A History of Cryptography - Introduction to Cryptography with Java Applets - page 19

By themselves, transposition ciphers are considered very weak ciphers. Anyone who has
played anagrams or has done unscrambling puzzles in the newspaper can testify to this.
However, when transposition is used in combination with substitution, one can produce
very powerful ciphers. Many modern ciphers are based on this idea.

1.15

POLYGRAM SUBSTITUTION CIPHERS
Mapping single letters to single letters is far too vulnerable to be useful. Thus, cryptogra-
phers eventually came up with the idea of mapping entire blocks of plaintext letters to blocks
of ciphertext letters. The ciphertext blocks didn't necessarily have the same length as the
plaintext blocks. For example, suppose we wish to map 8 letter blocks to 8 letter blocks. In
general, we could specify the mapping shown in Table 1.19.
There are clearly a lot of 8-letter plaintext blocks in the range AAAAAAAA through
ZZZZZZZZ (26 8 , exactly). If one wanted to do frequency analysis on such a scheme, he
would require a table of 26 8 = 208,827,064,576 blocks, and would have to know the rela-
tive percentages for which each 8-letter block appears in typical English text (if that is the
language being used). Then, he would need an enormous amount of ciphertext so that he
could determine the relative frequency of the 8-letter ciphertext blocks, and equate cipher-
text blocks to plaintext blocks. This is clearly infeasible, both in terms of the time and stor-
age requirements. Thus, doing frequency analysis on blocks of letters is much harder than
doing frequency analysis on individual letters. However, if the cryptosystem does not use
a sufficiently large block size, frequency analysis is still possible. An example follows.

1.16

THE PLAYFAIR CIPHER
The Playfair cipher was a cryptosystem that mapped digraphs (2-letter pairs) to digraphs.
The letters were arranged in a 5 5 square. There are 26 letters in the ordinary alphabet,

so the letters I and J were equated. This is the simplest 5 5 Playfair square:

A B C D E

F G H I/J K

L M N O P

Q R S T U

V W X Y Z

TABLE 1.19

AAAAAAAA maps to ZXCIJCDV

AAAAAAAB maps to APQODFIM

... ... ...

ZZZZZZZZ maps to SSTFQQWR