Introduction to modern cryptography offers its readers an in-depth, rigorous account of history, formal concepts, and definitions used today in the field of cryptography. Unlike other introductory texts, the authors strongly emphasize the importance of the mathematical foundations of cryptography.

The book is divided into three parts. The first part explores background and some basic formal definitions and principles about cryptography. Some of the basic mathematical foundations are described along with some of the most famous ciphers.

The second part of the book focuses on symmetric or private-key encryption. The authors formally define the concept of computational security, present alternatives to constructing secure encryption schemes, and then proceed to define secrecy and integrity, analyzing the construction of authentication codes and binding these concepts to encryption. Furthermore, in chapter 5 the reader gets important insights to the challenges of hash functions and their applications. When reaching the final chapters of this section, the authors have provided the reader with a complete set of definitions, theorems, proofs, and algorithms: enough to understand the dynamics of symmetric-key encryption.

The main topic of the third part is private-key or asymmetric encryption. This section handles public-key encryption with the same level of rigor and detail as the rest of the book. The first chapters present some background concepts, along with factoring problems and applications. Then, key management issues are introduced, before covering the schemes most common to public-key encryption and digital signatures.

The authors commit themselves to reinforcing the material presented in their text by offering challenging and insightful exercises at the end of each chapter. As a lone reader, I wish there were a forum for discussing the exercises and exchanging ideas with other readers. I could imagine that being part of a classroom could provide the sort of discussions that excite the student’s intellect.

The book is mostly suited for people seriously interested in cryptography. It is adequate for advanced undergraduate and graduate courses in the fields of computer science and mathematics. Although the authors try to explain the topic in a simple, comprehensible manner, a strong mathematical background is required to get the most out of the concepts, schemes, and strategies presented.

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