Cryptography is the foundation of any secure communication. It is essential for and enables e-commerce, the digitization of information, cloud computing, and the list goes on. Cryptography uses mathematical functions to scramble messages so that they become indistinguishable from random bit strings. To date, many cryptographic algorithms have been shown to be very effective, and they have become the backbone of modern computing. Also, cryptographic algorithms, because of their mathematical nature, can be proven to be correct; if implemented correctly, they are universally trusted.

Delfs and Knebl in this book focus on the mathematical aspects of cryptography. They are not concerned with the implementation of its algorithms, but instead attempt to teach the user the mathematical background of cryptography and then to prove the correctness of its algorithms. Because of its purely theoretical focus, I believe that this book is best suited for a graduate course in mathematics.

The book is organized in two parts. The first part has 11 chapters that cover the following topics: symmetric key cryptography, public-key cryptography, general cryptographic protocols, probabilistic algorithms, one-way functions, bit-security of one-way functions and pseudorandomness, provably secure encryption, unconditional security of cryptosystems, and provable secure digital signatures. This provides an overview over the main cryptographic algorithms and includes proofs of their correctness. The second part, the appendix, covers the mathematical background needed to understand the first part. Nevertheless, since the appendix with its mathematical theorems is separate from the rest of the book, a reader with little mathematical background would have to continuously go back and forth, making it very hard to read this book.

Because of this setup, I feel that this book is best suited for readers who already have the necessary background in number theory, abstract algebra, probability, and information theory. Since the appendix does not directly connect its material to the content of the main chapters, novice readers could become frustrated very easily. A mixed approach might have been better, where the mathematical background is covered just in time to explain a particular cryptographic algorithm. Because of this, I can really only recommend this book for readers with strong mathematical backgrounds who are interested in the foundations of the field.