#! /usr/local/bin/perl -w
use strict;
# --------------------------------------------------------------
# 	the essence of RSA algorithm -- assymetrical\public-key cryptography
# --------------------------------------------------------------
use Math::Pari qw(gcd PARI) ;
# --------------------------------------------------------------

# m -- message 
my $m = 'IBM' ;
print "original: $m\n" ;
my $tmpl = 'C*' ;
my @m = unpack($tmpl, $m) ;		# string -> unsigned char values
print "coded: @m\n" ;

# n = pq -- in RSA, p & q = prime, each 1024 bits/308 digits long
my $p = PARI("prime(".int(rand 50).")") ;
my $q = PARI("prime(".int(rand 50).")") ;
my $n = $p*$q ;			# $n = Pari's obj

# choose a random number r, s.t.
# 	1 < r < (p-1)(q-1) = b
# 	gcd(r, b) = 1 -- relative prime
my $b = ($p-1)*($q-1) ;
my $r ;
do {$r = int rand $b ; } until (gcd($r,$b) == 1) ;
$r = PARI $r ;

# rk = 1 mod (p-1)(q-1) -- d = private key; (n, r) public
my $k = (1/$r)%$b ;		# the math operators are Pari's, since vars = Pari

# encrypt -- c = (m ^ r) mod n
my @c ;
map { $c[$_] = ($m[$_]**$r)%$n } 0..$#m ;			# Perl uses ** for power
print "ciphered: @c\n" ;

# decrypt -- m = (c ^ k) mod n
my @d ; 
map { $d[$_] = PARI("($c[$_]^$k)%$n") } 0..$#c ; 	# Pari uses ^ for power
print "deciphered: @d\n" ;
print "decoded: " . pack($tmpl, @d) . "\n" ; 


# just checking....
print "\nprimes: $p, $q\n" ;
print "n: $n; (p-1)(q-1): $b\n" ;
print "rand: $r; key: $k\n"