148 | 14 TUNNy: HITlER’S BIGGEST fISH
The Tunny machine’s internal mechanisms produced a stream of letters that Bletchley Park
called the ‘key-stream’, or simply the ‘key’. Each letter of the ciphertext was produced by adding
a letter from the key-stream to a letter of the plaintext. For example, if the first letter of the
plaintext was H, and the first letter of the key-stream was W, then the first letter of the ciphertext
would be the result of adding W to H. Under the rules of dot-and-cross addition, adding W
(xx••x) to H (••x•x) produces U (xxx••):
U w H
x + x = •
x + x = •
x + • = x
- • = •
- x = x
H w U
- x = x
- x = x
x + • = x
- x = x
- • = •
x + x = •
- • = •
The German engineers selected these particular rules for dot-and-cross addition because
they wanted to arrange things so that adding one letter to another and then adding it again a
second time leaves you where you started. In symbols, (y + x) + x = y, for every pair of keyboard
characters x and y. For example, adding W to H produces U (as we have just seen), and then
adding W to U leads back to H:
This explains how the receiver’s Tunny decrypted the ciphertext. The ciphertext was the result
of adding key to the plaintext, so if the receiver’s machine added exactly the same letters of key
to the ciphertext, the encryption was wiped away and the plaintext was exposed.
For example, suppose that the plaintext was the single word HITLER. The stream of key
added to the plaintext by the sender’s Tunny might be WZTI/N. In the sender’s machine, these
characters were added serially to the letters in HITLER:
H + W I + Z T + T L + I E + / R + N.As you can check from Fig. 14.2, this produces UQ/HEI, which was then transmitted over the
radio link. The receiver’s Tunny added the same letters of key to the encrypted message:
U + W Q + Z /+ T H + I E + / I + N.This uncovers the letters HITLER.