Editors:
- Covers exciting new research directions on Gröbner bases and their applications
- Includes supplementary material: sn.pub/extras
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Table of contents (33 chapters)
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Front Matter
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Gröbner Bases, Coding, and Cryptography: a Guide to the State-of-Art
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Invited Papers
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Front Matter
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About this book
Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations.
This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will findthat all chapters fit nicely within a unified notation.
Editors and Affiliations
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Boole Centre for Research in Informatics, University College Cork, Cork, Ireland
Massimiliano Sala
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Faculty of Engineering Dept. Production Systems Engineering, Toyohashi University of Technology, Tempaku-cho, Japan
Shojiro Sakata
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Dipto. Matematica, Università Genova, Genova, Italy
Teo Mora
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Dipto. Matematica, Università Pisa, Pisa, Italy
Carlo Traverso
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LIP6, University of Paris VI, Paris, France
Ludovic Perret
Bibliographic Information
Book Title: Gröbner Bases, Coding, and Cryptography
Editors: Massimiliano Sala, Shojiro Sakata, Teo Mora, Carlo Traverso, Ludovic Perret
DOI: https://doi.org/10.1007/978-3-540-93806-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Hardcover ISBN: 978-3-540-93805-7Published: 05 June 2009
Softcover ISBN: 978-3-642-10100-7Published: 19 October 2010
eBook ISBN: 978-3-540-93806-4Published: 28 May 2009
Edition Number: 1
Number of Pages: XVI, 430
Topics: Algebra, Discrete Mathematics, Combinatorics, Cryptology, Mathematics of Computing, Theory of Computation