Secret Key Cryptography

15 Matrix methods

This chapter covers

• Ciphers using multiplication by a matrix of integers, or a matrix of ring elements
• Ciphers using multiplication by large and small integers
• Solving linear congruences
• Constructing rings and invertible matrices

Matrices are a tool well-suited for cryptography because they can encipher arbitrarily large blocks of text in one operation. Typically, each block in the message is treated as a vector of bytes, meaning integers modulo 256.

When Sandra uses a matrix to encipher a message, Riva must use the inverse of that matrix to decipher the message. Let’s begin the discussion of matrix methods with a technique ...