A First Look at Number Theory

Abstract

As we progress to more advanced forms of cryptography, we will need to use more and more mathematics. Many areas of mathematics are relevant to cryptography, and we will look at a few of those. However, by far the most important branch of mathematics for cryptography is number theory. In this chapter, we will see a few very ancient theorems and techniques in number theory, going back to ancient Greece. Some of the theorems and proofs here were already included in Euclid ’s Elements [Euc02], surely the most read math book in history. Later, we will return to number theory and look at more recent advances, going up to the 21st century.