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virtualx-engine/thirdparty/mbedtls/library/ecp_curves.c
Fabio Alessandrelli e375cbd094 Bump mbedTLS version to 2.28.0 (new LTS). 
Keep applying the windows entropy patch (UWP support).
Remove no longer needed padlock patch.
Update thirdparty README to reflect changes, and new source inclusion
criteria.
2021-12-21 13:26:02 +01:00

1478 lines
59 KiB
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/*
* Elliptic curves over GF(p): curve-specific data and functions
*
* Copyright The Mbed TLS Contributors
* 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.
*/
#include "common.h"
#if defined(MBEDTLS_ECP_C)
#include "mbedtls/ecp.h"
#include "mbedtls/platform_util.h"
#include "mbedtls/error.h"
#include "mbedtls/bn_mul.h"
#include "ecp_invasive.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
#define ECP_MPI_INIT(s, n, p) {s, (n), (mbedtls_mpi_uint *)(p)}
#define ECP_MPI_INIT_ARRAY(x) \
ECP_MPI_INIT(1, sizeof(x) / sizeof(mbedtls_mpi_uint), x)
/*
* 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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static const mbedtls_mpi_uint secp192r1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
};
static const mbedtls_mpi_uint secp192r1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
};
static const mbedtls_mpi_uint secp192r1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
};
static const mbedtls_mpi_uint secp192r1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
};
static const mbedtls_mpi_uint secp224r1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
MBEDTLS_BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
};
static const mbedtls_mpi_uint secp224r1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
MBEDTLS_BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
};
static const mbedtls_mpi_uint secp224r1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
MBEDTLS_BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
};
static const mbedtls_mpi_uint secp224r1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static const mbedtls_mpi_uint secp256r1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
};
static const mbedtls_mpi_uint secp256r1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
};
static const mbedtls_mpi_uint secp256r1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
};
static const mbedtls_mpi_uint secp256r1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static const mbedtls_mpi_uint secp384r1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
};
static const mbedtls_mpi_uint secp384r1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
};
static const mbedtls_mpi_uint secp384r1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
};
static const mbedtls_mpi_uint secp384r1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
};
static const mbedtls_mpi_uint secp521r1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
MBEDTLS_BYTES_TO_T_UINT_2( 0x51, 0x00 ),
};
static const mbedtls_mpi_uint secp521r1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
MBEDTLS_BYTES_TO_T_UINT_2( 0xC6, 0x00 ),
};
static const mbedtls_mpi_uint secp521r1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
MBEDTLS_BYTES_TO_T_UINT_2( 0x18, 0x01 ),
};
static const mbedtls_mpi_uint secp521r1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static const mbedtls_mpi_uint secp192k1_a[] = {
MBEDTLS_BYTES_TO_T_UINT_2( 0x00, 0x00 ),
};
static const mbedtls_mpi_uint secp192k1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_2( 0x03, 0x00 ),
};
static const mbedtls_mpi_uint secp192k1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ),
};
static const mbedtls_mpi_uint secp192k1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ),
};
static const mbedtls_mpi_uint secp192k1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
};
static const mbedtls_mpi_uint secp224k1_a[] = {
MBEDTLS_BYTES_TO_T_UINT_2( 0x00, 0x00 ),
};
static const mbedtls_mpi_uint secp224k1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_2( 0x05, 0x00 ),
};
static const mbedtls_mpi_uint secp224k1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ),
MBEDTLS_BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ),
};
static const mbedtls_mpi_uint secp224k1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ),
MBEDTLS_BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ),
};
static const mbedtls_mpi_uint secp224k1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
};
static const mbedtls_mpi_uint secp256k1_a[] = {
MBEDTLS_BYTES_TO_T_UINT_2( 0x00, 0x00 ),
};
static const mbedtls_mpi_uint secp256k1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_2( 0x07, 0x00 ),
};
static const mbedtls_mpi_uint secp256k1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ),
};
static const mbedtls_mpi_uint secp256k1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ),
};
static const mbedtls_mpi_uint secp256k1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
};
static const mbedtls_mpi_uint brainpoolP256r1_a[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
};
static const mbedtls_mpi_uint brainpoolP256r1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
};
static const mbedtls_mpi_uint brainpoolP256r1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
};
static const mbedtls_mpi_uint brainpoolP256r1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
};
static const mbedtls_mpi_uint brainpoolP256r1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
};
static const mbedtls_mpi_uint brainpoolP384r1_a[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
};
static const mbedtls_mpi_uint brainpoolP384r1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
};
static const mbedtls_mpi_uint brainpoolP384r1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
};
static const mbedtls_mpi_uint brainpoolP384r1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
};
static const mbedtls_mpi_uint brainpoolP384r1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
MBEDTLS_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[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
};
static const mbedtls_mpi_uint brainpoolP512r1_a[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
};
static const mbedtls_mpi_uint brainpoolP512r1_b[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
};
static const mbedtls_mpi_uint brainpoolP512r1_gx[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
};
static const mbedtls_mpi_uint brainpoolP512r1_gy[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
};
static const mbedtls_mpi_uint brainpoolP512r1_n[] = {
MBEDTLS_BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
MBEDTLS_BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
};
#endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
/* For these curves, we build the group parameters dynamically. */
#define ECP_LOAD_GROUP
#endif
#if defined(ECP_LOAD_GROUP)
/*
* 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 );
}
#endif /* ECP_LOAD_GROUP */
#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
#if defined(ECP_LOAD_GROUP)
#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 ) )
#endif /* ECP_LOAD_GROUP */
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
/* Constants used by ecp_use_curve25519() */
static const mbedtls_mpi_sint curve25519_a24 = 0x01DB42;
static const unsigned char curve25519_part_of_n[] = {
0x14, 0xDE, 0xF9, 0xDE, 0xA2, 0xF7, 0x9C, 0xD6,
0x58, 0x12, 0x63, 0x1A, 0x5C, 0xF5, 0xD3, 0xED,
};
/*
* Specialized function for creating the Curve25519 group
*/
static int ecp_use_curve25519( mbedtls_ecp_group *grp )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
/* Actually ( A + 2 ) / 4 */
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->A, curve25519_a24 ) );
/* 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_binary( &grp->N,
curve25519_part_of_n, sizeof( curve25519_part_of_n ) ) );
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)
/* Constants used by ecp_use_curve448() */
static const mbedtls_mpi_sint curve448_a24 = 0x98AA;
static const unsigned char curve448_part_of_n[] = {
0x83, 0x35, 0xDC, 0x16, 0x3B, 0xB1, 0x24,
0xB6, 0x51, 0x29, 0xC9, 0x6F, 0xDE, 0x93,
0x3D, 0x8D, 0x72, 0x3A, 0x70, 0xAA, 0xDC,
0x87, 0x3D, 0x6D, 0x54, 0xA7, 0xBB, 0x0D,
};
/*
* Specialized function for creating the Curve448 group
*/
static int ecp_use_curve448( mbedtls_ecp_group *grp )
{
mbedtls_mpi Ns;
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi_init( &Ns );
/* Actually ( A + 2 ) / 4 */
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->A, curve448_a24 ) );
/* 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_binary( &Ns,
curve448_part_of_n, sizeof( curve448_part_of_n ) ) );
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:
grp->id = MBEDTLS_ECP_DP_NONE;
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_ERR_ERROR_CORRUPTION_DETECTED;
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 );
#define ciL (sizeof(mbedtls_mpi_uint)) /* chars in limb */
#define biL (ciL << 3) /* bits in limb */
/*
* Helpers for the main 'loop'
*/
#define INIT( b ) \
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; \
signed char c = 0, cc; \
uint32_t cur; \
size_t i = 0, bits = (b); \
/* N is the size of the product of two b-bit numbers, plus one */ \
/* limb for fix_negative */ \
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, ( b ) * 2 / biL + 1 ) ); \
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 ) mbedtls_ecp_fix_negative( N, c, bits );
/*
* If the result is negative, we get it in the form
* c * 2^bits + N, with c negative and N positive shorter than 'bits'
*/
MBEDTLS_STATIC_TESTABLE
void mbedtls_ecp_fix_negative( mbedtls_mpi *N, signed char c, size_t bits )
{
size_t i;
/* Set N := 2^bits - 1 - N. We know that 0 <= N < 2^bits, so
* set the absolute value to 0xfff...fff - N. There is no carry
* since we're subtracting from all-bits-one. */
for( i = 0; i <= bits / 8 / sizeof( mbedtls_mpi_uint ); i++ )
{
N->p[i] = ~(mbedtls_mpi_uint)0 - N->p[i];
}
/* Add 1, taking care of the carry. */
i = 0;
do
++N->p[i];
while( N->p[i++] == 0 && i <= bits / 8 / sizeof( mbedtls_mpi_uint ) );
/* Invert the sign.
* Now N = N0 - 2^bits where N0 is the initial value of N. */
N->s = -1;
/* Add |c| * 2^bits to the absolute value. Since c and N are
* negative, this adds c * 2^bits. */
mbedtls_mpi_uint msw = (mbedtls_mpi_uint) -c;
#if defined(MBEDTLS_HAVE_INT64)
if( bits == 224 )
msw <<= 32;
#endif
N->p[bits / 8 / sizeof( mbedtls_mpi_uint)] += msw;
}
#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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
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 = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
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[] = {
MBEDTLS_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[] = {
MBEDTLS_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[] = {
MBEDTLS_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 */
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