As we entered World War II cryptology took center stage. Our success against
the German ENIGMA encryption machine makes a great story that I'm sure you
have heard before. When confronted with this problem it was quickly realized
that analysis and solution of the system was going to be orders of magnitude
harder than that of existing systems. Some even thought it was difficult to
the point of being undoable. Early progress against this system was made by
applying the power of group theory combined with the power of statistical
attack.