| /* |
| * 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 <polarssl_maintainer at polarssl.org> |
| * |
| * 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 */ |
| #if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED) |
| static int ecp_mod_p192( mpi * ); |
| #endif |
| #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) |
| static int ecp_mod_p224( mpi * ); |
| #endif |
| #if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) |
| static int ecp_mod_p256( mpi * ); |
| #endif |
| #if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) |
| static int ecp_mod_p384( mpi * ); |
| #endif |
| #if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED) |
| static int ecp_mod_p521( mpi * ); |
| #endif |
| #if defined(POLARSSL_ECP_DP_M255_ENABLED) |
| static int ecp_mod_p255( mpi * ); |
| #endif |
| |
| #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; |
| #else |
| #define NIST_MODP( P ) |
| #endif /* POLARSSL_ECP_NIST_OPTIM */ |
| |
| #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: |
| grp->modp = ecp_mod_p255; |
| 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 */ |
| |
| #if defined(POLARSSL_ECP_DP_M255_ENABLED) |
| |
| /* Size of p255 in terms of t_uint */ |
| #define P255_WIDTH ( 255 / 8 / sizeof( t_uint ) + 1 ) |
| |
| /* |
| * Fast quasi-reduction modulo p255 = 2^255 - 19 |
| * Write N as A1 + 2^255 A1, return A0 + 19 * A1 |
| */ |
| static int ecp_mod_p255( mpi *N ) |
| { |
| int ret; |
| size_t i; |
| mpi M; |
| t_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( t_uint ) ); |
| MPI_CHK( mpi_shift_r( &M, 255 % ( 8 * sizeof( t_uint ) ) ) ); |
| M.n++; /* Make room for multiplication by 19 */ |
| |
| /* N = A0 */ |
| mpi_set_bit( N, 255, 0 ); |
| for( i = P255_WIDTH; i < N->n; i++ ) |
| N->p[i] = 0; |
| |
| /* N = A0 + 19 * A1 */ |
| MPI_CHK( mpi_mul_int( &M, &M, 19 ) ); |
| MPI_CHK( mpi_add_abs( N, N, &M ) ); |
| |
| cleanup: |
| return( ret ); |
| } |
| #endif /* POLARSSL_ECP_DP_M255_ENABLED */ |
| |
| #endif |