On Diffie-Hellman key exchange

Question

The book I am reading, explains the algorithm as follows:

• 2 people think of 2 public "n and g" numbers both are aware of.
• 2 people think of 2 private "x and "y" numbers they keep secret.

Exchange happens as illustrated

I put together the following python code to see how this works and .... it does not. Please help me understand what am i missing:

 #!/usr/bin/python

 n=22 # publicly known 
 g=42 # publicly known

 x=13 # only Alice knows this 
 y=53 # only Bob knows this

 aliceSends = (g**x)%n 
 bobComputes = aliceSends**y 
 bobSends = (g**y)%n
 aliceComputes = bobSends**x


 print "Alice sends    ", aliceSends 
 print "Bob computes   ", bobComputes 
 print "Bob sends      ", bobSends 
 print "Alice computes ", aliceComputes

 print "In theory both should have ", (g**(x*y))%n

 ---

 Alice sends     14  
 Bob computes    5556302616191343498765890791686005349041729624255239232159744 
 Bob sends       14 
 Alice computes  793714773254144 

 In theory both should have  16

Answer 1

You forgot two more modulos:

>>> 5556302616191343498765890791686005349041729624255239232159744 % 22
16L
>>> 793714773254144 % 22
16

Answer 2

Roman is right. However, you'd better have a look at pow() three arguments function. Much faster and third argument is modulus