Code and ciphers: Julius Caesar, the Enigma and the internet

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chapter 9
This plethora of substitution alphabets provides good security but
that is not the end of the story, for before 16 900 letters have been enciphered
the three wired wheels can be removed and put back in a different
order on the common axle. In the original Enigma there were only three
wheels in the set which was provided with the machine and so they could
be ordered in six ways. The number of available simple substitution
alphabets was therefore
6�16 900�101 400.
In fact, since R2 can be started in any of its 26 positions, including Z, even
though it cannot move into position Z during normal operation unless
R1 also has previously been at Z, there are 6�26�26�26�105 456 possible
starting positions and simple substitution alphabets.
Assuming that a cryptanalyst had such an Enigma he would therefore
be faced with 105 456 possible wheel settings for the start of each message
and this, in the days before computers, would appear to present him with
an impossible task. If the cryptanalyst didn’t have an Enigma available,
and didn’t know the internal wirings of the three wheels and reflector, the
number of possibilities that he would have to try would be very much
larger for there are
25! (i.e. 25�24�23�22� ... �2�1)
possible wirings of each wheel, and this number is greater than
10 25 .
Three such wheels, therefore, can be wired in more than
10 75
ways. Furthermore, the cryptanalyst wouldn’t know the internal wiring
of the reflector and this multiplies the number of possibilities by a factor
of more than
10 12
(for the calculation of this number see M15). Consequently, the cryptanalyst
faced with messages enciphered on an Enigma with unknown
wirings would apparently have to try more than
10 87
decryptions before being sure of success. Cryptographers, however,
assume that the enemy will have acquired one of their machines on the