--- /dev/null
+/*
+ * Elliptic curves over GF(p): curve-specific data and functions
+ *
+ * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
+ * SPDX-License-Identifier: GPL-2.0
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License along
+ * with this program; if not, write to the Free Software Foundation, Inc.,
+ * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ *
+ * 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_CURVE448_ENABLED)
+static int ecp_mod_p448( mbedtls_mpi * );
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
+static int ecp_mod_p192k1( mbedtls_mpi * );
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
+static int ecp_mod_p224k1( mbedtls_mpi * );
+#endif
+#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+static int ecp_mod_p256k1( mbedtls_mpi * );
+#endif
+
+#define LOAD_GROUP_A( G ) ecp_group_load( grp, \
+ G ## _p, sizeof( G ## _p ), \
+ G ## _a, sizeof( G ## _a ), \
+ G ## _b, sizeof( G ## _b ), \
+ G ## _gx, sizeof( G ## _gx ), \
+ G ## _gy, sizeof( G ## _gy ), \
+ G ## _n, sizeof( G ## _n ) )
+
+#define LOAD_GROUP( G ) ecp_group_load( grp, \
+ G ## _p, sizeof( G ## _p ), \
+ NULL, 0, \
+ G ## _b, sizeof( G ## _b ), \
+ G ## _gx, sizeof( G ## _gx ), \
+ G ## _gy, sizeof( G ## _gy ), \
+ G ## _n, sizeof( G ## _n ) )
+
+#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+/*
+ * Specialized function for creating the Curve25519 group
+ */
+static int ecp_use_curve25519( mbedtls_ecp_group *grp )
+{
+ int ret;
+
+ /* Actually ( A + 2 ) / 4 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) );
+
+ /* P = 2^255 - 19 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) );
+ grp->pbits = mbedtls_mpi_bitlen( &grp->P );
+
+ /* N = 2^252 + 27742317777372353535851937790883648493 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16,
+ "14DEF9DEA2F79CD65812631A5CF5D3ED" ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) );
+
+ /* Y intentionally not set, since we use x/z coordinates.
+ * This is used as a marker to identify Montgomery curves! */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) );
+ mbedtls_mpi_free( &grp->G.Y );
+
+ /* Actually, the required msb for private keys */
+ grp->nbits = 254;
+
+cleanup:
+ if( ret != 0 )
+ mbedtls_ecp_group_free( grp );
+
+ return( ret );
+}
+#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
+/*
+ * Specialized function for creating the Curve448 group
+ */
+static int ecp_use_curve448( mbedtls_ecp_group *grp )
+{
+ mbedtls_mpi Ns;
+ int ret;
+
+ mbedtls_mpi_init( &Ns );
+
+ /* Actually ( A + 2 ) / 4 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) );
+
+ /* P = 2^448 - 2^224 - 1 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
+ grp->pbits = mbedtls_mpi_bitlen( &grp->P );
+
+ /* Y intentionally not set, since we use x/z coordinates.
+ * This is used as a marker to identify Montgomery curves! */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) );
+ mbedtls_mpi_free( &grp->G.Y );
+
+ /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16,
+ "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) );
+
+ /* Actually, the required msb for private keys */
+ grp->nbits = 447;
+
+cleanup:
+ mbedtls_mpi_free( &Ns );
+ if( ret != 0 )
+ mbedtls_ecp_group_free( grp );
+
+ return( ret );
+}
+#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
+
+/*
+ * Set a group using well-known domain parameters
+ */
+int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id )
+{
+ mbedtls_ecp_group_free( grp );
+
+ grp->id = id;
+
+ switch( id )
+ {
+#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
+ case MBEDTLS_ECP_DP_SECP192R1:
+ NIST_MODP( p192 );
+ return( LOAD_GROUP( secp192r1 ) );
+#endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
+ case MBEDTLS_ECP_DP_SECP224R1:
+ NIST_MODP( p224 );
+ return( LOAD_GROUP( secp224r1 ) );
+#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
+ case MBEDTLS_ECP_DP_SECP256R1:
+ NIST_MODP( p256 );
+ return( LOAD_GROUP( secp256r1 ) );
+#endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
+ case MBEDTLS_ECP_DP_SECP384R1:
+ NIST_MODP( p384 );
+ return( LOAD_GROUP( secp384r1 ) );
+#endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
+ case MBEDTLS_ECP_DP_SECP521R1:
+ NIST_MODP( p521 );
+ return( LOAD_GROUP( secp521r1 ) );
+#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
+ case MBEDTLS_ECP_DP_SECP192K1:
+ grp->modp = ecp_mod_p192k1;
+ return( LOAD_GROUP_A( secp192k1 ) );
+#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
+ case MBEDTLS_ECP_DP_SECP224K1:
+ grp->modp = ecp_mod_p224k1;
+ return( LOAD_GROUP_A( secp224k1 ) );
+#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+ case MBEDTLS_ECP_DP_SECP256K1:
+ grp->modp = ecp_mod_p256k1;
+ return( LOAD_GROUP_A( secp256k1 ) );
+#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
+ case MBEDTLS_ECP_DP_BP256R1:
+ return( LOAD_GROUP_A( brainpoolP256r1 ) );
+#endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
+ case MBEDTLS_ECP_DP_BP384R1:
+ return( LOAD_GROUP_A( brainpoolP384r1 ) );
+#endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
+ case MBEDTLS_ECP_DP_BP512R1:
+ return( LOAD_GROUP_A( brainpoolP512r1 ) );
+#endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+ case MBEDTLS_ECP_DP_CURVE25519:
+ grp->modp = ecp_mod_p255;
+ return( ecp_use_curve25519( grp ) );
+#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
+ case MBEDTLS_ECP_DP_CURVE448:
+ grp->modp = ecp_mod_p448;
+ return( ecp_use_curve448( grp ) );
+#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
+
+ default:
+ mbedtls_ecp_group_free( grp );
+ return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+ }
+}
+
+#if defined(MBEDTLS_ECP_NIST_OPTIM)
+/*
+ * Fast reduction modulo the primes used by the NIST curves.
+ *
+ * These functions are critical for speed, but not needed for correct
+ * operations. So, we make the choice to heavily rely on the internals of our
+ * bignum library, which creates a tight coupling between these functions and
+ * our MPI implementation. However, the coupling between the ECP module and
+ * MPI remains loose, since these functions can be deactivated at will.
+ */
+
+#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
+/*
+ * Compared to the way things are presented in FIPS 186-3 D.2,
+ * we proceed in columns, from right (least significant chunk) to left,
+ * adding chunks to N in place, and keeping a carry for the next chunk.
+ * This avoids moving things around in memory, and uselessly adding zeros,
+ * compared to the more straightforward, line-oriented approach.
+ *
+ * For this prime we need to handle data in chunks of 64 bits.
+ * Since this is always a multiple of our basic mbedtls_mpi_uint, we can
+ * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it.
+ */
+
+/* Add 64-bit chunks (dst += src) and update carry */
+static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry )
+{
+ unsigned char i;
+ mbedtls_mpi_uint c = 0;
+ for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ )
+ {
+ *dst += c; c = ( *dst < c );
+ *dst += *src; c += ( *dst < *src );
+ }
+ *carry += c;
+}
+
+/* Add carry to a 64-bit chunk and update carry */
+static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry )
+{
+ unsigned char i;
+ for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ )
+ {
+ *dst += *carry;
+ *carry = ( *dst < *carry );
+ }
+}
+
+#define WIDTH 8 / sizeof( mbedtls_mpi_uint )
+#define A( i ) N->p + i * WIDTH
+#define ADD( i ) add64( p, A( i ), &c )
+#define NEXT p += WIDTH; carry64( p, &c )
+#define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0
+
+/*
+ * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
+ */
+static int ecp_mod_p192( mbedtls_mpi *N )
+{
+ int ret;
+ mbedtls_mpi_uint c = 0;
+ mbedtls_mpi_uint *p, *end;
+
+ /* Make sure we have enough blocks so that A(5) is legal */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) );
+
+ p = N->p;
+ end = p + N->n;
+
+ ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5
+ ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5
+ ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5
+
+cleanup:
+ return( ret );
+}
+
+#undef WIDTH
+#undef A
+#undef ADD
+#undef NEXT
+#undef LAST
+#endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
+ defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
+ defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
+/*
+ * The reader is advised to first understand ecp_mod_p192() since the same
+ * general structure is used here, but with additional complications:
+ * (1) chunks of 32 bits, and (2) subtractions.
+ */
+
+/*
+ * For these primes, we need to handle data in chunks of 32 bits.
+ * This makes it more complicated if we use 64 bits limbs in MPI,
+ * which prevents us from using a uniform access method as for p192.
+ *
+ * So, we define a mini abstraction layer to access 32 bit chunks,
+ * load them in 'cur' for work, and store them back from 'cur' when done.
+ *
+ * While at it, also define the size of N in terms of 32-bit chunks.
+ */
+#define LOAD32 cur = A( i );
+
+#if defined(MBEDTLS_HAVE_INT32) /* 32 bit */
+
+#define MAX32 N->n
+#define A( j ) N->p[j]
+#define STORE32 N->p[i] = cur;
+
+#else /* 64-bit */
+
+#define MAX32 N->n * 2
+#define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
+#define STORE32 \
+ if( i % 2 ) { \
+ N->p[i/2] &= 0x00000000FFFFFFFF; \
+ N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \
+ } else { \
+ N->p[i/2] &= 0xFFFFFFFF00000000; \
+ N->p[i/2] |= (mbedtls_mpi_uint) cur; \
+ }
+
+#endif /* sizeof( mbedtls_mpi_uint ) */
+
+/*
+ * Helpers for addition and subtraction of chunks, with signed carry.
+ */
+static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
+{
+ *dst += src;
+ *carry += ( *dst < src );
+}
+
+static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
+{
+ *carry -= ( *dst < src );
+ *dst -= src;
+}
+
+#define ADD( j ) add32( &cur, A( j ), &c );
+#define SUB( j ) sub32( &cur, A( j ), &c );
+
+/*
+ * Helpers for the main 'loop'
+ * (see fix_negative for the motivation of C)
+ */
+#define INIT( b ) \
+ int ret; \
+ signed char c = 0, cc; \
+ uint32_t cur; \
+ size_t i = 0, bits = b; \
+ mbedtls_mpi C; \
+ mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \
+ \
+ C.s = 1; \
+ C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \
+ C.p = Cp; \
+ memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \
+ \
+ MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \
+ LOAD32;
+
+#define NEXT \
+ STORE32; i++; LOAD32; \
+ cc = c; c = 0; \
+ if( cc < 0 ) \
+ sub32( &cur, -cc, &c ); \
+ else \
+ add32( &cur, cc, &c ); \
+
+#define LAST \
+ STORE32; i++; \
+ cur = c > 0 ? c : 0; STORE32; \
+ cur = 0; while( ++i < MAX32 ) { STORE32; } \
+ if( c < 0 ) fix_negative( N, c, &C, bits );
+
+/*
+ * If the result is negative, we get it in the form
+ * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
+ */
+static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits )
+{
+ int ret;
+
+ /* C = - c * 2^(bits + 32) */
+#if !defined(MBEDTLS_HAVE_INT64)
+ ((void) bits);
+#else
+ if( bits == 224 )
+ C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32;
+ else
+#endif
+ C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c;
+
+ /* N = - ( C - N ) */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) );
+ N->s = -1;
+
+cleanup:
+
+ return( ret );
+}
+
+#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
+/*
+ * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
+ */
+static int ecp_mod_p224( mbedtls_mpi *N )
+{
+ INIT( 224 );
+
+ SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11
+ SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12
+ SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13
+ SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11
+ SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12
+ SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13
+ SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10
+
+cleanup:
+ return( ret );
+}
+#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
+/*
+ * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
+ */
+static int ecp_mod_p256( mbedtls_mpi *N )
+{
+ INIT( 256 );
+
+ ADD( 8 ); ADD( 9 );
+ SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0
+
+ ADD( 9 ); ADD( 10 );
+ SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1
+
+ ADD( 10 ); ADD( 11 );
+ SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2
+
+ ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
+ SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3
+
+ ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
+ SUB( 9 ); SUB( 10 ); NEXT; // A4
+
+ ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
+ SUB( 10 ); SUB( 11 ); NEXT; // A5
+
+ ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
+ SUB( 8 ); SUB( 9 ); NEXT; // A6
+
+ ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
+ SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7
+
+cleanup:
+ return( ret );
+}
+#endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
+/*
+ * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
+ */
+static int ecp_mod_p384( mbedtls_mpi *N )
+{
+ INIT( 384 );
+
+ ADD( 12 ); ADD( 21 ); ADD( 20 );
+ SUB( 23 ); NEXT; // A0
+
+ ADD( 13 ); ADD( 22 ); ADD( 23 );
+ SUB( 12 ); SUB( 20 ); NEXT; // A2
+
+ ADD( 14 ); ADD( 23 );
+ SUB( 13 ); SUB( 21 ); NEXT; // A2
+
+ ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
+ SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3
+
+ ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
+ SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4
+
+ ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
+ SUB( 16 ); NEXT; // A5
+
+ ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
+ SUB( 17 ); NEXT; // A6
+
+ ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
+ SUB( 18 ); NEXT; // A7
+
+ ADD( 20 ); ADD( 17 ); ADD( 16 );
+ SUB( 19 ); NEXT; // A8
+
+ ADD( 21 ); ADD( 18 ); ADD( 17 );
+ SUB( 20 ); NEXT; // A9
+
+ ADD( 22 ); ADD( 19 ); ADD( 18 );
+ SUB( 21 ); NEXT; // A10
+
+ ADD( 23 ); ADD( 20 ); ADD( 19 );
+ SUB( 22 ); LAST; // A11
+
+cleanup:
+ return( ret );
+}
+#endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
+
+#undef A
+#undef LOAD32
+#undef STORE32
+#undef MAX32
+#undef INIT
+#undef NEXT
+#undef LAST
+
+#endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED ||
+ MBEDTLS_ECP_DP_SECP256R1_ENABLED ||
+ MBEDTLS_ECP_DP_SECP384R1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
+/*
+ * Here we have an actual Mersenne prime, so things are more straightforward.
+ * However, chunks are aligned on a 'weird' boundary (521 bits).
+ */
+
+/* Size of p521 in terms of mbedtls_mpi_uint */
+#define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
+
+/* Bits to keep in the most significant mbedtls_mpi_uint */
+#define P521_MASK 0x01FF
+
+/*
+ * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
+ * Write N as A1 + 2^521 A0, return A0 + A1
+ */
+static int ecp_mod_p521( mbedtls_mpi *N )
+{
+ int ret;
+ size_t i;
+ mbedtls_mpi M;
+ mbedtls_mpi_uint Mp[P521_WIDTH + 1];
+ /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits:
+ * we need to hold bits 513 to 1056, which is 34 limbs, that is
+ * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
+
+ if( N->n < P521_WIDTH )
+ return( 0 );
+
+ /* M = A1 */
+ M.s = 1;
+ M.n = N->n - ( P521_WIDTH - 1 );
+ if( M.n > P521_WIDTH + 1 )
+ M.n = P521_WIDTH + 1;
+ M.p = Mp;
+ memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
+
+ /* N = A0 */
+ N->p[P521_WIDTH - 1] &= P521_MASK;
+ for( i = P521_WIDTH; i < N->n; i++ )
+ N->p[i] = 0;
+
+ /* N = A0 + A1 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
+
+cleanup:
+ return( ret );
+}
+
+#undef P521_WIDTH
+#undef P521_MASK
+#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
+
+#endif /* MBEDTLS_ECP_NIST_OPTIM */
+
+#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+
+/* Size of p255 in terms of mbedtls_mpi_uint */
+#define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
+
+/*
+ * Fast quasi-reduction modulo p255 = 2^255 - 19
+ * Write N as A0 + 2^255 A1, return A0 + 19 * A1
+ */
+static int ecp_mod_p255( mbedtls_mpi *N )
+{
+ int ret;
+ size_t i;
+ mbedtls_mpi M;
+ mbedtls_mpi_uint Mp[P255_WIDTH + 2];
+
+ if( N->n < P255_WIDTH )
+ return( 0 );
+
+ /* M = A1 */
+ M.s = 1;
+ M.n = N->n - ( P255_WIDTH - 1 );
+ if( M.n > P255_WIDTH + 1 )
+ return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+ M.p = Mp;
+ memset( Mp, 0, sizeof Mp );
+ memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
+ M.n++; /* Make room for multiplication by 19 */
+
+ /* N = A0 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) );
+ for( i = P255_WIDTH; i < N->n; i++ )
+ N->p[i] = 0;
+
+ /* N = A0 + 19 * A1 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
+
+cleanup:
+ return( ret );
+}
+#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
+
+/* Size of p448 in terms of mbedtls_mpi_uint */
+#define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) )
+
+/* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */
+#define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) )
+#define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) )
+#define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) )
+#define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 )
+
+/*
+ * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1
+ * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return
+ * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference
+ * implementation of Curve448, which uses its own special 56-bit limbs rather
+ * than a generic bignum library. We could squeeze some extra speed out on
+ * 32-bit machines by splitting N up into 32-bit limbs and doing the
+ * arithmetic using the limbs directly as we do for the NIST primes above,
+ * but for 64-bit targets it should use half the number of operations if we do
+ * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds.
+ */
+static int ecp_mod_p448( mbedtls_mpi *N )
+{
+ int ret;
+ size_t i;
+ mbedtls_mpi M, Q;
+ mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH];
+
+ if( N->n <= P448_WIDTH )
+ return( 0 );
+
+ /* M = A1 */
+ M.s = 1;
+ M.n = N->n - ( P448_WIDTH );
+ if( M.n > P448_WIDTH )
+ /* Shouldn't be called with N larger than 2^896! */
+ return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+ M.p = Mp;
+ memset( Mp, 0, sizeof( Mp ) );
+ memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) );
+
+ /* N = A0 */
+ for( i = P448_WIDTH; i < N->n; i++ )
+ N->p[i] = 0;
+
+ /* N += A1 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
+
+ /* Q = B1, N += B1 */
+ Q = M;
+ Q.p = Qp;
+ memcpy( Qp, Mp, sizeof( Qp ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) );
+
+ /* M = (B0 + B1) * 2^224, N += M */
+ if( sizeof( mbedtls_mpi_uint ) > 4 )
+ Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS );
+ for( i = P224_WIDTH_MAX; i < M.n; ++i )
+ Mp[i] = 0;
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) );
+ M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
+
+cleanup:
+ return( ret );
+}
+#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
+ defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
+ defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+/*
+ * Fast quasi-reduction modulo P = 2^s - R,
+ * with R about 33 bits, used by the Koblitz curves.
+ *
+ * Write N as A0 + 2^224 A1, return A0 + R * A1.
+ * Actually do two passes, since R is big.
+ */
+#define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P
+#define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R
+static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs,
+ size_t adjust, size_t shift, mbedtls_mpi_uint mask )
+{
+ int ret;
+ size_t i;
+ mbedtls_mpi M, R;
+ mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1];
+
+ if( N->n < p_limbs )
+ return( 0 );
+
+ /* Init R */
+ R.s = 1;
+ R.p = Rp;
+ R.n = P_KOBLITZ_R;
+
+ /* Common setup for M */
+ M.s = 1;
+ M.p = Mp;
+
+ /* M = A1 */
+ M.n = N->n - ( p_limbs - adjust );
+ if( M.n > p_limbs + adjust )
+ M.n = p_limbs + adjust;
+ memset( Mp, 0, sizeof Mp );
+ memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
+ if( shift != 0 )
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
+ M.n += R.n; /* Make room for multiplication by R */
+
+ /* N = A0 */
+ if( mask != 0 )
+ N->p[p_limbs - 1] &= mask;
+ for( i = p_limbs; i < N->n; i++ )
+ N->p[i] = 0;
+
+ /* N = A0 + R * A1 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
+
+ /* Second pass */
+
+ /* M = A1 */
+ M.n = N->n - ( p_limbs - adjust );
+ if( M.n > p_limbs + adjust )
+ M.n = p_limbs + adjust;
+ memset( Mp, 0, sizeof Mp );
+ memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
+ if( shift != 0 )
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
+ M.n += R.n; /* Make room for multiplication by R */
+
+ /* N = A0 */
+ if( mask != 0 )
+ N->p[p_limbs - 1] &= mask;
+ for( i = p_limbs; i < N->n; i++ )
+ N->p[i] = 0;
+
+ /* N = A0 + R * A1 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
+
+cleanup:
+ return( ret );
+}
+#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) ||
+ MBEDTLS_ECP_DP_SECP224K1_ENABLED) ||
+ MBEDTLS_ECP_DP_SECP256K1_ENABLED) */
+
+#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
+/*
+ * Fast quasi-reduction modulo p192k1 = 2^192 - R,
+ * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
+ */
+static int ecp_mod_p192k1( mbedtls_mpi *N )
+{
+ static mbedtls_mpi_uint Rp[] = {
+ BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
+
+ return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
+}
+#endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
+/*
+ * Fast quasi-reduction modulo p224k1 = 2^224 - R,
+ * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93
+ */
+static int ecp_mod_p224k1( mbedtls_mpi *N )
+{
+ static mbedtls_mpi_uint Rp[] = {
+ BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
+
+#if defined(MBEDTLS_HAVE_INT64)
+ return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) );
+#else
+ return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
+#endif
+}
+
+#endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
+
+#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+/*
+ * Fast quasi-reduction modulo p256k1 = 2^256 - R,
+ * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1
+ */
+static int ecp_mod_p256k1( mbedtls_mpi *N )
+{
+ static mbedtls_mpi_uint Rp[] = {
+ BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
+ return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
+}
+#endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
+
+#endif /* !MBEDTLS_ECP_ALT */
+
+#endif /* MBEDTLS_ECP_C */
projects / proxmark3-svn / blobdiff