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review.trustedfirmware.org / mirror / mbed-tls / refs/heads/2.28-sphinx-versioned-documentation / . / library / ecp_curves.c
blob: 6ce4f64c1636dd62c3812237a07e60d65fb73fdf [file] [log] [blame]
/*
* 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)
#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);
mbedtls_ecp_group_init(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 */