Cryptography Made Simple

Abstract

This is a reworking of my earlier book “Cryptography: An Introduction” which has been available online for over a decade. In the intervening years there have been major advances and changes in the subject which have led me to revisit much of the material in this book. In the main the book remains the same, in that it tries to present a non-rigorous treatment of modern cryptography, which is itself a highly rigorous area of computer science/mathematics. Thus the book acts as a stepping stone between more “traditional” courses which are taught to undergraduates around the world, and the more advanced rigorous courses taught in graduate school. The motivation for such a bridging book is that, in my view, the traditional courses (which deal with basic RSA encryption and signatures, and perhaps AES) are not a suitable starting point. They do not emphasize the importance of what it means for a system to be secure; and are often introduced into a curriculum as a means of demonstrating the applicability of mathematical theory as opposed to developing the material as a subject in its own right. However, most undergraduates could not cope with a full-on rigorous treatment from the start. After all one first needs to get a grasp of basic ideas before one can start building up a theoretical edifice. The main differences between this version and the Third Edition of “Cryptography: An Introduction” is in the ordering of material. Now security definitions are made central to the discussion of modern cryptography, and all discussions of attacks and weaknesses are related back to these definitions. We have found this to be a good way of presenting the material over the last few years in Bristol; hence the reordering. In addition many topics have been updated, and explanations improved. I have also made a number of the diagrams more pleasing to the eye. Cryptography courses are now taught at all major universities; sometimes these are taught in the context of a Mathematics degree, sometimes in the context of a Computer Science degree, and sometimes in the context of an Electrical Engineering degree. Indeed, a single course often needs to meet the requirements of all three types of students, plus maybe some from other subjects who are taking the course as an “open unit”. The backgrounds and needs of these students are different; some will require a quick overview of the algorithms currently in use, whilst others will want an introduction to current research directions. Hence, there seems to be a need for a textbook which starts from a low level and builds confidence in students until they are able to read the texts mentioned at the end of this Preface. The background I assume is what one could expect of a third or fourth year undergraduate in computer science. One can assume that such students have already met the basics of discrete mathematics (modular arithmetic) and a little probability. In addition, they will have at some point done (but probably forgotten) elementary calculus. Not that one needs calculus for cryptography, but the ability to happily deal with equations and symbols is certainly helpful. Apart from that I introduce everything needed from scratch. For those students who wish to dig into the mathematics a little more, or who need some further reading, I have provided an appendix which covers most of the basic algebra and notation needed to cope with modern cryptosystems.