Algebraic Geometry in Coding Theory and Cryptography

Niederreiter, Harald; Xing, Chaoping

ISBN 10: 0691102880 / ISBN 13: 9780691102887

Published by Princeton University Press, 2009

About this Item

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Bibliographic Details

Title: Algebraic Geometry in Coding Theory and ...

Publisher: Princeton University Press

Publication Date: 2009

Binding: Hardcover

Condition: As New

About this title

Synopsis:

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 cryptography. 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 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. 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

About the Author:

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".