# How did the cryptographers of Bletchley Park figure out the chi stream of the Lorenz cipher?

How did the Bletchley Park code breakers figure out the chi stream of the Lorenz cipher, that was obscured in the ciphertext, which British code breakers eventually decoded? It's written in The Rutherford Journal that John Tiltman deduced the key using a depth found on 30 August 1941. Since he couldn't figure how the key was generated, it was given to W.T. Tutte, who figured out how the key was generated without ever looking at the Lorenz cipher machine.

Jack Copeland writes in Colossus: The Secrets of Bletchley Park's Codebreaking Computers (p.364)

Here was a method of wheel setting! Δ(χ1+χ2) was a periodic sequence, supposed known, with a period of 41×31=1271. Lay it against Δ(C1+C2) in each of the 1271 possible relative positions and count the number of agreements for each one.

It's obvious that the British code breakers had the ciphertexts in hand, from which they could obtain the delta-ed version of the sum of the first and second impulse of an intercepted ciphertext, i.e., Δ(C1+C2). I would like to know how the code breakers figured out the delta-ed version of the chi stream of the Lorenz cipher machine, i.e., Δ(χ1+χ2).

• have you read en.wikipedia.org/wiki/Cryptanalysis_of_the_Lorenz_cipher? Dec 27, 2017 at 21:34
• Could you tell how codebreakers figured out the start positions of the chi wheel mentioned in the Cryptanalysis of the Lorenz machine. Dec 28, 2017 at 1:14
• The first paragraph you link to clearly says: " Initially, this was achieved by two messages having been sent in depth.". This means that they intercepted messages encrypted with the same settings. This is basically key re-use and leaks a lot of information.
– Marc
Dec 28, 2017 at 17:00
• @Marc: To be honest I couldn't get how code breakers figured out the start positions of the chi wheels even though they found a depth. I know that Tutte arranged the cipher text in rows of 41 after many attempts and came to see repetitions. Could you tell how Tutte figured out the start positions of the chi wheels. Dec 28, 2017 at 20:24