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CryptoSchool
von zur Gathen J., Springer International Publishing, New York, NY, 2015. 876 pp. Type: Book (978-3-662484-23-4)
Date Reviewed: May 6 2016

At almost 900 pages, this is actually almost two complete books: one on cryptography and cryptanalysis, and the other on the rich history of the subject. Cryptography is the art of making secure building blocks; cryptanalysis is the art of breaking them. In the work, the author intersperses with numbered designation aspects of the technology whereas cryptographic history is identified alphabetically; the separate topics and chapter nomenclature are rotated throughout.

The tools of modern cryptography are described, as well as more advanced topics, before completing the work with a toolbox. The author’s holistic view of cryptology provides a basis to equally present a history of the subject. The book can be used, and the author’s experience verifies this, as a one- or a two-semester course textbook. As they study, students can work their way through more than 240 exercises that the author describes as “fun.” Not surprisingly, the text is based on the author’s lecture notes.

The first modern cryptographic system of note was the advanced encryption standard (AES) in 1997. “This system is an example of a symmetric cryptosystem in which the two protagonists (sender and receiver) share the same key” (page 19). The security of AES is important as an example of a public-key cryptosystem, and a subsequent example of reliable cryptography is the key exchange protocol. In this protocol, “the goal is not to send a secret message,” but that two players interacting “agree on a common secret key.” The security of the protocol relies on computing discrete logarithms. A final example reviewed is visual cryptography in which two random pictures, when overlaid, reveal a secret message.

AES is critical to cryptography in that it is the standard for US government documentation. According to the author, AES defines “‘modern’ cryptography, whose current development started in the 1970s.” Modern cryptography then is the barometer or point of comparison for the historical portion of the work. Although many practitioners are no doubt more interested in the technical aspects of cryptography, the volume is much richer and fuller with the historical portion expanding on important developments such as those that led up to modern cryptography.

The work is an important contribution to the literature in that it is more detailed, abundantly illustrated, and more clearly explained and thorough than many other accounts. The text describes some of the most important systems in detail, including AES, Rivest-Shamir-Adleman (RSA), group-based and lattice-based cryptography, signatures, hash functions, and random generation, and provides detailed backgrounds for these topics as well. Each of these important areas is explained and demonstrated for those who lack knowledge in these aspects. For cryptanalysis, the author presents a number of basic tools such as the differential and linear methods and lattice attacks. In addition, since each salient point is then expanded with useful examples that are included in the text, the student can learn by doing. For example, one of the most critical aspects of cryptography is the question: What is secure?

More precisely, a system is secure when “the interaction of an adversary with the system is specified.” Security entails resisting any attack no matter what method is used or whether the attack system is known or unknown. Protection means security reductions by assuming that computational problems are hard to solve. Then, the security expert shows that if a certain system were to be broken, it would imply solving a stated, specific procedure. Since the procedure is difficult, no such break is possible and the system is defined as secure. This notion is described as axiomatic security. Axiomatic security complements empirical security in that arbitrary attacks, also unknown, are ruled out.

The interspersing of historical examples in this one volume is instructive. The history of cryptography is replete with “overly confident inventors and users” who, believing in the security of their systems, faced a rude awakening when their systems were violated. For example, as mentioned in the text, “Mary, Queen of Scots was beheaded in 1587, due to the cryptographic nonchalance of her secretaries and the skills of the cryptographers serving Queen Elizabeth I.” Also noted: “a cryptographic … blunder on the part of the German Foreign Office in 1917 hastened the end of World War I, and cryptographic negligence of the German military shortened World War II, most likely by a year or two.”

Two works can be compared to this volume: often seen as the definitive work of history, The codebreakers by David Khan [1], and, among recent works, one of the best on the technical aspects of cryptanalysis, Understanding cryptography by Christof Paar and Jan Pelzl [2].

Reviewer:  G. Mick Smith Review #: CR144385 (1607-0465)
1) Khan, D. The codebreakers: the comprehensive history of secret communication from ancient times to the Internet (revised & updated). Scribner, New York, NY, 1996.
2) Paar, C.; Pelzl, J. Understanding cryptography: a textbook for students and practitioners. Springer, New York, NY, 2010.
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