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

The Hagelin cipher machine 145
Example 10.4
The following stretch of key has been recovered from a mini-Hagelin with
three wheels of lengths 5, 8 and 9. Recover the kicks and pin patterns.
6 4 3 6 8 6 4 5 1 8 4 1 8 6 8 1 6 3 9 0 4 6 8 6 0.
Solution
We may apply the differencing operations in any order. If we begin with
interval 5 and then use interval 8 we will eliminate the contributions of
the 5- and 8-wheels and should obtain a stream of numbers all of which
are multiples (positive, negative or zero) of the kick on the 9-wheel. So:
Key 64368645�18�4�1868�1�6�3�9�04�68�6�0
Shift 5 6 4 3�68�6�4518�4�1�8�6�81�63�9�0
�5 002�50�2�3350�3�5�5�3�83�05�3�0
Shift 8 0 0�2�5�0�2�33�50�3�5
�8�5 50�5 10�5�5�50�55�0�5
The kick on the 9-wheel is obviously 5; note that the pattern begins to
repeat after 9 places. Note also that the doubly differenced key has one
value equal to twice the kick; this is a particular case of the following:
‘When the key stream is differenced N times a value of up to �2 (N�1)
times the kick may occur’ (for an explanation see M19).
We now find the kick on the 8-wheel. This involves differencing at
interval 5 and interval 9, in either order. Since we already have the key differenced
at interval 5 (i.e. �5 above) we need only difference that at interval
9:
�5 002�5 0�2 �3 350�3 5�5 3�8 �3 �0 5�3 �0
Shift 9 0 �0 2�5 0�2 �3 �3 5�0 �3
�9�5 0 �3 3�0 3�6 �6 �3 0�3 �3
The pattern begins to repeat after 8 places, as it should, and the kick on
the 8-wheel is obviously 3.
Similarly, by differencing the original key stream at interval 8 and
then at interval 9 we obtain
�9�8 0 1 �2 1 0 0 1 �2
The pattern begins to repeat after 5 places and the kick on the 5-wheel is
obviously 1.
We now have to find the patterns on the three wheels. We do this
by looking at the key values and seeing how they might arise from