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))
132 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
133 # include "sparc_arch.h"
134 extern unsigned int OPENSSL_sparcv9cap_P[];
135 # define SPARC_T4_MONT
138 /* maximum precomputation table size for *variable* sliding windows */
139 #define TABLE_SIZE 32
141 /* this one works - simple but works */
142 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
147 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
149 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
150 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
155 if ((r == a) || (r == p))
156 rr = BN_CTX_get(ctx);
160 if (rr == NULL || v == NULL) goto err;
162 if (BN_copy(v,a) == NULL) goto err;
166 { if (BN_copy(rr,a) == NULL) goto err; }
167 else { if (!BN_one(rr)) goto err; }
169 for (i=1; i<bits; i++)
171 if (!BN_sqr(v,v,ctx)) goto err;
172 if (BN_is_bit_set(p,i))
174 if (!BN_mul(rr,rr,v,ctx)) goto err;
179 if (r != rr) BN_copy(r,rr);
186 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
195 /* For even modulus m = 2^k*m_odd, it might make sense to compute
196 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
197 * exponentiation for the odd part), using appropriate exponent
198 * reductions, and combine the results using the CRT.
200 * For now, we use Montgomery only if the modulus is odd; otherwise,
201 * exponentiation using the reciprocal-based quick remaindering
204 * (Timing obtained with expspeed.c [computations a^p mod m
205 * where a, p, m are of the same length: 256, 512, 1024, 2048,
206 * 4096, 8192 bits], compared to the running time of the
207 * standard algorithm:
209 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
210 * 55 .. 77 % [UltraSparc processor, but
211 * debug-solaris-sparcv8-gcc conf.]
213 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
214 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
216 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
217 * at 2048 and more bits, but at 512 and 1024 bits, it was
218 * slower even than the standard algorithm!
220 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
221 * should be obtained when the new Montgomery reduction code
222 * has been integrated into OpenSSL.)
226 #define MONT_EXP_WORD
230 /* I have finally been able to take out this pre-condition of
231 * the top bit being set. It was caused by an error in BN_div
232 * with negatives. There was also another problem when for a^b%m
233 * a >= m. eay 07-May-97 */
234 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
238 # ifdef MONT_EXP_WORD
239 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
241 BN_ULONG A = a->d[0];
242 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
246 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
251 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
253 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
261 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
262 const BIGNUM *m, BN_CTX *ctx)
264 int i,j,bits,ret=0,wstart,wend,window,wvalue;
267 /* Table of variables obtained from 'ctx' */
268 BIGNUM *val[TABLE_SIZE];
271 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
273 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
274 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
287 aa = BN_CTX_get(ctx);
288 val[0] = BN_CTX_get(ctx);
289 if(!aa || !val[0]) goto err;
291 BN_RECP_CTX_init(&recp);
294 /* ignore sign of 'm' */
295 if (!BN_copy(aa, m)) goto err;
297 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
301 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
304 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
305 if (BN_is_zero(val[0]))
312 window = BN_window_bits_for_exponent_size(bits);
315 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
320 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
321 !BN_mod_mul_reciprocal(val[i],val[i-1],
327 start=1; /* This is used to avoid multiplication etc
328 * when there is only the value '1' in the
330 wvalue=0; /* The 'value' of the window */
331 wstart=bits-1; /* The top bit of the window */
332 wend=0; /* The bottom bit of the window */
334 if (!BN_one(r)) goto err;
338 if (BN_is_bit_set(p,wstart) == 0)
341 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
343 if (wstart == 0) break;
347 /* We now have wstart on a 'set' bit, we now need to work out
348 * how bit a window to do. To do this we need to scan
349 * forward until the last set bit before the end of the
354 for (i=1; i<window; i++)
356 if (wstart-i < 0) break;
357 if (BN_is_bit_set(p,wstart-i))
365 /* wend is the size of the current window */
367 /* add the 'bytes above' */
371 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
375 /* wvalue will be an odd number < 2^window */
376 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
379 /* move the 'window' down further */
383 if (wstart < 0) break;
388 BN_RECP_CTX_free(&recp);
394 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
395 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
397 int i,j,bits,ret=0,wstart,wend,window,wvalue;
401 /* Table of variables obtained from 'ctx' */
402 BIGNUM *val[TABLE_SIZE];
403 BN_MONT_CTX *mont=NULL;
405 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
407 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
416 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
429 val[0] = BN_CTX_get(ctx);
430 if (!d || !r || !val[0]) goto err;
432 /* If this is not done, things will break in the montgomery
439 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
440 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
443 if (a->neg || BN_ucmp(a,m) >= 0)
445 if (!BN_nnmod(val[0],a,m,ctx))
457 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
459 window = BN_window_bits_for_exponent_size(bits);
462 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
466 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
467 !BN_mod_mul_montgomery(val[i],val[i-1],
473 start=1; /* This is used to avoid multiplication etc
474 * when there is only the value '1' in the
476 wvalue=0; /* The 'value' of the window */
477 wstart=bits-1; /* The top bit of the window */
478 wend=0; /* The bottom bit of the window */
480 #if 1 /* by Shay Gueron's suggestion */
481 j = m->top; /* borrow j */
482 if (m->d[j-1] & (((BN_ULONG)1)<<(BN_BITS2-1)))
484 if (bn_wexpand(r,j) == NULL) goto err;
485 /* 2^(top*BN_BITS2) - m */
486 r->d[0] = (0-m->d[0])&BN_MASK2;
487 for(i=1;i<j;i++) r->d[i] = (~m->d[i])&BN_MASK2;
492 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
495 if (BN_is_bit_set(p,wstart) == 0)
499 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
502 if (wstart == 0) break;
506 /* We now have wstart on a 'set' bit, we now need to work out
507 * how bit a window to do. To do this we need to scan
508 * forward until the last set bit before the end of the
513 for (i=1; i<window; i++)
515 if (wstart-i < 0) break;
516 if (BN_is_bit_set(p,wstart-i))
524 /* wend is the size of the current window */
526 /* add the 'bytes above' */
530 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
534 /* wvalue will be an odd number < 2^window */
535 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
538 /* move the 'window' down further */
542 if (wstart < 0) break;
544 #if defined(SPARC_T4_MONT)
545 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
547 j = mont->N.top; /* borrow j */
548 val[0]->d[0] = 1; /* borrow val[0] */
549 for (i=1;i<j;i++) val[0]->d[i] = 0;
551 if (!BN_mod_mul_montgomery(rr,r,val[0],mont,ctx)) goto err;
555 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
558 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
564 #if defined(SPARC_T4_MONT)
565 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
570 wordpos = bitpos/BN_BITS2;
572 if (wordpos>=0 && wordpos < a->top)
574 ret = a->d[wordpos]&BN_MASK2;
578 if (++wordpos < a->top)
579 ret |= a->d[wordpos]<<(BN_BITS2-bitpos);
587 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
588 * so that accessing any of these table values shows the same access pattern as far
589 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
590 * from/to that table. */
592 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
597 top = b->top; /* this works because 'buf' is explicitly zeroed */
598 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
600 buf[j] = ((unsigned char*)b->d)[i];
606 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
610 if (bn_wexpand(b, top) == NULL)
613 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
615 ((unsigned char*)b->d)[i] = buf[j];
623 /* Given a pointer value, compute the next address that is a cache line multiple. */
624 #define MOD_EXP_CTIME_ALIGN(x_) \
625 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
627 /* This variant of BN_mod_exp_mont() uses fixed windows and the special
628 * precomputation memory layout to limit data-dependency to a minimum
629 * to protect secret exponents (cf. the hyper-threading timing attacks
630 * pointed out by Colin Percival,
631 * http://www.daemonology.net/hyperthreading-considered-harmful/)
633 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
634 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
636 int i,bits,ret=0,window,wvalue;
638 BN_MONT_CTX *mont=NULL;
641 unsigned char *powerbufFree=NULL;
643 unsigned char *powerbuf=NULL;
645 #if defined(SPARC_T4_MONT)
657 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
669 /* Allocate a montgomery context if it was not supplied by the caller.
670 * If this is not done, things will break in the montgomery part.
676 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
677 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
680 /* Get the window size to use with size of p. */
681 window = BN_window_bits_for_ctime_exponent_size(bits);
682 #if defined(SPARC_T4_MONT)
683 if (window>=5 && (top&15)==0 && top<=64 &&
684 (OPENSSL_sparcv9cap_P[1]&(CFR_MONTMUL|CFR_MONTSQR))==
685 (CFR_MONTMUL|CFR_MONTSQR) &&
686 (t4=OPENSSL_sparcv9cap_P[0]))
690 #if defined(OPENSSL_BN_ASM_MONT5)
691 if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */
695 /* Allocate a buffer large enough to hold all of the pre-computed
696 * powers of am, am itself and tmp.
698 numPowers = 1 << window;
699 powerbufLen = sizeof(m->d[0])*(top*numPowers +
700 ((2*top)>numPowers?(2*top):numPowers));
702 if (powerbufLen < 3072)
703 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
706 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
709 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
710 memset(powerbuf, 0, powerbufLen);
713 if (powerbufLen < 3072)
717 /* lay down tmp and am right after powers table */
718 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
720 tmp.top = am.top = 0;
721 tmp.dmax = am.dmax = top;
722 tmp.neg = am.neg = 0;
723 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
725 /* prepare a^0 in Montgomery domain */
726 #if 1 /* by Shay Gueron's suggestion */
727 if (m->d[top-1] & (((BN_ULONG)1)<<(BN_BITS2-1)))
729 /* 2^(top*BN_BITS2) - m */
730 tmp.d[0] = (0-m->d[0])&BN_MASK2;
731 for (i=1;i<top;i++) tmp.d[i] = (~m->d[i])&BN_MASK2;
736 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
738 /* prepare a^1 in Montgomery domain */
739 if (a->neg || BN_ucmp(a,m) >= 0)
741 if (!BN_mod(&am,a,m,ctx)) goto err;
742 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
744 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
746 #if defined(SPARC_T4_MONT)
749 typedef int (*bn_pwr5_mont_f)(BN_ULONG *tp,const BN_ULONG *np,
750 const BN_ULONG *n0,const void *table,int power,int bits);
751 int bn_pwr5_mont_t4_8(BN_ULONG *tp,const BN_ULONG *np,
752 const BN_ULONG *n0,const void *table,int power,int bits);
753 int bn_pwr5_mont_t4_16(BN_ULONG *tp,const BN_ULONG *np,
754 const BN_ULONG *n0,const void *table,int power,int bits);
755 int bn_pwr5_mont_t4_24(BN_ULONG *tp,const BN_ULONG *np,
756 const BN_ULONG *n0,const void *table,int power,int bits);
757 int bn_pwr5_mont_t4_32(BN_ULONG *tp,const BN_ULONG *np,
758 const BN_ULONG *n0,const void *table,int power,int bits);
759 static const bn_pwr5_mont_f pwr5_funcs[4] = {
760 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
761 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 };
762 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top/16-1];
764 typedef int (*bn_mul_mont_f)(BN_ULONG *rp,const BN_ULONG *ap,
765 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
766 int bn_mul_mont_t4_8(BN_ULONG *rp,const BN_ULONG *ap,
767 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
768 int bn_mul_mont_t4_16(BN_ULONG *rp,const BN_ULONG *ap,
769 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
770 int bn_mul_mont_t4_24(BN_ULONG *rp,const BN_ULONG *ap,
771 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
772 int bn_mul_mont_t4_32(BN_ULONG *rp,const BN_ULONG *ap,
773 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
774 static const bn_mul_mont_f mul_funcs[4] = {
775 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
776 bn_mul_mont_t4_24, bn_mul_mont_t4_32 };
777 bn_mul_mont_f mul_worker = mul_funcs[top/16-1];
779 void bn_mul_mont_vis3(BN_ULONG *rp,const BN_ULONG *ap,
780 const void *bp,const BN_ULONG *np,
781 const BN_ULONG *n0,int num);
782 void bn_mul_mont_t4(BN_ULONG *rp,const BN_ULONG *ap,
783 const void *bp,const BN_ULONG *np,
784 const BN_ULONG *n0,int num);
785 void bn_mul_mont_gather5_t4(BN_ULONG *rp,const BN_ULONG *ap,
786 const void *table,const BN_ULONG *np,
787 const BN_ULONG *n0,int num,int power);
788 void bn_flip_n_scatter5_t4(const BN_ULONG *inp,size_t num,
789 void *table,size_t power);
790 void bn_gather5_t4(BN_ULONG *out,size_t num,
791 void *table,size_t power);
792 void bn_flip_t4(BN_ULONG *dst,BN_ULONG *src,size_t num);
794 BN_ULONG *np=mont->N.d, *n0=mont->n0;
795 int stride = 5*(6-(top/16-1)); /* multiple of 5, but less than 32 */
797 /* BN_to_montgomery can contaminate words above .top
798 * [in BN_DEBUG[_DEBUG] build]... */
799 for (i=am.top; i<top; i++) am.d[i]=0;
800 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
802 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,0);
803 bn_flip_n_scatter5_t4(am.d,top,powerbuf,1);
804 if (!(*mul_worker)(tmp.d,am.d,am.d,np,n0) &&
805 !(*mul_worker)(tmp.d,am.d,am.d,np,n0))
806 bn_mul_mont_vis3(tmp.d,am.d,am.d,np,n0,top);
807 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,2);
811 /* Calculate a^i = a^(i-1) * a */
812 if (!(*mul_worker)(tmp.d,tmp.d,am.d,np,n0) &&
813 !(*mul_worker)(tmp.d,tmp.d,am.d,np,n0))
814 bn_mul_mont_vis3(tmp.d,tmp.d,am.d,np,n0,top);
815 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,i);
818 /* switch to 64-bit domain */
819 np = alloca(top*sizeof(BN_ULONG));
821 bn_flip_t4(np,mont->N.d,top);
824 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
825 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
826 bn_gather5_t4(tmp.d,top,powerbuf,wvalue);
828 /* Scan the exponent one window at a time starting from the most
833 if (bits < stride) stride = bits+1;
835 wvalue = bn_get_bits(p,bits+1);
837 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
838 /* retry once and fall back */
839 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
844 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
845 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
846 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
847 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
848 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
849 bn_mul_mont_gather5_t4(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
852 bn_flip_t4(tmp.d,tmp.d,top);
854 /* back to 32-bit domain */
856 bn_correct_top(&tmp);
857 OPENSSL_cleanse(np,top*sizeof(BN_ULONG));
861 #if defined(OPENSSL_BN_ASM_MONT5)
862 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
863 * specifically optimization of cache-timing attack countermeasures
864 * and pre-computation optimization. */
866 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
867 * 512-bit RSA is hardly relevant, we omit it to spare size... */
870 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
871 const void *table,const BN_ULONG *np,
872 const BN_ULONG *n0,int num,int power);
873 void bn_scatter5(const BN_ULONG *inp,size_t num,
874 void *table,size_t power);
875 void bn_gather5(BN_ULONG *out,size_t num,
876 void *table,size_t power);
878 BN_ULONG *np=mont->N.d, *n0=mont->n0;
880 /* BN_to_montgomery can contaminate words above .top
881 * [in BN_DEBUG[_DEBUG] build]... */
882 for (i=am.top; i<top; i++) am.d[i]=0;
883 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
885 bn_scatter5(tmp.d,top,powerbuf,0);
886 bn_scatter5(am.d,am.top,powerbuf,1);
887 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
888 bn_scatter5(tmp.d,top,powerbuf,2);
893 /* Calculate a^i = a^(i-1) * a */
894 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
895 bn_scatter5(tmp.d,top,powerbuf,i);
898 /* same as above, but uses squaring for 1/2 of operations */
899 for (i=4; i<32; i*=2)
901 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
902 bn_scatter5(tmp.d,top,powerbuf,i);
907 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
908 bn_scatter5(tmp.d,top,powerbuf,i);
909 for (j=2*i; j<32; j*=2)
911 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
912 bn_scatter5(tmp.d,top,powerbuf,j);
917 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
918 bn_scatter5(tmp.d,top,powerbuf,i);
919 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
920 bn_scatter5(tmp.d,top,powerbuf,2*i);
924 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
925 bn_scatter5(tmp.d,top,powerbuf,i);
929 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
930 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
931 bn_gather5(tmp.d,top,powerbuf,wvalue);
933 /* Scan the exponent one window at a time starting from the most
938 for (wvalue=0, i=0; i<5; i++,bits--)
939 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
941 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
942 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
943 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
944 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
945 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
946 bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
950 bn_correct_top(&tmp);
955 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
956 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
958 /* If the window size is greater than 1, then calculate
959 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
960 * (even powers could instead be computed as (a^(i/2))^2
961 * to use the slight performance advantage of sqr over mul).
965 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
966 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
967 for (i=3; i<numPowers; i++)
969 /* Calculate a^i = a^(i-1) * a */
970 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
972 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
977 for (wvalue=0, i=bits%window; i>=0; i--,bits--)
978 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
979 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
981 /* Scan the exponent one window at a time starting from the most
986 wvalue=0; /* The 'value' of the window */
988 /* Scan the window, squaring the result as we go */
989 for (i=0; i<window; i++,bits--)
991 if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err;
992 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
995 /* Fetch the appropriate pre-computed value from the pre-buf */
996 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
998 /* Multiply the result into the intermediate result */
999 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
1003 /* Convert the final result from montgomery to standard format */
1004 #if defined(SPARC_T4_MONT)
1005 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
1007 am.d[0] = 1; /* borrow am */
1008 for (i=1;i<top;i++) am.d[i] = 0;
1009 if (!BN_mod_mul_montgomery(rr,&tmp,&am,mont,ctx)) goto err;
1013 if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
1016 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1019 OPENSSL_cleanse(powerbuf,powerbufLen);
1020 if (powerbufFree) OPENSSL_free(powerbufFree);
1026 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1027 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1029 BN_MONT_CTX *mont = NULL;
1035 #define BN_MOD_MUL_WORD(r, w, m) \
1036 (BN_mul_word(r, (w)) && \
1037 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1038 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1039 /* BN_MOD_MUL_WORD is only used with 'w' large,
1040 * so the BN_ucmp test is probably more overhead
1041 * than always using BN_mod (which uses BN_copy if
1042 * a similar test returns true). */
1043 /* We can use BN_mod and do not need BN_nnmod because our
1044 * accumulator is never negative (the result of BN_mod does
1045 * not depend on the sign of the modulus).
1047 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1048 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1050 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1052 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1053 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1062 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
1066 a %= m->d[0]; /* make sure that 'a' is reduced */
1068 bits = BN_num_bits(p);
1071 /* x**0 mod 1 is still zero. */
1089 d = BN_CTX_get(ctx);
1090 r = BN_CTX_get(ctx);
1091 t = BN_CTX_get(ctx);
1092 if (d == NULL || r == NULL || t == NULL) goto err;
1094 if (in_mont != NULL)
1098 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
1099 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
1102 r_is_one = 1; /* except for Montgomery factor */
1106 /* The result is accumulated in the product r*w. */
1107 w = a; /* bit 'bits-1' of 'p' is always set */
1108 for (b = bits-2; b >= 0; b--)
1110 /* First, square r*w. */
1112 if ((next_w/w) != w) /* overflow */
1116 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1121 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1128 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
1131 /* Second, multiply r*w by 'a' if exponent bit is set. */
1132 if (BN_is_bit_set(p, b))
1135 if ((next_w/a) != w) /* overflow */
1139 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1144 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1152 /* Finally, set r:=r*w. */
1157 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1162 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1166 if (r_is_one) /* can happen only if a == 1*/
1168 if (!BN_one(rr)) goto err;
1172 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
1176 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1183 /* The old fallback, simple version :-) */
1184 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1185 const BIGNUM *m, BN_CTX *ctx)
1187 int i,j,bits,ret=0,wstart,wend,window,wvalue;
1190 /* Table of variables obtained from 'ctx' */
1191 BIGNUM *val[TABLE_SIZE];
1193 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1195 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1196 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1200 bits=BN_num_bits(p);
1209 d = BN_CTX_get(ctx);
1210 val[0] = BN_CTX_get(ctx);
1211 if(!d || !val[0]) goto err;
1213 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
1214 if (BN_is_zero(val[0]))
1221 window = BN_window_bits_for_exponent_size(bits);
1224 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
1229 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
1230 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
1235 start=1; /* This is used to avoid multiplication etc
1236 * when there is only the value '1' in the
1238 wvalue=0; /* The 'value' of the window */
1239 wstart=bits-1; /* The top bit of the window */
1240 wend=0; /* The bottom bit of the window */
1242 if (!BN_one(r)) goto err;
1246 if (BN_is_bit_set(p,wstart) == 0)
1249 if (!BN_mod_mul(r,r,r,m,ctx))
1251 if (wstart == 0) break;
1255 /* We now have wstart on a 'set' bit, we now need to work out
1256 * how bit a window to do. To do this we need to scan
1257 * forward until the last set bit before the end of the
1262 for (i=1; i<window; i++)
1264 if (wstart-i < 0) break;
1265 if (BN_is_bit_set(p,wstart-i))
1273 /* wend is the size of the current window */
1275 /* add the 'bytes above' */
1279 if (!BN_mod_mul(r,r,r,m,ctx))
1283 /* wvalue will be an odd number < 2^window */
1284 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
1287 /* move the 'window' down further */
1291 if (wstart < 0) break;