/* * 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 */