Exemplo n.º 1
0
 /**
  * Key Exchange
  *
  * @param String $kexinit_payload_server
  * @access private
  */
 function _key_exchange($kexinit_payload_server)
 {
     static $kex_algorithms = array('diffie-hellman-group1-sha1', 'diffie-hellman-group14-sha1');
     static $server_host_key_algorithms = array('ssh-rsa', 'ssh-dss');
     static $encryption_algorithms = array('arcfour256', 'arcfour128', 'arcfour', 'aes128-cbc', 'aes192-cbc', 'aes256-cbc', 'aes128-ctr', 'aes192-ctr', 'aes256-ctr', '3des-ctr', '3des-cbc', 'none');
     static $mac_algorithms = array('hmac-sha1-96', 'hmac-sha1', 'hmac-md5-96', 'hmac-md5', 'none');
     static $compression_algorithms = array('none');
     // some SSH servers have buggy implementations of some of the above algorithms
     switch ($this->server_identifier) {
         case 'SSH-2.0-SSHD':
             $mac_algorithms = array_values(array_diff($mac_algorithms, array('hmac-sha1-96', 'hmac-md5-96')));
     }
     static $str_kex_algorithms, $str_server_host_key_algorithms, $encryption_algorithms_server_to_client, $mac_algorithms_server_to_client, $compression_algorithms_server_to_client, $encryption_algorithms_client_to_server, $mac_algorithms_client_to_server, $compression_algorithms_client_to_server;
     if (empty($str_kex_algorithms)) {
         $str_kex_algorithms = implode(',', $kex_algorithms);
         $str_server_host_key_algorithms = implode(',', $server_host_key_algorithms);
         $encryption_algorithms_server_to_client = $encryption_algorithms_client_to_server = implode(',', $encryption_algorithms);
         $mac_algorithms_server_to_client = $mac_algorithms_client_to_server = implode(',', $mac_algorithms);
         $compression_algorithms_server_to_client = $compression_algorithms_client_to_server = implode(',', $compression_algorithms);
     }
     $client_cookie = '';
     for ($i = 0; $i < 16; $i++) {
         $client_cookie .= chr(crypt_random(0, 255));
     }
     $response = $kexinit_payload_server;
     $this->_string_shift($response, 1);
     // skip past the message number (it should be SSH_MSG_KEXINIT)
     $server_cookie = $this->_string_shift($response, 16);
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->kex_algorithms = explode(',', $this->_string_shift($response, $temp['length']));
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->server_host_key_algorithms = explode(',', $this->_string_shift($response, $temp['length']));
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->encryption_algorithms_client_to_server = explode(',', $this->_string_shift($response, $temp['length']));
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->encryption_algorithms_server_to_client = explode(',', $this->_string_shift($response, $temp['length']));
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->mac_algorithms_client_to_server = explode(',', $this->_string_shift($response, $temp['length']));
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->mac_algorithms_server_to_client = explode(',', $this->_string_shift($response, $temp['length']));
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->compression_algorithms_client_to_server = explode(',', $this->_string_shift($response, $temp['length']));
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->compression_algorithms_server_to_client = explode(',', $this->_string_shift($response, $temp['length']));
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->languages_client_to_server = explode(',', $this->_string_shift($response, $temp['length']));
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->languages_server_to_client = explode(',', $this->_string_shift($response, $temp['length']));
     extract(unpack('Cfirst_kex_packet_follows', $this->_string_shift($response, 1)));
     $first_kex_packet_follows = $first_kex_packet_follows != 0;
     // the sending of SSH2_MSG_KEXINIT could go in one of two places.  this is the second place.
     $kexinit_payload_client = pack('Ca*Na*Na*Na*Na*Na*Na*Na*Na*Na*Na*CN', NET_SSH2_MSG_KEXINIT, $client_cookie, strlen($str_kex_algorithms), $str_kex_algorithms, strlen($str_server_host_key_algorithms), $str_server_host_key_algorithms, strlen($encryption_algorithms_client_to_server), $encryption_algorithms_client_to_server, strlen($encryption_algorithms_server_to_client), $encryption_algorithms_server_to_client, strlen($mac_algorithms_client_to_server), $mac_algorithms_client_to_server, strlen($mac_algorithms_server_to_client), $mac_algorithms_server_to_client, strlen($compression_algorithms_client_to_server), $compression_algorithms_client_to_server, strlen($compression_algorithms_server_to_client), $compression_algorithms_server_to_client, 0, '', 0, '', 0, 0);
     if (!$this->_send_binary_packet($kexinit_payload_client)) {
         return false;
     }
     // here ends the second place.
     // we need to decide upon the symmetric encryption algorithms before we do the diffie-hellman key exchange
     for ($i = 0; $i < count($encryption_algorithms) && !in_array($encryption_algorithms[$i], $this->encryption_algorithms_server_to_client); $i++) {
     }
     if ($i == count($encryption_algorithms)) {
         user_error('No compatible server to client encryption algorithms found', E_USER_NOTICE);
         return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED);
     }
     // we don't initialize any crypto-objects, yet - we do that, later. for now, we need the lengths to make the
     // diffie-hellman key exchange as fast as possible
     $decrypt = $encryption_algorithms[$i];
     switch ($decrypt) {
         case '3des-cbc':
         case '3des-ctr':
             $decryptKeyLength = 24;
             // eg. 192 / 8
             break;
         case 'aes256-cbc':
         case 'aes256-ctr':
             $decryptKeyLength = 32;
             // eg. 256 / 8
             break;
         case 'aes192-cbc':
         case 'aes192-ctr':
             $decryptKeyLength = 24;
             // eg. 192 / 8
             break;
         case 'aes128-cbc':
         case 'aes128-ctr':
             $decryptKeyLength = 16;
             // eg. 128 / 8
             break;
         case 'arcfour':
         case 'arcfour128':
             $decryptKeyLength = 16;
             // eg. 128 / 8
             break;
         case 'arcfour256':
             $decryptKeyLength = 32;
             // eg. 128 / 8
             break;
         case 'none':
             $decryptKeyLength = 0;
     }
     for ($i = 0; $i < count($encryption_algorithms) && !in_array($encryption_algorithms[$i], $this->encryption_algorithms_client_to_server); $i++) {
     }
     if ($i == count($encryption_algorithms)) {
         user_error('No compatible client to server encryption algorithms found', E_USER_NOTICE);
         return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED);
     }
     $encrypt = $encryption_algorithms[$i];
     switch ($encrypt) {
         case '3des-cbc':
         case '3des-ctr':
             $encryptKeyLength = 24;
             break;
         case 'aes256-cbc':
         case 'aes256-ctr':
             $encryptKeyLength = 32;
             break;
         case 'aes192-cbc':
         case 'aes192-ctr':
             $encryptKeyLength = 24;
             break;
         case 'aes128-cbc':
         case 'aes128-ctr':
             $encryptKeyLength = 16;
             break;
         case 'arcfour':
         case 'arcfour128':
             $encryptKeyLength = 16;
             break;
         case 'arcfour256':
             $encryptKeyLength = 32;
             break;
         case 'none':
             $encryptKeyLength = 0;
     }
     $keyLength = $decryptKeyLength > $encryptKeyLength ? $decryptKeyLength : $encryptKeyLength;
     // through diffie-hellman key exchange a symmetric key is obtained
     for ($i = 0; $i < count($kex_algorithms) && !in_array($kex_algorithms[$i], $this->kex_algorithms); $i++) {
     }
     if ($i == count($kex_algorithms)) {
         user_error('No compatible key exchange algorithms found', E_USER_NOTICE);
         return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED);
     }
     switch ($kex_algorithms[$i]) {
         // see http://tools.ietf.org/html/rfc2409#section-6.2 and
         // http://tools.ietf.org/html/rfc2412, appendex E
         case 'diffie-hellman-group1-sha1':
             $p = pack('H256', 'FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74' . '020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F1437' . '4FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED' . 'EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE65381FFFFFFFFFFFFFFFF');
             $keyLength = $keyLength < 160 ? $keyLength : 160;
             $hash = 'sha1';
             break;
             // see http://tools.ietf.org/html/rfc3526#section-3
         // see http://tools.ietf.org/html/rfc3526#section-3
         case 'diffie-hellman-group14-sha1':
             $p = pack('H512', 'FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74' . '020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F1437' . '4FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED' . 'EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3DC2007CB8A163BF05' . '98DA48361C55D39A69163FA8FD24CF5F83655D23DCA3AD961C62F356208552BB' . '9ED529077096966D670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B' . 'E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718' . '3995497CEA956AE515D2261898FA051015728E5A8AACAA68FFFFFFFFFFFFFFFF');
             $keyLength = $keyLength < 160 ? $keyLength : 160;
             $hash = 'sha1';
     }
     $p = new Math_BigInteger($p, 256);
     //$q = $p->bitwise_rightShift(1);
     /* To increase the speed of the key exchange, both client and server may
                reduce the size of their private exponents.  It should be at least
                twice as long as the key material that is generated from the shared
                secret.  For more details, see the paper by van Oorschot and Wiener
                [VAN-OORSCHOT].
     
                -- http://tools.ietf.org/html/rfc4419#section-6.2 */
     $q = new Math_BigInteger(1);
     $q = $q->bitwise_leftShift(2 * $keyLength);
     $q = $q->subtract(new Math_BigInteger(1));
     $g = new Math_BigInteger(2);
     $x = new Math_BigInteger();
     $x->setRandomGenerator('crypt_random');
     $x = $x->random(new Math_BigInteger(1), $q);
     $e = $g->modPow($x, $p);
     $eBytes = $e->toBytes(true);
     $data = pack('CNa*', NET_SSH2_MSG_KEXDH_INIT, strlen($eBytes), $eBytes);
     if (!$this->_send_binary_packet($data)) {
         user_error('Connection closed by server', E_USER_NOTICE);
         return false;
     }
     $response = $this->_get_binary_packet();
     if ($response === false) {
         user_error('Connection closed by server', E_USER_NOTICE);
         return false;
     }
     extract(unpack('Ctype', $this->_string_shift($response, 1)));
     if ($type != NET_SSH2_MSG_KEXDH_REPLY) {
         user_error('Expected SSH_MSG_KEXDH_REPLY', E_USER_NOTICE);
         return false;
     }
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->server_public_host_key = $server_public_host_key = $this->_string_shift($response, $temp['length']);
     $temp = unpack('Nlength', $this->_string_shift($server_public_host_key, 4));
     $public_key_format = $this->_string_shift($server_public_host_key, $temp['length']);
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $fBytes = $this->_string_shift($response, $temp['length']);
     $f = new Math_BigInteger($fBytes, -256);
     $temp = unpack('Nlength', $this->_string_shift($response, 4));
     $this->signature = $this->_string_shift($response, $temp['length']);
     $temp = unpack('Nlength', $this->_string_shift($this->signature, 4));
     $this->signature_format = $this->_string_shift($this->signature, $temp['length']);
     $key = $f->modPow($x, $p);
     $keyBytes = $key->toBytes(true);
     $this->exchange_hash = pack('Na*Na*Na*Na*Na*Na*Na*Na*', strlen($this->identifier), $this->identifier, strlen($this->server_identifier), $this->server_identifier, strlen($kexinit_payload_client), $kexinit_payload_client, strlen($kexinit_payload_server), $kexinit_payload_server, strlen($this->server_public_host_key), $this->server_public_host_key, strlen($eBytes), $eBytes, strlen($fBytes), $fBytes, strlen($keyBytes), $keyBytes);
     $this->exchange_hash = pack('H*', $hash($this->exchange_hash));
     if ($this->session_id === false) {
         $this->session_id = $this->exchange_hash;
     }
     for ($i = 0; $i < count($server_host_key_algorithms) && !in_array($server_host_key_algorithms[$i], $this->server_host_key_algorithms); $i++) {
     }
     if ($i == count($server_host_key_algorithms)) {
         user_error('No compatible server host key algorithms found', E_USER_NOTICE);
         return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED);
     }
     if ($public_key_format != $server_host_key_algorithms[$i] || $this->signature_format != $server_host_key_algorithms[$i]) {
         user_error('Sever Host Key Algorithm Mismatch', E_USER_NOTICE);
         return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED);
     }
     $packet = pack('C', NET_SSH2_MSG_NEWKEYS);
     if (!$this->_send_binary_packet($packet)) {
         return false;
     }
     $response = $this->_get_binary_packet();
     if ($response === false) {
         user_error('Connection closed by server', E_USER_NOTICE);
         return false;
     }
     extract(unpack('Ctype', $this->_string_shift($response, 1)));
     if ($type != NET_SSH2_MSG_NEWKEYS) {
         user_error('Expected SSH_MSG_NEWKEYS', E_USER_NOTICE);
         return false;
     }
     switch ($encrypt) {
         case '3des-cbc':
             $this->encrypt = new Crypt_TripleDES();
             // $this->encrypt_block_size = 64 / 8 == the default
             break;
         case '3des-ctr':
             $this->encrypt = new Crypt_TripleDES(CRYPT_DES_MODE_CTR);
             // $this->encrypt_block_size = 64 / 8 == the default
             break;
         case 'aes256-cbc':
         case 'aes192-cbc':
         case 'aes128-cbc':
             $this->encrypt = new Crypt_AES();
             $this->encrypt_block_size = 16;
             // eg. 128 / 8
             break;
         case 'aes256-ctr':
         case 'aes192-ctr':
         case 'aes128-ctr':
             $this->encrypt = new Crypt_AES(CRYPT_AES_MODE_CTR);
             $this->encrypt_block_size = 16;
             // eg. 128 / 8
             break;
         case 'arcfour':
         case 'arcfour128':
         case 'arcfour256':
             $this->encrypt = new Crypt_RC4();
             break;
         case 'none':
             //$this->encrypt = new Crypt_Null();
     }
     switch ($decrypt) {
         case '3des-cbc':
             $this->decrypt = new Crypt_TripleDES();
             break;
         case '3des-ctr':
             $this->decrypt = new Crypt_TripleDES(CRYPT_DES_MODE_CTR);
             break;
         case 'aes256-cbc':
         case 'aes192-cbc':
         case 'aes128-cbc':
             $this->decrypt = new Crypt_AES();
             $this->decrypt_block_size = 16;
             break;
         case 'aes256-ctr':
         case 'aes192-ctr':
         case 'aes128-ctr':
             $this->decrypt = new Crypt_AES(CRYPT_AES_MODE_CTR);
             $this->decrypt_block_size = 16;
             break;
         case 'arcfour':
         case 'arcfour128':
         case 'arcfour256':
             $this->decrypt = new Crypt_RC4();
             break;
         case 'none':
             //$this->decrypt = new Crypt_Null();
     }
     $keyBytes = pack('Na*', strlen($keyBytes), $keyBytes);
     if ($this->encrypt) {
         $this->encrypt->enableContinuousBuffer();
         $this->encrypt->disablePadding();
         $iv = pack('H*', $hash($keyBytes . $this->exchange_hash . 'A' . $this->session_id));
         while ($this->encrypt_block_size > strlen($iv)) {
             $iv .= pack('H*', $hash($keyBytes . $this->exchange_hash . $iv));
         }
         $this->encrypt->setIV(substr($iv, 0, $this->encrypt_block_size));
         $key = pack('H*', $hash($keyBytes . $this->exchange_hash . 'C' . $this->session_id));
         while ($encryptKeyLength > strlen($key)) {
             $key .= pack('H*', $hash($keyBytes . $this->exchange_hash . $key));
         }
         $this->encrypt->setKey(substr($key, 0, $encryptKeyLength));
     }
     if ($this->decrypt) {
         $this->decrypt->enableContinuousBuffer();
         $this->decrypt->disablePadding();
         $iv = pack('H*', $hash($keyBytes . $this->exchange_hash . 'B' . $this->session_id));
         while ($this->decrypt_block_size > strlen($iv)) {
             $iv .= pack('H*', $hash($keyBytes . $this->exchange_hash . $iv));
         }
         $this->decrypt->setIV(substr($iv, 0, $this->decrypt_block_size));
         $key = pack('H*', $hash($keyBytes . $this->exchange_hash . 'D' . $this->session_id));
         while ($decryptKeyLength > strlen($key)) {
             $key .= pack('H*', $hash($keyBytes . $this->exchange_hash . $key));
         }
         $this->decrypt->setKey(substr($key, 0, $decryptKeyLength));
     }
     /* The "arcfour128" algorithm is the RC4 cipher, as described in
                [SCHNEIER], using a 128-bit key.  The first 1536 bytes of keystream
                generated by the cipher MUST be discarded, and the first byte of the
                first encrypted packet MUST be encrypted using the 1537th byte of
                keystream.
     
                -- http://tools.ietf.org/html/rfc4345#section-4 */
     if ($encrypt == 'arcfour128' || $encrypt == 'arcfour256') {
         $this->encrypt->encrypt(str_repeat("", 1536));
     }
     if ($decrypt == 'arcfour128' || $decrypt == 'arcfour256') {
         $this->decrypt->decrypt(str_repeat("", 1536));
     }
     for ($i = 0; $i < count($mac_algorithms) && !in_array($mac_algorithms[$i], $this->mac_algorithms_client_to_server); $i++) {
     }
     if ($i == count($mac_algorithms)) {
         user_error('No compatible client to server message authentication algorithms found', E_USER_NOTICE);
         return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED);
     }
     $createKeyLength = 0;
     // ie. $mac_algorithms[$i] == 'none'
     switch ($mac_algorithms[$i]) {
         case 'hmac-sha1':
             $this->hmac_create = new Crypt_Hash('sha1');
             $createKeyLength = 20;
             break;
         case 'hmac-sha1-96':
             $this->hmac_create = new Crypt_Hash('sha1-96');
             $createKeyLength = 20;
             break;
         case 'hmac-md5':
             $this->hmac_create = new Crypt_Hash('md5');
             $createKeyLength = 16;
             break;
         case 'hmac-md5-96':
             $this->hmac_create = new Crypt_Hash('md5-96');
             $createKeyLength = 16;
     }
     for ($i = 0; $i < count($mac_algorithms) && !in_array($mac_algorithms[$i], $this->mac_algorithms_server_to_client); $i++) {
     }
     if ($i == count($mac_algorithms)) {
         user_error('No compatible server to client message authentication algorithms found', E_USER_NOTICE);
         return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED);
     }
     $checkKeyLength = 0;
     $this->hmac_size = 0;
     switch ($mac_algorithms[$i]) {
         case 'hmac-sha1':
             $this->hmac_check = new Crypt_Hash('sha1');
             $checkKeyLength = 20;
             $this->hmac_size = 20;
             break;
         case 'hmac-sha1-96':
             $this->hmac_check = new Crypt_Hash('sha1-96');
             $checkKeyLength = 20;
             $this->hmac_size = 12;
             break;
         case 'hmac-md5':
             $this->hmac_check = new Crypt_Hash('md5');
             $checkKeyLength = 16;
             $this->hmac_size = 16;
             break;
         case 'hmac-md5-96':
             $this->hmac_check = new Crypt_Hash('md5-96');
             $checkKeyLength = 16;
             $this->hmac_size = 12;
     }
     $key = pack('H*', $hash($keyBytes . $this->exchange_hash . 'E' . $this->session_id));
     while ($createKeyLength > strlen($key)) {
         $key .= pack('H*', $hash($keyBytes . $this->exchange_hash . $key));
     }
     $this->hmac_create->setKey(substr($key, 0, $createKeyLength));
     $key = pack('H*', $hash($keyBytes . $this->exchange_hash . 'F' . $this->session_id));
     while ($checkKeyLength > strlen($key)) {
         $key .= pack('H*', $hash($keyBytes . $this->exchange_hash . $key));
     }
     $this->hmac_check->setKey(substr($key, 0, $checkKeyLength));
     for ($i = 0; $i < count($compression_algorithms) && !in_array($compression_algorithms[$i], $this->compression_algorithms_server_to_client); $i++) {
     }
     if ($i == count($compression_algorithms)) {
         user_error('No compatible server to client compression algorithms found', E_USER_NOTICE);
         return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED);
     }
     $this->decompress = $compression_algorithms[$i] == 'zlib';
     for ($i = 0; $i < count($compression_algorithms) && !in_array($compression_algorithms[$i], $this->compression_algorithms_client_to_server); $i++) {
     }
     if ($i == count($compression_algorithms)) {
         user_error('No compatible client to server compression algorithms found', E_USER_NOTICE);
         return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED);
     }
     $this->compress = $compression_algorithms[$i] == 'zlib';
     return true;
 }
Exemplo n.º 2
0
 /**
  * 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;
 }