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About this product
- Author(s)Chaoping Xing,Huaxiong Wang,San Ling
- PublisherTaylor & Francis Ltd
- Date of Publication30/04/2010
- Series TitleDiscrete Mathematics and Its Applications
- Country of PublicationUnited States
- ImprintChapman & Hall/CRC
- Content Note15 black & white illustrations, 4 black & white tables
- Weight612 g
- Width156 mm
- Height235 mm
- Format DetailsUnsewn / adhesive bound
- Table Of ContentsIntroduction 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
- Author BiographySan Ling is a professor in the Division of Mathematical Sciences, School of Physical and Mathematical Sciences at Nanyang Technological University. He received a PhD in mathematics from the University of California, Berkeley. His research interests include the arithmetic of modular curves and application of number theory to combinatorial designs, coding theory, cryptography, and sequences. Huaxiong Wang is an associate professor in the Division of Mathematical Sciences at Nanyang Technological University. He is also an honorary fellow at Macquarie University. He received a PhD in mathematics from the University of Haifa and a PhD in computer science from the University of Wollongong, Australia. His research interests include cryptography, information security, coding theory, combinatorics, and theoretical computer science. Chaoping Xing is a professor at Nanyang Technological University. He received a PhD from the University of Science and Technology of China. His research focuses on the areas of algebraic curves over finite fields, coding theory, cryptography, and quasi-Monte Carlo methods.
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