[SIGCIS-Members] Question about the Tiltman break in Lorenz cypher (1941)

[Brian E Carpenter]

Emmanuel,

On 24-May-21 09:47, E. Lazard wrote:
> Dear all,
> 
> I’m looking for some original information on the famous "Tiltman break" which led to the cryptanalysis of the Lorenz cipher en 1941.
> (https://en.wikipedia.org/wiki/Cryptanalysis_of_the_Lorenz_cipher <https://en.wikipedia.org/wiki/Cryptanalysis_of_the_Lorenz_cipher>)
> (http://www.eprg.org/computerphile/lorenz-combined.pdf <http://www.eprg.org/computerphile/lorenz-combined.pdf>)
> 
> The story is: the British intercepted two messages sent with the same key (HQIBPEXEZMUG) also called a "depth".
> When adding the two cipher texts with the exclusive-or function, the key cancels out and what is left is the exclusive-or of the two plain texts.
> From there, brigadier John Tiltman found the two messages by trying various likely pieces of plaintext and found that the first message started with the word SPRUCHNUMMER (message number) and that the second message also used the same word but shortened out as SPRUCHNR.
> 
> EVERY SINGLE WEBSITE and the Copeland book "Colossus" list the two intercepted cypher texts as:
> 
> C1 = JSH5N ZYMFS 01151 VKU1Y U4NCE JEGPB
> C2 = JSH5N ZYZY5 GLFRG XO5SQ 5DA1J JHD5O
> 
> and their exclusive-or as:
> 
> D  = ///// //FOU GF14M AQSG5 SEKZR /YWHE

Indeed,  S and 5 combine to give V according to
https://billtuttememorial.org.uk/codebreaking/teleprinter-code/
 
> My problem is that IT DOES NOT ADD UP!
> The U in 10th position is not the correct result, it should be a V.
> (S is 10100, 5 is 11011, so their exclusive-or is 01111 which is V)

However, there are two problems with your comment:

1) The code for 5 is actually 11110, the same as the code for T, but in figure shift. I assume that the Lorentz system removed the figure shift and letter shift codes before starting the crypto work.
11011 is indeed the figure shift code, so the actual bit stream would have contained 11011 11110 11111.

2) The appropriate operation is not XOR. It's what Bletchley Park called "addition", as described at the above web site. While that doesn't explain this U/V error, which I suppose started as a transcription error, it probably explains the other errors you mention.

Regards
   Brian Carpenter

> And I found other issues with all examples using the cypher text, the messages, the key… I always have several letters which are wrong.
> 
> So I’m wondering if I’ve misunderstood something or have the cypher texts been incorrectly written down once and everybody just copied them without checking?
> 
> Anybody has genuine information or can point me to some source?
> 
> Regards
> Emmanuel Lazard
> 
> 
> 
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