TheCodeBreakers
All of these situations have occurred often
enough for the cryptanalyst to exploit them.
That exploitation entails resolving the millions of secondary alphabets
into the few primary ones. It calls upon the resources of higher
mathematics, especially group theory, whose techniques are particularly
suited to handle the many unknowns involved in a rotor solution.
Basically these unknowns are the paths taken by the wires of each rotor
from one face to the other. The cryptanalyst-mathe-matician quantifies
them by measuring the distance, or displacement, between the input and
the output contacts. For example, a wire from input contact 3 to output
contact 10 marks a displacement of 7. Similarly, letters are given
numerical values, usually a = 0, 6 = l,...z = 25. Using his known or
assumed plaintext values, the cryptanalyst sets up equations in which
the displacements of the several rotors constitute the unknowns, and
then, using higher algebra, solves the equations for them
annaabi.ee 
