Alexander Kampmann
2119 lines
70 KiB
PHP
2119 lines
70 KiB
PHP
<?php
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/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */
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/**
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* Pure-PHP PKCS#1 (v2.1) compliant implementation of RSA.
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*
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* PHP versions 4 and 5
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*
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* Here's an example of how to encrypt and decrypt text with this library:
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* <code>
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* <?php
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* include('Crypt/RSA.php');
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*
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* $rsa = new Crypt_RSA();
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* extract($rsa->createKey());
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*
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* $plaintext = 'terrafrost';
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*
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* $rsa->loadKey($privatekey);
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* $ciphertext = $rsa->encrypt($plaintext);
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*
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* $rsa->loadKey($publickey);
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* echo $rsa->decrypt($ciphertext);
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* ?>
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* </code>
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*
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* Here's an example of how to create signatures and verify signatures with this library:
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* <code>
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* <?php
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* include('Crypt/RSA.php');
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*
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* $rsa = new Crypt_RSA();
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* extract($rsa->createKey());
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*
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* $plaintext = 'terrafrost';
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*
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* $rsa->loadKey($privatekey);
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* $signature = $rsa->sign($plaintext);
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*
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* $rsa->loadKey($publickey);
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* echo $rsa->verify($plaintext, $signature) ? 'verified' : 'unverified';
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* ?>
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* </code>
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*
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* LICENSE: This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library 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 GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston,
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* MA 02111-1307 USA
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*
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* @category Crypt
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* @package Crypt_RSA
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* @author Jim Wigginton <terrafrost@php.net>
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* @copyright MMIX Jim Wigginton
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* @license http://www.gnu.org/licenses/lgpl.txt
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* @version $Id: RSA.php,v 1.15 2010/04/10 15:57:02 terrafrost Exp $
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* @link http://phpseclib.sourceforge.net
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*/
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/**
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* Include Math_BigInteger
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*/
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require_once('Math/BigInteger.php');
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/**
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* Include Crypt_Random
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*/
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require_once('Crypt/Random.php');
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/**
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* Include Crypt_Hash
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*/
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require_once('Crypt/Hash.php');
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/**#@+
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* @access public
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* @see Crypt_RSA::encrypt()
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* @see Crypt_RSA::decrypt()
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*/
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/**
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* Use {@link http://en.wikipedia.org/wiki/Optimal_Asymmetric_Encryption_Padding Optimal Asymmetric Encryption Padding}
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* (OAEP) for encryption / decryption.
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*
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* Uses sha1 by default.
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*
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* @see Crypt_RSA::setHash()
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* @see Crypt_RSA::setMGFHash()
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*/
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define('CRYPT_RSA_ENCRYPTION_OAEP', 1);
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/**
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* Use PKCS#1 padding.
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*
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* Although CRYPT_RSA_ENCRYPTION_OAEP offers more security, including PKCS#1 padding is necessary for purposes of backwards
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* compatability with protocols (like SSH-1) written before OAEP's introduction.
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*/
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define('CRYPT_RSA_ENCRYPTION_PKCS1', 2);
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/**#@-*/
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/**#@+
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* @access public
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* @see Crypt_RSA::sign()
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* @see Crypt_RSA::verify()
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* @see Crypt_RSA::setHash()
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*/
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/**
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* Use the Probabilistic Signature Scheme for signing
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*
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* Uses sha1 by default.
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*
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* @see Crypt_RSA::setSaltLength()
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* @see Crypt_RSA::setMGFHash()
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*/
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define('CRYPT_RSA_SIGNATURE_PSS', 1);
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/**
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* Use the PKCS#1 scheme by default.
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*
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* Although CRYPT_RSA_SIGNATURE_PSS offers more security, including PKCS#1 signing is necessary for purposes of backwards
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* compatability with protocols (like SSH-2) written before PSS's introduction.
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*/
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define('CRYPT_RSA_SIGNATURE_PKCS1', 2);
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/**#@-*/
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/**#@+
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* @access private
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* @see Crypt_RSA::createKey()
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*/
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/**
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* ASN1 Integer
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*/
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define('CRYPT_RSA_ASN1_INTEGER', 2);
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/**
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* ASN1 Sequence (with the constucted bit set)
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*/
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define('CRYPT_RSA_ASN1_SEQUENCE', 48);
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/**#@-*/
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/**#@+
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* @access private
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* @see Crypt_RSA::Crypt_RSA()
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*/
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/**
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* To use the pure-PHP implementation
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*/
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define('CRYPT_RSA_MODE_INTERNAL', 1);
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/**
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* To use the OpenSSL library
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*
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* (if enabled; otherwise, the internal implementation will be used)
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*/
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define('CRYPT_RSA_MODE_OPENSSL', 2);
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/**#@-*/
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/**#@+
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* @access public
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* @see Crypt_RSA::createKey()
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* @see Crypt_RSA::setPrivateKeyFormat()
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*/
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/**
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* PKCS#1 formatted private key
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*
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* Used by OpenSSH
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*/
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define('CRYPT_RSA_PRIVATE_FORMAT_PKCS1', 0);
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/**#@-*/
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/**#@+
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* @access public
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* @see Crypt_RSA::createKey()
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* @see Crypt_RSA::setPublicKeyFormat()
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*/
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/**
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* Raw public key
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*
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* An array containing two Math_BigInteger objects.
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*
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* The exponent can be indexed with any of the following:
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*
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* 0, e, exponent, publicExponent
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*
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* The modulus can be indexed with any of the following:
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*
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* 1, n, modulo, modulus
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*/
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define('CRYPT_RSA_PUBLIC_FORMAT_RAW', 1);
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/**
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* PKCS#1 formatted public key
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*/
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define('CRYPT_RSA_PUBLIC_FORMAT_PKCS1', 2);
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/**
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* OpenSSH formatted public key
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*
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* Place in $HOME/.ssh/authorized_keys
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*/
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define('CRYPT_RSA_PUBLIC_FORMAT_OPENSSH', 3);
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/**#@-*/
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/**
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* Pure-PHP PKCS#1 compliant implementation of RSA.
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*
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* @author Jim Wigginton <terrafrost@php.net>
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* @version 0.1.0
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* @access public
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* @package Crypt_RSA
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*/
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class Crypt_RSA {
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/**
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* Precomputed Zero
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*
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* @var Array
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* @access private
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*/
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var $zero;
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/**
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* Precomputed One
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*
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* @var Array
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* @access private
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*/
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var $one;
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/**
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* Private Key Format
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*
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* @var Integer
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* @access private
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*/
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var $privateKeyFormat = CRYPT_RSA_PRIVATE_FORMAT_PKCS1;
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/**
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* Public Key Format
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*
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* @var Integer
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* @access public
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*/
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var $publicKeyFormat = CRYPT_RSA_PUBLIC_FORMAT_PKCS1;
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/**
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* Modulus (ie. n)
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*
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* @var Math_BigInteger
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* @access private
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*/
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var $modulus;
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/**
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* Modulus length
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*
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* @var Math_BigInteger
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* @access private
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*/
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var $k;
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/**
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* Exponent (ie. e or d)
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*
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* @var Math_BigInteger
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* @access private
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*/
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var $exponent;
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/**
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* Primes for Chinese Remainder Theorem (ie. p and q)
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*
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* @var Array
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* @access private
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*/
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var $primes;
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/**
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* Exponents for Chinese Remainder Theorem (ie. dP and dQ)
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*
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* @var Array
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* @access private
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*/
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var $exponents;
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/**
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* Coefficients for Chinese Remainder Theorem (ie. qInv)
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*
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* @var Array
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* @access private
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*/
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var $coefficients;
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/**
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* Hash name
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*
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* @var String
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* @access private
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*/
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var $hashName;
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/**
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* Hash function
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*
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* @var Crypt_Hash
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* @access private
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*/
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var $hash;
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/**
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* Length of hash function output
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*
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* @var Integer
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* @access private
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*/
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var $hLen;
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/**
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* Length of salt
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*
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* @var Integer
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* @access private
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*/
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var $sLen;
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/**
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* Hash function for the Mask Generation Function
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*
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* @var Crypt_Hash
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* @access private
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*/
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var $mgfHash;
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/**
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* Length of MGF hash function output
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*
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* @var Integer
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* @access private
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*/
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var $mgfHLen;
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/**
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* Encryption mode
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*
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* @var Integer
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* @access private
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*/
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var $encryptionMode = CRYPT_RSA_ENCRYPTION_OAEP;
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/**
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* Signature mode
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*
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* @var Integer
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* @access private
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*/
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var $signatureMode = CRYPT_RSA_SIGNATURE_PSS;
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/**
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* Public Exponent
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*
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* @var Mixed
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* @access private
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*/
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var $publicExponent = false;
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/**
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* Password
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*
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* @var String
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* @access private
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*/
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var $password = '';
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/**
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* The constructor
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*
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* If you want to make use of the openssl extension, you'll need to set the mode manually, yourself. The reason
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* Crypt_RSA doesn't do it is because OpenSSL doesn't fail gracefully. openssl_pkey_new(), in particular, requires
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* openssl.cnf be present somewhere and, unfortunately, the only real way to find out is too late.
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*
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* @return Crypt_RSA
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* @access public
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*/
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function Crypt_RSA()
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{
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if ( !defined('CRYPT_RSA_MODE') ) {
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switch (true) {
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//case extension_loaded('openssl') && version_compare(PHP_VERSION, '4.2.0', '>='):
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// define('CRYPT_RSA_MODE', CRYPT_RSA_MODE_OPENSSL);
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// break;
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default:
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define('CRYPT_RSA_MODE', CRYPT_RSA_MODE_INTERNAL);
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}
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}
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$this->zero = new Math_BigInteger();
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$this->one = new Math_BigInteger(1);
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$this->hash = new Crypt_Hash('sha1');
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$this->hLen = $this->hash->getLength();
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$this->hashName = 'sha1';
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$this->mgfHash = new Crypt_Hash('sha1');
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$this->mgfHLen = $this->mgfHash->getLength();
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}
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/**
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* Create public / private key pair
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*
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* Returns an array with the following three elements:
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* - 'privatekey': The private key.
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* - 'publickey': The public key.
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* - 'partialkey': A partially computed key (if the execution time exceeded $timeout).
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* Will need to be passed back to Crypt_RSA::createKey() as the third parameter for further processing.
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*
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* @access public
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* @param optional Integer $bits
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* @param optional Integer $timeout
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* @param optional Math_BigInteger $p
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*/
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function createKey($bits = 1024, $timeout = false, $partial = array())
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{
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if ( CRYPT_RSA_MODE == CRYPT_RSA_MODE_OPENSSL ) {
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$rsa = openssl_pkey_new(array('private_key_bits' => $bits));
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openssl_pkey_export($rsa, $privatekey);
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$publickey = openssl_pkey_get_details($rsa);
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$publickey = $publickey['key'];
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if ($this->privateKeyFormat != CRYPT_RSA_PRIVATE_FORMAT_PKCS1) {
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$privatekey = call_user_func_array(array($this, '_convertPrivateKey'), array_values($this->_parseKey($privatekey, CRYPT_RSA_PRIVATE_FORMAT_PKCS1)));
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$publickey = call_user_func_array(array($this, '_convertPublicKey'), array_values($this->_parseKey($publickey, CRYPT_RSA_PUBLIC_FORMAT_PKCS1)));
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}
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return array(
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'privatekey' => $privatekey,
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'publickey' => $publickey,
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'partialkey' => false
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);
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}
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static $e;
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if (!isset($e)) {
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if (!defined('CRYPT_RSA_EXPONENT')) {
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// http://en.wikipedia.org/wiki/65537_%28number%29
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define('CRYPT_RSA_EXPONENT', '65537');
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}
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if (!defined('CRYPT_RSA_COMMENT')) {
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define('CRYPT_RSA_COMMENT', 'phpseclib-generated-key');
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}
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// per <http://cseweb.ucsd.edu/~hovav/dist/survey.pdf#page=5>, this number ought not result in primes smaller
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// than 256 bits.
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if (!defined('CRYPT_RSA_SMALLEST_PRIME')) {
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define('CRYPT_RSA_SMALLEST_PRIME', 4096);
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}
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$e = new Math_BigInteger(CRYPT_RSA_EXPONENT);
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}
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extract($this->_generateMinMax($bits));
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$absoluteMin = $min;
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$temp = $bits >> 1;
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if ($temp > CRYPT_RSA_SMALLEST_PRIME) {
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$num_primes = floor($bits / CRYPT_RSA_SMALLEST_PRIME);
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$temp = CRYPT_RSA_SMALLEST_PRIME;
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} else {
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$num_primes = 2;
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}
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extract($this->_generateMinMax($temp + $bits % $temp));
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$finalMax = $max;
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extract($this->_generateMinMax($temp));
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$generator = new Math_BigInteger();
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$generator->setRandomGenerator('crypt_random');
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$n = $this->one->copy();
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if (!empty($partial)) {
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extract(unserialize($partial));
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} else {
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$exponents = $coefficients = $primes = array();
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$lcm = array(
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'top' => $this->one->copy(),
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'bottom' => false
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);
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}
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$start = time();
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$i0 = count($primes) + 1;
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do {
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for ($i = $i0; $i <= $num_primes; $i++) {
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if ($timeout !== false) {
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$timeout-= time() - $start;
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$start = time();
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if ($timeout <= 0) {
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return serialize(array(
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'privatekey' => '',
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'publickey' => '',
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'partialkey' => array(
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'primes' => $primes,
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'coefficients' => $coefficients,
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'lcm' => $lcm,
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'exponents' => $exponents
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)
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));
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}
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}
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if ($i == $num_primes) {
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list($min, $temp) = $absoluteMin->divide($n);
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if (!$temp->equals($this->zero)) {
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$min = $min->add($this->one); // ie. ceil()
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}
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$primes[$i] = $generator->randomPrime($min, $finalMax, $timeout);
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} else {
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$primes[$i] = $generator->randomPrime($min, $max, $timeout);
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}
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if ($primes[$i] === false) { // if we've reached the timeout
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return array(
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'privatekey' => '',
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'publickey' => '',
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'partialkey' => empty($primes) ? '' : serialize(array(
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'primes' => array_slice($primes, 0, $i - 1),
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'coefficients' => $coefficients,
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'lcm' => $lcm,
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'exponents' => $exponents
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))
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);
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}
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// the first coefficient is calculated differently from the rest
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// ie. instead of being $primes[1]->modInverse($primes[2]), it's $primes[2]->modInverse($primes[1])
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if ($i > 2) {
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$coefficients[$i] = $n->modInverse($primes[$i]);
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}
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$n = $n->multiply($primes[$i]);
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$temp = $primes[$i]->subtract($this->one);
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// textbook RSA implementations use Euler's totient function instead of the least common multiple.
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// see http://en.wikipedia.org/wiki/Euler%27s_totient_function
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$lcm['top'] = $lcm['top']->multiply($temp);
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$lcm['bottom'] = $lcm['bottom'] === false ? $temp : $lcm['bottom']->gcd($temp);
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$exponents[$i] = $e->modInverse($temp);
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}
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list($lcm) = $lcm['top']->divide($lcm['bottom']);
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$gcd = $lcm->gcd($e);
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$i0 = 1;
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} while (!$gcd->equals($this->one));
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$d = $e->modInverse($lcm);
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$coefficients[2] = $primes[2]->modInverse($primes[1]);
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|
|
// from <http://tools.ietf.org/html/rfc3447#appendix-A.1.2>:
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|
// RSAPrivateKey ::= SEQUENCE {
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|
// version Version,
|
|
// modulus INTEGER, -- n
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|
// publicExponent INTEGER, -- e
|
|
// privateExponent INTEGER, -- d
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|
// prime1 INTEGER, -- p
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// prime2 INTEGER, -- q
|
|
// exponent1 INTEGER, -- d mod (p-1)
|
|
// exponent2 INTEGER, -- d mod (q-1)
|
|
// coefficient INTEGER, -- (inverse of q) mod p
|
|
// otherPrimeInfos OtherPrimeInfos OPTIONAL
|
|
// }
|
|
|
|
return array(
|
|
'privatekey' => $this->_convertPrivateKey($n, $e, $d, $primes, $exponents, $coefficients),
|
|
'publickey' => $this->_convertPublicKey($n, $e),
|
|
'partialkey' => false
|
|
);
|
|
}
|
|
|
|
/**
|
|
* Convert a private key to the appropriate format.
|
|
*
|
|
* @access private
|
|
* @see setPrivateKeyFormat()
|
|
* @param String $RSAPrivateKey
|
|
* @return String
|
|
*/
|
|
function _convertPrivateKey($n, $e, $d, $primes, $exponents, $coefficients)
|
|
{
|
|
$num_primes = count($primes);
|
|
$raw = array(
|
|
'version' => $num_primes == 2 ? chr(0) : chr(1), // two-prime vs. multi
|
|
'modulus' => $n->toBytes(true),
|
|
'publicExponent' => $e->toBytes(true),
|
|
'privateExponent' => $d->toBytes(true),
|
|
'prime1' => $primes[1]->toBytes(true),
|
|
'prime2' => $primes[2]->toBytes(true),
|
|
'exponent1' => $exponents[1]->toBytes(true),
|
|
'exponent2' => $exponents[2]->toBytes(true),
|
|
'coefficient' => $coefficients[2]->toBytes(true)
|
|
);
|
|
|
|
// if the format in question does not support multi-prime rsa and multi-prime rsa was used,
|
|
// call _convertPublicKey() instead.
|
|
switch ($this->privateKeyFormat) {
|
|
default: // eg. CRYPT_RSA_PRIVATE_FORMAT_PKCS1
|
|
$components = array();
|
|
foreach ($raw as $name => $value) {
|
|
$components[$name] = pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($value)), $value);
|
|
}
|
|
|
|
$RSAPrivateKey = implode('', $components);
|
|
|
|
if ($num_primes > 2) {
|
|
$OtherPrimeInfos = '';
|
|
for ($i = 3; $i <= $num_primes; $i++) {
|
|
// OtherPrimeInfos ::= SEQUENCE SIZE(1..MAX) OF OtherPrimeInfo
|
|
//
|
|
// OtherPrimeInfo ::= SEQUENCE {
|
|
// prime INTEGER, -- ri
|
|
// exponent INTEGER, -- di
|
|
// coefficient INTEGER -- ti
|
|
// }
|
|
$OtherPrimeInfo = pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($primes[$i]->toBytes(true))), $primes[$i]->toBytes(true));
|
|
$OtherPrimeInfo.= pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($exponents[$i]->toBytes(true))), $exponents[$i]->toBytes(true));
|
|
$OtherPrimeInfo.= pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($coefficients[$i]->toBytes(true))), $coefficients[$i]->toBytes(true));
|
|
$OtherPrimeInfos.= pack('Ca*a*', CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($OtherPrimeInfo)), $OtherPrimeInfo);
|
|
}
|
|
$RSAPrivateKey.= pack('Ca*a*', CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($OtherPrimeInfos)), $OtherPrimeInfos);
|
|
}
|
|
|
|
$RSAPrivateKey = pack('Ca*a*', CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($RSAPrivateKey)), $RSAPrivateKey);
|
|
|
|
if (!empty($this->password)) {
|
|
$iv = $this->_random(8);
|
|
$symkey = pack('H*', md5($this->password . $iv)); // symkey is short for symmetric key
|
|
$symkey.= substr(pack('H*', md5($symkey . $this->password . $iv)), 0, 8);
|
|
if (!class_exists('Crypt_TripleDES')) {
|
|
require_once('Crypt/TripleDES.php');
|
|
}
|
|
$des = new Crypt_TripleDES();
|
|
$des->setKey($symkey);
|
|
$des->setIV($iv);
|
|
$iv = strtoupper(bin2hex($iv));
|
|
$RSAPrivateKey = "-----BEGIN RSA PRIVATE KEY-----\r\n" .
|
|
"Proc-Type: 4,ENCRYPTED\r\n" .
|
|
"DEK-Info: DES-EDE3-CBC,$iv\r\n" .
|
|
"\r\n" .
|
|
chunk_split(base64_encode($des->encrypt($RSAPrivateKey))) .
|
|
'-----END RSA PRIVATE KEY-----';
|
|
} else {
|
|
$RSAPrivateKey = "-----BEGIN RSA PRIVATE KEY-----\r\n" .
|
|
chunk_split(base64_encode($RSAPrivateKey)) .
|
|
'-----END RSA PRIVATE KEY-----';
|
|
}
|
|
|
|
return $RSAPrivateKey;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Convert a public key to the appropriate format
|
|
*
|
|
* @access private
|
|
* @see setPublicKeyFormat()
|
|
* @param String $RSAPrivateKey
|
|
* @return String
|
|
*/
|
|
function _convertPublicKey($n, $e)
|
|
{
|
|
$modulus = $n->toBytes(true);
|
|
$publicExponent = $e->toBytes(true);
|
|
|
|
switch ($this->publicKeyFormat) {
|
|
case CRYPT_RSA_PUBLIC_FORMAT_RAW:
|
|
return array('e' => $e->copy(), 'n' => $n->copy());
|
|
case CRYPT_RSA_PUBLIC_FORMAT_OPENSSH:
|
|
// from <http://tools.ietf.org/html/rfc4253#page-15>:
|
|
// string "ssh-rsa"
|
|
// mpint e
|
|
// mpint n
|
|
$RSAPublicKey = pack('Na*Na*Na*', strlen('ssh-rsa'), 'ssh-rsa', strlen($publicExponent), $publicExponent, strlen($modulus), $modulus);
|
|
$RSAPublicKey = 'ssh-rsa ' . base64_encode($RSAPublicKey) . ' ' . CRYPT_RSA_COMMENT;
|
|
|
|
return $RSAPublicKey;
|
|
default: // eg. CRYPT_RSA_PUBLIC_FORMAT_PKCS1
|
|
// from <http://tools.ietf.org/html/rfc3447#appendix-A.1.1>:
|
|
// RSAPublicKey ::= SEQUENCE {
|
|
// modulus INTEGER, -- n
|
|
// publicExponent INTEGER -- e
|
|
// }
|
|
$components = array(
|
|
'modulus' => pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($modulus)), $modulus),
|
|
'publicExponent' => pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($publicExponent)), $publicExponent)
|
|
);
|
|
|
|
$RSAPublicKey = pack('Ca*a*a*',
|
|
CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($components['modulus']) + strlen($components['publicExponent'])),
|
|
$components['modulus'], $components['publicExponent']
|
|
);
|
|
|
|
$RSAPublicKey = "-----BEGIN PUBLIC KEY-----\r\n" .
|
|
chunk_split(base64_encode($RSAPublicKey)) .
|
|
'-----END PUBLIC KEY-----';
|
|
|
|
return $RSAPublicKey;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Break a public or private key down into its constituant components
|
|
*
|
|
* @access private
|
|
* @see _convertPublicKey()
|
|
* @see _convertPrivateKey()
|
|
* @param String $key
|
|
* @param Integer $type
|
|
* @return Array
|
|
*/
|
|
function _parseKey($key, $type)
|
|
{
|
|
switch ($type) {
|
|
case CRYPT_RSA_PUBLIC_FORMAT_RAW:
|
|
if (!is_array($key)) {
|
|
return false;
|
|
}
|
|
$components = array();
|
|
switch (true) {
|
|
case isset($key['e']):
|
|
$components['publicExponent'] = $key['e']->copy();
|
|
break;
|
|
case isset($key['exponent']):
|
|
$components['publicExponent'] = $key['exponent']->copy();
|
|
break;
|
|
case isset($key['publicExponent']):
|
|
$components['publicExponent'] = $key['publicExponent']->copy();
|
|
break;
|
|
case isset($key[0]):
|
|
$components['publicExponent'] = $key[0]->copy();
|
|
}
|
|
switch (true) {
|
|
case isset($key['n']):
|
|
$components['modulus'] = $key['n']->copy();
|
|
break;
|
|
case isset($key['modulo']):
|
|
$components['modulus'] = $key['modulo']->copy();
|
|
break;
|
|
case isset($key['modulus']):
|
|
$components['modulus'] = $key['modulus']->copy();
|
|
break;
|
|
case isset($key[1]):
|
|
$components['modulus'] = $key[1]->copy();
|
|
}
|
|
return $components;
|
|
case CRYPT_RSA_PRIVATE_FORMAT_PKCS1:
|
|
case CRYPT_RSA_PUBLIC_FORMAT_PKCS1:
|
|
/* Although PKCS#1 proposes a format that public and private keys can use, encrypting them is
|
|
"outside the scope" of PKCS#1. PKCS#1 then refers you to PKCS#12 and PKCS#15 if you're wanting to
|
|
protect private keys, however, that's not what OpenSSL* does. OpenSSL protects private keys by adding
|
|
two new "fields" to the key - DEK-Info and Proc-Type. These fields are discussed here:
|
|
|
|
http://tools.ietf.org/html/rfc1421#section-4.6.1.1
|
|
http://tools.ietf.org/html/rfc1421#section-4.6.1.3
|
|
|
|
DES-EDE3-CBC as an algorithm, however, is not discussed anywhere, near as I can tell.
|
|
DES-CBC and DES-EDE are discussed in RFC1423, however, DES-EDE3-CBC isn't, nor is its key derivation
|
|
function. As is, the definitive authority on this encoding scheme isn't the IETF but rather OpenSSL's
|
|
own implementation. ie. the implementation *is* the standard and any bugs that may exist in that
|
|
implementation are part of the standard, as well.
|
|
|
|
* OpenSSL is the de facto standard. It's utilized by OpenSSH and other projects */
|
|
if (preg_match('#DEK-Info: (.+),(.+)#', $key, $matches)) {
|
|
$iv = pack('H*', trim($matches[2]));
|
|
$symkey = pack('H*', md5($this->password . $iv)); // symkey is short for symmetric key
|
|
$symkey.= substr(pack('H*', md5($symkey . $this->password . $iv)), 0, 8);
|
|
$ciphertext = preg_replace('#.+(\r|\n|\r\n)\1|[\r\n]|-.+-#s', '', $key);
|
|
$ciphertext = preg_match('#^[a-zA-Z\d/+]*={0,2}$#', $ciphertext) ? base64_decode($ciphertext) : false;
|
|
if ($ciphertext === false) {
|
|
$ciphertext = $key;
|
|
}
|
|
switch ($matches[1]) {
|
|
case 'DES-EDE3-CBC':
|
|
if (!class_exists('Crypt_TripleDES')) {
|
|
require_once('Crypt/TripleDES.php');
|
|
}
|
|
$crypto = new Crypt_TripleDES();
|
|
break;
|
|
case 'DES-CBC':
|
|
if (!class_exists('Crypt_DES')) {
|
|
require_once('Crypt/DES.php');
|
|
}
|
|
$crypto = new Crypt_DES();
|
|
break;
|
|
default:
|
|
return false;
|
|
}
|
|
$crypto->setKey($symkey);
|
|
$crypto->setIV($iv);
|
|
$decoded = $crypto->decrypt($ciphertext);
|
|
} else {
|
|
$decoded = preg_replace('#-.+-|[\r\n]#', '', $key);
|
|
$decoded = preg_match('#^[a-zA-Z\d/+]*={0,2}$#', $decoded) ? base64_decode($decoded) : false;
|
|
}
|
|
|
|
if ($decoded !== false) {
|
|
$key = $decoded;
|
|
}
|
|
|
|
$components = array();
|
|
|
|
if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_SEQUENCE) {
|
|
return false;
|
|
}
|
|
if ($this->_decodeLength($key) != strlen($key)) {
|
|
return false;
|
|
}
|
|
|
|
$tag = ord($this->_string_shift($key));
|
|
if ($tag == CRYPT_RSA_ASN1_SEQUENCE) {
|
|
/* intended for keys for which OpenSSL's asn1parse returns the following:
|
|
|
|
0:d=0 hl=4 l= 290 cons: SEQUENCE
|
|
4:d=1 hl=2 l= 13 cons: SEQUENCE
|
|
6:d=2 hl=2 l= 9 prim: OBJECT :rsaEncryption
|
|
17:d=2 hl=2 l= 0 prim: NULL
|
|
19:d=1 hl=4 l= 271 prim: BIT STRING */
|
|
$this->_string_shift($key, $this->_decodeLength($key));
|
|
$this->_string_shift($key); // skip over the BIT STRING tag
|
|
$this->_decodeLength($key); // skip over the BIT STRING length
|
|
// "The initial octet shall encode, as an unsigned binary integer wtih bit 1 as the least significant bit, the number of
|
|
// unused bits in teh final subsequent octet. The number shall be in the range zero to seven."
|
|
// -- http://www.itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdf (section 8.6.2.2)
|
|
$this->_string_shift($key);
|
|
if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_SEQUENCE) {
|
|
return false;
|
|
}
|
|
if ($this->_decodeLength($key) != strlen($key)) {
|
|
return false;
|
|
}
|
|
$tag = ord($this->_string_shift($key));
|
|
}
|
|
if ($tag != CRYPT_RSA_ASN1_INTEGER) {
|
|
return false;
|
|
}
|
|
|
|
$length = $this->_decodeLength($key);
|
|
$temp = $this->_string_shift($key, $length);
|
|
if (strlen($temp) != 1 || ord($temp) > 2) {
|
|
$components['modulus'] = new Math_BigInteger($temp, -256);
|
|
$this->_string_shift($key); // skip over CRYPT_RSA_ASN1_INTEGER
|
|
$length = $this->_decodeLength($key);
|
|
$components[$type == CRYPT_RSA_PUBLIC_FORMAT_PKCS1 ? 'publicExponent' : 'privateExponent'] = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
|
|
return $components;
|
|
}
|
|
if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_INTEGER) {
|
|
return false;
|
|
}
|
|
$length = $this->_decodeLength($key);
|
|
$components['modulus'] = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
$this->_string_shift($key);
|
|
$length = $this->_decodeLength($key);
|
|
$components['publicExponent'] = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
$this->_string_shift($key);
|
|
$length = $this->_decodeLength($key);
|
|
$components['privateExponent'] = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
$this->_string_shift($key);
|
|
$length = $this->_decodeLength($key);
|
|
$components['primes'] = array(1 => new Math_BigInteger($this->_string_shift($key, $length), -256));
|
|
$this->_string_shift($key);
|
|
$length = $this->_decodeLength($key);
|
|
$components['primes'][] = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
$this->_string_shift($key);
|
|
$length = $this->_decodeLength($key);
|
|
$components['exponents'] = array(1 => new Math_BigInteger($this->_string_shift($key, $length), -256));
|
|
$this->_string_shift($key);
|
|
$length = $this->_decodeLength($key);
|
|
$components['exponents'][] = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
$this->_string_shift($key);
|
|
$length = $this->_decodeLength($key);
|
|
$components['coefficients'] = array(2 => new Math_BigInteger($this->_string_shift($key, $length), -256));
|
|
|
|
if (!empty($key)) {
|
|
if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_SEQUENCE) {
|
|
return false;
|
|
}
|
|
$this->_decodeLength($key);
|
|
while (!empty($key)) {
|
|
if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_SEQUENCE) {
|
|
return false;
|
|
}
|
|
$this->_decodeLength($key);
|
|
$key = substr($key, 1);
|
|
$length = $this->_decodeLength($key);
|
|
$components['primes'][] = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
$this->_string_shift($key);
|
|
$length = $this->_decodeLength($key);
|
|
$components['exponents'][] = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
$this->_string_shift($key);
|
|
$length = $this->_decodeLength($key);
|
|
$components['coefficients'][] = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
}
|
|
}
|
|
|
|
return $components;
|
|
case CRYPT_RSA_PUBLIC_FORMAT_OPENSSH:
|
|
$key = base64_decode(preg_replace('#^ssh-rsa | .+$#', '', $key));
|
|
if ($key === false) {
|
|
return false;
|
|
}
|
|
|
|
$cleanup = substr($key, 0, 11) == "\0\0\0\7ssh-rsa";
|
|
|
|
extract(unpack('Nlength', $this->_string_shift($key, 4)));
|
|
$publicExponent = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
extract(unpack('Nlength', $this->_string_shift($key, 4)));
|
|
$modulus = new Math_BigInteger($this->_string_shift($key, $length), -256);
|
|
|
|
if ($cleanup && strlen($key)) {
|
|
extract(unpack('Nlength', $this->_string_shift($key, 4)));
|
|
return array(
|
|
'modulus' => new Math_BigInteger($this->_string_shift($key, $length), -256),
|
|
'publicExponent' => $modulus
|
|
);
|
|
} else {
|
|
return array(
|
|
'modulus' => $modulus,
|
|
'publicExponent' => $publicExponent
|
|
);
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Loads a public or private key
|
|
*
|
|
* Returns true on success and false on failure (ie. an incorrect password was provided or the key was malformed)
|
|
*
|
|
* @access public
|
|
* @param String $key
|
|
* @param Integer $type optional
|
|
*/
|
|
function loadKey($key, $type = CRYPT_RSA_PRIVATE_FORMAT_PKCS1)
|
|
{
|
|
$components = $this->_parseKey($key, $type);
|
|
if ($components === false) {
|
|
return false;
|
|
}
|
|
|
|
$this->modulus = $components['modulus'];
|
|
$this->k = strlen($this->modulus->toBytes());
|
|
$this->exponent = isset($components['privateExponent']) ? $components['privateExponent'] : $components['publicExponent'];
|
|
if (isset($components['primes'])) {
|
|
$this->primes = $components['primes'];
|
|
$this->exponents = $components['exponents'];
|
|
$this->coefficients = $components['coefficients'];
|
|
$this->publicExponent = $components['publicExponent'];
|
|
} else {
|
|
$this->primes = array();
|
|
$this->exponents = array();
|
|
$this->coefficients = array();
|
|
$this->publicExponent = false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
/**
|
|
* Sets the password
|
|
*
|
|
* Private keys can be encrypted with a password. To unset the password, pass in the empty string or false.
|
|
* Or rather, pass in $password such that empty($password) is true.
|
|
*
|
|
* @see createKey()
|
|
* @see loadKey()
|
|
* @access public
|
|
* @param String $password
|
|
*/
|
|
function setPassword($password)
|
|
{
|
|
$this->password = $password;
|
|
}
|
|
|
|
/**
|
|
* Defines the public key
|
|
*
|
|
* Some private key formats define the public exponent and some don't. Those that don't define it are problematic when
|
|
* used in certain contexts. For example, in SSH-2, RSA authentication works by sending the public key along with a
|
|
* message signed by the private key to the server. The SSH-2 server looks the public key up in an index of public keys
|
|
* and if it's present then proceeds to verify the signature. Problem is, if your private key doesn't include the public
|
|
* exponent this won't work unless you manually add the public exponent.
|
|
*
|
|
* Do note that when a new key is loaded the index will be cleared.
|
|
*
|
|
* Returns true on success, false on failure
|
|
*
|
|
* @see getPublicKey()
|
|
* @access public
|
|
* @param String $key
|
|
* @param Integer $type optional
|
|
* @return Boolean
|
|
*/
|
|
function setPublicKey($key, $type = CRYPT_RSA_PUBLIC_FORMAT_PKCS1)
|
|
{
|
|
$components = $this->_parseKey($key, $type);
|
|
if (empty($this->modulus) || !$this->modulus->equals($components['modulus'])) {
|
|
return false;
|
|
}
|
|
$this->publicExponent = $components['publicExponent'];
|
|
}
|
|
|
|
/**
|
|
* Returns the public key
|
|
*
|
|
* The public key is only returned under two circumstances - if the private key had the public key embedded within it
|
|
* or if the public key was set via setPublicKey(). If the currently loaded key is supposed to be the public key this
|
|
* function won't return it since this library, for the most part, doesn't distinguish between public and private keys.
|
|
*
|
|
* @see getPublicKey()
|
|
* @access public
|
|
* @param String $key
|
|
* @param Integer $type optional
|
|
*/
|
|
function getPublicKey($type = CRYPT_RSA_PUBLIC_FORMAT_PKCS1)
|
|
{
|
|
if (empty($this->modulus) || empty($this->publicExponent)) {
|
|
return false;
|
|
}
|
|
|
|
$oldFormat = $this->publicKeyFormat;
|
|
$this->publicKeyFormat = $type;
|
|
$temp = $this->_convertPublicKey($this->modulus, $this->publicExponent);
|
|
$this->publicKeyFormat = $oldFormat;
|
|
return $temp;
|
|
}
|
|
|
|
/**
|
|
* Generates the smallest and largest numbers requiring $bits bits
|
|
*
|
|
* @access private
|
|
* @param Integer $bits
|
|
* @return Array
|
|
*/
|
|
function _generateMinMax($bits)
|
|
{
|
|
$bytes = $bits >> 3;
|
|
$min = str_repeat(chr(0), $bytes);
|
|
$max = str_repeat(chr(0xFF), $bytes);
|
|
$msb = $bits & 7;
|
|
if ($msb) {
|
|
$min = chr(1 << ($msb - 1)) . $min;
|
|
$max = chr((1 << $msb) - 1) . $max;
|
|
} else {
|
|
$min[0] = chr(0x80);
|
|
}
|
|
|
|
return array(
|
|
'min' => new Math_BigInteger($min, 256),
|
|
'max' => new Math_BigInteger($max, 256)
|
|
);
|
|
}
|
|
|
|
/**
|
|
* DER-decode the length
|
|
*
|
|
* DER supports lengths up to (2**8)**127, however, we'll only support lengths up to (2**8)**4. See
|
|
* {@link http://itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdf#p=13 X.690 � 8.1.3} for more information.
|
|
*
|
|
* @access private
|
|
* @param String $string
|
|
* @return Integer
|
|
*/
|
|
function _decodeLength(&$string)
|
|
{
|
|
$length = ord($this->_string_shift($string));
|
|
if ( $length & 0x80 ) { // definite length, long form
|
|
$length&= 0x7F;
|
|
$temp = $this->_string_shift($string, $length);
|
|
list(, $length) = unpack('N', substr(str_pad($temp, 4, chr(0), STR_PAD_LEFT), -4));
|
|
}
|
|
return $length;
|
|
}
|
|
|
|
/**
|
|
* DER-encode the length
|
|
*
|
|
* DER supports lengths up to (2**8)**127, however, we'll only support lengths up to (2**8)**4. See
|
|
* {@link http://itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdf#p=13 X.690 � 8.1.3} for more information.
|
|
*
|
|
* @access private
|
|
* @param Integer $length
|
|
* @return String
|
|
*/
|
|
function _encodeLength($length)
|
|
{
|
|
if ($length <= 0x7F) {
|
|
return chr($length);
|
|
}
|
|
|
|
$temp = ltrim(pack('N', $length), chr(0));
|
|
return pack('Ca*', 0x80 | strlen($temp), $temp);
|
|
}
|
|
|
|
/**
|
|
* String Shift
|
|
*
|
|
* Inspired by array_shift
|
|
*
|
|
* @param String $string
|
|
* @param optional Integer $index
|
|
* @return String
|
|
* @access private
|
|
*/
|
|
function _string_shift(&$string, $index = 1)
|
|
{
|
|
$substr = substr($string, 0, $index);
|
|
$string = substr($string, $index);
|
|
return $substr;
|
|
}
|
|
|
|
/**
|
|
* Determines the private key format
|
|
*
|
|
* @see createKey()
|
|
* @access public
|
|
* @param Integer $format
|
|
*/
|
|
function setPrivateKeyFormat($format)
|
|
{
|
|
$this->privateKeyFormat = $format;
|
|
}
|
|
|
|
/**
|
|
* Determines the public key format
|
|
*
|
|
* @see createKey()
|
|
* @access public
|
|
* @param Integer $format
|
|
*/
|
|
function setPublicKeyFormat($format)
|
|
{
|
|
$this->publicKeyFormat = $format;
|
|
}
|
|
|
|
/**
|
|
* Determines which hashing function should be used
|
|
*
|
|
* Used with signature production / verification and (if the encryption mode is CRYPT_RSA_ENCRYPTION_OAEP) encryption and
|
|
* decryption. If $hash isn't supported, sha1 is used.
|
|
*
|
|
* @access public
|
|
* @param String $hash
|
|
*/
|
|
function setHash($hash)
|
|
{
|
|
// Crypt_Hash supports algorithms that PKCS#1 doesn't support. md5-96 and sha1-96, for example.
|
|
switch ($hash) {
|
|
case 'md2':
|
|
case 'md5':
|
|
case 'sha1':
|
|
case 'sha256':
|
|
case 'sha384':
|
|
case 'sha512':
|
|
$this->hash = new Crypt_Hash($hash);
|
|
$this->hashName = $hash;
|
|
break;
|
|
default:
|
|
$this->hash = new Crypt_Hash('sha1');
|
|
$this->hashName = 'sha1';
|
|
}
|
|
$this->hLen = $this->hash->getLength();
|
|
}
|
|
|
|
/**
|
|
* Determines which hashing function should be used for the mask generation function
|
|
*
|
|
* The mask generation function is used by CRYPT_RSA_ENCRYPTION_OAEP and CRYPT_RSA_SIGNATURE_PSS and although it's
|
|
* best if Hash and MGFHash are set to the same thing this is not a requirement.
|
|
*
|
|
* @access public
|
|
* @param String $hash
|
|
*/
|
|
function setMGFHash($hash)
|
|
{
|
|
// Crypt_Hash supports algorithms that PKCS#1 doesn't support. md5-96 and sha1-96, for example.
|
|
switch ($hash) {
|
|
case 'md2':
|
|
case 'md5':
|
|
case 'sha1':
|
|
case 'sha256':
|
|
case 'sha384':
|
|
case 'sha512':
|
|
$this->mgfHash = new Crypt_Hash($hash);
|
|
break;
|
|
default:
|
|
$this->mgfHash = new Crypt_Hash('sha1');
|
|
}
|
|
$this->mgfHLen = $this->mgfHash->getLength();
|
|
}
|
|
|
|
/**
|
|
* Determines the salt length
|
|
*
|
|
* To quote from {@link http://tools.ietf.org/html/rfc3447#page-38 RFC3447#page-38}:
|
|
*
|
|
* Typical salt lengths in octets are hLen (the length of the output
|
|
* of the hash function Hash) and 0.
|
|
*
|
|
* @access public
|
|
* @param Integer $format
|
|
*/
|
|
function setSaltLength($sLen)
|
|
{
|
|
$this->sLen = $sLen;
|
|
}
|
|
|
|
/**
|
|
* Generates a random string x bytes long
|
|
*
|
|
* @access public
|
|
* @param Integer $bytes
|
|
* @param optional Integer $nonzero
|
|
* @return String
|
|
*/
|
|
function _random($bytes, $nonzero = false)
|
|
{
|
|
$temp = '';
|
|
if ($nonzero) {
|
|
for ($i = 0; $i < $bytes; $i++) {
|
|
$temp.= chr(crypt_random(1, 255));
|
|
}
|
|
} else {
|
|
$ints = ($bytes + 1) >> 2;
|
|
for ($i = 0; $i < $ints; $i++) {
|
|
$temp.= pack('N', crypt_random());
|
|
}
|
|
$temp = substr($temp, 0, $bytes);
|
|
}
|
|
return $temp;
|
|
}
|
|
|
|
/**
|
|
* Integer-to-Octet-String primitive
|
|
*
|
|
* See {@link http://tools.ietf.org/html/rfc3447#section-4.1 RFC3447#section-4.1}.
|
|
*
|
|
* @access private
|
|
* @param Math_BigInteger $x
|
|
* @param Integer $xLen
|
|
* @return String
|
|
*/
|
|
function _i2osp($x, $xLen)
|
|
{
|
|
$x = $x->toBytes();
|
|
if (strlen($x) > $xLen) {
|
|
user_error('Integer too large', E_USER_NOTICE);
|
|
return false;
|
|
}
|
|
return str_pad($x, $xLen, chr(0), STR_PAD_LEFT);
|
|
}
|
|
|
|
/**
|
|
* Octet-String-to-Integer primitive
|
|
*
|
|
* See {@link http://tools.ietf.org/html/rfc3447#section-4.2 RFC3447#section-4.2}.
|
|
*
|
|
* @access private
|
|
* @param String $x
|
|
* @return Math_BigInteger
|
|
*/
|
|
function _os2ip($x)
|
|
{
|
|
return new Math_BigInteger($x, 256);
|
|
}
|
|
|
|
/**
|
|
* Exponentiate with or without Chinese Remainder Theorem
|
|
*
|
|
* See {@link http://tools.ietf.org/html/rfc3447#section-5.1.1 RFC3447#section-5.1.2}.
|
|
*
|
|
* @access private
|
|
* @param Math_BigInteger $x
|
|
* @return Math_BigInteger
|
|
*/
|
|
function _exponentiate($x)
|
|
{
|
|
if (empty($this->primes) || empty($this->coefficients) || empty($this->exponents)) {
|
|
return $x->modPow($this->exponent, $this->modulus);
|
|
}
|
|
|
|
$num_primes = count($this->primes);
|
|
|
|
if (defined('CRYPT_RSA_DISABLE_BLINDING')) {
|
|
$m_i = array(
|
|
1 => $x->modPow($this->exponents[1], $this->primes[1]),
|
|
2 => $x->modPow($this->exponents[2], $this->primes[2])
|
|
);
|
|
$h = $m_i[1]->subtract($m_i[2]);
|
|
$h = $h->multiply($this->coefficients[2]);
|
|
list(, $h) = $h->divide($this->primes[1]);
|
|
$m = $m_i[2]->add($h->multiply($this->primes[2]));
|
|
|
|
$r = $this->primes[1];
|
|
for ($i = 3; $i <= $num_primes; $i++) {
|
|
$m_i = $x->modPow($this->exponents[$i], $this->primes[$i]);
|
|
|
|
$r = $r->multiply($this->primes[$i - 1]);
|
|
|
|
$h = $m_i->subtract($m);
|
|
$h = $h->multiply($this->coefficients[$i]);
|
|
list(, $h) = $h->divide($this->primes[$i]);
|
|
|
|
$m = $m->add($r->multiply($h));
|
|
}
|
|
} else {
|
|
$smallest = $this->primes[1];
|
|
for ($i = 2; $i <= $num_primes; $i++) {
|
|
if ($smallest->compare($this->primes[$i]) > 0) {
|
|
$smallest = $this->primes[$i];
|
|
}
|
|
}
|
|
|
|
$one = new Math_BigInteger(1);
|
|
$one->setRandomGenerator('crypt_random');
|
|
|
|
$r = $one->random($one, $smallest->subtract($one));
|
|
|
|
$m_i = array(
|
|
1 => $this->_blind($x, $r, 1),
|
|
2 => $this->_blind($x, $r, 2)
|
|
);
|
|
$h = $m_i[1]->subtract($m_i[2]);
|
|
$h = $h->multiply($this->coefficients[2]);
|
|
list(, $h) = $h->divide($this->primes[1]);
|
|
$m = $m_i[2]->add($h->multiply($this->primes[2]));
|
|
|
|
$r = $this->primes[1];
|
|
for ($i = 3; $i <= $num_primes; $i++) {
|
|
$m_i = $this->_blind($x, $r, $i);
|
|
|
|
$r = $r->multiply($this->primes[$i - 1]);
|
|
|
|
$h = $m_i->subtract($m);
|
|
$h = $h->multiply($this->coefficients[$i]);
|
|
list(, $h) = $h->divide($this->primes[$i]);
|
|
|
|
$m = $m->add($r->multiply($h));
|
|
}
|
|
}
|
|
|
|
return $m;
|
|
}
|
|
|
|
/**
|
|
* Performs RSA Blinding
|
|
*
|
|
* Protects against timing attacks by employing RSA Blinding.
|
|
* Returns $x->modPow($this->exponents[$i], $this->primes[$i])
|
|
*
|
|
* @access private
|
|
* @param Math_BigInteger $x
|
|
* @param Math_BigInteger $r
|
|
* @param Integer $i
|
|
* @return Math_BigInteger
|
|
*/
|
|
function _blind($x, $r, $i)
|
|
{
|
|
$x = $x->multiply($r->modPow($this->publicExponent, $this->primes[$i]));
|
|
|
|
$x = $x->modPow($this->exponents[$i], $this->primes[$i]);
|
|
|
|
$r = $r->modInverse($this->primes[$i]);
|
|
$x = $x->multiply($r);
|
|
list(, $x) = $x->divide($this->primes[$i]);
|
|
|
|
return $x;
|
|
}
|
|
|
|
/**
|
|
* RSAEP
|
|
*
|
|
* See {@link http://tools.ietf.org/html/rfc3447#section-5.1.1 RFC3447#section-5.1.1}.
|
|
*
|
|
* @access private
|
|
* @param Math_BigInteger $m
|
|