Algebraic curves in cryptography
 Responsibility
 San Ling, Huaxiong Wang, Chaoping Xing.
 Language
 English.
 Publication
 Boca Raton, FL : CRC Press, [2013]
 Physical description
 xvii, 321 pages : illustrations ; 25 cm.
 Series
 Discrete mathematics and its applications.
Access
Creators/Contributors
 Author/Creator
 Ling, San, 1964
 Contributor
 Wang, Huaxiong.
 Xing, Chaoping, 1963
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 301313) and index.
 Contents

 Introduction to Algebraic Curves Plane Curves Algebraic Curves and Their Function Fields Smooth Curves RiemannRoch Theorem Rational Points and Zeta Functions Introduction to ErrorCorrecting Codes Introduction Linear Codes Bounds Algebraic Geometry Codes Asymptotic Behavior of Codes Elliptic Curves and Their Applications to Cryptography Basic Introduction Maps between Elliptic Curves The Group E(Fq) and Its Torsion Subgroups Computational Considerations on Elliptic Curves Pairings on an Elliptic Curve Elliptic Curve Cryptography Secret Sharing Schemes The Shamir Threshold Scheme Other Threshold Schemes General Secret Sharing Schemes Information Rate QuasiPerfect Secret Sharing Schemes Linear Secret Sharing Schemes Multiplicative Linear Secret Sharing Schemes Secret Sharing from ErrorCorrecting Codes Secret Sharing from Algebraic Geometry Codes Authentication Codes Authentication Codes Bounds of ACodes ACodes and ErrorCorrecting Codes Universal Hash Families and ACodes ACodes from Algebraic Curves Linear Authentication Codes Frameproof Codes Introduction Constructions of Frameproof Codes without Algebraic Geometry Asymptotic Bounds and Constructions from Algebraic Geometry Improvements to the Asymptotic Bound Key Distribution Schemes Key Predistribution Key Predistribution Schemes with Optimal Information Rates Linear Key Predistribution Schemes Key Predistribution Schemes from Algebraic Geometry Key Predistribution Schemes from CoverFree Families Perfect Hash Families and Algebraic Geometry Broadcast Encryption and Multicast Security OneTime Broadcast Encryption Multicast ReKeying Schemes ReKeying Schemes with Dynamic Group Controllers Some Applications from Algebraic Geometry Sequences Introduction Linear Feedback Shift Register Sequences Constructions of Almost Perfect Sequences Constructions of Multisequences Sequences with Low Correlation and Large Linear Complexity Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 selfcontained 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 errorcorrecting 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.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2013
 Series
 Discrete mathematics and its applications
 ISBN
 9781420079463 (hardback)
 1420079468 (hardback)