Digraphic ciphers based on linear transformations—matrices

We have seen in the previous chapters that various techniques associated with the frequencies of individual letters and their combinations enable the cryptanalyst to cope with different kinds of substitution ciphers. Conceivably this may remain true even for more sophisticated methods of cryptography so long as the unit of cryptography remains a single letter. Perhaps the way for the cryptographer to prevent the cryptanalyst's successes with letter frequencies might be to make the unit of encipherment a group of letters instead of just one. A system of cryptography in which a group of n plain text letters is replaced as a unit by a group of n cipher letters is called a polygraphic system.

In the simplest case, n = 2, the system is called digraphic. Each pair of plain text letters is replaced by a cipher digraph.

There are many different ways to set up the plain-cipher relationships for a digraphic system. For example, a 26 × 26 square can be constructed with the 262 = 676 possible digraphs entered randomly into the cells of the square. Normal alphabets across the top of the square and down the left side serve as plain language coordinates. The cipher equivalent of the plain digraph P1P2 is found in the cell on row P1 and in column P2. A portion of such a square is shown in Figure 4.1. For example, the cipher equivalents for AC, BE, CD are RA, AS, YE.