<?php
/*
 * PHP implementation of the RSA algorithm
 * (C) Copyright 2004 Edsko de Vries, Ireland
 *
 * Licensed under the GNU Public License (GPL)
 *
 * This implementation has been verified against [3] 
 * (tested Java/PHP interoperability).
 *
 * References:
 * [1] "Applied Cryptography", Bruce Schneier, John Wiley & Sons, 1996
 * [2] "Prime Number Hide-and-Seek", Brian Raiter, Muppetlabs (online)
 * [3] "The Bouncy Castle Crypto Package", Legion of the Bouncy Castle,
 *      (open source cryptography library for Java, online)
 * [4] "PKCS #1: RSA Encryption Standard", RSA Laboratories Technical Note,
 *      version 1.5, revised November 1, 1993
 */

/*
 * Functions that are meant to be used by the user of this PHP module.
 *
 * Notes:
 * - $key and $modulus should be numbers in (decimal) string format
 * - $message is expected to be binary data
 * - $keylength should be a multiple of 8, and should be in bits
 * - For rsa_encrypt/rsa_sign, the length of $message should not exceed 
 *   ($keylength / 8) - 11 (as mandated by [4]).
 * - rsa_encrypt and rsa_sign will automatically add padding to the message. 
 *   For rsa_encrypt, this padding will consist of random values; for rsa_sign,
 *   padding will consist of the appropriate number of 0xFF values (see [4])
 * - rsa_decrypt and rsa_verify will automatically remove message padding.
 * - Blocks for decoding (rsa_decrypt, rsa_verify) should be exactly 
 *   ($keylength / 8) bytes long.
 * - rsa_encrypt and rsa_verify expect a public key; rsa_decrypt and rsa_sign
 *   expect a private key.
 */

function rsa_encrypt($message, $public_key, $modulus, $keylength)
{
	$padded = add_PKCS1_padding($message, true, $keylength / 8);
	$number = binary_to_number($padded);
	$encrypted = pow_mod($number, $public_key, $modulus);
	$result = number_to_binary($encrypted, $keylength / 8);
	
	return $result;
}

function rsa_decrypt($message, $private_key, $modulus, $keylength)
{
	$number = binary_to_number($message);
	$decrypted = pow_mod($number, $private_key, $modulus);
	$result = number_to_binary($decrypted, $keylength / 8);

	return remove_PKCS1_padding($result, $keylength / 8);
}

function rsa_sign($message, $private_key, $modulus, $keylength)
{
	$padded = add_PKCS1_padding($message, false, $keylength / 8);
	$number = binary_to_number($padded);
	$signed = pow_mod($number, $private_key, $modulus);
	$result = number_to_binary($signed, $keylength / 8);

	return $result;
}

function rsa_verify($message, $public_key, $modulus, $keylength)
{
	return rsa_decrypt($message, $public_key, $modulus, $keylength);
}

function rsa_kyp_verify($message, $public_key, $modulus, $keylength)
{
	$number = binary_to_number($message);
	$decrypted = pow_mod($number, $public_key, $modulus);
	$result = number_to_binary($decrypted, $keylength / 8);

	return remove_KYP_padding($result, $keylength / 8);
}

/*
 * Some constants
 */

define("BCCOMP_LARGER", 1);

/*
 * The actual implementation.
 * Requires BCMath support in PHP (compile with --enable-bcmath)
 */

//--
// Calculate (p ^ q) mod r 
//
// We need some trickery to [2]:
//   (a) Avoid calculating (p ^ q) before (p ^ q) mod r, because for typical RSA
//       applications, (p ^ q) is going to be _WAY_ too large.
//       (I mean, __WAY__ too large - won't fit in your computer's memory.)
//   (b) Still be reasonably efficient.
//
// We assume p, q and r are all positive, and that r is non-zero.
//
// Note that the more simple algorithm of multiplying $p by itself $q times, and
// applying "mod $r" at every step is also valid, but is O($q), whereas this
// algorithm is O(log $q). Big difference.
//
// As far as I can see, the algorithm I use is optimal; there is no redundancy
// in the calculation of the partial results. 
//--
function pow_mod($p, $q, $r)
{
	// Extract powers of 2 from $q
	$factors = array();
	$div = $q;
	$power_of_two = 0;
	while(bccomp($div, "0") == BCCOMP_LARGER)
	{
		$rem = bcmod($div, 2);
		$div = bcdiv($div, 2);
	
		if($rem) array_push($factors, $power_of_two);
		$power_of_two++;
	}

	// Calculate partial results for each factor, using each partial result as a
	// starting point for the next. This depends of the factors of two being
	// generated in increasing order.
	$partial_results = array();
	$part_res = $p;
	$idx = 0;
	foreach($factors as $factor)
	{
		while($idx < $factor)
		{
			$part_res = bcpow($part_res, "2");
			$part_res = bcmod($part_res, $r);

			$idx++;
		}
		
		array_push($partial_results, $part_res);
	}

	// Calculate final result
	$result = "1";
	foreach($partial_results as $part_res)
	{
		$result = bcmul($result, $part_res);
		$result = bcmod($result, $r);
	}

	return $result;
}

//--
// Function to add padding to a decrypted string
// We need to know if this is a private or a public key operation [4]
//--
function add_PKCS1_padding($data, $isPublicKey, $blocksize)
{
	$pad_length = $blocksize - 3 - strlen($data);

	if($isPublicKey)
	{
		$block_type = "\x02";
	
		$padding = "";
		for($i = 0; $i < $pad_length; $i++)
		{
			$rnd = mt_rand(1, 255);
			$padding .= chr($rnd);
		}
	}
	else
	{
		$block_type = "\x01";
		$padding = str_repeat("\xFF", $pad_length);
	}
	
	return "\x00" . $block_type . $padding . "\x00" . $data;
}

//--
// Remove padding from a decrypted string
// See [4] for more details.
//--
function remove_PKCS1_padding($data, $blocksize)
{
	assert(strlen($data) == $blocksize);
	$data = substr($data, 1);

	// We cannot deal with block type 0
	if($data{0} == '\0')
		die("Block type 0 not implemented.");

	// Then the block type must be 1 or 2 
	assert(($data{0} == "\x01") || ($data{0} == "\x02"));

	// Remove the padding
	$offset = strpos($data, "\0", 1);
	return substr($data, $offset + 1);
}

//--
// Remove "kyp" padding
// (Non standard)
//--
function remove_KYP_padding($data, $blocksize)
{
	assert(strlen($data) == $blocksize);
	
	$offset = strpos($data, "\0");
	return substr($data, 0, $offset);
}

//--
// Convert binary data to a decimal number
//--
function binary_to_number($data)
{
	$base = "256";
	$radix = "1";
	$result = "0";

	for($i = strlen($data) - 1; $i >= 0; $i--)
	{
		$digit = ord($data{$i});
		$part_res = bcmul($digit, $radix);
		$result = bcadd($result, $part_res);
		$radix = bcmul($radix, $base);
	}

	return $result;
}

//--
// Convert a number back into binary form
//--
function number_to_binary($number, $blocksize)
{
	$base = "256";
	$result = "";

	$div = $number;
	while($div > 0)
	{
		$mod = bcmod($div, $base);
		$div = bcdiv($div, $base);
		
		$result = chr($mod) . $result;
	}

	return str_pad($result, $blocksize, "\x00", STR_PAD_LEFT);
}
?>