Code and ciphers: Julius Caesar, the Enigma and the internet

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chapter 9
H) and (C, Q) are such pairs, and, if R2 doesn’t move during the indicator
encipherment, we can hope to identify R1 and its setting.
Since (i) is always true and (ii) holds about 80% of the time the prospects
of success, using the method to be described, are good if enough
information is available. Even if R2 does move the attack may still succeed
for if R2 moves between the second and third letters (say) then the third
and sixth letters (C and Q in the example) will have been produced by the
same letter on a machine on which only R1 has moved. In the worst case,
where R2 turns between the third and fourth letters, the attack is invalid,
but the fact that it fails tells the cryptanalyst that R2 has probably moved
and this may be helpful in a different attack.
Before describing the method for finding the identity and setting of
R1 it is helpful to look at a small scale example. In this example the indicator
consists of just one letter which is immediately repeated, rather
than three letters repeated as in the Enigma itself. The cryptanalytic
attack is the same in both cases. The chains are formed from the cipher
pairs at positions 1 and 2 rather than those at positions 1 and 4 (and (2, 5)
and (3, 6) for the Enigma).
Example 9.1 (Mini-Enigma)
The following 12 pairs of cipher letters are the result of enciphering the
12 plaintext letter-pairs AA, BB, ..., KK, LL (in an unknown order) at consecutive
positions, and at a common ground setting, through a 12-letter
Enigma-type cipher machine:
AK, BL, CI, DD, EB, FG, GE, HH, IA, JC, KJ, LF.
We form ‘chains’ from these pairs by joining pairs where the second letter
of one pair is the same as the first letter of another pair, stopping when a
letter is repeated:
AKJCI
BLFGE
DD
HH
We see that there are two chains of 5 different letters and two chains of
just 1 letter. Is this a coincidence? No; it is not. The Polish cryptanalysts
discovered that encipherment of pairs of the same letter at positions one
or more places apart when only R1 moves will always produce chains
which occur in pairs. The proof of this is not very difficult and the