Description
This text is a comprehensive introduction to codes and cryptography, covering the fundamental ideas of information theory, compact encoding of messages, and the theory of error-correcting codes. It also covers modern cryptographic methods, including public key cryptography and digital signatures. The text is aimed at readers with a variety of interests and backgrounds, and includes extensive problems and solutions.
This text unifies the concepts of information, codes and cryptography as first studied by Shannon in his seminal papers on communication and secrecy systems. The first five chapters cover the fundamental ideas of information theory, compact encoding of messages and the theory of error-correcting codes. After a discussion of mathematical models of English, there is an introduction to the classical Shannon model of cryptography. This is followed by a brief survey of those aspects of computational complexity needed for an understanding of modern cryptographic methods and the recent advances in public key cryptography, password systems and authentication techniques. Because the aim of the text is to make this exciting branch of modern applied mathematics available to readers with a variety of interests and backgrounds, the mathematical prerequisites have been kept to an absolute minimum. Problems and solutions are included.
Dominic Welsh's
Codes and Cryptography takes a wide approach and explores the mathematical foundations of this field, considering information theory, entropy, and the encoding of messages. From these roots in information and communication theory, Welsh then moves on to topics in cryptography, including public key cryptography and digital signatures. The text also offers practice exercises along with their solutions. There is plenty of mathematics here, making this a book for specialists (a result of the author's experience teaching undergraduates at Oxford). Between the formulas, though, the author conveys a genuine enthusiasm for his subject and for the history of cryptography. The text includes an extensive bibliography of sources in the field.
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