122 | 12 BOmBES
The letter to which E is connected is called E’s ‘plugboard-mate’ (Turing’s term was E’s
‘Stecker value’). It is E’s plugboard-mate (not E itself ) that we need to input into our chain of
replica Enigmas, and we want to drive the Enigmas into a loop so that E’s plugboard-mate (and
not E) emerges at the other end of the chain. Since we do not know what E’s plugboard-mate
is—this is one of the pieces of information that we are trying to discover—we proceed by first
examining the possibility that E’s plugboard-mate is A: we continually input A into the chain
and keep turning the wheels, trying to put the Enigmas into a loop so that A emerges at the
other end of the chain.
If we fail to create a loop leading from A to A, even after turning the wheels through all their
possible positions, then E’s plugboard-mate cannot have been A. So now we try B, proceeding
as before, and so on. Suppose that our luck is out and we don’t find the loop until our final
try, when we input Z into the chain and manage to get Z out again. The existence of this loop,
the one and only loop to give us the same letter at the start and the finish, establishes that E’s
plugboard-mate was Z.
milking the loops
Note that the identity of E’s plugboard-mate is not all that we have established. As explained
earlier, we now know the position of the sender’s wheels at the start of the message. And there is
more. Once we have located the loop, the letter that exits the wheels of the first replica Enigma
must be M’s plugboard-mate, since at the first step of the loop, E is enciphered as M. Other
Enigmas in the chain similarly yield up information about the plugboard—for example, the
letter exiting the wheels of the third replica Enigma must be Q’s plugboard-mate, since Z was
enciphered as Q at the third step of the loop. So, as required, Turing’s method has supplied not
only the starting position of the sender’s wheels, but also a quantity of information about the
plugboard.
So far, so good. There is a difficulty, however. In practice, many different wheel positions will
drive the chain of Enigmas into a loop, and there will be many candidates for E’s plugboard-
mate. It is rather too easy to find ways of making the input letter light up at the end of the chain.
To counter this embarrassment of riches, Turing used other loops in the crib. As Fig. 12.6
shows, the ‘Keine Zusaetze’ crib of Fig. 12.8 contains more than half-a-dozen loops with central
letter E. A separate chain of Enigmas was set up within the bombe for each loop; and the same
letter, A for example, was continuously input into every chain. The bombe’s electrical motors
would turn the wheels of all the Enigmas in the chains, searching for a way of making A light up
at the end of every chain, and if a way of doing so was found, the bombe would automatically
stop. The more loops there were in play, the fewer ways there would be of getting the input letter
to light up at the end of each chain, and so the fewer stops there would be.
Given enough loops, this procedure of Turing’s usually produced a manageably small num-
ber of stops. Each time that the bombe stopped, information was automatically extracted from
the chains of Enigmas and displayed by the machine for the Wren operators to read. The Wrens
passed the readings on by telephone. Bombe operator Jean Valentine remembers that she had
no idea who she was telephoning from Hut 11A or where the readings were going. ‘Secrecy was
the order of the day’, she explains. Long after the war, she discovered that she was phoning the
information to Hut 6, only 10 yards away. If a naval message were being attacked, the readings
would be telephoned to Hut 8.