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 #if defined(OPENSSL_BN_ASM_MONT) && defined(__sparc__)
130 # include "sparc_arch.h"
131 extern unsigned int OPENSSL_sparcv9cap_P[];
134 /* maximum precomputation table size for *variable* sliding windows */
135 #define TABLE_SIZE 32
137 /* this one works - simple but works */
138 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
143 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
145 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
146 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
151 if ((r == a) || (r == p))
152 rr = BN_CTX_get(ctx);
156 if (rr == NULL || v == NULL) goto err;
158 if (BN_copy(v,a) == NULL) goto err;
162 { if (BN_copy(rr,a) == NULL) goto err; }
163 else { if (!BN_one(rr)) goto err; }
165 for (i=1; i<bits; i++)
167 if (!BN_sqr(v,v,ctx)) goto err;
168 if (BN_is_bit_set(p,i))
170 if (!BN_mul(rr,rr,v,ctx)) goto err;
175 if (r != rr) BN_copy(r,rr);
182 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
191 /* For even modulus m = 2^k*m_odd, it might make sense to compute
192 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
193 * exponentiation for the odd part), using appropriate exponent
194 * reductions, and combine the results using the CRT.
196 * For now, we use Montgomery only if the modulus is odd; otherwise,
197 * exponentiation using the reciprocal-based quick remaindering
200 * (Timing obtained with expspeed.c [computations a^p mod m
201 * where a, p, m are of the same length: 256, 512, 1024, 2048,
202 * 4096, 8192 bits], compared to the running time of the
203 * standard algorithm:
205 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
206 * 55 .. 77 % [UltraSparc processor, but
207 * debug-solaris-sparcv8-gcc conf.]
209 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
210 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
212 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
213 * at 2048 and more bits, but at 512 and 1024 bits, it was
214 * slower even than the standard algorithm!
216 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
217 * should be obtained when the new Montgomery reduction code
218 * has been integrated into OpenSSL.)
222 #define MONT_EXP_WORD
226 /* I have finally been able to take out this pre-condition of
227 * the top bit being set. It was caused by an error in BN_div
228 * with negatives. There was also another problem when for a^b%m
229 * a >= m. eay 07-May-97 */
230 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
234 # ifdef MONT_EXP_WORD
235 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
237 BN_ULONG A = a->d[0];
238 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
242 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
247 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
249 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
257 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
258 const BIGNUM *m, BN_CTX *ctx)
260 int i,j,bits,ret=0,wstart,wend,window,wvalue;
263 /* Table of variables obtained from 'ctx' */
264 BIGNUM *val[TABLE_SIZE];
267 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
269 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
270 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
283 aa = BN_CTX_get(ctx);
284 val[0] = BN_CTX_get(ctx);
285 if(!aa || !val[0]) goto err;
287 BN_RECP_CTX_init(&recp);
290 /* ignore sign of 'm' */
291 if (!BN_copy(aa, m)) goto err;
293 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
297 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
300 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
301 if (BN_is_zero(val[0]))
308 window = BN_window_bits_for_exponent_size(bits);
311 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
316 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
317 !BN_mod_mul_reciprocal(val[i],val[i-1],
323 start=1; /* This is used to avoid multiplication etc
324 * when there is only the value '1' in the
326 wvalue=0; /* The 'value' of the window */
327 wstart=bits-1; /* The top bit of the window */
328 wend=0; /* The bottom bit of the window */
330 if (!BN_one(r)) goto err;
334 if (BN_is_bit_set(p,wstart) == 0)
337 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
339 if (wstart == 0) break;
343 /* We now have wstart on a 'set' bit, we now need to work out
344 * how bit a window to do. To do this we need to scan
345 * forward until the last set bit before the end of the
350 for (i=1; i<window; i++)
352 if (wstart-i < 0) break;
353 if (BN_is_bit_set(p,wstart-i))
361 /* wend is the size of the current window */
363 /* add the 'bytes above' */
367 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
371 /* wvalue will be an odd number < 2^window */
372 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
375 /* move the 'window' down further */
379 if (wstart < 0) break;
384 BN_RECP_CTX_free(&recp);
390 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
391 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
393 int i,j,bits,ret=0,wstart,wend,window,wvalue;
397 /* Table of variables obtained from 'ctx' */
398 BIGNUM *val[TABLE_SIZE];
399 BN_MONT_CTX *mont=NULL;
401 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
403 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
412 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
425 val[0] = BN_CTX_get(ctx);
426 if (!d || !r || !val[0]) goto err;
428 /* If this is not done, things will break in the montgomery
435 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
436 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
439 if (a->neg || BN_ucmp(a,m) >= 0)
441 if (!BN_nnmod(val[0],a,m,ctx))
453 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
455 window = BN_window_bits_for_exponent_size(bits);
458 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
462 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
463 !BN_mod_mul_montgomery(val[i],val[i-1],
469 start=1; /* This is used to avoid multiplication etc
470 * when there is only the value '1' in the
472 wvalue=0; /* The 'value' of the window */
473 wstart=bits-1; /* The top bit of the window */
474 wend=0; /* The bottom bit of the window */
476 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
479 if (BN_is_bit_set(p,wstart) == 0)
483 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
486 if (wstart == 0) break;
490 /* We now have wstart on a 'set' bit, we now need to work out
491 * how bit a window to do. To do this we need to scan
492 * forward until the last set bit before the end of the
497 for (i=1; i<window; i++)
499 if (wstart-i < 0) break;
500 if (BN_is_bit_set(p,wstart-i))
508 /* wend is the size of the current window */
510 /* add the 'bytes above' */
514 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
518 /* wvalue will be an odd number < 2^window */
519 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
522 /* move the 'window' down further */
526 if (wstart < 0) break;
528 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
531 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
538 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
539 * so that accessing any of these table values shows the same access pattern as far
540 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
541 * from/to that table. */
543 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
548 top = b->top; /* this works because 'buf' is explicitly zeroed */
549 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
551 buf[j] = ((unsigned char*)b->d)[i];
557 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
561 if (bn_wexpand(b, top) == NULL)
564 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
566 ((unsigned char*)b->d)[i] = buf[j];
574 /* Given a pointer value, compute the next address that is a cache line multiple. */
575 #define MOD_EXP_CTIME_ALIGN(x_) \
576 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
578 /* This variant of BN_mod_exp_mont() uses fixed windows and the special
579 * precomputation memory layout to limit data-dependency to a minimum
580 * to protect secret exponents (cf. the hyper-threading timing attacks
581 * pointed out by Colin Percival,
582 * http://www.daemonology.net/hyperthreading-considered-harmful/)
584 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
585 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
587 int i,bits,ret=0,window,wvalue;
589 BN_MONT_CTX *mont=NULL;
592 unsigned char *powerbufFree=NULL;
594 unsigned char *powerbuf=NULL;
596 #if defined(OPENSSL_BN_ASM_MONT) && defined(__sparc__)
608 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
620 /* Allocate a montgomery context if it was not supplied by the caller.
621 * If this is not done, things will break in the montgomery part.
627 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
628 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
631 /* Get the window size to use with size of p. */
632 window = BN_window_bits_for_ctime_exponent_size(bits);
633 #if defined(OPENSSL_BN_ASM_MONT) && defined(__sparc__)
634 if (window>=5 && (top&15)==0 && top<=64 &&
635 (OPENSSL_sparcv9cap_P[1]&(CFR_MONTMUL|CFR_MONTSQR))==
636 (CFR_MONTMUL|CFR_MONTSQR) &&
637 (t4=OPENSSL_sparcv9cap_P[0]))
641 #if defined(OPENSSL_BN_ASM_MONT5)
642 if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */
646 /* Allocate a buffer large enough to hold all of the pre-computed
647 * powers of am, am itself and tmp.
649 numPowers = 1 << window;
650 powerbufLen = sizeof(m->d[0])*(top*numPowers +
651 ((2*top)>numPowers?(2*top):numPowers));
653 if (powerbufLen < 3072)
654 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
657 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
660 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
661 memset(powerbuf, 0, powerbufLen);
664 if (powerbufLen < 3072)
668 /* lay down tmp and am right after powers table */
669 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
671 tmp.top = am.top = 0;
672 tmp.dmax = am.dmax = top;
673 tmp.neg = am.neg = 0;
674 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
676 /* prepare a^0 in Montgomery domain */
678 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
680 tmp.d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */
682 tmp.d[i] = (~m->d[i])&BN_MASK2;
686 /* prepare a^1 in Montgomery domain */
687 if (a->neg || BN_ucmp(a,m) >= 0)
689 if (!BN_mod(&am,a,m,ctx)) goto err;
690 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
692 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
694 #if defined(OPENSSL_BN_ASM_MONT) && defined(__sparc__)
697 typedef int (*bn_pwr5_mont_f)(BN_ULONG *tp,const BN_ULONG *np,
698 const BN_ULONG *n0,const void *table,int power);
699 int bn_pwr5_mont_t4_8(BN_ULONG *tp,const BN_ULONG *np,
700 const BN_ULONG *n0,const void *table,int power);
701 int bn_pwr5_mont_t4_16(BN_ULONG *tp,const BN_ULONG *np,
702 const BN_ULONG *n0,const void *table,int power);
703 int bn_pwr5_mont_t4_24(BN_ULONG *tp,const BN_ULONG *np,
704 const BN_ULONG *n0,const void *table,int power);
705 int bn_pwr5_mont_t4_32(BN_ULONG *tp,const BN_ULONG *np,
706 const BN_ULONG *n0,const void *table,int power);
707 static const bn_pwr5_mont_f funcs[4] = {
708 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
709 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 };
710 bn_pwr5_mont_f worker = funcs[top/16-1];
712 void bn_mul_mont_t4(BN_ULONG *rp,const BN_ULONG *ap,
713 const void *bp,const BN_ULONG *np,
714 const BN_ULONG *n0,int num);
715 void bn_mul_mont_gather5_t4(BN_ULONG *rp,const BN_ULONG *ap,
716 const void *table,const BN_ULONG *np,
717 const BN_ULONG *n0,int num,int power);
718 void bn_scatter5_t4(const BN_ULONG *inp,size_t num,
719 void *table,size_t power);
720 void bn_gather5_t4(BN_ULONG *out,size_t num,
721 void *table,size_t power);
722 void bn_flip_t4(BN_ULONG *dst,BN_ULONG *src,size_t num);
724 BN_ULONG *np=alloca(top*sizeof(BN_ULONG)), *n0=mont->n0;
726 /* BN_to_montgomery can contaminate words above .top
727 * [in BN_DEBUG[_DEBUG] build]... */
728 for (i=am.top; i<top; i++) am.d[i]=0;
729 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
731 /* switch to 64-bit domain */
733 bn_flip_t4(np,mont->N.d,top);
734 bn_flip_t4(tmp.d,tmp.d,top);
735 bn_flip_t4(am.d,am.d,top);
737 bn_scatter5_t4(tmp.d,top,powerbuf,0);
738 bn_scatter5_t4(am.d,top,powerbuf,1);
739 bn_mul_mont_t4(tmp.d,am.d,am.d,np,n0,top);
740 bn_scatter5_t4(tmp.d,top,powerbuf,2);
744 /* Calculate a^i = a^(i-1) * a */
745 bn_mul_mont_gather5_t4(tmp.d,am.d,powerbuf,np,n0,top,i-1);
746 bn_scatter5_t4(tmp.d,top,powerbuf,i);
750 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
751 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
752 bn_gather5_t4(tmp.d,top,powerbuf,wvalue);
754 /* Scan the exponent one window at a time starting from the most
759 for (wvalue=0, i=0; i<5; i++,bits--)
760 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
762 if ((*worker)(tmp.d,np,n0,powerbuf,wvalue)) continue;
763 /* retry once and fall back */
764 if ((*worker)(tmp.d,np,n0,powerbuf,wvalue)) continue;
765 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
766 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
767 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
768 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
769 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
770 bn_mul_mont_gather5_t4(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
773 bn_flip_t4(tmp.d,tmp.d,top);
775 /* back to 32-bit domain */
777 bn_correct_top(&tmp);
778 OPENSSL_cleanse(np,top*sizeof(BN_ULONG));
782 #if defined(OPENSSL_BN_ASM_MONT5)
783 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
784 * specifically optimization of cache-timing attack countermeasures
785 * and pre-computation optimization. */
787 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
788 * 512-bit RSA is hardly relevant, we omit it to spare size... */
791 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
792 const void *table,const BN_ULONG *np,
793 const BN_ULONG *n0,int num,int power);
794 void bn_scatter5(const BN_ULONG *inp,size_t num,
795 void *table,size_t power);
796 void bn_gather5(BN_ULONG *out,size_t num,
797 void *table,size_t power);
799 BN_ULONG *np=mont->N.d, *n0=mont->n0;
801 /* BN_to_montgomery can contaminate words above .top
802 * [in BN_DEBUG[_DEBUG] build]... */
803 for (i=am.top; i<top; i++) am.d[i]=0;
804 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
806 bn_scatter5(tmp.d,top,powerbuf,0);
807 bn_scatter5(am.d,am.top,powerbuf,1);
808 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
809 bn_scatter5(tmp.d,top,powerbuf,2);
814 /* Calculate a^i = a^(i-1) * a */
815 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
816 bn_scatter5(tmp.d,top,powerbuf,i);
819 /* same as above, but uses squaring for 1/2 of operations */
820 for (i=4; i<32; i*=2)
822 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
823 bn_scatter5(tmp.d,top,powerbuf,i);
828 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
829 bn_scatter5(tmp.d,top,powerbuf,i);
830 for (j=2*i; j<32; j*=2)
832 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
833 bn_scatter5(tmp.d,top,powerbuf,j);
838 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
839 bn_scatter5(tmp.d,top,powerbuf,i);
840 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
841 bn_scatter5(tmp.d,top,powerbuf,2*i);
845 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
846 bn_scatter5(tmp.d,top,powerbuf,i);
850 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
851 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
852 bn_gather5(tmp.d,top,powerbuf,wvalue);
854 /* Scan the exponent one window at a time starting from the most
859 for (wvalue=0, i=0; i<5; i++,bits--)
860 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
862 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
863 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
864 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
865 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
866 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
867 bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
871 bn_correct_top(&tmp);
876 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
877 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
879 /* If the window size is greater than 1, then calculate
880 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
881 * (even powers could instead be computed as (a^(i/2))^2
882 * to use the slight performance advantage of sqr over mul).
886 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
887 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
888 for (i=3; i<numPowers; i++)
890 /* Calculate a^i = a^(i-1) * a */
891 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
893 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
898 for (wvalue=0, i=bits%window; i>=0; i--,bits--)
899 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
900 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
902 /* Scan the exponent one window at a time starting from the most
907 wvalue=0; /* The 'value' of the window */
909 /* Scan the window, squaring the result as we go */
910 for (i=0; i<window; i++,bits--)
912 if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err;
913 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
916 /* Fetch the appropriate pre-computed value from the pre-buf */
917 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
919 /* Multiply the result into the intermediate result */
920 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
924 /* Convert the final result from montgomery to standard format */
925 if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
928 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
931 OPENSSL_cleanse(powerbuf,powerbufLen);
932 if (powerbufFree) OPENSSL_free(powerbufFree);
938 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
939 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
941 BN_MONT_CTX *mont = NULL;
947 #define BN_MOD_MUL_WORD(r, w, m) \
948 (BN_mul_word(r, (w)) && \
949 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
950 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
951 /* BN_MOD_MUL_WORD is only used with 'w' large,
952 * so the BN_ucmp test is probably more overhead
953 * than always using BN_mod (which uses BN_copy if
954 * a similar test returns true). */
955 /* We can use BN_mod and do not need BN_nnmod because our
956 * accumulator is never negative (the result of BN_mod does
957 * not depend on the sign of the modulus).
959 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
960 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
962 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
964 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
965 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
974 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
978 a %= m->d[0]; /* make sure that 'a' is reduced */
980 bits = BN_num_bits(p);
997 if (d == NULL || r == NULL || t == NULL) goto err;
1003 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
1004 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
1007 r_is_one = 1; /* except for Montgomery factor */
1011 /* The result is accumulated in the product r*w. */
1012 w = a; /* bit 'bits-1' of 'p' is always set */
1013 for (b = bits-2; b >= 0; b--)
1015 /* First, square r*w. */
1017 if ((next_w/w) != w) /* overflow */
1021 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1026 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1033 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
1036 /* Second, multiply r*w by 'a' if exponent bit is set. */
1037 if (BN_is_bit_set(p, b))
1040 if ((next_w/a) != w) /* overflow */
1044 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1049 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1057 /* Finally, set r:=r*w. */
1062 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1067 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1071 if (r_is_one) /* can happen only if a == 1*/
1073 if (!BN_one(rr)) goto err;
1077 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
1081 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1088 /* The old fallback, simple version :-) */
1089 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1090 const BIGNUM *m, BN_CTX *ctx)
1092 int i,j,bits,ret=0,wstart,wend,window,wvalue;
1095 /* Table of variables obtained from 'ctx' */
1096 BIGNUM *val[TABLE_SIZE];
1098 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1100 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1101 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1105 bits=BN_num_bits(p);
1114 d = BN_CTX_get(ctx);
1115 val[0] = BN_CTX_get(ctx);
1116 if(!d || !val[0]) goto err;
1118 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
1119 if (BN_is_zero(val[0]))
1126 window = BN_window_bits_for_exponent_size(bits);
1129 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
1134 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
1135 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
1140 start=1; /* This is used to avoid multiplication etc
1141 * when there is only the value '1' in the
1143 wvalue=0; /* The 'value' of the window */
1144 wstart=bits-1; /* The top bit of the window */
1145 wend=0; /* The bottom bit of the window */
1147 if (!BN_one(r)) goto err;
1151 if (BN_is_bit_set(p,wstart) == 0)
1154 if (!BN_mod_mul(r,r,r,m,ctx))
1156 if (wstart == 0) break;
1160 /* We now have wstart on a 'set' bit, we now need to work out
1161 * how bit a window to do. To do this we need to scan
1162 * forward until the last set bit before the end of the
1167 for (i=1; i<window; i++)
1169 if (wstart-i < 0) break;
1170 if (BN_is_bit_set(p,wstart-i))
1178 /* wend is the size of the current window */
1180 /* add the 'bytes above' */
1184 if (!BN_mod_mul(r,r,r,m,ctx))
1188 /* wvalue will be an odd number < 2^window */
1189 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
1192 /* move the 'window' down further */
1196 if (wstart < 0) break;