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Gröbner bases, coding, and cryptography

Author: Massimiliano Sala
Publisher: Berlin : Springer ; [Place of publication not identified] : RISC, ©2009.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This text presents 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.
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Genre/Form: Kongress
Linz (2006)
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Massimiliano Sala
ISBN: 9783540938057 3540938052 9783540938064 3540938060
OCLC Number: 297148417
Description: xvi, 430 ; 24 cm
Contents: Part I: Invited Talks1 Teo Mora: Groebner technology,2 Teo Mora: The FGLM problem and Moeller's algorithm on zero-dimensional ideals,3 Daniel Augot, Emanuele Betti, Emmanuela Orsini: An introduction to linear and cyclic codes,4 Teo Mora, Emmanuela Orsini: Decoding cyclic codes: the Cooper philosophy,5 Douglas A. Leonard: A tutorial on AG code construction from a Groebner basis perspective,6 John Little: Automorphisms and encoding of AG and order domain codes,7 Olav Geil: Algebraic geometry codes from order domains,8 Shojiro Sakata: The BMS algorithm,9 Shojiro Sakata: The BMS Algorithm and decoding of algebraic geometry codes,10 Douglas A. Leonard: A tutorial on AG code decoding from a Groebner basis perspective,11 Eleonora Guerrini,Anna Rimoldi: FGLM-like decoding: from Fitzpatrick's approach to recent developments,12 Marcus Greferath: An introduction to ring-linear coding theory,13 Eimear Byrne, Teo Mora: Groebner bases over commutative Artin chain rings and applications to coding theory,14 Olivier Billet and Jintai Ding: Overview of cryptanalysis techniques in multivariate public key cryptography15 Francoise Levy-dit-Vehel, Maria Grazia Marinari, Ludovic Perret, Carlo Traverso: A survey on Polly-Cracker systems,16 Carlos Cid, Ralf Weinmann: Block ciphers: algebraic cryptanalysis and Groebner bases,17 Frederik Armknecht, Gwenole Ars: Algebraic attacks on stream ciphers with Groebner bases, Part II: Notes 1 Kristine Lally: Canonical representation of quasicyclic codes using Groebner basis theory,2 Marta Giorgetti: About the nth-root codes,3 Stanislav Bulygin, Ruud Pellikaan: Decoding linear error-correcting codes up to half the minimum distance withGroebner bases,4 Eleonora Guerrini, Emmanuela Orsini, Ilaria Simonetti: Groebner bases for the distance distribution of systematic codes,5 Jon-Lark Kim: A Prize Problem in Coding Theory,6 Mijail Borges-Quintana, Miguel A. Borges-Trenard, Edgar Martinez-Moro: An application of Moeller's Algorithm to Coding Theory,7 Edgar Martinez-Moro, Diego Ruano: Mattson Solomon transform and algebra codes,8 Peter Beelen, Kristian Brander: Decoding folded Reed-Solomon codes using Hensel lifting,9 Daniel Augot, Michael Stepanov: A note on the generalisation of the Guruswami-Sudan list decoding 10 Gretchen L. Matthews: Viewing multipoint codes as subcodes of one-point codes11 Heide Gluesing-Luerssen, Barbara Langfeld, Wiland Schmale: A short introduction to cyclic convolutional codes,12 Ilaria Simonetti: On the non-linearity of Boolean functions13 Danilo Gligoroski, Vesna Dimitrova, Smile Markovski: Quasigroups as Boolean functions, their equation systems and Groebner bases14 Danilo Gligoroski, Smile Markovski, Svein J. Knapskog: A new measure to estimate pseudo-randomness of Boolean functions and relations with Groebner bases15 Ryutaroh Matsumoto: Radical computation for small characteristics
Responsibility: Massimiliano Sala [and others].

Abstract:

This book is the first ever to give a comprehensive overview of the application of commutative algebra to coding theory and cryptography. In it, all important properties of algebraic/geometric coding  Read more...

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