3 - Polyalphabetic Substitution

Summary

Polyalphabetic ciphers

The preceding chapter has indicated how a monoalphabetic cipher can be solved. Even if the original word lengths are concealed and the substitution alphabet is random, it is possible to find a solution by using frequency data, repetition patterns and information about the way letters combine with one another. What makes the solution possible is the fact that a given plain language letter is always represented by the same cipher letter. As a consequence, all the properties of plain language such as frequencies and combinations are carried over into the cipher and may be utilized for solution. In effect we could say that all such properties are invariant except that the names of the letters have been changed.

It would seem then that one way to obtain greater security would be to use more than one alphabet in enciphering a message. The general system could be one that uses a number of different alphabets for encipherment, with an understanding between the correspondents of the order in which the alphabets are to be used.

As an illustration of a classic procedure, consider the method that was devised by the French cryptographer Vigenère. It utilizes the encipherment square which is known by his name—the Vigenère square—described in Chapter 1 (Figure 1.2). This square, whose successive rows consist of the normal alphabet shifted by 1 place, 2 places, etc., can be easily constructed whenever it is needed.