2009

Gröbner Bases, Coding, and Cryptography

ISBN: 978-3-540-93805-7 (Print) 978-3-540-93806-4 (Online)

Table of contents (33 chapters)

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  1. Front Matter

    Pages 1-16

  2. Gröbner Bases, Coding, and Cryptography: a Guide to the State-of-Art

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      Book Chapter

      Pages 1-8

      Gröbner Bases, Coding, and Cryptography: a Guide to the State-of-Art

  3. Invited Papers

    1. Front Matter

      Pages 9-9

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      Book Chapter

      Pages 11-25

      Gröbner Technology

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      Book Chapter

      Pages 27-45

      The FGLM Problem and Möller’s Algorithm on Zero-dimensional Ideals

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      Book Chapter

      Pages 47-68

      An Introduction to Linear and Cyclic Codes

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      Book Chapter

      Pages 69-91

      Decoding Cyclic Codes: the Cooper Philosophy

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      Book Chapter

      Pages 93-106

      A Tutorial on AG Code Construction from a Gröbner Basis Perspective

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      Book Chapter

      Pages 107-120

      Automorphisms and Encoding of AG and Order Domain Codes

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      Book Chapter

      Pages 121-141

      Algebraic Geometry Codes from Order Domains

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      Book Chapter

      Pages 143-163

      The BMS Algorithm

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      Book Chapter

      Pages 165-185

      The BMS Algorithm and Decoding of AG Codes

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      Book Chapter

      Pages 187-196

      A Tutorial on AG Code Decoding from a Gröbner Basis Perspective

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      Book Chapter

      Pages 197-218

      FGLM-Like Decoding: from Fitzpatrick’s Approach to Recent Developments

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      Book Chapter

      Pages 219-238

      An Introduction to Ring-Linear Coding Theory

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      Book Chapter

      Pages 239-261

      Gröbner Bases over Commutative Rings and Applications to Coding Theory

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      Book Chapter

      Pages 263-283

      Overview of Cryptanalysis Techniques in Multivariate Public Key Cryptography

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      Book Chapter

      Pages 285-305

      A Survey on Polly Cracker Systems

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      Book Chapter

      Pages 307-327

      Block Ciphers: Algebraic Cryptanalysis and Gröbner Bases

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      Book Chapter

      Pages 329-348

      Algebraic Attacks on Stream Ciphers with Gröbner Bases

  4. Notes

    1. Front Matter

      Pages 349-349

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      Book Chapter

      Pages 351-355

      Canonical Representation of Quasicyclic Codes Using Gröbner Bases Theory

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      Book Chapter

      Pages 357-360

      About the nth-Root Codes: a Gröbner Basis Approach to the Weight Computation

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