The Turing Guide

120 | 12 BOmBES

DAEDAQOZSIQMMKBILGMPWHAIV from KEINEZUSAETZEZUMVORBERIQT. In
the real world, however, it would take the bombe impossibly long to search through the astro-
nomical number of possible combinations. The challenge facing Turing was to find a faster
method.

How it worked

The key to understanding Turing’s method is his observation that if a crib involves a number
of ‘loops’, these can be exploited to find the plugboard wiring and the starting position of the
wheels, as well as which three wheels are in the Enigma.^64 (Turing himself used the term ‘closed
chain’ for what I call a loop.)
The crib in Fig. 12.8 contains several loops. One occurs at steps 2 and 5: at step 2 E leads to A
(that is, E enciphers as A), and at step 5 A leads back down again to E (so A deciphers as E). This
short loop is depicted in Fig. 12.10. Figure 12.11 depicts a longer loop occurring at steps 10, 23,
and 5: E is linked with I, I is linked with A, and A is linked with E. (Notice that ‘linked with’ is
reversible: if X is linked with Y, then Y is linked with X. This is because, in Enigma, if X encodes
as Y at some step, then Y would encode as X at the same step.) Steps 13, 12, 6, 24, and 10 contain
a monster loop: E is linked with M at step 13, M is linked with Z at step 12, Z is linked with Q at
step 6, Q is linked with I at step 24, and I is linked with E at step 10. Turing called E the ‘central
letter’ of these three different loops.^65
Turing’s great insight was that loops give away information. He put it like this, using the
German word ‘Stecker’ for the plugboard connections: loops correspond to ‘characteristics of
the crib which are independent of the Stecker’.^66 He realized that a crib’s loops can be milked
for information by using a short chain of replica Enigmas linked nose to tail. Let’s focus on the
longest of the three loops just mentioned, E → M → Z → Q → I → E. To milk this five-step loop, we
connect five replica Enigmas together in such a way that the output from the first Enigma—i.e.

WETTERFURDIENACHT

.... HPZEMUGBNATPRUKAI ....

bombe searched for a pattern of wiring at figure 12.9 The bombe’s function. The Settings x, y, z

the plugboard and wheel start positions

that encrypted the crib correctly.

E

A

2 5

figure 12.10 A loop

involving two letters.