492 lines
16 KiB
C
492 lines
16 KiB
C
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/* crypto/bn/bn_lcl.h */
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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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#ifndef HEADER_BN_LCL_H
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#define HEADER_BN_LCL_H
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#include <openssl/bn.h>
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#ifdef __cplusplus
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extern "C" {
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#endif
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/*
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* BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
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*
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*
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* For window size 'w' (w >= 2) and a random 'b' bits exponent,
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* the number of multiplications is a constant plus on average
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*
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* 2^(w-1) + (b-w)/(w+1);
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*
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* here 2^(w-1) is for precomputing the table (we actually need
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* entries only for windows that have the lowest bit set), and
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* (b-w)/(w+1) is an approximation for the expected number of
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* w-bit windows, not counting the first one.
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*
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* Thus we should use
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*
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* w >= 6 if b > 671
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* w = 5 if 671 > b > 239
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* w = 4 if 239 > b > 79
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* w = 3 if 79 > b > 23
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* w <= 2 if 23 > b
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*
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* (with draws in between). Very small exponents are often selected
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* with low Hamming weight, so we use w = 1 for b <= 23.
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*/
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#if 1
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#define BN_window_bits_for_exponent_size(b) \
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((b) > 671 ? 6 : \
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(b) > 239 ? 5 : \
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(b) > 79 ? 4 : \
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(b) > 23 ? 3 : 1)
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#else
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/* Old SSLeay/OpenSSL table.
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* Maximum window size was 5, so this table differs for b==1024;
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* but it coincides for other interesting values (b==160, b==512).
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*/
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#define BN_window_bits_for_exponent_size(b) \
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((b) > 255 ? 5 : \
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(b) > 127 ? 4 : \
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(b) > 17 ? 3 : 1)
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#endif
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/* BN_mod_exp_mont_conttime is based on the assumption that the
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* L1 data cache line width of the target processor is at least
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* the following value.
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*/
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#define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
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#define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
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/* Window sizes optimized for fixed window size modular exponentiation
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* algorithm (BN_mod_exp_mont_consttime).
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*
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* To achieve the security goals of BN_mode_exp_mont_consttime, the
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* maximum size of the window must not exceed
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* log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
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*
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* Window size thresholds are defined for cache line sizes of 32 and 64,
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* cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A
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* window size of 7 should only be used on processors that have a 128
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* byte or greater cache line size.
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*/
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#if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
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# define BN_window_bits_for_ctime_exponent_size(b) \
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((b) > 937 ? 6 : \
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(b) > 306 ? 5 : \
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(b) > 89 ? 4 : \
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(b) > 22 ? 3 : 1)
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# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
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#elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
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# define BN_window_bits_for_ctime_exponent_size(b) \
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((b) > 306 ? 5 : \
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(b) > 89 ? 4 : \
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(b) > 22 ? 3 : 1)
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# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
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#endif
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/* Pentium pro 16,16,16,32,64 */
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/* Alpha 16,16,16,16.64 */
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#define BN_MULL_SIZE_NORMAL (16) /* 32 */
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#define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */
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#define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */
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#define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */
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#define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */
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#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
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/*
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* BN_UMULT_HIGH section.
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*
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* No, I'm not trying to overwhelm you when stating that the
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* product of N-bit numbers is 2*N bits wide:-) No, I don't expect
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* you to be impressed when I say that if the compiler doesn't
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* support 2*N integer type, then you have to replace every N*N
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* multiplication with 4 (N/2)*(N/2) accompanied by some shifts
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* and additions which unavoidably results in severe performance
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* penalties. Of course provided that the hardware is capable of
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* producing 2*N result... That's when you normally start
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* considering assembler implementation. However! It should be
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* pointed out that some CPUs (most notably Alpha, PowerPC and
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* upcoming IA-64 family:-) provide *separate* instruction
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* calculating the upper half of the product placing the result
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* into a general purpose register. Now *if* the compiler supports
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* inline assembler, then it's not impossible to implement the
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* "bignum" routines (and have the compiler optimize 'em)
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* exhibiting "native" performance in C. That's what BN_UMULT_HIGH
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* macro is about:-)
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*
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* <appro@fy.chalmers.se>
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*/
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# if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
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# if defined(__DECC)
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# include <c_asm.h>
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# define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
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# elif defined(__GNUC__)
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# define BN_UMULT_HIGH(a,b) ({ \
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register BN_ULONG ret; \
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asm ("umulh %1,%2,%0" \
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: "=r"(ret) \
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: "r"(a), "r"(b)); \
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ret; })
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# endif /* compiler */
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# elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
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# if defined(__GNUC__)
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# define BN_UMULT_HIGH(a,b) ({ \
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register BN_ULONG ret; \
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asm ("mulhdu %0,%1,%2" \
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: "=r"(ret) \
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: "r"(a), "r"(b)); \
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ret; })
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# endif /* compiler */
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# elif (defined(__x86_64) || defined(__x86_64__)) && \
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(defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
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# if defined(__GNUC__)
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# define BN_UMULT_HIGH(a,b) ({ \
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register BN_ULONG ret,discard; \
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asm ("mulq %3" \
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: "=a"(discard),"=d"(ret) \
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: "a"(a), "g"(b) \
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: "cc"); \
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ret; })
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# define BN_UMULT_LOHI(low,high,a,b) \
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asm ("mulq %3" \
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: "=a"(low),"=d"(high) \
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: "a"(a),"g"(b) \
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: "cc");
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# endif
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# elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
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# if defined(_MSC_VER) && _MSC_VER>=1400
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unsigned __int64 __umulh (unsigned __int64 a,unsigned __int64 b);
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unsigned __int64 _umul128 (unsigned __int64 a,unsigned __int64 b,
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unsigned __int64 *h);
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# pragma intrinsic(__umulh,_umul128)
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# define BN_UMULT_HIGH(a,b) __umulh((a),(b))
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# define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
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# endif
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# endif /* cpu */
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#endif /* OPENSSL_NO_ASM */
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/*************************************************************
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* Using the long long type
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*/
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#define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
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#define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
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#ifdef BN_DEBUG_RAND
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#define bn_clear_top2max(a) \
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{ \
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int ind = (a)->dmax - (a)->top; \
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BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
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for (; ind != 0; ind--) \
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*(++ftl) = 0x0; \
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}
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#else
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#define bn_clear_top2max(a)
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#endif
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#ifdef BN_LLONG
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#define mul_add(r,a,w,c) { \
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BN_ULLONG t; \
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t=(BN_ULLONG)w * (a) + (r) + (c); \
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(r)= Lw(t); \
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(c)= Hw(t); \
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}
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#define mul(r,a,w,c) { \
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BN_ULLONG t; \
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t=(BN_ULLONG)w * (a) + (c); \
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(r)= Lw(t); \
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(c)= Hw(t); \
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}
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#define sqr(r0,r1,a) { \
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BN_ULLONG t; \
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t=(BN_ULLONG)(a)*(a); \
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(r0)=Lw(t); \
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(r1)=Hw(t); \
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}
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#elif defined(BN_UMULT_LOHI)
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#define mul_add(r,a,w,c) { \
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BN_ULONG high,low,ret,tmp=(a); \
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ret = (r); \
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BN_UMULT_LOHI(low,high,w,tmp); \
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ret += (c); \
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(c) = (ret<(c))?1:0; \
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(c) += high; \
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ret += low; \
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||
|
|
(c) += (ret<low)?1:0; \
|
||
|
|
(r) = ret; \
|
||
|
|
}
|
||
|
|
|
||
|
|
#define mul(r,a,w,c) { \
|
||
|
|
BN_ULONG high,low,ret,ta=(a); \
|
||
|
|
BN_UMULT_LOHI(low,high,w,ta); \
|
||
|
|
ret = low + (c); \
|
||
|
|
(c) = high; \
|
||
|
|
(c) += (ret<low)?1:0; \
|
||
|
|
(r) = ret; \
|
||
|
|
}
|
||
|
|
|
||
|
|
#define sqr(r0,r1,a) { \
|
||
|
|
BN_ULONG tmp=(a); \
|
||
|
|
BN_UMULT_LOHI(r0,r1,tmp,tmp); \
|
||
|
|
}
|
||
|
|
|
||
|
|
#elif defined(BN_UMULT_HIGH)
|
||
|
|
#define mul_add(r,a,w,c) { \
|
||
|
|
BN_ULONG high,low,ret,tmp=(a); \
|
||
|
|
ret = (r); \
|
||
|
|
high= BN_UMULT_HIGH(w,tmp); \
|
||
|
|
ret += (c); \
|
||
|
|
low = (w) * tmp; \
|
||
|
|
(c) = (ret<(c))?1:0; \
|
||
|
|
(c) += high; \
|
||
|
|
ret += low; \
|
||
|
|
(c) += (ret<low)?1:0; \
|
||
|
|
(r) = ret; \
|
||
|
|
}
|
||
|
|
|
||
|
|
#define mul(r,a,w,c) { \
|
||
|
|
BN_ULONG high,low,ret,ta=(a); \
|
||
|
|
low = (w) * ta; \
|
||
|
|
high= BN_UMULT_HIGH(w,ta); \
|
||
|
|
ret = low + (c); \
|
||
|
|
(c) = high; \
|
||
|
|
(c) += (ret<low)?1:0; \
|
||
|
|
(r) = ret; \
|
||
|
|
}
|
||
|
|
|
||
|
|
#define sqr(r0,r1,a) { \
|
||
|
|
BN_ULONG tmp=(a); \
|
||
|
|
(r0) = tmp * tmp; \
|
||
|
|
(r1) = BN_UMULT_HIGH(tmp,tmp); \
|
||
|
|
}
|
||
|
|
|
||
|
|
#else
|
||
|
|
/*************************************************************
|
||
|
|
* No long long type
|
||
|
|
*/
|
||
|
|
|
||
|
|
#define LBITS(a) ((a)&BN_MASK2l)
|
||
|
|
#define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
|
||
|
|
#define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
|
||
|
|
|
||
|
|
#define LLBITS(a) ((a)&BN_MASKl)
|
||
|
|
#define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
|
||
|
|
#define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
|
||
|
|
|
||
|
|
#define mul64(l,h,bl,bh) \
|
||
|
|
{ \
|
||
|
|
BN_ULONG m,m1,lt,ht; \
|
||
|
|
\
|
||
|
|
lt=l; \
|
||
|
|
ht=h; \
|
||
|
|
m =(bh)*(lt); \
|
||
|
|
lt=(bl)*(lt); \
|
||
|
|
m1=(bl)*(ht); \
|
||
|
|
ht =(bh)*(ht); \
|
||
|
|
m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
|
||
|
|
ht+=HBITS(m); \
|
||
|
|
m1=L2HBITS(m); \
|
||
|
|
lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
|
||
|
|
(l)=lt; \
|
||
|
|
(h)=ht; \
|
||
|
|
}
|
||
|
|
|
||
|
|
#define sqr64(lo,ho,in) \
|
||
|
|
{ \
|
||
|
|
BN_ULONG l,h,m; \
|
||
|
|
\
|
||
|
|
h=(in); \
|
||
|
|
l=LBITS(h); \
|
||
|
|
h=HBITS(h); \
|
||
|
|
m =(l)*(h); \
|
||
|
|
l*=l; \
|
||
|
|
h*=h; \
|
||
|
|
h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
|
||
|
|
m =(m&BN_MASK2l)<<(BN_BITS4+1); \
|
||
|
|
l=(l+m)&BN_MASK2; if (l < m) h++; \
|
||
|
|
(lo)=l; \
|
||
|
|
(ho)=h; \
|
||
|
|
}
|
||
|
|
|
||
|
|
#define mul_add(r,a,bl,bh,c) { \
|
||
|
|
BN_ULONG l,h; \
|
||
|
|
\
|
||
|
|
h= (a); \
|
||
|
|
l=LBITS(h); \
|
||
|
|
h=HBITS(h); \
|
||
|
|
mul64(l,h,(bl),(bh)); \
|
||
|
|
\
|
||
|
|
/* non-multiply part */ \
|
||
|
|
l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
|
||
|
|
(c)=(r); \
|
||
|
|
l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
|
||
|
|
(c)=h&BN_MASK2; \
|
||
|
|
(r)=l; \
|
||
|
|
}
|
||
|
|
|
||
|
|
#define mul(r,a,bl,bh,c) { \
|
||
|
|
BN_ULONG l,h; \
|
||
|
|
\
|
||
|
|
h= (a); \
|
||
|
|
l=LBITS(h); \
|
||
|
|
h=HBITS(h); \
|
||
|
|
mul64(l,h,(bl),(bh)); \
|
||
|
|
\
|
||
|
|
/* non-multiply part */ \
|
||
|
|
l+=(c); if ((l&BN_MASK2) < (c)) h++; \
|
||
|
|
(c)=h&BN_MASK2; \
|
||
|
|
(r)=l&BN_MASK2; \
|
||
|
|
}
|
||
|
|
#endif /* !BN_LLONG */
|
||
|
|
|
||
|
|
void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb);
|
||
|
|
void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
|
||
|
|
void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
|
||
|
|
void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
|
||
|
|
void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a);
|
||
|
|
void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a);
|
||
|
|
int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n);
|
||
|
|
int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
|
||
|
|
int cl, int dl);
|
||
|
|
void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
|
||
|
|
int dna,int dnb,BN_ULONG *t);
|
||
|
|
void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,
|
||
|
|
int n,int tna,int tnb,BN_ULONG *t);
|
||
|
|
void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t);
|
||
|
|
void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n);
|
||
|
|
void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
|
||
|
|
BN_ULONG *t);
|
||
|
|
void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2,
|
||
|
|
BN_ULONG *t);
|
||
|
|
BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
|
||
|
|
int cl, int dl);
|
||
|
|
BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
|
||
|
|
int cl, int dl);
|
||
|
|
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0, int num);
|
||
|
|
|
||
|
|
#ifdef __cplusplus
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#endif
|