Arithmetic of Finite Fields

1. Front Matter

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2. Structures in Finite Fields

   1. Interpolation of the Double Discrete Logarithm

      • Gerasimos C. Meletiou, Arne Winterhof

      Pages 1-10

   2. Finite Dedekind Sums

      • Yoshinori Hamahata

      Pages 11-18

   3. Transitive q-Ary Functions over Finite Fields or Finite Sets: Counts, Properties and Applications

      • Marc Mouffron

      Pages 19-35

3. Efficient Finite Field Arithmetic

   1. Fast Point Multiplication on Elliptic Curves without Precomputation

      • Marc Joye

      Pages 36-46

   2. Optimal Extension Field Inversion in the Frequency Domain

      • Selçuk Baktır, Berk Sunar

      Pages 47-61

   3. Efficient Finite Fields in the Maxima Computer Algebra System

      • Fabrizio Caruso, Jacopo D’Aurizio, Alasdair McAndrew

      Pages 62-76

4. Efficient Implementation and Architectures

   1. Modular Reduction in GF(2ⁿ) without Pre-computational Phase

      • M. Knežević, K. Sakiyama, J. Fan, I. Verbauwhede

      Pages 77-87

   2. Subquadratic Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation

      • M. Anwar Hasan, Christophe Negre

      Pages 88-102

   3. Digit-Serial Structures for the Shifted Polynomial Basis Multiplication over Binary Extension Fields

      • Arash Hariri, Arash Reyhani-Masoleh

      Pages 103-116

5. Classification and Construction of Mappings over Finite Fields

   1. Some Theorems on Planar Mappings

      • Gohar M. Kyureghyan, Alexander Pott

      Pages 117-122

   2. Classifying 8-Bit to 8-Bit S-Boxes Based on Power Mappings from the Point of DDT and LAT Distributions

      • Bora Aslan, M. Tolga Sakalli, Ercan Bulus

      Pages 123-133

   3. EA and CCZ Equivalence of Functions over GF(2ⁿ)

      • K. J. Horadam

      Pages 134-143

6. Codes and Cryptography

   1. On the Number of Two-Weight Cyclic Codes with Composite Parity-Check Polynomials

      • Gerardo Vega

      Pages 144-156

   2. On Field Size and Success Probability in Network Coding

      • Olav Geil, Ryutaroh Matsumoto, Casper Thomsen

      Pages 157-173

   3. Montgomery Ladder for All Genus 2 Curves in Characteristic 2

      • Sylvain Duquesne

      Pages 174-188

   4. On Cryptographically Significant Mappings over GF(2ⁿ)

      • Enes Pasalic

      Pages 189-204

7. Back Matter

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This book constitutes the refereed proceedings of the Second International Workshop on the Arithmetic of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008. The 16 revised full papers presented were carefully reviewed and selected from 34 submissions. The papers are organized in topical sections on structures in finite fields, efficient finite field arithmetic, efficient implementation and architectures, classification and construction of mappings over finite fields, and codes and cryptography.

• Algebra
• LA
• algebraic computation
• algebraic number theory
• algorithmic number theory
• binary polynomials
• classification
• complexity
• computational algebra
• computational number theory
• computer algebra
• cryptographic codes
• cryptography
• curve-based cryptography
• cyclic codes
• algorithm analysis and problem complexity

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