Grbner Bases, Coding, and Cryptography (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
430
Utgivningsdatum
2009-06-05
Upplaga
2009 ed.
Förlag
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Medarbetare
Sala, Massimiliano
Illustrationer
XVI, 430 p.
Dimensioner
234 x 156 x 25 mm
Vikt
799 g
Antal komponenter
1
Komponenter
1 Hardback
ISBN
9783540938057

Grbner Bases, Coding, and Cryptography

av Massimiliano Sala, Teo Mora, Ludovic Perret, Shojiro Sakata, Carlo Traverso
Inbunden,  Engelska, 2009-06-05
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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. Grbner 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.
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Massimiliano Sala, Teo Mora, Ludovic Perret, Shojiro Sakata, Carlo Traverso

Innehållsförteckning

Grbner Bases, Coding, and Cryptography: a Guide to the State-of-Art.- Grbner Bases, Coding, and Cryptography: a Guide to the State-of-Art.- Invited Papers.- Grbner Technology.- The FGLM Problem and Mllers Algorithm on Zero-dimensional Ideals.- An Introduction to Linear and Cyclic Codes.- Decoding Cyclic Codes: the Cooper Philosophy.- A Tutorial on AG Code Construction from a Grbner Basis Perspective.- Automorphisms and Encoding of AG and Order Domain Codes.- Algebraic Geometry Codes from Order Domains.- The BMS Algorithm.- The BMS Algorithm and Decoding of AG Codes.- A Tutorial on AG Code Decoding from a Grbner Basis Perspective.- FGLM-Like Decoding: from Fitzpatricks Approach to Recent Developments.- An Introduction to Ring-Linear Coding Theory.- Grbner Bases over Commutative Rings and Applications to Coding Theory.- Overview of Cryptanalysis Techniques in Multivariate Public Key Cryptography.- A Survey on Polly Cracker Systems.- Block Ciphers: Algebraic Cryptanalysis and Grbner Bases.- Algebraic Attacks on Stream Ciphers with Grbner Bases.- Notes.- Canonical Representation of Quasicyclic Codes Using Grbner Bases Theory.- About the nth-Root Codes: a Grbner Basis Approach to the Weight Computation.- Decoding Linear Error-Correcting Codes up to Half the Minimum Distance with Grbner Bases.- Grbner Bases for the Distance Distribution of Systematic Codes.- A Prize Problem in Coding Theory.- An Application of Mllers Algorithm to Coding Theory.- Mattson Solomon Transform and Algebra Codes.- Decoding Folded ReedSolomon Codes Using Hensel-Lifting.- A Note on the Generalisation of the GuruswamiSudan List Decoding Algorithm to ReedMuller Codes.- Viewing Multipoint Codes as Subcodes of One-Point Codes.- A Short Introduction to Cyclic Convolutional Codes.- On the Non-linearity of Boolean Functions.- Quasigroups as Boolean Functions, Their Equation Systems and Grbner Bases.- A New Measure to Estimate Pseudo-Randomness of Boolean Functions and Relations withGrbner Bases.- Radical Computation for Small Characteristics.

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