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Reviewer: Carla Iran SanchezAguilar

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. More reviews about this item: Amazon Online Computing Reviews Service

Reviewer: G. Smith

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]. More reviews about this item: Amazon Online Computing Reviews Service

Reviewer: Alasdair McAndrew

In contrast to many introductory cryptography texts, this one concentrates on the theory of cryptography: what is in fact meant by security__?__ How can security be measured__?__ What are the conditions under which a cryptosystem (or hash function, or any other cryptographic primitive) can be said to be secure__?__ The book is in three sections: the first consists of two short chapters and is introductory and discursive; the second (chapters 3 to 7) investigates security as applied to secret-key cryptography; and the third discusses public key cryptography. The language of probability pervades this text, as it should. For example, suppose one of two messages is encrypted and the ciphertext passed to an "adversary." If the adversary cannot determine which of the two plaintexts corresponds to the ciphertext with probability greater than 1/2, the system is "perfectly secure." A slightly weaker definition, but more useful in practice, is to define security as the probability of the adversary choosing the correct plaintext being no greater than 1/2 + negl( n ), where negl is a "negligible function" (one that is asymptotically less than the reciprocal of any positive polynomial, such as 2- n ), and n is a parameter defined in terms of the lengths of the plaintext and ciphertext. There are discussions on security based on information held by the adversary: chosen plaintext attack (CPA)-secure and chosen ciphertext attack (CCA)-secure. It is shown, for example, what it means for a cryptosystem to be secure against such an attack. The five chapters of the Part 2 expand upon this definition (which is very clearly and precisely stated) and its ramifications to hash functions, secret-key systems, encryption modes, and other cryptographic primitives. Chapters 6 and 7 introduce some practical systems: the data encryption standard (DES) and its variants; the advanced encryption standard (AES); the hash functions MD5 and SHA-0 to SHA-3; and pseudorandom generators. Although DES might seem to have been discussed to death in pretty much every cryptography text published in the last few decades, the authors provide here a refreshingly different approach: one in which the various building blocks (in particular the Feistel structure) are each carefully analyzed for the security they provide. This means, for example, that there can be a discussion on attacking DES with fewer rounds, as well as an (optional) section on differential and linear cryptanalysis. The text also clearly differentiates theoretical from practical attacks. The birthday attack for hash functions, in its most theoretical form, requires a great deal of memory, which is noted to be "in general, a scarcer resource than time." For such an attack to be practical, some means must be found to minimize the storage requirements, which leads to "small-space birthday attacks." This is in fact only a small part of the text, but it nicely illustrates the book's structure, its attention to detail, and its rigor. The second half of the text investigates public-key cryptography, again defining security probabilistically, and very carefully showing how that definition can be used to show that a public-key system is secure. One example, which neatly sums up the flavor of the book, is theorem 11.8, which states: "If the DDH problem is hard relative to G , then the El Gamal encryption scheme is CPA-secure." Here G is the polynomial-time algorithm that outputs a description of a cyclic group of order n and a generator, over which the El Gamal system is defined. DDH is the decisional Diffie-Hellman problem, and its "hardness" is again carefully described using probability. A particularly elegant example is the RSA cryptosystem, which would seem to be secure simply because of the difficulty of factoring large numbers. But this is not true; since RSA is deterministic (same input produces the same output), in its basic form it is trivially insecure against a chosen plaintext attack. This raises the question: how secure is RSA__?__ This text carefully investigates security assumptions and foundations (using the random oracle model) to precisely define how a public-key system can be said to be secure. Examples of cryptosystems are scattered throughout the book-DES, AES, RSA, El Gamal, Rabin, Paillier, and Goldwasser-Micali, for example-but in fact these are not the main aim of the text. This text is not a compendium of cryptosystems, with a nod in the direction of their security, but instead sits at a more profoundly fundamental level. It is, as the authors are careful to point out, a text about the theory of modern cryptography. Cryptography can be an abstruse science: notationally complex and with definitions requiring particular precision and care. A cryptosystem can't be said to be "secure" without a firm foundation as to the meaning of security, and the context in which it is being applied. It is easy for authors to be confused in their discussions and imprecise in their reasoning. I think that Katz and Lindell have done a remarkable job in maintaining clarity and rigor, without sacrificing approachability. The text is even pleasantly chatty and discursive when needed. The authors aim to be "accessible," and I think the text is so, given the subtlety of its material. For a course of study, it would be suited to upper undergraduate or beginning postgraduate students: a mathematics student (or indeed, anybody else with some mathematics background) wishing to come to grips with modern cryptographic theory could do a great deal worse than this text. 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