程序代码：

<?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)
{
   
   
    $data = substr($data, 1);

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




    // Remove the padding
    $i=1;
    while (1){
        $offset = strpos($data, "\0", $i);
        if(!$offset){
            $offset=$i;
            break;
        }
        $i=$offset+1;
    }
   
    return substr($data, $offset);
}

//--
// 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);
}
?>