RSA and Public-Key Cryptography

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Publisher: Chapman&Hall/CRC Press, Boca Raton.

ISBN#: 1-58488-338-3

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TABLE OF CONTENTS:

BRIEF OVERVIEW:

This book is intended for a second course in cryptography at the undergraduate level, where the student is assumed to have had a course in introductory number theory. Also, the book is intended as a source book for those in the cryptography business, who will find collected together herein numerous facts that are currently scattered throughout the literature on public-key cryptography and related issues described in the Table of Contents. The impetus for the writing of this text arose from the author's involvement in the establishment of an iCORE (Informatics Circle of Research Excellence) Chair in cryptography at the University of Calgary in September of 2001, and the launching of an associated Centre for Information Security and Cryptography (CISAC). In addition to the education of numerous graduate students and postdoctoral fellows in cryptology, we have an ongoing commitment to the development of a new stream of cryptography courses for the Mathematics Department. This text will serve as the text for one of them at the senior undergraduate level. No suitable text for that course was on the market, nor is there one at the time of this writing, hence the appearance of this one.

Features of This Text:

The book is ideal for the student since it offers a wealth of exercises with 350 problems. The more challenging exercises are marked with a star symbol. Also, complete and detailed solutions to all of the odd-numbered exercises are provided at the back of the text. Complete and detailed solutions of the even-numbered exercises are included in a Solutions Manual, which is available from the publisher for the instructor who adopts the text for a course. Moreover, the exercises are presented at the end of each section, rather than at the end of each chapter.

The text is accessible to anyone from the senior undergraduate to the research scientist, and all levels of readers will find challenging and inspirational data. To ensure that the book is as self-contained as possible, we have three appendices of relevant background information. Appendix A has a brief, but highly informative, overview of letter frequency analysis (of the English language) to assist in our cryptanalytic travels. Appendix B has a solid background review and analysis of elementary complexity theory to provide us with the necessary tools for algorithmic analysis and related phenomena. Lastly, Appendix C contains the fundamentals of the number-theoretic results used in the text together with any other relevant information that we will need such as vector space basics, matrix theory fundamentals, and some facts on continued fractions.

There are over 100 footnotes containing nearly 40 biographies of the individuals who helped develop cryptologic concepts, together with historical data of interest, as well as other information which the discerning reader may want to explore at leisure. These are woven throughout the text, to give a human face to the cryptology being presented. A knowledge of the lives of these individuals can only deepen our appreciation of the development of PKC and related concepts. The footnote presentation of this material allows the reader to have immediate information at will, or to treat them as digressions, and access them later without significantly interfering with the main discussion.

There are optional topics, denoted by a pointing hand symbol which add additional material for the more advanced reader or the reader requiring more challenging material which goes beyond the basics presented in the core data.

There are more than 60 examples, diagrams, figures, and tables throughout the text to illustrate the concepts presented.

For ease of search, the reader will find consecutive numbering, namely object N.m is the m-th object in Chapter N (or Appendix N), exclusive of footnotes and exercises, which are numbered separately and consecutively unto themselves. Thus, for instance, Diagram 3.5 is the 5-th numbered object in Chapter Three; exclusive of footnotes and exercises; Exercise 4.37 is the 37-th exercise in Chapter Four; and Footnote 9.2 is the second footnote in Chapter Nine.

The bibliography contains nearly 250 references for further reading.

The index has more than 2,000 entries, and has been devised in such a way to ensure that there is maximum ease in getting information from the text.

Reviews

The author has brought together the most relevant topics about Public-Key Cryptography (PKC) and Public-Key Infrastructure (PKI).

In the author's words ``this book is intended for a second course in cryptography at the undergraduate level''. However the book incorporates a wealth of additional materials that make the book interesting for a much wider public spectrum.

In spite of the title, the RSA cryptosystem does not monopolize the work: the description takes only four pages of Chapter 3 (Public-Key Cryptography, where the cryptosystems based on the so-called discrete logarithm problem are also studied) while Chapter 6 analyzes its security. Chapters 4 and 5 (Probabilistic Primality Tests and Factoring respectively) are also related to RSA.

The rest of the book examines the usual PKI protocols (authentication, digital signatures, certification, integrity, etc.), and other security applications (electronic cash, secret broadcasting, smart cards, biometrics, etc.). The main topic not included is the use of elliptic curves in public-key cryptography (the book only mentions it in a footnote). The development of the topics treated is elementary yet rigorous, and the book, as others of the author, is clear and well written.

To make the book as self-contained as possible it includes three appendices (with background information about the English letter frequency, complexity theory and some algebraic and arithmetic elementary results). At the end of each section exercises are included (350 in all), and as usual in the books of the author solutions of the odd-numbered exercises are provided at the end of the book.

The text is also supplemented with 100 footnotes, of which about 40 trace the biographical profile of highlighted people in cryptography.

Juan Tena Ayuso (Valladolid)

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From Mathematics of Computation:

This textbook is a welcome addition to the existing cryptographic literature. Instead of trying to produce a universal manual covering all possible (and impossible) aspects of cryptography, the author concentrates and provides an in-depth treatment of a single topic, the RSA cryptosystem. The matter is traced from its number theoretic roots up to practical protocols, which one can rarely find in more traditional cryptographic textbooks. It provides all the necessary preliminaries, such as primality testing and integer factorisation algorithms. Additionally, such practically important issues as timing and power attacks as well as small public exponent attacks are described. The last three chapters of the book give a treatment of several practical applications of RSA, including such very recently emerged applications as digital cash, electronic commerce, and WLAN (wireless local area network).

The book also contains a carefully selected set of exercises with solutions to the odd numbered ones.

IGOR SHPARLINSKI

 Last updated: June 20, 2009