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

[Mark Priestley]

Emmanuel -

I think you are right. On page 372 of the Copeland "Colossus" anthology,
Friedrich Bauer presents the two cipher streams and their sum as you do, in
particular showing S + 5 = U. He writes: "The subtractions can be verified
by means of the Table in Appendix 3, remembering that for this cipher
system addition and subtraction are the same thing". The table, however,
shows that S + 5 = V. So anyone using Bauer's article as a source - and I
don't recall seeing the details anywhere else - will likely have reproduced
the error.

As Tom Haigh pointed out, there is an error in Copeland's reproduction of
the teleprinter alphabet in Appendix 2 - the 5th impulse of I should be a
dot rather than a cross - but that's not in play in this example. I'm not
aware of any errors in the addition table in appendix 3, so it looks like
it's a simple typo on Bauer's part.

The Fish section called the two basic symbols DOT and CROSS. In various
physical manifestations, CROSS might be a hole in a paper tape, or a
certain voltage, or a certain position of a cam on the rim of one of the
wheels of the Lorentz machine. But they didn't know this, and for crypto
purposes it didn't matter. The "General Report on Tunny" section 11B says:

Teleprinter letters are added by summing corresponding impulses according
to the rules:
DOT plus DOT equals DOT
CROSS plus CROSS equals DOT
DOT plus CROSS equals CROSS
CROSS plus DOT equals CROSS

Usually, now, we write DOT as 0 and CROSS as 1, giving:

0 + 0 = 0; 1 + 1 = 0; 0 + 1 = 1; 1 + 0 = 1

which does look like XOR (or binary addition w/o carry). The opposite
convention, which Brian Carpenter uses in his Python script, gives

1 + 1 = 1; 0 + 0 = 1; 1 + 0 = 0; 0 + 1 = 0

and would work equally well, but does look odd. But really DOT and CROSS
represent neither numbers nor truth values, so these aren't truth tables,
and describing the combining operation as "addition" is really a useful
metaphor deployed by the codebreakers, I think.

Finally: 28 of the 32 symbols in the teleprinter alphabet had two
interpretations depending on which "mode" the message was in: "figure
shift" or "letter shift". *5* (also written *+*) moved the message to
"figure shift" mode; *8* (or *-*) moved it to "letter shift" mode.
Punctuation symbols were in figure shift, so to put a full stop in a
message you'd have to do *SOMETHING9LIKE9THIS5M8* (*9* represented a space
in both modes, and *M* represented a full stop in figure shift). The *5*s
and *8*s were left in the message, and were crucial to the cryptanalysis
(and, indeed, to simply reading it correctly). Apparently German operators
often doubled the shift characters in case one of them got corrupted - *5*
and *8* are idempotent, so a full stop could also be *55M88* or *555M888*
etc - and this sort of thing helped the codebreakers.

(I'm using boldface here to distinguish the conventional names of the
letters in the teleprinter alphabet from their interpretation as symbols of
normal printed text. *T* represented "T" in letter shift and "5" in figure
shift, for example. The "shift keys" *5*  and *8* don't represent any
printed character. If a *5* appears when you're already in figure shift, it
has no effect.)

All the best,
Mark


On Sun, 23 May 2021 at 22:50, E. Lazard <Emmanuel.Lazard at dauphine.psl.eu>
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)
> (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
>
> 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)
> 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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