diff options
Diffstat (limited to 'thirdparty/mbedtls/library/ecp_curves.c')
| -rw-r--r-- | thirdparty/mbedtls/library/ecp_curves.c | 1329 |
1 files changed, 1329 insertions, 0 deletions
diff --git a/thirdparty/mbedtls/library/ecp_curves.c b/thirdparty/mbedtls/library/ecp_curves.c new file mode 100644 index 0000000000..df5ac3eea5 --- /dev/null +++ b/thirdparty/mbedtls/library/ecp_curves.c @@ -0,0 +1,1329 @@ +/* + * Elliptic curves over GF(p): curve-specific data and functions + * + * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the "License"); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + * + * This file is part of mbed TLS (https://tls.mbed.org) + */ + +#if !defined(MBEDTLS_CONFIG_FILE) +#include "mbedtls/config.h" +#else +#include MBEDTLS_CONFIG_FILE +#endif + +#if defined(MBEDTLS_ECP_C) + +#include "mbedtls/ecp.h" + +#include <string.h> + +#if !defined(MBEDTLS_ECP_ALT) + +#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ + !defined(inline) && !defined(__cplusplus) +#define inline __inline +#endif + +/* + * Conversion macros for embedded constants: + * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2 + */ +#if defined(MBEDTLS_HAVE_INT32) + +#define BYTES_TO_T_UINT_4( a, b, c, d ) \ + ( (mbedtls_mpi_uint) a << 0 ) | \ + ( (mbedtls_mpi_uint) b << 8 ) | \ + ( (mbedtls_mpi_uint) c << 16 ) | \ + ( (mbedtls_mpi_uint) d << 24 ) + +#define BYTES_TO_T_UINT_2( a, b ) \ + BYTES_TO_T_UINT_4( a, b, 0, 0 ) + +#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ + BYTES_TO_T_UINT_4( a, b, c, d ), \ + BYTES_TO_T_UINT_4( e, f, g, h ) + +#else /* 64-bits */ + +#define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ + ( (mbedtls_mpi_uint) a << 0 ) | \ + ( (mbedtls_mpi_uint) b << 8 ) | \ + ( (mbedtls_mpi_uint) c << 16 ) | \ + ( (mbedtls_mpi_uint) d << 24 ) | \ + ( (mbedtls_mpi_uint) e << 32 ) | \ + ( (mbedtls_mpi_uint) f << 40 ) | \ + ( (mbedtls_mpi_uint) g << 48 ) | \ + ( (mbedtls_mpi_uint) h << 56 ) + +#define BYTES_TO_T_UINT_4( a, b, c, d ) \ + BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 ) + +#define BYTES_TO_T_UINT_2( a, b ) \ + BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 ) + +#endif /* bits in mbedtls_mpi_uint */ + +/* + * Note: the constants are in little-endian order + * to be directly usable in MPIs + */ + +/* + * Domain parameters for secp192r1 + */ +#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) +static const mbedtls_mpi_uint secp192r1_p[] = { + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +static const mbedtls_mpi_uint secp192r1_b[] = { + BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ), + BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ), + BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ), +}; +static const mbedtls_mpi_uint secp192r1_gx[] = { + BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ), + BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ), + BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ), +}; +static const mbedtls_mpi_uint secp192r1_gy[] = { + BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ), + BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ), + BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ), +}; +static const mbedtls_mpi_uint secp192r1_n[] = { + BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ), + BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +#endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ + +/* + * Domain parameters for secp224r1 + */ +#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) +static const mbedtls_mpi_uint secp224r1_p[] = { + BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), + BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), +}; +static const mbedtls_mpi_uint secp224r1_b[] = { + BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ), + BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ), + BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ), + BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ), +}; +static const mbedtls_mpi_uint secp224r1_gx[] = { + BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ), + BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ), + BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ), + BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ), +}; +static const mbedtls_mpi_uint secp224r1_gy[] = { + BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ), + BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ), + BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ), + BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ), +}; +static const mbedtls_mpi_uint secp224r1_n[] = { + BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ), + BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), +}; +#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ + +/* + * Domain parameters for secp256r1 + */ +#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) +static const mbedtls_mpi_uint secp256r1_p[] = { + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), + BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), + BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +static const mbedtls_mpi_uint secp256r1_b[] = { + BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ), + BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ), + BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ), + BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ), +}; +static const mbedtls_mpi_uint secp256r1_gx[] = { + BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ), + BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ), + BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ), + BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ), +}; +static const mbedtls_mpi_uint secp256r1_gy[] = { + BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ), + BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ), + BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ), + BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ), +}; +static const mbedtls_mpi_uint secp256r1_n[] = { + BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ), + BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +#endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ + +/* + * Domain parameters for secp384r1 + */ +#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) +static const mbedtls_mpi_uint secp384r1_p[] = { + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), + BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +static const mbedtls_mpi_uint secp384r1_b[] = { + BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ), + BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ), + BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ), + BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ), + BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ), + BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ), +}; +static const mbedtls_mpi_uint secp384r1_gx[] = { + BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ), + BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ), + BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ), + BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ), + BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ), + BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ), +}; +static const mbedtls_mpi_uint secp384r1_gy[] = { + BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ), + BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ), + BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ), + BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ), + BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ), + BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ), +}; +static const mbedtls_mpi_uint secp384r1_n[] = { + BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ), + BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ), + BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +#endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ + +/* + * Domain parameters for secp521r1 + */ +#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) +static const mbedtls_mpi_uint secp521r1_p[] = { + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_2( 0xFF, 0x01 ), +}; +static const mbedtls_mpi_uint secp521r1_b[] = { + BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ), + BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ), + BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ), + BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ), + BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ), + BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ), + BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ), + BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ), + BYTES_TO_T_UINT_2( 0x51, 0x00 ), +}; +static const mbedtls_mpi_uint secp521r1_gx[] = { + BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ), + BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ), + BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ), + BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ), + BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ), + BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ), + BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ), + BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ), + BYTES_TO_T_UINT_2( 0xC6, 0x00 ), +}; +static const mbedtls_mpi_uint secp521r1_gy[] = { + BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ), + BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ), + BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ), + BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ), + BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ), + BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ), + BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ), + BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ), + BYTES_TO_T_UINT_2( 0x18, 0x01 ), +}; +static const mbedtls_mpi_uint secp521r1_n[] = { + BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ), + BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ), + BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ), + BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ), + BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_2( 0xFF, 0x01 ), +}; +#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) +static const mbedtls_mpi_uint secp192k1_p[] = { + BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +static const mbedtls_mpi_uint secp192k1_a[] = { + BYTES_TO_T_UINT_2( 0x00, 0x00 ), +}; +static const mbedtls_mpi_uint secp192k1_b[] = { + BYTES_TO_T_UINT_2( 0x03, 0x00 ), +}; +static const mbedtls_mpi_uint secp192k1_gx[] = { + BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ), + BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ), + BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ), +}; +static const mbedtls_mpi_uint secp192k1_gy[] = { + BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ), + BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ), + BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ), +}; +static const mbedtls_mpi_uint secp192k1_n[] = { + BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ), + BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) +static const mbedtls_mpi_uint secp224k1_p[] = { + BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), +}; +static const mbedtls_mpi_uint secp224k1_a[] = { + BYTES_TO_T_UINT_2( 0x00, 0x00 ), +}; +static const mbedtls_mpi_uint secp224k1_b[] = { + BYTES_TO_T_UINT_2( 0x05, 0x00 ), +}; +static const mbedtls_mpi_uint secp224k1_gx[] = { + BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ), + BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ), + BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ), + BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ), +}; +static const mbedtls_mpi_uint secp224k1_gy[] = { + BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ), + BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ), + BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ), + BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ), +}; +static const mbedtls_mpi_uint secp224k1_n[] = { + BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ), + BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ), + BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), + BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ), +}; +#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) +static const mbedtls_mpi_uint secp256k1_p[] = { + BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +static const mbedtls_mpi_uint secp256k1_a[] = { + BYTES_TO_T_UINT_2( 0x00, 0x00 ), +}; +static const mbedtls_mpi_uint secp256k1_b[] = { + BYTES_TO_T_UINT_2( 0x07, 0x00 ), +}; +static const mbedtls_mpi_uint secp256k1_gx[] = { + BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ), + BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ), + BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ), + BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ), +}; +static const mbedtls_mpi_uint secp256k1_gy[] = { + BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ), + BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ), + BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ), + BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ), +}; +static const mbedtls_mpi_uint secp256k1_n[] = { + BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ), + BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ), + BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), + BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), +}; +#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ + +/* + * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) + */ +#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) +static const mbedtls_mpi_uint brainpoolP256r1_p[] = { + BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ), + BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ), + BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), + BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), +}; +static const mbedtls_mpi_uint brainpoolP256r1_a[] = { + BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ), + BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ), + BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ), + BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ), +}; +static const mbedtls_mpi_uint brainpoolP256r1_b[] = { + BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ), + BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ), + BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ), + BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ), +}; +static const mbedtls_mpi_uint brainpoolP256r1_gx[] = { + BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ), + BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ), + BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ), + BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ), +}; +static const mbedtls_mpi_uint brainpoolP256r1_gy[] = { + BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ), + BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ), + BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ), + BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ), +}; +static const mbedtls_mpi_uint brainpoolP256r1_n[] = { + BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ), + BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ), + BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), + BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), +}; +#endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ + +/* + * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) + */ +#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) +static const mbedtls_mpi_uint brainpoolP384r1_p[] = { + BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ), + BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ), + BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ), + BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), + BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), + BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), +}; +static const mbedtls_mpi_uint brainpoolP384r1_a[] = { + BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), + BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ), + BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ), + BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ), + BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ), + BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ), +}; +static const mbedtls_mpi_uint brainpoolP384r1_b[] = { + BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ), + BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ), + BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ), + BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ), + BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ), + BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), +}; +static const mbedtls_mpi_uint brainpoolP384r1_gx[] = { + BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ), + BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ), + BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ), + BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ), + BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ), + BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ), +}; +static const mbedtls_mpi_uint brainpoolP384r1_gy[] = { + BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ), + BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ), + BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ), + BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ), + BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ), + BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ), +}; +static const mbedtls_mpi_uint brainpoolP384r1_n[] = { + BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ), + BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ), + BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ), + BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), + BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), + BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), +}; +#endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ + +/* + * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) + */ +#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) +static const mbedtls_mpi_uint brainpoolP512r1_p[] = { + BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ), + BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ), + BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ), + BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ), + BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), + BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), + BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), + BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), +}; +static const mbedtls_mpi_uint brainpoolP512r1_a[] = { + BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ), + BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ), + BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ), + BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ), + BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ), + BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ), + BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ), + BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ), +}; +static const mbedtls_mpi_uint brainpoolP512r1_b[] = { + BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ), + BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ), + BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ), + BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ), + BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ), + BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ), + BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ), + BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ), +}; +static const mbedtls_mpi_uint brainpoolP512r1_gx[] = { + BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ), + BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ), + BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ), + BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ), + BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ), + BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ), + BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ), + BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ), +}; +static const mbedtls_mpi_uint brainpoolP512r1_gy[] = { + BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ), + BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ), + BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ), + BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ), + BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ), + BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ), + BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ), + BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ), +}; +static const mbedtls_mpi_uint brainpoolP512r1_n[] = { + BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ), + BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ), + BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ), + BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ), + BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), + BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), + BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), + BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), +}; +#endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ + +/* + * Create an MPI from embedded constants + * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint) + */ +static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len ) +{ + X->s = 1; + X->n = len / sizeof( mbedtls_mpi_uint ); + X->p = (mbedtls_mpi_uint *) p; +} + +/* + * Set an MPI to static value 1 + */ +static inline void ecp_mpi_set1( mbedtls_mpi *X ) +{ + static mbedtls_mpi_uint one[] = { 1 }; + X->s = 1; + X->n = 1; + X->p = one; +} + +/* + * Make group available from embedded constants + */ +static int ecp_group_load( mbedtls_ecp_group *grp, + const mbedtls_mpi_uint *p, size_t plen, + const mbedtls_mpi_uint *a, size_t alen, + const mbedtls_mpi_uint *b, size_t blen, + const mbedtls_mpi_uint *gx, size_t gxlen, + const mbedtls_mpi_uint *gy, size_t gylen, + const mbedtls_mpi_uint *n, size_t nlen) +{ + ecp_mpi_load( &grp->P, p, plen ); + if( a != NULL ) + ecp_mpi_load( &grp->A, a, alen ); + ecp_mpi_load( &grp->B, b, blen ); + ecp_mpi_load( &grp->N, n, nlen ); + + ecp_mpi_load( &grp->G.X, gx, gxlen ); + ecp_mpi_load( &grp->G.Y, gy, gylen ); + ecp_mpi_set1( &grp->G.Z ); + + grp->pbits = mbedtls_mpi_bitlen( &grp->P ); + grp->nbits = mbedtls_mpi_bitlen( &grp->N ); + + grp->h = 1; + + return( 0 ); +} + +#if defined(MBEDTLS_ECP_NIST_OPTIM) +/* Forward declarations */ +#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) +static int ecp_mod_p192( mbedtls_mpi * ); +#endif +#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) +static int ecp_mod_p224( mbedtls_mpi * ); +#endif +#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) +static int ecp_mod_p256( mbedtls_mpi * ); +#endif +#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) +static int ecp_mod_p384( mbedtls_mpi * ); +#endif +#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) +static int ecp_mod_p521( mbedtls_mpi * ); +#endif + +#define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; +#else +#define NIST_MODP( P ) +#endif /* MBEDTLS_ECP_NIST_OPTIM */ + +/* Additional forward declarations */ +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) +static int ecp_mod_p255( mbedtls_mpi * ); +#endif +#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) +static int ecp_mod_p192k1( mbedtls_mpi * ); +#endif +#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) +static int ecp_mod_p224k1( mbedtls_mpi * ); +#endif +#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) +static int ecp_mod_p256k1( mbedtls_mpi * ); +#endif + +#define LOAD_GROUP_A( G ) ecp_group_load( grp, \ + G ## _p, sizeof( G ## _p ), \ + G ## _a, sizeof( G ## _a ), \ + G ## _b, sizeof( G ## _b ), \ + G ## _gx, sizeof( G ## _gx ), \ + G ## _gy, sizeof( G ## _gy ), \ + G ## _n, sizeof( G ## _n ) ) + +#define LOAD_GROUP( G ) ecp_group_load( grp, \ + G ## _p, sizeof( G ## _p ), \ + NULL, 0, \ + G ## _b, sizeof( G ## _b ), \ + G ## _gx, sizeof( G ## _gx ), \ + G ## _gy, sizeof( G ## _gy ), \ + G ## _n, sizeof( G ## _n ) ) + +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) +/* + * Specialized function for creating the Curve25519 group + */ +static int ecp_use_curve25519( mbedtls_ecp_group *grp ) +{ + int ret; + + /* Actually ( A + 2 ) / 4 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) ); + + /* P = 2^255 - 19 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) ); + grp->pbits = mbedtls_mpi_bitlen( &grp->P ); + + /* Y intentionaly 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 */ + +/* + * Set a group using well-known domain parameters + */ +int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ) +{ + mbedtls_ecp_group_free( grp ); + + grp->id = id; + + switch( id ) + { +#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) + case MBEDTLS_ECP_DP_SECP192R1: + NIST_MODP( p192 ); + return( LOAD_GROUP( secp192r1 ) ); +#endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) + case MBEDTLS_ECP_DP_SECP224R1: + NIST_MODP( p224 ); + return( LOAD_GROUP( secp224r1 ) ); +#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) + case MBEDTLS_ECP_DP_SECP256R1: + NIST_MODP( p256 ); + return( LOAD_GROUP( secp256r1 ) ); +#endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) + case MBEDTLS_ECP_DP_SECP384R1: + NIST_MODP( p384 ); + return( LOAD_GROUP( secp384r1 ) ); +#endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) + case MBEDTLS_ECP_DP_SECP521R1: + NIST_MODP( p521 ); + return( LOAD_GROUP( secp521r1 ) ); +#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) + case MBEDTLS_ECP_DP_SECP192K1: + grp->modp = ecp_mod_p192k1; + return( LOAD_GROUP_A( secp192k1 ) ); +#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) + case MBEDTLS_ECP_DP_SECP224K1: + grp->modp = ecp_mod_p224k1; + return( LOAD_GROUP_A( secp224k1 ) ); +#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) + case MBEDTLS_ECP_DP_SECP256K1: + grp->modp = ecp_mod_p256k1; + return( LOAD_GROUP_A( secp256k1 ) ); +#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) + case MBEDTLS_ECP_DP_BP256R1: + return( LOAD_GROUP_A( brainpoolP256r1 ) ); +#endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) + case MBEDTLS_ECP_DP_BP384R1: + return( LOAD_GROUP_A( brainpoolP384r1 ) ); +#endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) + case MBEDTLS_ECP_DP_BP512R1: + return( LOAD_GROUP_A( brainpoolP512r1 ) ); +#endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) + case MBEDTLS_ECP_DP_CURVE25519: + grp->modp = ecp_mod_p255; + return( ecp_use_curve25519( grp ) ); +#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ + + default: + mbedtls_ecp_group_free( grp ); + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); + } +} + +#if defined(MBEDTLS_ECP_NIST_OPTIM) +/* + * Fast reduction modulo the primes used by the NIST curves. + * + * These functions are critical for speed, but not needed for correct + * operations. So, we make the choice to heavily rely on the internals of our + * bignum library, which creates a tight coupling between these functions and + * our MPI implementation. However, the coupling between the ECP module and + * MPI remains loose, since these functions can be deactivated at will. + */ + +#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) +/* + * Compared to the way things are presented in FIPS 186-3 D.2, + * we proceed in columns, from right (least significant chunk) to left, + * adding chunks to N in place, and keeping a carry for the next chunk. + * This avoids moving things around in memory, and uselessly adding zeros, + * compared to the more straightforward, line-oriented approach. + * + * For this prime we need to handle data in chunks of 64 bits. + * Since this is always a multiple of our basic mbedtls_mpi_uint, we can + * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it. + */ + +/* Add 64-bit chunks (dst += src) and update carry */ +static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry ) +{ + unsigned char i; + mbedtls_mpi_uint c = 0; + for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ ) + { + *dst += c; c = ( *dst < c ); + *dst += *src; c += ( *dst < *src ); + } + *carry += c; +} + +/* Add carry to a 64-bit chunk and update carry */ +static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry ) +{ + unsigned char i; + for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ ) + { + *dst += *carry; + *carry = ( *dst < *carry ); + } +} + +#define WIDTH 8 / sizeof( mbedtls_mpi_uint ) +#define A( i ) N->p + i * WIDTH +#define ADD( i ) add64( p, A( i ), &c ) +#define NEXT p += WIDTH; carry64( p, &c ) +#define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0 + +/* + * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1) + */ +static int ecp_mod_p192( mbedtls_mpi *N ) +{ + int ret; + mbedtls_mpi_uint c = 0; + mbedtls_mpi_uint *p, *end; + + /* Make sure we have enough blocks so that A(5) is legal */ + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) ); + + p = N->p; + end = p + N->n; + + ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5 + ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5 + ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5 + +cleanup: + return( ret ); +} + +#undef WIDTH +#undef A +#undef ADD +#undef NEXT +#undef LAST +#endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ + defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ + defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) +/* + * The reader is advised to first understand ecp_mod_p192() since the same + * general structure is used here, but with additional complications: + * (1) chunks of 32 bits, and (2) subtractions. + */ + +/* + * For these primes, we need to handle data in chunks of 32 bits. + * This makes it more complicated if we use 64 bits limbs in MPI, + * which prevents us from using a uniform access method as for p192. + * + * So, we define a mini abstraction layer to access 32 bit chunks, + * load them in 'cur' for work, and store them back from 'cur' when done. + * + * While at it, also define the size of N in terms of 32-bit chunks. + */ +#define LOAD32 cur = A( i ); + +#if defined(MBEDTLS_HAVE_INT32) /* 32 bit */ + +#define MAX32 N->n +#define A( j ) N->p[j] +#define STORE32 N->p[i] = cur; + +#else /* 64-bit */ + +#define MAX32 N->n * 2 +#define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] ) +#define STORE32 \ + if( i % 2 ) { \ + N->p[i/2] &= 0x00000000FFFFFFFF; \ + N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \ + } else { \ + N->p[i/2] &= 0xFFFFFFFF00000000; \ + N->p[i/2] |= (mbedtls_mpi_uint) cur; \ + } + +#endif /* sizeof( mbedtls_mpi_uint ) */ + +/* + * Helpers for addition and subtraction of chunks, with signed carry. + */ +static inline void add32( uint32_t *dst, uint32_t src, signed char *carry ) +{ + *dst += src; + *carry += ( *dst < src ); +} + +static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry ) +{ + *carry -= ( *dst < src ); + *dst -= src; +} + +#define ADD( j ) add32( &cur, A( j ), &c ); +#define SUB( j ) sub32( &cur, A( j ), &c ); + +/* + * Helpers for the main 'loop' + * (see fix_negative for the motivation of C) + */ +#define INIT( b ) \ + int ret; \ + signed char c = 0, cc; \ + uint32_t cur; \ + size_t i = 0, bits = b; \ + mbedtls_mpi C; \ + mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \ + \ + C.s = 1; \ + C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \ + C.p = Cp; \ + memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \ + \ + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \ + LOAD32; + +#define NEXT \ + STORE32; i++; LOAD32; \ + cc = c; c = 0; \ + if( cc < 0 ) \ + sub32( &cur, -cc, &c ); \ + else \ + add32( &cur, cc, &c ); \ + +#define LAST \ + STORE32; i++; \ + cur = c > 0 ? c : 0; STORE32; \ + cur = 0; while( ++i < MAX32 ) { STORE32; } \ + if( c < 0 ) fix_negative( N, c, &C, bits ); + +/* + * If the result is negative, we get it in the form + * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits' + */ +static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits ) +{ + int ret; + + /* C = - c * 2^(bits + 32) */ +#if !defined(MBEDTLS_HAVE_INT64) + ((void) bits); +#else + if( bits == 224 ) + C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32; + else +#endif + C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c; + + /* N = - ( C - N ) */ + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) ); + N->s = -1; + +cleanup: + + return( ret ); +} + +#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) +/* + * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) + */ +static int ecp_mod_p224( mbedtls_mpi *N ) +{ + INIT( 224 ); + + SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11 + SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12 + SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13 + SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11 + SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12 + SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13 + SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10 + +cleanup: + return( ret ); +} +#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) +/* + * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) + */ +static int ecp_mod_p256( mbedtls_mpi *N ) +{ + INIT( 256 ); + + ADD( 8 ); ADD( 9 ); + SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0 + + ADD( 9 ); ADD( 10 ); + SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1 + + ADD( 10 ); ADD( 11 ); + SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2 + + ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 ); + SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3 + + ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 ); + SUB( 9 ); SUB( 10 ); NEXT; // A4 + + ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 ); + SUB( 10 ); SUB( 11 ); NEXT; // A5 + + ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 ); + SUB( 8 ); SUB( 9 ); NEXT; // A6 + + ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 ); + SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7 + +cleanup: + return( ret ); +} +#endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) +/* + * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) + */ +static int ecp_mod_p384( mbedtls_mpi *N ) +{ + INIT( 384 ); + + ADD( 12 ); ADD( 21 ); ADD( 20 ); + SUB( 23 ); NEXT; // A0 + + ADD( 13 ); ADD( 22 ); ADD( 23 ); + SUB( 12 ); SUB( 20 ); NEXT; // A2 + + ADD( 14 ); ADD( 23 ); + SUB( 13 ); SUB( 21 ); NEXT; // A2 + + ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 ); + SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3 + + ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 ); + SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4 + + ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 ); + SUB( 16 ); NEXT; // A5 + + ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 ); + SUB( 17 ); NEXT; // A6 + + ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 ); + SUB( 18 ); NEXT; // A7 + + ADD( 20 ); ADD( 17 ); ADD( 16 ); + SUB( 19 ); NEXT; // A8 + + ADD( 21 ); ADD( 18 ); ADD( 17 ); + SUB( 20 ); NEXT; // A9 + + ADD( 22 ); ADD( 19 ); ADD( 18 ); + SUB( 21 ); NEXT; // A10 + + ADD( 23 ); ADD( 20 ); ADD( 19 ); + SUB( 22 ); LAST; // A11 + +cleanup: + return( ret ); +} +#endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ + +#undef A +#undef LOAD32 +#undef STORE32 +#undef MAX32 +#undef INIT +#undef NEXT +#undef LAST + +#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED || + MBEDTLS_ECP_DP_SECP256R1_ENABLED || + MBEDTLS_ECP_DP_SECP384R1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) +/* + * Here we have an actual Mersenne prime, so things are more straightforward. + * However, chunks are aligned on a 'weird' boundary (521 bits). + */ + +/* Size of p521 in terms of mbedtls_mpi_uint */ +#define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) + +/* Bits to keep in the most significant mbedtls_mpi_uint */ +#define P521_MASK 0x01FF + +/* + * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) + * Write N as A1 + 2^521 A0, return A0 + A1 + */ +static int ecp_mod_p521( mbedtls_mpi *N ) +{ + int ret; + size_t i; + mbedtls_mpi M; + mbedtls_mpi_uint Mp[P521_WIDTH + 1]; + /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits: + * we need to hold bits 513 to 1056, which is 34 limbs, that is + * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ + + if( N->n < P521_WIDTH ) + return( 0 ); + + /* M = A1 */ + M.s = 1; + M.n = N->n - ( P521_WIDTH - 1 ); + if( M.n > P521_WIDTH + 1 ) + M.n = P521_WIDTH + 1; + M.p = Mp; + memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); + + /* N = A0 */ + N->p[P521_WIDTH - 1] &= P521_MASK; + for( i = P521_WIDTH; i < N->n; i++ ) + N->p[i] = 0; + + /* N = A0 + A1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); + +cleanup: + return( ret ); +} + +#undef P521_WIDTH +#undef P521_MASK +#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ + +#endif /* MBEDTLS_ECP_NIST_OPTIM */ + +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) + +/* Size of p255 in terms of mbedtls_mpi_uint */ +#define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) + +/* + * Fast quasi-reduction modulo p255 = 2^255 - 19 + * Write N as A0 + 2^255 A1, return A0 + 19 * A1 + */ +static int ecp_mod_p255( mbedtls_mpi *N ) +{ + int ret; + size_t i; + mbedtls_mpi M; + mbedtls_mpi_uint Mp[P255_WIDTH + 2]; + + if( N->n < P255_WIDTH ) + return( 0 ); + + /* M = A1 */ + M.s = 1; + M.n = N->n - ( P255_WIDTH - 1 ); + if( M.n > P255_WIDTH + 1 ) + M.n = P255_WIDTH + 1; + 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_SECP192K1_ENABLED) || \ + defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ + defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) +/* + * Fast quasi-reduction modulo P = 2^s - R, + * with R about 33 bits, used by the Koblitz curves. + * + * Write N as A0 + 2^224 A1, return A0 + R * A1. + * Actually do two passes, since R is big. + */ +#define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P +#define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R +static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs, + size_t adjust, size_t shift, mbedtls_mpi_uint mask ) +{ + int ret; + size_t i; + mbedtls_mpi M, R; + mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1]; + + if( N->n < p_limbs ) + return( 0 ); + + /* Init R */ + R.s = 1; + R.p = Rp; + R.n = P_KOBLITZ_R; + + /* Common setup for M */ + M.s = 1; + M.p = Mp; + + /* M = A1 */ + M.n = N->n - ( p_limbs - adjust ); + if( M.n > p_limbs + adjust ) + M.n = p_limbs + adjust; + memset( Mp, 0, sizeof Mp ); + memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); + if( shift != 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); + M.n += R.n; /* Make room for multiplication by R */ + + /* N = A0 */ + if( mask != 0 ) + N->p[p_limbs - 1] &= mask; + for( i = p_limbs; i < N->n; i++ ) + N->p[i] = 0; + + /* N = A0 + R * A1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); + + /* Second pass */ + + /* M = A1 */ + M.n = N->n - ( p_limbs - adjust ); + if( M.n > p_limbs + adjust ) + M.n = p_limbs + adjust; + memset( Mp, 0, sizeof Mp ); + memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); + if( shift != 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); + M.n += R.n; /* Make room for multiplication by R */ + + /* N = A0 */ + if( mask != 0 ) + N->p[p_limbs - 1] &= mask; + for( i = p_limbs; i < N->n; i++ ) + N->p[i] = 0; + + /* N = A0 + R * A1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); + +cleanup: + return( ret ); +} +#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) || + MBEDTLS_ECP_DP_SECP224K1_ENABLED) || + MBEDTLS_ECP_DP_SECP256K1_ENABLED) */ + +#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) +/* + * Fast quasi-reduction modulo p192k1 = 2^192 - R, + * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119 + */ +static int ecp_mod_p192k1( mbedtls_mpi *N ) +{ + static mbedtls_mpi_uint Rp[] = { + BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; + + return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); +} +#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) +/* + * Fast quasi-reduction modulo p224k1 = 2^224 - R, + * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93 + */ +static int ecp_mod_p224k1( mbedtls_mpi *N ) +{ + static mbedtls_mpi_uint Rp[] = { + BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; + +#if defined(MBEDTLS_HAVE_INT64) + return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) ); +#else + return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); +#endif +} + +#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ + +#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) +/* + * Fast quasi-reduction modulo p256k1 = 2^256 - R, + * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1 + */ +static int ecp_mod_p256k1( mbedtls_mpi *N ) +{ + static mbedtls_mpi_uint Rp[] = { + BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; + return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); +} +#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ + +#endif /* !MBEDTLS_ECP_ALT */ + +#endif /* MBEDTLS_ECP_C */ |