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

18
chapter 2
which is written in mathematics, for convenience, as 26!, called factorial
26. This is an enormous number, bigger than 10 to the 26th power, (or
10 26 as it is commonly written) so that even a computer capable of testing
one thousand million (i.e. 10 9 ) alphabets every second would take several
hundred million years to complete the task. Evidently, the method of
trying all possibilities, which works satisfactorily with Julius Caesar
ciphers, where there are only 25 of them, is quite impracticable here.
The practical method for solving this type of cipher is as follows.
(1) Make a frequency count of the letters occurring in the cipher, i.e. count
how many times A, B, C, ..., X, Y, Z occur.
(2) Attempt to identify which cipher character represents ‘space’. This
should be easy unless the cipher message is very short, since ‘space’ and
punctuation symbols account for between 15% and 20% of a typical
text in English with ‘space’ itself accounting for most of this. It is
highly likely that the most frequently occurring cipher letter
represents ‘space’. Furthermore, if this assumption is correct, the
cipher letter which represents ‘space’ will appear after every few
characters, with no really long gaps.
(3) Having identified ‘space’, rewrite the text with the spaces replacing the
cipher character representing it. The text will now appear as a
collection of separated ‘words’ which are of the same length and
structure as the plaintext words. So, for example, if a plaintext word
has a repeated letter so will its cipher version.
(4) Attempt to identify the cipher representations of some of the high
frequency letters such as E, T, A, I, O and N which will together
typically account for over 40% of the entire text, with E being by far the
most common letter in most texts.
A table of typical frequencies of letters in English is a great help at
this point and such a table is given as Table 2.4; a second table, based
upon a much larger sample, will be found in Chapter 7; either will
suffice for solving simple substitution ciphers. The tables should only
be treated as guides; the higher letter frequencies are reasonably
consistent from one sample to another but low letter frequencies are of
little value. In the table of English letter frequencies printed below, the
letters J, X and Z are shown as having frequencies of 1 in 1000 but in
any particular sample of 1000 letters any one of them may occur
several times or not at all. Similar remarks apply to letter frequencies
in most languages.
(5) With some parts of words identified in this way look for short words
with one or two letters still unknown, for example if we know T and E
and see a three-letter word with an unknown letter between T and E