Applications Of Permutations And Substitutions To Cryptography

Abstract

This honors thesis explores two different encrypting methods, permutations and substitutions, and how they are combined to form two famous cryptosystems, the Enigma and DES. Permutations and substitutions have been used in cryptography for the past two thousand years, dating back to Julius Caesar and the Egyptians. The algorithms themselves are very simple, yet when multiple permutations and substitutions are combined, some ofthe most sophisticated and complex coding methods of our time are produced. In this paper we first review the basic permutation and substitution ciphers. We then see how these ciphers are used in two very modem and complex applications. The first is the Enigma machine, used by the Germans in World War II. We explain how this “unbreakable” coding method was finally broken. The second application of permutation and substitution ciphers that is discussed is the Data Encryption Standard (DES). We briefly state the controversy surrounding the use of DES and mention a few of its successors designed to overcome these perceived problems.