Browse Books

Reviewer: Burkhard Englert

Despite frequent news reports about information security problems, most users take the secure transmission of messages over insecure networks for granted. They trust in the security of the protocols that enable this message exchange. This trust is based on confidence in the underlying cryptographic protocols. In the first volume of this already classic, groundbreaking book, Goldreich provides rigorous justification for this trust. The volume's theme is the basic cryptographic tools, particularly one-way functions, pseudorandom generators, and zero-knowledge proofs. The book begins with a brief introduction in chapter 1 that includes a review of basic probability theory and basic complexity theory, and a justification for the rigorous treatment of the subject. In the second chapter, one-way functions are discussed. Intuitively speaking, a one-way function is easy to compute but hard to invert. In this sense, the definition of one-way functions captures the fact that without the existence of some computational hardness or difficulty and the ability to generate hard problems, there is no cryptography. Goldreich then carefully and skillfully develops the theory of one-way functions, always trying to steer the reader toward the essential core of the subject. The reader never gets the feeling of being left alone with a difficult subject. Goldreich does not hesitate to emphasize techniques and ideas that are critical to master the subject. The proof that shows that the existence of weak one-way functions implies the existence of strong one-way functions, for example, receives special attention, since it contains many of the essential techniques and ideas that will allow the reader to actively engage in the subject. The chapter also contains a discussion of some variations and of hard-core predicates. Chapter 3 is dedicated, with equal care, to pseudorandom generators. Such generators are able to extend randomly selected seeds into pseudorandom sequences that are computationally indistinguishable from truly random sequences. The fourth and final chapter discusses zero-knowledge proofs. A zero-knowledge proof system has the property of being convincing without giving anything away besides the validity of the assumption. All chapters conclude with exercises. The book is targeted to graduate students, and can be used by researchers as a reference manual. Reading and appreciating it requires a significant level of mathematical maturity. Inexperienced readers may potentially become frustrated since proofs are dense and require the reader's full attention. On the other hand, Goldreich never tires in providing examples that illustrate the concepts discussed. The book clearly grew out of a teaching environment and is targeted at a teaching environment. There are many teaching tips throughout the book. Some passages feel like a textbook and instructor's manual all in one. Many similar textbooks suffer from a writing style that is not able to hold the reader's attention. Not so with this book. Goldreich aims to be in a continuous dialog with the readers and is willing to take them by the hand, always helping them dissect the difficult material. For readers already familiar with the material, this book is simply a joy to read, a true classic. Online Computing Reviews Service