The Lorenz

The Lorenz cipher was known to the Allies as Tunny because they had no idea what machine was generating the cipher and so gave it a name.  The Lorenz had 12 wheels: 5 Chi wheels, 5 Psi wheels and 2 Motor wheels. Their movement was as follows:

5 Chi Wheels	Always moved (the second chi wheel only turning once the first chi wheel had completed a full revolution, the third wheel only turning after the second wheel had completed a full revolution and so on)
5 Psi Wheels	Either all 5 wheels moved together in one step or they stayed still
2 Motor Wheels	Caused the Psi wheels to move.

The key is generated either solely by the Chi wheels or by a combined effort of the Chi and Psi wheels. See Enciphering with Lorenz for further information.

German operators would set their Lorenz machine by setting the pins around each wheel to operative or inoperative (these settings changed once a month) and also setting the wheel start positions (these changed for each message).

A Lorenz could be set up: 104,970795,887142,501519,944408,859713,937438,238568,341584,154526,205632,598745,732639,647278,021173,163831,071764,896225,159592,365198,842461,226688,733330,753486,243770,471723,522422,795262,754816 different ways.

That’s 100 million million million million million million million million million million million million million million million million million million million million million million million million million million million million.

Lorenz was used to send high grade strategic information between Hitler and his generals. Approximately 13,508 Lorenz messages were deciphered at Bletchley Park from November 1942 to 8 May 1945 (see page 394 of the General Report on Tunny). 

Enigma

In comparison to Lorenz, an Enigma machine had three or four wheels (rotors). Although Enigma was less complicated than Lorenz, Enigma was more widely used because it was portable and so was easily taken into the field and on board U-Boats. Enigma was a tactical code to break, whereas Lorenz was mostly strategic.

A standard three rotor Enigma with plug board could be set up 158,962555,217826,360000 different ways, that’s almost 159 million million million. Three rotor Enigma machines were used by the German Army and Air Force, and four rotor Enigma machines by the Navy.

In the video below Dr James Grime introduces the Lorenz cipher, explains the complex mathematics of the machine and how the cipher was broken.