The volume is intended as a textbook, which also includes classroom exercises. As a result, it can be evaluated on that basis and then compared to other works in the field. The question is why write another textbook on cryptography? The authors note that they wrote this new textbook to be both rigorous and accessible for the study of modern cryptography.

Let me define modern cryptography as that scientific discipline which began in the 1980s. In terms of definition, modern cryptography is characterized by the ability to describe security in order to design it. In modern cryptography, the assumptions are clearly stated and are unambiguously defined; prior to modern scholarship, cryptography was more of an art than a science for students to learn.

Since the volume is addressed to students, there is an emphasis on practice. The student should understand discrete math as well as have exposure to proofs at the college level, an upper-level math course, or a course on algorithms or computability theory. The work is geared toward a one-semester 35-hour undergraduate course. The core components of the volume are highlighted with stars; however, there is added material for a more detailed explanation of the content or flexibly for extra work if needed.

Helpfully, the authors point out how modern cryptography is to be defined. To wit, “modern cryptography involves the study of mathematical techniques for securing digital information, systems, and distributed computations against adversarial attacks” (p. 3). Post 1980s modern cryptography enabled the rigorous study of cryptography as a science and a mathematical discipline as opposed to the art of classical cryptography. The major shift in cryptography also has spread to the ordinary computer user who utilizes the discipline for passwords and financial transactions.

Classical cryptography prioritizes private encryption wherein two parties share a key that they use to communicate securely. The assumption is then that an eavesdropper can monitor the transmissions, but without the key they cannot understand the private messages. Over time, another common setting of private-key cryptography is that a single user stores data securely and continuously. The syntax of encryption encrypts a message and the decrypts are the resulting cipher text using the same key that yields the original message. In the late 19th century, Auguste Kerckhoffs developed the principle demanding that “security rely solely on secrecy of the key” (p. 7).

However, the key-space principle noted above provides a necessary condition for security, but not a sufficient one. On the other hand, the mono-alphabetic substitution cipher does ensure sufficiency. The key is arbitrary so that decryption is possible. Nonetheless, the mono-alphabetic substitution cipher can be quickly broken; in fact, to demonstrate the utility of their key points, one of the strengths of the volume is that a handy exercise is placed directly after making these points. In this case, the student can perform an improved attack on the aforementioned shift cipher through the use of the supplied letter-frequency table (Figure 1.3).

The Vigenère (poly-alphabetic shift) cipher thwarts mono-alphabetic analysis where the key defines a mapping that is applied on blocks of plaintext characters. This historic cypher was invented in the 16th century, thought to be unbreakable, and indeed it was until a systematic attack on the scheme was devised hundreds of years later.

In summary, these few historical ciphers illustrate important lessons. Arguably, the most important lesson is that designing secure ciphers is arduous. Far more complex ciphers have been designed and yet all historical schemes have been broken.

The core of the work is in modern cryptography, which is a science as opposed to the bulk of historical examples that were more of an art. The practice of the art allowed the scheme to be broken, fixed, or patched, and the process repeated. There was no agreed upon manner to secure a scheme. Modern cryptography now aspires to provide rigorous proof of a secure construction and the means to do so. In order to articulate these proofs, formal definitions pinpoint exactly what secure means. The emphasis on definitions, assumptions, and proofs distinguishes modern cryptography from the historical art.

The actual test of a volume of this type’s worth is to compare it to others in the same genre. The work is comprehensive, rigorous, and yet accessible for dedicated students. In the case of this text, the work may be favorably compared to two other standard works in the field [1,2].

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