Cryptography for Secure Encryption

Writing coded messages so that only the writer knows what is said has existed for hundreds of years, especially during wartime.  Secure encryption has been a goal of mathematicians and now computer scientists every bit as long.  It is essential for all business practices and as such has gained attention in the press, often in the context of cybercrimes. 

 

As the author says, the book is divided into essentially two parts after the introduction in the first chapter.  Chapters 2-7 provides a brief synopsis of the mathematics needed to understand the rest of the book, namely topics in probability, entropy, complexity theory, and the algebra of groups, rings, and fields.   The remaining chapters talk about standard cryptography topics, such as symmetric key cryptography, public key cryptography, digital signatures, key generation and distribution.  Lastly, the more recent work on elliptic curves and their extensions are considered.  Since I view this book as a graduate text for mathematics and computer science graduate students that will have had courses in algebra, probability, and analysis as undergraduates and more advanced courses as graduate students, these chapters seem at best unnecessary, and at worst, distractions to the primary goals of the book and the development of secure encryption . If I were I to teach a graduate course in cryptography, I would use chapters 1, maybe 4 on complexity, 8-12, and with time an introduction to elliptic curves as found in chapter 13.

 

One of the strengths of the book is the exercises.  They get at the essence of the material in the chapter with easier to harder problems.  The book assumes that some students will be able to program and as such the book exercises provide opportunities for programming solutions. The exercises not only test the student’s knowledge of the material in the chapter, but are fun to work on. I enjoyed the chapter on digital signatures the most, but be aware I am an applied mathematician and I love the application of RSA and more to digital signatures.

 

I believe that a book that is designed for graduate level students in more than one discipline, as this one is, needs an extensive up to date set of references.  The references here are very dated, from the 40’s, 70’s, 80’s and so on.  For a topic that has become so important today, there need to be current references.  The only one that truly meets this requirement is the Childs book. A student should be able to find the newest applications in the references.  The book by Keith Martin is an obvious book that should be included, among others.

  

Underwood states that he leaves out Quantum Cryptography, but he does not say why, nor why he leaves out topics like steganography.  He leaves out any mention of the history of cryptography, even though a sentence here and there would help the student understand its importance

Overall, Cryptography for Secure Encryption is an interesting theoretical book for mathematics and computer science students with solid backgrounds in mathematics. The exercises make the book very appealing.  It is clear that faculty teaching the course will ask for a solutions manual for the exercises, at least for the odd numbered exercises.

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Margaret Cozzens is a Distinguished Research Professor at Rutgers University.