1.1. Introduction

It is rather difficult to give a precise definition of cryptography. Loosely speaking, it is the science (or art or technology) of preventing access to sensitive data by parties who are not authorized to access the data. Secure transmission of messages over a public channel is the first, simplest and oldest example of a cryptographic protocol. For assessing the security of these protocols, one studies their possible weak points, namely the strategies for breaking them. This study is commonly referred to as cryptanalysis. And, finally, the study of both cryptography and cryptanalysis is known as cryptology.

The science of cryptology is rather old. It naturally developed as and when human beings felt the need for privacy and secrecy. The rapid deployment of the Internet in the current years demands that we look into this subject with a renewed interest. Newer requirements tailored to Internet applications have started cropping up and as a result newer methods, protocols and algorithms are coming up. The most startling discoveries include that of the key-exchange protocol by Diffie and Hellman in 1976 and that of the RSA cryptosystem by Rivest, Shamir and Adleman in 1978. They opened up a new branch of cryptology, namely public-key cryptology. Historically, public-key technology came earlier than the Internet, but it is the latter that makes an extensive use of the former.

This book is an attempt to introduce to the reader the vast and interesting branch of public-key cryptology. One of the most distinguishing features of public-key cryptology is that it involves a reasonable amount of abstract mathematics which often comes in the way of a complete understanding to an uninitiated reader. This book tries to bridge the gap. We develop the required mathematics in necessary and sufficient details.

This chapter is an overview of the topics that the rest of the book deals with. We start with a description of the most common cryptographic protocols. Then we introduce the public-key paradigm and discuss the source of its security. We use certain mathematical terms and notations throughout this chapter. If the reader is not already familiar with these terms, there is nothing to worry about. As we have just claimed, we will introduce the mathematics in the later chapters. The exposition of this chapter is expected to give the reader an overview of the area of public-key cryptography and also the requisite motivation for learning the mathematical tools that follow.