## Cryptography

#### The History and Mathematics of Codes and Code Breaking

Here's John's paper on the Lorenz cipher machine [PDF].

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1. #### Rachel Lundberg

You did a really good job of explaining the Vernam method. The whole thing totally made sense to me after I read it. The example was useful, and the red parts made it easier to understand. I also liked how you sort of built on the concepts of the Enigma machine to explain Lorenz, and showed the advantages Lorenz had over Enigma. It really put in perspective how the Germans advanced their cipher machines.

You made some great "big picture" points in this paper. Making the connection between the cryptanalysis of Lorenz and the development of the modern computer got right to the heart of the historical importance of your topic. The point you make about powerful ciphers weakened by improper use was also very good. It would have been nice to see a connection between the mistake made with Lorenz and some of those made with Enigma (repetition of the key, cillies, etc.).

The only area I felt could use some more expansion was the cryptanalysis section. You explain how Tiltman had an excellent crib, but don't really go into how he used it to infer the machine's design to the point where the British could build their own. How did the psi and chi wheels give Tutte a clue? Why did he shift the ciphertext over?

Overall, it's a good read--the details are well attended to, the comparisons are appropriate and helpful, and the conclusions are well thought out. I was wondering about Lorenz when it was mentioned in Singh, and I'm glad I got to read about it here.

2. #### Max Gillett

I felt that the Vernam method, the method responsible for the Lorenz cipher, was very clearly explained and easy to understand, but that the explanation of how the Lorenz enhanced the Vernam method was hard to follow. Some diagrams (like those present in the paragraph about the Vernam method) would have aided my understanding better.

How did the Lorenz machine come to be employed by the top military officials in Germany? Was its origin similar to that of the Enigma? If the Lorenz was considered to be unbreakable, why did only the high-ranking German command use it? Why was it not used in battles in which time was of the essence?

It's amazing how fast and advanced the Collosus machine was. It seems that so many people in history and in the field of cryptography (i.e. Babbage, Turing, Rejewski) have either come up with blueprints or implementations of rudimentary computers, but never realized the true implications of their device.