82b2f57e30
the same thing. Also, I have some stuff on the back-burner related to some BN_CTX notes from Peter Gutmann about his cryptlib hacks to the bignum code. The BN_CTX comments are there to remind me of some relevant points in the code.
754 lines
19 KiB
C
754 lines
19 KiB
C
/* crypto/bn/bn_exp.c */
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/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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* All rights reserved.
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*
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* This package is an SSL implementation written
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* by Eric Young (eay@cryptsoft.com).
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* The implementation was written so as to conform with Netscapes SSL.
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*
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* This library is free for commercial and non-commercial use as long as
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* the following conditions are aheared to. The following conditions
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* apply to all code found in this distribution, be it the RC4, RSA,
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* lhash, DES, etc., code; not just the SSL code. The SSL documentation
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* included with this distribution is covered by the same copyright terms
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* except that the holder is Tim Hudson (tjh@cryptsoft.com).
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*
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* Copyright remains Eric Young's, and as such any Copyright notices in
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* the code are not to be removed.
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* If this package is used in a product, Eric Young should be given attribution
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* as the author of the parts of the library used.
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* This can be in the form of a textual message at program startup or
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* in documentation (online or textual) provided with the package.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* "This product includes cryptographic software written by
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* Eric Young (eay@cryptsoft.com)"
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* The word 'cryptographic' can be left out if the rouines from the library
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* being used are not cryptographic related :-).
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* 4. If you include any Windows specific code (or a derivative thereof) from
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* the apps directory (application code) you must include an acknowledgement:
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* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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*
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* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* The licence and distribution terms for any publically available version or
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* derivative of this code cannot be changed. i.e. this code cannot simply be
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* copied and put under another distribution licence
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* [including the GNU Public Licence.]
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*/
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/* ====================================================================
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* Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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*
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* 3. All advertising materials mentioning features or use of this
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* software must display the following acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
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*
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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* endorse or promote products derived from this software without
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* prior written permission. For written permission, please contact
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* openssl-core@openssl.org.
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*
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* 5. Products derived from this software may not be called "OpenSSL"
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* nor may "OpenSSL" appear in their names without prior written
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* permission of the OpenSSL Project.
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*
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* 6. Redistributions of any form whatsoever must retain the following
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* acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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*
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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* ====================================================================
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*
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* This product includes cryptographic software written by Eric Young
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* (eay@cryptsoft.com). This product includes software written by Tim
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* Hudson (tjh@cryptsoft.com).
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*
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*/
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#include "cryptlib.h"
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#include "bn_lcl.h"
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#define TABLE_SIZE 32
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/* this one works - simple but works */
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int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
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{
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int i,bits,ret=0;
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BIGNUM *v,*rr;
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BN_CTX_start(ctx);
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if ((r == a) || (r == p))
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rr = BN_CTX_get(ctx);
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else
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rr = r;
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if ((v = BN_CTX_get(ctx)) == NULL) goto err;
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if (BN_copy(v,a) == NULL) goto err;
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bits=BN_num_bits(p);
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if (BN_is_odd(p))
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{ if (BN_copy(rr,a) == NULL) goto err; }
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else { if (!BN_one(rr)) goto err; }
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for (i=1; i<bits; i++)
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{
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if (!BN_sqr(v,v,ctx)) goto err;
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if (BN_is_bit_set(p,i))
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{
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if (!BN_mul(rr,rr,v,ctx)) goto err;
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}
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}
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ret=1;
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err:
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if (r != rr) BN_copy(r,rr);
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BN_CTX_end(ctx);
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bn_check_top(r);
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return(ret);
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}
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int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
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BN_CTX *ctx)
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{
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int ret;
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bn_check_top(a);
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bn_check_top(p);
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bn_check_top(m);
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/* For even modulus m = 2^k*m_odd, it might make sense to compute
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* a^p mod m_odd and a^p mod 2^k separately (with Montgomery
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* exponentiation for the odd part), using appropriate exponent
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* reductions, and combine the results using the CRT.
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*
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* For now, we use Montgomery only if the modulus is odd; otherwise,
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* exponentiation using the reciprocal-based quick remaindering
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* algorithm is used.
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*
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* (Timing obtained with expspeed.c [computations a^p mod m
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* where a, p, m are of the same length: 256, 512, 1024, 2048,
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* 4096, 8192 bits], compared to the running time of the
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* standard algorithm:
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*
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* BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
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* 55 .. 77 % [UltraSparc processor, but
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* debug-solaris-sparcv8-gcc conf.]
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*
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* BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
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* 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
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*
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* On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
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* at 2048 and more bits, but at 512 and 1024 bits, it was
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* slower even than the standard algorithm!
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*
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* "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
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* should be obtained when the new Montgomery reduction code
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* has been integrated into OpenSSL.)
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*/
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#define MONT_MUL_MOD
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#define MONT_EXP_WORD
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#define RECP_MUL_MOD
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#ifdef MONT_MUL_MOD
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/* I have finally been able to take out this pre-condition of
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* the top bit being set. It was caused by an error in BN_div
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* with negatives. There was also another problem when for a^b%m
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* a >= m. eay 07-May-97 */
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/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
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if (BN_is_odd(m))
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{
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# ifdef MONT_EXP_WORD
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if (a->top == 1 && !a->neg)
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{
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BN_ULONG A = a->d[0];
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ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
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}
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else
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# endif
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ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
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}
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else
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#endif
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#ifdef RECP_MUL_MOD
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{ ret=BN_mod_exp_recp(r,a,p,m,ctx); }
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#else
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{ ret=BN_mod_exp_simple(r,a,p,m,ctx); }
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#endif
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bn_check_top(r);
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return(ret);
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}
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int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
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const BIGNUM *m, BN_CTX *ctx)
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{
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int i,j,bits,ret=0,wstart,wend,window,wvalue;
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int start=1,ts=0;
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BIGNUM *aa;
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BIGNUM val[TABLE_SIZE];
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BN_RECP_CTX recp;
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bits=BN_num_bits(p);
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if (bits == 0)
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{
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ret = BN_one(r);
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return ret;
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}
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BN_CTX_start(ctx);
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if ((aa = BN_CTX_get(ctx)) == NULL) goto err;
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BN_RECP_CTX_init(&recp);
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if (m->neg)
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{
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/* ignore sign of 'm' */
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if (!BN_copy(aa, m)) goto err;
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aa->neg = 0;
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if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
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}
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else
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{
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if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
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}
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BN_init(&(val[0]));
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ts=1;
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if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
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if (BN_is_zero(&(val[0])))
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{
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ret = BN_zero(r);
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goto err;
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}
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window = BN_window_bits_for_exponent_size(bits);
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if (window > 1)
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{
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if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
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goto err; /* 2 */
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j=1<<(window-1);
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for (i=1; i<j; i++)
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{
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BN_init(&val[i]);
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if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
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goto err;
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}
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ts=i;
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}
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start=1; /* This is used to avoid multiplication etc
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* when there is only the value '1' in the
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* buffer. */
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wvalue=0; /* The 'value' of the window */
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wstart=bits-1; /* The top bit of the window */
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wend=0; /* The bottom bit of the window */
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if (!BN_one(r)) goto err;
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for (;;)
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{
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if (BN_is_bit_set(p,wstart) == 0)
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{
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if (!start)
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if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
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goto err;
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if (wstart == 0) break;
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wstart--;
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continue;
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}
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/* We now have wstart on a 'set' bit, we now need to work out
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* how bit a window to do. To do this we need to scan
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* forward until the last set bit before the end of the
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* window */
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j=wstart;
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wvalue=1;
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wend=0;
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for (i=1; i<window; i++)
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{
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if (wstart-i < 0) break;
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if (BN_is_bit_set(p,wstart-i))
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{
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wvalue<<=(i-wend);
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wvalue|=1;
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wend=i;
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}
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}
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/* wend is the size of the current window */
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j=wend+1;
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/* add the 'bytes above' */
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if (!start)
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for (i=0; i<j; i++)
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{
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if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
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goto err;
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}
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/* wvalue will be an odd number < 2^window */
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if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
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goto err;
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/* move the 'window' down further */
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wstart-=wend+1;
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wvalue=0;
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start=0;
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if (wstart < 0) break;
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}
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ret=1;
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err:
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BN_CTX_end(ctx);
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for (i=0; i<ts; i++)
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BN_clear_free(&(val[i]));
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BN_RECP_CTX_free(&recp);
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bn_check_top(r);
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return(ret);
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}
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int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
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const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
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{
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int i,j,bits,ret=0,wstart,wend,window,wvalue;
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int start=1,ts=0;
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BIGNUM *d,*r;
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const BIGNUM *aa;
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/* TODO: BN_CTX??? */
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BIGNUM val[TABLE_SIZE];
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BN_MONT_CTX *mont=NULL;
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bn_check_top(a);
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bn_check_top(p);
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bn_check_top(m);
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if (!BN_is_odd(m))
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{
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BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
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return(0);
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}
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bits=BN_num_bits(p);
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if (bits == 0)
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{
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ret = BN_one(rr);
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return ret;
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}
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BN_CTX_start(ctx);
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d = BN_CTX_get(ctx);
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r = BN_CTX_get(ctx);
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if (d == NULL || r == NULL) goto err;
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/* If this is not done, things will break in the montgomery
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* part */
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if (in_mont != NULL)
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mont=in_mont;
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else
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{
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if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
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if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
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}
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BN_init(&val[0]);
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ts=1;
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if (a->neg || BN_ucmp(a,m) >= 0)
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{
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if (!BN_nnmod(&(val[0]),a,m,ctx))
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goto err;
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aa= &(val[0]);
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|
}
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|
else
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aa=a;
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if (BN_is_zero(aa))
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{
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ret = BN_zero(rr);
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goto err;
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|
}
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if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */
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window = BN_window_bits_for_exponent_size(bits);
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if (window > 1)
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{
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if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
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j=1<<(window-1);
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for (i=1; i<j; i++)
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{
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BN_init(&(val[i]));
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if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
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goto err;
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|
}
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|
ts=i;
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|
}
|
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|
|
start=1; /* This is used to avoid multiplication etc
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* when there is only the value '1' in the
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|
* buffer. */
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wvalue=0; /* The 'value' of the window */
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|
wstart=bits-1; /* The top bit of the window */
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|
wend=0; /* The bottom bit of the window */
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|
|
|
if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
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|
for (;;)
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|
{
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|
if (BN_is_bit_set(p,wstart) == 0)
|
|
{
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|
if (!start)
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|
{
|
|
if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
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|
goto err;
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|
}
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|
if (wstart == 0) break;
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|
wstart--;
|
|
continue;
|
|
}
|
|
/* We now have wstart on a 'set' bit, we now need to work out
|
|
* how bit a window to do. To do this we need to scan
|
|
* forward until the last set bit before the end of the
|
|
* window */
|
|
j=wstart;
|
|
wvalue=1;
|
|
wend=0;
|
|
for (i=1; i<window; i++)
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|
{
|
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if (wstart-i < 0) break;
|
|
if (BN_is_bit_set(p,wstart-i))
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|
{
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wvalue<<=(i-wend);
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wvalue|=1;
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wend=i;
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|
}
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|
}
|
|
|
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/* wend is the size of the current window */
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|
j=wend+1;
|
|
/* add the 'bytes above' */
|
|
if (!start)
|
|
for (i=0; i<j; i++)
|
|
{
|
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if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
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|
goto err;
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|
}
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|
|
|
/* wvalue will be an odd number < 2^window */
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|
if (!BN_mod_mul_montgomery(r,r,&(val[wvalue>>1]),mont,ctx))
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|
goto err;
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|
|
|
/* move the 'window' down further */
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|
wstart-=wend+1;
|
|
wvalue=0;
|
|
start=0;
|
|
if (wstart < 0) break;
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|
}
|
|
if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
|
|
ret=1;
|
|
err:
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|
if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
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|
BN_CTX_end(ctx);
|
|
for (i=0; i<ts; i++)
|
|
BN_clear_free(&(val[i]));
|
|
bn_check_top(rr);
|
|
return(ret);
|
|
}
|
|
|
|
int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
|
|
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
|
|
{
|
|
BN_MONT_CTX *mont = NULL;
|
|
int b, bits, ret=0;
|
|
int r_is_one;
|
|
BN_ULONG w, next_w;
|
|
BIGNUM *d, *r, *t;
|
|
BIGNUM *swap_tmp;
|
|
#define BN_MOD_MUL_WORD(r, w, m) \
|
|
(BN_mul_word(r, (w)) && \
|
|
(/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
|
|
(BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
|
|
/* BN_MOD_MUL_WORD is only used with 'w' large,
|
|
* so the BN_ucmp test is probably more overhead
|
|
* than always using BN_mod (which uses BN_copy if
|
|
* a similar test returns true). */
|
|
/* We can use BN_mod and do not need BN_nnmod because our
|
|
* accumulator is never negative (the result of BN_mod does
|
|
* not depend on the sign of the modulus).
|
|
*/
|
|
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
|
|
(BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
|
|
|
|
bn_check_top(p);
|
|
bn_check_top(m);
|
|
|
|
if (!BN_is_odd(m))
|
|
{
|
|
BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
|
|
return(0);
|
|
}
|
|
if (m->top == 1)
|
|
a %= m->d[0]; /* make sure that 'a' is reduced */
|
|
|
|
bits = BN_num_bits(p);
|
|
if (bits == 0)
|
|
{
|
|
ret = BN_one(rr);
|
|
return ret;
|
|
}
|
|
if (a == 0)
|
|
{
|
|
ret = BN_zero(rr);
|
|
return ret;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
d = BN_CTX_get(ctx);
|
|
r = BN_CTX_get(ctx);
|
|
t = BN_CTX_get(ctx);
|
|
if (d == NULL || r == NULL || t == NULL) goto err;
|
|
|
|
if (in_mont != NULL)
|
|
mont=in_mont;
|
|
else
|
|
{
|
|
if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
|
|
if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
|
|
}
|
|
|
|
r_is_one = 1; /* except for Montgomery factor */
|
|
|
|
/* bits-1 >= 0 */
|
|
|
|
/* The result is accumulated in the product r*w. */
|
|
w = a; /* bit 'bits-1' of 'p' is always set */
|
|
for (b = bits-2; b >= 0; b--)
|
|
{
|
|
/* First, square r*w. */
|
|
next_w = w*w;
|
|
if ((next_w/w) != w) /* overflow */
|
|
{
|
|
if (r_is_one)
|
|
{
|
|
if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
|
|
r_is_one = 0;
|
|
}
|
|
else
|
|
{
|
|
if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
|
|
}
|
|
next_w = 1;
|
|
}
|
|
w = next_w;
|
|
if (!r_is_one)
|
|
{
|
|
if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
|
|
}
|
|
|
|
/* Second, multiply r*w by 'a' if exponent bit is set. */
|
|
if (BN_is_bit_set(p, b))
|
|
{
|
|
next_w = w*a;
|
|
if ((next_w/a) != w) /* overflow */
|
|
{
|
|
if (r_is_one)
|
|
{
|
|
if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
|
|
r_is_one = 0;
|
|
}
|
|
else
|
|
{
|
|
if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
|
|
}
|
|
next_w = a;
|
|
}
|
|
w = next_w;
|
|
}
|
|
}
|
|
|
|
/* Finally, set r:=r*w. */
|
|
if (w != 1)
|
|
{
|
|
if (r_is_one)
|
|
{
|
|
if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
|
|
r_is_one = 0;
|
|
}
|
|
else
|
|
{
|
|
if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
|
|
}
|
|
}
|
|
|
|
if (r_is_one) /* can happen only if a == 1*/
|
|
{
|
|
if (!BN_one(rr)) goto err;
|
|
}
|
|
else
|
|
{
|
|
if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
|
|
}
|
|
ret = 1;
|
|
err:
|
|
if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(rr);
|
|
return(ret);
|
|
}
|
|
|
|
|
|
/* The old fallback, simple version :-) */
|
|
int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
|
|
const BIGNUM *m, BN_CTX *ctx)
|
|
{
|
|
int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
|
|
int start=1;
|
|
BIGNUM *d;
|
|
/* TODO: BN_CTX?? */
|
|
BIGNUM val[TABLE_SIZE];
|
|
|
|
bits=BN_num_bits(p);
|
|
|
|
if (bits == 0)
|
|
{
|
|
ret = BN_one(r);
|
|
return ret;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
if ((d = BN_CTX_get(ctx)) == NULL) goto err;
|
|
|
|
BN_init(&(val[0]));
|
|
ts=1;
|
|
if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
|
|
if (BN_is_zero(&(val[0])))
|
|
{
|
|
ret = BN_zero(r);
|
|
goto err;
|
|
}
|
|
|
|
window = BN_window_bits_for_exponent_size(bits);
|
|
if (window > 1)
|
|
{
|
|
if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
|
|
goto err; /* 2 */
|
|
j=1<<(window-1);
|
|
for (i=1; i<j; i++)
|
|
{
|
|
BN_init(&(val[i]));
|
|
if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
|
|
goto err;
|
|
}
|
|
ts=i;
|
|
}
|
|
|
|
start=1; /* This is used to avoid multiplication etc
|
|
* when there is only the value '1' in the
|
|
* buffer. */
|
|
wvalue=0; /* The 'value' of the window */
|
|
wstart=bits-1; /* The top bit of the window */
|
|
wend=0; /* The bottom bit of the window */
|
|
|
|
if (!BN_one(r)) goto err;
|
|
|
|
for (;;)
|
|
{
|
|
if (BN_is_bit_set(p,wstart) == 0)
|
|
{
|
|
if (!start)
|
|
if (!BN_mod_mul(r,r,r,m,ctx))
|
|
goto err;
|
|
if (wstart == 0) break;
|
|
wstart--;
|
|
continue;
|
|
}
|
|
/* We now have wstart on a 'set' bit, we now need to work out
|
|
* how bit a window to do. To do this we need to scan
|
|
* forward until the last set bit before the end of the
|
|
* window */
|
|
j=wstart;
|
|
wvalue=1;
|
|
wend=0;
|
|
for (i=1; i<window; i++)
|
|
{
|
|
if (wstart-i < 0) break;
|
|
if (BN_is_bit_set(p,wstart-i))
|
|
{
|
|
wvalue<<=(i-wend);
|
|
wvalue|=1;
|
|
wend=i;
|
|
}
|
|
}
|
|
|
|
/* wend is the size of the current window */
|
|
j=wend+1;
|
|
/* add the 'bytes above' */
|
|
if (!start)
|
|
for (i=0; i<j; i++)
|
|
{
|
|
if (!BN_mod_mul(r,r,r,m,ctx))
|
|
goto err;
|
|
}
|
|
|
|
/* wvalue will be an odd number < 2^window */
|
|
if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
|
|
goto err;
|
|
|
|
/* move the 'window' down further */
|
|
wstart-=wend+1;
|
|
wvalue=0;
|
|
start=0;
|
|
if (wstart < 0) break;
|
|
}
|
|
ret=1;
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
for (i=0; i<ts; i++)
|
|
BN_clear_free(&(val[i]));
|
|
bn_check_top(r);
|
|
return(ret);
|
|
}
|
|
|