/* | |
* Elliptic curves over GF(p): curve-specific data and functions | |
* | |
* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved | |
* SPDX-License-Identifier: Apache-2.0 | |
* | |
* Licensed under the Apache License, Version 2.0 (the "License"); you may | |
* not use this file except in compliance with the License. | |
* You may obtain a copy of the License at | |
* | |
* http://www.apache.org/licenses/LICENSE-2.0 | |
* | |
* Unless required by applicable law or agreed to in writing, software | |
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT | |
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
* See the License for the specific language governing permissions and | |
* limitations under the License. | |
* | |
* This file is part of mbed TLS (https://tls.mbed.org) | |
*/ | |
#if !defined(MBEDTLS_CONFIG_FILE) | |
#include "mbedtls/config.h" | |
#else | |
#include MBEDTLS_CONFIG_FILE | |
#endif | |
#if defined(MBEDTLS_ECP_C) | |
#include "mbedtls/ecp.h" | |
#include "mbedtls/platform_util.h" | |
#include <string.h> | |
#if !defined(MBEDTLS_ECP_ALT) | |
/* Parameter validation macros based on platform_util.h */ | |
#define ECP_VALIDATE_RET( cond ) \ | |
MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA ) | |
#define ECP_VALIDATE( cond ) \ | |
MBEDTLS_INTERNAL_VALIDATE( cond ) | |
#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ | |
!defined(inline) && !defined(__cplusplus) | |
#define inline __inline | |
#endif | |
/* | |
* Conversion macros for embedded constants: | |
* build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2 | |
*/ | |
#if defined(MBEDTLS_HAVE_INT32) | |
#define BYTES_TO_T_UINT_4( a, b, c, d ) \ | |
( (mbedtls_mpi_uint) (a) << 0 ) | \ | |
( (mbedtls_mpi_uint) (b) << 8 ) | \ | |
( (mbedtls_mpi_uint) (c) << 16 ) | \ | |
( (mbedtls_mpi_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 ) \ | |
( (mbedtls_mpi_uint) (a) << 0 ) | \ | |
( (mbedtls_mpi_uint) (b) << 8 ) | \ | |
( (mbedtls_mpi_uint) (c) << 16 ) | \ | |
( (mbedtls_mpi_uint) (d) << 24 ) | \ | |
( (mbedtls_mpi_uint) (e) << 32 ) | \ | |
( (mbedtls_mpi_uint) (f) << 40 ) | \ | |
( (mbedtls_mpi_uint) (g) << 48 ) | \ | |
( (mbedtls_mpi_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 mbedtls_mpi_uint */ | |
/* | |
* Note: the constants are in little-endian order | |
* to be directly usable in MPIs | |
*/ | |
/* | |
* Domain parameters for secp192r1 | |
*/ | |
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ | |
/* | |
* Domain parameters for secp224r1 | |
*/ | |
#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ | |
/* | |
* Domain parameters for secp256r1 | |
*/ | |
#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ | |
/* | |
* Domain parameters for secp384r1 | |
*/ | |
#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ | |
/* | |
* Domain parameters for secp521r1 | |
*/ | |
#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_uint secp192k1_a[] = { | |
BYTES_TO_T_UINT_2( 0x00, 0x00 ), | |
}; | |
static const mbedtls_mpi_uint secp192k1_b[] = { | |
BYTES_TO_T_UINT_2( 0x03, 0x00 ), | |
}; | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_uint secp224k1_a[] = { | |
BYTES_TO_T_UINT_2( 0x00, 0x00 ), | |
}; | |
static const mbedtls_mpi_uint secp224k1_b[] = { | |
BYTES_TO_T_UINT_2( 0x05, 0x00 ), | |
}; | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_uint secp256k1_a[] = { | |
BYTES_TO_T_UINT_2( 0x00, 0x00 ), | |
}; | |
static const mbedtls_mpi_uint secp256k1_b[] = { | |
BYTES_TO_T_UINT_2( 0x07, 0x00 ), | |
}; | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ | |
/* | |
* Domain parameters for brainpoolP256r1 (RFC 5639 3.4) | |
*/ | |
#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ | |
/* | |
* Domain parameters for brainpoolP384r1 (RFC 5639 3.6) | |
*/ | |
#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ | |
/* | |
* Domain parameters for brainpoolP512r1 (RFC 5639 3.7) | |
*/ | |
#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) | |
static const mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 mbedtls_mpi_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 /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ | |
/* | |
* Create an MPI from embedded constants | |
* (assumes len is an exact multiple of sizeof mbedtls_mpi_uint) | |
*/ | |
static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len ) | |
{ | |
X->s = 1; | |
X->n = len / sizeof( mbedtls_mpi_uint ); | |
X->p = (mbedtls_mpi_uint *) p; | |
} | |
/* | |
* Set an MPI to static value 1 | |
*/ | |
static inline void ecp_mpi_set1( mbedtls_mpi *X ) | |
{ | |
static mbedtls_mpi_uint one[] = { 1 }; | |
X->s = 1; | |
X->n = 1; | |
X->p = one; | |
} | |
/* | |
* Make group available from embedded constants | |
*/ | |
static int ecp_group_load( mbedtls_ecp_group *grp, | |
const mbedtls_mpi_uint *p, size_t plen, | |
const mbedtls_mpi_uint *a, size_t alen, | |
const mbedtls_mpi_uint *b, size_t blen, | |
const mbedtls_mpi_uint *gx, size_t gxlen, | |
const mbedtls_mpi_uint *gy, size_t gylen, | |
const mbedtls_mpi_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 = mbedtls_mpi_bitlen( &grp->P ); | |
grp->nbits = mbedtls_mpi_bitlen( &grp->N ); | |
grp->h = 1; | |
return( 0 ); | |
} | |
#if defined(MBEDTLS_ECP_NIST_OPTIM) | |
/* Forward declarations */ | |
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) | |
static int ecp_mod_p192( mbedtls_mpi * ); | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) | |
static int ecp_mod_p224( mbedtls_mpi * ); | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) | |
static int ecp_mod_p256( mbedtls_mpi * ); | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) | |
static int ecp_mod_p384( mbedtls_mpi * ); | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) | |
static int ecp_mod_p521( mbedtls_mpi * ); | |
#endif | |
#define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; | |
#else | |
#define NIST_MODP( P ) | |
#endif /* MBEDTLS_ECP_NIST_OPTIM */ | |
/* Additional forward declarations */ | |
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) | |
static int ecp_mod_p255( mbedtls_mpi * ); | |
#endif | |
#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) | |
static int ecp_mod_p448( mbedtls_mpi * ); | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) | |
static int ecp_mod_p192k1( mbedtls_mpi * ); | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) | |
static int ecp_mod_p224k1( mbedtls_mpi * ); | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) | |
static int ecp_mod_p256k1( mbedtls_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(MBEDTLS_ECP_DP_CURVE25519_ENABLED) | |
/* | |
* Specialized function for creating the Curve25519 group | |
*/ | |
static int ecp_use_curve25519( mbedtls_ecp_group *grp ) | |
{ | |
int ret; | |
/* Actually ( A + 2 ) / 4 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) ); | |
/* P = 2^255 - 19 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) ); | |
grp->pbits = mbedtls_mpi_bitlen( &grp->P ); | |
/* N = 2^252 + 27742317777372353535851937790883648493 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16, | |
"14DEF9DEA2F79CD65812631A5CF5D3ED" ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) ); | |
/* Y intentionally not set, since we use x/z coordinates. | |
* This is used as a marker to identify Montgomery curves! */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); | |
mbedtls_mpi_free( &grp->G.Y ); | |
/* Actually, the required msb for private keys */ | |
grp->nbits = 254; | |
cleanup: | |
if( ret != 0 ) | |
mbedtls_ecp_group_free( grp ); | |
return( ret ); | |
} | |
#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) | |
/* | |
* Specialized function for creating the Curve448 group | |
*/ | |
static int ecp_use_curve448( mbedtls_ecp_group *grp ) | |
{ | |
mbedtls_mpi Ns; | |
int ret; | |
mbedtls_mpi_init( &Ns ); | |
/* Actually ( A + 2 ) / 4 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) ); | |
/* P = 2^448 - 2^224 - 1 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); | |
grp->pbits = mbedtls_mpi_bitlen( &grp->P ); | |
/* Y intentionally not set, since we use x/z coordinates. | |
* This is used as a marker to identify Montgomery curves! */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); | |
mbedtls_mpi_free( &grp->G.Y ); | |
/* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16, | |
"8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) ); | |
/* Actually, the required msb for private keys */ | |
grp->nbits = 447; | |
cleanup: | |
mbedtls_mpi_free( &Ns ); | |
if( ret != 0 ) | |
mbedtls_ecp_group_free( grp ); | |
return( ret ); | |
} | |
#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ | |
/* | |
* Set a group using well-known domain parameters | |
*/ | |
int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ) | |
{ | |
ECP_VALIDATE_RET( grp != NULL ); | |
mbedtls_ecp_group_free( grp ); | |
grp->id = id; | |
switch( id ) | |
{ | |
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) | |
case MBEDTLS_ECP_DP_SECP192R1: | |
NIST_MODP( p192 ); | |
return( LOAD_GROUP( secp192r1 ) ); | |
#endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) | |
case MBEDTLS_ECP_DP_SECP224R1: | |
NIST_MODP( p224 ); | |
return( LOAD_GROUP( secp224r1 ) ); | |
#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) | |
case MBEDTLS_ECP_DP_SECP256R1: | |
NIST_MODP( p256 ); | |
return( LOAD_GROUP( secp256r1 ) ); | |
#endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) | |
case MBEDTLS_ECP_DP_SECP384R1: | |
NIST_MODP( p384 ); | |
return( LOAD_GROUP( secp384r1 ) ); | |
#endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) | |
case MBEDTLS_ECP_DP_SECP521R1: | |
NIST_MODP( p521 ); | |
return( LOAD_GROUP( secp521r1 ) ); | |
#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) | |
case MBEDTLS_ECP_DP_SECP192K1: | |
grp->modp = ecp_mod_p192k1; | |
return( LOAD_GROUP_A( secp192k1 ) ); | |
#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) | |
case MBEDTLS_ECP_DP_SECP224K1: | |
grp->modp = ecp_mod_p224k1; | |
return( LOAD_GROUP_A( secp224k1 ) ); | |
#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) | |
case MBEDTLS_ECP_DP_SECP256K1: | |
grp->modp = ecp_mod_p256k1; | |
return( LOAD_GROUP_A( secp256k1 ) ); | |
#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) | |
case MBEDTLS_ECP_DP_BP256R1: | |
return( LOAD_GROUP_A( brainpoolP256r1 ) ); | |
#endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) | |
case MBEDTLS_ECP_DP_BP384R1: | |
return( LOAD_GROUP_A( brainpoolP384r1 ) ); | |
#endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) | |
case MBEDTLS_ECP_DP_BP512R1: | |
return( LOAD_GROUP_A( brainpoolP512r1 ) ); | |
#endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) | |
case MBEDTLS_ECP_DP_CURVE25519: | |
grp->modp = ecp_mod_p255; | |
return( ecp_use_curve25519( grp ) ); | |
#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) | |
case MBEDTLS_ECP_DP_CURVE448: | |
grp->modp = ecp_mod_p448; | |
return( ecp_use_curve448( grp ) ); | |
#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ | |
default: | |
mbedtls_ecp_group_free( grp ); | |
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); | |
} | |
} | |
#if defined(MBEDTLS_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(MBEDTLS_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 mbedtls_mpi_uint, we can | |
* use a mbedtls_mpi_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( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry ) | |
{ | |
unsigned char i; | |
mbedtls_mpi_uint c = 0; | |
for( i = 0; i < 8 / sizeof( mbedtls_mpi_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( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry ) | |
{ | |
unsigned char i; | |
for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ ) | |
{ | |
*dst += *carry; | |
*carry = ( *dst < *carry ); | |
} | |
} | |
#define WIDTH 8 / sizeof( mbedtls_mpi_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( mbedtls_mpi *N ) | |
{ | |
int ret; | |
mbedtls_mpi_uint c = 0; | |
mbedtls_mpi_uint *p, *end; | |
/* Make sure we have enough blocks so that A(5) is legal */ | |
MBEDTLS_MPI_CHK( mbedtls_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 /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ | |
defined(MBEDTLS_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(MBEDTLS_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] |= ((mbedtls_mpi_uint) cur) << 32; \ | |
} else { \ | |
N->p[i/2] &= 0xFFFFFFFF00000000; \ | |
N->p[i/2] |= (mbedtls_mpi_uint) cur; \ | |
} | |
#endif /* sizeof( mbedtls_mpi_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); \ | |
mbedtls_mpi C; \ | |
mbedtls_mpi_uint Cp[ (b) / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \ | |
\ | |
C.s = 1; \ | |
C.n = (b) / 8 / sizeof( mbedtls_mpi_uint) + 1; \ | |
C.p = Cp; \ | |
memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \ | |
\ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, (b) * 2 / 8 / \ | |
sizeof( mbedtls_mpi_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( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits ) | |
{ | |
int ret; | |
/* C = - c * 2^(bits + 32) */ | |
#if !defined(MBEDTLS_HAVE_INT64) | |
((void) bits); | |
#else | |
if( bits == 224 ) | |
C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32; | |
else | |
#endif | |
C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c; | |
/* N = - ( C - N ) */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) ); | |
N->s = -1; | |
cleanup: | |
return( ret ); | |
} | |
#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) | |
/* | |
* Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) | |
*/ | |
static int ecp_mod_p224( mbedtls_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 /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) | |
/* | |
* Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) | |
*/ | |
static int ecp_mod_p256( mbedtls_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 /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) | |
/* | |
* Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) | |
*/ | |
static int ecp_mod_p384( mbedtls_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 /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ | |
#undef A | |
#undef LOAD32 | |
#undef STORE32 | |
#undef MAX32 | |
#undef INIT | |
#undef NEXT | |
#undef LAST | |
#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED || | |
MBEDTLS_ECP_DP_SECP256R1_ENABLED || | |
MBEDTLS_ECP_DP_SECP384R1_ENABLED */ | |
#if defined(MBEDTLS_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 mbedtls_mpi_uint */ | |
#define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) | |
/* Bits to keep in the most significant mbedtls_mpi_uint */ | |
#define P521_MASK 0x01FF | |
/* | |
* 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( mbedtls_mpi *N ) | |
{ | |
int ret; | |
size_t i; | |
mbedtls_mpi M; | |
mbedtls_mpi_uint Mp[P521_WIDTH + 1]; | |
/* Worst case for the size of M is when mbedtls_mpi_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( mbedtls_mpi_uint ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_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 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); | |
cleanup: | |
return( ret ); | |
} | |
#undef P521_WIDTH | |
#undef P521_MASK | |
#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ | |
#endif /* MBEDTLS_ECP_NIST_OPTIM */ | |
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) | |
/* Size of p255 in terms of mbedtls_mpi_uint */ | |
#define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_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( mbedtls_mpi *N ) | |
{ | |
int ret; | |
size_t i; | |
mbedtls_mpi M; | |
mbedtls_mpi_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 ) | |
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); | |
M.p = Mp; | |
memset( Mp, 0, sizeof Mp ); | |
memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); | |
M.n++; /* Make room for multiplication by 19 */ | |
/* N = A0 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) ); | |
for( i = P255_WIDTH; i < N->n; i++ ) | |
N->p[i] = 0; | |
/* N = A0 + 19 * A1 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); | |
cleanup: | |
return( ret ); | |
} | |
#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) | |
/* Size of p448 in terms of mbedtls_mpi_uint */ | |
#define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) ) | |
/* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */ | |
#define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) ) | |
#define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) ) | |
#define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) ) | |
#define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 ) | |
/* | |
* Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1 | |
* Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return | |
* A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference | |
* implementation of Curve448, which uses its own special 56-bit limbs rather | |
* than a generic bignum library. We could squeeze some extra speed out on | |
* 32-bit machines by splitting N up into 32-bit limbs and doing the | |
* arithmetic using the limbs directly as we do for the NIST primes above, | |
* but for 64-bit targets it should use half the number of operations if we do | |
* the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds. | |
*/ | |
static int ecp_mod_p448( mbedtls_mpi *N ) | |
{ | |
int ret; | |
size_t i; | |
mbedtls_mpi M, Q; | |
mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH]; | |
if( N->n <= P448_WIDTH ) | |
return( 0 ); | |
/* M = A1 */ | |
M.s = 1; | |
M.n = N->n - ( P448_WIDTH ); | |
if( M.n > P448_WIDTH ) | |
/* Shouldn't be called with N larger than 2^896! */ | |
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); | |
M.p = Mp; | |
memset( Mp, 0, sizeof( Mp ) ); | |
memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) ); | |
/* N = A0 */ | |
for( i = P448_WIDTH; i < N->n; i++ ) | |
N->p[i] = 0; | |
/* N += A1 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); | |
/* Q = B1, N += B1 */ | |
Q = M; | |
Q.p = Qp; | |
memcpy( Qp, Mp, sizeof( Qp ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) ); | |
/* M = (B0 + B1) * 2^224, N += M */ | |
if( sizeof( mbedtls_mpi_uint ) > 4 ) | |
Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS ); | |
for( i = P224_WIDTH_MAX; i < M.n; ++i ) | |
Mp[i] = 0; | |
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) ); | |
M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); | |
cleanup: | |
return( ret ); | |
} | |
#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ | |
#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ | |
defined(MBEDTLS_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( mbedtls_mpi_uint ) ) // Max limbs in P | |
#define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R | |
static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs, | |
size_t adjust, size_t shift, mbedtls_mpi_uint mask ) | |
{ | |
int ret; | |
size_t i; | |
mbedtls_mpi M, R; | |
mbedtls_mpi_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( mbedtls_mpi_uint ) ); | |
if( shift != 0 ) | |
MBEDTLS_MPI_CHK( mbedtls_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 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); | |
MBEDTLS_MPI_CHK( mbedtls_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( mbedtls_mpi_uint ) ); | |
if( shift != 0 ) | |
MBEDTLS_MPI_CHK( mbedtls_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 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); | |
cleanup: | |
return( ret ); | |
} | |
#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) || | |
MBEDTLS_ECP_DP_SECP224K1_ENABLED) || | |
MBEDTLS_ECP_DP_SECP256K1_ENABLED) */ | |
#if defined(MBEDTLS_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( mbedtls_mpi *N ) | |
{ | |
static mbedtls_mpi_uint Rp[] = { | |
BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; | |
return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); | |
} | |
#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ | |
#if defined(MBEDTLS_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( mbedtls_mpi *N ) | |
{ | |
static mbedtls_mpi_uint Rp[] = { | |
BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; | |
#if defined(MBEDTLS_HAVE_INT64) | |
return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) ); | |
#else | |
return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); | |
#endif | |
} | |
#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ | |
#if defined(MBEDTLS_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( mbedtls_mpi *N ) | |
{ | |
static mbedtls_mpi_uint Rp[] = { | |
BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; | |
return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); | |
} | |
#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ | |
#endif /* !MBEDTLS_ECP_ALT */ | |
#endif /* MBEDTLS_ECP_C */ |