890 lines
30 KiB
C
890 lines
30 KiB
C
/* crypto/bn/bn_nist.c */
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/*
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* Written by Nils Larsch for the OpenSSL project
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*/
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/* ====================================================================
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* Copyright (c) 1998-2005 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 "bn_lcl.h"
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#include "cryptlib.h"
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#define BN_NIST_192_TOP (192+BN_BITS2-1)/BN_BITS2
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#define BN_NIST_224_TOP (224+BN_BITS2-1)/BN_BITS2
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#define BN_NIST_256_TOP (256+BN_BITS2-1)/BN_BITS2
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#define BN_NIST_384_TOP (384+BN_BITS2-1)/BN_BITS2
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#define BN_NIST_521_TOP (521+BN_BITS2-1)/BN_BITS2
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/* pre-computed tables are "carry-less" values of modulus*(i+1) */
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#if BN_BITS2 == 64
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static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
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{0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFFULL},
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{0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL},
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{0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFCULL, 0xFFFFFFFFFFFFFFFFULL}
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};
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static const BN_ULONG _nist_p_192_sqr[] = {
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0x0000000000000001ULL, 0x0000000000000002ULL, 0x0000000000000001ULL,
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0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL
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};
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static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
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{0x0000000000000001ULL, 0xFFFFFFFF00000000ULL,
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0xFFFFFFFFFFFFFFFFULL, 0x00000000FFFFFFFFULL},
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{0x0000000000000002ULL, 0xFFFFFFFE00000000ULL,
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0xFFFFFFFFFFFFFFFFULL, 0x00000001FFFFFFFFULL} /* this one is
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* "carry-full" */
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};
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static const BN_ULONG _nist_p_224_sqr[] = {
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0x0000000000000001ULL, 0xFFFFFFFE00000000ULL,
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0xFFFFFFFFFFFFFFFFULL, 0x0000000200000000ULL,
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0x0000000000000000ULL, 0xFFFFFFFFFFFFFFFEULL,
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0xFFFFFFFFFFFFFFFFULL
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};
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static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
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{0xFFFFFFFFFFFFFFFFULL, 0x00000000FFFFFFFFULL,
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0x0000000000000000ULL, 0xFFFFFFFF00000001ULL},
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{0xFFFFFFFFFFFFFFFEULL, 0x00000001FFFFFFFFULL,
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0x0000000000000000ULL, 0xFFFFFFFE00000002ULL},
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{0xFFFFFFFFFFFFFFFDULL, 0x00000002FFFFFFFFULL,
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0x0000000000000000ULL, 0xFFFFFFFD00000003ULL},
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{0xFFFFFFFFFFFFFFFCULL, 0x00000003FFFFFFFFULL,
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0x0000000000000000ULL, 0xFFFFFFFC00000004ULL},
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{0xFFFFFFFFFFFFFFFBULL, 0x00000004FFFFFFFFULL,
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0x0000000000000000ULL, 0xFFFFFFFB00000005ULL},
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};
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static const BN_ULONG _nist_p_256_sqr[] = {
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0x0000000000000001ULL, 0xFFFFFFFE00000000ULL,
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0xFFFFFFFFFFFFFFFFULL, 0x00000001FFFFFFFEULL,
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0x00000001FFFFFFFEULL, 0x00000001FFFFFFFEULL,
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0xFFFFFFFE00000001ULL, 0xFFFFFFFE00000002ULL
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};
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static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
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{0x00000000FFFFFFFFULL, 0xFFFFFFFF00000000ULL, 0xFFFFFFFFFFFFFFFEULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
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{0x00000001FFFFFFFEULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFDULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
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{0x00000002FFFFFFFDULL, 0xFFFFFFFD00000000ULL, 0xFFFFFFFFFFFFFFFCULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
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{0x00000003FFFFFFFCULL, 0xFFFFFFFC00000000ULL, 0xFFFFFFFFFFFFFFFBULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
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{0x00000004FFFFFFFBULL, 0xFFFFFFFB00000000ULL, 0xFFFFFFFFFFFFFFFAULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
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};
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static const BN_ULONG _nist_p_384_sqr[] = {
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0xFFFFFFFE00000001ULL, 0x0000000200000000ULL, 0xFFFFFFFE00000000ULL,
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0x0000000200000000ULL, 0x0000000000000001ULL, 0x0000000000000000ULL,
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0x00000001FFFFFFFEULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFDULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL
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};
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static const BN_ULONG _nist_p_521[] =
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{ 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
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0x00000000000001FFULL
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};
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static const BN_ULONG _nist_p_521_sqr[] = {
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0x0000000000000001ULL, 0x0000000000000000ULL, 0x0000000000000000ULL,
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0x0000000000000000ULL, 0x0000000000000000ULL, 0x0000000000000000ULL,
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0x0000000000000000ULL, 0x0000000000000000ULL, 0xFFFFFFFFFFFFFC00ULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
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0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
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0xFFFFFFFFFFFFFFFFULL, 0x000000000003FFFFULL
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};
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#elif BN_BITS2 == 32
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static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
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{0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
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{0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
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{0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
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};
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static const BN_ULONG _nist_p_192_sqr[] = {
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0x00000001, 0x00000000, 0x00000002, 0x00000000, 0x00000001, 0x00000000,
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0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF
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};
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static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
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{0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
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{0x00000002, 0x00000000, 0x00000000, 0xFFFFFFFE,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
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};
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static const BN_ULONG _nist_p_224_sqr[] = {
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0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE,
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0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000002,
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0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF
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};
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static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
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{0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000,
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0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF},
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{0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000001,
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0x00000000, 0x00000000, 0x00000002, 0xFFFFFFFE},
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{0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000002,
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0x00000000, 0x00000000, 0x00000003, 0xFFFFFFFD},
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{0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000003,
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0x00000000, 0x00000000, 0x00000004, 0xFFFFFFFC},
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{0xFFFFFFFB, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000004,
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0x00000000, 0x00000000, 0x00000005, 0xFFFFFFFB},
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};
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static const BN_ULONG _nist_p_256_sqr[] = {
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0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0x00000001,
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0xFFFFFFFE, 0x00000001, 0xFFFFFFFE, 0x00000001,
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0x00000001, 0xFFFFFFFE, 0x00000002, 0xFFFFFFFE
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};
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static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
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{0xFFFFFFFF, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
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{0xFFFFFFFE, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
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{0xFFFFFFFD, 0x00000002, 0x00000000, 0xFFFFFFFD, 0xFFFFFFFC, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
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{0xFFFFFFFC, 0x00000003, 0x00000000, 0xFFFFFFFC, 0xFFFFFFFB, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
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{0xFFFFFFFB, 0x00000004, 0x00000000, 0xFFFFFFFB, 0xFFFFFFFA, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
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};
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static const BN_ULONG _nist_p_384_sqr[] = {
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0x00000001, 0xFFFFFFFE, 0x00000000, 0x00000002, 0x00000000, 0xFFFFFFFE,
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0x00000000, 0x00000002, 0x00000001, 0x00000000, 0x00000000, 0x00000000,
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0xFFFFFFFE, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF
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};
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static const BN_ULONG _nist_p_521[] = { 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
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0xFFFFFFFF, 0x000001FF
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};
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static const BN_ULONG _nist_p_521_sqr[] = {
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0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
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0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
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0x00000000, 0x00000000, 0x00000000, 0x00000000, 0xFFFFFC00, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
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0xFFFFFFFF, 0xFFFFFFFF, 0x0003FFFF
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};
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#else
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# error "unsupported BN_BITS2"
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#endif
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static const BIGNUM _bignum_nist_p_192 = {
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(BN_ULONG *)_nist_p_192[0],
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BN_NIST_192_TOP,
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BN_NIST_192_TOP,
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0,
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BN_FLG_STATIC_DATA
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};
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static const BIGNUM _bignum_nist_p_224 = {
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(BN_ULONG *)_nist_p_224[0],
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BN_NIST_224_TOP,
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BN_NIST_224_TOP,
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0,
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BN_FLG_STATIC_DATA
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};
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static const BIGNUM _bignum_nist_p_256 = {
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(BN_ULONG *)_nist_p_256[0],
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BN_NIST_256_TOP,
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BN_NIST_256_TOP,
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0,
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BN_FLG_STATIC_DATA
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};
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static const BIGNUM _bignum_nist_p_384 = {
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(BN_ULONG *)_nist_p_384[0],
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BN_NIST_384_TOP,
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BN_NIST_384_TOP,
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0,
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BN_FLG_STATIC_DATA
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};
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static const BIGNUM _bignum_nist_p_521 = {
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(BN_ULONG *)_nist_p_521,
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BN_NIST_521_TOP,
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BN_NIST_521_TOP,
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0,
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BN_FLG_STATIC_DATA
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};
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const BIGNUM *BN_get0_nist_prime_192(void)
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{
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return &_bignum_nist_p_192;
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}
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const BIGNUM *BN_get0_nist_prime_224(void)
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{
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return &_bignum_nist_p_224;
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}
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const BIGNUM *BN_get0_nist_prime_256(void)
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{
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return &_bignum_nist_p_256;
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}
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const BIGNUM *BN_get0_nist_prime_384(void)
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{
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return &_bignum_nist_p_384;
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}
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const BIGNUM *BN_get0_nist_prime_521(void)
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{
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return &_bignum_nist_p_521;
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}
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static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
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{
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int i;
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BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
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#ifdef BN_DEBUG
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OPENSSL_assert(top <= max);
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#endif
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for (i = (top); i != 0; i--)
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*_tmp1++ = *_tmp2++;
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for (i = (max) - (top); i != 0; i--)
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*_tmp1++ = (BN_ULONG)0;
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}
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static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
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{
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int i;
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BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
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for (i = (top); i != 0; i--)
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*_tmp1++ = *_tmp2++;
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}
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#if BN_BITS2 == 64
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# define bn_cp_64(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
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# define bn_64_set_0(to, n) (to)[n] = (BN_ULONG)0;
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/*
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* two following macros are implemented under assumption that they
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* are called in a sequence with *ascending* n, i.e. as they are...
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*/
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# define bn_cp_32_naked(to, n, from, m) (((n)&1)?(to[(n)/2]|=((m)&1)?(from[(m)/2]&BN_MASK2h):(from[(m)/2]<<32))\
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:(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
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# define bn_32_set_0(to, n) (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
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# define bn_cp_32(to,n,from,m) ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
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#else
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# define bn_cp_64(to, n, from, m) \
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{ \
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bn_cp_32(to, (n)*2, from, (m)*2); \
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bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
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}
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# define bn_64_set_0(to, n) \
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{ \
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bn_32_set_0(to, (n)*2); \
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bn_32_set_0(to, (n)*2+1); \
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}
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# if BN_BITS2 == 32
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# define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
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# define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0;
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# endif
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#endif /* BN_BITS2 != 64 */
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#define nist_set_192(to, from, a1, a2, a3) \
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{ \
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bn_cp_64(to, 0, from, (a3) - 3) \
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bn_cp_64(to, 1, from, (a2) - 3) \
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bn_cp_64(to, 2, from, (a1) - 3) \
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}
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int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
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BN_CTX *ctx)
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{
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int top = a->top, i;
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int carry;
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register BN_ULONG *r_d, *a_d = a->d;
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BN_ULONG t_d[BN_NIST_192_TOP],
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buf[BN_NIST_192_TOP], c_d[BN_NIST_192_TOP], *res;
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PTR_SIZE_INT mask;
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static const BIGNUM _bignum_nist_p_192_sqr = {
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(BN_ULONG *)_nist_p_192_sqr,
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sizeof(_nist_p_192_sqr) / sizeof(_nist_p_192_sqr[0]),
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sizeof(_nist_p_192_sqr) / sizeof(_nist_p_192_sqr[0]),
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0, BN_FLG_STATIC_DATA
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};
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field = &_bignum_nist_p_192; /* just to make sure */
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if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_192_sqr) >= 0)
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return BN_nnmod(r, a, field, ctx);
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i = BN_ucmp(field, a);
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if (i == 0) {
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BN_zero(r);
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return 1;
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} else if (i > 0)
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return (r == a) ? 1 : (BN_copy(r, a) != NULL);
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if (r != a) {
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if (!bn_wexpand(r, BN_NIST_192_TOP))
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return 0;
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r_d = r->d;
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nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
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} else
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r_d = a_d;
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nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP,
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BN_NIST_192_TOP);
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nist_set_192(t_d, buf, 0, 3, 3);
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carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
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nist_set_192(t_d, buf, 4, 4, 0);
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carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
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nist_set_192(t_d, buf, 5, 5, 5)
|
|
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
|
|
|
|
if (carry > 0)
|
|
carry =
|
|
(int)bn_sub_words(r_d, r_d, _nist_p_192[carry - 1],
|
|
BN_NIST_192_TOP);
|
|
else
|
|
carry = 1;
|
|
|
|
/*
|
|
* we need 'if (carry==0 || result>=modulus) result-=modulus;'
|
|
* as comparison implies subtraction, we can write
|
|
* 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
|
|
* this is what happens below, but without explicit if:-) a.
|
|
*/
|
|
mask =
|
|
0 - (PTR_SIZE_INT) bn_sub_words(c_d, r_d, _nist_p_192[0],
|
|
BN_NIST_192_TOP);
|
|
mask &= 0 - (PTR_SIZE_INT) carry;
|
|
res = (BN_ULONG *)
|
|
(((PTR_SIZE_INT) c_d & ~mask) | ((PTR_SIZE_INT) r_d & mask));
|
|
nist_cp_bn(r_d, res, BN_NIST_192_TOP);
|
|
r->top = BN_NIST_192_TOP;
|
|
bn_correct_top(r);
|
|
|
|
return 1;
|
|
}
|
|
|
|
typedef BN_ULONG (*bn_addsub_f) (BN_ULONG *, const BN_ULONG *,
|
|
const BN_ULONG *, int);
|
|
|
|
#define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
|
|
{ \
|
|
bn_cp_32(to, 0, from, (a7) - 7) \
|
|
bn_cp_32(to, 1, from, (a6) - 7) \
|
|
bn_cp_32(to, 2, from, (a5) - 7) \
|
|
bn_cp_32(to, 3, from, (a4) - 7) \
|
|
bn_cp_32(to, 4, from, (a3) - 7) \
|
|
bn_cp_32(to, 5, from, (a2) - 7) \
|
|
bn_cp_32(to, 6, from, (a1) - 7) \
|
|
}
|
|
|
|
int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
|
|
BN_CTX *ctx)
|
|
{
|
|
int top = a->top, i;
|
|
int carry;
|
|
BN_ULONG *r_d, *a_d = a->d;
|
|
BN_ULONG t_d[BN_NIST_224_TOP],
|
|
buf[BN_NIST_224_TOP], c_d[BN_NIST_224_TOP], *res;
|
|
PTR_SIZE_INT mask;
|
|
union {
|
|
bn_addsub_f f;
|
|
PTR_SIZE_INT p;
|
|
} u;
|
|
static const BIGNUM _bignum_nist_p_224_sqr = {
|
|
(BN_ULONG *)_nist_p_224_sqr,
|
|
sizeof(_nist_p_224_sqr) / sizeof(_nist_p_224_sqr[0]),
|
|
sizeof(_nist_p_224_sqr) / sizeof(_nist_p_224_sqr[0]),
|
|
0, BN_FLG_STATIC_DATA
|
|
};
|
|
|
|
field = &_bignum_nist_p_224; /* just to make sure */
|
|
|
|
if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_224_sqr) >= 0)
|
|
return BN_nnmod(r, a, field, ctx);
|
|
|
|
i = BN_ucmp(field, a);
|
|
if (i == 0) {
|
|
BN_zero(r);
|
|
return 1;
|
|
} else if (i > 0)
|
|
return (r == a) ? 1 : (BN_copy(r, a) != NULL);
|
|
|
|
if (r != a) {
|
|
if (!bn_wexpand(r, BN_NIST_224_TOP))
|
|
return 0;
|
|
r_d = r->d;
|
|
nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
|
|
} else
|
|
r_d = a_d;
|
|
|
|
#if BN_BITS2==64
|
|
/* copy upper 256 bits of 448 bit number ... */
|
|
nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP - 1),
|
|
top - (BN_NIST_224_TOP - 1), BN_NIST_224_TOP);
|
|
/* ... and right shift by 32 to obtain upper 224 bits */
|
|
nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
|
|
/* truncate lower part to 224 bits too */
|
|
r_d[BN_NIST_224_TOP - 1] &= BN_MASK2l;
|
|
#else
|
|
nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP,
|
|
BN_NIST_224_TOP);
|
|
#endif
|
|
nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
|
|
carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
|
|
nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
|
|
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
|
|
nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
|
|
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
|
|
nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
|
|
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
|
|
|
|
#if BN_BITS2==64
|
|
carry = (int)(r_d[BN_NIST_224_TOP - 1] >> 32);
|
|
#endif
|
|
u.f = bn_sub_words;
|
|
if (carry > 0) {
|
|
carry =
|
|
(int)bn_sub_words(r_d, r_d, _nist_p_224[carry - 1],
|
|
BN_NIST_224_TOP);
|
|
#if BN_BITS2==64
|
|
carry = (int)(~(r_d[BN_NIST_224_TOP - 1] >> 32)) & 1;
|
|
#endif
|
|
} else if (carry < 0) {
|
|
/*
|
|
* it's a bit more comlicated logic in this case. if bn_add_words
|
|
* yields no carry, then result has to be adjusted by unconditionally
|
|
* *adding* the modulus. but if it does, then result has to be
|
|
* compared to the modulus and conditionally adjusted by
|
|
* *subtracting* the latter.
|
|
*/
|
|
carry =
|
|
(int)bn_add_words(r_d, r_d, _nist_p_224[-carry - 1],
|
|
BN_NIST_224_TOP);
|
|
mask = 0 - (PTR_SIZE_INT) carry;
|
|
u.p = ((PTR_SIZE_INT) bn_sub_words & mask) |
|
|
((PTR_SIZE_INT) bn_add_words & ~mask);
|
|
} else
|
|
carry = 1;
|
|
|
|
/* otherwise it's effectively same as in BN_nist_mod_192... */
|
|
mask =
|
|
0 - (PTR_SIZE_INT) (*u.f) (c_d, r_d, _nist_p_224[0], BN_NIST_224_TOP);
|
|
mask &= 0 - (PTR_SIZE_INT) carry;
|
|
res = (BN_ULONG *)(((PTR_SIZE_INT) c_d & ~mask) |
|
|
((PTR_SIZE_INT) r_d & mask));
|
|
nist_cp_bn(r_d, res, BN_NIST_224_TOP);
|
|
r->top = BN_NIST_224_TOP;
|
|
bn_correct_top(r);
|
|
|
|
return 1;
|
|
}
|
|
|
|
#define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
|
|
{ \
|
|
bn_cp_32(to, 0, from, (a8) - 8) \
|
|
bn_cp_32(to, 1, from, (a7) - 8) \
|
|
bn_cp_32(to, 2, from, (a6) - 8) \
|
|
bn_cp_32(to, 3, from, (a5) - 8) \
|
|
bn_cp_32(to, 4, from, (a4) - 8) \
|
|
bn_cp_32(to, 5, from, (a3) - 8) \
|
|
bn_cp_32(to, 6, from, (a2) - 8) \
|
|
bn_cp_32(to, 7, from, (a1) - 8) \
|
|
}
|
|
|
|
int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
|
|
BN_CTX *ctx)
|
|
{
|
|
int i, top = a->top;
|
|
int carry = 0;
|
|
register BN_ULONG *a_d = a->d, *r_d;
|
|
BN_ULONG t_d[BN_NIST_256_TOP],
|
|
buf[BN_NIST_256_TOP], c_d[BN_NIST_256_TOP], *res;
|
|
PTR_SIZE_INT mask;
|
|
union {
|
|
bn_addsub_f f;
|
|
PTR_SIZE_INT p;
|
|
} u;
|
|
static const BIGNUM _bignum_nist_p_256_sqr = {
|
|
(BN_ULONG *)_nist_p_256_sqr,
|
|
sizeof(_nist_p_256_sqr) / sizeof(_nist_p_256_sqr[0]),
|
|
sizeof(_nist_p_256_sqr) / sizeof(_nist_p_256_sqr[0]),
|
|
0, BN_FLG_STATIC_DATA
|
|
};
|
|
|
|
field = &_bignum_nist_p_256; /* just to make sure */
|
|
|
|
if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_256_sqr) >= 0)
|
|
return BN_nnmod(r, a, field, ctx);
|
|
|
|
i = BN_ucmp(field, a);
|
|
if (i == 0) {
|
|
BN_zero(r);
|
|
return 1;
|
|
} else if (i > 0)
|
|
return (r == a) ? 1 : (BN_copy(r, a) != NULL);
|
|
|
|
if (r != a) {
|
|
if (!bn_wexpand(r, BN_NIST_256_TOP))
|
|
return 0;
|
|
r_d = r->d;
|
|
nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
|
|
} else
|
|
r_d = a_d;
|
|
|
|
nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP,
|
|
BN_NIST_256_TOP);
|
|
|
|
/*
|
|
* S1
|
|
*/
|
|
nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
|
|
/*
|
|
* S2
|
|
*/
|
|
nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
|
|
carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
|
|
/* left shift */
|
|
{
|
|
register BN_ULONG *ap, t, c;
|
|
ap = t_d;
|
|
c = 0;
|
|
for (i = BN_NIST_256_TOP; i != 0; --i) {
|
|
t = *ap;
|
|
*(ap++) = ((t << 1) | c) & BN_MASK2;
|
|
c = (t & BN_TBIT) ? 1 : 0;
|
|
}
|
|
carry <<= 1;
|
|
carry |= c;
|
|
}
|
|
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
|
|
/*
|
|
* S3
|
|
*/
|
|
nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
|
|
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
|
|
/*
|
|
* S4
|
|
*/
|
|
nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
|
|
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
|
|
/*
|
|
* D1
|
|
*/
|
|
nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
|
|
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
|
|
/*
|
|
* D2
|
|
*/
|
|
nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
|
|
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
|
|
/*
|
|
* D3
|
|
*/
|
|
nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
|
|
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
|
|
/*
|
|
* D4
|
|
*/
|
|
nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
|
|
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
|
|
|
|
/* see BN_nist_mod_224 for explanation */
|
|
u.f = bn_sub_words;
|
|
if (carry > 0)
|
|
carry =
|
|
(int)bn_sub_words(r_d, r_d, _nist_p_256[carry - 1],
|
|
BN_NIST_256_TOP);
|
|
else if (carry < 0) {
|
|
carry =
|
|
(int)bn_add_words(r_d, r_d, _nist_p_256[-carry - 1],
|
|
BN_NIST_256_TOP);
|
|
mask = 0 - (PTR_SIZE_INT) carry;
|
|
u.p = ((PTR_SIZE_INT) bn_sub_words & mask) |
|
|
((PTR_SIZE_INT) bn_add_words & ~mask);
|
|
} else
|
|
carry = 1;
|
|
|
|
mask =
|
|
0 - (PTR_SIZE_INT) (*u.f) (c_d, r_d, _nist_p_256[0], BN_NIST_256_TOP);
|
|
mask &= 0 - (PTR_SIZE_INT) carry;
|
|
res = (BN_ULONG *)(((PTR_SIZE_INT) c_d & ~mask) |
|
|
((PTR_SIZE_INT) r_d & mask));
|
|
nist_cp_bn(r_d, res, BN_NIST_256_TOP);
|
|
r->top = BN_NIST_256_TOP;
|
|
bn_correct_top(r);
|
|
|
|
return 1;
|
|
}
|
|
|
|
#define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
|
|
{ \
|
|
bn_cp_32(to, 0, from, (a12) - 12) \
|
|
bn_cp_32(to, 1, from, (a11) - 12) \
|
|
bn_cp_32(to, 2, from, (a10) - 12) \
|
|
bn_cp_32(to, 3, from, (a9) - 12) \
|
|
bn_cp_32(to, 4, from, (a8) - 12) \
|
|
bn_cp_32(to, 5, from, (a7) - 12) \
|
|
bn_cp_32(to, 6, from, (a6) - 12) \
|
|
bn_cp_32(to, 7, from, (a5) - 12) \
|
|
bn_cp_32(to, 8, from, (a4) - 12) \
|
|
bn_cp_32(to, 9, from, (a3) - 12) \
|
|
bn_cp_32(to, 10, from, (a2) - 12) \
|
|
bn_cp_32(to, 11, from, (a1) - 12) \
|
|
}
|
|
|
|
int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
|
|
BN_CTX *ctx)
|
|
{
|
|
int i, top = a->top;
|
|
int carry = 0;
|
|
register BN_ULONG *r_d, *a_d = a->d;
|
|
BN_ULONG t_d[BN_NIST_384_TOP],
|
|
buf[BN_NIST_384_TOP], c_d[BN_NIST_384_TOP], *res;
|
|
PTR_SIZE_INT mask;
|
|
union {
|
|
bn_addsub_f f;
|
|
PTR_SIZE_INT p;
|
|
} u;
|
|
static const BIGNUM _bignum_nist_p_384_sqr = {
|
|
(BN_ULONG *)_nist_p_384_sqr,
|
|
sizeof(_nist_p_384_sqr) / sizeof(_nist_p_384_sqr[0]),
|
|
sizeof(_nist_p_384_sqr) / sizeof(_nist_p_384_sqr[0]),
|
|
0, BN_FLG_STATIC_DATA
|
|
};
|
|
|
|
field = &_bignum_nist_p_384; /* just to make sure */
|
|
|
|
if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_384_sqr) >= 0)
|
|
return BN_nnmod(r, a, field, ctx);
|
|
|
|
i = BN_ucmp(field, a);
|
|
if (i == 0) {
|
|
BN_zero(r);
|
|
return 1;
|
|
} else if (i > 0)
|
|
return (r == a) ? 1 : (BN_copy(r, a) != NULL);
|
|
|
|
if (r != a) {
|
|
if (!bn_wexpand(r, BN_NIST_384_TOP))
|
|
return 0;
|
|
r_d = r->d;
|
|
nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
|
|
} else
|
|
r_d = a_d;
|
|
|
|
nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP,
|
|
BN_NIST_384_TOP);
|
|
|
|
/*
|
|
* S1
|
|
*/
|
|
nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23 - 4, 22 - 4, 21 - 4);
|
|
/* left shift */
|
|
{
|
|
register BN_ULONG *ap, t, c;
|
|
ap = t_d;
|
|
c = 0;
|
|
for (i = 3; i != 0; --i) {
|
|
t = *ap;
|
|
*(ap++) = ((t << 1) | c) & BN_MASK2;
|
|
c = (t & BN_TBIT) ? 1 : 0;
|
|
}
|
|
*ap = c;
|
|
}
|
|
carry = (int)bn_add_words(r_d + (128 / BN_BITS2), r_d + (128 / BN_BITS2),
|
|
t_d, BN_NIST_256_TOP);
|
|
/*
|
|
* S2
|
|
*/
|
|
carry += (int)bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
|
|
/*
|
|
* S3
|
|
*/
|
|
nist_set_384(t_d, buf, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21);
|
|
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
|
|
/*
|
|
* S4
|
|
*/
|
|
nist_set_384(t_d, buf, 19, 18, 17, 16, 15, 14, 13, 12, 20, 0, 23, 0);
|
|
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
|
|
/*
|
|
* S5
|
|
*/
|
|
nist_set_384(t_d, buf, 0, 0, 0, 0, 23, 22, 21, 20, 0, 0, 0, 0);
|
|
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
|
|
/*
|
|
* S6
|
|
*/
|
|
nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 23, 22, 21, 0, 0, 20);
|
|
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
|
|
/*
|
|
* D1
|
|
*/
|
|
nist_set_384(t_d, buf, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23);
|
|
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
|
|
/*
|
|
* D2
|
|
*/
|
|
nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 0, 23, 22, 21, 20, 0);
|
|
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
|
|
/*
|
|
* D3
|
|
*/
|
|
nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 0, 23, 23, 0, 0, 0);
|
|
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
|
|
|
|
/* see BN_nist_mod_224 for explanation */
|
|
u.f = bn_sub_words;
|
|
if (carry > 0)
|
|
carry =
|
|
(int)bn_sub_words(r_d, r_d, _nist_p_384[carry - 1],
|
|
BN_NIST_384_TOP);
|
|
else if (carry < 0) {
|
|
carry =
|
|
(int)bn_add_words(r_d, r_d, _nist_p_384[-carry - 1],
|
|
BN_NIST_384_TOP);
|
|
mask = 0 - (PTR_SIZE_INT) carry;
|
|
u.p = ((PTR_SIZE_INT) bn_sub_words & mask) |
|
|
((PTR_SIZE_INT) bn_add_words & ~mask);
|
|
} else
|
|
carry = 1;
|
|
|
|
mask =
|
|
0 - (PTR_SIZE_INT) (*u.f) (c_d, r_d, _nist_p_384[0], BN_NIST_384_TOP);
|
|
mask &= 0 - (PTR_SIZE_INT) carry;
|
|
res = (BN_ULONG *)(((PTR_SIZE_INT) c_d & ~mask) |
|
|
((PTR_SIZE_INT) r_d & mask));
|
|
nist_cp_bn(r_d, res, BN_NIST_384_TOP);
|
|
r->top = BN_NIST_384_TOP;
|
|
bn_correct_top(r);
|
|
|
|
return 1;
|
|
}
|
|
|
|
#define BN_NIST_521_RSHIFT (521%BN_BITS2)
|
|
#define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
|
|
#define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
|
|
|
|
int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
|
|
BN_CTX *ctx)
|
|
{
|
|
int top = a->top, i;
|
|
BN_ULONG *r_d, *a_d = a->d, t_d[BN_NIST_521_TOP], val, tmp, *res;
|
|
PTR_SIZE_INT mask;
|
|
static const BIGNUM _bignum_nist_p_521_sqr = {
|
|
(BN_ULONG *)_nist_p_521_sqr,
|
|
sizeof(_nist_p_521_sqr) / sizeof(_nist_p_521_sqr[0]),
|
|
sizeof(_nist_p_521_sqr) / sizeof(_nist_p_521_sqr[0]),
|
|
0, BN_FLG_STATIC_DATA
|
|
};
|
|
|
|
field = &_bignum_nist_p_521; /* just to make sure */
|
|
|
|
if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_521_sqr) >= 0)
|
|
return BN_nnmod(r, a, field, ctx);
|
|
|
|
i = BN_ucmp(field, a);
|
|
if (i == 0) {
|
|
BN_zero(r);
|
|
return 1;
|
|
} else if (i > 0)
|
|
return (r == a) ? 1 : (BN_copy(r, a) != NULL);
|
|
|
|
if (r != a) {
|
|
if (!bn_wexpand(r, BN_NIST_521_TOP))
|
|
return 0;
|
|
r_d = r->d;
|
|
nist_cp_bn(r_d, a_d, BN_NIST_521_TOP);
|
|
} else
|
|
r_d = a_d;
|
|
|
|
/* upper 521 bits, copy ... */
|
|
nist_cp_bn_0(t_d, a_d + (BN_NIST_521_TOP - 1),
|
|
top - (BN_NIST_521_TOP - 1), BN_NIST_521_TOP);
|
|
/* ... and right shift */
|
|
for (val = t_d[0], i = 0; i < BN_NIST_521_TOP - 1; i++) {
|
|
t_d[i] = (val >> BN_NIST_521_RSHIFT |
|
|
(tmp = t_d[i + 1]) << BN_NIST_521_LSHIFT) & BN_MASK2;
|
|
val = tmp;
|
|
}
|
|
t_d[i] = val >> BN_NIST_521_RSHIFT;
|
|
/* lower 521 bits */
|
|
r_d[i] &= BN_NIST_521_TOP_MASK;
|
|
|
|
bn_add_words(r_d, r_d, t_d, BN_NIST_521_TOP);
|
|
mask =
|
|
0 - (PTR_SIZE_INT) bn_sub_words(t_d, r_d, _nist_p_521,
|
|
BN_NIST_521_TOP);
|
|
res =
|
|
(BN_ULONG *)(((PTR_SIZE_INT) t_d & ~mask) |
|
|
((PTR_SIZE_INT) r_d & mask));
|
|
nist_cp_bn(r_d, res, BN_NIST_521_TOP);
|
|
r->top = BN_NIST_521_TOP;
|
|
bn_correct_top(r);
|
|
|
|
return 1;
|
|
}
|