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) && \
133 (defined(__x86_64) || defined(__x86_64__) || \
134 defined(_M_AMD64) || defined(_M_X64))
135 # include "rsaz_exp.h"
136 # define RSAZ_ENABLED
140 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
141 # include "sparc_arch.h"
142 extern unsigned int OPENSSL_sparcv9cap_P[];
143 # define SPARC_T4_MONT
146 /* maximum precomputation table size for *variable* sliding windows */
147 #define TABLE_SIZE 32
149 /* this one works - simple but works */
150 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
155 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
157 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
158 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
163 if ((r == a) || (r == p))
164 rr = BN_CTX_get(ctx);
168 if (rr == NULL || v == NULL) goto err;
170 if (BN_copy(v,a) == NULL) goto err;
174 { if (BN_copy(rr,a) == NULL) goto err; }
175 else { if (!BN_one(rr)) goto err; }
177 for (i=1; i<bits; i++)
179 if (!BN_sqr(v,v,ctx)) goto err;
180 if (BN_is_bit_set(p,i))
182 if (!BN_mul(rr,rr,v,ctx)) goto err;
187 if (r != rr) BN_copy(r,rr);
194 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
203 /* For even modulus m = 2^k*m_odd, it might make sense to compute
204 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
205 * exponentiation for the odd part), using appropriate exponent
206 * reductions, and combine the results using the CRT.
208 * For now, we use Montgomery only if the modulus is odd; otherwise,
209 * exponentiation using the reciprocal-based quick remaindering
212 * (Timing obtained with expspeed.c [computations a^p mod m
213 * where a, p, m are of the same length: 256, 512, 1024, 2048,
214 * 4096, 8192 bits], compared to the running time of the
215 * standard algorithm:
217 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
218 * 55 .. 77 % [UltraSparc processor, but
219 * debug-solaris-sparcv8-gcc conf.]
221 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
222 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
224 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
225 * at 2048 and more bits, but at 512 and 1024 bits, it was
226 * slower even than the standard algorithm!
228 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
229 * should be obtained when the new Montgomery reduction code
230 * has been integrated into OpenSSL.)
234 #define MONT_EXP_WORD
238 /* I have finally been able to take out this pre-condition of
239 * the top bit being set. It was caused by an error in BN_div
240 * with negatives. There was also another problem when for a^b%m
241 * a >= m. eay 07-May-97 */
242 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
246 # ifdef MONT_EXP_WORD
247 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
249 BN_ULONG A = a->d[0];
250 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
254 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
259 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
261 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
269 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
270 const BIGNUM *m, BN_CTX *ctx)
272 int i,j,bits,ret=0,wstart,wend,window,wvalue;
275 /* Table of variables obtained from 'ctx' */
276 BIGNUM *val[TABLE_SIZE];
279 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
281 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
282 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
295 aa = BN_CTX_get(ctx);
296 val[0] = BN_CTX_get(ctx);
297 if(!aa || !val[0]) goto err;
299 BN_RECP_CTX_init(&recp);
302 /* ignore sign of 'm' */
303 if (!BN_copy(aa, m)) goto err;
305 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
309 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
312 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
313 if (BN_is_zero(val[0]))
320 window = BN_window_bits_for_exponent_size(bits);
323 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
328 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
329 !BN_mod_mul_reciprocal(val[i],val[i-1],
335 start=1; /* This is used to avoid multiplication etc
336 * when there is only the value '1' in the
338 wvalue=0; /* The 'value' of the window */
339 wstart=bits-1; /* The top bit of the window */
340 wend=0; /* The bottom bit of the window */
342 if (!BN_one(r)) goto err;
346 if (BN_is_bit_set(p,wstart) == 0)
349 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
351 if (wstart == 0) break;
355 /* We now have wstart on a 'set' bit, we now need to work out
356 * how bit a window to do. To do this we need to scan
357 * forward until the last set bit before the end of the
362 for (i=1; i<window; i++)
364 if (wstart-i < 0) break;
365 if (BN_is_bit_set(p,wstart-i))
373 /* wend is the size of the current window */
375 /* add the 'bytes above' */
379 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
383 /* wvalue will be an odd number < 2^window */
384 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
387 /* move the 'window' down further */
391 if (wstart < 0) break;
396 BN_RECP_CTX_free(&recp);
402 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
403 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
405 int i,j,bits,ret=0,wstart,wend,window,wvalue;
409 /* Table of variables obtained from 'ctx' */
410 BIGNUM *val[TABLE_SIZE];
411 BN_MONT_CTX *mont=NULL;
413 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
415 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
424 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
437 val[0] = BN_CTX_get(ctx);
438 if (!d || !r || !val[0]) goto err;
440 /* If this is not done, things will break in the montgomery
447 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
448 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
451 if (a->neg || BN_ucmp(a,m) >= 0)
453 if (!BN_nnmod(val[0],a,m,ctx))
465 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
467 window = BN_window_bits_for_exponent_size(bits);
470 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
474 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
475 !BN_mod_mul_montgomery(val[i],val[i-1],
481 start=1; /* This is used to avoid multiplication etc
482 * when there is only the value '1' in the
484 wvalue=0; /* The 'value' of the window */
485 wstart=bits-1; /* The top bit of the window */
486 wend=0; /* The bottom bit of the window */
488 #if 1 /* by Shay Gueron's suggestion */
489 j = m->top; /* borrow j */
490 if (m->d[j-1] & (((BN_ULONG)1)<<(BN_BITS2-1)))
492 if (bn_wexpand(r,j) == NULL) goto err;
493 /* 2^(top*BN_BITS2) - m */
494 r->d[0] = (0-m->d[0])&BN_MASK2;
495 for(i=1;i<j;i++) r->d[i] = (~m->d[i])&BN_MASK2;
497 /* Upper words will be zero if the corresponding words of 'm'
498 * were 0xfff[...], so decrement r->top accordingly. */
503 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
506 if (BN_is_bit_set(p,wstart) == 0)
510 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
513 if (wstart == 0) break;
517 /* We now have wstart on a 'set' bit, we now need to work out
518 * how bit a window to do. To do this we need to scan
519 * forward until the last set bit before the end of the
524 for (i=1; i<window; i++)
526 if (wstart-i < 0) break;
527 if (BN_is_bit_set(p,wstart-i))
535 /* wend is the size of the current window */
537 /* add the 'bytes above' */
541 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
545 /* wvalue will be an odd number < 2^window */
546 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
549 /* move the 'window' down further */
553 if (wstart < 0) break;
555 #if defined(SPARC_T4_MONT)
556 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
558 j = mont->N.top; /* borrow j */
559 val[0]->d[0] = 1; /* borrow val[0] */
560 for (i=1;i<j;i++) val[0]->d[i] = 0;
562 if (!BN_mod_mul_montgomery(rr,r,val[0],mont,ctx)) goto err;
566 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
569 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
575 #if defined(SPARC_T4_MONT)
576 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
581 wordpos = bitpos/BN_BITS2;
583 if (wordpos>=0 && wordpos < a->top)
585 ret = a->d[wordpos]&BN_MASK2;
589 if (++wordpos < a->top)
590 ret |= a->d[wordpos]<<(BN_BITS2-bitpos);
598 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
599 * so that accessing any of these table values shows the same access pattern as far
600 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
601 * from/to that table. */
603 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
608 top = b->top; /* this works because 'buf' is explicitly zeroed */
609 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
611 buf[j] = ((unsigned char*)b->d)[i];
617 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
621 if (bn_wexpand(b, top) == NULL)
624 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
626 ((unsigned char*)b->d)[i] = buf[j];
634 /* Given a pointer value, compute the next address that is a cache line multiple. */
635 #define MOD_EXP_CTIME_ALIGN(x_) \
636 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
638 /* This variant of BN_mod_exp_mont() uses fixed windows and the special
639 * precomputation memory layout to limit data-dependency to a minimum
640 * to protect secret exponents (cf. the hyper-threading timing attacks
641 * pointed out by Colin Percival,
642 * http://www.daemonology.net/hyperthreading-considered-harmful/)
644 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
645 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
647 int i,bits,ret=0,window,wvalue;
649 BN_MONT_CTX *mont=NULL;
652 unsigned char *powerbufFree=NULL;
654 unsigned char *powerbuf=NULL;
656 #if defined(SPARC_T4_MONT)
668 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
680 /* Allocate a montgomery context if it was not supplied by the caller.
681 * If this is not done, things will break in the montgomery part.
687 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
688 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
693 * If the size of the operands allow it, perform the optimized
694 * RSAZ exponentiation. For further information see
695 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
697 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
698 && rsaz_avx2_eligible())
700 if (NULL == bn_wexpand(rr, 16)) goto err;
701 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, mont->n0[0]);
708 else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512))
710 if (NULL == bn_wexpand(rr,8)) goto err;
711 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
720 /* Get the window size to use with size of p. */
721 window = BN_window_bits_for_ctime_exponent_size(bits);
722 #if defined(SPARC_T4_MONT)
723 if (window>=5 && (top&15)==0 && top<=64 &&
724 (OPENSSL_sparcv9cap_P[1]&(CFR_MONTMUL|CFR_MONTSQR))==
725 (CFR_MONTMUL|CFR_MONTSQR) &&
726 (t4=OPENSSL_sparcv9cap_P[0]))
730 #if defined(OPENSSL_BN_ASM_MONT5)
733 window=5; /* ~5% improvement for RSA2048 sign, and even for RSA4096 */
734 if ((top&7)==0) powerbufLen += 2*top*sizeof(m->d[0]);
739 /* Allocate a buffer large enough to hold all of the pre-computed
740 * powers of am, am itself and tmp.
742 numPowers = 1 << window;
743 powerbufLen += sizeof(m->d[0])*(top*numPowers +
744 ((2*top)>numPowers?(2*top):numPowers));
746 if (powerbufLen < 3072)
747 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
750 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
753 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
754 memset(powerbuf, 0, powerbufLen);
757 if (powerbufLen < 3072)
761 /* lay down tmp and am right after powers table */
762 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
764 tmp.top = am.top = 0;
765 tmp.dmax = am.dmax = top;
766 tmp.neg = am.neg = 0;
767 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
769 /* prepare a^0 in Montgomery domain */
770 #if 1 /* by Shay Gueron's suggestion */
771 if (m->d[top-1] & (((BN_ULONG)1)<<(BN_BITS2-1)))
773 /* 2^(top*BN_BITS2) - m */
774 tmp.d[0] = (0-m->d[0])&BN_MASK2;
775 for (i=1;i<top;i++) tmp.d[i] = (~m->d[i])&BN_MASK2;
780 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
782 /* prepare a^1 in Montgomery domain */
783 if (a->neg || BN_ucmp(a,m) >= 0)
785 if (!BN_mod(&am,a,m,ctx)) goto err;
786 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
788 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
790 #if defined(SPARC_T4_MONT)
793 typedef int (*bn_pwr5_mont_f)(BN_ULONG *tp,const BN_ULONG *np,
794 const BN_ULONG *n0,const void *table,int power,int bits);
795 int bn_pwr5_mont_t4_8(BN_ULONG *tp,const BN_ULONG *np,
796 const BN_ULONG *n0,const void *table,int power,int bits);
797 int bn_pwr5_mont_t4_16(BN_ULONG *tp,const BN_ULONG *np,
798 const BN_ULONG *n0,const void *table,int power,int bits);
799 int bn_pwr5_mont_t4_24(BN_ULONG *tp,const BN_ULONG *np,
800 const BN_ULONG *n0,const void *table,int power,int bits);
801 int bn_pwr5_mont_t4_32(BN_ULONG *tp,const BN_ULONG *np,
802 const BN_ULONG *n0,const void *table,int power,int bits);
803 static const bn_pwr5_mont_f pwr5_funcs[4] = {
804 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
805 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 };
806 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top/16-1];
808 typedef int (*bn_mul_mont_f)(BN_ULONG *rp,const BN_ULONG *ap,
809 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
810 int bn_mul_mont_t4_8(BN_ULONG *rp,const BN_ULONG *ap,
811 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
812 int bn_mul_mont_t4_16(BN_ULONG *rp,const BN_ULONG *ap,
813 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
814 int bn_mul_mont_t4_24(BN_ULONG *rp,const BN_ULONG *ap,
815 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
816 int bn_mul_mont_t4_32(BN_ULONG *rp,const BN_ULONG *ap,
817 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
818 static const bn_mul_mont_f mul_funcs[4] = {
819 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
820 bn_mul_mont_t4_24, bn_mul_mont_t4_32 };
821 bn_mul_mont_f mul_worker = mul_funcs[top/16-1];
823 void bn_mul_mont_vis3(BN_ULONG *rp,const BN_ULONG *ap,
824 const void *bp,const BN_ULONG *np,
825 const BN_ULONG *n0,int num);
826 void bn_mul_mont_t4(BN_ULONG *rp,const BN_ULONG *ap,
827 const void *bp,const BN_ULONG *np,
828 const BN_ULONG *n0,int num);
829 void bn_mul_mont_gather5_t4(BN_ULONG *rp,const BN_ULONG *ap,
830 const void *table,const BN_ULONG *np,
831 const BN_ULONG *n0,int num,int power);
832 void bn_flip_n_scatter5_t4(const BN_ULONG *inp,size_t num,
833 void *table,size_t power);
834 void bn_gather5_t4(BN_ULONG *out,size_t num,
835 void *table,size_t power);
836 void bn_flip_t4(BN_ULONG *dst,BN_ULONG *src,size_t num);
838 BN_ULONG *np=mont->N.d, *n0=mont->n0;
839 int stride = 5*(6-(top/16-1)); /* multiple of 5, but less than 32 */
841 /* BN_to_montgomery can contaminate words above .top
842 * [in BN_DEBUG[_DEBUG] build]... */
843 for (i=am.top; i<top; i++) am.d[i]=0;
844 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
846 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,0);
847 bn_flip_n_scatter5_t4(am.d,top,powerbuf,1);
848 if (!(*mul_worker)(tmp.d,am.d,am.d,np,n0) &&
849 !(*mul_worker)(tmp.d,am.d,am.d,np,n0))
850 bn_mul_mont_vis3(tmp.d,am.d,am.d,np,n0,top);
851 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,2);
855 /* Calculate a^i = a^(i-1) * a */
856 if (!(*mul_worker)(tmp.d,tmp.d,am.d,np,n0) &&
857 !(*mul_worker)(tmp.d,tmp.d,am.d,np,n0))
858 bn_mul_mont_vis3(tmp.d,tmp.d,am.d,np,n0,top);
859 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,i);
862 /* switch to 64-bit domain */
863 np = alloca(top*sizeof(BN_ULONG));
865 bn_flip_t4(np,mont->N.d,top);
868 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
869 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
870 bn_gather5_t4(tmp.d,top,powerbuf,wvalue);
872 /* Scan the exponent one window at a time starting from the most
877 if (bits < stride) stride = bits+1;
879 wvalue = bn_get_bits(p,bits+1);
881 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
882 /* retry once and fall back */
883 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
888 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
889 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
890 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
891 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
892 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
893 bn_mul_mont_gather5_t4(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
896 bn_flip_t4(tmp.d,tmp.d,top);
898 /* back to 32-bit domain */
900 bn_correct_top(&tmp);
901 OPENSSL_cleanse(np,top*sizeof(BN_ULONG));
905 #if defined(OPENSSL_BN_ASM_MONT5)
906 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
907 * specifically optimization of cache-timing attack countermeasures
908 * and pre-computation optimization. */
910 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
911 * 512-bit RSA is hardly relevant, we omit it to spare size... */
912 if (window==5 && top>1)
914 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
915 const void *table,const BN_ULONG *np,
916 const BN_ULONG *n0,int num,int power);
917 void bn_scatter5(const BN_ULONG *inp,size_t num,
918 void *table,size_t power);
919 void bn_gather5(BN_ULONG *out,size_t num,
920 void *table,size_t power);
921 void bn_power5(BN_ULONG *rp,const BN_ULONG *ap,
922 const void *table,const BN_ULONG *np,
923 const BN_ULONG *n0,int num,int power);
924 int bn_get_bits5(const BN_ULONG *ap,int off);
925 int bn_from_montgomery(BN_ULONG *rp,const BN_ULONG *ap,
926 const BN_ULONG *not_used,const BN_ULONG *np,
927 const BN_ULONG *n0,int num);
929 BN_ULONG *np=mont->N.d, *n0=mont->n0, *np2;
931 /* BN_to_montgomery can contaminate words above .top
932 * [in BN_DEBUG[_DEBUG] build]... */
933 for (i=am.top; i<top; i++) am.d[i]=0;
934 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
939 for (np2=am.d+top,i=0; i<top; i++) np2[2*i]=np[i];
941 bn_scatter5(tmp.d,top,powerbuf,0);
942 bn_scatter5(am.d,am.top,powerbuf,1);
943 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
944 bn_scatter5(tmp.d,top,powerbuf,2);
949 /* Calculate a^i = a^(i-1) * a */
950 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
951 bn_scatter5(tmp.d,top,powerbuf,i);
954 /* same as above, but uses squaring for 1/2 of operations */
955 for (i=4; i<32; i*=2)
957 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
958 bn_scatter5(tmp.d,top,powerbuf,i);
963 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
964 bn_scatter5(tmp.d,top,powerbuf,i);
965 for (j=2*i; j<32; j*=2)
967 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
968 bn_scatter5(tmp.d,top,powerbuf,j);
973 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
974 bn_scatter5(tmp.d,top,powerbuf,i);
975 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
976 bn_scatter5(tmp.d,top,powerbuf,2*i);
980 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
981 bn_scatter5(tmp.d,top,powerbuf,i);
985 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
986 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
987 bn_gather5(tmp.d,top,powerbuf,wvalue);
989 /* Scan the exponent one window at a time starting from the most
995 for (wvalue=0, i=0; i<5; i++,bits--)
996 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
998 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
999 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
1000 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
1001 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
1002 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
1003 bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
1009 wvalue = bn_get_bits5(p->d,bits-4);
1011 bn_power5(tmp.d,tmp.d,powerbuf,np2,n0,top,wvalue);
1015 ret=bn_from_montgomery(tmp.d,tmp.d,NULL,np2,n0,top);
1017 bn_correct_top(&tmp);
1020 if (!BN_copy(rr,&tmp)) ret=0;
1021 goto err; /* non-zero ret means it's not error */
1027 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
1028 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
1030 /* If the window size is greater than 1, then calculate
1031 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
1032 * (even powers could instead be computed as (a^(i/2))^2
1033 * to use the slight performance advantage of sqr over mul).
1037 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
1038 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
1039 for (i=3; i<numPowers; i++)
1041 /* Calculate a^i = a^(i-1) * a */
1042 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
1044 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
1049 for (wvalue=0, i=bits%window; i>=0; i--,bits--)
1050 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
1051 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
1053 /* Scan the exponent one window at a time starting from the most
1058 wvalue=0; /* The 'value' of the window */
1060 /* Scan the window, squaring the result as we go */
1061 for (i=0; i<window; i++,bits--)
1063 if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err;
1064 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
1067 /* Fetch the appropriate pre-computed value from the pre-buf */
1068 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
1070 /* Multiply the result into the intermediate result */
1071 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
1075 /* Convert the final result from montgomery to standard format */
1076 #if defined(SPARC_T4_MONT)
1077 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
1079 am.d[0] = 1; /* borrow am */
1080 for (i=1;i<top;i++) am.d[i] = 0;
1081 if (!BN_mod_mul_montgomery(rr,&tmp,&am,mont,ctx)) goto err;
1085 if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
1088 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1091 OPENSSL_cleanse(powerbuf,powerbufLen);
1092 if (powerbufFree) OPENSSL_free(powerbufFree);
1098 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1099 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1101 BN_MONT_CTX *mont = NULL;
1107 #define BN_MOD_MUL_WORD(r, w, m) \
1108 (BN_mul_word(r, (w)) && \
1109 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1110 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1111 /* BN_MOD_MUL_WORD is only used with 'w' large,
1112 * so the BN_ucmp test is probably more overhead
1113 * than always using BN_mod (which uses BN_copy if
1114 * a similar test returns true). */
1115 /* We can use BN_mod and do not need BN_nnmod because our
1116 * accumulator is never negative (the result of BN_mod does
1117 * not depend on the sign of the modulus).
1119 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1120 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1122 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1124 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1125 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1134 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
1138 a %= m->d[0]; /* make sure that 'a' is reduced */
1140 bits = BN_num_bits(p);
1143 /* x**0 mod 1 is still zero. */
1161 d = BN_CTX_get(ctx);
1162 r = BN_CTX_get(ctx);
1163 t = BN_CTX_get(ctx);
1164 if (d == NULL || r == NULL || t == NULL) goto err;
1166 if (in_mont != NULL)
1170 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
1171 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
1174 r_is_one = 1; /* except for Montgomery factor */
1178 /* The result is accumulated in the product r*w. */
1179 w = a; /* bit 'bits-1' of 'p' is always set */
1180 for (b = bits-2; b >= 0; b--)
1182 /* First, square r*w. */
1184 if ((next_w/w) != w) /* overflow */
1188 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1193 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1200 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
1203 /* Second, multiply r*w by 'a' if exponent bit is set. */
1204 if (BN_is_bit_set(p, b))
1207 if ((next_w/a) != w) /* overflow */
1211 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1216 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1224 /* Finally, set r:=r*w. */
1229 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1234 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1238 if (r_is_one) /* can happen only if a == 1*/
1240 if (!BN_one(rr)) goto err;
1244 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
1248 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1255 /* The old fallback, simple version :-) */
1256 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1257 const BIGNUM *m, BN_CTX *ctx)
1259 int i,j,bits,ret=0,wstart,wend,window,wvalue;
1262 /* Table of variables obtained from 'ctx' */
1263 BIGNUM *val[TABLE_SIZE];
1265 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1267 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1268 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1272 bits=BN_num_bits(p);
1281 d = BN_CTX_get(ctx);
1282 val[0] = BN_CTX_get(ctx);
1283 if(!d || !val[0]) goto err;
1285 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
1286 if (BN_is_zero(val[0]))
1293 window = BN_window_bits_for_exponent_size(bits);
1296 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
1301 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
1302 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
1307 start=1; /* This is used to avoid multiplication etc
1308 * when there is only the value '1' in the
1310 wvalue=0; /* The 'value' of the window */
1311 wstart=bits-1; /* The top bit of the window */
1312 wend=0; /* The bottom bit of the window */
1314 if (!BN_one(r)) goto err;
1318 if (BN_is_bit_set(p,wstart) == 0)
1321 if (!BN_mod_mul(r,r,r,m,ctx))
1323 if (wstart == 0) break;
1327 /* We now have wstart on a 'set' bit, we now need to work out
1328 * how bit a window to do. To do this we need to scan
1329 * forward until the last set bit before the end of the
1334 for (i=1; i<window; i++)
1336 if (wstart-i < 0) break;
1337 if (BN_is_bit_set(p,wstart-i))
1345 /* wend is the size of the current window */
1347 /* add the 'bytes above' */
1351 if (!BN_mod_mul(r,r,r,m,ctx))
1355 /* wvalue will be an odd number < 2^window */
1356 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
1359 /* move the 'window' down further */
1363 if (wstart < 0) break;