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  • © 2009

Gröbner Bases, Coding, and Cryptography

  • Covers exciting new research directions on Gröbner bases and their applications
  • Includes supplementary material: sn.pub/extras

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Table of contents (33 chapters)

  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. Gröbner Technology

      • Teo Mora
      Pages 11-25
    3. An Introduction to Linear and Cyclic Codes

      • Daniel Augot, Emanuele Betti, Emmanuela Orsini
      Pages 47-68
    4. Decoding Cyclic Codes: the Cooper Philosophy

      • Teo Mora, Emmanuela Orsini
      Pages 69-91
    5. The BMS Algorithm

      • Shojiro Sakata
      Pages 143-163
    6. The BMS Algorithm and Decoding of AG Codes

      • Shojiro Sakata
      Pages 165-185
    7. FGLM-Like Decoding: from Fitzpatrick’s Approach to Recent Developments

      • Eleonora Guerrini, Anna Rimoldi
      Pages 197-218
    8. An Introduction to Ring-Linear Coding Theory

      • Marcus Greferath
      Pages 219-238
    9. A Survey on Polly Cracker Systems

      • Françoise Levy-dit-Vehel, Maria Grazia Marinari, Ludovic Perret, Carlo Traverso
      Pages 285-305
    10. Block Ciphers: Algebraic Cryptanalysis and Gröbner Bases

      • Carlos Cid, Ralf-Philipp Weinmann
      Pages 307-327
    11. Algebraic Attacks on Stream Ciphers with Gröbner Bases

      • Frederik Armknecht, Gwenolé Ars
      Pages 329-348

About this book

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 findthat all chapters fit nicely within a unified notation.

Editors and Affiliations

  • Boole Centre for Research in Informatics, University College Cork, Cork, Ireland

    Massimiliano Sala

  • Faculty of Engineering Dept. Production Systems Engineering, Toyohashi University of Technology, Tempaku-cho, Japan

    Shojiro Sakata

  • Dipto. Matematica, Università Genova, Genova, Italy

    Teo Mora

  • Dipto. Matematica, Università Pisa, Pisa, Italy

    Carlo Traverso

  • LIP6, University of Paris VI, Paris, France

    Ludovic Perret

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access