php下的RSA算法实现

/*
* 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);
}

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