/* * Elliptic curves over GF(p): curve-specific data and functions * * Copyright (C) 2006-2013, Brainspark B.V. * * This file is part of PolarSSL (http://www.polarssl.org) * Lead Maintainer: Paul Bakker * * All rights reserved. * * 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. */ #include "polarssl/config.h" #if defined(POLARSSL_ECP_C) #include "polarssl/ecp.h" #if defined(_MSC_VER) && !defined(inline) #define inline _inline #else #if defined(__ARMCC_VERSION) && !defined(inline) #define inline __inline #endif /* __ARMCC_VERSION */ #endif /*_MSC_VER */ /* * Domain parameters for secp192r1 */ static unsigned char secp192r1_p[] = { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF }; static unsigned char *secp192r1_a = NULL; static unsigned char secp192r1_b[] = { 0x64, 0x21, 0x05, 0x19, 0xE5, 0x9C, 0x80, 0xE7, 0x0F, 0xA7, 0xE9, 0xAB, 0x72, 0x24, 0x30, 0x49, 0xFE, 0xB8, 0xDE, 0xEC, 0xC1, 0x46, 0xB9, 0xB1 }; static unsigned char secp192r1_gx[] = { 0x18, 0x8D, 0xA8, 0x0E, 0xB0, 0x30, 0x90, 0xF6, 0x7C, 0xBF, 0x20, 0xEB, 0x43, 0xA1, 0x88, 0x00, 0xF4, 0xFF, 0x0A, 0xFD, 0x82, 0xFF, 0x10, 0x12 }; static unsigned char secp192r1_gy[] = { 0x07, 0x19, 0x2B, 0x95, 0xFF, 0xC8, 0xDA, 0x78, 0x63, 0x10, 0x11, 0xED, 0x6B, 0x24, 0xCD, 0xD5, 0x73, 0xF9, 0x77, 0xA1, 0x1E, 0x79, 0x48, 0x11 }; static unsigned char secp192r1_n[] = { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x99, 0xDE, 0xF8, 0x36, 0x14, 0x6B, 0xC9, 0xB1, 0xB4, 0xD2, 0x28, 0x31 }; /* * Domain parameters for secp224r1 */ static unsigned char secp224r1_p[] = { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01 }; static unsigned char *secp224r1_a = NULL; static unsigned char secp224r1_b[] = { 0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4 }; static unsigned char secp224r1_gx[] = { 0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21 }; static unsigned char secp224r1_gy[] = { 0xBD, 0x37, 0x63, 0x88, 0xB5, 0xF7, 0x23, 0xFB, 0x4C, 0x22, 0xDF, 0xE6, 0xCD, 0x43, 0x75, 0xA0, 0x5A, 0x07, 0x47, 0x64, 0x44, 0xD5, 0x81, 0x99, 0x85, 0x00, 0x7E, 0x34 }; static unsigned char secp224r1_n[] = { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x16, 0xA2, 0xE0, 0xB8, 0xF0, 0x3E, 0x13, 0xDD, 0x29, 0x45, 0x5C, 0x5C, 0x2A, 0x3D }; /* * Domain parameters for secp256r1 */ static unsigned char secp256r1_p[] = { 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF }; static unsigned char *secp256r1_a = NULL; static unsigned char secp256r1_b[] = { 0x5A, 0xC6, 0x35, 0xD8, 0xAA, 0x3A, 0x93, 0xE7, 0xB3, 0xEB, 0xBD, 0x55, 0x76, 0x98, 0x86, 0xBC, 0x65, 0x1D, 0x06, 0xB0, 0xCC, 0x53, 0xB0, 0xF6, 0x3B, 0xCE, 0x3C, 0x3E, 0x27, 0xD2, 0x60, 0x4B }; static unsigned char secp256r1_gx[] = { 0x6B, 0x17, 0xD1, 0xF2, 0xE1, 0x2C, 0x42, 0x47, 0xF8, 0xBC, 0xE6, 0xE5, 0x63, 0xA4, 0x40, 0xF2, 0x77, 0x03, 0x7D, 0x81, 0x2D, 0xEB, 0x33, 0xA0, 0xF4, 0xA1, 0x39, 0x45, 0xD8, 0x98, 0xC2, 0x96 }; static unsigned char secp256r1_gy[] = { 0x4F, 0xE3, 0x42, 0xE2, 0xFE, 0x1A, 0x7F, 0x9B, 0x8E, 0xE7, 0xEB, 0x4A, 0x7C, 0x0F, 0x9E, 0x16, 0x2B, 0xCE, 0x33, 0x57, 0x6B, 0x31, 0x5E, 0xCE, 0xCB, 0xB6, 0x40, 0x68, 0x37, 0xBF, 0x51, 0xF5 }; static unsigned char secp256r1_n[] = { 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xBC, 0xE6, 0xFA, 0xAD, 0xA7, 0x17, 0x9E, 0x84, 0xF3, 0xB9, 0xCA, 0xC2, 0xFC, 0x63, 0x25, 0x51 }; /* * Domain parameters for secp384r1 */ static unsigned char secp384r1_p[] = { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF }; static unsigned char *secp384r1_a = NULL; static unsigned char secp384r1_b[] = { 0xB3, 0x31, 0x2F, 0xA7, 0xE2, 0x3E, 0xE7, 0xE4, 0x98, 0x8E, 0x05, 0x6B, 0xE3, 0xF8, 0x2D, 0x19, 0x18, 0x1D, 0x9C, 0x6E, 0xFE, 0x81, 0x41, 0x12, 0x03, 0x14, 0x08, 0x8F, 0x50, 0x13, 0x87, 0x5A, 0xC6, 0x56, 0x39, 0x8D, 0x8A, 0x2E, 0xD1, 0x9D, 0x2A, 0x85, 0xC8, 0xED, 0xD3, 0xEC, 0x2A, 0xEF }; static unsigned char secp384r1_gx[] = { 0xAA, 0x87, 0xCA, 0x22, 0xBE, 0x8B, 0x05, 0x37, 0x8E, 0xB1, 0xC7, 0x1E, 0xF3, 0x20, 0xAD, 0x74, 0x6E, 0x1D, 0x3B, 0x62, 0x8B, 0xA7, 0x9B, 0x98, 0x59, 0xF7, 0x41, 0xE0, 0x82, 0x54, 0x2A, 0x38, 0x55, 0x02, 0xF2, 0x5D, 0xBF, 0x55, 0x29, 0x6C, 0x3A, 0x54, 0x5E, 0x38, 0x72, 0x76, 0x0A, 0xB7 }; static unsigned char secp384r1_gy[] = { 0x36, 0x17, 0xDE, 0x4A, 0x96, 0x26, 0x2C, 0x6F, 0x5D, 0x9E, 0x98, 0xBF, 0x92, 0x92, 0xDC, 0x29, 0xF8, 0xF4, 0x1D, 0xBD, 0x28, 0x9A, 0x14, 0x7C, 0xE9, 0xDA, 0x31, 0x13, 0xB5, 0xF0, 0xB8, 0xC0, 0x0A, 0x60, 0xB1, 0xCE, 0x1D, 0x7E, 0x81, 0x9D, 0x7A, 0x43, 0x1D, 0x7C, 0x90, 0xEA, 0x0E, 0x5F }; static unsigned char secp384r1_n[] = { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xC7, 0x63, 0x4D, 0x81, 0xF4, 0x37, 0x2D, 0xDF, 0x58, 0x1A, 0x0D, 0xB2, 0x48, 0xB0, 0xA7, 0x7A, 0xEC, 0xEC, 0x19, 0x6A, 0xCC, 0xC5, 0x29, 0x73 }; /* * Domain parameters for secp521r1 */ static unsigned char secp521r1_p[] = { 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF }; static unsigned char *secp521r1_a = NULL; static unsigned char secp521r1_b[] = { 0x00, 0x51, 0x95, 0x3E, 0xB9, 0x61, 0x8E, 0x1C, 0x9A, 0x1F, 0x92, 0x9A, 0x21, 0xA0, 0xB6, 0x85, 0x40, 0xEE, 0xA2, 0xDA, 0x72, 0x5B, 0x99, 0xB3, 0x15, 0xF3, 0xB8, 0xB4, 0x89, 0x91, 0x8E, 0xF1, 0x09, 0xE1, 0x56, 0x19, 0x39, 0x51, 0xEC, 0x7E, 0x93, 0x7B, 0x16, 0x52, 0xC0, 0xBD, 0x3B, 0xB1, 0xBF, 0x07, 0x35, 0x73, 0xDF, 0x88, 0x3D, 0x2C, 0x34, 0xF1, 0xEF, 0x45, 0x1F, 0xD4, 0x6B, 0x50, 0x3F, 0x00 }; static unsigned char secp521r1_gx[] = { 0x00, 0xC6, 0x85, 0x8E, 0x06, 0xB7, 0x04, 0x04, 0xE9, 0xCD, 0x9E, 0x3E, 0xCB, 0x66, 0x23, 0x95, 0xB4, 0x42, 0x9C, 0x64, 0x81, 0x39, 0x05, 0x3F, 0xB5, 0x21, 0xF8, 0x28, 0xAF, 0x60, 0x6B, 0x4D, 0x3D, 0xBA, 0xA1, 0x4B, 0x5E, 0x77, 0xEF, 0xE7, 0x59, 0x28, 0xFE, 0x1D, 0xC1, 0x27, 0xA2, 0xFF, 0xA8, 0xDE, 0x33, 0x48, 0xB3, 0xC1, 0x85, 0x6A, 0x42, 0x9B, 0xF9, 0x7E, 0x7E, 0x31, 0xC2, 0xE5, 0xBD, 0x66 }; static unsigned char secp521r1_gy[] = { 0x01, 0x18, 0x39, 0x29, 0x6A, 0x78, 0x9A, 0x3B, 0xC0, 0x04, 0x5C, 0x8A, 0x5F, 0xB4, 0x2C, 0x7D, 0x1B, 0xD9, 0x98, 0xF5, 0x44, 0x49, 0x57, 0x9B, 0x44, 0x68, 0x17, 0xAF, 0xBD, 0x17, 0x27, 0x3E, 0x66, 0x2C, 0x97, 0xEE, 0x72, 0x99, 0x5E, 0xF4, 0x26, 0x40, 0xC5, 0x50, 0xB9, 0x01, 0x3F, 0xAD, 0x07, 0x61, 0x35, 0x3C, 0x70, 0x86, 0xA2, 0x72, 0xC2, 0x40, 0x88, 0xBE, 0x94, 0x76, 0x9F, 0xD1, 0x66, 0x50 }; static unsigned char secp521r1_n[] = { 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFA, 0x51, 0x86, 0x87, 0x83, 0xBF, 0x2F, 0x96, 0x6B, 0x7F, 0xCC, 0x01, 0x48, 0xF7, 0x09, 0xA5, 0xD0, 0x3B, 0xB5, 0xC9, 0xB8, 0x89, 0x9C, 0x47, 0xAE, 0xBB, 0x6F, 0xB7, 0x1E, 0x91, 0x38, 0x64, 0x09 }; /* * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) */ static unsigned char brainpoolP256r1_p[] = { 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, 0xD5, 0x26, 0x20, 0x28, 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, 0x53, 0x77 }; static unsigned char brainpoolP256r1_a[] = { 0x7D, 0x5A, 0x09, 0x75, 0xFC, 0x2C, 0x30, 0x57, 0xEE, 0xF6, 0x75, 0x30, 0x41, 0x7A, 0xFF, 0xE7, 0xFB, 0x80, 0x55, 0xC1, 0x26, 0xDC, 0x5C, 0x6C, 0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, 0xB5, 0xD9 }; static unsigned char brainpoolP256r1_b[] = { 0x26, 0xDC, 0x5C, 0x6C, 0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, 0xB5, 0xD9, 0xBB, 0xD7, 0x7C, 0xBF, 0x95, 0x84, 0x16, 0x29, 0x5C, 0xF7, 0xE1, 0xCE, 0x6B, 0xCC, 0xDC, 0x18, 0xFF, 0x8C, 0x07, 0xB6 }; static unsigned char brainpoolP256r1_gx[] = { 0x8B, 0xD2, 0xAE, 0xB9, 0xCB, 0x7E, 0x57, 0xCB, 0x2C, 0x4B, 0x48, 0x2F, 0xFC, 0x81, 0xB7, 0xAF, 0xB9, 0xDE, 0x27, 0xE1, 0xE3, 0xBD, 0x23, 0xC2, 0x3A, 0x44, 0x53, 0xBD, 0x9A, 0xCE, 0x32, 0x62 }; static unsigned char brainpoolP256r1_gy[] = { 0x54, 0x7E, 0xF8, 0x35, 0xC3, 0xDA, 0xC4, 0xFD, 0x97, 0xF8, 0x46, 0x1A, 0x14, 0x61, 0x1D, 0xC9, 0xC2, 0x77, 0x45, 0x13, 0x2D, 0xED, 0x8E, 0x54, 0x5C, 0x1D, 0x54, 0xC7, 0x2F, 0x04, 0x69, 0x97 }; static unsigned char brainpoolP256r1_n[] = { 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, 0x0A, 0x90, 0x9D, 0x83, 0x8D, 0x71, 0x8C, 0x39, 0x7A, 0xA3, 0xB5, 0x61, 0xA6, 0xF7, 0x90, 0x1E, 0x0E, 0x82, 0x97, 0x48, 0x56, 0xA7 }; /* * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) */ static unsigned char brainpoolP384r1_p[] = { 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, 0xED, 0x54, 0x56, 0xB4, 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, 0x90, 0x1D, 0x1A, 0x71, 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x53 }; static unsigned char brainpoolP384r1_a[] = { 0x7B, 0xC3, 0x82, 0xC6, 0x3D, 0x8C, 0x15, 0x0C, 0x3C, 0x72, 0x08, 0x0A, 0xCE, 0x05, 0xAF, 0xA0, 0xC2, 0xBE, 0xA2, 0x8E, 0x4F, 0xB2, 0x27, 0x87, 0x13, 0x91, 0x65, 0xEF, 0xBA, 0x91, 0xF9, 0x0F, 0x8A, 0xA5, 0x81, 0x4A, 0x50, 0x3A, 0xD4, 0xEB, 0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26 }; static unsigned char brainpoolP384r1_b[] = { 0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26, 0x8B, 0x39, 0xB5, 0x54, 0x16, 0xF0, 0x44, 0x7C, 0x2F, 0xB7, 0x7D, 0xE1, 0x07, 0xDC, 0xD2, 0xA6, 0x2E, 0x88, 0x0E, 0xA5, 0x3E, 0xEB, 0x62, 0xD5, 0x7C, 0xB4, 0x39, 0x02, 0x95, 0xDB, 0xC9, 0x94, 0x3A, 0xB7, 0x86, 0x96, 0xFA, 0x50, 0x4C, 0x11 }; static unsigned char brainpoolP384r1_gx[] = { 0x1D, 0x1C, 0x64, 0xF0, 0x68, 0xCF, 0x45, 0xFF, 0xA2, 0xA6, 0x3A, 0x81, 0xB7, 0xC1, 0x3F, 0x6B, 0x88, 0x47, 0xA3, 0xE7, 0x7E, 0xF1, 0x4F, 0xE3, 0xDB, 0x7F, 0xCA, 0xFE, 0x0C, 0xBD, 0x10, 0xE8, 0xE8, 0x26, 0xE0, 0x34, 0x36, 0xD6, 0x46, 0xAA, 0xEF, 0x87, 0xB2, 0xE2, 0x47, 0xD4, 0xAF, 0x1E }; static unsigned char brainpoolP384r1_gy[] = { 0x8A, 0xBE, 0x1D, 0x75, 0x20, 0xF9, 0xC2, 0xA4, 0x5C, 0xB1, 0xEB, 0x8E, 0x95, 0xCF, 0xD5, 0x52, 0x62, 0xB7, 0x0B, 0x29, 0xFE, 0xEC, 0x58, 0x64, 0xE1, 0x9C, 0x05, 0x4F, 0xF9, 0x91, 0x29, 0x28, 0x0E, 0x46, 0x46, 0x21, 0x77, 0x91, 0x81, 0x11, 0x42, 0x82, 0x03, 0x41, 0x26, 0x3C, 0x53, 0x15 }; static unsigned char brainpoolP384r1_n[] = { 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, 0x6F, 0x7E, 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, 0xED, 0x54, 0x56, 0xB3, 0x1F, 0x16, 0x6E, 0x6C, 0xAC, 0x04, 0x25, 0xA7, 0xCF, 0x3A, 0xB6, 0xAF, 0x6B, 0x7F, 0xC3, 0x10, 0x3B, 0x88, 0x32, 0x02, 0xE9, 0x04, 0x65, 0x65 }; /* * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) */ static unsigned char brainpoolP512r1_p[] = { 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, 0x9B, 0xC6, 0x68, 0x42, 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, 0x28, 0x81, 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, 0x58, 0x3A, 0x48, 0xF3 }; static unsigned char brainpoolP512r1_a[] = { 0x78, 0x30, 0xA3, 0x31, 0x8B, 0x60, 0x3B, 0x89, 0xE2, 0x32, 0x71, 0x45, 0xAC, 0x23, 0x4C, 0xC5, 0x94, 0xCB, 0xDD, 0x8D, 0x3D, 0xF9, 0x16, 0x10, 0xA8, 0x34, 0x41, 0xCA, 0xEA, 0x98, 0x63, 0xBC, 0x2D, 0xED, 0x5D, 0x5A, 0xA8, 0x25, 0x3A, 0xA1, 0x0A, 0x2E, 0xF1, 0xC9, 0x8B, 0x9A, 0xC8, 0xB5, 0x7F, 0x11, 0x17, 0xA7, 0x2B, 0xF2, 0xC7, 0xB9, 0xE7, 0xC1, 0xAC, 0x4D, 0x77, 0xFC, 0x94, 0xCA }; static unsigned char brainpoolP512r1_b[] = { 0x3D, 0xF9, 0x16, 0x10, 0xA8, 0x34, 0x41, 0xCA, 0xEA, 0x98, 0x63, 0xBC, 0x2D, 0xED, 0x5D, 0x5A, 0xA8, 0x25, 0x3A, 0xA1, 0x0A, 0x2E, 0xF1, 0xC9, 0x8B, 0x9A, 0xC8, 0xB5, 0x7F, 0x11, 0x17, 0xA7, 0x2B, 0xF2, 0xC7, 0xB9, 0xE7, 0xC1, 0xAC, 0x4D, 0x77, 0xFC, 0x94, 0xCA, 0xDC, 0x08, 0x3E, 0x67, 0x98, 0x40, 0x50, 0xB7, 0x5E, 0xBA, 0xE5, 0xDD, 0x28, 0x09, 0xBD, 0x63, 0x80, 0x16, 0xF7, 0x23 }; static unsigned char brainpoolP512r1_gx[] = { 0x81, 0xAE, 0xE4, 0xBD, 0xD8, 0x2E, 0xD9, 0x64, 0x5A, 0x21, 0x32, 0x2E, 0x9C, 0x4C, 0x6A, 0x93, 0x85, 0xED, 0x9F, 0x70, 0xB5, 0xD9, 0x16, 0xC1, 0xB4, 0x3B, 0x62, 0xEE, 0xF4, 0xD0, 0x09, 0x8E, 0xFF, 0x3B, 0x1F, 0x78, 0xE2, 0xD0, 0xD4, 0x8D, 0x50, 0xD1, 0x68, 0x7B, 0x93, 0xB9, 0x7D, 0x5F, 0x7C, 0x6D, 0x50, 0x47, 0x40, 0x6A, 0x5E, 0x68, 0x8B, 0x35, 0x22, 0x09, 0xBC, 0xB9, 0xF8, 0x22 }; static unsigned char brainpoolP512r1_gy[] = { 0x7D, 0xDE, 0x38, 0x5D, 0x56, 0x63, 0x32, 0xEC, 0xC0, 0xEA, 0xBF, 0xA9, 0xCF, 0x78, 0x22, 0xFD, 0xF2, 0x09, 0xF7, 0x00, 0x24, 0xA5, 0x7B, 0x1A, 0xA0, 0x00, 0xC5, 0x5B, 0x88, 0x1F, 0x81, 0x11, 0xB2, 0xDC, 0xDE, 0x49, 0x4A, 0x5F, 0x48, 0x5E, 0x5B, 0xCA, 0x4B, 0xD8, 0x8A, 0x27, 0x63, 0xAE, 0xD1, 0xCA, 0x2B, 0x2F, 0xA8, 0xF0, 0x54, 0x06, 0x78, 0xCD, 0x1E, 0x0F, 0x3A, 0xD8, 0x08, 0x92 }; static unsigned char brainpoolP512r1_n[] = { 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, 0xE6, 0xAE, 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, 0xB3, 0xC9, 0xD2, 0x0E, 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, 0x08, 0x70, 0x55, 0x3E, 0x5C, 0x41, 0x4C, 0xA9, 0x26, 0x19, 0x41, 0x86, 0x61, 0x19, 0x7F, 0xAC, 0x10, 0x47, 0x1D, 0xB1, 0xD3, 0x81, 0x08, 0x5D, 0xDA, 0xDD, 0xB5, 0x87, 0x96, 0x82, 0x9C, 0xA9, 0x00, 0x69 }; /* * Import an ECP group from binary */ static int ecp_group_read_binary( ecp_group *grp, const unsigned char *p, size_t plen, const unsigned char *a, size_t alen, const unsigned char *b, size_t blen, const unsigned char *gx, size_t gxlen, const unsigned char *gy, size_t gylen, const unsigned char *n, size_t nlen) { int ret; MPI_CHK( mpi_read_binary( &grp->P, p, plen ) ); if( a != NULL ) MPI_CHK( mpi_read_binary( &grp->A, a, alen ) ); else MPI_CHK( mpi_sub_int( &grp->A, &grp->P, 3 ) ); MPI_CHK( mpi_read_binary( &grp->B, b, blen ) ); MPI_CHK( mpi_read_binary( &grp->N, n, nlen ) ); MPI_CHK( mpi_read_binary( &grp->G.X, gx, gxlen ) ); MPI_CHK( mpi_read_binary( &grp->G.Y, gy, gylen ) ); MPI_CHK( mpi_lset( &grp->G.Z, 1 ) ); grp->pbits = mpi_msb( &grp->P ); grp->nbits = mpi_msb( &grp->N ); cleanup: if( ret != 0 ) ecp_group_free( grp ); return( ret ); } #if defined(POLARSSL_ECP_NIST_OPTIM) /* Forward declarations */ static int ecp_mod_p192( mpi * ); static int ecp_mod_p224( mpi * ); static int ecp_mod_p256( mpi * ); static int ecp_mod_p384( mpi * ); static int ecp_mod_p521( mpi * ); #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; #else #define NIST_MODP( P ) #endif #define LOAD_GROUP( G ) ecp_group_read_binary( 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 ) ) /* * Specialized function for creating the Curve25519 group */ static int ecp_use_curve25519( ecp_group *grp ) { int ret; /* Actually ( A + 2 ) / 4 */ MPI_CHK( mpi_read_string( &grp->A, 16, "01DB42" ) ); /* P = 2^255 - 19 */ MPI_CHK( mpi_lset( &grp->P, 1 ) ); MPI_CHK( mpi_shift_l( &grp->P, 255 ) ); MPI_CHK( mpi_sub_int( &grp->P, &grp->P, 19 ) ); grp->pbits = mpi_msb( &grp->P ); /* Y intentionaly not set, since we use x/z coordinates. * This is used as a marker to identify Montgomery curves! */ MPI_CHK( mpi_lset( &grp->G.X, 9 ) ); MPI_CHK( mpi_lset( &grp->G.Z, 1 ) ); mpi_free( &grp->G.Y ); /* Actually, the required msb for private keys */ grp->nbits = 254; cleanup: if( ret != 0 ) ecp_group_free( grp ); return( ret ); } /* * Set a group using well-known domain parameters */ int ecp_use_known_dp( ecp_group *grp, ecp_group_id id ) { ecp_group_free( grp ); grp->id = id; switch( id ) { #if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED) case POLARSSL_ECP_DP_SECP192R1: NIST_MODP( p192 ); return( LOAD_GROUP( secp192r1 ) ); #endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */ #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) case POLARSSL_ECP_DP_SECP224R1: NIST_MODP( p224 ); return( LOAD_GROUP( secp224r1 ) ); #endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */ #if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) case POLARSSL_ECP_DP_SECP256R1: NIST_MODP( p256 ); return( LOAD_GROUP( secp256r1 ) ); #endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */ #if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) case POLARSSL_ECP_DP_SECP384R1: NIST_MODP( p384 ); return( LOAD_GROUP( secp384r1 ) ); #endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */ #if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED) case POLARSSL_ECP_DP_SECP521R1: NIST_MODP( p521 ); return( LOAD_GROUP( secp521r1 ) ); #endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */ #if defined(POLARSSL_ECP_DP_BP256R1_ENABLED) case POLARSSL_ECP_DP_BP256R1: return( LOAD_GROUP( brainpoolP256r1 ) ); #endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */ #if defined(POLARSSL_ECP_DP_BP384R1_ENABLED) case POLARSSL_ECP_DP_BP384R1: return( LOAD_GROUP( brainpoolP384r1 ) ); #endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */ #if defined(POLARSSL_ECP_DP_BP512R1_ENABLED) case POLARSSL_ECP_DP_BP512R1: return( LOAD_GROUP( brainpoolP512r1 ) ); #endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */ #if defined(POLARSSL_ECP_DP_M255_ENABLED) case POLARSSL_ECP_DP_M255: return( ecp_use_curve25519( grp ) ); #endif /* POLARSSL_ECP_DP_M255_ENABLED */ default: ecp_group_free( grp ); return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE ); } } #if defined(POLARSSL_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(POLARSSL_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 t_uint, we can * use a t_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( t_uint *dst, t_uint *src, t_uint *carry ) { unsigned char i; t_uint c = 0; for( i = 0; i < 8 / sizeof( t_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( t_uint *dst, t_uint *carry ) { unsigned char i; for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++ ) { *dst += *carry; *carry = ( *dst < *carry ); } } #define WIDTH 8 / sizeof( t_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( mpi *N ) { int ret; t_uint c = 0; t_uint *p, *end; /* Make sure we have enough blocks so that A(5) is legal */ MPI_CHK( 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 /* POLARSSL_ECP_DP_SECP192R1_ENABLED */ #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) || \ defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) || \ defined(POLARSSL_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(POLARSSL_HAVE_INT8) /* 8 bit */ #define MAX32 N->n / 4 #define A( j ) (uint32_t)( N->p[4*j+0] ) | \ ( N->p[4*j+1] << 8 ) | \ ( N->p[4*j+2] << 16 ) | \ ( N->p[4*j+3] << 24 ) #define STORE32 N->p[4*i+0] = (t_uint)( cur ); \ N->p[4*i+1] = (t_uint)( cur >> 8 ); \ N->p[4*i+2] = (t_uint)( cur >> 16 ); \ N->p[4*i+3] = (t_uint)( cur >> 24 ); #elif defined(POLARSSL_HAVE_INT16) /* 16 bit */ #define MAX32 N->n / 2 #define A( j ) (uint32_t)( N->p[2*j] ) | ( N->p[2*j+1] << 16 ) #define STORE32 N->p[2*i+0] = (t_uint)( cur ); \ N->p[2*i+1] = (t_uint)( cur >> 16 ); #elif defined(POLARSSL_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] |= ((t_uint) cur) << 32; \ } else { \ N->p[i/2] &= 0xFFFFFFFF00000000; \ N->p[i/2] |= (t_uint) cur; \ } #endif /* sizeof( t_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; \ mpi C; \ t_uint Cp[ b / 8 / sizeof( t_uint) + 1 ]; \ \ C.s = 1; \ C.n = b / 8 / sizeof( t_uint) + 1; \ C.p = Cp; \ memset( Cp, 0, C.n * sizeof( t_uint ) ); \ \ MPI_CHK( mpi_grow( N, b * 2 / 8 / sizeof( t_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( mpi *N, signed char c, mpi *C, size_t bits ) { int ret; /* C = - c * 2^(bits + 32) */ #if !defined(POLARSSL_HAVE_INT64) ((void) bits); #else if( bits == 224 ) C->p[ C->n - 1 ] = ((t_uint) -c) << 32; else #endif C->p[ C->n - 1 ] = (t_uint) -c; /* N = - ( C - N ) */ MPI_CHK( mpi_sub_abs( N, C, N ) ); N->s = -1; cleanup: return( ret ); } #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) /* * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) */ static int ecp_mod_p224( 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 /* POLARSSL_ECP_DP_SECP224R1_ENABLED */ #if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) /* * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) */ static int ecp_mod_p256( 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 /* POLARSSL_ECP_DP_SECP256R1_ENABLED */ #if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) /* * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) */ static int ecp_mod_p384( 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 /* POLARSSL_ECP_DP_SECP384R1_ENABLED */ #undef A #undef LOAD32 #undef STORE32 #undef MAX32 #undef INIT #undef NEXT #undef LAST #endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED || POLARSSL_ECP_DP_SECP256R1_ENABLED || POLARSSL_ECP_DP_SECP384R1_ENABLED */ #if defined(POLARSSL_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 t_uint */ #define P521_WIDTH ( 521 / 8 / sizeof( t_uint ) + 1 ) /* Bits to keep in the most significant t_uint */ #if defined(POLARSSL_HAVE_INT8) #define P521_MASK 0x01 #else #define P521_MASK 0x01FF #endif /* * 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( mpi *N ) { int ret; size_t i; mpi M; t_uint Mp[P521_WIDTH + 1]; /* Worst case for the size of M is when t_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( t_uint ) ); MPI_CHK( mpi_shift_r( &M, 521 % ( 8 * sizeof( t_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 */ MPI_CHK( mpi_add_abs( N, N, &M ) ); cleanup: return( ret ); } #undef P521_WIDTH #undef P521_MASK #endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */ #endif /* POLARSSL_ECP_NIST_OPTIM */ #endif