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;
500 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
503 if (BN_is_bit_set(p,wstart) == 0)
507 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
510 if (wstart == 0) break;
514 /* We now have wstart on a 'set' bit, we now need to work out
515 * how bit a window to do. To do this we need to scan
516 * forward until the last set bit before the end of the
521 for (i=1; i<window; i++)
523 if (wstart-i < 0) break;
524 if (BN_is_bit_set(p,wstart-i))
532 /* wend is the size of the current window */
534 /* add the 'bytes above' */
538 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
542 /* wvalue will be an odd number < 2^window */
543 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
546 /* move the 'window' down further */
550 if (wstart < 0) break;
552 #if defined(SPARC_T4_MONT)
553 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
555 j = mont->N.top; /* borrow j */
556 val[0]->d[0] = 1; /* borrow val[0] */
557 for (i=1;i<j;i++) val[0]->d[i] = 0;
559 if (!BN_mod_mul_montgomery(rr,r,val[0],mont,ctx)) goto err;
563 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
566 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
572 #if defined(SPARC_T4_MONT)
573 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
578 wordpos = bitpos/BN_BITS2;
580 if (wordpos>=0 && wordpos < a->top)
582 ret = a->d[wordpos]&BN_MASK2;
586 if (++wordpos < a->top)
587 ret |= a->d[wordpos]<<(BN_BITS2-bitpos);
595 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
596 * so that accessing any of these table values shows the same access pattern as far
597 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
598 * from/to that table. */
600 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
605 top = b->top; /* this works because 'buf' is explicitly zeroed */
606 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
608 buf[j] = ((unsigned char*)b->d)[i];
614 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
618 if (bn_wexpand(b, top) == NULL)
621 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
623 ((unsigned char*)b->d)[i] = buf[j];
631 /* Given a pointer value, compute the next address that is a cache line multiple. */
632 #define MOD_EXP_CTIME_ALIGN(x_) \
633 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
635 /* This variant of BN_mod_exp_mont() uses fixed windows and the special
636 * precomputation memory layout to limit data-dependency to a minimum
637 * to protect secret exponents (cf. the hyper-threading timing attacks
638 * pointed out by Colin Percival,
639 * http://www.daemonology.net/hyperthreading-considered-harmful/)
641 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
642 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
644 int i,bits,ret=0,window,wvalue;
646 BN_MONT_CTX *mont=NULL;
649 unsigned char *powerbufFree=NULL;
651 unsigned char *powerbuf=NULL;
653 #if defined(SPARC_T4_MONT)
665 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
677 /* Allocate a montgomery context if it was not supplied by the caller.
678 * If this is not done, things will break in the montgomery part.
684 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
685 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
690 * If the size of the operands allow it, perform the optimized
691 * RSAZ exponentiation. For further information see
692 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
694 if (((OPENSSL_ia32cap_P[2]&0x80100) != 0x80100) /* check for MULX/AD*X */
695 && (16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
696 && rsaz_avx2_eligible())
698 if (NULL == bn_wexpand(rr, 16)) goto err;
699 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, mont->n0[0]);
706 else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512))
708 if (NULL == bn_wexpand(rr,8)) goto err;
709 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
718 /* Get the window size to use with size of p. */
719 window = BN_window_bits_for_ctime_exponent_size(bits);
720 #if defined(SPARC_T4_MONT)
721 if (window>=5 && (top&15)==0 && top<=64 &&
722 (OPENSSL_sparcv9cap_P[1]&(CFR_MONTMUL|CFR_MONTSQR))==
723 (CFR_MONTMUL|CFR_MONTSQR) &&
724 (t4=OPENSSL_sparcv9cap_P[0]))
728 #if defined(OPENSSL_BN_ASM_MONT5)
731 window=5; /* ~5% improvement for RSA2048 sign, and even for RSA4096 */
732 if ((top&7)==0) powerbufLen += 2*top*sizeof(m->d[0]);
737 /* Allocate a buffer large enough to hold all of the pre-computed
738 * powers of am, am itself and tmp.
740 numPowers = 1 << window;
741 powerbufLen += sizeof(m->d[0])*(top*numPowers +
742 ((2*top)>numPowers?(2*top):numPowers));
744 if (powerbufLen < 3072)
745 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
748 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
751 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
752 memset(powerbuf, 0, powerbufLen);
755 if (powerbufLen < 3072)
759 /* lay down tmp and am right after powers table */
760 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
762 tmp.top = am.top = 0;
763 tmp.dmax = am.dmax = top;
764 tmp.neg = am.neg = 0;
765 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
767 /* prepare a^0 in Montgomery domain */
768 #if 1 /* by Shay Gueron's suggestion */
769 if (m->d[top-1] & (((BN_ULONG)1)<<(BN_BITS2-1)))
771 /* 2^(top*BN_BITS2) - m */
772 tmp.d[0] = (0-m->d[0])&BN_MASK2;
773 for (i=1;i<top;i++) tmp.d[i] = (~m->d[i])&BN_MASK2;
778 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
780 /* prepare a^1 in Montgomery domain */
781 if (a->neg || BN_ucmp(a,m) >= 0)
783 if (!BN_mod(&am,a,m,ctx)) goto err;
784 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
786 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
788 #if defined(SPARC_T4_MONT)
791 typedef int (*bn_pwr5_mont_f)(BN_ULONG *tp,const BN_ULONG *np,
792 const BN_ULONG *n0,const void *table,int power,int bits);
793 int bn_pwr5_mont_t4_8(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_16(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_24(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_32(BN_ULONG *tp,const BN_ULONG *np,
800 const BN_ULONG *n0,const void *table,int power,int bits);
801 static const bn_pwr5_mont_f pwr5_funcs[4] = {
802 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
803 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32 };
804 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top/16-1];
806 typedef int (*bn_mul_mont_f)(BN_ULONG *rp,const BN_ULONG *ap,
807 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
808 int bn_mul_mont_t4_8(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_16(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_24(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_32(BN_ULONG *rp,const BN_ULONG *ap,
815 const void *bp,const BN_ULONG *np,const BN_ULONG *n0);
816 static const bn_mul_mont_f mul_funcs[4] = {
817 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
818 bn_mul_mont_t4_24, bn_mul_mont_t4_32 };
819 bn_mul_mont_f mul_worker = mul_funcs[top/16-1];
821 void bn_mul_mont_vis3(BN_ULONG *rp,const BN_ULONG *ap,
822 const void *bp,const BN_ULONG *np,
823 const BN_ULONG *n0,int num);
824 void bn_mul_mont_t4(BN_ULONG *rp,const BN_ULONG *ap,
825 const void *bp,const BN_ULONG *np,
826 const BN_ULONG *n0,int num);
827 void bn_mul_mont_gather5_t4(BN_ULONG *rp,const BN_ULONG *ap,
828 const void *table,const BN_ULONG *np,
829 const BN_ULONG *n0,int num,int power);
830 void bn_flip_n_scatter5_t4(const BN_ULONG *inp,size_t num,
831 void *table,size_t power);
832 void bn_gather5_t4(BN_ULONG *out,size_t num,
833 void *table,size_t power);
834 void bn_flip_t4(BN_ULONG *dst,BN_ULONG *src,size_t num);
836 BN_ULONG *np=mont->N.d, *n0=mont->n0;
837 int stride = 5*(6-(top/16-1)); /* multiple of 5, but less than 32 */
839 /* BN_to_montgomery can contaminate words above .top
840 * [in BN_DEBUG[_DEBUG] build]... */
841 for (i=am.top; i<top; i++) am.d[i]=0;
842 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
844 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,0);
845 bn_flip_n_scatter5_t4(am.d,top,powerbuf,1);
846 if (!(*mul_worker)(tmp.d,am.d,am.d,np,n0) &&
847 !(*mul_worker)(tmp.d,am.d,am.d,np,n0))
848 bn_mul_mont_vis3(tmp.d,am.d,am.d,np,n0,top);
849 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,2);
853 /* Calculate a^i = a^(i-1) * a */
854 if (!(*mul_worker)(tmp.d,tmp.d,am.d,np,n0) &&
855 !(*mul_worker)(tmp.d,tmp.d,am.d,np,n0))
856 bn_mul_mont_vis3(tmp.d,tmp.d,am.d,np,n0,top);
857 bn_flip_n_scatter5_t4(tmp.d,top,powerbuf,i);
860 /* switch to 64-bit domain */
861 np = alloca(top*sizeof(BN_ULONG));
863 bn_flip_t4(np,mont->N.d,top);
866 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
867 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
868 bn_gather5_t4(tmp.d,top,powerbuf,wvalue);
870 /* Scan the exponent one window at a time starting from the most
875 if (bits < stride) stride = bits+1;
877 wvalue = bn_get_bits(p,bits+1);
879 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
880 /* retry once and fall back */
881 if ((*pwr5_worker)(tmp.d,np,n0,powerbuf,wvalue,stride)) continue;
886 bn_mul_mont_t4(tmp.d,tmp.d,tmp.d,np,n0,top);
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_gather5_t4(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
894 bn_flip_t4(tmp.d,tmp.d,top);
896 /* back to 32-bit domain */
898 bn_correct_top(&tmp);
899 OPENSSL_cleanse(np,top*sizeof(BN_ULONG));
903 #if defined(OPENSSL_BN_ASM_MONT5)
904 /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
905 * specifically optimization of cache-timing attack countermeasures
906 * and pre-computation optimization. */
908 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
909 * 512-bit RSA is hardly relevant, we omit it to spare size... */
912 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
913 const void *table,const BN_ULONG *np,
914 const BN_ULONG *n0,int num,int power);
915 void bn_scatter5(const BN_ULONG *inp,size_t num,
916 void *table,size_t power);
917 void bn_gather5(BN_ULONG *out,size_t num,
918 void *table,size_t power);
919 void bn_power5(BN_ULONG *rp,const BN_ULONG *ap,
920 const void *table,const BN_ULONG *np,
921 const BN_ULONG *n0,int num,int power);
922 int bn_get_bits5(const BN_ULONG *ap,int off);
923 int bn_from_montgomery(BN_ULONG *rp,const BN_ULONG *ap,
924 const BN_ULONG *not_used,const BN_ULONG *np,
925 const BN_ULONG *n0,int num);
927 BN_ULONG *np=mont->N.d, *n0=mont->n0, *np2;
929 /* BN_to_montgomery can contaminate words above .top
930 * [in BN_DEBUG[_DEBUG] build]... */
931 for (i=am.top; i<top; i++) am.d[i]=0;
932 for (i=tmp.top; i<top; i++) tmp.d[i]=0;
937 for (np2=am.d+top,i=0; i<top; i++) np2[2*i]=np[i];
939 bn_scatter5(tmp.d,top,powerbuf,0);
940 bn_scatter5(am.d,am.top,powerbuf,1);
941 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
942 bn_scatter5(tmp.d,top,powerbuf,2);
947 /* Calculate a^i = a^(i-1) * a */
948 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
949 bn_scatter5(tmp.d,top,powerbuf,i);
952 /* same as above, but uses squaring for 1/2 of operations */
953 for (i=4; i<32; i*=2)
955 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
956 bn_scatter5(tmp.d,top,powerbuf,i);
961 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
962 bn_scatter5(tmp.d,top,powerbuf,i);
963 for (j=2*i; j<32; j*=2)
965 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
966 bn_scatter5(tmp.d,top,powerbuf,j);
971 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
972 bn_scatter5(tmp.d,top,powerbuf,i);
973 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
974 bn_scatter5(tmp.d,top,powerbuf,2*i);
978 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
979 bn_scatter5(tmp.d,top,powerbuf,i);
983 for (wvalue=0, i=bits%5; i>=0; i--,bits--)
984 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
985 bn_gather5(tmp.d,top,powerbuf,wvalue);
987 /* Scan the exponent one window at a time starting from the most
993 for (wvalue=0, i=0; i<5; i++,bits--)
994 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
996 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
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_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
1007 wvalue = bn_get_bits5(p->d,bits-4);
1009 bn_power5(tmp.d,tmp.d,powerbuf,np2,n0,top,wvalue);
1013 ret=bn_from_montgomery(tmp.d,tmp.d,NULL,np2,n0,top);
1015 bn_correct_top(&tmp);
1018 if (!BN_copy(rr,&tmp)) ret=0;
1019 goto err; /* non-zero ret means it's not error */
1025 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
1026 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
1028 /* If the window size is greater than 1, then calculate
1029 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
1030 * (even powers could instead be computed as (a^(i/2))^2
1031 * to use the slight performance advantage of sqr over mul).
1035 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
1036 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
1037 for (i=3; i<numPowers; i++)
1039 /* Calculate a^i = a^(i-1) * a */
1040 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
1042 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
1047 for (wvalue=0, i=bits%window; i>=0; i--,bits--)
1048 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
1049 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
1051 /* Scan the exponent one window at a time starting from the most
1056 wvalue=0; /* The 'value' of the window */
1058 /* Scan the window, squaring the result as we go */
1059 for (i=0; i<window; i++,bits--)
1061 if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err;
1062 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
1065 /* Fetch the appropriate pre-computed value from the pre-buf */
1066 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
1068 /* Multiply the result into the intermediate result */
1069 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
1073 /* Convert the final result from montgomery to standard format */
1074 #if defined(SPARC_T4_MONT)
1075 if (OPENSSL_sparcv9cap_P[0]&(SPARCV9_VIS3|SPARCV9_PREFER_FPU))
1077 am.d[0] = 1; /* borrow am */
1078 for (i=1;i<top;i++) am.d[i] = 0;
1079 if (!BN_mod_mul_montgomery(rr,&tmp,&am,mont,ctx)) goto err;
1083 if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
1086 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1089 OPENSSL_cleanse(powerbuf,powerbufLen);
1090 if (powerbufFree) OPENSSL_free(powerbufFree);
1096 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1097 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1099 BN_MONT_CTX *mont = NULL;
1105 #define BN_MOD_MUL_WORD(r, w, m) \
1106 (BN_mul_word(r, (w)) && \
1107 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1108 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1109 /* BN_MOD_MUL_WORD is only used with 'w' large,
1110 * so the BN_ucmp test is probably more overhead
1111 * than always using BN_mod (which uses BN_copy if
1112 * a similar test returns true). */
1113 /* We can use BN_mod and do not need BN_nnmod because our
1114 * accumulator is never negative (the result of BN_mod does
1115 * not depend on the sign of the modulus).
1117 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1118 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1120 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1122 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1123 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1132 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
1136 a %= m->d[0]; /* make sure that 'a' is reduced */
1138 bits = BN_num_bits(p);
1141 /* x**0 mod 1 is still zero. */
1159 d = BN_CTX_get(ctx);
1160 r = BN_CTX_get(ctx);
1161 t = BN_CTX_get(ctx);
1162 if (d == NULL || r == NULL || t == NULL) goto err;
1164 if (in_mont != NULL)
1168 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
1169 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
1172 r_is_one = 1; /* except for Montgomery factor */
1176 /* The result is accumulated in the product r*w. */
1177 w = a; /* bit 'bits-1' of 'p' is always set */
1178 for (b = bits-2; b >= 0; b--)
1180 /* First, square r*w. */
1182 if ((next_w/w) != w) /* overflow */
1186 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1191 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1198 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
1201 /* Second, multiply r*w by 'a' if exponent bit is set. */
1202 if (BN_is_bit_set(p, b))
1205 if ((next_w/a) != w) /* overflow */
1209 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1214 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1222 /* Finally, set r:=r*w. */
1227 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
1232 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
1236 if (r_is_one) /* can happen only if a == 1*/
1238 if (!BN_one(rr)) goto err;
1242 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
1246 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
1253 /* The old fallback, simple version :-) */
1254 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1255 const BIGNUM *m, BN_CTX *ctx)
1257 int i,j,bits,ret=0,wstart,wend,window,wvalue;
1260 /* Table of variables obtained from 'ctx' */
1261 BIGNUM *val[TABLE_SIZE];
1263 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
1265 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1266 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1270 bits=BN_num_bits(p);
1279 d = BN_CTX_get(ctx);
1280 val[0] = BN_CTX_get(ctx);
1281 if(!d || !val[0]) goto err;
1283 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
1284 if (BN_is_zero(val[0]))
1291 window = BN_window_bits_for_exponent_size(bits);
1294 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
1299 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
1300 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
1305 start=1; /* This is used to avoid multiplication etc
1306 * when there is only the value '1' in the
1308 wvalue=0; /* The 'value' of the window */
1309 wstart=bits-1; /* The top bit of the window */
1310 wend=0; /* The bottom bit of the window */
1312 if (!BN_one(r)) goto err;
1316 if (BN_is_bit_set(p,wstart) == 0)
1319 if (!BN_mod_mul(r,r,r,m,ctx))
1321 if (wstart == 0) break;
1325 /* We now have wstart on a 'set' bit, we now need to work out
1326 * how bit a window to do. To do this we need to scan
1327 * forward until the last set bit before the end of the
1332 for (i=1; i<window; i++)
1334 if (wstart-i < 0) break;
1335 if (BN_is_bit_set(p,wstart-i))
1343 /* wend is the size of the current window */
1345 /* add the 'bytes above' */
1349 if (!BN_mod_mul(r,r,r,m,ctx))
1353 /* wvalue will be an odd number < 2^window */
1354 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
1357 /* move the 'window' down further */
1361 if (wstart < 0) break;