The foundations of cryptography [1], assembled from the lecture notes of Oded Goldreich, is widely known for its high value in cryptographic research. Just like its name, the book discusses many pivotal problems of cryptology in depth. Therefore, it may be very hard for leaders in this area to understand even the motivation for writing this book.

To celebrate Goldreich’s 60th birthday (and 20 years since the publication of his essay “On the foundations of modern cryptography” [2]), his students present this book, which consists of tutorials on certain topics in cryptology. The book includes seven chapters that rearrange topics on garble circuits, the complexity of public-key cryptography, pseudorandom functions (PRFs), entropies in one-way functions, homomorphic encryption, the simulation proof technique, and differential privacy. All of these topics are inherited from the foundations of cryptography and play important roles in both academic research and industrial practice.

Although this book is called a “tutorial,” it is not a companion to Goldreich’s original book [1]. The contents of this book are totally rewritten. The authors deliberately select the latest published results on the discussed topics, and make new comparisons and analyses to Goldreich’s ideas in the original book; this illuminates a whole new understanding of the foundation of cryptography that Goldreich wants to build.

For my personal research interests, I thoroughly read chapter 3 (“Pseudorandom Functions: Three Decades Later”). In particular, feasibility results and constructions of PRFs are proposed. For example, in Section 3.8, the authors provide contemporary constructions of PRFs: key-homomorphic PRFs and puncturable PRFs. It should be emphasized that the PRFs described here are not formally used to build pseudorandom number generators (PRNGs); however, they will play a pivotal role in the design of public-key algorithms, such as proxy re-encryption and public-key encryption in/without random oracles. Moreover, some open problems are pointed out. Engineers might be disappointed about the so-called feasibility. But just like the other chapters of this book, the authors focus on building the foundations of cryptography rather than simple explanations. Thus, this book is just for people who want to investigate the very basis of cryptography.