575 /* Given a pointer value, compute the next address that is a cache line multiple. */
576 #define MOD_EXP_CTIME_ALIGN(x_) \
577 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
579 /* This variant of BN_mod_exp_mont() uses fixed windows and the special
580 * precomputation memory layout to limit data-dependency to a minimum
581 * to protect secret exponents (cf. the hyper-threading timing attacks
582 * pointed out by Colin Percival,
583 * http://www.daemonology.net/hyperthreading-considered-harmful/)
585 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
586 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
588 int i,bits,ret=0,window,wvalue;
591 BN_MONT_CTX *mont=NULL;
594 unsigned char *powerbufFree=NULL;
596 unsigned char *powerbuf=NULL;
597 BIGNUM computeTemp, *am=NULL;
607 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
617 /* Initialize BIGNUM context and allocate intermediate result */
620 if (r == NULL) goto err;
622 /* Allocate a montgomery context if it was not supplied by the caller.
623 * If this is not done, things will break in the montgomery part.
629 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
630 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
633 /* Get the window size to use with size of p. */
634 window = BN_window_bits_for_ctime_exponent_size(bits);
635 #if defined(OPENSSL_BN_ASM_MONT5)
636 if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */
638 /* Adjust the number of bits up to a multiple of the window size.
639 * If the exponent length is not a multiple of the window size, then
640 * this pads the most significant bits with zeros to normalize the
641 * scanning loop to there's no special cases.
643 * * NOTE: Making the window size a power of two less than the native
644 * * word size ensures that the padded bits won't go past the last
645 * * word in the internal BIGNUM structure. Going past the end will
646 * * still produce the correct result, but causes a different branch
647 * * to be taken in the BN_is_bit_set function.
649 bits = ((bits+window-1)/window)*window;
651 /* Allocate a buffer large enough to hold all of the pre-computed
652 * powers of a, plus computeTemp.
654 numPowers = 1 << window;
655 powerbufLen = sizeof(m->d[0])*(top*numPowers +
656 (top>numPowers?top:numPowers));
657 if (powerbufLen < 3072)
658 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
659 else if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
662 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
663 memset(powerbuf, 0, powerbufLen);
665 if (powerbufLen < 3072)
668 computeTemp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
669 computeTemp.top = computeTemp.dmax = top;
671 computeTemp.flags = BN_FLG_STATIC_DATA;
673 /* Initialize the intermediate result. Do this early to save double conversion,
674 * once each for a^0 and intermediate result.
676 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
678 /* Initialize computeTemp as a^1 with montgomery precalcs */
679 am = BN_CTX_get(ctx);
680 if (am==NULL) goto err;
682 if (a->neg || BN_ucmp(a,m) >= 0)
684 if (!BN_mod(am,a,m,ctx)) goto err;
685 if (!BN_to_montgomery(am,am,mont,ctx)) goto err;
687 else if (!BN_to_montgomery(am,a,mont,ctx)) goto err;
689 if (!BN_copy(&computeTemp, am)) goto err;
691 if (bn_wexpand(am,top)==NULL || bn_wexpand(r,top)==NULL)
694 #if defined(OPENSSL_BN_ASM_MONT5)
695 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
696 * specifically optimization of cache-timing attack countermeasures
697 * and pre-computation optimization. */
699 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
700 * 512-bit RSA is hardly relevant, we omit it to spare size... */
703 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
704 const void *table,const BN_ULONG *np,
705 const BN_ULONG *n0,int num,int power);
706 void bn_scatter5(const BN_ULONG *inp,size_t num,
707 void *table,size_t power);
709 BN_ULONG *acc, *np=mont->N.d, *n0=mont->n0;
711 bn_scatter5(r->d,r->top,powerbuf,0);
712 bn_scatter5(am->d,am->top,powerbuf,1);
718 bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
719 bn_scatter5(acc,top,powerbuf,i);
722 /* same as above, but uses squaring for 1/2 of operations */
723 for (i=2; i<32; i*=2)
725 bn_mul_mont(acc,acc,acc,np,n0,top);
726 bn_scatter5(acc,top,powerbuf,i);
731 bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
732 bn_scatter5(acc,top,powerbuf,i);
733 for (j=2*i; j<32; j*=2)
735 bn_mul_mont(acc,acc,acc,np,n0,top);
736 bn_scatter5(acc,top,powerbuf,j);
741 bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
742 bn_scatter5(acc,top,powerbuf,i);
743 bn_mul_mont(acc,acc,acc,np,n0,top);
744 bn_scatter5(acc,top,powerbuf,2*i);
748 bn_mul_mont_gather5(acc,am->d,powerbuf,np,n0,top,i-1);
749 bn_scatter5(acc,top,powerbuf,i);
754 /* Scan the exponent one window at a time starting from the most
760 for (wvalue=0, i=0; i<5; i++,bits--)
761 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
763 bn_mul_mont(acc,acc,acc,np,n0,top);
764 bn_mul_mont(acc,acc,acc,np,n0,top);
765 bn_mul_mont(acc,acc,acc,np,n0,top);
766 bn_mul_mont(acc,acc,acc,np,n0,top);
767 bn_mul_mont(acc,acc,acc,np,n0,top);
768 bn_mul_mont_gather5(acc,acc,powerbuf,np,n0,top,wvalue);
777 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err;
778 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err;
780 /* If the window size is greater than 1, then calculate
781 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
782 * (even powers could instead be computed as (a^(i/2))^2
783 * to use the slight performance advantage of sqr over mul).
787 for (i=2; i<numPowers; i++)
789 /* Calculate a^i = a^(i-1) * a */
790 if (!BN_mod_mul_montgomery(&computeTemp,am,&computeTemp,mont,ctx))
792 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&computeTemp, top, powerbuf, i, numPowers)) goto err;
796 /* Scan the exponent one window at a time starting from the most
802 wvalue=0; /* The 'value' of the window */
804 /* Scan the window, squaring the result as we go */
805 for (i=0; i<window; i++,bits--)
807 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) goto err;
808 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
811 /* Fetch the appropriate pre-computed value from the pre-buf */
812 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&computeTemp, top, powerbuf, wvalue, numPowers)) goto err;
814 /* Multiply the result into the intermediate result */
815 if (!BN_mod_mul_montgomery(r,r,&computeTemp,mont,ctx)) goto err;
819 /* Convert the final result from montgomery to standard format */
820 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
823 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
826 OPENSSL_cleanse(powerbuf,powerbufLen);
827 if (powerbufFree) OPENSSL_free(powerbufFree);
829 if (am!=NULL) BN_clear(am);
834 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
835 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
837 BN_MONT_CTX *mont = NULL;
843 #define BN_MOD_MUL_WORD(r, w, m) \
844 (BN_mul_word(r, (w)) && \
845 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
846 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
847 /* BN_MOD_MUL_WORD is only used with 'w' large,
848 * so the BN_ucmp test is probably more overhead
849 * than always using BN_mod (which uses BN_copy if
850 * a similar test returns true). */
851 /* We can use BN_mod and do not need BN_nnmod because our
852 * accumulator is never negative (the result of BN_mod does
853 * not depend on the sign of the modulus).
855 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
856 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
858 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
860 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
861 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
870 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
874 a %= m->d[0]; /* make sure that 'a' is reduced */
876 bits = BN_num_bits(p);
893 if (d == NULL || r == NULL || t == NULL) goto err;
899 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
900 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
903 r_is_one = 1; /* except for Montgomery factor */
907 /* The result is accumulated in the product r*w. */
908 w = a; /* bit 'bits-1' of 'p' is always set */
909 for (b = bits-2; b >= 0; b--)
911 /* First, square r*w. */
913 if ((next_w/w) != w) /* overflow */
917 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
922 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
929 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
932 /* Second, multiply r*w by 'a' if exponent bit is set. */
933 if (BN_is_bit_set(p, b))
936 if ((next_w/a) != w) /* overflow */
940 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
945 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
953 /* Finally, set r:=r*w. */
958 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
963 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
967 if (r_is_one) /* can happen only if a == 1*/
969 if (!BN_one(rr)) goto err;
973 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
977 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
984 /* The old fallback, simple version :-) */
985 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
986 const BIGNUM *m, BN_CTX *ctx)
988 int i,j,bits,ret=0,wstart,wend,window,wvalue;
991 /* Table of variables obtained from 'ctx' */
992 BIGNUM *val[TABLE_SIZE];
994 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
996 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
997 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1001 bits=BN_num_bits(p);
1010 d = BN_CTX_get(ctx);
1011 val[0] = BN_CTX_get(ctx);
1012 if(!d || !val[0]) goto err;
1014 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
1015 if (BN_is_zero(val[0]))
1022 window = BN_window_bits_for_exponent_size(bits);
1025 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
1030 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
1031 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
1036 start=1; /* This is used to avoid multiplication etc
1037 * when there is only the value '1' in the
1039 wvalue=0; /* The 'value' of the window */
1040 wstart=bits-1; /* The top bit of the window */
1041 wend=0; /* The bottom bit of the window */
1043 if (!BN_one(r)) goto err;
1047 if (BN_is_bit_set(p,wstart) == 0)
1050 if (!BN_mod_mul(r,r,r,m,ctx))
1052 if (wstart == 0) break;
1056 /* We now have wstart on a 'set' bit, we now need to work out
1057 * how bit a window to do. To do this we need to scan
1058 * forward until the last set bit before the end of the
1063 for (i=1; i<window; i++)
1065 if (wstart-i < 0) break;
1066 if (BN_is_bit_set(p,wstart-i))
1074 /* wend is the size of the current window */
1076 /* add the 'bytes above' */
1080 if (!BN_mod_mul(r,r,r,m,ctx))
1084 /* wvalue will be an odd number < 2^window */
1085 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
1088 /* move the 'window' down further */
1092 if (wstart < 0) break;