Lorenz Cipher - Structure

Structure

The logical functioning of the Tunny system was worked out well before the Bletchley Park cryptanalysts saw one of the machines—which only happened in 1945, shortly before the allied victory in Europe.

The SZ machine served as an in-line attachment to a standard Lorenz teleprinter. It had a metal base 19 in (48 cm) × 15.5 in (39 cm) and was 17 in (43 cm) high. The teleprinter characters consisted of five data bits, encoded in the International Telegraphy Alphabet No. 2 (ITA2). The enciphering machine generated a pseudorandom character-by-character key that was XOR-ed with the input characters to form the output characters.

Each of the five bits (or "impulses") of the key for each character was generated by the relevant wheels in two parts of the machine. The Bletchley Park analysts called these the ("chi") wheels, and the ("psi") wheels. Each wheel had a series of cams (or "pins") around them. These cams could be set in a raised (active) or lowered (inactive) position. In the raised position they generated a '1', in the lowered position they generated a '0'.

The chi wheels all moved on one position for each character. The psi wheels also all moved together, but not after each character. Their movement was controlled by the two ("mu") or "motor" wheels. The SZ40 61 wheel moved one position with each character, but the 37 wheel moved on only when the cam on the 61 wheel was in the active position. If the cam on the 37 wheel was in the active position, all five psi wheels then moved. The SZ42A and SZ42B models had additional complexity to this mechanism, known at Bletchley Park as Limitations.

The key stream generated by the SZ machines thus had a chi component and a psi component that were combined together with the XOR function. Symbolically, the key that was combined with the plaintext for enciphering—or with the ciphertext for deciphering—can be represented as follows.

Key = Chi-Key ⊕ Psi-Key

The number of cams on each wheel equalled the number of impulses needed to cause them to complete a full rotation. It should be noted that these numbers are all co-prime with each other, giving the longest possible time before the pattern repeated. With a total of 501 cams this equals 2501 which is approximately 10151, an astronomically large number. However, if the five impulses are considered independently, the numbers are much more manageable. The product of the rotation period of any pair of chi wheels gives numbers between 41×31=1271 and 26×23=598.