Historical Cryptosystems - Everyday Cryptography - page 59

2. Allow the same plaintext letter to be encrypted to different ciphertext letters .
Letter frequency analysis is easy to perform on monoalphabetic ciphers. If we
allow several ciphertext letters to represent the same plaintext letter then letter
frequency analysis becomes more difficult.
3. Make the choice of ciphertext letter that is used to encrypt a plaintext letter
depend on the position that the plaintext letter occupies within the plaintext .
This is a particular example of the previous approach. By introducing a
dependency on the position that a letter occupieswithin the plaintext ( positional
dependency ) then a letter occurring in two different positions within the
plaintext is likely to be encrypted into two different ciphertext letters, again
helping to defeat letter frequency analysis.
We now look at three historical cryptosystems, each of which uses one or more of
these techniques in order to defeat single letter frequency analysis.

2.2.2 Playfair Cipher

The Playfair Cipher is an unusual cryptosystem because it operates on pairs of
letters ( bigrams ). The Playfair Cipher consists of a preprocessing stage and then
an encryption stage.

PREPROCESSING FOR THE PLAYFAIR CIPHER
The plaintext requires a degree of preprocessing before it can be encrypted. We
now describe this process and explain why each step is necessary.

1. Replace J's with I's : The Playfair Cipher is based on a 5 5 square grid (the

Playfair Square ) with 25 positions, each of which contains a different letter of
the alphabet. Thus one letter of the alphabet cannot appear in this grid and
must be discarded. It makes most sense for this to be a fairly uncommon letter.
There is nothing special about the selection of the letter J, other than it does not
occur often in English. The choice of replacement of the letter J by the letter I is
because of the superficial resemblance between these two letters. A number
of variants of the Playfair Cipher could be designed that remove a different
unpopular letter and replace it by another of the remaining letters.
2. Write out the plaintext in pairs of letters : This is done because the Playfair
Cipher operates on bigrams, and hence processes the plaintext in 'blocks' of
two letters.
3. Split identical pairs by inserting a Z between them : The Playfair Cipher relies on
the two letters in each plaintext bigram being different. If a plaintext bigram
currently consists of two identical letters then the letter Z is inserted between
them in the plaintext in order to separate them. There is nothing special about
the selection of the letter Z. Any other unpopular letter could be chosen instead.
Indeed, if two Z's occur together in a bigram of the plaintext then some other
letter must be inserted between them.

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