Many Rational Points: Coding Theory and Algebraic Geometry / Edition 1

Many Rational Points: Coding Theory and Algebraic Geometry / Edition 1

by N.E. Hurt
     
 

This monograph presents a comprehensive treatment of recent results on algebraic geometry as they apply to coding theory and cryptography, with the goal the study of algebraic curves and varieties with many rational points. They book surveys recent developments on abelian varieties, in particular the classification of abelian surfaces, hyperelliptic curves, modular

See more details below

Overview

This monograph presents a comprehensive treatment of recent results on algebraic geometry as they apply to coding theory and cryptography, with the goal the study of algebraic curves and varieties with many rational points. They book surveys recent developments on abelian varieties, in particular the classification of abelian surfaces, hyperelliptic curves, modular towers, Kloosterman curves and codes, Shimura curves and modular jacobian surfaces. Applications of abelian varieties to cryptography are presented including a discussion of hyperelliptic curve cryptosystems. The inter-relationship of codes and curves is developed building on Goppa's results on algebraic-geometry cods. The volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators.

Product Details

ISBN-13:
9789048164967
Publisher:
Springer Netherlands
Publication date:
12/07/2010
Series:
Mathematics and Its Applications (closed) Series, #564
Edition description:
Softcover reprint of hardcover 1st ed. 2004
Pages:
346
Product dimensions:
6.14(w) x 9.21(h) x 0.77(d)

Table of Contents

Abelian Varieties.- Refined Bounds.- Codes and Curves.- Deligne-Lusztig Spaces.- Drinfeld Modules.- Shimura Curves.- Cryptography and Applications.- References.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >