/** * Performs modular exponentiation. * * Here's an example: * <code> * <?php * $a = new \Topxia\Service\Util\Phpsec\Math\BigInteger('10'); * $b = new \Topxia\Service\Util\Phpsec\Math\BigInteger('20'); * $c = new \Topxia\Service\Util\Phpsec\Math\BigInteger('30'); * * $c = $a->modPow($b, $c); * * echo $c->toString(); // outputs 10 * ?> * </code> * * @access public * @internal The most naive approach to modular exponentiation has very unreasonable requirements, and * and although the approach involving repeated squaring does vastly better, it, too, is impractical * for our purposes. The reason being that division - by far the most complicated and time-consuming * of the basic operations (eg. +,-,*,/) - occurs multiple times within it. * * Modular reductions resolve this issue. Although an individual modular reduction takes more time * then an individual division, when performed in succession (with the same modulo), they're a lot faster. * * The two most commonly used modular reductions are Barrett and Montgomery reduction. Montgomery reduction, * although faster, only works when the gcd of the modulo and of the base being used is 1. In RSA, when the * base is a power of two, the modulo - a product of two primes - is always going to have a gcd of 1 (because * the product of two odd numbers is odd), but what about when RSA isn't used? * * In contrast, Barrett reduction has no such constraint. As such, some bigint implementations perform a * Barrett reduction after every operation in the modpow function. Others perform Barrett reductions when the * modulo is even and Montgomery reductions when the modulo is odd. BigInteger.java's modPow method, however, * uses a trick involving the Chinese Remainder Theorem to factor the even modulo into two numbers - one odd and * the other, a power of two - and recombine them, later. This is the method that this modPow function uses. * {@link http://islab.oregonstate.edu/papers/j34monex.pdf Montgomery Reduction with Even Modulus} elaborates. * @param \Topxia\Service\Util\Phpsec\Math\BigInteger $e * @param \Topxia\Service\Util\Phpsec\Math\BigInteger $n * @return \Topxia\Service\Util\Phpsec\Math\BigInteger */ public function modPow($e, $n) { $n = $this->bitmask !== false && $this->bitmask->compare($n) < 0 ? $this->bitmask : $n->abs(); if ($e->compare(new static()) < 0) { $e = $e->abs(); $temp = $this->modInverse($n); if ($temp === false) { return false; } return $this->_normalize($temp->modPow($e, $n)); } if (MATH_BIGINTEGER_MODE == self::MODE_GMP) { $temp = new static(); $temp->value = gmp_powm($this->value, $e->value, $n->value); return $this->_normalize($temp); } if ($this->compare(new static()) < 0 || $this->compare($n) > 0) { list(, $temp) = $this->divide($n); return $temp->modPow($e, $n); } if (defined('MATH_BIGINTEGER_OPENSSL_ENABLED')) { $components = array('modulus' => $n->toBytes(true), 'publicExponent' => $e->toBytes(true)); $components = array('modulus' => pack('Ca*a*', 2, $this->_encodeASN1Length(strlen($components['modulus'])), $components['modulus']), 'publicExponent' => pack('Ca*a*', 2, $this->_encodeASN1Length(strlen($components['publicExponent'])), $components['publicExponent'])); $RSAPublicKey = pack('Ca*a*a*', 48, $this->_encodeASN1Length(strlen($components['modulus']) + strlen($components['publicExponent'])), $components['modulus'], $components['publicExponent']); $rsaOID = pack('H*', '300d06092a864886f70d0101010500'); // hex version of MA0GCSqGSIb3DQEBAQUA $RSAPublicKey = chr(0) . $RSAPublicKey; $RSAPublicKey = chr(3) . $this->_encodeASN1Length(strlen($RSAPublicKey)) . $RSAPublicKey; $encapsulated = pack('Ca*a*', 48, $this->_encodeASN1Length(strlen($rsaOID . $RSAPublicKey)), $rsaOID . $RSAPublicKey); $RSAPublicKey = "-----BEGIN PUBLIC KEY-----\r\n" . chunk_split(base64_encode($encapsulated)) . '-----END PUBLIC KEY-----'; $plaintext = str_pad($this->toBytes(), strlen($n->toBytes(true)) - 1, "", STR_PAD_LEFT); if (openssl_public_encrypt($plaintext, $result, $RSAPublicKey, OPENSSL_NO_PADDING)) { return new static($result, 256); } } if (MATH_BIGINTEGER_MODE == self::MODE_BCMATH) { $temp = new static(); $temp->value = bcpowmod($this->value, $e->value, $n->value, 0); return $this->_normalize($temp); } if (empty($e->value)) { $temp = new static(); $temp->value = array(1); return $this->_normalize($temp); } if ($e->value == array(1)) { list(, $temp) = $this->divide($n); return $this->_normalize($temp); } if ($e->value == array(2)) { $temp = new static(); $temp->value = $this->_square($this->value); list(, $temp) = $temp->divide($n); return $this->_normalize($temp); } return $this->_normalize($this->_slidingWindow($e, $n, self::BARRETT)); // the following code, although not callable, can be run independently of the above code // although the above code performed better in my benchmarks the following could might // perform better under different circumstances. in lieu of deleting it it's just been // made uncallable // is the modulo odd? if ($n->value[0] & 1) { return $this->_normalize($this->_slidingWindow($e, $n, self::MONTGOMERY)); } // if it's not, it's even // find the lowest set bit (eg. the max pow of 2 that divides $n) for ($i = 0; $i < count($n->value); ++$i) { if ($n->value[$i]) { $temp = decbin($n->value[$i]); $j = strlen($temp) - strrpos($temp, '1') - 1; $j += 26 * $i; break; } } // at this point, 2^$j * $n/(2^$j) == $n $mod1 = $n->copy(); $mod1->_rshift($j); $mod2 = new static(); $mod2->value = array(1); $mod2->_lshift($j); $part1 = $mod1->value != array(1) ? $this->_slidingWindow($e, $mod1, self::MONTGOMERY) : new static(); $part2 = $this->_slidingWindow($e, $mod2, self::POWEROF2); $y1 = $mod2->modInverse($mod1); $y2 = $mod1->modInverse($mod2); $result = $part1->multiply($mod2); $result = $result->multiply($y1); $temp = $part2->multiply($mod1); $temp = $temp->multiply($y2); $result = $result->add($temp); list(, $result) = $result->divide($n); return $this->_normalize($result); }
/** * Connect to an SSHv1 server * * @access private * @return Boolean */ public function _connect() { $this->fsock = @fsockopen($this->host, $this->port, $errno, $errstr, $this->connectionTimeout); if (!$this->fsock) { user_error(rtrim("Cannot connect to {$this->host}:{$this->port}. Error {$errno}. {$errstr}")); return false; } $this->server_identification = $init_line = fgets($this->fsock, 255); if (defined('NET_SSH1_LOGGING')) { $this->_append_log('<-', $this->server_identification); $this->_append_log('->', $this->identifier . "\r\n"); } if (!preg_match('#SSH-([0-9\\.]+)-(.+)#', $init_line, $parts)) { user_error('Can only connect to SSH servers'); return false; } if ($parts[1][0] != 1) { user_error("Cannot connect to SSH {$parts['1']} servers"); return false; } fputs($this->fsock, $this->identifier . "\r\n"); $response = $this->_get_binary_packet(); if ($response[self::RESPONSE_TYPE] != NET_SSH1_SMSG_PUBLIC_KEY) { user_error('Expected SSH_SMSG_PUBLIC_KEY'); return false; } $anti_spoofing_cookie = $this->_string_shift($response[self::RESPONSE_DATA], 8); $this->_string_shift($response[self::RESPONSE_DATA], 4); $temp = unpack('nlen', $this->_string_shift($response[self::RESPONSE_DATA], 2)); $server_key_public_exponent = new BigInteger($this->_string_shift($response[self::RESPONSE_DATA], ceil($temp['len'] / 8)), 256); $this->server_key_public_exponent = $server_key_public_exponent; $temp = unpack('nlen', $this->_string_shift($response[self::RESPONSE_DATA], 2)); $server_key_public_modulus = new BigInteger($this->_string_shift($response[self::RESPONSE_DATA], ceil($temp['len'] / 8)), 256); $this->server_key_public_modulus = $server_key_public_modulus; $this->_string_shift($response[self::RESPONSE_DATA], 4); $temp = unpack('nlen', $this->_string_shift($response[self::RESPONSE_DATA], 2)); $host_key_public_exponent = new BigInteger($this->_string_shift($response[self::RESPONSE_DATA], ceil($temp['len'] / 8)), 256); $this->host_key_public_exponent = $host_key_public_exponent; $temp = unpack('nlen', $this->_string_shift($response[self::RESPONSE_DATA], 2)); $host_key_public_modulus = new BigInteger($this->_string_shift($response[self::RESPONSE_DATA], ceil($temp['len'] / 8)), 256); $this->host_key_public_modulus = $host_key_public_modulus; $this->_string_shift($response[self::RESPONSE_DATA], 4); // get a list of the supported ciphers extract(unpack('Nsupported_ciphers_mask', $this->_string_shift($response[self::RESPONSE_DATA], 4))); foreach ($this->supported_ciphers as $mask => $name) { if (($supported_ciphers_mask & 1 << $mask) == 0) { unset($this->supported_ciphers[$mask]); } } // get a list of the supported authentications extract(unpack('Nsupported_authentications_mask', $this->_string_shift($response[self::RESPONSE_DATA], 4))); foreach ($this->supported_authentications as $mask => $name) { if (($supported_authentications_mask & 1 << $mask) == 0) { unset($this->supported_authentications[$mask]); } } $session_id = pack('H*', md5($host_key_public_modulus->toBytes() . $server_key_public_modulus->toBytes() . $anti_spoofing_cookie)); $session_key = Random::string(32); $double_encrypted_session_key = $session_key ^ str_pad($session_id, 32, chr(0)); if ($server_key_public_modulus->compare($host_key_public_modulus) < 0) { $double_encrypted_session_key = $this->_rsa_crypt($double_encrypted_session_key, array($server_key_public_exponent, $server_key_public_modulus)); $double_encrypted_session_key = $this->_rsa_crypt($double_encrypted_session_key, array($host_key_public_exponent, $host_key_public_modulus)); } else { $double_encrypted_session_key = $this->_rsa_crypt($double_encrypted_session_key, array($host_key_public_exponent, $host_key_public_modulus)); $double_encrypted_session_key = $this->_rsa_crypt($double_encrypted_session_key, array($server_key_public_exponent, $server_key_public_modulus)); } $cipher = isset($this->supported_ciphers[$this->cipher]) ? $this->cipher : self::CIPHER_3DES; $data = pack('C2a*na*N', NET_SSH1_CMSG_SESSION_KEY, $cipher, $anti_spoofing_cookie, 8 * strlen($double_encrypted_session_key), $double_encrypted_session_key, 0); if (!$this->_send_binary_packet($data)) { user_error('Error sending SSH_CMSG_SESSION_KEY'); return false; } switch ($cipher) { //case self::CIPHER_NONE: // $this->crypto = new \Topxia\Service\Util\Phpsec\Crypt\Null(); // break; case self::CIPHER_DES: $this->crypto = new DES(); $this->crypto->disablePadding(); $this->crypto->enableContinuousBuffer(); $this->crypto->setKey(substr($session_key, 0, 8)); break; case self::CIPHER_3DES: $this->crypto = new TripleDES(TripleDES::MODE_3CBC); $this->crypto->disablePadding(); $this->crypto->enableContinuousBuffer(); $this->crypto->setKey(substr($session_key, 0, 24)); break; //case self::CIPHER_RC4: // $this->crypto = new RC4(); // $this->crypto->enableContinuousBuffer(); // $this->crypto->setKey(substr($session_key, 0, 16)); // break; } $response = $this->_get_binary_packet(); if ($response[self::RESPONSE_TYPE] != NET_SSH1_SMSG_SUCCESS) { user_error('Expected SSH_SMSG_SUCCESS'); return false; } $this->bitmap = self::MASK_CONNECTED; return true; }
/** * Returns the server public host key. * * Caching this the first time you connect to a server and checking the result on subsequent connections * is recommended. Returns false if the server signature is not signed correctly with the public host key. * * @access public * @return Mixed */ public function getServerPublicHostKey() { if (!($this->bitmap & self::MASK_CONSTRUCTOR)) { if (!$this->_connect()) { return false; } } $signature = $this->signature; $server_public_host_key = $this->server_public_host_key; extract(unpack('Nlength', $this->_string_shift($server_public_host_key, 4))); $this->_string_shift($server_public_host_key, $length); if ($this->signature_validated) { return $this->bitmap ? $this->signature_format . ' ' . base64_encode($this->server_public_host_key) : false; } $this->signature_validated = true; switch ($this->signature_format) { case 'ssh-dss': $zero = new BigInteger(); $temp = unpack('Nlength', $this->_string_shift($server_public_host_key, 4)); $p = new BigInteger($this->_string_shift($server_public_host_key, $temp['length']), -256); $temp = unpack('Nlength', $this->_string_shift($server_public_host_key, 4)); $q = new BigInteger($this->_string_shift($server_public_host_key, $temp['length']), -256); $temp = unpack('Nlength', $this->_string_shift($server_public_host_key, 4)); $g = new BigInteger($this->_string_shift($server_public_host_key, $temp['length']), -256); $temp = unpack('Nlength', $this->_string_shift($server_public_host_key, 4)); $y = new BigInteger($this->_string_shift($server_public_host_key, $temp['length']), -256); /* The value for 'dss_signature_blob' is encoded as a string containing r, followed by s (which are 160-bit integers, without lengths or padding, unsigned, and in network byte order). */ $temp = unpack('Nlength', $this->_string_shift($signature, 4)); if ($temp['length'] != 40) { user_error('Invalid signature'); return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED); } $r = new BigInteger($this->_string_shift($signature, 20), 256); $s = new BigInteger($this->_string_shift($signature, 20), 256); switch (true) { case $r->equals($zero): case $r->compare($q) >= 0: case $s->equals($zero): case $s->compare($q) >= 0: user_error('Invalid signature'); return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED); } $w = $s->modInverse($q); $u1 = $w->multiply(new BigInteger(sha1($this->exchange_hash), 16)); list(, $u1) = $u1->divide($q); $u2 = $w->multiply($r); list(, $u2) = $u2->divide($q); $g = $g->modPow($u1, $p); $y = $y->modPow($u2, $p); $v = $g->multiply($y); list(, $v) = $v->divide($p); list(, $v) = $v->divide($q); if (!$v->equals($r)) { user_error('Bad server signature'); return $this->_disconnect(NET_SSH2_DISCONNECT_HOST_KEY_NOT_VERIFIABLE); } break; case 'ssh-rsa': $temp = unpack('Nlength', $this->_string_shift($server_public_host_key, 4)); $e = new BigInteger($this->_string_shift($server_public_host_key, $temp['length']), -256); $temp = unpack('Nlength', $this->_string_shift($server_public_host_key, 4)); $rawN = $this->_string_shift($server_public_host_key, $temp['length']); $n = new BigInteger($rawN, -256); $nLength = strlen(ltrim($rawN, "")); /* $temp = unpack('Nlength', $this->_string_shift($signature, 4)); $signature = $this->_string_shift($signature, $temp['length']); $rsa = new RSA(); $rsa->setSignatureMode(RSA::SIGNATURE_PKCS1); $rsa->loadKey(array('e' => $e, 'n' => $n), RSA::PUBLIC_FORMAT_RAW); if (!$rsa->verify($this->exchange_hash, $signature)) { user_error('Bad server signature'); return $this->_disconnect(NET_SSH2_DISCONNECT_HOST_KEY_NOT_VERIFIABLE); } */ $temp = unpack('Nlength', $this->_string_shift($signature, 4)); $s = new BigInteger($this->_string_shift($signature, $temp['length']), 256); // validate an RSA signature per "8.2 RSASSA-PKCS1-v1_5", "5.2.2 RSAVP1", and "9.1 EMSA-PSS" in the // following URL: // ftp://ftp.rsasecurity.com/pub/pkcs/pkcs-1/pkcs-1v2-1.pdf // also, see SSHRSA.c (rsa2_verifysig) in PuTTy's source. if ($s->compare(new BigInteger()) < 0 || $s->compare($n->subtract(new BigInteger(1))) > 0) { user_error('Invalid signature'); return $this->_disconnect(NET_SSH2_DISCONNECT_KEY_EXCHANGE_FAILED); } $s = $s->modPow($e, $n); $s = $s->toBytes(); $h = pack('N4H*', 0x302130, 0x906052b, 0xe03021a, 0x5000414, sha1($this->exchange_hash)); $h = chr(0x1) . str_repeat(chr(0xff), $nLength - 2 - strlen($h)) . $h; if ($s != $h) { user_error('Bad server signature'); return $this->_disconnect(NET_SSH2_DISCONNECT_HOST_KEY_NOT_VERIFIABLE); } break; default: user_error('Unsupported signature format'); return $this->_disconnect(NET_SSH2_DISCONNECT_HOST_KEY_NOT_VERIFIABLE); } return $this->signature_format . ' ' . base64_encode($this->server_public_host_key); }