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);
}
?>