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

158
chapter 11
Solution
Plaintext letter (S) 1 0 1 0 0
Set A pin values 0 1 0 1 1
(mod 2) sum 1 1 1 1 1
Set C pin values 1 0 0 1 0
(mod 2) sum 0 1 1 0 1�P.
So the cipher letter will be P. If we now start with the cipher letter, P,
then, with the same pin values the decipherment process gives
Cipher letter (P) 0 1 1 0 1
Set A pin values 0 1 0 1 1
(mod 2) sum 0 0 1 1 0
Set C pin values 1 0 0 1 0
(mod 2) sum 1 0 1 0 0�S,
confirming the original plaintext letter.
Breaking and setting the SZ42
Assuming that the cryptanalyst knew the design details of the SZ42, as
given in Figure 11.1, and that it was being used, how many possibilities
would he have to consider before he could be certain of being able to
decipher a message? The answer is easily obtained. The motion of the
wheels and the encipherment are completely determined by the pins on
the 12 wheels. Since there are 501 pins in all and each of them can be
placed in either of two states, ‘active’ or ‘inactive’, the number of possibilities
is
2 501 � 10 151 .
This is the ‘breaking work factor’ and it is so large that if every particle in
the Universe was a computer and had been assigned full time ever since
the ‘Big Bang’ to trying all the possibilities the solution would still not
have been found. Clearly, a ‘brute force attack’ approach to breaking the
SZ42 is hopeless.
If the cryptanalyst knew all of the pin patterns and a new message
appeared he would have the ‘easier’ task of finding the settings of the 12
wheels at the start of the message. The number of possibilities that he
would have to try is the product of the wheel lengths, viz:
23�26�29�31�37�41�43�47�51�53�59�61