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Gröbner Bases, Coding, and Cryptography

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Table of Contents

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    Book Overview
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    Chapter 1 Gröbner Bases, Coding, and Cryptography: a Guide to the State-of-Art
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    Chapter 2 Gröbner Technology
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    Chapter 3 The FGLM Problem and Möller’s Algorithm on Zero-dimensional Ideals
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    Chapter 4 An Introduction to Linear and Cyclic Codes
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    Chapter 5 Decoding Cyclic Codes: the Cooper Philosophy
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    Chapter 6 A Tutorial on AG Code Construction from a Gröbner Basis Perspective
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    Chapter 7 Automorphisms and Encoding of AG and Order Domain Codes
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    Chapter 8 Algebraic Geometry Codes from Order Domains
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    Chapter 9 The BMS Algorithm
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    Chapter 10 The BMS Algorithm and Decoding of AG Codes
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    Chapter 11 A Tutorial on AG Code Decoding from a Gröbner Basis Perspective
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    Chapter 12 FGLM-Like Decoding: from Fitzpatrick’s Approach to Recent Developments
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    Chapter 13 An Introduction to Ring-Linear Coding Theory
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    Chapter 14 Gröbner Bases, Coding, and Cryptography
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    Chapter 15 Overview of Cryptanalysis Techniques in Multivariate Public Key Cryptography
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    Chapter 16 A Survey on Polly Cracker Systems
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    Chapter 17 Block Ciphers: Algebraic Cryptanalysis and Gröbner Bases
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    Chapter 18 Algebraic Attacks on Stream Ciphers with Gröbner Bases
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    Chapter 19 Canonical Representation of Quasicyclic Codes Using Gröbner Bases Theory
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    Chapter 20 About the n th-Root Codes: a Gröbner Basis Approach to the Weight Computation
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    Chapter 21 Decoding Linear Error-Correcting Codes up to Half the Minimum Distance with Gröbner Bases
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    Chapter 22 Gröbner Bases for the Distance Distribution of Systematic Codes
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    Chapter 23 A Prize Problem in Coding Theory
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    Chapter 24 An Application of Möller’s Algorithm to Coding Theory
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    Chapter 25 Mattson Solomon Transform and Algebra Codes
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    Chapter 26 Decoding Folded Reed–Solomon Codes Using Hensel-Lifting
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    Chapter 27 A Note on the Generalisation of the Guruswami–Sudan List Decoding Algorithm to Reed–Muller Codes
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    Chapter 28 Viewing Multipoint Codes as Subcodes of One-Point Codes
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    Chapter 29 A Short Introduction to Cyclic Convolutional Codes
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    Chapter 30 On the Non-linearity of Boolean Functions
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    Chapter 31 Quasigroups as Boolean Functions, Their Equation Systems and Gröbner Bases
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    Chapter 32 A New Measure to Estimate Pseudo-Randomness of Boolean Functions and Relations with Gröbner Bases
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    Chapter 33 Radical Computation for Small Characteristics
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Citations

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Title
Gröbner Bases, Coding, and Cryptography
Published by
Springer Nature, January 2009
DOI 10.1007/978-3-540-93806-4
ISBNs
978-3-54-093805-7, 978-3-54-093806-4
Editors

Sala, Massimiliano, Sakata, Shojiro, Mora, Teo, Traverso, Carlo, Perret, Ludovic

Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 36 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Italy 1 3%
Unknown 35 97%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 9 25%
Student > Master 6 17%
Researcher 4 11%
Professor > Associate Professor 3 8%
Student > Bachelor 2 6%
Other 6 17%
Unknown 6 17%
Readers by discipline Count As %
Mathematics 15 42%
Computer Science 11 31%
Physics and Astronomy 1 3%
Social Sciences 1 3%
Engineering 1 3%
Other 0 0%
Unknown 7 19%