A Survey of Modern Mathematical Cryptology

Much of modern applied mathematics, and in particular modern applied algebra, has focused on creating algorithms by which two parties can securely communicate information. Numerous such algorithms have been published in the past thirty years; some have been shown as insecure whereas others have withstood scrutiny for many years. A class of these algorithms, known as key agreement protocols, are of particular importance because of their utility in secure, rapid encryption. In this paper, we will explore some of the ideas behind some public-key cryptosystems; in particular, we will analyze an algorithm that was proposed in [2].