Overview

Cryptography is the science of information and communication security. It entered in mass product markets quite recently and every citizen from developed countries uses it daily. It is used for authentication and encryption (bank cards, wireless telephone, e-commerce, pay-TV), access control (car lock systems, ski lifts), payment (prepaid telephone cards, e-cash), and may become the fundamental instrument of democracy with the advent of e-voting systems. To master cryptographic tools becomes a requirement for most engineers. The present book aims at presenting fundamentals on modern cryptography.

Cryptography is a puzzling kaleidoscope where we have to face and use malice at the same time, to rationalize irrational behaviors, to prove unprovability, and to twist mathematics to make it fit applications. We easily switch from theoretical questions on elliptic curves to standardization problems such as how to represent a number in a communication protocol. One needs to juggle with assembly code on chips and distributed systems over the Internet. We are concerned about commercial aspects such as patents or mass products, as well as communication aspects since cryptography is more and more exposed in media, novels, and movies. Since I first started to work on cryptography, I always summarized how fun it was by the slogan La crypto c'est rigolo! ^[1] My wish is that the reader appreciates the malicious beauty of this puzzling science throughout this textbook.

When writing the preamble of textbooks, authors usually try to justify themselves for introducing yet-another-book. Actually, I had to set up a...