Secure, Reliable Information

Abstract

This chapter introduces “clock arithmetic”, or modular arithmetic, using the division theorem and the concept of least non-negative residue. These ideas are used to describe some historic examples of the two main applications of the book. Cryptology, or the study of methods of making information secret except to persons with special knowledge, is illustrated by additive Caesar ciphers, and Vigenere and Vernam (one-time pad) cryptosystems. Coding, or the study of methods to add redundancy to a message to determine if it is compromised by errors, is illustrated by check digits in several settings, and by repetition coding, a special case of which has historically been known as triple modular redundancy.