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

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chapter 9
Table 9.3
Setting 1 Setting 2
DH →GA DH →CD
AB →KF AL →AF
IL →DL IF →BK
CF →BH CG →GI
JG →IC JE →EH
KE →EJ KB →JL
These produce several contradictions: eg Setting 1 implies that (A, G) are
paired in the composite reflector whereas Setting 2 tells us that (A, F) are
paired. Therefore R1 is not at Setting 1.
(2) We repeat the exercise but this time encipher the pairs at Settings 2
and 3: Table 9.4.
Table 9.4
Setting 2 Setting 3
DH →CD DH →HJ
AB →AL AL →GK
IL →BF IF →EI
CF →GK CG →AL
JG →EI JE →CD
KE →JH KB →FB
The two sets are in complete agreement and we conclude that we have
identified R1 and that it was set at position 2 at the beginning of the
encryption. We also now know that the pairings of the 12 letters in the
composite reflector are
(A, L), (B, F), (C, D), (E, I), (G, K) and (H, J).
Since R1 and the actual reflector (U) are known the cryptanalyst would
now try to find which combinations of U and two other wheels could
produce these pairs. The original Enigma had only three wheels in its set
and so, since R1 has been identified, there would be ‘only’ 2�26�26�
1352 possibilities to be examined. Whilst this may seem a large number it
is small in comparison with the 105 456 cases which the cryptanalyst
would have faced initially. Other lines of attack would now also be used,
such as trying some possible plaintext beginnings for some of the messages.