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))
131 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
132 # include "sparc_arch.h"
133 extern unsigned int OPENSSL_sparcv9cap_P[];
136 /* maximum precomputation table size for *variable* sliding windows */
137 #define TABLE_SIZE 32
139 /* this one works - simple but works */
140 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
145 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
147 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
148 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
153 if ((r == a) || (r == p))
154 rr = BN_CTX_get(ctx);
158 if (rr == NULL || v == NULL) goto err;
160 if (BN_copy(v,a) == NULL) goto err;
164 { if (BN_copy(rr,a) == NULL) goto err; }
165 else { if (!BN_one(rr)) goto err; }
167 for (i=1; i<bits; i++)
169 if (!BN_sqr(v,v,ctx)) goto err;
170 if (BN_is_bit_set(p,i))
172 if (!BN_mul(rr,rr,v,ctx)) goto err;
177 if (r != rr) BN_copy(r,rr);
184 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
193 /* For even modulus m = 2^k*m_odd, it might make sense to compute
194 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
195 * exponentiation for the odd part), using appropriate exponent
196 * reductions, and combine the results using the CRT.
198 * For now, we use Montgomery only if the modulus is odd; otherwise,
199 * exponentiation using the reciprocal-based quick remaindering
202 * (Timing obtained with expspeed.c [computations a^p mod m
203 * where a, p, m are of the same length: 256, 512, 1024, 2048,
204 * 4096, 8192 bits], compared to the running time of the
205 * standard algorithm:
207 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
208 * 55 .. 77 % [UltraSparc processor, but
209 * debug-solaris-sparcv8-gcc conf.]
211 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
212 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
214 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
215 * at 2048 and more bits, but at 512 and 1024 bits, it was
216 * slower even than the standard algorithm!
218 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
219 * should be obtained when the new Montgomery reduction code
220 * has been integrated into OpenSSL.)
224 #define MONT_EXP_WORD
228 /* I have finally been able to take out this pre-condition of
229 * the top bit being set. It was caused by an error in BN_div
230 * with negatives. There was also another problem when for a^b%m
231 * a >= m. eay 07-May-97 */
232 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
236 # ifdef MONT_EXP_WORD
237 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
239 BN_ULONG A = a->d[0];
240 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
244 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
249 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
251 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
259 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
260 const BIGNUM *m, BN_CTX *ctx)
262 int i,j,bits,ret=0,wstart,wend,window,wvalue;
265 /* Table of variables obtained from 'ctx' */
266 BIGNUM *val[TABLE_SIZE];
269 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
271 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
272 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
285 aa = BN_CTX_get(ctx);
286 val[0] = BN_CTX_get(ctx);
287 if(!aa || !val[0]) goto err;
289 BN_RECP_CTX_init(&recp);
292 /* ignore sign of 'm' */
293 if (!BN_copy(aa, m)) goto err;
295 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
299 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
302 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
303 if (BN_is_zero(val[0]))
310 window = BN_window_bits_for_exponent_size(bits);
313 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
318 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
319 !BN_mod_mul_reciprocal(val[i],val[i-1],
325 start=1; /* This is used to avoid multiplication etc
326 * when there is only the value '1' in the
328 wvalue=0; /* The 'value' of the window */
329 wstart=bits-1; /* The top bit of the window */
330 wend=0; /* The bottom bit of the window */
332 if (!BN_one(r)) goto err;
336 if (BN_is_bit_set(p,wstart) == 0)
339 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
341 if (wstart == 0) break;
345 /* We now have wstart on a 'set' bit, we now need to work out
346 * how bit a window to do. To do this we need to scan
347 * forward until the last set bit before the end of the
352 for (i=1; i<window; i++)
354 if (wstart-i < 0) break;
355 if (BN_is_bit_set(p,wstart-i))
363 /* wend is the size of the current window */
365 /* add the 'bytes above' */
369 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
373 /* wvalue will be an odd number < 2^window */
374 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
377 /* move the 'window' down further */
381 if (wstart < 0) break;
386 BN_RECP_CTX_free(&recp);
392 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
393 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
395 int i,j,bits,ret=0,wstart,wend,window,wvalue;
399 /* Table of variables obtained from 'ctx' */
400 BIGNUM *val[TABLE_SIZE];
401 BN_MONT_CTX *mont=NULL;
403 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
405 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
414 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
427 val[0] = BN_CTX_get(ctx);
428 if (!d || !r || !val[0]) goto err;
430 /* If this is not done, things will break in the montgomery
437 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
438 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
441 if (a->neg || BN_ucmp(a,m) >= 0)
443 if (!BN_nnmod(val[0],a,m,ctx))
455 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
457 window = BN_window_bits_for_exponent_size(bits);
460 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
464 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
465 !BN_mod_mul_montgomery(val[i],val[i-1],
471 start=1; /* This is used to avoid multiplication etc
472 * when there is only the value '1' in the
474 wvalue=0; /* The 'value' of the window */
475 wstart=bits-1; /* The top bit of the window */
476 wend=0; /* The bottom bit of the window */
478 #if 1 /* by Shay Gueron's suggestion */
479 j = mont->N.top; /* borrow j */
480 if (bn_wexpand(r,j) == NULL) goto err;
481 r->d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */
482 for(i=1;i<j;i++) r->d[i] = (~m->d[i])&BN_MASK2;
485 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
489 if (BN_is_bit_set(p,wstart) == 0)
493 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
496 if (wstart == 0) break;
500 /* We now have wstart on a 'set' bit, we now need to work out
501 * how bit a window to do. To do this we need to scan
502 * forward until the last set bit before the end of the
507 for (i=1; i<window; i++)
509 if (wstart-i < 0) break;
510 if (BN_is_bit_set(p,wstart-i))
518 /* wend is the size of the current window */
520 /* add the 'bytes above' */
524 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
528 /* wvalue will be an odd number < 2^window */
529 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
532 /* move the 'window' down further */
536 if (wstart < 0) break;
538 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
539 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
541 j = mont->N.top; /* borrow j */
542 val[0]->d[0] = 1; /* borrow val[0] */
543 for (i=1;i<j;i++) val[0]->d[i] = 0;
545 if (!BN_mod_mul_montgomery(rr,r,val[0],mont,ctx)) goto err;
549 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
552 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
558 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
559 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
564 wordpos = bitpos/BN_BITS2;
566 if (wordpos>=0 && wordpos < a->top)
568 ret = a->d[wordpos]&BN_MASK2;
572 if (++wordpos < a->top)
573 ret |= a->d[wordpos]<<(BN_BITS2-bitpos);
581 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
582 * so that accessing any of these table values shows the same access pattern as far
583 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
584 * from/to that table. */
586 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
591 top = b->top; /* this works because 'buf' is explicitly zeroed */
592 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
594 buf[j] = ((unsigned char*)b->d)[i];
600 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
604 if (bn_wexpand(b, top) == NULL)
607 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
609 ((unsigned char*)b->d)[i] = buf[j];
617 /* Given a pointer value, compute the next address that is a cache line multiple. */
618 #define MOD_EXP_CTIME_ALIGN(x_) \
619 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
621 /* This variant of BN_mod_exp_mont() uses fixed windows and the special
622 * precomputation memory layout to limit data-dependency to a minimum
623 * to protect secret exponents (cf. the hyper-threading timing attacks
624 * pointed out by Colin Percival,
625 * http://www.daemonology.net/hyperthreading-considered-harmful/)
627 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
628 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
630 int i,bits,ret=0,window,wvalue;
632 BN_MONT_CTX *mont=NULL;
635 unsigned char *powerbufFree=NULL;
637 unsigned char *powerbuf=NULL;
639 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
651 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
663 /* Allocate a montgomery context if it was not supplied by the caller.
664 * If this is not done, things will break in the montgomery part.
670 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
671 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
674 /* Get the window size to use with size of p. */
675 window = BN_window_bits_for_ctime_exponent_size(bits);
676 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
677 if (window>=5 && (top&15)==0 && top<=64 &&
678 (OPENSSL_sparcv9cap_P[1]&(CFR_MONTMUL|CFR_MONTSQR))==
679 (CFR_MONTMUL|CFR_MONTSQR) &&
680 (t4=OPENSSL_sparcv9cap_P[0]))
684 #if defined(OPENSSL_BN_ASM_MONT5)
685 if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */
689 /* Allocate a buffer large enough to hold all of the pre-computed
690 * powers of am, am itself and tmp.
692 numPowers = 1 << window;
693 powerbufLen = sizeof(m->d[0])*(top*numPowers +
694 ((2*top)>numPowers?(2*top):numPowers));
696 if (powerbufLen < 3072)
697 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
700 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
703 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
704 memset(powerbuf, 0, powerbufLen);
707 if (powerbufLen < 3072)
711 /* lay down tmp and am right after powers table */
712 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
714 tmp.top = am.top = 0;
715 tmp.dmax = am.dmax = top;
716 tmp.neg = am.neg = 0;
717 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
719 /* prepare a^0 in Montgomery domain */
720 #if 1 /* by Shay Gueron's suggestion */
721 tmp.d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */
723 tmp.d[i] = (~m->d[i])&BN_MASK2;
726 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
729 /* prepare a^1 in Montgomery domain */
730 if (a->neg || BN_ucmp(a,m) >= 0)
732 if (!BN_mod(&am,a,m,ctx)) goto err;
733 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
735 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
737 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
740 typedef int (*bn_pwr5_mont_f)(BN_ULONG *tp,const BN_ULONG *np,
741 const BN_ULONG *n0,const void *table,int power,int bits);
742 int bn_pwr5_mont_t4_8(BN_ULONG *tp,const BN_ULONG *np,
743 const BN_ULONG *n0,const void *table,int power,int bits);
744 int bn_pwr5_mont_t4_16(BN_ULONG *tp,const BN_ULONG *np,
745 const BN_ULONG *n0,const void *table,int power,int bits);
746 int bn_pwr5_mont_t4_24(BN_ULONG *tp,const BN_ULONG *np,
747 const BN_ULONG *n0,const void *table,int power,int bits);
748 int bn_pwr5_mont_t4_32(BN_ULONG *tp,const BN_ULONG *np,
749 const BN_ULONG *n0,const void *table,int power,int bits);
750 static const bn_pwr5_mont_f pwr5_funcs[4] = {
751 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
752 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 };
753 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top/16-1];
755 typedef int (*bn_mul_mont_f)(BN_ULONG *rp,const BN_ULONG *ap,
756 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
757 int bn_mul_mont_t4_8(BN_ULONG *rp,const BN_ULONG *ap,
758 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
759 int bn_mul_mont_t4_16(BN_ULONG *rp,const BN_ULONG *ap,
760 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
761 int bn_mul_mont_t4_24(BN_ULONG *rp,const BN_ULONG *ap,
762 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
763 int bn_mul_mont_t4_32(BN_ULONG *rp,const BN_ULONG *ap,
764 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
765 static const bn_mul_mont_f mul_funcs[4] = {
766 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
767 bn_mul_mont_t4_24, bn_mul_mont_t4_32 };
768 bn_mul_mont_f mul_worker = mul_funcs[top/16-1];
770 void bn_mul_mont_vis3(BN_ULONG *rp,const BN_ULONG *ap,
771 const void *bp,const BN_ULONG *np,
772 const BN_ULONG *n0,int num);
773 void bn_mul_mont_t4(BN_ULONG *rp,const BN_ULONG *ap,
774 const void *bp,const BN_ULONG *np,
775 const BN_ULONG *n0,int num);
776 void bn_mul_mont_gather5_t4(BN_ULONG *rp,const BN_ULONG *ap,
777 const void *table,const BN_ULONG *np,
778 const BN_ULONG *n0,int num,int power);
779 void bn_flip_n_scatter5_t4(const BN_ULONG *inp,size_t num,
780 void *table,size_t power);
781 void bn_gather5_t4(BN_ULONG *out,size_t num,
782 void *table,size_t power);
783 void bn_flip_t4(BN_ULONG *dst,BN_ULONG *src,size_t num);
785 BN_ULONG *np=mont->N.d, *n0=mont->n0;
786 int stride = 5*(6-(top/16-1)); /* multiple of 5, but less than 32 */
788 /* BN_to_montgomery can contaminate words above .top
789 * [in BN_DEBUG[_DEBUG] build]... */
790 for (i=am.top; i<top; i++) am.d[i]=0;
791 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
793 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,0);
794 bn_flip_n_scatter5_t4(am.d,top,powerbuf,1);
795 if (!(*mul_worker)(tmp.d,am.d,am.d,np,n0) &&
796 !(*mul_worker)(tmp.d,am.d,am.d,np,n0))
797 bn_mul_mont_vis3(tmp.d,am.d,am.d,np,n0,top);
798 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,2);
802 /* Calculate a^i = a^(i-1) * a */
803 if (!(*mul_worker)(tmp.d,tmp.d,am.d,np,n0) &&
804 !(*mul_worker)(tmp.d,tmp.d,am.d,np,n0))
805 bn_mul_mont_vis3(tmp.d,tmp.d,am.d,np,n0,top);
806 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,i);
809 /* switch to 64-bit domain */
810 np = alloca(top*sizeof(BN_ULONG));
812 bn_flip_t4(np,mont->N.d,top);
815 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
816 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
817 bn_gather5_t4(tmp.d,top,powerbuf,wvalue);
819 /* Scan the exponent one window at a time starting from the most
824 if (bits < stride) stride = bits+1;
826 wvalue = bn_get_bits(p,bits+1);
828 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
829 /* retry once and fall back */
830 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
835 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
836 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
837 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
838 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
839 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
840 bn_mul_mont_gather5_t4(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
843 bn_flip_t4(tmp.d,tmp.d,top);
845 /* back to 32-bit domain */
847 bn_correct_top(&tmp);
848 OPENSSL_cleanse(np,top*sizeof(BN_ULONG));
852 #if defined(OPENSSL_BN_ASM_MONT5)
853 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
854 * specifically optimization of cache-timing attack countermeasures
855 * and pre-computation optimization. */
857 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
858 * 512-bit RSA is hardly relevant, we omit it to spare size... */
861 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
862 const void *table,const BN_ULONG *np,
863 const BN_ULONG *n0,int num,int power);
864 void bn_scatter5(const BN_ULONG *inp,size_t num,
865 void *table,size_t power);
866 void bn_gather5(BN_ULONG *out,size_t num,
867 void *table,size_t power);
869 BN_ULONG *np=mont->N.d, *n0=mont->n0;
871 /* BN_to_montgomery can contaminate words above .top
872 * [in BN_DEBUG[_DEBUG] build]... */
873 for (i=am.top; i<top; i++) am.d[i]=0;
874 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
876 bn_scatter5(tmp.d,top,powerbuf,0);
877 bn_scatter5(am.d,am.top,powerbuf,1);
878 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
879 bn_scatter5(tmp.d,top,powerbuf,2);
884 /* Calculate a^i = a^(i-1) * a */
885 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
886 bn_scatter5(tmp.d,top,powerbuf,i);
889 /* same as above, but uses squaring for 1/2 of operations */
890 for (i=4; i<32; i*=2)
892 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
893 bn_scatter5(tmp.d,top,powerbuf,i);
898 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
899 bn_scatter5(tmp.d,top,powerbuf,i);
900 for (j=2*i; j<32; j*=2)
902 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
903 bn_scatter5(tmp.d,top,powerbuf,j);
908 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
909 bn_scatter5(tmp.d,top,powerbuf,i);
910 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
911 bn_scatter5(tmp.d,top,powerbuf,2*i);
915 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
916 bn_scatter5(tmp.d,top,powerbuf,i);
920 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
921 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
922 bn_gather5(tmp.d,top,powerbuf,wvalue);
924 /* Scan the exponent one window at a time starting from the most
929 for (wvalue=0, i=0; i<5; i++,bits--)
930 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
932 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
933 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
934 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
935 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
936 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
937 bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
941 bn_correct_top(&tmp);
946 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
947 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
949 /* If the window size is greater than 1, then calculate
950 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
951 * (even powers could instead be computed as (a^(i/2))^2
952 * to use the slight performance advantage of sqr over mul).
956 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
957 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
958 for (i=3; i<numPowers; i++)
960 /* Calculate a^i = a^(i-1) * a */
961 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
963 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
968 for (wvalue=0, i=bits%window; i>=0; i--,bits--)
969 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
970 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
972 /* Scan the exponent one window at a time starting from the most
977 wvalue=0; /* The 'value' of the window */
979 /* Scan the window, squaring the result as we go */
980 for (i=0; i<window; i++,bits--)
982 if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err;
983 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
986 /* Fetch the appropriate pre-computed value from the pre-buf */
987 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
989 /* Multiply the result into the intermediate result */
990 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
994 /* Convert the final result from montgomery to standard format */
995 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
996 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
998 am.d[0] = 1; /* borrow am */
999 for (i=1;i<top;i++) am.d[i] = 0;
1000 if (!BN_mod_mul_montgomery(rr,&tmp,&am,mont,ctx)) goto err;
1004 if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
1007 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1010 OPENSSL_cleanse(powerbuf,powerbufLen);
1011 if (powerbufFree) OPENSSL_free(powerbufFree);
1017 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1018 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1020 BN_MONT_CTX *mont = NULL;
1026 #define BN_MOD_MUL_WORD(r, w, m) \
1027 (BN_mul_word(r, (w)) && \
1028 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1029 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1030 /* BN_MOD_MUL_WORD is only used with 'w' large,
1031 * so the BN_ucmp test is probably more overhead
1032 * than always using BN_mod (which uses BN_copy if
1033 * a similar test returns true). */
1034 /* We can use BN_mod and do not need BN_nnmod because our
1035 * accumulator is never negative (the result of BN_mod does
1036 * not depend on the sign of the modulus).
1038 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1039 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1041 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1043 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1044 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1053 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
1057 a %= m->d[0]; /* make sure that 'a' is reduced */
1059 bits = BN_num_bits(p);
1062 /* x**0 mod 1 is still zero. */
1080 d = BN_CTX_get(ctx);
1081 r = BN_CTX_get(ctx);
1082 t = BN_CTX_get(ctx);
1083 if (d == NULL || r == NULL || t == NULL) goto err;
1085 if (in_mont != NULL)
1089 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
1090 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
1093 r_is_one = 1; /* except for Montgomery factor */
1097 /* The result is accumulated in the product r*w. */
1098 w = a; /* bit 'bits-1' of 'p' is always set */
1099 for (b = bits-2; b >= 0; b--)
1101 /* First, square r*w. */
1103 if ((next_w/w) != w) /* overflow */
1107 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1112 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1119 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
1122 /* Second, multiply r*w by 'a' if exponent bit is set. */
1123 if (BN_is_bit_set(p, b))
1126 if ((next_w/a) != w) /* overflow */
1130 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1135 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1143 /* Finally, set r:=r*w. */
1148 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1153 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1157 if (r_is_one) /* can happen only if a == 1*/
1159 if (!BN_one(rr)) goto err;
1163 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
1167 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1174 /* The old fallback, simple version :-) */
1175 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1176 const BIGNUM *m, BN_CTX *ctx)
1178 int i,j,bits,ret=0,wstart,wend,window,wvalue;
1181 /* Table of variables obtained from 'ctx' */
1182 BIGNUM *val[TABLE_SIZE];
1184 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1186 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1187 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1191 bits=BN_num_bits(p);
1200 d = BN_CTX_get(ctx);
1201 val[0] = BN_CTX_get(ctx);
1202 if(!d || !val[0]) goto err;
1204 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
1205 if (BN_is_zero(val[0]))
1212 window = BN_window_bits_for_exponent_size(bits);
1215 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
1220 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
1221 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
1226 start=1; /* This is used to avoid multiplication etc
1227 * when there is only the value '1' in the
1229 wvalue=0; /* The 'value' of the window */
1230 wstart=bits-1; /* The top bit of the window */
1231 wend=0; /* The bottom bit of the window */
1233 if (!BN_one(r)) goto err;
1237 if (BN_is_bit_set(p,wstart) == 0)
1240 if (!BN_mod_mul(r,r,r,m,ctx))
1242 if (wstart == 0) break;
1246 /* We now have wstart on a 'set' bit, we now need to work out
1247 * how bit a window to do. To do this we need to scan
1248 * forward until the last set bit before the end of the
1253 for (i=1; i<window; i++)
1255 if (wstart-i < 0) break;
1256 if (BN_is_bit_set(p,wstart-i))
1264 /* wend is the size of the current window */
1266 /* add the 'bytes above' */
1270 if (!BN_mod_mul(r,r,r,m,ctx))
1274 /* wvalue will be an odd number < 2^window */
1275 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
1278 /* move the 'window' down further */
1282 if (wstart < 0) break;