800 lines
31 KiB
C
800 lines
31 KiB
C
/*
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* Elliptic curves over GF(p): curve-specific data and functions
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*
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* Copyright (C) 2006-2013, Brainspark B.V.
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*
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* This file is part of PolarSSL (http://www.polarssl.org)
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* Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
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*
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* All rights reserved.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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#include "polarssl/config.h"
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#if defined(POLARSSL_ECP_C)
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#include "polarssl/ecp.h"
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/*
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* Domain parameters for secp192r1
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*/
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static unsigned char secp192r1_p[] = {
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF };
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static unsigned char *secp192r1_a = NULL;
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static unsigned char secp192r1_b[] = {
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0x64, 0x21, 0x05, 0x19, 0xE5, 0x9C, 0x80, 0xE7, 0x0F, 0xA7, 0xE9, 0xAB,
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0x72, 0x24, 0x30, 0x49, 0xFE, 0xB8, 0xDE, 0xEC, 0xC1, 0x46, 0xB9, 0xB1 };
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static unsigned char secp192r1_gx[] = {
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0x18, 0x8D, 0xA8, 0x0E, 0xB0, 0x30, 0x90, 0xF6, 0x7C, 0xBF, 0x20, 0xEB,
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0x43, 0xA1, 0x88, 0x00, 0xF4, 0xFF, 0x0A, 0xFD, 0x82, 0xFF, 0x10, 0x12 };
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static unsigned char secp192r1_gy[] = {
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0x07, 0x19, 0x2B, 0x95, 0xFF, 0xC8, 0xDA, 0x78, 0x63, 0x10, 0x11, 0xED,
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0x6B, 0x24, 0xCD, 0xD5, 0x73, 0xF9, 0x77, 0xA1, 0x1E, 0x79, 0x48, 0x11 };
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static unsigned char secp192r1_n[] = {
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0x99, 0xDE, 0xF8, 0x36, 0x14, 0x6B, 0xC9, 0xB1, 0xB4, 0xD2, 0x28, 0x31 };
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/*
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* Domain parameters for secp224r1
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*/
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static unsigned char secp224r1_p[] = {
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x01 };
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static unsigned char *secp224r1_a = NULL;
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static unsigned char secp224r1_b[] = {
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0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, 0x32, 0x56,
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0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, 0x27, 0x0B, 0x39, 0x43,
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0x23, 0x55, 0xFF, 0xB4 };
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static unsigned char secp224r1_gx[] = {
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0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, 0x90, 0xB9,
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0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xD6,
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0x11, 0x5C, 0x1D, 0x21 };
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static unsigned char secp224r1_gy[] = {
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0xBD, 0x37, 0x63, 0x88, 0xB5, 0xF7, 0x23, 0xFB, 0x4C, 0x22, 0xDF, 0xE6,
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0xCD, 0x43, 0x75, 0xA0, 0x5A, 0x07, 0x47, 0x64, 0x44, 0xD5, 0x81, 0x99,
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0x85, 0x00, 0x7E, 0x34 };
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static unsigned char secp224r1_n[] = {
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0x16, 0xA2, 0xE0, 0xB8, 0xF0, 0x3E, 0x13, 0xDD, 0x29, 0x45,
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0x5C, 0x5C, 0x2A, 0x3D };
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/*
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* Domain parameters for secp256r1
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*/
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static unsigned char secp256r1_p[] = {
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0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF };
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static unsigned char *secp256r1_a = NULL;
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static unsigned char secp256r1_b[] = {
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0x5A, 0xC6, 0x35, 0xD8, 0xAA, 0x3A, 0x93, 0xE7, 0xB3, 0xEB, 0xBD, 0x55,
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0x76, 0x98, 0x86, 0xBC, 0x65, 0x1D, 0x06, 0xB0, 0xCC, 0x53, 0xB0, 0xF6,
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0x3B, 0xCE, 0x3C, 0x3E, 0x27, 0xD2, 0x60, 0x4B };
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static unsigned char secp256r1_gx[] = {
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0x6B, 0x17, 0xD1, 0xF2, 0xE1, 0x2C, 0x42, 0x47, 0xF8, 0xBC, 0xE6, 0xE5,
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0x63, 0xA4, 0x40, 0xF2, 0x77, 0x03, 0x7D, 0x81, 0x2D, 0xEB, 0x33, 0xA0,
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0xF4, 0xA1, 0x39, 0x45, 0xD8, 0x98, 0xC2, 0x96 };
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static unsigned char secp256r1_gy[] = {
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0x4F, 0xE3, 0x42, 0xE2, 0xFE, 0x1A, 0x7F, 0x9B, 0x8E, 0xE7, 0xEB, 0x4A,
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0x7C, 0x0F, 0x9E, 0x16, 0x2B, 0xCE, 0x33, 0x57, 0x6B, 0x31, 0x5E, 0xCE,
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0xCB, 0xB6, 0x40, 0x68, 0x37, 0xBF, 0x51, 0xF5 };
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static unsigned char secp256r1_n[] = {
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0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xBC, 0xE6, 0xFA, 0xAD, 0xA7, 0x17, 0x9E, 0x84,
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0xF3, 0xB9, 0xCA, 0xC2, 0xFC, 0x63, 0x25, 0x51 };
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/*
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* Domain parameters for secp384r1
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*/
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static unsigned char secp384r1_p[] = {
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF };
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static unsigned char *secp384r1_a = NULL;
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static unsigned char secp384r1_b[] = {
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0xB3, 0x31, 0x2F, 0xA7, 0xE2, 0x3E, 0xE7, 0xE4, 0x98, 0x8E, 0x05, 0x6B,
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0xE3, 0xF8, 0x2D, 0x19, 0x18, 0x1D, 0x9C, 0x6E, 0xFE, 0x81, 0x41, 0x12,
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0x03, 0x14, 0x08, 0x8F, 0x50, 0x13, 0x87, 0x5A, 0xC6, 0x56, 0x39, 0x8D,
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0x8A, 0x2E, 0xD1, 0x9D, 0x2A, 0x85, 0xC8, 0xED, 0xD3, 0xEC, 0x2A, 0xEF };
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static unsigned char secp384r1_gx[] = {
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0xAA, 0x87, 0xCA, 0x22, 0xBE, 0x8B, 0x05, 0x37, 0x8E, 0xB1, 0xC7, 0x1E,
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0xF3, 0x20, 0xAD, 0x74, 0x6E, 0x1D, 0x3B, 0x62, 0x8B, 0xA7, 0x9B, 0x98,
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0x59, 0xF7, 0x41, 0xE0, 0x82, 0x54, 0x2A, 0x38, 0x55, 0x02, 0xF2, 0x5D,
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0xBF, 0x55, 0x29, 0x6C, 0x3A, 0x54, 0x5E, 0x38, 0x72, 0x76, 0x0A, 0xB7 };
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static unsigned char secp384r1_gy[] = {
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0x36, 0x17, 0xDE, 0x4A, 0x96, 0x26, 0x2C, 0x6F, 0x5D, 0x9E, 0x98, 0xBF,
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0x92, 0x92, 0xDC, 0x29, 0xF8, 0xF4, 0x1D, 0xBD, 0x28, 0x9A, 0x14, 0x7C,
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0xE9, 0xDA, 0x31, 0x13, 0xB5, 0xF0, 0xB8, 0xC0, 0x0A, 0x60, 0xB1, 0xCE,
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0x1D, 0x7E, 0x81, 0x9D, 0x7A, 0x43, 0x1D, 0x7C, 0x90, 0xEA, 0x0E, 0x5F };
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static unsigned char secp384r1_n[] = {
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xC7, 0x63, 0x4D, 0x81, 0xF4, 0x37, 0x2D, 0xDF, 0x58, 0x1A, 0x0D, 0xB2,
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0x48, 0xB0, 0xA7, 0x7A, 0xEC, 0xEC, 0x19, 0x6A, 0xCC, 0xC5, 0x29, 0x73 };
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/*
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* Domain parameters for secp521r1
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*/
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static unsigned char secp521r1_p[] = {
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0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF };
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static unsigned char *secp521r1_a = NULL;
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static unsigned char secp521r1_b[] = {
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0x00, 0x51, 0x95, 0x3E, 0xB9, 0x61, 0x8E, 0x1C, 0x9A, 0x1F, 0x92, 0x9A,
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0x21, 0xA0, 0xB6, 0x85, 0x40, 0xEE, 0xA2, 0xDA, 0x72, 0x5B, 0x99, 0xB3,
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0x15, 0xF3, 0xB8, 0xB4, 0x89, 0x91, 0x8E, 0xF1, 0x09, 0xE1, 0x56, 0x19,
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0x39, 0x51, 0xEC, 0x7E, 0x93, 0x7B, 0x16, 0x52, 0xC0, 0xBD, 0x3B, 0xB1,
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0xBF, 0x07, 0x35, 0x73, 0xDF, 0x88, 0x3D, 0x2C, 0x34, 0xF1, 0xEF, 0x45,
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0x1F, 0xD4, 0x6B, 0x50, 0x3F, 0x00 };
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static unsigned char secp521r1_gx[] = {
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0x00, 0xC6, 0x85, 0x8E, 0x06, 0xB7, 0x04, 0x04, 0xE9, 0xCD, 0x9E, 0x3E,
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0xCB, 0x66, 0x23, 0x95, 0xB4, 0x42, 0x9C, 0x64, 0x81, 0x39, 0x05, 0x3F,
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0xB5, 0x21, 0xF8, 0x28, 0xAF, 0x60, 0x6B, 0x4D, 0x3D, 0xBA, 0xA1, 0x4B,
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0x5E, 0x77, 0xEF, 0xE7, 0x59, 0x28, 0xFE, 0x1D, 0xC1, 0x27, 0xA2, 0xFF,
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0xA8, 0xDE, 0x33, 0x48, 0xB3, 0xC1, 0x85, 0x6A, 0x42, 0x9B, 0xF9, 0x7E,
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0x7E, 0x31, 0xC2, 0xE5, 0xBD, 0x66 };
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static unsigned char secp521r1_gy[] = {
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0x01, 0x18, 0x39, 0x29, 0x6A, 0x78, 0x9A, 0x3B, 0xC0, 0x04, 0x5C, 0x8A,
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0x5F, 0xB4, 0x2C, 0x7D, 0x1B, 0xD9, 0x98, 0xF5, 0x44, 0x49, 0x57, 0x9B,
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0x44, 0x68, 0x17, 0xAF, 0xBD, 0x17, 0x27, 0x3E, 0x66, 0x2C, 0x97, 0xEE,
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0x72, 0x99, 0x5E, 0xF4, 0x26, 0x40, 0xC5, 0x50, 0xB9, 0x01, 0x3F, 0xAD,
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0x07, 0x61, 0x35, 0x3C, 0x70, 0x86, 0xA2, 0x72, 0xC2, 0x40, 0x88, 0xBE,
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0x94, 0x76, 0x9F, 0xD1, 0x66, 0x50 };
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static unsigned char secp521r1_n[] = {
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0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFA, 0x51, 0x86,
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0x87, 0x83, 0xBF, 0x2F, 0x96, 0x6B, 0x7F, 0xCC, 0x01, 0x48, 0xF7, 0x09,
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0xA5, 0xD0, 0x3B, 0xB5, 0xC9, 0xB8, 0x89, 0x9C, 0x47, 0xAE, 0xBB, 0x6F,
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0xB7, 0x1E, 0x91, 0x38, 0x64, 0x09 };
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/*
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* Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
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*/
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static unsigned char brainpoolP256r1_p[] = {
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0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, 0x0A, 0x90,
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0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, 0xD5, 0x26, 0x20, 0x28,
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0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, 0x53, 0x77 };
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static unsigned char brainpoolP256r1_a[] = {
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0x7D, 0x5A, 0x09, 0x75, 0xFC, 0x2C, 0x30, 0x57, 0xEE, 0xF6, 0x75, 0x30,
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0x41, 0x7A, 0xFF, 0xE7, 0xFB, 0x80, 0x55, 0xC1, 0x26, 0xDC, 0x5C, 0x6C,
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0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, 0xB5, 0xD9 };
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static unsigned char brainpoolP256r1_b[] = {
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0x26, 0xDC, 0x5C, 0x6C, 0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, 0xB5, 0xD9,
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0xBB, 0xD7, 0x7C, 0xBF, 0x95, 0x84, 0x16, 0x29, 0x5C, 0xF7, 0xE1, 0xCE,
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0x6B, 0xCC, 0xDC, 0x18, 0xFF, 0x8C, 0x07, 0xB6 };
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static unsigned char brainpoolP256r1_gx[] = {
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0x8B, 0xD2, 0xAE, 0xB9, 0xCB, 0x7E, 0x57, 0xCB, 0x2C, 0x4B, 0x48, 0x2F,
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0xFC, 0x81, 0xB7, 0xAF, 0xB9, 0xDE, 0x27, 0xE1, 0xE3, 0xBD, 0x23, 0xC2,
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0x3A, 0x44, 0x53, 0xBD, 0x9A, 0xCE, 0x32, 0x62 };
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static unsigned char brainpoolP256r1_gy[] = {
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0x54, 0x7E, 0xF8, 0x35, 0xC3, 0xDA, 0xC4, 0xFD, 0x97, 0xF8, 0x46, 0x1A,
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0x14, 0x61, 0x1D, 0xC9, 0xC2, 0x77, 0x45, 0x13, 0x2D, 0xED, 0x8E, 0x54,
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0x5C, 0x1D, 0x54, 0xC7, 0x2F, 0x04, 0x69, 0x97 };
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static unsigned char brainpoolP256r1_n[] = {
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0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, 0x0A, 0x90,
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0x9D, 0x83, 0x8D, 0x71, 0x8C, 0x39, 0x7A, 0xA3, 0xB5, 0x61, 0xA6, 0xF7,
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0x90, 0x1E, 0x0E, 0x82, 0x97, 0x48, 0x56, 0xA7 };
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/*
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* Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
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*/
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static unsigned char brainpoolP384r1_p[] = {
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0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, 0x6F, 0x7E,
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0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, 0xED, 0x54, 0x56, 0xB4,
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0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29,
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0x90, 0x1D, 0x1A, 0x71, 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x53 };
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static unsigned char brainpoolP384r1_a[] = {
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0x7B, 0xC3, 0x82, 0xC6, 0x3D, 0x8C, 0x15, 0x0C, 0x3C, 0x72, 0x08, 0x0A,
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0xCE, 0x05, 0xAF, 0xA0, 0xC2, 0xBE, 0xA2, 0x8E, 0x4F, 0xB2, 0x27, 0x87,
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0x13, 0x91, 0x65, 0xEF, 0xBA, 0x91, 0xF9, 0x0F, 0x8A, 0xA5, 0x81, 0x4A,
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0x50, 0x3A, 0xD4, 0xEB, 0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26 };
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static unsigned char brainpoolP384r1_b[] = {
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0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26, 0x8B, 0x39, 0xB5, 0x54,
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0x16, 0xF0, 0x44, 0x7C, 0x2F, 0xB7, 0x7D, 0xE1, 0x07, 0xDC, 0xD2, 0xA6,
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0x2E, 0x88, 0x0E, 0xA5, 0x3E, 0xEB, 0x62, 0xD5, 0x7C, 0xB4, 0x39, 0x02,
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0x95, 0xDB, 0xC9, 0x94, 0x3A, 0xB7, 0x86, 0x96, 0xFA, 0x50, 0x4C, 0x11 };
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static unsigned char brainpoolP384r1_gx[] = {
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0x1D, 0x1C, 0x64, 0xF0, 0x68, 0xCF, 0x45, 0xFF, 0xA2, 0xA6, 0x3A, 0x81,
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0xB7, 0xC1, 0x3F, 0x6B, 0x88, 0x47, 0xA3, 0xE7, 0x7E, 0xF1, 0x4F, 0xE3,
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0xDB, 0x7F, 0xCA, 0xFE, 0x0C, 0xBD, 0x10, 0xE8, 0xE8, 0x26, 0xE0, 0x34,
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0x36, 0xD6, 0x46, 0xAA, 0xEF, 0x87, 0xB2, 0xE2, 0x47, 0xD4, 0xAF, 0x1E };
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static unsigned char brainpoolP384r1_gy[] = {
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|
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 ) )
|
|
|
|
/*
|
|
* Set a group using well-known domain parameters
|
|
*/
|
|
int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
|
|
{
|
|
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 */
|
|
|
|
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
|