Algebraic Curves in Cryptography
1st Edition
Published on 13. June 2013
Book
Hardback
340 pages
978-1-4200-7946-3 (ISBN)
Description
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.
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.
Reviews / Votes
"This is a self-contained book intended for researchers and graduate students in mathematics and computer science interested in different topics in cryptography involving algebraic curves ... The authors of this book make an exhaustive review on some other topics where algebraic curves, mainly in higher genus, are important as well."-Zentralblatt MATH 1282
"The book is written in a user-friendly style, with good coverage of the background, many examples, and a detailed bibliography of over 180 items. It is mainly directed towards graduate students and researchers, but some parts of the book are even accessible for advanced undergraduate students. The book is highly recommended for readers interested in the manifold applications of algebraic curves over finite fields."
-Harald Niederreiter, Mathematical Reviews, March 2014
"The book is filled with examples to illustrate the various constructions and, assuming a basic knowledge of combinatorics and algebraic geometry, it is almost self-contained."
-Felipe Zaldivar, MAA Reviews, September 2013
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
Professional and scholarly
Product notice
Paper over boards
Illustrations
15 s/w Abbildungen, 4 s/w Tabellen
4 Tables, black and white; 15 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Weight
660 gr
ISBN-13
978-1-4200-7946-3 (9781420079463)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
San Ling | Huaxiong Wang | Chaoping Xing
Algebraic Curves in Cryptography
Book
06/2019
1st Edition
CRC Press
€94.30
Shipment within 10-20 days
San Ling | Huaxiong Wang | Chaoping Xing
Algebraic Curves in Cryptography
E-Book
06/2013
1st Edition
Chapman & Hall/CRC
€86.99
Available for download
San Ling | Huaxiong Wang | Chaoping Xing
Algebraic Curves in Cryptography
E-Book
06/2013
Chapman and Hall
€86.99
Available for download
Persons
San 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.
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.
Content
Introduction to Algebraic Curves. Introduction to Error-Correcting Codes. Elliptic Curves and Their Applications to Cryptography. Secret Sharing Schemes. Authentication Codes. Frameproof Codes. Key Distribution Schemes. Broadcast Encryption and Multicast Security. Sequences. Bibliography. Index.