Even though the mathematical rigor and depth exhibited in this text falls short of what one might expect from such a title, this monograph provides excellent coverage of the major research questions that have arisen in the field of cryptology over the last ten years. The author’s purpose in writing this book is to provide, in one reference book, both an introduction to modern cryptology and a springboard for the discussion of and possible extension of contemporary results. This book contains ten chapters and six appendices, together with an excellent bibliography.
Chapter 1 gives a brief survey of cryptography before 1970. Using a historical perspective, this chapter addresses such topics as transposition and substitution cryptosystems, frequency analysis, and rotor machines.
The Data Encryption Standard (DES) is the topic of the second chapter. Patterson delineates the DES algorithm with a full complement of permutation tables and S-boxes. Group properties of DES and potential attacks on DES are mentioned.
Chapter 3 is a three-page motivation for a public-key cryptosystem (PKC). It is based on the inherent difficulties of using DES, namely, the key distribution and authentication problems.
The knapsack approach to public-key cryptography is presented in chapter 4. The original Merkle-Hellman knapsack, or PKC, together with several variations on it, is described; and the idea of using an NP-complete problem as the basis for a PKC is introduced.
Chapter 5 addresses the difficult problem of factoring large integers and introduces the Rivest-Shamir-Adleman (RSA) algorithm. Probabilistic techniques for the testing of large primes are also considered here.
The sixth chapter continues the chronological development of modern cryptosystems by considering the cryptanalysis or breaking of knapsacks. The work of Shamir, and Lagarias and Odlyzko, as well as that of Brickell are mentioned, along with an appropriate example of how a small knapsack may be broken.
The Chor-Rivest algorithm and other proposed PKCs are the subject of chapter 7. Some of the approaches covered are the error-correcting code scheme of McEliece, the Cooper-Patterson knapsack method, and Wagner’s use of combinatorial group theory.
Chapter 8 addresses problems closely related to the classical problem of cryptography. Foremost among these is the authentication problem. Other topics considered in this chapter include the oblivious transfer problem, one-way encryption functions, and a variety of threshold schemes.
The attempts by the International Standards Organization (the Working Group on Public Key Cryptosystems and Applications) to define PKCs are documented in chapter 9.
The last chapter discusses some of the most recent attempts to cryptanalyze the DES. Group-theoretic properties of DES are presented along with the MIT Cycling Experiments and Shamir’s Remarkable Symmetries.
While the ten chapters preserve the chronological development of many of the recent efforts in cryptology, the intent of the six appendices is to provide the background needed to understand the mathematical underpinnings of the cryptographic methods. The first five appendices cover modular arithmetic, groups, elementary number theory, computational complexity, and Galois fields, respectively. These appendices are appropriately referenced in the text when the prerequisite knowledge is required. I found the material in these appendices to be shallow, but the necessary references for a more in-depth study of any one of these areas are given. Appendix 6 gives a useful set of 14 well-documented Pascal programs. Among these are programs for implementing DES, RSA, the Lehmann and Peralta Primality Test, and Fast Exponentiation.
The most impressive strength of this book is the extensive overview of the major issues in cryptography that have occurred in recent years. The book is easy to read and has an excellent bibliography and index. The selected Pascal programs will make life easier for the practitioner.
The book also has its drawbacks. For any particular topic covered, there is most certainly another source that would cover that topic in more depth, a necessary consideration in an academic environment. Numerous typos and inconsistencies limit the readability of the monograph. For example, on page 115 the author says that “the RSA cryptosystems can be adapted for authentication as well as for secrecy (not at the same time, however)” and only a few lines later on page 116 he says that “RSA can simultaneously provide secrecy and authentication.” The group properties of DES given on page 156 are almost a rehash of those given on page 32. Also, notational inaccuracies like the ones on page 161 (which should be xi = Tai−1(u) and yj = Tbj(c)) tend to slow the reading comprehension rate. Additionally, the text offers only a limited number of exercises.
In summary, this book--despite the drawbacks--is a readable exposition of the major issues in cryptography over the last decade; and in this sense, the author has achieved his purpose.
