Algebraic Curves in Cryptography

By: Chaoping Xing, San Ling, Huaxiong Wang

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Paperback | 12 June 2019 | Edition Number 1

At a Glance

Paperback
340 Pages

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23.4 x 15.6 x 1.8

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The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sharing, frameproof codes, and broadcast encryption.

Suitable for researchers and graduate students in mathematics and computer science, this self-contained book is one of the first to focus on many topics in cryptography involving algebraic curves. After supplying the necessary background on algebraic curves, the authors discuss error-correcting codes, including algebraic geometry codes, and provide an introduction to elliptic curves. Each chapter in the remainder of the book deals with a selected topic in cryptography (other than elliptic curve cryptography). The topics covered include secret sharing schemes, authentication codes, frameproof codes, key distribution schemes, broadcast encryption, and sequences. Chapters begin with introductory material before featuring the application of algebraic curves.

Industry Reviews

"This is a self-contained book intended for researchers and graduate students in mathematics and computer science interested in different topics in cryptography involving algebraic curves ... The authors of this book make an exhaustive review on some other topics where algebraic curves, mainly in higher genus, are important as well."
-Zentralblatt MATH 1282

"The book is written in a user-friendly style, with good coverage of the background, many examples, and a detailed bibliography of over 180 items. It is mainly directed towards graduate students and researchers, but some parts of the book are even accessible for advanced undergraduate students. The book is highly recommended for readers interested in the manifold applications of algebraic curves over finite fields."
-Harald Niederreiter, Mathematical Reviews, March 2014

"The book is filled with examples to illustrate the various constructions and, assuming a basic knowledge of combinatorics and algebraic geometry, it is almost self-contained."
-Felipe Zaldivar, MAA Reviews, September 2013

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