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5d9224e11c
mbedtls/library/ecp_curves.c
Janos Follath f5ffc79896 ECP: Prevent freeing a buffer on stack 
The function ecp_mod_koblitz computed the space for the result of a
multiplication optimally for that specific case, but unfortunately
the function mbedtls_mpi_mul_mpi performs a generic, suboptimal
calculation and needs one more limb for the result. Since the result's
buffer is on the stack, the best case scenario is that the program
stops.

This only happened on 64 bit platforms.

Fixes #569
2017-02-28 20:24:52 +00:00

1377 lines
51 KiB
C
Raw Blame History

/*
* Elliptic curves over GF(p): curve-specific data and functions
*
* Copyright (C) 2006-2014, ARM Limited, All Rights Reserved
*
* This file is part of mbed TLS (https://tls.mbed.org)
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#if !defined(POLARSSL_CONFIG_FILE)
#include "polarssl/config.h"
#else
#include POLARSSL_CONFIG_FILE
#endif
#if defined(POLARSSL_ECP_C)
#include "polarssl/ecp.h"
#include <string.h>
#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
!defined(inline) && !defined(__cplusplus)
#define inline __inline
#endif
/*
* Conversion macros for embedded constants:
* build lists of t_uint's from lists of unsigned char's grouped by 8, 4 or 2
*/
#if defined(POLARSSL_HAVE_INT8)
#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
a, b, c, d, e, f, g, h
#define BYTES_TO_T_UINT_4( a, b, c, d ) \
a, b, c, d
#define BYTES_TO_T_UINT_2( a, b ) \
a, b
#elif defined(POLARSSL_HAVE_INT16)
#define BYTES_TO_T_UINT_2( a, b ) \
( (t_uint) a << 0 ) | \
( (t_uint) b << 8 )
#define BYTES_TO_T_UINT_4( a, b, c, d ) \
BYTES_TO_T_UINT_2( a, b ), \
BYTES_TO_T_UINT_2( c, d )
#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
BYTES_TO_T_UINT_2( a, b ), \
BYTES_TO_T_UINT_2( c, d ), \
BYTES_TO_T_UINT_2( e, f ), \
BYTES_TO_T_UINT_2( g, h )
#elif defined(POLARSSL_HAVE_INT32)
#define BYTES_TO_T_UINT_4( a, b, c, d ) \
( (t_uint) a << 0 ) | \
( (t_uint) b << 8 ) | \
( (t_uint) c << 16 ) | \
( (t_uint) d << 24 )
#define BYTES_TO_T_UINT_2( a, b ) \
BYTES_TO_T_UINT_4( a, b, 0, 0 )
#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
BYTES_TO_T_UINT_4( a, b, c, d ), \
BYTES_TO_T_UINT_4( e, f, g, h )
#else /* 64-bits */
#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
( (t_uint) a << 0 ) | \
( (t_uint) b << 8 ) | \
( (t_uint) c << 16 ) | \
( (t_uint) d << 24 ) | \
( (t_uint) e << 32 ) | \
( (t_uint) f << 40 ) | \
( (t_uint) g << 48 ) | \
( (t_uint) h << 56 )
#define BYTES_TO_T_UINT_4( a, b, c, d ) \
BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 )
#define BYTES_TO_T_UINT_2( a, b ) \
BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 )
#endif /* bits in t_uint */
/*
* Note: the constants are in little-endian order
* to be directly usable in MPIs
*/
/*
* Domain parameters for secp192r1
*/
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
static const t_uint secp192r1_p[] = {
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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 ),
};
static const t_uint secp192r1_b[] = {
BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
};
static const t_uint secp192r1_gx[] = {
BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
};
static const t_uint secp192r1_gy[] = {
BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
};
static const t_uint secp192r1_n[] = {
BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
/*
* Domain parameters for secp224r1
*/
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
static const t_uint secp224r1_p[] = {
BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 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, 0x00, 0x00, 0x00, 0x00 ),
};
static const t_uint secp224r1_b[] = {
BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
};
static const t_uint secp224r1_gx[] = {
BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
};
static const t_uint secp224r1_gy[] = {
BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
};
static const t_uint secp224r1_n[] = {
BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
};
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
/*
* Domain parameters for secp256r1
*/
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
static const t_uint secp256r1_p[] = {
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static const t_uint secp256r1_b[] = {
BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
};
static const t_uint secp256r1_gx[] = {
BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
};
static const t_uint secp256r1_gy[] = {
BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
};
static const t_uint secp256r1_n[] = {
BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
};
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
/*
* Domain parameters for secp384r1
*/
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
static const t_uint secp384r1_p[] = {
BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
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 ),
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 secp384r1_b[] = {
BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
};
static const t_uint secp384r1_gx[] = {
BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
};
static const t_uint secp384r1_gy[] = {
BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
};
static const t_uint secp384r1_n[] = {
BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
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 ),
};
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
/*
* Domain parameters for secp521r1
*/
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
static const t_uint secp521r1_p[] = {
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_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_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 ),
};
static const t_uint secp521r1_b[] = {
BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
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 + 1];
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; /* 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; /* 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 );
}
#endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED) ||
POLARSSL_ECP_DP_SECP224K1_ENABLED) ||
POLARSSL_ECP_DP_SECP256K1_ENABLED) */
#if defined(POLARSSL_ECP_DP_SECP192K1_ENABLED)
/*
* Fast quasi-reduction modulo p192k1 = 2^192 - R,
* with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
*/
static int ecp_mod_p192k1( mpi *N )
{
static t_uint Rp[] = {
BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( t_uint ), 0, 0, 0 ) );
}
#endif /* POLARSSL_ECP_DP_SECP192K1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP224K1_ENABLED)
/*
* 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
*/
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)
return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) );
#else
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 */
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