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

show how, in a typical encipherment, the plaintext letter D might become
the cipher letter Q. The key point to note is that if, as shown in the
diagram, D is enciphered to I and Q is enciphered to P by R1, then IP is a
pair in the composite reflector, which means that during the six-letter
encipherment any letter entering the composite reflector as I will emerge
from it as P, and vice versa.
The indicator ‘chains’ in the Enigma
The Enigma cipher machine 125
We have seen, in Figure 9.3, how the encipherment of a letter involves one
of the 13 pairs in the composite reflector; in the typical example shown in
Figure 9.3 the plaintext letter D was changed to I by R1 and so entered the
composite reflector as I. After being changed to K then B then P then U
respectively by R2, R3, U and R3 it emerges from R2, and hence from the
composite reflector as P before finally passing back through R1 and producing
cipher letter Q, since the entry wheel, being wired in alphabetical
order, will leave the letter emerging from R1 unchanged. If, therefore, we
knew the identity, internal wiring and starting position of R1 and enciphered
D, to give I, and enciphered Q, giving P, we would discover one of the
13 pairs of the composite reflector. If we had a large number of such
plain–cipher pairs we would find that if we had correctly identified both
the wheel R1 and its initial setting we would always have got one of these
13 pairs of letters from the composite reflector. If, on the other hand, we
had used the wrong wheel as R1, or the correct wheel but at an incorrect
setting, we would have found not just 13 pairs but many more, since
there are 325 possible pairings of 26 letters, and we would get contradictions
such as ‘IP is a pair but so is IM’. In this way we would soon know
when we had found the correct wheel and its setting.
The problem is: we don’t know the identity of the plaintext input letter
(D in the example) although we do know the cipher output letter (Q); so
how do we progress? The answer is that there is a feature of the six-letter
indicators, originally discovered by the Polish cryptanalysts in 1932, that
enables us to identify the correct R1 and its setting by this method,
without knowing the input letters. The discovery relies upon two facts:
(i) plain–cipher pairs are reversible; e.g. if A enciphers to M (say) then M
enciphers to A at the same wheel settings;
(ii) the six-letter indicator provides three cases where the same letter has
been enciphered at positions in the text which are three apart so, in the
example above where the enciphered indicator was LOCWHQ, (L, W), (O,