## Chapter 1 Introduction

Welcome to Cryptology by Discovery. In this course, you will study the mathematics behind encrypting and decrypting secret messages. We will primarily follow a historical approach, beginning with the simplest methods of encoding messages, and work up to some of the more complicated present day cryptographic systems, which are used in web and electronic security. We will also discuss methods of breaking these codes and which ones are secure. Mathematics has played an important role in developing and breaking codes. We will study a variety of mathematical topics from discrete mathematics, number theory, probability, permutations and matrices as necessary to understand these codes. We begin with some definitions and terminology.