Preface to the Second Edition

WELCOME, New Co-author

It is a privilege to welcome back our readers, past, present, and future to this second edition. We are delighted to introduce a third author, Dr. James McQuillan from Western Illinois University. We now have as co-authors a mathematician, a computer scientist, and an engineer which, we feel, provides a good balance.

Intended Readership, Connections Between the Areas

This new edition, like the first edition, is intended for a broad audience and our goals have not changed. Over the last 15 years, the three areas in the title have become more unified. For example, cryptographer A might exchange a key with B using public key cryptography. But in doing so, both would want to use error correction ensuring accuracy of transmission. Now that they have the common secret key they might use a symmetric-key protocol such as DES or AES to exchange messages or even a one-time pad. They need to know about security, and how it is measured, which brings in probability and entropy. This example is but the tip of the iceberg.

This book arose out of courses in cryptography and information theory at the University of Calgary. It is used as a text or a reference at universities in North America and Europe and of course can be used for self-study. Parts of the material have also been presented at various industrial gatherings. Material related to some of the topics in the book has been patented and used in the energy sector.

Problems with Solutions

The second edition has well over 350 worked examples and problems with solutions.

Style

As with the first edition, we have made a considerable effort to ensure that the chapters are as accessible as possible. We wanted this new edition to also have both depth and breadth, to read with ease, and to explain the content clearly. We feel that the updates, the incorporation of new applications of basic principles, and the new examples and worked problems added to this edition greatly enhance and complete the book. We hope that it will be an excellent source for academics (including undergraduate and graduate students!) and practitioners that want to understand the mathematical principles and their real-world consequences.

In a 2005 review of the first edition for the Mathematical Association of America, Dr. William Satzer states that the book is "lively and engaging, written with palpable enthusiasm." He mentions the ". clearly communicated sense of interconnections among the [three] parts [of the book]." In a review for Mathematical Reviews (MR2131191), Dr. Andrea Sgarro from the University of Trieste, Italy, noted that the first edition ". is meant for a wide audience . and it can be used at various levels, both as a reference text and as a text for undergraduate and graduate courses; worked examples and problems are provided."

Possible Courses

Each chapter covers a lot of ground so a course might only cover part of it. For a basic course in cryptography, one could start with Chapter 2 having taken a quick look at Chapter 1. Chapter 2 introduces basic ideas on keys and security. Some of the material relates to weaknesses due to letter frequencies and requires some sophisticated mathematics described more fully in Beutelspacher, [Beu94]. Chapter 3 covers public key cryptography algorithms such as RSA and key-exchanges such as Diffie-Hellman, Elliptic curve cryptography and quantum cryptography are discussed in Chapter 6. Symmetric cryptography involving DES, AES, shift registers and perfect secrecy is discussed in Chapters 2, 4, 5, 15, 16 and 21. Various attacks are covered in Chapter 7 Part II of the book is devoted to information theory and Part III mainly deals with error-correction. However, along the way all these topics, i.e., cryptography, information theory and error-correction merge. The unity is beautifully illustrated in Chapters 24, 25 and 26.

Recent algorithms related to some in industry are discussed in Chapter 24. For applications to Bitcoin, there is Chapter 26. There are lots of options in the book for an undergraduate or graduate course for a term or a year in all three topics.

On the more applied side, the book can be used for courses in Cybersecurity Foundations, IT Systems, Data Security, and Cryptanalysis which might include topics such as HTTP, SSL/TLS, brute-force, and birthday attacks.

What's New

We refer also to the preface of the first edition. Many new developments have taken place in this dynamic area since the first edition in 2005 and we have tried to cover them and to provide good references in this new edition. Chapters in the first edition have been updated. We have six new chapters dealing with Compression and Applications (Chapter 17), New Identities for the Shannon Function and an Application (Chapter 25), Blockchain and Bitcoin (Chapter 26), IoT, the Internet of Things (Chapter 27), In the Cloud (Chapter 28), and Review Problems and Solutions (Chapter 29). We touch only on a few of the changes and additions that have been made in various chapters, as follows:

• Chapter 4: homomorphic encryption is introduced, the discussion on quantum encryption is enlarged and post-quantum cryptography is discussed.
• Chapter 6 extends the usual algorithm for ECC and demonstrates corresponding new geometrical results.
• Chapter 7 contains details of many new attacks.
• Chapter 9 has a new extended discussion on entropy in weighing problems.
• Chapter 11 has an improved treatment of source coding.
• Chapter 12 now contains a full proof of the Fundamental Theorem of Information Theory.
• Chapter 13 features a more user-friendly approach to continuous signals and the Information Capacity Theorem for Band-Limited channels.
• The exposition for Chapter 15 has been polished and simplified.
• Chapter 16 includes background and full details of the Berlekamp-Massey algorithm.
• Chapter 17 has details of the WKdm algorithms.
• Chapter 18 outlines the proof by one of the authors on a long-standing conjecture regarding the next-to-minimum weights of Reed-Muller codes.
• Chapter 21 features a fresh approach to cyclic linear codes and culminates with a new user-friendly proof of a powerful result on the periodicity of shift registers in Peterson and Weldon, [PW72].
• The study of MDS codes leads to a very interesting and basic "inverse" problem in linear algebra over any field. It could be discussed in a first year linear algebra class. See Chapter 23 for the details.
• Chapter 24 introduces a new hash function and improvements to the main algorithm in the chapter.
• Chapter 25 brings readers of this book to the very forefront of research by exhibiting infinitely many new identities for the Shannon function.
• Chapter 26 features a simple new proof of the security of Bitcoin in the matter of double spending, avoiding the assumptions of the approximation by a continuous random variable in the original paper by Nakamoto ([Nak08]).
• Chapter 27 discusses privacy and security concerns relating to the Internet of Things (IoT). Important questions include: Who has access to the information that your smart device is collecting? Could someone remotely access your smart device?
• Chapter 28 focuses on the availability of data stored in the cloud and on homomorphic encryption, which allows computations to be done on data while it is in an encrypted form.
• Chapter 29 features another approach to MDS codes and, we hope, a very interesting discussion of the venerable topic of mutually orthogonal latin squares. There are also exercises in modular arithmetic, finite fields, linear algebra, and other topics to elucidate theoretical results in previous chapters, along with solutions.

Hardcover and eBook

The second edition will be available both as a hardcover book and as an eBook. The content will be the same in both. Besides traditional formatting for items in the bibliography, most of the items have accompanying URLs.

The eBook will have clickable links, including links to chapter and section numbers, to theorem numbers, from problems to their solutions, and to items in the bibliography. The URLs in the bibliography will also be clickable in the eBook.

Numbering of Definitions, Examples, Results.

When referring to a definition or result, we list the chapter number, a dot and then a number from an increasing counter for that chapter. For instance, Example 10.7 is the seventh numbered item in Chapter 10. Theorem 10.8 comes after Example 10.7 and is the eight such numbered item in Chapter 10.

Numbering of Problems, Solutions.

Most chapters have a section called Problems followed immediately by a corresponding section called Solutions at the end of the chapter. Problems and Solutions at the end of the chapter have their own counters. So, Problem 10.6 is the sixth problem in the Problems section (Section 10.15) of Chapter 10 and Solution 10.6 has the solution to that problem. It can be found in the...