#!/usr/bin/perl

use strict;
use warnings;
use Math::BigInt lib => 'GMP';

my $g = new Math::BigInt('5'); # typically 2 or 5
my $p = new Math::BigInt(
  "537139360602477525125655043677356597740" .
  "672426915294213641576278281056255413159" .
  "9074907426010737503501" # any 100+ digit prime will do
);

my $a = new Math::BigInt(join("", 
  map(chr(48+int rand 10), 
  1 .. 50))); # $a is the lhs secret

my $b = new Math::BigInt(join("", 
  map(chr(48+int rand 10), 
  1 .. 50))); # $b is the rhs secret

my ($A, $B, $Kab, $Kba);

print "g=$g\n"; # $p and $g generate a group
print "p=$p\n"; # cyclic group G
print "a=$a\n"; # $p and $g are chosen in the clear
print "b=$b\n";

print "\n";

# it's safe to send A=g^a mod p in the clear
$A = $g->copy->bmodpow( $a, $p );

# it's safe to send B=g^b mod p in the clear
$B = $g->copy->bmodpow( $b, $p );

# g^b^a mod p should be equal to g^a^b mod p
$Kba = $B->copy->bmodpow( $a, $p );
$Kab = $A->copy->bmodpow( $b, $p );

# so we both know the secret without transmitting it!
# magic!
print "These better be equal:\n\t$Kab\n\t$Kba\n\n";