Cryptography, Information Theory, and Error-Correction. Aiden A. Bruen

      Dedicated to the memory of my late parents, Edward A. Bruen and Brid Bean de Brún and to the memory of my late sister Antoinette.

      Dedicated also to my siblings Phil and Bernard, to my beloved wife Katri, and to our children Trevor, Robin, and Merike. (Aiden A. Bruen)

      Also dedicated to my parents, Alberto Forcinito and Olga Swystun de Forcinito, my beloved wife Claudia, and our children Dante, Lucas, and Diego. (Mario A. Forcinito)

      Also dedicated to my parents, Archie and Muriel McQuillan, my siblings Dan, Mary, and Ian, my beloved wife Joy, and our children Anna and Christopher. (James M. McQuillan)

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.