For some reason: the display looks like this:
3 to the power of x mod 17 is 19. This is called v.
Shared person a (v):
19
and in the script, it looks like this (this script is used to describe Diffie-Hellman key exchange algorithm.):
$p="17";
$g="3";
$px=gmp_nextprime(rand());
$x=gmp_strval($px);
$a=$g^$x%$p;
echo "$g to the power of x mod $p is $a. This is called v.<br>";
echo "<br>Shared person a (v):<br>";
echo "$a <br>";
Wondering if this is kind of a PHP glitch, because:
if{x mod y=z}, z<y
Now my questions: How to fix this? Had I done anything wrong? Is this a PHP glitch?
(The code needs a clean up, I know.)
Additional notes: $x = 2047401017
Well, ^ is not the power operator and modulo precedes both of them; besides, GMP has a function for power-modulo already:
$p="17";
$g="3";
$px=gmp_nextprime(rand());
$a = gmp_powm($g, $px, $p);
echo "$g to the power of x mod $p is $a. This is called v.<br>";
echo "<br>Shared person a (v):<br>";
echo "$a <br>";
^ is not the exponent operator, it's the bitwise XOR operator. As of PHP 5.6, the exponent operator is **. So it should be either
$a = ($g ** $x) % $p;
or
$a = $g ** ($x % $p);
The exponent operator was added in PHP 5.6. Prior to this, you need to use the pow() function:
$a = pow($g, $x) % $p;