Note: I didn’t really make these classes to be portable, so in the RSA_Handler class, there are a few things that I did my own way (mostly in the generate_keys and encrypt functions), but you should still be able to see how it works. If you want the most basic usage, use an RSA_keymaker object and the make_keys function. The function will return an array of keys (in number form) where $keys[0] is the public key, $keys[1] is the private key and $keys[2] is the modulo. The keys generated with the default function are around 1024 bits (a 310 digit modulo).

In the future I’ll probably tweak these so that they’re useable on any PHP build (after 4.0 or so).

EDIT: I have updated the code! It is now 100% portable and full functioning. The only thing I have left out is the ability to encrypt the private key, but there are several pure PHP implementations of AES, DES3, Blowfish etc. which can be used to encrypt a private key for storage. This is released under the GPL Licence. Do whatever you want with it, but know there’s no warranty express or implied. My work here is done

UPDATE: The code is now more efficient, and uses number of bits to determine key sizes (instead of number of digits). The version number is included in the code so you can always check to see if there is a newer version available (but don’t hold your breath)
{code type=php}
// Stevish RSA version 2.1

// Copyright 2009, Stevish.com (with mad props to te developers of the PEAR RSA extension)
// This script is distributed under the terms of the GNU General Public License (GPL)
// See http://www.gnu.org/licenses/gpl.txt for license details

// Please use, distribute, modify, rip-off, sell or destroy this script however you see fit
// I only ask that you remove my copyright if you modify and re-release this.
// To make sure you have the genuine, up-to-date version, visit http://stevish.com/rsa-encryption-in-pure-php

// To use:
//
// $text = “Peter Piper picked a peck of pickled peppers”;
// $RSA = new RSA_Handler();
// $keys = $RSA->generate_keypair(1024);
// $encrypted = $RSA->encrypt($text, $keys[0]);
// $decrypted = $RSA->decrypt($encrypted, $keys[1]);
// echo $decrypted; //Will print Peter Piper picked a peck of pickled peppers

class RSA_Handler {
function encrypt($text, $key) {
list($p, $r, $keysize) = unserialize(base64_decode($key));
$in = $this->blockify($text, $keysize);
$out = ”;
foreach($in as $block) {
if($block) {
$cryptblock = $this->crypt_num($this->txt2num($block), $p, $r);
$out .= $this->long_base_convert($cryptblock, 10, 145) . ” “;
}
}
return $out;
}

function decrypt($code, $key) {
list($q, $r) = unserialize(base64_decode($key));
$in = explode(” “, $code);
$out = ”;
foreach($in as $block) {
if($block) {
$block = $this->long_base_convert($block, 145, 10);
$out .= $this->num2txt($this->crypt_num($block, $q, $r));
}
}
return $out;
}

function generate_keypair($bits = 1024) {
$km = new RSA_keymaker();
$keys = $km->make_keys($bits);
//The keys are separated into arrays and then serialized and encoded in base64
//This makes it easier to store and transmit them
//
//The private key should probably be encrypted with a user-supplied key (in AES or DES3)…
//This way it can be stored on the server, yet still be secure. The user-supplied key should not be stored.
$pub = base64_encode(serialize(array($keys[0], $keys[2], $bits)));
$priv = base64_encode(serialize(array($keys[1], $keys[2], $bits)));
return array($pub, $priv);
}

function crypt_num($num, $key, $mod) {
//The powerhorse function. This is where the encryption/decryption actually happens.
//This function is used whether you are encrypting or decrypting.
return $this->powmod($num, $key, $mod);
}

function long_base_convert ($numstring, $frombase, $tobase) {
//Converts a long integer (passed as a string) to/from any base from 2 to 145
$chars = “0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOP QRSTUVWXYZ_-+=!@#$%^*(){[}]|:,.?/`~•¤¶§Çüéâà ¤Ã Ã¥Ã§ÃªÃ«Ã¨Ã¯Ã®Ã¬Ã„ÅÉæÆôöòûùÿÖÜ¢£¥ƒ áíóúñѪº¿¬½¼¡«»¯ßµ±÷;<>“;
$fromstring = substr($chars, 0, $frombase);
$tostring = substr($chars, 0, $tobase);

$length = strlen($numstring);
$result = ”;
for ($i = 0; $i < $length; $i++) {
$number[$i] = strpos($fromstring, $numstring{$i});
}
do {
$divide = 0;
$newlen = 0;
for ($i = 0; $i < $length; $i++) {
$divide = $divide * $frombase + $number[$i];
if ($divide >= $tobase) {
$number[$newlen++] = (int)($divide / $tobase);
$divide = $divide % $tobase;
} elseif ($newlen > 0) {
$number[$newlen++] = 0;
}
}
$length = $newlen;
$result = $tostring{$divide} . $result;
} while ($newlen != 0);
return $result;
}

function blockify($in, $keysize) {
//Calculate blocksize by keysize
$b_len = floor($keysize/8);
return str_split($in, $b_len);
}

function txt2num($str) {
//Turns regular text into a number that can be manipulated by the RSA algorithm
$result = ’0′;
$n = strlen($str);
do {
$result = bcadd(bcmul($result, ’256′), ord($str{–$n}));
} while ($n > 0);
return $result;
}

function num2txt($num) {
//Turns the numeric representation of text (as output by txt2num) back into text
$result = ”;
do {
$result .= chr(bcmod($num, ’256′));
$num = bcdiv($num, ’256′);
} while (bccomp($num, ’0′));
return $result;
}

function powmod($num, $pow, $mod) {
if (function_exists(‘bcpowmod’)) {
// bcpowmod is only available under PHP5
return bcpowmod($num, $pow, $mod);
}

// emulate bcpowmod
$result = ’1′;
do {
if (!bccomp(bcmod($pow, ’2′), ’1′)) {
$result = bcmod(bcmul($result, $num), $mod);
}
$num = bcmod(bcpow($num, ’2′), $mod);

$pow = bcdiv($pow, ’2′);
} while (bccomp($pow, ’0′));
return $result;
}
}

class RSA_keymaker {

static $primes = null;

function __construct() {
if(is_null($this->primes)) {
//Make $this->primes an array of all primes under 20,000
//We will use this list to rule out the “easy” composite (non-prime) numbers

for ($i = 0; $i < 20000; $i++) {
$numbers[] = $i;
}
$numbers[0] = $numbers[1] = 0; //Zero and one are not primes
foreach ($numbers as $i => $num) {
if(!$num) {
continue;
}
$j = $i;

for ($j += $i; $j < 20000; $j += $i) {
//Jump to each multiple of the current number and set it to 0 (not prime)
$numbers[$j] = 0;
}
}
foreach($numbers as $num) {
//Take all the prime numbers and fill the primes array
if ($num) {
$this->primes[] = $num;
}
}
}
}

function make_keys($bits = 1024, $u = false, $v = false) {
//If not provided, select 2 random prime numbers each at about half the bit size of our key
//We keep a possible variant of 2 bits so that there are a wider range of primes that can be used
$variant = rand(0,2);
if(!$u)
$u = $this->make_prime(ceil($bits/2) + $variant);
if(!$v)
$v = $this->make_prime(floor($bits/2) – $variant);
while(substr($u, -16, 2) < (substr($v, -16, 2) + 2) && substr($u, -16, 2) > (substr($v, -16, 2) – 2) ) {
//Make sure the 2 primes are at least 1 quadrillion numbers apart
$v = $pm->make_prime(intval($digits/2));
}

//Find our modulo r and phi(r)
$r = bcmul($u, $v);
$phir = bcmul(bcsub($u, 1), bcsub($v, 1));

//Pick a value for p (The Public key). We will make it 17 bits or smaller.
$psize = ($bits > 51) ? 17 : intval($bits/3);
$p = $this->make_prime($psize);

//Find the inverse of p mod phi(r) using the Extended Euclidian Algorithm
$q = $this->euclid($p, $phir);

return array($p, $q, $r);
}

function make_prime($bits) {
//This function should not be used to generate primes less than 18 bits

$min = bcpow(2, $bits – 1);
$max = bcsub(bcmul($min, 2), 1);
$digits = strlen($max);
while(strlen($min) < $digits)
$min = "0" . $min;
$ent = $this->entropyarray($digits);
$maxed = true;
$mined = true;
$num = ”;
for($i = 0; $i < $digits; $i++) {
//Create a long integer between $min and $max starting with the entropy number
$thismax = 9;
$thismin = 0;
if($maxed)
$thismax = substr($max, $i, 1);
if($mined)
$thismin = substr($min, $i, 1);

//Add random numbers (mod 10) until the number meets the constraints
$thisdigit = ($ent[$i] + rand(0,9)) % 10;
if($i == $digits - 1) //The last digit should be a 1, 3, 7 or 9
while($thisdigit != 1 && $thisdigit != 3 && $thisdigit != 7 && $thisdigit != 9 && $thisdigit <= $thismax && $thisdigit >= $thismin)
$thisdigit = ($thisdigit + rand(0,9)) % 10;
else
while($thisdigit < = $thismax && $thisdigit >= $thismin)
$thisdigit = ($thisdigit + rand(0,9)) % 10;
$num .= $thisdigit;
if($maxed && $thisdigit < $thismax)
$maxed = false;
if($mined && $thisdigit > $thismin)
$mined = false;
}

//Check if the number is prime
while(!$this->is_prime($num)) {
//If the number is not prime, add 2 or 4 (since it is currently an odd number)
//This will keep the number odd and skip 5 to speed up the primality testing
if(substr($num, -1, 1) == 3)
$num = bcadd($num, 4);
else
$num = bcadd($num, 2);
$tries++;
}
return $num;
}

function entropyarray($digits) {
//create a long number based on as much entropy as possible
$a = base_convert(md5(microtime()), 16, 10);
$b = base_convert(sha1(@exec(‘uptime’)), 16, 10);
$c = mt_rand();
$d = disk_total_space(“/”);
$e = rand();
$f = memory_get_usage();

//Make sure it is only numbers, scramble it and make it the right length
$num = str_shuffle(preg_replace(“[^0-9]“, ”, $a . $b . $c . $d . $e));
if(strlen($num) > $digits)
$num = substr($num, 0, $digits);
else
while(strlen($num) < $digits)
$num = str_shuffle(substr(base_convert(md5($num), 16, 10), 3, 1) . $num);

//Turn the number into an array and return it
$ent_array = str_split($num);
return $ent_array;
}

function is_prime($num) {
if(bccomp($num, 1) < 1)
return false;
//Clear the easy stuff (divide by all primes under 20,000)
foreach($this->primes as $prime) {
if(bccomp($num, $prime) == 0)
return true;
if(!bcmod($num, $prime))
return false;
}

//Try the more complex method with the first 7 primes as bases
for($i = 0; $i < 7; $i++) {
if(!$this->_millerTest($num, $this->primes[$i]))
return false; //Number is composite
}

//Strong probability that the number is prime
return true;
}

function _millerTest($num, $base) {
if(!bccomp($num, ’1′)) {
// 1 is not prime
return false;
}
$tmp = bcsub($num, ’1′);

$zero_bits = 0;
while (!bccomp(bcmod($tmp, ’2′), ’0′)) {
$zero_bits++;
$tmp = bcdiv($tmp, ’2′);
}

$tmp = $this->powmod($base, $tmp, $num);
if (!bccomp($tmp, ’1′)) {
// $num is probably prime
return true;
}

while ($zero_bits–) {
if (!bccomp(bcadd($tmp, ’1′), $num)) {
// $num is probably prime
return true;
}
$tmp = $this->powmod($tmp, ’2′, $num);
}
// $num is composite
return false;
}

function euclid($num, $mod) {
//The Extended Euclidian Algorithm
$x = ’1′;
$y = ’0′;
$num1 = $mod;
do {
$tmp = bcmod($num, $num1);
$q = bcdiv($num, $num1);
$num = $num1;
$num1 = $tmp;

$tmp = bcsub($x, bcmul($y, $q));
$x = $y;
$y = $tmp;
} while (bccomp($num1, ’0′));
if (bccomp($x, ’0′) < 0) {
$x = bcadd($x, $mod);
}
return $x;
}

function powmod($num, $pow, $mod) {
if (function_exists('bcpowmod')) {
// bcpowmod is only available under PHP5
return bcpowmod($num, $pow, $mod);
}

// emulate bcpowmod
$result = '1';
do {
if (!bccomp(bcmod($pow, '2'), '1')) {
$result = bcmod(bcmul($result, $num), $mod);
}
$num = bcmod(bcpow($num, '2'), $mod);

$pow = bcdiv($pow, '2');
} while (bccomp($pow, '0'));
return $result;
}
}
{/code}
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