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Gröbner Bases, Coding, and Cryptography

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

Table of contents

  1. Front Matter
    Pages 1-16
  2. Gröbner Bases, Coding, and Cryptography: a Guide to the State-of-Art

  3. Invited Papers

    1. Front Matter
      Pages 9-9
    2. Teo Mora
      Pages 11-25
    3. Daniel Augot, Emanuele Betti, Emmanuela Orsini
      Pages 47-68
    4. Teo Mora, Emmanuela Orsini
      Pages 69-91
    5. Shojiro Sakata
      Pages 143-163
    6. Shojiro Sakata
      Pages 165-185
    7. Eleonora Guerrini, Anna Rimoldi
      Pages 197-218
    8. Marcus Greferath
      Pages 219-238
    9. Françoise Levy-dit-Vehel, Maria Grazia Marinari, Ludovic Perret, Carlo Traverso
      Pages 285-305
    10. Carlos Cid, Ralf-Philipp Weinmann
      Pages 307-327
    11. Frederik Armknecht, Gwenolé Ars
      Pages 329-348
  4. Notes

    1. Front Matter
      Pages 349-349
    2. Eleonora Guerrini, Emmanuela Orsini, Ilaria Simonetti
      Pages 367-372
    3. Jon-Lark Kim
      Pages 373-377
    4. M. Borges-Quintana, M. A. Borges-Trenard, E. Martínez-Moro
      Pages 379-384
    5. Edgar Martínez-Moro, Diego Ruano
      Pages 385-388
    6. Peter Beelen, Kristian Brander
      Pages 389-394
    7. Heide Gluesing-Luerssen, Barbara Langfeld, Wiland Schmale
      Pages 403-408
    8. Ilaria Simonetti
      Pages 409-413
    9. D. Gligoroski, V. Dimitrova, S. Markovski
      Pages 415-420
    10. Danilo Gligoroski, Smile Markovski, Svein Johan Knapskog
      Pages 421-425
    11. Ryutaroh Matsumoto
      Pages 427-430

About this book

Introduction

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 find that all chapters fit nicely within a unified notation.

Keywords

Algebra Code Coding Theory Cryptography DES Error-correcting Code Graph Groebner bases Gröbner basis Sim algorithms communication computer algebra data transmission

Editors and affiliations

  • Massimiliano Sala
    • 1
  • Shojiro Sakata
    • 2
  • Teo Mora
    • 3
  • Carlo Traverso
    • 4
  • Ludovic Perret
    • 5
  1. 1.Boole Centre for Research in InformaticsUniversity College CorkCorkIreland
  2. 2.Faculty of Engineering Dept. Production Systems EngineeringToyohashi University of TechnologyTempaku-choJapan
  3. 3.Dipto. MatematicaUniversità GenovaGenovaItaly
  4. 4.Dipto. MatematicaUniversità PisaPisaItaly
  5. 5.LIP6University of Paris VIParisFrance

Bibliographic information