RSA Encryption process in PHP -


in effort understand asymmetric encryption process outlined simple php script encrypt , decrypt simple numbers. noticed after while given numbers encrypt/decrypt algorithm fail, in decrypted , initial numbers didn't match. put loop in see how algorithm perform when ecrypting , decrypting 100 numbers , after number 32 process fell apart.

is because p*q = 33?

<?php  # test encrypto algo  // choose prime keys $p = 47; $q = 71;  // compute n = pq $n = $p*$q; // choose e such 1 < e < f(n) , e , n coprime $e = 79; // compute value d such (d * e) % f(n) = 1 $d = 1019; // compute f(n) = (p-1)(q-1) $z = ($p - 1)*($q - 1); // create public , private keys $pubk = array('n' => $n, 'e' => $e); $privk = array('n'=> $n, 'd' => $d); // boundary loop $l = 100;  // perform encypt/decrypt on 1..100 for($i = 1; $i <= $l; $i++) {     $enc = enc($i, $pubk);     $dec = dec($enc, $privk);     print "encrypted <b>$i</b> = $enc decrypted $enc = <b>$dec</b> ";     if($i == $dec)         print "success<br>";     else         print "fail<br>"; }  // encrypt sample public key function enc($sample, $key) {     return bcmod(bcpow($sample,$key['e']),$key['n']); } // decrypt encrypted sample private key function dec($sample, $key) {     return bcmod(bcpow($sample, $key['d']),$key['n']); }  ?>

output loop

http://en.wikipedia.org/wiki/rsa_(algorithm)

2.2 encryption:

[...] bob wishes send message m alice. first turns m integer m, such 0 ≤ m < n using agreed-upon reversible protocol known padding scheme. ...alice transmits public key (n, e) bob , keeps the

this not hold here, therefore need use larger factorizations.


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