1380 lines
51 KiB
C
1380 lines
51 KiB
C
/*
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* Elliptic curves over GF(p): curve-specific data and functions
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*
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* Copyright (C) 2006-2014, Brainspark B.V.
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*
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* This file is part of PolarSSL (http://www.polarssl.org)
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* Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
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*
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* All rights reserved.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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#if !defined(POLARSSL_CONFIG_FILE)
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#include "polarssl/config.h"
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#else
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#include POLARSSL_CONFIG_FILE
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#endif
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#if defined(POLARSSL_ECP_C)
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#include "polarssl/ecp.h"
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#if defined(_MSC_VER) && !defined(inline)
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#define inline _inline
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#else
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#if defined(__ARMCC_VERSION) && !defined(inline)
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#define inline __inline
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#endif /* __ARMCC_VERSION */
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#endif /*_MSC_VER */
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/*
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* Conversion macros for embedded constants:
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* build lists of t_uint's from lists of unsigned char's grouped by 8, 4 or 2
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*/
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#if defined(POLARSSL_HAVE_INT8)
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#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
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a, b, c, d, e, f, g, h
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#define BYTES_TO_T_UINT_4( a, b, c, d ) \
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a, b, c, d
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#define BYTES_TO_T_UINT_2( a, b ) \
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a, b
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#elif defined(POLARSSL_HAVE_INT16)
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#define BYTES_TO_T_UINT_2( a, b ) \
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( (t_uint) a << 0 ) | \
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( (t_uint) b << 8 )
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#define BYTES_TO_T_UINT_4( a, b, c, d ) \
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BYTES_TO_T_UINT_2( a, b ), \
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BYTES_TO_T_UINT_2( c, d )
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#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
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BYTES_TO_T_UINT_2( a, b ), \
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BYTES_TO_T_UINT_2( c, d ), \
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BYTES_TO_T_UINT_2( e, f ), \
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BYTES_TO_T_UINT_2( g, h )
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#elif defined(POLARSSL_HAVE_INT32)
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#define BYTES_TO_T_UINT_4( a, b, c, d ) \
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( (t_uint) a << 0 ) | \
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( (t_uint) b << 8 ) | \
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( (t_uint) c << 16 ) | \
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( (t_uint) d << 24 )
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#define BYTES_TO_T_UINT_2( a, b ) \
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BYTES_TO_T_UINT_4( a, b, 0, 0 )
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#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
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BYTES_TO_T_UINT_4( a, b, c, d ), \
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BYTES_TO_T_UINT_4( e, f, g, h )
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#else /* 64-bits */
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#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
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( (t_uint) a << 0 ) | \
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( (t_uint) b << 8 ) | \
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( (t_uint) c << 16 ) | \
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( (t_uint) d << 24 ) | \
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( (t_uint) e << 32 ) | \
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( (t_uint) f << 40 ) | \
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( (t_uint) g << 48 ) | \
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( (t_uint) h << 56 )
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#define BYTES_TO_T_UINT_4( a, b, c, d ) \
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BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 )
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#define BYTES_TO_T_UINT_2( a, b ) \
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BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 )
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#endif /* bits in t_uint */
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/*
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* Note: the constants are in little-endian order
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* to be directly usable in MPIs
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*/
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/*
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* Domain parameters for secp192r1
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*/
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#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
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static const t_uint secp192r1_p[] = {
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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};
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static const t_uint secp192r1_b[] = {
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BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
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BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
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BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
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};
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static const t_uint secp192r1_gx[] = {
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BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
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BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
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BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
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};
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static const t_uint secp192r1_gy[] = {
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BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
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BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
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BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
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};
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static const t_uint secp192r1_n[] = {
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BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
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BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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};
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#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
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/*
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* Domain parameters for secp224r1
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*/
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#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
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static const t_uint secp224r1_p[] = {
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BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
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BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
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};
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static const t_uint secp224r1_b[] = {
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BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
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BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
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BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
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BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
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};
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static const t_uint secp224r1_gx[] = {
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BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
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BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
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BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
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BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
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};
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static const t_uint secp224r1_gy[] = {
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BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
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BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
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BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
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BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
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};
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static const t_uint secp224r1_n[] = {
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BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
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BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
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};
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#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
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/*
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* Domain parameters for secp256r1
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*/
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#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
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static const t_uint secp256r1_p[] = {
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
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BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
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BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
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};
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static const t_uint secp256r1_b[] = {
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BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
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BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
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BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
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BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
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};
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static const t_uint secp256r1_gx[] = {
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BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
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BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
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BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
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BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
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};
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static const t_uint secp256r1_gy[] = {
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BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
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BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
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BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
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BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
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};
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static const t_uint secp256r1_n[] = {
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BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
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BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
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};
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#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
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/*
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* Domain parameters for secp384r1
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*/
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#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
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static const t_uint secp384r1_p[] = {
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
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BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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};
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static const t_uint secp384r1_b[] = {
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BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
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BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
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BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
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BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
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BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
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BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
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};
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static const t_uint secp384r1_gx[] = {
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BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
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BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
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BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
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BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
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BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
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BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
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};
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static const t_uint secp384r1_gy[] = {
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BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
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BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
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BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
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BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
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BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
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BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
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};
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static const t_uint secp384r1_n[] = {
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BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
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BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
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BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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};
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#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
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/*
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* Domain parameters for secp521r1
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*/
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#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
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static const t_uint secp521r1_p[] = {
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
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};
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static const t_uint secp521r1_b[] = {
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BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
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BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
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BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
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BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
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BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
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BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
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BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
|
|
BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
|
|
BYTES_TO_T_UINT_2( 0x51, 0x00 ),
|
|
};
|
|
static const t_uint secp521r1_gx[] = {
|
|
BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
|
|
BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
|
|
BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
|
|
BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
|
|
BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
|
|
BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
|
|
BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
|
|
BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
|
|
BYTES_TO_T_UINT_2( 0xC6, 0x00 ),
|
|
};
|
|
static const t_uint secp521r1_gy[] = {
|
|
BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
|
|
BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
|
|
BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
|
|
BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
|
|
BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
|
|
BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
|
|
BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
|
|
BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
|
|
BYTES_TO_T_UINT_2( 0x18, 0x01 ),
|
|
};
|
|
static const t_uint secp521r1_n[] = {
|
|
BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
|
|
BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
|
|
BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
|
|
BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
|
|
BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
|
|
};
|
|
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED)
|
|
static const t_uint secp192k1_p[] = {
|
|
BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
};
|
|
static const t_uint secp192k1_a[] = {
|
|
BYTES_TO_T_UINT_2( 0x00, 0x00 ),
|
|
};
|
|
static const t_uint secp192k1_b[] = {
|
|
BYTES_TO_T_UINT_2( 0x03, 0x00 ),
|
|
};
|
|
static const t_uint secp192k1_gx[] = {
|
|
BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ),
|
|
BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ),
|
|
BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ),
|
|
};
|
|
static const t_uint secp192k1_gy[] = {
|
|
BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ),
|
|
BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ),
|
|
BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ),
|
|
};
|
|
static const t_uint secp192k1_n[] = {
|
|
BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ),
|
|
BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
};
|
|
#endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED)
|
|
static const t_uint secp224k1_p[] = {
|
|
BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
};
|
|
static const t_uint secp224k1_a[] = {
|
|
BYTES_TO_T_UINT_2( 0x00, 0x00 ),
|
|
};
|
|
static const t_uint secp224k1_b[] = {
|
|
BYTES_TO_T_UINT_2( 0x05, 0x00 ),
|
|
};
|
|
static const t_uint secp224k1_gx[] = {
|
|
BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ),
|
|
BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ),
|
|
BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ),
|
|
BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ),
|
|
};
|
|
static const t_uint secp224k1_gy[] = {
|
|
BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ),
|
|
BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ),
|
|
BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ),
|
|
BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ),
|
|
};
|
|
static const t_uint secp224k1_n[] = {
|
|
BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ),
|
|
BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ),
|
|
BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
|
|
BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ),
|
|
};
|
|
#endif /* POLARSSL_ECP_DP_SECP224K1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED)
|
|
static const t_uint secp256k1_p[] = {
|
|
BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
};
|
|
static const t_uint secp256k1_a[] = {
|
|
BYTES_TO_T_UINT_2( 0x00, 0x00 ),
|
|
};
|
|
static const t_uint secp256k1_b[] = {
|
|
BYTES_TO_T_UINT_2( 0x07, 0x00 ),
|
|
};
|
|
static const t_uint secp256k1_gx[] = {
|
|
BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ),
|
|
BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ),
|
|
BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ),
|
|
BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ),
|
|
};
|
|
static const t_uint secp256k1_gy[] = {
|
|
BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ),
|
|
BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ),
|
|
BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ),
|
|
BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ),
|
|
};
|
|
static const t_uint secp256k1_n[] = {
|
|
BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ),
|
|
BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ),
|
|
BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
|
};
|
|
#endif /* POLARSSL_ECP_DP_SECP256K1_ENABLED */
|
|
|
|
/*
|
|
* Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
|
|
*/
|
|
#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
|
|
static const t_uint brainpoolP256r1_p[] = {
|
|
BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
|
|
BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
|
|
BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
|
|
BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
|
|
};
|
|
static const t_uint brainpoolP256r1_a[] = {
|
|
BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
|
|
BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
|
|
BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
|
|
BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
|
|
};
|
|
static const t_uint brainpoolP256r1_b[] = {
|
|
BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
|
|
BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
|
|
BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
|
|
BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
|
|
};
|
|
static const t_uint brainpoolP256r1_gx[] = {
|
|
BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
|
|
BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
|
|
BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
|
|
BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
|
|
};
|
|
static const t_uint brainpoolP256r1_gy[] = {
|
|
BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
|
|
BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
|
|
BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
|
|
BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
|
|
};
|
|
static const t_uint brainpoolP256r1_n[] = {
|
|
BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
|
|
BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
|
|
BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
|
|
BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
|
|
};
|
|
#endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */
|
|
|
|
/*
|
|
* Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
|
|
*/
|
|
#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
|
|
static const t_uint brainpoolP384r1_p[] = {
|
|
BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
|
|
BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
|
|
BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
|
|
BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
|
|
BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
|
|
BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
|
|
};
|
|
static const t_uint brainpoolP384r1_a[] = {
|
|
BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
|
|
BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
|
|
BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
|
|
BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
|
|
BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
|
|
BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
|
|
};
|
|
static const t_uint brainpoolP384r1_b[] = {
|
|
BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
|
|
BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
|
|
BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
|
|
BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
|
|
BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
|
|
BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
|
|
};
|
|
static const t_uint brainpoolP384r1_gx[] = {
|
|
BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
|
|
BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
|
|
BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
|
|
BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
|
|
BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
|
|
BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
|
|
};
|
|
static const t_uint brainpoolP384r1_gy[] = {
|
|
BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
|
|
BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
|
|
BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
|
|
BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
|
|
BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
|
|
BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
|
|
};
|
|
static const t_uint brainpoolP384r1_n[] = {
|
|
BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
|
|
BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
|
|
BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
|
|
BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
|
|
BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
|
|
BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
|
|
};
|
|
#endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */
|
|
|
|
/*
|
|
* Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
|
|
*/
|
|
#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
|
|
static const t_uint brainpoolP512r1_p[] = {
|
|
BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
|
|
BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
|
|
BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
|
|
BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
|
|
BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
|
|
BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
|
|
BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
|
|
BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
|
|
};
|
|
static const t_uint brainpoolP512r1_a[] = {
|
|
BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
|
|
BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
|
|
BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
|
|
BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
|
|
BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
|
|
BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
|
|
BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
|
|
BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
|
|
};
|
|
static const t_uint brainpoolP512r1_b[] = {
|
|
BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
|
|
BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
|
|
BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
|
|
BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
|
|
BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
|
|
BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
|
|
BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
|
|
BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
|
|
};
|
|
static const t_uint brainpoolP512r1_gx[] = {
|
|
BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
|
|
BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
|
|
BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
|
|
BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
|
|
BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
|
|
BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
|
|
BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
|
|
BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
|
|
};
|
|
static const t_uint brainpoolP512r1_gy[] = {
|
|
BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
|
|
BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
|
|
BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
|
|
BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
|
|
BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
|
|
BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
|
|
BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
|
|
BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
|
|
};
|
|
static const t_uint brainpoolP512r1_n[] = {
|
|
BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
|
|
BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
|
|
BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
|
|
BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
|
|
BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
|
|
BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
|
|
BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
|
|
BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
|
|
};
|
|
#endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */
|
|
|
|
/*
|
|
* Create an MPI from embedded constants
|
|
* (assumes len is an exact multiple of sizeof t_uint)
|
|
*/
|
|
static inline void ecp_mpi_load( mpi *X, const t_uint *p, size_t len )
|
|
{
|
|
X->s = 1;
|
|
X->n = len / sizeof( t_uint );
|
|
X->p = (t_uint *) p;
|
|
}
|
|
|
|
/*
|
|
* Set an MPI to static value 1
|
|
*/
|
|
static inline void ecp_mpi_set1( mpi *X )
|
|
{
|
|
static t_uint one[] = { 1 };
|
|
X->s = 1;
|
|
X->n = 1;
|
|
X->p = one;
|
|
}
|
|
|
|
/*
|
|
* Make group available from embedded constants
|
|
*/
|
|
static int ecp_group_load( ecp_group *grp,
|
|
const t_uint *p, size_t plen,
|
|
const t_uint *a, size_t alen,
|
|
const t_uint *b, size_t blen,
|
|
const t_uint *gx, size_t gxlen,
|
|
const t_uint *gy, size_t gylen,
|
|
const t_uint *n, size_t nlen)
|
|
{
|
|
ecp_mpi_load( &grp->P, p, plen );
|
|
if( a != NULL )
|
|
ecp_mpi_load( &grp->A, a, alen );
|
|
ecp_mpi_load( &grp->B, b, blen );
|
|
ecp_mpi_load( &grp->N, n, nlen );
|
|
|
|
ecp_mpi_load( &grp->G.X, gx, gxlen );
|
|
ecp_mpi_load( &grp->G.Y, gy, gylen );
|
|
ecp_mpi_set1( &grp->G.Z );
|
|
|
|
grp->pbits = mpi_msb( &grp->P );
|
|
grp->nbits = mpi_msb( &grp->N );
|
|
|
|
grp->h = 1;
|
|
|
|
return( 0 );
|
|
}
|
|
|
|
#if defined(POLARSSL_ECP_NIST_OPTIM)
|
|
/* Forward declarations */
|
|
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
|
|
static int ecp_mod_p192( mpi * );
|
|
#endif
|
|
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
|
|
static int ecp_mod_p224( mpi * );
|
|
#endif
|
|
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
|
|
static int ecp_mod_p256( mpi * );
|
|
#endif
|
|
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
|
|
static int ecp_mod_p384( mpi * );
|
|
#endif
|
|
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
|
|
static int ecp_mod_p521( mpi * );
|
|
#endif
|
|
|
|
#define NIST_MODP( P ) grp->modp = ecp_mod_ ## P;
|
|
#else
|
|
#define NIST_MODP( P )
|
|
#endif /* POLARSSL_ECP_NIST_OPTIM */
|
|
|
|
/* Additional forward declarations */
|
|
#if defined(POLARSSL_ECP_DP_M255_ENABLED)
|
|
static int ecp_mod_p255( mpi * );
|
|
#endif
|
|
#if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED)
|
|
static int ecp_mod_p192k1( mpi * );
|
|
#endif
|
|
#if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED)
|
|
static int ecp_mod_p224k1( mpi * );
|
|
#endif
|
|
#if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED)
|
|
static int ecp_mod_p256k1( mpi * );
|
|
#endif
|
|
|
|
#define LOAD_GROUP_A( G ) ecp_group_load( grp, \
|
|
G ## _p, sizeof( G ## _p ), \
|
|
G ## _a, sizeof( G ## _a ), \
|
|
G ## _b, sizeof( G ## _b ), \
|
|
G ## _gx, sizeof( G ## _gx ), \
|
|
G ## _gy, sizeof( G ## _gy ), \
|
|
G ## _n, sizeof( G ## _n ) )
|
|
|
|
#define LOAD_GROUP( G ) ecp_group_load( grp, \
|
|
G ## _p, sizeof( G ## _p ), \
|
|
NULL, 0, \
|
|
G ## _b, sizeof( G ## _b ), \
|
|
G ## _gx, sizeof( G ## _gx ), \
|
|
G ## _gy, sizeof( G ## _gy ), \
|
|
G ## _n, sizeof( G ## _n ) )
|
|
|
|
#if defined(POLARSSL_ECP_DP_M255_ENABLED)
|
|
/*
|
|
* Specialized function for creating the Curve25519 group
|
|
*/
|
|
static int ecp_use_curve25519( ecp_group *grp )
|
|
{
|
|
int ret;
|
|
|
|
/* Actually ( A + 2 ) / 4 */
|
|
MPI_CHK( mpi_read_string( &grp->A, 16, "01DB42" ) );
|
|
|
|
/* P = 2^255 - 19 */
|
|
MPI_CHK( mpi_lset( &grp->P, 1 ) );
|
|
MPI_CHK( mpi_shift_l( &grp->P, 255 ) );
|
|
MPI_CHK( mpi_sub_int( &grp->P, &grp->P, 19 ) );
|
|
grp->pbits = mpi_msb( &grp->P );
|
|
|
|
/* Y intentionaly not set, since we use x/z coordinates.
|
|
* This is used as a marker to identify Montgomery curves! */
|
|
MPI_CHK( mpi_lset( &grp->G.X, 9 ) );
|
|
MPI_CHK( mpi_lset( &grp->G.Z, 1 ) );
|
|
mpi_free( &grp->G.Y );
|
|
|
|
/* Actually, the required msb for private keys */
|
|
grp->nbits = 254;
|
|
|
|
cleanup:
|
|
if( ret != 0 )
|
|
ecp_group_free( grp );
|
|
|
|
return( ret );
|
|
}
|
|
#endif /* POLARSSL_ECP_DP_M255_ENABLED */
|
|
|
|
/*
|
|
* Set a group using well-known domain parameters
|
|
*/
|
|
int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
|
|
{
|
|
ecp_group_free( grp );
|
|
|
|
grp->id = id;
|
|
|
|
switch( id )
|
|
{
|
|
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
|
|
case POLARSSL_ECP_DP_SECP192R1:
|
|
NIST_MODP( p192 );
|
|
return( LOAD_GROUP( secp192r1 ) );
|
|
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
|
|
case POLARSSL_ECP_DP_SECP224R1:
|
|
NIST_MODP( p224 );
|
|
return( LOAD_GROUP( secp224r1 ) );
|
|
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
|
|
case POLARSSL_ECP_DP_SECP256R1:
|
|
NIST_MODP( p256 );
|
|
return( LOAD_GROUP( secp256r1 ) );
|
|
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
|
|
case POLARSSL_ECP_DP_SECP384R1:
|
|
NIST_MODP( p384 );
|
|
return( LOAD_GROUP( secp384r1 ) );
|
|
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
|
|
case POLARSSL_ECP_DP_SECP521R1:
|
|
NIST_MODP( p521 );
|
|
return( LOAD_GROUP( secp521r1 ) );
|
|
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED)
|
|
case POLARSSL_ECP_DP_SECP192K1:
|
|
grp->modp = ecp_mod_p192k1;
|
|
return( LOAD_GROUP_A( secp192k1 ) );
|
|
#endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED)
|
|
case POLARSSL_ECP_DP_SECP224K1:
|
|
grp->modp = ecp_mod_p224k1;
|
|
return( LOAD_GROUP_A( secp224k1 ) );
|
|
#endif /* POLARSSL_ECP_DP_SECP224K1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED)
|
|
case POLARSSL_ECP_DP_SECP256K1:
|
|
grp->modp = ecp_mod_p256k1;
|
|
return( LOAD_GROUP_A( secp256k1 ) );
|
|
#endif /* POLARSSL_ECP_DP_SECP256K1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
|
|
case POLARSSL_ECP_DP_BP256R1:
|
|
return( LOAD_GROUP_A( brainpoolP256r1 ) );
|
|
#endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
|
|
case POLARSSL_ECP_DP_BP384R1:
|
|
return( LOAD_GROUP_A( brainpoolP384r1 ) );
|
|
#endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
|
|
case POLARSSL_ECP_DP_BP512R1:
|
|
return( LOAD_GROUP_A( brainpoolP512r1 ) );
|
|
#endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_M255_ENABLED)
|
|
case POLARSSL_ECP_DP_M255:
|
|
grp->modp = ecp_mod_p255;
|
|
return( ecp_use_curve25519( grp ) );
|
|
#endif /* POLARSSL_ECP_DP_M255_ENABLED */
|
|
|
|
default:
|
|
ecp_group_free( grp );
|
|
return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE );
|
|
}
|
|
}
|
|
|
|
#if defined(POLARSSL_ECP_NIST_OPTIM)
|
|
/*
|
|
* Fast reduction modulo the primes used by the NIST curves.
|
|
*
|
|
* These functions are critical for speed, but not needed for correct
|
|
* operations. So, we make the choice to heavily rely on the internals of our
|
|
* bignum library, which creates a tight coupling between these functions and
|
|
* our MPI implementation. However, the coupling between the ECP module and
|
|
* MPI remains loose, since these functions can be deactivated at will.
|
|
*/
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
|
|
/*
|
|
* Compared to the way things are presented in FIPS 186-3 D.2,
|
|
* we proceed in columns, from right (least significant chunk) to left,
|
|
* adding chunks to N in place, and keeping a carry for the next chunk.
|
|
* This avoids moving things around in memory, and uselessly adding zeros,
|
|
* compared to the more straightforward, line-oriented approach.
|
|
*
|
|
* For this prime we need to handle data in chunks of 64 bits.
|
|
* Since this is always a multiple of our basic t_uint, we can
|
|
* use a t_uint * to designate such a chunk, and small loops to handle it.
|
|
*/
|
|
|
|
/* Add 64-bit chunks (dst += src) and update carry */
|
|
static inline void add64( t_uint *dst, t_uint *src, t_uint *carry )
|
|
{
|
|
unsigned char i;
|
|
t_uint c = 0;
|
|
for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++, src++ )
|
|
{
|
|
*dst += c; c = ( *dst < c );
|
|
*dst += *src; c += ( *dst < *src );
|
|
}
|
|
*carry += c;
|
|
}
|
|
|
|
/* Add carry to a 64-bit chunk and update carry */
|
|
static inline void carry64( t_uint *dst, t_uint *carry )
|
|
{
|
|
unsigned char i;
|
|
for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++ )
|
|
{
|
|
*dst += *carry;
|
|
*carry = ( *dst < *carry );
|
|
}
|
|
}
|
|
|
|
#define WIDTH 8 / sizeof( t_uint )
|
|
#define A( i ) N->p + i * WIDTH
|
|
#define ADD( i ) add64( p, A( i ), &c )
|
|
#define NEXT p += WIDTH; carry64( p, &c )
|
|
#define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0
|
|
|
|
/*
|
|
* Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
|
|
*/
|
|
static int ecp_mod_p192( mpi *N )
|
|
{
|
|
int ret;
|
|
t_uint c = 0;
|
|
t_uint *p, *end;
|
|
|
|
/* Make sure we have enough blocks so that A(5) is legal */
|
|
MPI_CHK( mpi_grow( N, 6 * WIDTH ) );
|
|
|
|
p = N->p;
|
|
end = p + N->n;
|
|
|
|
ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5
|
|
ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5
|
|
ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
#undef WIDTH
|
|
#undef A
|
|
#undef ADD
|
|
#undef NEXT
|
|
#undef LAST
|
|
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) || \
|
|
defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) || \
|
|
defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
|
|
/*
|
|
* The reader is advised to first understand ecp_mod_p192() since the same
|
|
* general structure is used here, but with additional complications:
|
|
* (1) chunks of 32 bits, and (2) subtractions.
|
|
*/
|
|
|
|
/*
|
|
* For these primes, we need to handle data in chunks of 32 bits.
|
|
* This makes it more complicated if we use 64 bits limbs in MPI,
|
|
* which prevents us from using a uniform access method as for p192.
|
|
*
|
|
* So, we define a mini abstraction layer to access 32 bit chunks,
|
|
* load them in 'cur' for work, and store them back from 'cur' when done.
|
|
*
|
|
* While at it, also define the size of N in terms of 32-bit chunks.
|
|
*/
|
|
#define LOAD32 cur = A( i );
|
|
|
|
#if defined(POLARSSL_HAVE_INT8) /* 8 bit */
|
|
|
|
#define MAX32 N->n / 4
|
|
#define A( j ) (uint32_t)( N->p[4*j+0] ) | \
|
|
( N->p[4*j+1] << 8 ) | \
|
|
( N->p[4*j+2] << 16 ) | \
|
|
( N->p[4*j+3] << 24 )
|
|
#define STORE32 N->p[4*i+0] = (t_uint)( cur ); \
|
|
N->p[4*i+1] = (t_uint)( cur >> 8 ); \
|
|
N->p[4*i+2] = (t_uint)( cur >> 16 ); \
|
|
N->p[4*i+3] = (t_uint)( cur >> 24 );
|
|
|
|
#elif defined(POLARSSL_HAVE_INT16) /* 16 bit */
|
|
|
|
#define MAX32 N->n / 2
|
|
#define A( j ) (uint32_t)( N->p[2*j] ) | ( N->p[2*j+1] << 16 )
|
|
#define STORE32 N->p[2*i+0] = (t_uint)( cur ); \
|
|
N->p[2*i+1] = (t_uint)( cur >> 16 );
|
|
|
|
#elif defined(POLARSSL_HAVE_INT32) /* 32 bit */
|
|
|
|
#define MAX32 N->n
|
|
#define A( j ) N->p[j]
|
|
#define STORE32 N->p[i] = cur;
|
|
|
|
#else /* 64-bit */
|
|
|
|
#define MAX32 N->n * 2
|
|
#define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
|
|
#define STORE32 \
|
|
if( i % 2 ) { \
|
|
N->p[i/2] &= 0x00000000FFFFFFFF; \
|
|
N->p[i/2] |= ((t_uint) cur) << 32; \
|
|
} else { \
|
|
N->p[i/2] &= 0xFFFFFFFF00000000; \
|
|
N->p[i/2] |= (t_uint) cur; \
|
|
}
|
|
|
|
#endif /* sizeof( t_uint ) */
|
|
|
|
/*
|
|
* Helpers for addition and subtraction of chunks, with signed carry.
|
|
*/
|
|
static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
|
|
{
|
|
*dst += src;
|
|
*carry += ( *dst < src );
|
|
}
|
|
|
|
static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
|
|
{
|
|
*carry -= ( *dst < src );
|
|
*dst -= src;
|
|
}
|
|
|
|
#define ADD( j ) add32( &cur, A( j ), &c );
|
|
#define SUB( j ) sub32( &cur, A( j ), &c );
|
|
|
|
/*
|
|
* Helpers for the main 'loop'
|
|
* (see fix_negative for the motivation of C)
|
|
*/
|
|
#define INIT( b ) \
|
|
int ret; \
|
|
signed char c = 0, cc; \
|
|
uint32_t cur; \
|
|
size_t i = 0, bits = b; \
|
|
mpi C; \
|
|
t_uint Cp[ b / 8 / sizeof( t_uint) + 1 ]; \
|
|
\
|
|
C.s = 1; \
|
|
C.n = b / 8 / sizeof( t_uint) + 1; \
|
|
C.p = Cp; \
|
|
memset( Cp, 0, C.n * sizeof( t_uint ) ); \
|
|
\
|
|
MPI_CHK( mpi_grow( N, b * 2 / 8 / sizeof( t_uint ) ) ); \
|
|
LOAD32;
|
|
|
|
#define NEXT \
|
|
STORE32; i++; LOAD32; \
|
|
cc = c; c = 0; \
|
|
if( cc < 0 ) \
|
|
sub32( &cur, -cc, &c ); \
|
|
else \
|
|
add32( &cur, cc, &c ); \
|
|
|
|
#define LAST \
|
|
STORE32; i++; \
|
|
cur = c > 0 ? c : 0; STORE32; \
|
|
cur = 0; while( ++i < MAX32 ) { STORE32; } \
|
|
if( c < 0 ) fix_negative( N, c, &C, bits );
|
|
|
|
/*
|
|
* If the result is negative, we get it in the form
|
|
* c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
|
|
*/
|
|
static inline int fix_negative( mpi *N, signed char c, mpi *C, size_t bits )
|
|
{
|
|
int ret;
|
|
|
|
/* C = - c * 2^(bits + 32) */
|
|
#if !defined(POLARSSL_HAVE_INT64)
|
|
((void) bits);
|
|
#else
|
|
if( bits == 224 )
|
|
C->p[ C->n - 1 ] = ((t_uint) -c) << 32;
|
|
else
|
|
#endif
|
|
C->p[ C->n - 1 ] = (t_uint) -c;
|
|
|
|
/* N = - ( C - N ) */
|
|
MPI_CHK( mpi_sub_abs( N, C, N ) );
|
|
N->s = -1;
|
|
|
|
cleanup:
|
|
|
|
return( ret );
|
|
}
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
|
|
/*
|
|
* Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
|
|
*/
|
|
static int ecp_mod_p224( mpi *N )
|
|
{
|
|
INIT( 224 );
|
|
|
|
SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11
|
|
SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12
|
|
SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13
|
|
SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11
|
|
SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12
|
|
SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13
|
|
SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
|
|
/*
|
|
* Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
|
|
*/
|
|
static int ecp_mod_p256( mpi *N )
|
|
{
|
|
INIT( 256 );
|
|
|
|
ADD( 8 ); ADD( 9 );
|
|
SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0
|
|
|
|
ADD( 9 ); ADD( 10 );
|
|
SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1
|
|
|
|
ADD( 10 ); ADD( 11 );
|
|
SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2
|
|
|
|
ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
|
|
SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3
|
|
|
|
ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
|
|
SUB( 9 ); SUB( 10 ); NEXT; // A4
|
|
|
|
ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
|
|
SUB( 10 ); SUB( 11 ); NEXT; // A5
|
|
|
|
ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
|
|
SUB( 8 ); SUB( 9 ); NEXT; // A6
|
|
|
|
ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
|
|
SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
|
|
/*
|
|
* Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
|
|
*/
|
|
static int ecp_mod_p384( mpi *N )
|
|
{
|
|
INIT( 384 );
|
|
|
|
ADD( 12 ); ADD( 21 ); ADD( 20 );
|
|
SUB( 23 ); NEXT; // A0
|
|
|
|
ADD( 13 ); ADD( 22 ); ADD( 23 );
|
|
SUB( 12 ); SUB( 20 ); NEXT; // A2
|
|
|
|
ADD( 14 ); ADD( 23 );
|
|
SUB( 13 ); SUB( 21 ); NEXT; // A2
|
|
|
|
ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
|
|
SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3
|
|
|
|
ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
|
|
SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4
|
|
|
|
ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
|
|
SUB( 16 ); NEXT; // A5
|
|
|
|
ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
|
|
SUB( 17 ); NEXT; // A6
|
|
|
|
ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
|
|
SUB( 18 ); NEXT; // A7
|
|
|
|
ADD( 20 ); ADD( 17 ); ADD( 16 );
|
|
SUB( 19 ); NEXT; // A8
|
|
|
|
ADD( 21 ); ADD( 18 ); ADD( 17 );
|
|
SUB( 20 ); NEXT; // A9
|
|
|
|
ADD( 22 ); ADD( 19 ); ADD( 18 );
|
|
SUB( 21 ); NEXT; // A10
|
|
|
|
ADD( 23 ); ADD( 20 ); ADD( 19 );
|
|
SUB( 22 ); LAST; // A11
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
|
|
|
|
#undef A
|
|
#undef LOAD32
|
|
#undef STORE32
|
|
#undef MAX32
|
|
#undef INIT
|
|
#undef NEXT
|
|
#undef LAST
|
|
|
|
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED ||
|
|
POLARSSL_ECP_DP_SECP256R1_ENABLED ||
|
|
POLARSSL_ECP_DP_SECP384R1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
|
|
/*
|
|
* Here we have an actual Mersenne prime, so things are more straightforward.
|
|
* However, chunks are aligned on a 'weird' boundary (521 bits).
|
|
*/
|
|
|
|
/* Size of p521 in terms of t_uint */
|
|
#define P521_WIDTH ( 521 / 8 / sizeof( t_uint ) + 1 )
|
|
|
|
/* Bits to keep in the most significant t_uint */
|
|
#if defined(POLARSSL_HAVE_INT8)
|
|
#define P521_MASK 0x01
|
|
#else
|
|
#define P521_MASK 0x01FF
|
|
#endif
|
|
|
|
/*
|
|
* Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
|
|
* Write N as A1 + 2^521 A0, return A0 + A1
|
|
*/
|
|
static int ecp_mod_p521( mpi *N )
|
|
{
|
|
int ret;
|
|
size_t i;
|
|
mpi M;
|
|
t_uint Mp[P521_WIDTH + 1];
|
|
/* Worst case for the size of M is when t_uint is 16 bits:
|
|
* we need to hold bits 513 to 1056, which is 34 limbs, that is
|
|
* P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
|
|
|
|
if( N->n < P521_WIDTH )
|
|
return( 0 );
|
|
|
|
/* M = A1 */
|
|
M.s = 1;
|
|
M.n = N->n - ( P521_WIDTH - 1 );
|
|
if( M.n > P521_WIDTH + 1 )
|
|
M.n = P521_WIDTH + 1;
|
|
M.p = Mp;
|
|
memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( t_uint ) );
|
|
MPI_CHK( mpi_shift_r( &M, 521 % ( 8 * sizeof( t_uint ) ) ) );
|
|
|
|
/* N = A0 */
|
|
N->p[P521_WIDTH - 1] &= P521_MASK;
|
|
for( i = P521_WIDTH; i < N->n; i++ )
|
|
N->p[i] = 0;
|
|
|
|
/* N = A0 + A1 */
|
|
MPI_CHK( mpi_add_abs( N, N, &M ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
#undef P521_WIDTH
|
|
#undef P521_MASK
|
|
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
|
|
|
|
#endif /* POLARSSL_ECP_NIST_OPTIM */
|
|
|
|
#if defined(POLARSSL_ECP_DP_M255_ENABLED)
|
|
|
|
/* Size of p255 in terms of t_uint */
|
|
#define P255_WIDTH ( 255 / 8 / sizeof( t_uint ) + 1 )
|
|
|
|
/*
|
|
* Fast quasi-reduction modulo p255 = 2^255 - 19
|
|
* Write N as A0 + 2^255 A1, return A0 + 19 * A1
|
|
*/
|
|
static int ecp_mod_p255( mpi *N )
|
|
{
|
|
int ret;
|
|
size_t i;
|
|
mpi M;
|
|
t_uint Mp[P255_WIDTH + 2];
|
|
|
|
if( N->n < P255_WIDTH )
|
|
return( 0 );
|
|
|
|
/* M = A1 */
|
|
M.s = 1;
|
|
M.n = N->n - ( P255_WIDTH - 1 );
|
|
if( M.n > P255_WIDTH + 1 )
|
|
M.n = P255_WIDTH + 1;
|
|
M.p = Mp;
|
|
memset( Mp, 0, sizeof Mp );
|
|
memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( t_uint ) );
|
|
MPI_CHK( mpi_shift_r( &M, 255 % ( 8 * sizeof( t_uint ) ) ) );
|
|
M.n++; /* Make room for multiplication by 19 */
|
|
|
|
/* N = A0 */
|
|
MPI_CHK( mpi_set_bit( N, 255, 0 ) );
|
|
for( i = P255_WIDTH; i < N->n; i++ )
|
|
N->p[i] = 0;
|
|
|
|
/* N = A0 + 19 * A1 */
|
|
MPI_CHK( mpi_mul_int( &M, &M, 19 ) );
|
|
MPI_CHK( mpi_add_abs( N, N, &M ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
#endif /* POLARSSL_ECP_DP_M255_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED) || \
|
|
defined(POLARSSL_ECP_DP_SECP224K1_ENABLED) || \
|
|
defined(POLARSSL_ECP_DP_SECP256K1_ENABLED)
|
|
/*
|
|
* Fast quasi-reduction modulo P = 2^s - R,
|
|
* with R about 33 bits, used by the Koblitz curves.
|
|
*
|
|
* Write N as A0 + 2^224 A1, return A0 + R * A1.
|
|
* Actually do two passes, since R is big.
|
|
*/
|
|
#define P_KOBLITZ_MAX ( 256 / 8 / sizeof( t_uint ) ) // Max limbs in P
|
|
#define P_KOBLITZ_R ( 8 / sizeof( t_uint ) ) // Limbs in R
|
|
static inline int ecp_mod_koblitz( mpi *N, t_uint *Rp, size_t p_limbs,
|
|
size_t adjust, size_t shift, t_uint mask )
|
|
{
|
|
int ret;
|
|
size_t i;
|
|
mpi M, R;
|
|
t_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R];
|
|
|
|
if( N->n < p_limbs )
|
|
return( 0 );
|
|
|
|
/* Init R */
|
|
R.s = 1;
|
|
R.p = Rp;
|
|
R.n = P_KOBLITZ_R;
|
|
|
|
/* Common setup for M */
|
|
M.s = 1;
|
|
M.p = Mp;
|
|
|
|
/* M = A1 */
|
|
M.n = N->n - ( p_limbs - adjust );
|
|
if( M.n > p_limbs + adjust )
|
|
M.n = p_limbs + adjust;
|
|
memset( Mp, 0, sizeof Mp );
|
|
memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( t_uint ) );
|
|
if( shift != 0 )
|
|
MPI_CHK( mpi_shift_r( &M, shift ) );
|
|
M.n += R.n - adjust; /* Make room for multiplication by R */
|
|
|
|
/* N = A0 */
|
|
if( mask != 0 )
|
|
N->p[p_limbs - 1] &= mask;
|
|
for( i = p_limbs; i < N->n; i++ )
|
|
N->p[i] = 0;
|
|
|
|
/* N = A0 + R * A1 */
|
|
MPI_CHK( mpi_mul_mpi( &M, &M, &R ) );
|
|
MPI_CHK( mpi_add_abs( N, N, &M ) );
|
|
|
|
/* Second pass */
|
|
|
|
/* M = A1 */
|
|
M.n = N->n - ( p_limbs - adjust );
|
|
if( M.n > p_limbs + adjust )
|
|
M.n = p_limbs + adjust;
|
|
memset( Mp, 0, sizeof Mp );
|
|
memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( t_uint ) );
|
|
if( shift != 0 )
|
|
MPI_CHK( mpi_shift_r( &M, shift ) );
|
|
M.n += R.n - adjust; /* Make room for multiplication by R */
|
|
|
|
/* N = A0 */
|
|
if( mask != 0 )
|
|
N->p[p_limbs - 1] &= mask;
|
|
for( i = p_limbs; i < N->n; i++ )
|
|
N->p[i] = 0;
|
|
|
|
/* N = A0 + R * A1 */
|
|
MPI_CHK( mpi_mul_mpi( &M, &M, &R ) );
|
|
MPI_CHK( mpi_add_abs( N, N, &M ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
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}
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#endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED) ||
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POLARSSL_ECP_DP_SECP224K1_ENABLED) ||
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POLARSSL_ECP_DP_SECP256K1_ENABLED) */
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|
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#if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED)
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/*
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* Fast quasi-reduction modulo p192k1 = 2^192 - R,
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* with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
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*/
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static int ecp_mod_p192k1( mpi *N )
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{
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static t_uint Rp[] = {
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BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
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|
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return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( t_uint ), 0, 0, 0 ) );
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}
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#endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED */
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|
|
|
#if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED)
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|
/*
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|
* Fast quasi-reduction modulo p224k1 = 2^224 - R,
|
|
* with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93
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|
*/
|
|
static int ecp_mod_p224k1( mpi *N )
|
|
{
|
|
static t_uint Rp[] = {
|
|
BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
|
|
|
|
#if defined(POLARSSL_HAVE_INT64)
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return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) );
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|
#else
|
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return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( t_uint ), 0, 0, 0 ) );
|
|
#endif
|
|
}
|
|
|
|
#endif /* POLARSSL_ECP_DP_SECP224K1_ENABLED */
|
|
|
|
#if defined(POLARSSL_ECP_DP_SECP256K1_ENABLED)
|
|
/*
|
|
* Fast quasi-reduction modulo p256k1 = 2^256 - R,
|
|
* with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1
|
|
*/
|
|
static int ecp_mod_p256k1( mpi *N )
|
|
{
|
|
static t_uint Rp[] = {
|
|
BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
|
|
return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( t_uint ), 0, 0, 0 ) );
|
|
}
|
|
#endif /* POLARSSL_ECP_DP_SECP256K1_ENABLED */
|
|
|
|
#endif /* POLARSSL_ECP_C */
|