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tgseclib/phpseclib/Crypt/RSA.php
terrafrost 6ca7323401 Merge branch '2.0'
2017-05-29 06:33:24 -05:00

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<?php
/**
* Pure-PHP PKCS#1 (v2.1) compliant implementation of RSA.
*
* PHP version 5
*
* Here's an example of how to encrypt and decrypt text with this library:
* <code>
* <?php
* include 'vendor/autoload.php';
*
* extract(\phpseclib\Crypt\RSA::createKey());
*
* $plaintext = 'terrafrost';
*
* $ciphertext = $publickey->encrypt($plaintext);
*
* echo $privatekey->decrypt($ciphertext);
* ?>
* </code>
*
* Here's an example of how to create signatures and verify signatures with this library:
* <code>
* <?php
* include 'vendor/autoload.php';
*
* extract(\phpseclib\Crypt\RSA::createKey());
*
* $plaintext = 'terrafrost';
*
* $signature = $privatekey->sign($plaintext);
*
* echo $publickey->verify($plaintext, $signature) ? 'verified' : 'unverified';
* ?>
* </code>
*
* @category Crypt
* @package RSA
* @author Jim Wigginton <terrafrost@php.net>
* @copyright 2009 Jim Wigginton
* @license http://www.opensource.org/licenses/mit-license.html MIT License
* @link http://phpseclib.sourceforge.net
*/
namespace phpseclib\Crypt;
use ParagonIE\ConstantTime\Base64;
use phpseclib\File\ASN1;
use phpseclib\Math\BigInteger;
use phpseclib\Common\Functions\Strings;
use phpseclib\File\ASN1\Maps\DigestInfo;
use phpseclib\Crypt\Common\AsymmetricKey;
use phpseclib\Exception\UnsupportedAlgorithmException;
/**
* Pure-PHP PKCS#1 compliant implementation of RSA.
*
* @package RSA
* @author Jim Wigginton <terrafrost@php.net>
* @access public
*/
class RSA extends AsymmetricKey
{
/**
* Algorithm Name
*
* @var string
* @access private
*/
const ALGORITHM = 'RSA';
/**#@+
* @access public
* @see self::encrypt()
* @see self::decrypt()
*/
/**
* Use {@link http://en.wikipedia.org/wiki/Optimal_Asymmetric_Encryption_Padding Optimal Asymmetric Encryption Padding}
* (OAEP) for encryption / decryption.
*
* Uses sha256 by default
*
* @see self::setHash()
* @see self::setMGFHash()
*/
const PADDING_OAEP = 1;
/**
* Use PKCS#1 padding.
*
* Although self::PADDING_OAEP / self::PADDING_PSS offers more security, including PKCS#1 padding is necessary for purposes of backwards
* compatibility with protocols (like SSH-1) written before OAEP's introduction.
*/
const PADDING_PKCS1 = 2;
/**
* Do not use any padding
*
* Although this method is not recommended it can none-the-less sometimes be useful if you're trying to decrypt some legacy
* stuff, if you're trying to diagnose why an encrypted message isn't decrypting, etc.
*/
const PADDING_NONE = 3;
/**
* Use PKCS#1 padding with PKCS1 v1.5 compatibility
*
* A PKCS1 v2.1 encrypted message may not successfully decrypt with a PKCS1 v1.5 implementation (such as OpenSSL).
*/
const PADDING_PKCS15_COMPAT = 6;
/**#@-*/
/**#@+
* @access public
* @see self::sign()
* @see self::verify()
* @see self::setHash()
*/
/**
* Use the Probabilistic Signature Scheme for signing
*
* Uses sha256 and 0 as the salt length
*
* @see self::setSaltLength()
* @see self::setMGFHash()
* @see self::setHash()
*/
const PADDING_PSS = 4;
/**
* Use a relaxed version of PKCS#1 padding for signature verification
*/
const PADDING_RELAXED_PKCS1 = 5;
/**#@-*/
/**
* Modulus (ie. n)
*
* @var \phpseclib\Math\BigInteger
* @access private
*/
private $modulus;
/**
* Modulus length
*
* @var \phpseclib\Math\BigInteger
* @access private
*/
private $k;
/**
* Exponent (ie. e or d)
*
* @var \phpseclib\Math\BigInteger
* @access private
*/
private $exponent;
/**
* Primes for Chinese Remainder Theorem (ie. p and q)
*
* @var array
* @access private
*/
private $primes;
/**
* Exponents for Chinese Remainder Theorem (ie. dP and dQ)
*
* @var array
* @access private
*/
private $exponents;
/**
* Coefficients for Chinese Remainder Theorem (ie. qInv)
*
* @var array
* @access private
*/
private $coefficients;
/**
* Hash name
*
* @var string
* @access private
*/
private $hashName;
/**
* Length of hash function output
*
* @var int
* @access private
*/
private $hLen;
/**
* Length of salt
*
* @var int
* @access private
*/
private $sLen;
/**
* Hash function for the Mask Generation Function
*
* @var \phpseclib\Crypt\Hash
* @access private
*/
private $mgfHash;
/**
* Length of MGF hash function output
*
* @var int
* @access private
*/
private $mgfHLen;
/**
* Public Exponent
*
* @var mixed
* @access private
*/
private $publicExponent = false;
/**
* Public exponent
*
* @var int
* @link http://en.wikipedia.org/wiki/65537_%28number%29
* @access private
*/
private static $defaultExponent = 65537;
/**
* Smallest Prime
*
* Per <http://cseweb.ucsd.edu/~hovav/dist/survey.pdf#page=5>, this number ought not result in primes smaller
* than 256 bits. As a consequence if the key you're trying to create is 1024 bits and you've set smallestPrime
* to 384 bits then you're going to get a 384 bit prime and a 640 bit prime (384 + 1024 % 384). At least if
* engine is set to self::ENGINE_INTERNAL. If Engine is set to self::ENGINE_OPENSSL then smallest Prime is
* ignored (ie. multi-prime RSA support is more intended as a way to speed up RSA key generation when there's
* a chance neither gmp nor OpenSSL are installed)
*
* @var int
* @access private
*/
private static $smallestPrime = 4096;
/**
* The constructor
*
* If you want to make use of the openssl extension, you'll need to set the mode manually, yourself. The reason
* \phpseclib\Crypt\RSA doesn't do it is because OpenSSL doesn't fail gracefully. openssl_pkey_new(), in particular, requires
* openssl.cnf be present somewhere and, unfortunately, the only real way to find out is too late.
*
* @return \phpseclib\Crypt\RSA
* @access public
*/
public function __construct()
{
parent::__construct();
//$this->hash = new Hash('sha256');
$this->hLen = $this->hash->getLengthInBytes();
$this->hashName = 'sha256';
$this->mgfHash = new Hash('sha256');
$this->mgfHLen = $this->mgfHash->getLengthInBytes();
}
/**
* Sets the public exponent
*
* This will be 65537 unless changed.
*
* @access public
* @param int $val
*/
public static function setExponent($val)
{
self::$defaultExponent = $val;
}
/**
* Sets the smallest prime number in bits
*
* This will be 4096 unless changed.
*
* @access public
* @param int $val
*/
public static function setSmallestPrime($val)
{
self::$smallestPrime = $val;
}
/**
* Create public / private key pair
*
* Returns an array with the following two elements:
* - 'privatekey': The private key.
* - 'publickey': The public key.
*
* @access public
* @param int $bits
* @param array $p
*/
public static function createKey($bits = 2048)
{
self::initialize_static_variables();
if (!isset(self::$engine)) {
self::setPreferredEngine(self::ENGINE_OPENSSL);
}
// OpenSSL uses 65537 as the exponent and requires RSA keys be 384 bits minimum
if (self::$engine == self::ENGINE_OPENSSL && $bits >= 384 && self::$defaultExponent == 65537) {
$config = [];
if (isset(self::$configFile)) {
$config['config'] = self::$configFile;
}
$rsa = openssl_pkey_new(['private_key_bits' => $bits] + $config);
openssl_pkey_export($rsa, $privatekeystr, null, $config);
$privatekey = new RSA();
$privatekey->load($privatekeystr);
$publickeyarr = openssl_pkey_get_details($rsa);
$publickey = new RSA();
$publickey->load($publickeyarr['key']);
$publickey->setPublicKey();
// clear the buffer of error strings stemming from a minimalistic openssl.cnf
while (openssl_error_string() !== false) {
}
return compact('privatekey', 'publickey');
}
static $e;
if (!isset($e)) {
$e = new BigInteger(self::$defaultExponent);
}
$regSize = $bits >> 1; // divide by two to see how many bits P and Q would be
if ($regSize > self::$smallestPrime) {
$num_primes = floor($bits / self::$smallestPrime);
$regSize = self::$smallestPrime;
} else {
$num_primes = 2;
}
$n = clone self::$one;
$exponents = $coefficients = $primes = [];
$lcm = [
'top' => clone self::$one,
'bottom' => false
];
do {
for ($i = 1; $i <= $num_primes; $i++) {
if ($i != $num_primes) {
$primes[$i] = BigInteger::randomPrime($regSize);
} else {
extract(BigInteger::minMaxBits($bits));
list($min) = $min->divide($n);
$min = $min->add(self::$one);
list($max) = $max->divide($n);
$primes[$i] = BigInteger::randomRangePrime($min, $max);
}
// the first coefficient is calculated differently from the rest
// ie. instead of being $primes[1]->modInverse($primes[2]), it's $primes[2]->modInverse($primes[1])
if ($i > 2) {
$coefficients[$i] = $n->modInverse($primes[$i]);
}
$n = $n->multiply($primes[$i]);
$temp = $primes[$i]->subtract(self::$one);
// textbook RSA implementations use Euler's totient function instead of the least common multiple.
// see http://en.wikipedia.org/wiki/Euler%27s_totient_function
$lcm['top'] = $lcm['top']->multiply($temp);
$lcm['bottom'] = $lcm['bottom'] === false ? $temp : $lcm['bottom']->gcd($temp);
}
list($temp) = $lcm['top']->divide($lcm['bottom']);
$gcd = $temp->gcd($e);
$i0 = 1;
} while (!$gcd->equals(self::$one));
$coefficients[2] = $primes[2]->modInverse($primes[1]);
$d = $e->modInverse($temp);
foreach ($primes as $i => $prime) {
$temp = $prime->subtract(self::$one);
$exponents[$i] = $e->modInverse($temp);
}
// from <http://tools.ietf.org/html/rfc3447#appendix-A.1.2>:
// RSAPrivateKey ::= SEQUENCE {
// version Version,
// modulus INTEGER, -- n
// publicExponent INTEGER, -- e
// privateExponent INTEGER, -- d
// prime1 INTEGER, -- p
// 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
// }
$privatekey = new RSA();
$privatekey->modulus = $n;
$privatekey->k = $bits >> 3;
$privatekey->publicExponent = $e;
$privatekey->exponent = $d;
$privatekey->privateExponent = $e;
$privatekey->primes = $primes;
$privatekey->exponents = $exponents;
$privatekey->coefficients = $coefficients;
$publickey = new RSA();
$publickey->modulus = $n;
$publickey->k = $bits >> 3;
$publickey->exponent = $e;
$publickey->publicExponent = $e;
return compact('privatekey', 'publickey');
}
/**
* 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 int $type optional
*/
public function load($key, $type = false)
{
if ($key instanceof RSA) {
$this->privateKeyFormat = $key->privateKeyFormat;
$this->publicKeyFormat = $key->publicKeyFormat;
$this->format = $key->format;
$this->k = $key->k;
$this->hLen = $key->hLen;
$this->sLen = $key->sLen;
$this->mgfHLen = $key->mgfHLen;
$this->password = $key->password;
if (is_object($key->hash)) {
$this->hash = new Hash($key->hash->getHash());
}
if (is_object($key->mgfHash)) {
$this->mgfHash = new Hash($key->mgfHash->getHash());
}
if (is_object($key->modulus)) {
$this->modulus = clone $key->modulus;
}
if (is_object($key->exponent)) {
$this->exponent = clone $key->exponent;
}
if (is_object($key->publicExponent)) {
$this->publicExponent = clone $key->publicExponent;
}
$this->primes = [];
$this->exponents = [];
$this->coefficients = [];
foreach ($this->primes as $prime) {
$this->primes[] = clone $prime;
}
foreach ($this->exponents as $exponent) {
$this->exponents[] = clone $exponent;
}
foreach ($this->coefficients as $coefficient) {
$this->coefficients[] = clone $coefficient;
}
return true;
}
$components = parent::load($key, $type);
if ($components === false) {
$this->comment = null;
$this->modulus = null;
$this->k = null;
$this->exponent = null;
$this->primes = null;
$this->exponents = null;
$this->coefficients = null;
$this->publicExponent = null;
return false;
}
$this->modulus = $components['modulus'];
$this->k = $this->modulus->getLengthInBytes();
$this->exponent = isset($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 = [];
$this->exponents = [];
$this->coefficients = [];
$this->publicExponent = false;
}
if ($components['isPublicKey']) {
$this->setPublicKey();
}
return true;
}
/**
* Returns the private key
*
* The private key is only returned if the currently loaded key contains the constituent prime numbers.
*
* @see self::getPublicKey()
* @access public
* @param string $type optional
* @return mixed
*/
public function getPrivateKey($type = 'PKCS8')
{
$type = self::validatePlugin('Keys', $type, 'savePrivateKey');
if ($type === false) {
return false;
}
if (empty($this->primes)) {
return false;
}
return $type::savePrivateKey($this->modulus, $this->publicExponent, $this->exponent, $this->primes, $this->exponents, $this->coefficients, $this->password);
/*
$key = $type::savePrivateKey($this->modulus, $this->publicExponent, $this->exponent, $this->primes, $this->exponents, $this->coefficients, $this->password);
if ($key !== false || count($this->primes) == 2) {
return $key;
}
$nSize = $this->getSize() >> 1;
$primes = [1 => clone self::$one, clone self::$one];
$i = 1;
foreach ($this->primes as $prime) {
$primes[$i] = $primes[$i]->multiply($prime);
if ($primes[$i]->getLength() >= $nSize) {
$i++;
}
}
$exponents = [];
$coefficients = [2 => $primes[2]->modInverse($primes[1])];
foreach ($primes as $i => $prime) {
$temp = $prime->subtract(self::$one);
$exponents[$i] = $this->modulus->modInverse($temp);
}
return $type::savePrivateKey($this->modulus, $this->publicExponent, $this->exponent, $primes, $exponents, $coefficients, $this->password);
*/
}
/**
* Returns a minimalistic private key
*
* Returns the private key without the prime number constituants. Structurally identical to a public key that
* hasn't been set as the public key
*
* @see self::getPrivateKey()
* @access private
* @param string $type optional
* @return mixed
*/
protected function getPrivatePublicKey($type = 'PKCS8')
{
$type = self::validatePlugin('Keys', $type, 'savePublicKey');
if ($type === false) {
return false;
}
if (empty($this->modulus) || empty($this->exponent)) {
return false;
}
$oldFormat = $this->publicKeyFormat;
$this->publicKeyFormat = $type;
$temp = $type::savePublicKey($this->modulus, $this->exponent);
$this->publicKeyFormat = $oldFormat;
return $temp;
}
/**
* Returns the key size
*
* More specifically, this returns the size of the modulo in bits.
*
* @access public
* @return int
*/
public function getLength()
{
return !isset($this->modulus) ? 0 : $this->modulus->getLength();
}
/**
* 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. phpseclib tries to guess if the key being used
* is the public key but in the event that it guesses incorrectly you might still want to explicitly set the key as being
* public.
*
* Do note that when a new key is loaded the index will be cleared.
*
* Returns true on success, false on failure
*
* @see self::getPublicKey()
* @access public
* @param string $key optional
* @param int $type optional
* @return bool
*/
public function setPublicKey($key = false, $type = false)
{
// if a public key has already been loaded return false
if (!empty($this->publicExponent)) {
return false;
}
if ($key === false && !empty($this->modulus)) {
$this->publicExponent = $this->exponent;
return true;
}
$components = parent::setPublicKey($key, $type);
if ($components === false) {
return false;
}
if (empty($this->modulus) || !$this->modulus->equals($components['modulus'])) {
$this->modulus = $components['modulus'];
$this->exponent = $this->publicExponent = $components['publicExponent'];
return true;
}
$this->publicExponent = $components['publicExponent'];
return true;
}
/**
* Defines the private key
*
* If phpseclib guessed a private key was a public key and loaded it as such it might be desirable to force
* phpseclib to treat the key as a private key. This function will do that.
*
* Do note that when a new key is loaded the index will be cleared.
*
* Returns true on success, false on failure
*
* @see self::getPublicKey()
* @access public
* @param string $key optional
* @param int $type optional
* @return bool
*/
public function setPrivateKey($key = false, $type = false)
{
if ($key === false && !empty($this->publicExponent)) {
$this->publicExponent = false;
return true;
}
$rsa = new RSA();
if (!$rsa->load($key, $type)) {
return false;
}
$rsa->publicExponent = false;
// don't overwrite the old key if the new key is invalid
$this->load($rsa);
return true;
}
/**
* 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 self::getPrivateKey()
* @access public
* @param string $type optional
* @return mixed
*/
public function getPublicKey($type = 'PKCS8')
{
$type = self::validatePlugin('Keys', $type, 'savePublicKey');
if ($type === false) {
return false;
}
if (empty($this->modulus) || empty($this->publicExponent)) {
return false;
}
return $type::savePublicKey($this->modulus, $this->publicExponent);
}
/**
* __toString() magic method
*
* @access public
* @return string
*/
public function __toString()
{
try {
$key = $this->getPrivateKey($this->privateKeyFormat);
if (is_string($key)) {
return $key;
}
$key = $this->getPrivatePublicKey($this->publicKeyFormat);
return is_string($key) ? $key : '';
} catch (\Exception $e) {
return '';
}
}
/**
* Determines which hashing function should be used
*
* Used with signature production / verification and (if the encryption mode is self::PADDING_OAEP) encryption and
* decryption.
*
* @access public
* @param string $hash
*/
public function setHash($hash)
{
// \phpseclib\Crypt\Hash supports algorithms that PKCS#1 doesn't support. md5-96 and sha1-96, for example.
switch (strtolower($hash)) {
case 'md2':
case 'md5':
case 'sha1':
case 'sha256':
case 'sha384':
case 'sha512':
case 'sha224':
case 'sha512/224':
case 'sha512/256':
$this->hash = new Hash($hash);
$this->hashName = $hash;
break;
default:
throw new UnsupportedAlgorithmException(
'The only supported hash algorithms are: md2, md5, sha1, sha256, sha384, sha512, sha224, sha512/224, sha512/256'
);
}
$this->hLen = $this->hash->getLengthInBytes();
}
/**
* Determines which hashing function should be used for the mask generation function
*
* The mask generation function is used by self::PADDING_OAEP and self::PADDING_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 $hash
*/
public function setMGFHash($hash)
{
// \phpseclib\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':
case 'sha224':
case 'sha512/224':
case 'sha512/256':
$this->mgfHash = new Hash($hash);
break;
default:
$this->mgfHash = new Hash('sha256');
}
$this->mgfHLen = $this->mgfHash->getLengthInBytes();
}
/**
* 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 int $format
*/
public function setSaltLength($sLen)
{
$this->sLen = $sLen;
}
/**
* Integer-to-Octet-String primitive
*
* See {@link http://tools.ietf.org/html/rfc3447#section-4.1 RFC3447#section-4.1}.
*
* @access private
* @param bool|\phpseclib\Math\BigInteger $x
* @param int $xLen
* @return bool|string
*/
private function i2osp($x, $xLen)
{
if ($x === false) {
return false;
}
$x = $x->toBytes();
if (strlen($x) > $xLen) {
return false;
}
return str_pad($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 $x
* @return \phpseclib\Math\BigInteger
*/
private function os2ip($x)
{
return new 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 \phpseclib\Math\BigInteger $x
* @return \phpseclib\Math\BigInteger
*/
private function exponentiate($x)
{
switch (true) {
case empty($this->primes):
case $this->primes[1]->equals(self::$zero):
case empty($this->coefficients):
case $this->coefficients[2]->equals(self::$zero):
case empty($this->exponents):
case $this->exponents[1]->equals(self::$zero):
return $x->modPow($this->exponent, $this->modulus);
}
$num_primes = count($this->primes);
if (defined('CRYPT_RSA_DISABLE_BLINDING')) {
$m_i = [
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];
}
}
$r = BigInteger::randomRange(self::$one, $smallest->subtract(self::$one));
$m_i = [
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 \phpseclib\Math\BigInteger $x
* @param \phpseclib\Math\BigInteger $r
* @param int $i
* @return \phpseclib\Math\BigInteger
*/
private function blind($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 \phpseclib\Math\BigInteger $m
* @return bool|\phpseclib\Math\BigInteger
*/
private function rsaep($m)
{
if ($m->compare(self::$zero) < 0 || $m->compare($this->modulus) > 0) {
return false;
}
return $this->exponentiate($m);
}
/**
* RSADP
*
* See {@link http://tools.ietf.org/html/rfc3447#section-5.1.2 RFC3447#section-5.1.2}.
*
* @access private
* @param \phpseclib\Math\BigInteger $c
* @return bool|\phpseclib\Math\BigInteger
*/
private function rsadp($c)
{
if ($c->compare(self::$zero) < 0 || $c->compare($this->modulus) > 0) {
return false;
}
return $this->exponentiate($c);
}
/**
* RSASP1
*
* See {@link http://tools.ietf.org/html/rfc3447#section-5.2.1 RFC3447#section-5.2.1}.
*
* @access private
* @param \phpseclib\Math\BigInteger $m
* @return bool|\phpseclib\Math\BigInteger
*/
private function rsasp1($m)
{
if ($m->compare(self::$zero) < 0 || $m->compare($this->modulus) > 0) {
return false;
}
return $this->exponentiate($m);
}
/**
* RSAVP1
*
* See {@link http://tools.ietf.org/html/rfc3447#section-5.2.2 RFC3447#section-5.2.2}.
*
* @access private
* @param \phpseclib\Math\BigInteger $s
* @return bool|\phpseclib\Math\BigInteger
*/
private function rsavp1($s)
{
if ($s->compare(self::$zero) < 0 || $s->compare($this->modulus) > 0) {
return false;
}
return $this->exponentiate($s);
}
/**
* MGF1
*
* See {@link http://tools.ietf.org/html/rfc3447#appendix-B.2.1 RFC3447#appendix-B.2.1}.
*
* @access private
* @param string $mgfSeed
* @param int $mgfLen
* @return string
*/
private function mgf1($mgfSeed, $maskLen)
{
// if $maskLen would yield strings larger than 4GB, PKCS#1 suggests a "Mask too long" error be output.
$t = '';
$count = ceil($maskLen / $this->mgfHLen);
for ($i = 0; $i < $count; $i++) {
$c = pack('N', $i);
$t.= $this->mgfHash->hash($mgfSeed . $c);
}
return substr($t, 0, $maskLen);
}
/**
* RSAES-OAEP-ENCRYPT
*
* See {@link http://tools.ietf.org/html/rfc3447#section-7.1.1 RFC3447#section-7.1.1} and
* {http://en.wikipedia.org/wiki/Optimal_Asymmetric_Encryption_Padding OAES}.
*
* @access private
* @param string $m
* @param string $l
* @throws \OutOfBoundsException if strlen($m) > $this->k - 2 * $this->hLen - 2
* @return string
*/
private function rsaes_oaep_encrypt($m, $l = '')
{
$mLen = strlen($m);
// Length checking
// if $l is larger than two million terrabytes and you're using sha1, PKCS#1 suggests a "Label too long" error
// be output.
if ($mLen > $this->k - 2 * $this->hLen - 2) {
throw new \OutOfBoundsException('Message too long');
}
// EME-OAEP encoding
$lHash = $this->hash->hash($l);
$ps = str_repeat(chr(0), $this->k - $mLen - 2 * $this->hLen - 2);
$db = $lHash . $ps . chr(1) . $m;
$seed = Random::string($this->hLen);
$dbMask = $this->mgf1($seed, $this->k - $this->hLen - 1);
$maskedDB = $db ^ $dbMask;
$seedMask = $this->mgf1($maskedDB, $this->hLen);
$maskedSeed = $seed ^ $seedMask;
$em = chr(0) . $maskedSeed . $maskedDB;
// RSA encryption
$m = $this->os2ip($em);
$c = $this->rsaep($m);
$c = $this->i2osp($c, $this->k);
// Output the ciphertext C
return $c;
}
/**
* RSAES-OAEP-DECRYPT
*
* See {@link http://tools.ietf.org/html/rfc3447#section-7.1.2 RFC3447#section-7.1.2}. The fact that the error
* messages aren't distinguishable from one another hinders debugging, but, to quote from RFC3447#section-7.1.2:
*
* Note. Care must be taken to ensure that an opponent cannot
* distinguish the different error conditions in Step 3.g, whether by
* error message or timing, or, more generally, learn partial
* information about the encoded message EM. Otherwise an opponent may
* be able to obtain useful information about the decryption of the
* ciphertext C, leading to a chosen-ciphertext attack such as the one
* observed by Manger [36].
*
* As for $l... to quote from {@link http://tools.ietf.org/html/rfc3447#page-17 RFC3447#page-17}:
*
* Both the encryption and the decryption operations of RSAES-OAEP take
* the value of a label L as input. In this version of PKCS #1, L is
* the empty string; other uses of the label are outside the scope of
* this document.
*
* @access private
* @param string $c
* @param string $l
* @return bool|string
*/
private function rsaes_oaep_decrypt($c, $l = '')
{
// Length checking
// if $l is larger than two million terrabytes and you're using sha1, PKCS#1 suggests a "Label too long" error
// be output.
if (strlen($c) != $this->k || $this->k < 2 * $this->hLen + 2) {
return false;
}
// RSA decryption
$c = $this->os2ip($c);
$m = $this->rsadp($c);
$em = $this->i2osp($m, $this->k);
if ($em === false) {
return false;
}
// EME-OAEP decoding
$lHash = $this->hash->hash($l);
$y = ord($em[0]);
$maskedSeed = substr($em, 1, $this->hLen);
$maskedDB = substr($em, $this->hLen + 1);
$seedMask = $this->mgf1($maskedDB, $this->hLen);
$seed = $maskedSeed ^ $seedMask;
$dbMask = $this->mgf1($seed, $this->k - $this->hLen - 1);
$db = $maskedDB ^ $dbMask;
$lHash2 = substr($db, 0, $this->hLen);
$m = substr($db, $this->hLen);
if (!Strings::equals($lHash, $lHash2)) {
return false;
}
$m = ltrim($m, chr(0));
if (ord($m[0]) != 1) {
return false;
}
// Output the message M
return substr($m, 1);
}
/**
* Raw Encryption / Decryption
*
* Doesn't use padding and is not recommended.
*
* @access private
* @param string $m
* @return bool|string
* @throws \OutOfBoundsException if strlen($m) > $this->k
*/
private function raw_encrypt($m)
{
if (strlen($m) > $this->k) {
throw new \OutOfBoundsException('Message too long');
}
$temp = $this->os2ip($m);
$temp = $this->rsaep($temp);
return $this->i2osp($temp, $this->k);
}
/**
* RSAES-PKCS1-V1_5-ENCRYPT
*
* See {@link http://tools.ietf.org/html/rfc3447#section-7.2.1 RFC3447#section-7.2.1}.
*
* @access private
* @param string $m
* @param bool $pkcs15_compat optional
* @throws \OutOfBoundsException if strlen($m) > $this->k - 11
* @return bool|string
*/
private function rsaes_pkcs1_v1_5_encrypt($m, $pkcs15_compat = false)
{
$mLen = strlen($m);
// Length checking
if ($mLen > $this->k - 11) {
throw new \OutOfBoundsException('Message too long');
}
// EME-PKCS1-v1_5 encoding
$psLen = $this->k - $mLen - 3;
$ps = '';
while (strlen($ps) != $psLen) {
$temp = Random::string($psLen - strlen($ps));
$temp = str_replace("\x00", '', $temp);
$ps.= $temp;
}
$type = 2;
// see the comments of _rsaes_pkcs1_v1_5_decrypt() to understand why this is being done
if ($pkcs15_compat && (!isset($this->publicExponent) || $this->exponent !== $this->publicExponent)) {
$type = 1;
// "The padding string PS shall consist of k-3-||D|| octets. ... for block type 01, they shall have value FF"
$ps = str_repeat("\xFF", $psLen);
}
$em = chr(0) . chr($type) . $ps . chr(0) . $m;
// RSA encryption
$m = $this->os2ip($em);
$c = $this->rsaep($m);
$c = $this->i2osp($c, $this->k);
// Output the ciphertext C
return $c;
}
/**
* RSAES-PKCS1-V1_5-DECRYPT
*
* See {@link http://tools.ietf.org/html/rfc3447#section-7.2.2 RFC3447#section-7.2.2}.
*
* For compatibility purposes, this function departs slightly from the description given in RFC3447.
* The reason being that RFC2313#section-8.1 (PKCS#1 v1.5) states that ciphertext's encrypted by the
* private key should have the second byte set to either 0 or 1 and that ciphertext's encrypted by the
* public key should have the second byte set to 2. In RFC3447 (PKCS#1 v2.1), the second byte is supposed
* to be 2 regardless of which key is used. For compatibility purposes, we'll just check to make sure the
* second byte is 2 or less. If it is, we'll accept the decrypted string as valid.
*
* As a consequence of this, a private key encrypted ciphertext produced with \phpseclib\Crypt\RSA may not decrypt
* with a strictly PKCS#1 v1.5 compliant RSA implementation. Public key encrypted ciphertext's should but
* not private key encrypted ciphertext's.
*
* @access private
* @param string $c
* @return bool|string
*/
private function rsaes_pkcs1_v1_5_decrypt($c)
{
// Length checking
if (strlen($c) != $this->k) { // or if k < 11
return false;
}
// RSA decryption
$c = $this->os2ip($c);
$m = $this->rsadp($c);
$em = $this->i2osp($m, $this->k);
if ($em === false) {
return false;
}
// EME-PKCS1-v1_5 decoding
if (ord($em[0]) != 0 || ord($em[1]) > 2) {
return false;
}
$ps = substr($em, 2, strpos($em, chr(0), 2) - 2);
$m = substr($em, strlen($ps) + 3);
if (strlen($ps) < 8) {
return false;
}
// Output M
return $m;
}
/**
* EMSA-PSS-ENCODE
*
* See {@link http://tools.ietf.org/html/rfc3447#section-9.1.1 RFC3447#section-9.1.1}.
*
* @access private
* @param string $m
* @throws \RuntimeException on encoding error
* @param int $emBits
*/
private function emsa_pss_encode($m, $emBits)
{
// if $m is larger than two million terrabytes and you're using sha1, PKCS#1 suggests a "Label too long" error
// be output.
$emLen = ($emBits + 1) >> 3; // ie. ceil($emBits / 8)
$sLen = $this->sLen !== null ? $this->sLen : $this->hLen;
$mHash = $this->hash->hash($m);
if ($emLen < $this->hLen + $sLen + 2) {
return false;
}
$salt = Random::string($sLen);
$m2 = "\0\0\0\0\0\0\0\0" . $mHash . $salt;
$h = $this->hash->hash($m2);
$ps = str_repeat(chr(0), $emLen - $sLen - $this->hLen - 2);
$db = $ps . chr(1) . $salt;
$dbMask = $this->mgf1($h, $emLen - $this->hLen - 1);
$maskedDB = $db ^ $dbMask;
$maskedDB[0] = ~chr(0xFF << ($emBits & 7)) & $maskedDB[0];
$em = $maskedDB . $h . chr(0xBC);
return $em;
}
/**
* EMSA-PSS-VERIFY
*
* See {@link http://tools.ietf.org/html/rfc3447#section-9.1.2 RFC3447#section-9.1.2}.
*
* @access private
* @param string $m
* @param string $em
* @param int $emBits
* @return string
*/
private function emsa_pss_verify($m, $em, $emBits)
{
// if $m is larger than two million terrabytes and you're using sha1, PKCS#1 suggests a "Label too long" error
// be output.
$emLen = ($emBits + 1) >> 3; // ie. ceil($emBits / 8);
$sLen = $this->sLen !== null ? $this->sLen : $this->hLen;
$mHash = $this->hash->hash($m);
if ($emLen < $this->hLen + $sLen + 2) {
return false;
}
if ($em[strlen($em) - 1] != chr(0xBC)) {
return false;
}
$maskedDB = substr($em, 0, -$this->hLen - 1);
$h = substr($em, -$this->hLen - 1, $this->hLen);
$temp = chr(0xFF << ($emBits & 7));
if ((~$maskedDB[0] & $temp) != $temp) {
return false;
}
$dbMask = $this->mgf1($h, $emLen - $this->hLen - 1);
$db = $maskedDB ^ $dbMask;
$db[0] = ~chr(0xFF << ($emBits & 7)) & $db[0];
$temp = $emLen - $this->hLen - $sLen - 2;
if (substr($db, 0, $temp) != str_repeat(chr(0), $temp) || ord($db[$temp]) != 1) {
return false;
}
$salt = substr($db, $temp + 1); // should be $sLen long
$m2 = "\0\0\0\0\0\0\0\0" . $mHash . $salt;
$h2 = $this->hash->hash($m2);
return Strings::equals($h, $h2);
}
/**
* RSASSA-PSS-SIGN
*
* See {@link http://tools.ietf.org/html/rfc3447#section-8.1.1 RFC3447#section-8.1.1}.
*
* @access private
* @param string $m
* @return bool|string
*/
private function rsassa_pss_sign($m)
{
// EMSA-PSS encoding
$em = $this->emsa_pss_encode($m, 8 * $this->k - 1);
// RSA signature
$m = $this->os2ip($em);
$s = $this->rsasp1($m);
$s = $this->i2osp($s, $this->k);
// Output the signature S
return $s;
}
/**
* RSASSA-PSS-VERIFY
*
* See {@link http://tools.ietf.org/html/rfc3447#section-8.1.2 RFC3447#section-8.1.2}.
*
* @access private
* @param string $m
* @param string $s
* @return bool|string
*/
private function rsassa_pss_verify($m, $s)
{
// Length checking
if (strlen($s) != $this->k) {
return false;
}
// RSA verification
$modBits = 8 * $this->k;
$s2 = $this->os2ip($s);
$m2 = $this->rsavp1($s2);
$em = $this->i2osp($m2, $modBits >> 3);
if ($em === false) {
return false;
}
// EMSA-PSS verification
return $this->emsa_pss_verify($m, $em, $modBits - 1);
}
/**
* EMSA-PKCS1-V1_5-ENCODE
*
* See {@link http://tools.ietf.org/html/rfc3447#section-9.2 RFC3447#section-9.2}.
*
* @access private
* @param string $m
* @param int $emLen
* @throws \LengthException if the intended encoded message length is too short
* @return string
*/
private function emsa_pkcs1_v1_5_encode($m, $emLen)
{
$h = $this->hash->hash($m);
// see http://tools.ietf.org/html/rfc3447#page-43
switch ($this->hashName) {
case 'md2':
$t = "\x30\x20\x30\x0c\x06\x08\x2a\x86\x48\x86\xf7\x0d\x02\x02\x05\x00\x04\x10";
break;
case 'md5':
$t = "\x30\x20\x30\x0c\x06\x08\x2a\x86\x48\x86\xf7\x0d\x02\x05\x05\x00\x04\x10";
break;
case 'sha1':
$t = "\x30\x21\x30\x09\x06\x05\x2b\x0e\x03\x02\x1a\x05\x00\x04\x14";
break;
case 'sha256':
$t = "\x30\x31\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x01\x05\x00\x04\x20";
break;
case 'sha384':
$t = "\x30\x41\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x02\x05\x00\x04\x30";
break;
case 'sha512':
$t = "\x30\x51\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x03\x05\x00\x04\x40";
break;
// from https://www.emc.com/collateral/white-papers/h11300-pkcs-1v2-2-rsa-cryptography-standard-wp.pdf#page=40
case 'sha224':
$t = "\x30\x2d\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x04\x05\x00\x04\x1c";
break;
case 'sha512/224':
$t = "\x30\x2d\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x05\x05\x00\x04\x1c";
break;
case 'sha512/256':
$t = "\x30\x31\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x06\x05\x00\x04\x20";
}
$t.= $h;
$tLen = strlen($t);
if ($emLen < $tLen + 11) {
throw new \LengthException('Intended encoded message length too short');
}
$ps = str_repeat(chr(0xFF), $emLen - $tLen - 3);
$em = "\0\1$ps\0$t";
return $em;
}
/**
* RSASSA-PKCS1-V1_5-SIGN
*
* See {@link http://tools.ietf.org/html/rfc3447#section-8.2.1 RFC3447#section-8.2.1}.
*
* @access private
* @param string $m
* @throws \LengthException if the RSA modulus is too short
* @return bool|string
*/
private function rsassa_pkcs1_v1_5_sign($m)
{
// EMSA-PKCS1-v1_5 encoding
// If the encoding operation outputs "intended encoded message length too short," output "RSA modulus
// too short" and stop.
try {
$em = $this->emsa_pkcs1_v1_5_encode($m, $this->k);
} catch (\LengthException $e) {
throw new \LengthException('RSA modulus too short');
}
// RSA signature
$m = $this->os2ip($em);
$s = $this->rsasp1($m);
$s = $this->i2osp($s, $this->k);
// Output the signature S
return $s;
}
/**
* RSASSA-PKCS1-V1_5-VERIFY
*
* See {@link http://tools.ietf.org/html/rfc3447#section-8.2.2 RFC3447#section-8.2.2}.
*
* @access private
* @param string $m
* @param string $s
* @throws \LengthException if the RSA modulus is too short
* @return bool
*/
private function rsassa_pkcs1_v1_5_verify($m, $s)
{
// Length checking
if (strlen($s) != $this->k) {
return false;
}
// RSA verification
$s = $this->os2ip($s);
$m2 = $this->rsavp1($s);
$em = $this->i2osp($m2, $this->k);
if ($em === false) {
return false;
}
// EMSA-PKCS1-v1_5 encoding
// If the encoding operation outputs "intended encoded message length too short," output "RSA modulus
// too short" and stop.
try {
$em2 = $this->emsa_pkcs1_v1_5_encode($m, $this->k);
} catch (\LengthException $e) {
throw new \LengthException('RSA modulus too short');
}
// Compare
return Strings::equals($em, $em2);
}
/**
* RSASSA-PKCS1-V1_5-VERIFY (relaxed matching)
*
* Per {@link http://tools.ietf.org/html/rfc3447#page-43 RFC3447#page-43} PKCS1 v1.5
* specified the use BER encoding rather than DER encoding that PKCS1 v2.0 specified.
* This means that under rare conditions you can have a perfectly valid v1.5 signature
* that fails to validate with _rsassa_pkcs1_v1_5_verify(). PKCS1 v2.1 also recommends
* that if you're going to validate these types of signatures you "should indicate
* whether the underlying BER encoding is a DER encoding and hence whether the signature
* is valid with respect to the specification given in [PKCS1 v2.0+]". so if you do
* $rsa->getLastPadding() and get RSA::PADDING_RELAXED_PKCS1 back instead of
* RSA::PADDING_PKCS1... that means BER encoding was used.
*
* @access private
* @param string $m
* @param string $s
* @return bool
*/
private function rsassa_pkcs1_v1_5_relaxed_verify($m, $s)
{
// Length checking
if (strlen($s) != $this->k) {
return false;
}
// RSA verification
$s = $this->os2ip($s);
$m2 = $this->rsavp1($s);
if ($m2 === false) {
return false;
}
$em = $this->i2osp($m2, $this->k);
if ($em === false) {
return false;
}
if (Strings::shift($em, 2) != "\0\1") {
return false;
}
$em = ltrim($em, "\xFF");
if (Strings::shift($em) != "\0") {
return false;
}
$decoded = ASN1::decodeBER($em);
if (!is_array($decoded) || empty($decoded[0]) || strlen($em) > $decoded[0]['length']) {
return false;
}
static $oids;
if (!isset($oids)) {
$oids = [
'1.2.840.113549.2.2' => 'md2',
'1.2.840.113549.2.4' => 'md4', // from PKCS1 v1.5
'1.2.840.113549.2.5' => 'md5',
'1.3.14.3.2.26' => 'id-sha1',
'2.16.840.1.101.3.4.2.1' => 'id-sha256',
'2.16.840.1.101.3.4.2.2' => 'id-sha384',
'2.16.840.1.101.3.4.2.3' => 'id-sha512',
// from PKCS1 v2.2
'2.16.840.1.101.3.4.2.4' => 'id-sha224',
'2.16.840.1.101.3.4.2.5' => 'id-sha512/224',
'2.16.840.1.101.3.4.2.6' => 'id-sha512/256',
];
ASN1::loadOIDs($oids);
}
$decoded = ASN1::asn1map($decoded[0], DigestInfo::MAP);
if (!isset($decoded) || $decoded === false) {
return false;
}
if (!in_array($decoded['digestAlgorithm']['algorithm'], $oids)) {
return false;
}
$hash = $decoded['digestAlgorithm']['algorithm'];
$hash = substr($hash, 0, 3) == 'id-' ?
substr($hash, 3) :
$hash;
$hash = new Hash($hash);
$em = $hash->hash($m);
$em2 = $decoded['digest'];
return Strings::equals($em, $em2);
}
/**
* Encryption
*
* Both self::PADDING_OAEP and self::PADDING_PKCS1 both place limits on how long $plaintext can be.
* If $plaintext exceeds those limits it will be broken up so that it does and the resultant ciphertext's will
* be concatenated together.
*
* @see self::decrypt()
* @access public
* @param string $plaintext
* @param int $padding optional
* @return bool|string
* @throws \LengthException if the RSA modulus is too short
*/
public function encrypt($plaintext, $padding = self::PADDING_OAEP)
{
switch ($padding) {
case self::PADDING_NONE:
return $this->raw_encrypt($plaintext);
case self::PADDING_PKCS15_COMPAT:
case self::PADDING_PKCS1:
return $this->rsaes_pkcs1_v1_5_encrypt($plaintext, $padding == self::PADDING_PKCS15_COMPAT);
//case self::PADDING_OAEP:
default:
return $this->rsaes_oaep_encrypt($plaintext);
}
}
/**
* Decryption
*
* @see self::encrypt()
* @access public
* @param string $plaintext
* @param int $padding optional
* @return bool|string
*/
public function decrypt($ciphertext, $padding = self::PADDING_OAEP)
{
switch ($padding) {
case self::PADDING_NONE:
return $this->raw_encrypt($ciphertext);
case self::PADDING_PKCS1:
return $this->rsaes_pkcs1_v1_5_decrypt($ciphertext);
//case self::PADDING_OAEP:
default:
return $this->rsaes_oaep_decrypt($ciphertext);
}
}
/**
* Create a signature
*
* @see self::verify()
* @access public
* @param string $message
* @param int $padding optional
* @return string
*/
public function sign($message, $padding = self::PADDING_PSS)
{
if (empty($this->modulus) || empty($this->exponent)) {
return false;
}
switch ($padding) {
case self::PADDING_PKCS1:
case self::PADDING_RELAXED_PKCS1:
return $this->rsassa_pkcs1_v1_5_sign($message);
//case self::PADDING_PSS:
default:
return $this->rsassa_pss_sign($message);
}
}
/**
* Verifies a signature
*
* @see self::sign()
* @access public
* @param string $message
* @param string $signature
* @param int $padding optional
* @return bool
*/
public function verify($message, $signature, $padding = self::PADDING_PSS)
{
if (empty($this->modulus) || empty($this->exponent)) {
return false;
}
switch ($padding) {
case self::PADDING_RELAXED_PKCS1:
return $this->rsassa_pkcs1_v1_5_relaxed_verify($message, $signature);
case self::PADDING_PKCS1:
return $this->rsassa_pkcs1_v1_5_verify($message, $signature);
//case self::PADDING_PSS:
default:
return $this->rsassa_pss_verify($message, $signature);
}
}
}
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