Enhanced descriptions from Syndetics:

This book is intended as a text for a course on cryptography with emphasis on algebraic methods. It is written so as to be accessible to graduate or advanced undergraduate students, as well as to scientists in other fields. The first three chapters form a self-contained introduction to basic concepts and techniques. Here my approach is intuitive and informal. For example, the treatment of computational complexity in Chapter 2, while lacking formalistic rigor, emphasizes the aspects of the subject that are most important in cryptography. Chapters 4-6 and the Appendix contain material that for the most part has not previously appeared in textbook form. A novel feature is the inclusion of three types of cryptography - "hidden monomial" systems, combinatorial-algebraic sys­ tems, and hyperelliptic systems - that are at an early stage of development. It is too soon to know which, if any, of these cryptosystems will ultimately be of practical use. But in the rapidly growing field of cryptography it is worthwhile to continually explore new one-way constructions coming from different areas of mathematics. Perhaps some of the readers will contribute to the research that still needs to be done. This book is designed not as a comprehensive reference work, but rather as a selective textbook. The many exercises (with answers at the back of the book) make it suitable for use in a math or computer science course or in a program of independent study.

Reviews provided by Syndetics

CHOICE Review

Mathematical cryptography has a holy grail: the creation of provably secure communication protocols. A previous work by Koblitz, A Course in Number Theory and Cryptography (1987), described the basics of finite field arithmetic and the mechanics of well-known cryptosystems such as RSA. The present volume rapidly summarizes the basics of cryptography, complexity, and relevant abstract algebra and then turns to some recent developments heretofore unavailable in book form. Chapter 4 describes the Imai-Matsumoto system, the successful attack against it by Patarin, refinements of the system, attacks against those, and further refinements that so far resist attack. Chapter 5 examines recent attempts to circumvent a 1979 theorem of Brassard usually understood as saying that given a cryptosystem, the problem of breaking it cannot belong to NP-hard, that class of computational problems for which computer scientists feel they have the best evidence of intractability. Finally, chapter 6 describes cryptosystems based on elliptic and hyperelliptic curves, as opposed to finite field multiplicative groups, which offer resistance to certain increasingly successful lines of attack based on successes with the discrete log problem. The battles between cryptographers and cryptanalysts lend a drama to this subject quite evident in Koblitz's self-contained and very readable account. Highly recommended. Upper-division undergraduates. D. V. Feldman; University of New Hampshire