Historical Cryptosystems - Everyday Cryptography - page 63

LESSONS FROM THE PLAYFAIR CIPHER
There are several important lessons to be learnt from the Playfair Cipher.
Avoiding the monoalphabetic property makes frequency analysis harder .
Cryptanalysis is nowmuch harder. Letter frequency analysis has been rendered
ineffective by designing an encryption algorithm that does not encrypt
plaintext letters by the same ciphertext letter each time they occur. The main
technique for achieving this has been to encrypt the plaintext in pairs of letters,
thus increasing the size of the plaintext (and ciphertext) alphabet from 26
single letters to 600 plaintext bigrams. The cost of this progress has been a
more complex encryption and decryption process.
Avoiding the monoalphabetic property is not enough . We have seen that
although single letter frequency analysis is defeated, cryptanalysis is only
slightly harder. Assuming that a sufficiently long ciphertext is observed, it
is still possible to conduct an analysis of the ciphertext based on this enlarged
plaintext alphabet, by analysing frequencies of ciphertext bigrams.
Efficiency can be traded-off against security . The design of the Playfair Cipher
represents an efficiency-security tradeoff, where we gain security at a slight cost
to efficiency. It is possible to imagine that we could invent a generalisation of the
Playfair Cipher that operates on trigrams (triples of plaintext letters). It would
be evenmore complex to specify and encrypt than the Playfair Cipher, but if we
designed it well then it might defeat bigram frequency analysis. However, it will
itself be prone to trigram frequency analysis (harder to conduct, but possible
using computers). For example, given enough ciphertext then it should be
possible to identify the common English trigram THE.
We will see many more efficiency-security tradeoffs in the rest of our study of
cryptography. We will also see that frequency analysis (of blocks of bits) is a
relevant attack on modern cryptosystems, so our discussion of the Playfair Cipher
is of much more than just historical interest.
2.2.3 Homophonic encoding
An alternative means of defeating single letter frequency analysis is to tackle the
letter frequencies head on. The idea behind homophonic encoding is to encrypt
plaintext letters by a number of different ciphertext characters in order to directly
confuse the ciphertext symbol frequency statistics (we say symbol rather than
letter here because, after homophonic encoding has been applied, there are many
more ciphertext symbols than there are letters in the alphabet). This technique is
best explained by means of an example.
EXAMPLE OF HOMOPHONIC ENCODING
The aim of homophonic encoding is to design a cryptosystem whose ciphertext
alphabet histogram is close to being 'flat' (in other words, every ciphertext symbol