## Homework 7 (due 6/2) CSC 233

Remember: the detailed outline of your paper is due this Thursday (see final requirements).

We talked about the Enigma cipher including the Polish break into the Enigma (Rejewski's Theorem); and, more superficially, how Turing built on that in his work at Bletchley Park. Singh's  book explains both parts excellently, you can read up on it there. If you want deeper details on how Enigma is broken, Bauer's Decrypted Secrets will be your best source.

A detailed account of the history of rotor machines, and their cryptanalysis (with more material on the Enigma) is

Cipher A. Deavours, Louis Kruh. Machine Cryptography and Modern Cryptanalysis.

On the historical side, there is David Kahn's "Seizing the Enigma".

1. [Enigma-Decryption, 10pt] Your day settings are: 321, A/D, K/L, and rotor orientation TFF. You have received the signal

"YCBHJ WOIJI PGOYB IHKAE TSEPK SA"

Decrypt (use the enigma simulator we saw in class). (Remember the use of session keys, see pg. 147/148 of the book.)

2. (Tagesschluessel, 20pt) Determine the lengths of the cycles in the permutation generated by letters in positions 3/6 of the Tagesschluessel we discussed in class (see Enigma handout for the key sequences).

a) Construct the permutation for the letters in positions 3,6. E.g. the first sequence AUQ AMN means that Q->N, so you start with

ABCDEFGHIJKLMNOPQRSTUVWXYXZ
................N..........

b) Find all the cycles in this permutation. E.g. for the letters in position 1/4, we had a cycle B->C of length 2.

c) What are the lengths of the cycles (for 1/4 we had lengths 1, 2, and 10).

Marcus Schaefer
Last updated: May 26th, 2011.