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tackling Tunny. He had very little to go on. Tunny was believed to encipher teleprinter mes-
sages. It also seemed likely that Tunny was an ‘additive’ cipher machine. An additive machine
adds key to the plaintext to form the ciphertext, as already described. Symbolically, P + K = Z,
where P is the plaintext, K is the key, and Z is the ciphertext.
Sometimes the sending Tunny operator would foolishly use the same setting for two mes-
sages: at Bletchley Park this was called a depth. Depths were often the result of something going
wrong during the encryption and transmission of a message—radio interference perhaps, or a
jammed or torn paper tape. So the sending operator would start again from the beginning of the
message. If, instead of selecting new starting positions for the wheels, he stupidly used the same
ones, a depth resulted. However, if the message was repeated identically on the second transmis-
sion, the depth would be of no help to the codebreakers—they simply ended up with two copies
of the same ciphertext. But if the sending operator introduced typing errors during the second
attempt, or abbreviations, or other variations, then the depth would consist of two not-quite-
identical messages, both encrypted by means of exactly the same key—a codebreaker’s dream.
It was such a depth that Tiltman decrypted in the late summer of 1941, giving the codebreak-
ers their first entry into Tunny. On the hypothesis that Tunny was additive, he added the two
intercepted ciphertexts—call them Z 1 and Z 2. If Tunny were indeed an additive machine, this
would have the effect of cancelling out the key, and would produce a sequence of approximately
4000 letters that consisted of the two plaintexts, P 1 and P 2 , added together character by charac-
ter. This is because
Z 1 + Z 2 = (P 1 + K) + (P 2 + K) = (P 1 + P 2 ) + (K + K) = P 1 + P 2.
Tiltman managed to prise the two separate plaintexts out of the sequence P 1 + P 2. It took
him 10 days. He had to guess at words in each message, and Tiltman was a very good guesser.
Each time he guessed a word from one message, he added it to the characters at the appropri-
ate place in the P 1 + P 2 sequence, and if the guess were correct an intelligible fragment of the
second message would pop out. For example, adding the probable word ‘geheim’ (secret) at
a particular place in the P 1 + P 2 sequence revealed the plausible fragment ‘eratta’.^3 This short
break could then be extended to the left and right. More letters of the second message were
obtained by guessing that ‘eratta’ is part of ‘militaerattache’ (military attaché), and if these letters
were added to their counterparts in the P 1 + P 2 sequence, further letters of the first message
were revealed—and so on.
Eventually, Tiltman achieved enough of these local breaks to realize that long stretches of
each message were the same, and so he was able to decrypt the whole thing. By adding one of
the resulting plaintexts to its ciphertext, he was then able to extract the 4000 or so characters
of key that had been used to encrypt the message (since P + Z = K).
Tutte and Turing join the attack
However, breaking one message was a far cry from knowing how the Tunny machine worked.
The codebreakers still had no idea how the machine produced the key that Tiltman had
extracted. In the case of Enigma, Bletchley Park knew the internal workings of the machine
before the war even began, thanks to Poland’s codebreakers, and then once the fighting started a
number of Enigmas were captured on land and sea. Tunny, on the other hand, was an unknown
quantity: no machine had been captured, and nor would one be until the war was almost over.