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(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
543 top = b->top; /* this works because 'buf' is explicitly zeroed */
544 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
546 buf[j] = ((unsigned char*)b->d)[i];
552 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
556 if (bn_wexpand(b, top) == NULL)
559 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
561 ((unsigned char*)b->d)[i] = buf[j];
569 /* Given a pointer value, compute the next address that is a cache line multiple. */
570 #define MOD_EXP_CTIME_ALIGN(x_) \
571 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
573 /* This variant of BN_mod_exp_mont() uses fixed windows and the special
574 * precomputation memory layout to limit data-dependency to a minimum
575 * to protect secret exponents (cf. the hyper-threading timing attacks
576 * pointed out by Colin Percival,
577 * http://www.daemonology.net/hyperthreading-considered-harmful/)
579 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
580 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
582 int i,bits,ret=0,window,wvalue;
584 BN_MONT_CTX *mont=NULL;
587 unsigned char *powerbufFree=NULL;
589 unsigned char *powerbuf=NULL;
600 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
612 /* Allocate a montgomery context if it was not supplied by the caller.
613 * If this is not done, things will break in the montgomery part.
619 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
620 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
623 /* Get the window size to use with size of p. */
624 window = BN_window_bits_for_ctime_exponent_size(bits);
625 #if defined(OPENSSL_BN_ASM_MONT5)
626 if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */
629 /* Allocate a buffer large enough to hold all of the pre-computed
630 * powers of am, am itself and tmp.
632 numPowers = 1 << window;
633 powerbufLen = sizeof(m->d[0])*(top*numPowers +
634 ((2*top)>numPowers?(2*top):numPowers));
636 if (powerbufLen < 3072)
637 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
640 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
643 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
644 memset(powerbuf, 0, powerbufLen);
647 if (powerbufLen < 3072)
651 /* lay down tmp and am right after powers table */
652 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
654 tmp.top = am.top = 0;
655 tmp.dmax = am.dmax = top;
656 tmp.neg = am.neg = 0;
657 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
659 /* prepare a^0 in Montgomery domain */
661 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
663 tmp.d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */
665 tmp.d[i] = (~m->d[i])&BN_MASK2;
669 /* prepare a^1 in Montgomery domain */
670 if (a->neg || BN_ucmp(a,m) >= 0)
672 if (!BN_mod(&am,a,m,ctx)) goto err;
673 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
675 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
677 #if defined(OPENSSL_BN_ASM_MONT5)
678 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
679 * specifically optimization of cache-timing attack countermeasures
680 * and pre-computation optimization. */
682 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
683 * 512-bit RSA is hardly relevant, we omit it to spare size... */
686 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
687 const void *table,const BN_ULONG *np,
688 const BN_ULONG *n0,int num,int power);
689 void bn_scatter5(const BN_ULONG *inp,size_t num,
690 void *table,size_t power);
691 void bn_gather5(BN_ULONG *out,size_t num,
692 void *table,size_t power);
694 BN_ULONG *np=mont->N.d, *n0=mont->n0;
696 /* BN_to_montgomery can contaminate words above .top
697 * [in BN_DEBUG[_DEBUG] build]... */
698 for (i=am.top; i<top; i++) am.d[i]=0;
699 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
701 bn_scatter5(tmp.d,top,powerbuf,0);
702 bn_scatter5(am.d,am.top,powerbuf,1);
703 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
704 bn_scatter5(tmp.d,top,powerbuf,2);
709 /* Calculate a^i = a^(i-1) * a */
710 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
711 bn_scatter5(tmp.d,top,powerbuf,i);
714 /* same as above, but uses squaring for 1/2 of operations */
715 for (i=4; i<32; i*=2)
717 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
718 bn_scatter5(tmp.d,top,powerbuf,i);
723 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
724 bn_scatter5(tmp.d,top,powerbuf,i);
725 for (j=2*i; j<32; j*=2)
727 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
728 bn_scatter5(tmp.d,top,powerbuf,j);
733 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
734 bn_scatter5(tmp.d,top,powerbuf,i);
735 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
736 bn_scatter5(tmp.d,top,powerbuf,2*i);
740 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
741 bn_scatter5(tmp.d,top,powerbuf,i);
745 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
746 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
747 bn_gather5(tmp.d,top,powerbuf,wvalue);
749 /* Scan the exponent one window at a time starting from the most
754 for (wvalue=0, i=0; i<5; i++,bits--)
755 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
757 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
758 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
759 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
760 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
761 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
762 bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
766 bn_correct_top(&tmp);
771 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
772 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
774 /* If the window size is greater than 1, then calculate
775 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
776 * (even powers could instead be computed as (a^(i/2))^2
777 * to use the slight performance advantage of sqr over mul).
781 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
782 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
783 for (i=3; i<numPowers; i++)
785 /* Calculate a^i = a^(i-1) * a */
786 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
788 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
793 for (wvalue=0, i=bits%window; i>=0; i--,bits--)
794 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
795 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
797 /* 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(&tmp,&tmp,&tmp,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(&am, top, powerbuf, wvalue, numPowers)) goto err;
814 /* Multiply the result into the intermediate result */
815 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
819 /* Convert the final result from montgomery to standard format */
820 if (!BN_from_montgomery(rr,&tmp,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);
833 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
834 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
836 BN_MONT_CTX *mont = NULL;
842 #define BN_MOD_MUL_WORD(r, w, m) \
843 (BN_mul_word(r, (w)) && \
844 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
845 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
846 /* BN_MOD_MUL_WORD is only used with 'w' large,
847 * so the BN_ucmp test is probably more overhead
848 * than always using BN_mod (which uses BN_copy if
849 * a similar test returns true). */
850 /* We can use BN_mod and do not need BN_nnmod because our
851 * accumulator is never negative (the result of BN_mod does
852 * not depend on the sign of the modulus).
854 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
855 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
857 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
859 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
860 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
869 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
873 a %= m->d[0]; /* make sure that 'a' is reduced */
875 bits = BN_num_bits(p);
892 if (d == NULL || r == NULL || t == NULL) goto err;
898 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
899 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
902 r_is_one = 1; /* except for Montgomery factor */
906 /* The result is accumulated in the product r*w. */
907 w = a; /* bit 'bits-1' of 'p' is always set */
908 for (b = bits-2; b >= 0; b--)
910 /* First, square r*w. */
912 if ((next_w/w) != w) /* overflow */
916 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
921 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
928 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
931 /* Second, multiply r*w by 'a' if exponent bit is set. */
932 if (BN_is_bit_set(p, b))
935 if ((next_w/a) != w) /* overflow */
939 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
944 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
952 /* Finally, set r:=r*w. */
957 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
962 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
966 if (r_is_one) /* can happen only if a == 1*/
968 if (!BN_one(rr)) goto err;
972 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
976 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
983 /* The old fallback, simple version :-) */
984 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
985 const BIGNUM *m, BN_CTX *ctx)
987 int i,j,bits,ret=0,wstart,wend,window,wvalue;
990 /* Table of variables obtained from 'ctx' */
991 BIGNUM *val[TABLE_SIZE];
993 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
995 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
996 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1000 bits=BN_num_bits(p);
1009 d = BN_CTX_get(ctx);
1010 val[0] = BN_CTX_get(ctx);
1011 if(!d || !val[0]) goto err;
1013 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
1014 if (BN_is_zero(val[0]))
1021 window = BN_window_bits_for_exponent_size(bits);
1024 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
1029 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
1030 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
1035 start=1; /* This is used to avoid multiplication etc
1036 * when there is only the value '1' in the
1038 wvalue=0; /* The 'value' of the window */
1039 wstart=bits-1; /* The top bit of the window */
1040 wend=0; /* The bottom bit of the window */
1042 if (!BN_one(r)) goto err;
1046 if (BN_is_bit_set(p,wstart) == 0)
1049 if (!BN_mod_mul(r,r,r,m,ctx))
1051 if (wstart == 0) break;
1055 /* We now have wstart on a 'set' bit, we now need to work out
1056 * how bit a window to do. To do this we need to scan
1057 * forward until the last set bit before the end of the
1062 for (i=1; i<window; i++)
1064 if (wstart-i < 0) break;
1065 if (BN_is_bit_set(p,wstart-i))
1073 /* wend is the size of the current window */
1075 /* add the 'bytes above' */
1079 if (!BN_mod_mul(r,r,r,m,ctx))
1083 /* wvalue will be an odd number < 2^window */
1084 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
1087 /* move the 'window' down further */
1091 if (wstart < 0) break;