Mathematical Foundations of Cryptography

Abstract

This chapter introduces some basic mathematical concepts necessary to understand the design of modern cryptographic algorithms and protocols. It begins with definitions of such algebraic structures as groups, rings, and finite fields, followed by some of their applications. This part also includes fundamental number theoretic definitions and properties playing an important role in cryptographic applications: the integer divisibility relation, the greatest common divisor, the least common multiple, the prime numbers, Euler’s totient function, the congruence relation, and their basic properties.