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

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appendix
Verification
If such a recurrence exists it takes the form
U n �aU (n�1) �bU (n�2) �cU (n�3) .
The data then give the equations
a � b � 0,
b � c � 1,
a � c � 0.
Adding the first and second equations (mod 2) we get
a�c�1
which contradicts the third equation. The equations are therefore inconsistent
and no solution of order 3 exists.
M13 Generation of pseudo-random numbers
In a typical application, such as where we require random numbers which
are uniformly distributed over the interval [0, 1], the integers generated
by the recurrence are divided by the modulus. The 16 integers in Example
8.4 would thus be divided by 17 to give the following 16 pseudo-random
numbers (to two decimal places):
0.29, 0.12, 0.59, 0.00, 0.24, 0.94, 0.06, 0.41, 0.47, 0.65, 0.18, 0.76,
0.53, 0.82, 0.71, 0.35.
In realistic-sized applications it would be necessary to use a very large
modulus and, even better, to utilise more than one linear recurrence and
then combine the results in some way, to provide a less predictable set of
values. For a useful discussion of these matters, suggested sets of values
for the modulus, multiplier and increment, as well as relevant computer
programs, see Chapter 7 of [8.4].
Chapter 9
M14 Wheel wirings in the Enigma
The simple substitution alphabets provided by an Enigma wired wheel at
eachofthe26positionsofthatwheelcanberepresentedbya26�26matrix.
The first column of the matrix shows the encipherment of the 26 letters at
setting 1 of the wheel, the second column shows the encipherment of