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

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chapter 3
A Vigenère cipher is a particular, and rather special, case of a polyalphabetic
system in which, as the name implies, a number of different substitution
alphabets are used rather than just one, as in simple substitution systems.
The number of substitution alphabets used may be anything from 2 to
many thousands; in the enigma for example it is effectively 16 900, and
these are simple substitutions, not Julius Caesar type shifted alphabets as
in Vigenère ciphers, as we shall see in Chapter 9.
How to solve a Vigenère cipher
The first step in solving a Vigenère cipher is to determine the length of the
key and, assuming that there is sufficient cipher text available, we do this
by looking for repeated combinations of letters, polygraphs as they are
called, and noting how far apart they are in the text. If these repetitions are
genuine, that is if they are cipher versions of the same plaintext, then they
will be separated by multiples of the length of the key which should then
be identified or, at least, reduced to one of a small number of possibilities.
The longer the repeated polygraphs are the better the situation for the
cryptanalyst, but even digraphs, two-letter combinations, can be helpful.
Example 3.1
A cipher message of 157 characters enciphered by a Vigenère cipher with
Z used as ‘space’ is
HQEOT FNMKP ELTEL UEZSI KTFYG STNME GNDGL
PUJCH QWFEX FEEPR PGKZY EHHQV PSRGN YGYSL
EDBRX LWKPE ZMYPU EWLFG LESVR PGJLY QJGNY
GYSLE XVWYP SRGFY KECVF XGFMV ZEGKT LQOZE
LUIKS FYLXK HQWGI LF
(1) Find the length of the key.
(2) Find the key and decrypt the message.
Solution
(1) We examine the text and find that six digraphs occur three times or
more, viz:
EL at positions 11, 14 and 140;
FY at positions 23, 119 and 146;
GN at positions 31, 64 and 103;
HQ at positions 1, 40, 58 and 151;
LE at positions 70, 91 and 109;
YG at positions 24, 66 and 105.