Cryptography Reference
In-Depth Information
Figure 2.5:
The Enigma ciphering machine (courtesy of M. Swimmer, IBM).
four rotors, since the positions of submarines had to be kept particularly
secret. The first three rotors could be selected from a total of five (chang-
ing rotors, however, is said not to have been easy). From 1943 onwards, a
sixth rotor was available to the navy, which could take the fourth position.
Finally, there was a total of eight rotors, partly with deviating movement prop-
erties.
Enigma's key consisted of the selection and arrangement of three or four rotors,
their ground positions, and the description of the plugboard.
The army Enigma had 26
3
possibilities for the three rotor positions, multiplied
by 10 possibilities to select three rotors out of five, each multiplied by 3!
=
6
possible rotor sequences. This resulted in a total of 1 054 560 possible keys.
And we haven't considered the permutations on the plugboard yet. Twenty-
six letters could be grouped in pairs in 26!/(13!*2
13
)
ways, i.e., in roughly
eight billion ways. This resulted in a total of about eight trillion (8*10
18
)
possible keys for the Enigma (and not 265 749 120 as stated in the file
enigma-
wiring.txt
; the author forgot a few multiplications). That's an extremely large
number of possibilities, even for current computer technology. By the way,
though several reversing drums existed, they were never changed in a perma-
nent machine.
This sort of number-crunching game had impressed the cryptologists and cer-
tainly the top Nazi echelon. Anyhow, the German Wehrmacht thought the
Enigma was perfectly secure. The Enigma almost gained a monopoly; estimates
state that between 40 000 and 200 000 machines were built. It was perhaps the
first time that so much depended on one single algorithm. The Enigma was the
basis for secure radio communications in the entire Wehrmacht.
