Gröbner Bases, Coding, and Cryptography

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

Gröbner Bases, Coding, and Cryptography

Edited by Massimiliano Sala (), Shojiro Sakata (), Teo Mora (), Carlo Traverso () and Ludovic Perret ()

in Springer Books from Springer

Date: 2009
ISBN: 978-3-540-93806-4
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Chapters in this book:

Gröbner Bases, Coding, and Cryptography: a Guide to the State-of-Art: Massimiliano Sala
Gröbner Technology: Teo Mora
The FGLM Problem and Möller’s Algorithm on Zero-dimensional Ideals: Teo Mora
An Introduction to Linear and Cyclic Codes: Daniel Augot, Emanuele Betti and Emmanuela Orsini
Decoding Cyclic Codes: the Cooper Philosophy: Teo Mora and Emmanuela Orsini
A Tutorial on AG Code Construction from a Gröbner Basis Perspective: Douglas A. Leonard
Automorphisms and Encoding of AG and Order Domain Codes: John B. Little
Algebraic Geometry Codes from Order Domains: Olav Geil
The BMS Algorithm: Shojiro Sakata
The BMS Algorithm and Decoding of AG Codes: Shojiro Sakata
A Tutorial on AG Code Decoding from a Gröbner Basis Perspective: Douglas A. Leonard
FGLM-Like Decoding: from Fitzpatrick’s Approach to Recent Developments: Eleonora Guerrini and Anna Rimoldi
An Introduction to Ring-Linear Coding Theory: Marcus Greferath
Gröbner Bases over Commutative Rings and Applications to Coding Theory: Eimear Byrne and Teo Mora
Overview of Cryptanalysis Techniques in Multivariate Public Key Cryptography: Olivier Billet and Jintai Ding
A Survey on Polly Cracker Systems: Françoise Levy-dit-Vehel, Maria Grazia Marinari, Ludovic Perret and Carlo Traverso
Block Ciphers: Algebraic Cryptanalysis and Gröbner Bases: Carlos Cid and Ralf-Philipp Weinmann
Algebraic Attacks on Stream Ciphers with Gröbner Bases: Frederik Armknecht and Gwenolé Ars
Canonical Representation of Quasicyclic Codes Using Gröbner Bases Theory: Kristine Lally
About the nth-Root Codes: a Gröbner Basis Approach to the Weight Computation: Marta Giorgetti
Decoding Linear Error-Correcting Codes up to Half the Minimum Distance with Gröbner Bases: Stanislav Bulygin and Ruud Pellikaan
Gröbner Bases for the Distance Distribution of Systematic Codes: Eleonora Guerrini, Emmanuela Orsini and Ilaria Simonetti
A Prize Problem in Coding Theory: Jon-Lark Kim
An Application of Möller’s Algorithm to Coding Theory: M. Borges-Quintana, M. A. Borges-Trenard and E. Martínez-Moro
Mattson Solomon Transform and Algebra Codes: Edgar Martínez-Moro and Diego Ruano
Decoding Folded Reed–Solomon Codes Using Hensel-Lifting: Peter Beelen and Kristian Brander
A Note on the Generalisation of the Guruswami–Sudan List Decoding Algorithm to Reed–Muller Codes: Daniel Augot and Michael Stepanov
Viewing Multipoint Codes as Subcodes of One-Point Codes: Gretchen L. Matthews
A Short Introduction to Cyclic Convolutional Codes: Heide Gluesing-Luerssen, Barbara Langfeld and Wiland Schmale
On the Non-linearity of Boolean Functions: Ilaria Simonetti
Quasigroups as Boolean Functions, Their Equation Systems and Gröbner Bases: D. Gligoroski, V. Dimitrova and S. Markovski
A New Measure to Estimate Pseudo-Randomness of Boolean Functions and Relations with Gröbner Bases: Danilo Gligoroski, Smile Markovski and Svein Johan Knapskog
Radical Computation for Small Characteristics: Ryutaroh Matsumoto

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DOI: 10.1007/978-3-540-93806-4

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