Algebraic Geometry in Coding Theory and Cryptography
|Rating||:||4.65 (750 Votes)|
|Number of Pages||:||272 Pages|
Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available.Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and crypto
Harald Niederreiter is professor of mathematics and computer science at the National University of Singapore. Chaoping Xing is professor of mathematics at the Nanyang Technological University in Singapore. They are the authors of "Rational Points on Curves over Finite Fields: Theory and Applications."
This book is certainly an important addition to the literature in this area and a serious candidate for becoming one of the standard textbooks in related courses."--Cicero Carvalho, Mathematical Reviews. "Coding theory has a rapidly growing corpus of knowledge, and now appears explicitly in several classifications in the MSC
Clear, Concise and Comprehensive Amazon Customer Algebraic geometry is a beautiful subject and have found nice applications in many areas of mathematics/CS.Coding theory and Cryptography are two such areas.There are many great books available on each of these areas. They focus either on Coding theory, or on Cryptography.This book however, builds on keeping algebraic geometry in the first place.It isolates out the relevant algebraic