Mathematical Background

This chapter introduces the basic mathematical background for better understanding cryptography that is applied in wireless security. It provides an overview on basic concepts in modern algebra and number theory. In mathematics, number theory is the study of the set of integers and integer‐valued functions. Groups, rings, and fields are the basic elements in modern algebra. Besides group axioms, there are several other concepts related to groups. The chapter defines an abelian group and a cyclic group. It also introduces prime numbers, modular arithmetic and divisors. The chapter examines finite field and Galois field. Finite fields are used in a variety of cryptography algorithms such as the AES encryption algorithm and public key cryptography. The chapter outlines polynomial arithmetic, followed by Fermat's little theorem, Euler's totient function, Euler's theory, primality testing, Chinese remainder theorem, and discrete logarithm.