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).
113 #include "cryptlib.h"
120 # define alloca _alloca
122 #elif defined(__GNUC__)
124 # define alloca(s) __builtin_alloca((s))
131 #if defined(OPENSSL_BN_ASM_MONT) && \
132 (defined(__x86_64) || defined(__x86_64__) || \
133 defined(_M_AMD64) || defined(_M_X64))
134 # include "rsaz_exp.h"
135 # define RSAZ_ENABLED
139 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
140 # include "sparc_arch.h"
141 extern unsigned int OPENSSL_sparcv9cap_P[];
142 # define SPARC_T4_MONT
145 /* maximum precomputation table size for *variable* sliding windows */
146 #define TABLE_SIZE 32
148 /* this one works - simple but works */
149 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
154 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
156 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
157 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
162 if ((r == a) || (r == p))
163 rr = BN_CTX_get(ctx);
167 if (rr == NULL || v == NULL) goto err;
169 if (BN_copy(v,a) == NULL) goto err;
173 { if (BN_copy(rr,a) == NULL) goto err; }
174 else { if (!BN_one(rr)) goto err; }
176 for (i=1; i<bits; i++)
178 if (!BN_sqr(v,v,ctx)) goto err;
179 if (BN_is_bit_set(p,i))
181 if (!BN_mul(rr,rr,v,ctx)) goto err;
186 if (r != rr) BN_copy(r,rr);
193 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
202 /* For even modulus m = 2^k*m_odd, it might make sense to compute
203 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
204 * exponentiation for the odd part), using appropriate exponent
205 * reductions, and combine the results using the CRT.
207 * For now, we use Montgomery only if the modulus is odd; otherwise,
208 * exponentiation using the reciprocal-based quick remaindering
211 * (Timing obtained with expspeed.c [computations a^p mod m
212 * where a, p, m are of the same length: 256, 512, 1024, 2048,
213 * 4096, 8192 bits], compared to the running time of the
214 * standard algorithm:
216 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
217 * 55 .. 77 % [UltraSparc processor, but
218 * debug-solaris-sparcv8-gcc conf.]
220 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
221 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
223 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
224 * at 2048 and more bits, but at 512 and 1024 bits, it was
225 * slower even than the standard algorithm!
227 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
228 * should be obtained when the new Montgomery reduction code
229 * has been integrated into OpenSSL.)
233 #define MONT_EXP_WORD
237 /* I have finally been able to take out this pre-condition of
238 * the top bit being set. It was caused by an error in BN_div
239 * with negatives. There was also another problem when for a^b%m
240 * a >= m. eay 07-May-97 */
241 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
245 # ifdef MONT_EXP_WORD
246 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
248 BN_ULONG A = a->d[0];
249 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
253 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
258 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
260 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
268 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
269 const BIGNUM *m, BN_CTX *ctx)
271 int i,j,bits,ret=0,wstart,wend,window,wvalue;
274 /* Table of variables obtained from 'ctx' */
275 BIGNUM *val[TABLE_SIZE];
278 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
280 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
281 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
294 aa = BN_CTX_get(ctx);
295 val[0] = BN_CTX_get(ctx);
296 if(!aa || !val[0]) goto err;
298 BN_RECP_CTX_init(&recp);
301 /* ignore sign of 'm' */
302 if (!BN_copy(aa, m)) goto err;
304 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
308 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
311 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
312 if (BN_is_zero(val[0]))
319 window = BN_window_bits_for_exponent_size(bits);
322 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
327 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
328 !BN_mod_mul_reciprocal(val[i],val[i-1],
334 start=1; /* This is used to avoid multiplication etc
335 * when there is only the value '1' in the
337 wvalue=0; /* The 'value' of the window */
338 wstart=bits-1; /* The top bit of the window */
339 wend=0; /* The bottom bit of the window */
341 if (!BN_one(r)) goto err;
345 if (BN_is_bit_set(p,wstart) == 0)
348 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
350 if (wstart == 0) break;
354 /* We now have wstart on a 'set' bit, we now need to work out
355 * how bit a window to do. To do this we need to scan
356 * forward until the last set bit before the end of the
361 for (i=1; i<window; i++)
363 if (wstart-i < 0) break;
364 if (BN_is_bit_set(p,wstart-i))
372 /* wend is the size of the current window */
374 /* add the 'bytes above' */
378 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
382 /* wvalue will be an odd number < 2^window */
383 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
386 /* move the 'window' down further */
390 if (wstart < 0) break;
395 BN_RECP_CTX_free(&recp);
401 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
402 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
404 int i,j,bits,ret=0,wstart,wend,window,wvalue;
408 /* Table of variables obtained from 'ctx' */
409 BIGNUM *val[TABLE_SIZE];
410 BN_MONT_CTX *mont=NULL;
412 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
414 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
423 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
436 val[0] = BN_CTX_get(ctx);
437 if (!d || !r || !val[0]) goto err;
439 /* If this is not done, things will break in the montgomery
446 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
447 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
450 if (a->neg || BN_ucmp(a,m) >= 0)
452 if (!BN_nnmod(val[0],a,m,ctx))
464 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
466 window = BN_window_bits_for_exponent_size(bits);
469 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
473 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
474 !BN_mod_mul_montgomery(val[i],val[i-1],
480 start=1; /* This is used to avoid multiplication etc
481 * when there is only the value '1' in the
483 wvalue=0; /* The 'value' of the window */
484 wstart=bits-1; /* The top bit of the window */
485 wend=0; /* The bottom bit of the window */
487 #if 1 /* by Shay Gueron's suggestion */
488 j = m->top; /* borrow j */
489 if (m->d[j-1] & (((BN_ULONG)1)<<(BN_BITS2-1)))
491 if (bn_wexpand(r,j) == NULL) goto err;
492 /* 2^(top*BN_BITS2) - m */
493 r->d[0] = (0-m->d[0])&BN_MASK2;
494 for(i=1;i<j;i++) r->d[i] = (~m->d[i])&BN_MASK2;
496 /* Upper words will be zero if the corresponding words of 'm'
497 * were 0xfff[...], so decrement r->top accordingly. */
502 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
505 if (BN_is_bit_set(p,wstart) == 0)
509 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
512 if (wstart == 0) break;
516 /* We now have wstart on a 'set' bit, we now need to work out
517 * how bit a window to do. To do this we need to scan
518 * forward until the last set bit before the end of the
523 for (i=1; i<window; i++)
525 if (wstart-i < 0) break;
526 if (BN_is_bit_set(p,wstart-i))
534 /* wend is the size of the current window */
536 /* add the 'bytes above' */
540 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
544 /* wvalue will be an odd number < 2^window */
545 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
548 /* move the 'window' down further */
552 if (wstart < 0) break;
554 #if defined(SPARC_T4_MONT)
555 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
557 j = mont->N.top; /* borrow j */
558 val[0]->d[0] = 1; /* borrow val[0] */
559 for (i=1;i<j;i++) val[0]->d[i] = 0;
561 if (!BN_mod_mul_montgomery(rr,r,val[0],mont,ctx)) goto err;
565 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
568 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
574 #if defined(SPARC_T4_MONT)
575 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
580 wordpos = bitpos/BN_BITS2;
582 if (wordpos>=0 && wordpos < a->top)
584 ret = a->d[wordpos]&BN_MASK2;
588 if (++wordpos < a->top)
589 ret |= a->d[wordpos]<<(BN_BITS2-bitpos);
597 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
598 * so that accessing any of these table values shows the same access pattern as far
599 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
600 * from/to that table. */
602 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
607 top = b->top; /* this works because 'buf' is explicitly zeroed */
608 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
610 buf[j] = ((unsigned char*)b->d)[i];
616 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
620 if (bn_wexpand(b, top) == NULL)
623 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
625 ((unsigned char*)b->d)[i] = buf[j];
633 /* Given a pointer value, compute the next address that is a cache line multiple. */
634 #define MOD_EXP_CTIME_ALIGN(x_) \
635 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
637 /* This variant of BN_mod_exp_mont() uses fixed windows and the special
638 * precomputation memory layout to limit data-dependency to a minimum
639 * to protect secret exponents (cf. the hyper-threading timing attacks
640 * pointed out by Colin Percival,
641 * http://www.daemonology.net/hyperthreading-considered-harmful/)
643 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
644 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
646 int i,bits,ret=0,window,wvalue;
648 BN_MONT_CTX *mont=NULL;
651 unsigned char *powerbufFree=NULL;
653 unsigned char *powerbuf=NULL;
655 #if defined(SPARC_T4_MONT)
667 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
679 /* Allocate a montgomery context if it was not supplied by the caller.
680 * If this is not done, things will break in the montgomery part.
686 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
687 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
692 * If the size of the operands allow it, perform the optimized
693 * RSAZ exponentiation. For further information see
694 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
696 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
697 && rsaz_avx2_eligible())
699 if (NULL == bn_wexpand(rr, 16)) goto err;
700 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, mont->n0[0]);
707 else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512))
709 if (NULL == bn_wexpand(rr,8)) goto err;
710 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
719 /* Get the window size to use with size of p. */
720 window = BN_window_bits_for_ctime_exponent_size(bits);
721 #if defined(SPARC_T4_MONT)
722 if (window>=5 && (top&15)==0 && top<=64 &&
723 (OPENSSL_sparcv9cap_P[1]&(CFR_MONTMUL|CFR_MONTSQR))==
724 (CFR_MONTMUL|CFR_MONTSQR) &&
725 (t4=OPENSSL_sparcv9cap_P[0]))
729 #if defined(OPENSSL_BN_ASM_MONT5)
732 window=5; /* ~5% improvement for RSA2048 sign, and even for RSA4096 */
733 if ((top&7)==0) powerbufLen += 2*top*sizeof(m->d[0]);
738 /* Allocate a buffer large enough to hold all of the pre-computed
739 * powers of am, am itself and tmp.
741 numPowers = 1 << window;
742 powerbufLen += sizeof(m->d[0])*(top*numPowers +
743 ((2*top)>numPowers?(2*top):numPowers));
745 if (powerbufLen < 3072)
746 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
749 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
752 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
753 memset(powerbuf, 0, powerbufLen);
756 if (powerbufLen < 3072)
760 /* lay down tmp and am right after powers table */
761 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
763 tmp.top = am.top = 0;
764 tmp.dmax = am.dmax = top;
765 tmp.neg = am.neg = 0;
766 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
768 /* prepare a^0 in Montgomery domain */
769 #if 1 /* by Shay Gueron's suggestion */
770 if (m->d[top-1] & (((BN_ULONG)1)<<(BN_BITS2-1)))
772 /* 2^(top*BN_BITS2) - m */
773 tmp.d[0] = (0-m->d[0])&BN_MASK2;
774 for (i=1;i<top;i++) tmp.d[i] = (~m->d[i])&BN_MASK2;
779 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
781 /* prepare a^1 in Montgomery domain */
782 if (a->neg || BN_ucmp(a,m) >= 0)
784 if (!BN_mod(&am,a,m,ctx)) goto err;
785 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
787 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
789 #if defined(SPARC_T4_MONT)
792 typedef int (*bn_pwr5_mont_f)(BN_ULONG *tp,const BN_ULONG *np,
793 const BN_ULONG *n0,const void *table,int power,int bits);
794 int bn_pwr5_mont_t4_8(BN_ULONG *tp,const BN_ULONG *np,
795 const BN_ULONG *n0,const void *table,int power,int bits);
796 int bn_pwr5_mont_t4_16(BN_ULONG *tp,const BN_ULONG *np,
797 const BN_ULONG *n0,const void *table,int power,int bits);
798 int bn_pwr5_mont_t4_24(BN_ULONG *tp,const BN_ULONG *np,
799 const BN_ULONG *n0,const void *table,int power,int bits);
800 int bn_pwr5_mont_t4_32(BN_ULONG *tp,const BN_ULONG *np,
801 const BN_ULONG *n0,const void *table,int power,int bits);
802 static const bn_pwr5_mont_f pwr5_funcs[4] = {
803 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
804 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 };
805 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top/16-1];
807 typedef int (*bn_mul_mont_f)(BN_ULONG *rp,const BN_ULONG *ap,
808 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
809 int bn_mul_mont_t4_8(BN_ULONG *rp,const BN_ULONG *ap,
810 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
811 int bn_mul_mont_t4_16(BN_ULONG *rp,const BN_ULONG *ap,
812 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
813 int bn_mul_mont_t4_24(BN_ULONG *rp,const BN_ULONG *ap,
814 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
815 int bn_mul_mont_t4_32(BN_ULONG *rp,const BN_ULONG *ap,
816 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
817 static const bn_mul_mont_f mul_funcs[4] = {
818 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
819 bn_mul_mont_t4_24, bn_mul_mont_t4_32 };
820 bn_mul_mont_f mul_worker = mul_funcs[top/16-1];
822 void bn_mul_mont_vis3(BN_ULONG *rp,const BN_ULONG *ap,
823 const void *bp,const BN_ULONG *np,
824 const BN_ULONG *n0,int num);
825 void bn_mul_mont_t4(BN_ULONG *rp,const BN_ULONG *ap,
826 const void *bp,const BN_ULONG *np,
827 const BN_ULONG *n0,int num);
828 void bn_mul_mont_gather5_t4(BN_ULONG *rp,const BN_ULONG *ap,
829 const void *table,const BN_ULONG *np,
830 const BN_ULONG *n0,int num,int power);
831 void bn_flip_n_scatter5_t4(const BN_ULONG *inp,size_t num,
832 void *table,size_t power);
833 void bn_gather5_t4(BN_ULONG *out,size_t num,
834 void *table,size_t power);
835 void bn_flip_t4(BN_ULONG *dst,BN_ULONG *src,size_t num);
837 BN_ULONG *np=mont->N.d, *n0=mont->n0;
838 int stride = 5*(6-(top/16-1)); /* multiple of 5, but less than 32 */
840 /* BN_to_montgomery can contaminate words above .top
841 * [in BN_DEBUG[_DEBUG] build]... */
842 for (i=am.top; i<top; i++) am.d[i]=0;
843 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
845 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,0);
846 bn_flip_n_scatter5_t4(am.d,top,powerbuf,1);
847 if (!(*mul_worker)(tmp.d,am.d,am.d,np,n0) &&
848 !(*mul_worker)(tmp.d,am.d,am.d,np,n0))
849 bn_mul_mont_vis3(tmp.d,am.d,am.d,np,n0,top);
850 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,2);
854 /* Calculate a^i = a^(i-1) * a */
855 if (!(*mul_worker)(tmp.d,tmp.d,am.d,np,n0) &&
856 !(*mul_worker)(tmp.d,tmp.d,am.d,np,n0))
857 bn_mul_mont_vis3(tmp.d,tmp.d,am.d,np,n0,top);
858 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,i);
861 /* switch to 64-bit domain */
862 np = alloca(top*sizeof(BN_ULONG));
864 bn_flip_t4(np,mont->N.d,top);
867 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
868 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
869 bn_gather5_t4(tmp.d,top,powerbuf,wvalue);
871 /* Scan the exponent one window at a time starting from the most
876 if (bits < stride) stride = bits+1;
878 wvalue = bn_get_bits(p,bits+1);
880 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
881 /* retry once and fall back */
882 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
887 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
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_gather5_t4(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
895 bn_flip_t4(tmp.d,tmp.d,top);
897 /* back to 32-bit domain */
899 bn_correct_top(&tmp);
900 OPENSSL_cleanse(np,top*sizeof(BN_ULONG));
904 #if defined(OPENSSL_BN_ASM_MONT5)
905 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
906 * specifically optimization of cache-timing attack countermeasures
907 * and pre-computation optimization. */
909 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
910 * 512-bit RSA is hardly relevant, we omit it to spare size... */
911 if (window==5 && top>1)
913 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
914 const void *table,const BN_ULONG *np,
915 const BN_ULONG *n0,int num,int power);
916 void bn_scatter5(const BN_ULONG *inp,size_t num,
917 void *table,size_t power);
918 void bn_gather5(BN_ULONG *out,size_t num,
919 void *table,size_t power);
920 void bn_power5(BN_ULONG *rp,const BN_ULONG *ap,
921 const void *table,const BN_ULONG *np,
922 const BN_ULONG *n0,int num,int power);
923 int bn_get_bits5(const BN_ULONG *ap,int off);
924 int bn_from_montgomery(BN_ULONG *rp,const BN_ULONG *ap,
925 const BN_ULONG *not_used,const BN_ULONG *np,
926 const BN_ULONG *n0,int num);
928 BN_ULONG *np=mont->N.d, *n0=mont->n0, *np2;
930 /* BN_to_montgomery can contaminate words above .top
931 * [in BN_DEBUG[_DEBUG] build]... */
932 for (i=am.top; i<top; i++) am.d[i]=0;
933 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
938 for (np2=am.d+top,i=0; i<top; i++) np2[2*i]=np[i];
940 bn_scatter5(tmp.d,top,powerbuf,0);
941 bn_scatter5(am.d,am.top,powerbuf,1);
942 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
943 bn_scatter5(tmp.d,top,powerbuf,2);
948 /* Calculate a^i = a^(i-1) * a */
949 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
950 bn_scatter5(tmp.d,top,powerbuf,i);
953 /* same as above, but uses squaring for 1/2 of operations */
954 for (i=4; i<32; i*=2)
956 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
957 bn_scatter5(tmp.d,top,powerbuf,i);
962 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
963 bn_scatter5(tmp.d,top,powerbuf,i);
964 for (j=2*i; j<32; j*=2)
966 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
967 bn_scatter5(tmp.d,top,powerbuf,j);
972 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
973 bn_scatter5(tmp.d,top,powerbuf,i);
974 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
975 bn_scatter5(tmp.d,top,powerbuf,2*i);
979 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
980 bn_scatter5(tmp.d,top,powerbuf,i);
984 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
985 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
986 bn_gather5(tmp.d,top,powerbuf,wvalue);
988 /* Scan the exponent one window at a time starting from the most
994 for (wvalue=0, i=0; i<5; i++,bits--)
995 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
997 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
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_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
1008 wvalue = bn_get_bits5(p->d,bits-4);
1010 bn_power5(tmp.d,tmp.d,powerbuf,np2,n0,top,wvalue);
1014 ret=bn_from_montgomery(tmp.d,tmp.d,NULL,np2,n0,top);
1016 bn_correct_top(&tmp);
1019 if (!BN_copy(rr,&tmp)) ret=0;
1020 goto err; /* non-zero ret means it's not error */
1026 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
1027 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
1029 /* If the window size is greater than 1, then calculate
1030 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
1031 * (even powers could instead be computed as (a^(i/2))^2
1032 * to use the slight performance advantage of sqr over mul).
1036 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
1037 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
1038 for (i=3; i<numPowers; i++)
1040 /* Calculate a^i = a^(i-1) * a */
1041 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
1043 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
1048 for (wvalue=0, i=bits%window; i>=0; i--,bits--)
1049 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
1050 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
1052 /* Scan the exponent one window at a time starting from the most
1057 wvalue=0; /* The 'value' of the window */
1059 /* Scan the window, squaring the result as we go */
1060 for (i=0; i<window; i++,bits--)
1062 if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err;
1063 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
1066 /* Fetch the appropriate pre-computed value from the pre-buf */
1067 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
1069 /* Multiply the result into the intermediate result */
1070 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
1074 /* Convert the final result from montgomery to standard format */
1075 #if defined(SPARC_T4_MONT)
1076 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
1078 am.d[0] = 1; /* borrow am */
1079 for (i=1;i<top;i++) am.d[i] = 0;
1080 if (!BN_mod_mul_montgomery(rr,&tmp,&am,mont,ctx)) goto err;
1084 if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
1087 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1090 OPENSSL_cleanse(powerbuf,powerbufLen);
1091 if (powerbufFree) OPENSSL_free(powerbufFree);
1097 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1098 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1100 BN_MONT_CTX *mont = NULL;
1106 #define BN_MOD_MUL_WORD(r, w, m) \
1107 (BN_mul_word(r, (w)) && \
1108 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1109 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1110 /* BN_MOD_MUL_WORD is only used with 'w' large,
1111 * so the BN_ucmp test is probably more overhead
1112 * than always using BN_mod (which uses BN_copy if
1113 * a similar test returns true). */
1114 /* We can use BN_mod and do not need BN_nnmod because our
1115 * accumulator is never negative (the result of BN_mod does
1116 * not depend on the sign of the modulus).
1118 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1119 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1121 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1123 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1124 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1133 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
1137 a %= m->d[0]; /* make sure that 'a' is reduced */
1139 bits = BN_num_bits(p);
1142 /* x**0 mod 1 is still zero. */
1160 d = BN_CTX_get(ctx);
1161 r = BN_CTX_get(ctx);
1162 t = BN_CTX_get(ctx);
1163 if (d == NULL || r == NULL || t == NULL) goto err;
1165 if (in_mont != NULL)
1169 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
1170 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
1173 r_is_one = 1; /* except for Montgomery factor */
1177 /* The result is accumulated in the product r*w. */
1178 w = a; /* bit 'bits-1' of 'p' is always set */
1179 for (b = bits-2; b >= 0; b--)
1181 /* First, square r*w. */
1183 if ((next_w/w) != w) /* overflow */
1187 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1192 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1199 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
1202 /* Second, multiply r*w by 'a' if exponent bit is set. */
1203 if (BN_is_bit_set(p, b))
1206 if ((next_w/a) != w) /* overflow */
1210 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1215 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1223 /* Finally, set r:=r*w. */
1228 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1233 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1237 if (r_is_one) /* can happen only if a == 1*/
1239 if (!BN_one(rr)) goto err;
1243 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
1247 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1254 /* The old fallback, simple version :-) */
1255 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1256 const BIGNUM *m, BN_CTX *ctx)
1258 int i,j,bits,ret=0,wstart,wend,window,wvalue;
1261 /* Table of variables obtained from 'ctx' */
1262 BIGNUM *val[TABLE_SIZE];
1264 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1266 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1267 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1271 bits=BN_num_bits(p);
1280 d = BN_CTX_get(ctx);
1281 val[0] = BN_CTX_get(ctx);
1282 if(!d || !val[0]) goto err;
1284 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
1285 if (BN_is_zero(val[0]))
1292 window = BN_window_bits_for_exponent_size(bits);
1295 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
1300 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
1301 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
1306 start=1; /* This is used to avoid multiplication etc
1307 * when there is only the value '1' in the
1309 wvalue=0; /* The 'value' of the window */
1310 wstart=bits-1; /* The top bit of the window */
1311 wend=0; /* The bottom bit of the window */
1313 if (!BN_one(r)) goto err;
1317 if (BN_is_bit_set(p,wstart) == 0)
1320 if (!BN_mod_mul(r,r,r,m,ctx))
1322 if (wstart == 0) break;
1326 /* We now have wstart on a 'set' bit, we now need to work out
1327 * how bit a window to do. To do this we need to scan
1328 * forward until the last set bit before the end of the
1333 for (i=1; i<window; i++)
1335 if (wstart-i < 0) break;
1336 if (BN_is_bit_set(p,wstart-i))
1344 /* wend is the size of the current window */
1346 /* add the 'bytes above' */
1350 if (!BN_mod_mul(r,r,r,m,ctx))
1354 /* wvalue will be an odd number < 2^window */
1355 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
1358 /* move the 'window' down further */
1362 if (wstart < 0) break;