Fully homomorphic encryption is one of the most exciting results in cryptography of the last few years. It allows for arbitrary computations to be carried out on ciphertext to produce an encrypted result that, when decrypted, matches the result of the same computation performed on the corresponding plaintext. This is a very desirable feature in many modern communication system architectures. It allows one, for example, to chain together several services without having to disclose the data that these services operate on to any of them. Natural applications are also in cloud computing applications to allow for computations on encrypted data while protecting, at all times, the confidentiality of the data.

This book presents the basic homomorphic encryption techniques and their applications. The book begins in chapter 1 with a brief historical overview of classic ciphers, and secret key and public key encryption schemes. Chapter 2 discusses four different partially homomorphic encryption schemes. Fully homomorphic encryption schemes are presented in chapter 3. The remaining chapters discuss applications of other homomorphic encryption schemes: a remote end-to-end voting scheme (chapter 4), nearest neighbor queries with location privacy (chapter 5), and private searching on streaming data (chapter 6).

This is a short book that provides a quick overview of this topic. It is best suited for undergraduate students in computer science or mathematics with a basic background in cryptography who have taken a course in abstract algebra. For researchers, however, the book lacks sufficient detail. Most readers will also likely want to skip chapter 1, which discusses very basic background material; in addition, with its color figures, it is visually disconnected from the rest of the book.

Overall, I can recommend this book as a general reference for possible independent study.