Algebraic curves in cryptography
QA268 .L545 2013
- Unknown QA268 .L545 2013
- Includes bibliographical references (pages 301-313) and index.
- Introduction to Algebraic Curves Plane Curves Algebraic Curves and Their Function Fields Smooth Curves Riemann-Roch Theorem Rational Points and Zeta Functions Introduction to Error-Correcting 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 Quasi-Perfect Secret Sharing Schemes Linear Secret Sharing Schemes Multiplicative Linear Secret Sharing Schemes Secret Sharing from Error-Correcting Codes Secret Sharing from Algebraic Geometry Codes Authentication Codes Authentication Codes Bounds of A-Codes A-Codes and Error-Correcting Codes Universal Hash Families and A-Codes A-Codes 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 Cover-Free Families Perfect Hash Families and Algebraic Geometry Broadcast Encryption and Multicast Security One-Time Broadcast Encryption Multicast Re-Keying Schemes Re-Keying 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 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.
(source: Nielsen Book Data)
- Publication date
- San Ling, Huaxiong Wang, Chaoping Xing.
- Discrete mathematics and its applications