Arithmetic of Finite Fields: Second International Workshop, WAIFI 2008, Siena, Italy, July 6-9, 2008, Proceedings

ISBN-13: 9783540694984 / Angielski / Miękka / 2008 / 205 str.

Joachim von zur Gathen;José Luis Imana;Cetin Kaya Koc

Opis

These are the proceedings of WAIFI 2008, the second workshop on the Ari- metic of Finite Fields, that was held in Siena, Italy, July 6-9, 2008. The ?rst workshop, WAIFI 2007, which was held in Madrid (Spain), was received quite enthusiasticallybymathematicians, computerscientists, engineersandphysicists who are performing research on ?nite ?eld arithmetic. We believe that there is a need for a workshop series bridging the gap between the mathematical theory of ?nite ?elds and their hardware/software implementations and technical - plications. We hope that the WAIFI workshopseries, which from now on will be held on even years, will help to ?ll this gap. Therewere 34 submissionsto WAIFI 2008, of which the ProgramCommittee selected 16 for presentation. Each submission was reviewed by at least three reviewers. Our thanks go to the Program Committee members for their many contributionsandhardwork.Wearealsogratefultotheexternalreviewerslisted below for their expertise and assistance in the deliberations. In addition to the contributions appearing in these proceedings, the workshop program included an invited lecture given by Amin Shokrollahi. Special compliments go out to Enrico Martinelli, General Co-chair, and to Roberto Giorgi and Sandro Bartolini, local organizers of WAIFI 2008, who broughtthe workshopto Siena, oneofthe mostbeautiful citiesofTuscany, Italy. WAIFI 2008 was organized by the Dipartimento di Ingegneria dell'Informazione of the University of Siena, Italy. The submission and selection of papers were done using the iChair software, developed at EPFL by Thomas Baign eres and Matthieu Finiasz. We also thank Deniz Karakoyunlu for his help in this matter.

Spis treści

Structures in Finite Fields.- Interpolation of the Double Discrete Logarithm.- Finite Dedekind Sums.- Transitive q-Ary Functions over Finite Fields or Finite Sets: Counts, Properties and Applications.- Efficient Finite Field Arithmetic.- Fast Point Multiplication on Elliptic Curves without Precomputation.- Optimal Extension Field Inversion in the Frequency Domain.- Efficient Finite Fields in the Maxima Computer Algebra System.- Efficient Implementation and Architectures.- Modular Reduction in GF(2 n ) without Pre-computational Phase.- Subquadratic Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation.- Digit-Serial Structures for the Shifted Polynomial Basis Multiplication over Binary Extension Fields.- Classification and Construction of Mappings over Finite Fields.- Some Theorems on Planar Mappings.- Classifying 8-Bit to 8-Bit S-Boxes Based on Power Mappings from the Point of DDT and LAT Distributions.- EA and CCZ Equivalence of Functions over GF(2 n ).- Codes and Cryptography.- On the Number of Two-Weight Cyclic Codes with Composite Parity-Check Polynomials.- On Field Size and Success Probability in Network Coding.- Montgomery Ladder for All Genus 2 Curves in Characteristic 2.- On Cryptographically Significant Mappings over GF(2 n ).

Blurb

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.