(*
   Eugene Wallingford 2013-1203

   This program demonstrates how we can factor large numbers
   that are the products of large primes.  This is one way
   in which public-key cryptography can work.

   http://en.wikipedia.org/wiki/Public-key_cryptography
*)

function main( publicKey  : integer,
               privateKey : integer ) : integer
  if publicKey = 0               (* as a flag for no arguments *)
  then factor( 2147481647,       (* public key  *)
               2047483747 )      (* private key *)
  else factor( publicKey,
               privateKey )

(*
   gcd(publicKey, privateKey) should work, even if
   you have a small stack space and no optimization!
*)

function factor( publicKey  : integer,
                 privateKey : integer ) : integer
  displayAndPrint( publicKey,
                   privateKey,
                   gcd(publicKey, privateKey) )

function displayAndPrint( publicKey    : integer,
                          privateKey   : integer,
                          commonFactor : integer ) : integer
  print( publicKey  / commonFactor )
  print( privateKey / commonFactor )
  commonFactor

(*
   finds the greatest common divisor using Euclid's algorithm
*)

function gcd(a : integer, b : integer) : integer
  if b = 0 then
     a
  else
     gcd(b, remainder(a, b))

function remainder(a : integer, b : integer) : integer
  if a < b then
     a
  else
     remainder(a-b, b)