<?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); } /* * 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); $idx++; } array_pus($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, $offset + 1); } //-- // Convert binary data to a decimal number //-- function binary_to_number($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); } ?>