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

going into the mathematical criteria for deciding if a sequence is random
a suitable definition for our purposes is
Definition 8.1
A binary sequence is considered to be random if, no matter how many
digits we have seen, the probability that the next digit will be 0 is 0.5.
This is the situation that should apply if one spins an ‘unbiased’ coin many
times: no matter what has already happened the probability that it will
come down ‘heads’ next time should be 0.5, or in terms of odds, ‘evens’.
There is nothing special about binary sequences; our definition of randomness
can be applied with only slight modification to sequences of
decimal digits or letters.
Definition 8.2
A sequence of decimal digits is considered to be random if, no matter how
many digits we have seen, the probability that the next digit will have a
particular value is 0.1.
Definition 8.3
A sequence of letters from the English alphabet is considered to be
random if, no matter how many letters we have seen, the probability that
the next letter will be a particular one is 1/26.
Producing random sequences
A truly random sequence can only be generated by a truly random process
and so, in particular, cannot be generated by any mathematical formula,
for knowledge of the formula and sufficient initial values (i.e. of numbers
already generated by the formula) would enable someone to predict the
next value with certainty. There are, however, formulae which can
produce a long sequence of numbers which satisfy many randomness criteria
before they start to repeat; such sequences are called ‘pseudorandom’
and we describe some of these below, but first we look at some
ways of generating truly random sequences.
Coin spinning
Producing random numbers and letters 95
If we spin a ‘fair’ coin many times and write down ‘1’ each time it comes
up ‘heads’ and ‘0’ each time it comes up ‘tails’ we ought to get a random
binary sequence. In practice, perhaps because of some regularity about