Lorenz cipher

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The Lorenz SZ42 machine with its covers removed.





The Vernam cipher[edit]

Main article: Gilbert Vernam

Gilbert Vernam was an AT&T Bell Labs research engineer who, in 1917, invented a cipher system that used the Boolean "exclusive or" (XOR) function, symbolized by ⊕.[6] This is represented by the following "truth table", where 1 represents "true" and 0 represents "false".

0 0 0
0 1 1
1 0 1
1 1 0



Plaintext ⊕ Key = Ciphertext


Ciphertext ⊕ Key = Plaintext





BP wheel name[10] \psi1 \psi2 \psi3 \psi4 \psi5 \mu37 \mu61 \chi1 \chi2 \chi3 \chi4 \chi5


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 ("chi") wheels, and the \psi ("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 ("mu") or "motor" wheels.[11] The SZ40 \mu61 wheel moved one position with each character, but the \mu37 wheel moved on only when the cam on the \mu61 wheel was in the active position. If the cam on the \mu37 wheel was in the active position, all five psi wheels then moved.[11] The SZ42A and SZ42B models had additional complexity to this mechanism, known at Bletchley Park as Limitations.[12]

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.[11]

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.[13] 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.


Each "Tunny" link had four SZ machines with a transmitting and a receiving teleprinter at each end. For enciphering and deciphering to work, the transmitting and receiving machines had to be set up identically. There were two components to this; setting the patterns of cams on the wheels and rotating the wheels for the start of enciphering a message. The cam settings were changed less frequently before the Summer of 1944. The psi wheel cams were initially only changed quarterly, but later monthly, the chi wheels were changed monthly but the motor wheel patterns were changed daily. From 1 August 1944, all wheel patterns were changed daily.[14]






Tunny traffic was known by Y Station operators used to listening to Morse code transmission as "new music". Its interception was originally concentrated at the Foreign Office Y Station operated by the Metropolitan Police at Denmark Hill in Camberwell, London. But due to lack of resources at this time (~1941), it was given a low priority. A new Y Station, Knockholt in Kent, was later constructed specifically to intercept Tunny traffic so that the messages could be efficiently recorded and sent to Bletchley Park.[17] The head of Y station, Harold Kenworthy, moved to head up Knockholt. He was later promoted to head the Foreign Office Research and Development Establishment (F.O.R.D.E).

Code breaking[edit]



Decryption machines[edit]

Several complex machines were built by the British to aid the attack on Tunny. The first was the British Tunny.[20][21] This machine was designed by Bletchley Park, based on the reverse engineering work done by Tiltman's team in the Testery, to emulate the Lorenz Cipher Machine. When the pin wheel settings were found by the Testery, the Tunny machine was set up and run so that the messages could be printed.

A family of machines known as "Robinsons" were built for the Newmanry. These used two paper tapes, along with logic circuitry, to find the settings of the chi pin wheels of the Lorenz machine.[22] The Robinsons had major problems keeping the two paper tapes synchronized and were relatively slow, reading only 2000 characters per second.


Testery executives and Tunny codebreakers[edit]

  • Ralph Tester linguist and head of Testery
  • Jerry Roberts shift-leader, linguist and senior codebreaker
  • Peter Ericsson shift-leader, linguist and senior codebreaker
  • Victor Masters shift-leader
  • Denis Oswald linguist and senior codebreaker
  • Peter Hilton codebreaker and mathematician
  • Peter Benenson codebreaker
  • Peter Edgerley codebreaker
  • John Christie codebreaker
  • John Thompson codebreaker
  • Roy Jenkins codebreaker
  • Tom Colvill general manager

By the end of the war, the Testery had grown to 9 cryptographers, 24 ATS girls (as the women serving that role were then called) with a total staff of 118, organised in 3 shifts working round the clock.

Surviving machines[edit]


In Germany, examples may be seen at the Heinz Nixdorf MuseumsForum, a computer museum in Paderborn and the Deutsches Museum, a museum of science and technology in Munich.[26] A Lorenz machine is also displayed at Bletchley Park in the United Kingdom and at the National Cryptologic Museum in the United States.

See also[edit]


  1. ^ Hinsley 1993, p. 141
  2. ^ Hinsley 1993, p. 142
  3. ^ Copeland 2006, pp. 38, 39
  5. ^ Good 1993, pp. 160–165
  6. ^ Klein, p. 2
  7. ^ Klein, p. 3
  12. ^ Good, Michie & Timms 1945, p. 8 of German Tunny
  13. ^ Churchhouse 2002, p. 158
  14. ^ Good, Michie & Timms 1945, p. 14 of German Tunny
  15. ^ Copeland 2006, p. 45
  16. ^ Churchhouse 2002, p. 34
  17. ^ Good, Michie & Timms 1945, p. 281 in Knockholt
  18. ^ Tutte 1998, pp. 356, 357
  19. ^ Roberts 2009
  20. ^ Halton 1993
  21. ^ Bletchley Park completes epic Tunny machine The Register, 26th May 2011, Accessed may 2011
  22. ^ Copeland 2006, p. 66
  23. ^ Flowers 2006, p. 100
  25. ^ Copeland 2006, p. 173
  26. ^ "Cryptology". Dsutches Museum. Retrieved 30 October 2014. 


Further reading[edit]


External links[edit]