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

Cryptanalytic aspects of Playfair
Playfair encipherment has certain properties that a cryptanalyst might
exploit including the following.
(i) A letter cannot encipher to itself.
(ii) A letter can only encipher to one of 5 other letters which are the 4 other
letters in its row and the letter below it in its column.
(iii) A letter is twice as likely to encipher to the letter immediately to its
right than to any other letter. So, for example, in the square used in
Example 5.6 (Table 5.5), if the second letter of a digraph beginning
with M is not in the same row or column as M then M enciphers as E, F, H
or O. If the second letter of the digraph is in the same row as M then M
enciphers as O and if the second letter is in the same column as M then M
enciphers as S. It follows that of the 24 possibilities for letters which
can follow M in the plaintext (since J is not included and M would cause
a dummy to be introduced) E, F, H, O, I, D, T and Z each cause O to
occur as the cipher letter whereas the other 16 letters will cause E, F, H,
and S each to occur four times. So in this case M will encipher to O twice
as often as to any other letter and the same feature will hold for any
other letter.
(iv) There is reciprocity between plain and cipher digraphs unless the
letters are in the same row or column; that is, if CR, say, enciphers to PJ
then PJ enciphers to CR and, furthermore, RC enciphers to JP and vice
versa.
The usual method of attack on a Playfair cipher is via the digraphs.
With a sufficiently long text a count of the cipher digraphs should reveal
likely candidates for the cipher equivalents of high frequency plaintext
digraphs such as TH, HE, IN and ER and since the reversals of two of these
digraphs, HT and EH, have very low frequencies identification is made that
much easier. Having identified the relative positions of some letters it
may be possible to deduce which letters are in the keyword and then to
reconstruct the Playfair square. An example of such a solution using a
text of over eleven hundred digraphs is given in [5.3].
Double Playfair
Two-letter ciphers 61
Playfair encipherment was used by the British for some of their military
ciphers up to and including the 1914–18 war and the Germans had considerable
success in reading the messages. In World War II the German
Army, knowing the weakness of the single Playfair cipher, used a double