A Cryptographic Machine

In a recent textbook (1) on the theory of numbers Professor B. M. Stewart suggests the usefulness of the algebra of matrices over a finite field for encoding messages. The procedure is as follows. First the message is written as a normal message. Then each letter of the alphabet and each punctuation mark is associated with an element of a finite field F. Then the message is broken up into blocks, each block being a square matrix, and each matrix is premultiplied (or postmultiplied) by a non-singular scrambling matrix C whose elements are in the field, F. Each resulting matrix is translated into its alphabetical and punctuated form and the resulting code message is transmitted. On the receiving end, the code message is translated into a collection of matrices again and the matrices are premultiplied (or postmultipled) by the inverse of C. The resulting matrices are translated into blocks of punctuated and spaced words forming the message. Of course, C must be nonsingular and C-1 must be known to the receiver