Safety in Numbers: Modern Cryptography from Ancient Arithmetic

Abstract

This chapter shifts the focus on cryptography from historical ciphers to their present day replacements. The content is split into two parts. First, the fundamentals of number theory (a branch of pure Mathematics) is introduced; the main topic is that of modular arithmetic, including a range of simple algorithms used to compute results. Using this starting point, it then describes two modern cryptographic schemes (the RSA encryption, and Diffie-Hellman key exchange schemes) that more or less all of us rely on every day. For example, both form components within the Secure Sockets Layer (SSL) which supports secure web-browsing.