Arithmetic of Finite Fields: Second International Workshop, WAIFI 2008, Siena, Italy, July 6-9, 2008, ProceedingsThis 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. |
Contents
Interpolation of the Double Discrete Logarithm | 1 |
Finite Dedekind Sums | 11 |
Counts Properties and Applications | 19 |
Fast Point Multiplication on Elliptic Curves without Precomputation | 36 |
Optimal Extension Field Inversion in the Frequency Domain | 47 |
Efficient Finite Fields in the Maxima Computer Algebra System | 62 |
Modular Reduction in GF2n without Precomputational Phase | 77 |
Subquadratic Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation | 88 |
Some Theorems on Planar Mappings | 117 |
Classifying 8Bit to 8Bit SBoxes Based on Power Mappings from the Point of DDT and LAT Distributions | 123 |
EA and CCZ Equivalence of Functions over GF2n | 134 |
On the Number of TwoWeight Cyclic Codes with Composite ParityCheck Polynomials | 144 |
On Field Size and Success Probability in Network Coding | 157 |
Montgomery Ladder for All Genus 2 Curves in Characteristic 2 | 174 |
On Cryptographically Significant Mappings over GF2n | 189 |
| 205 | |
DigitSerial Structures for the Shifted Polynomial Basis Multiplication over Binary Extension Fields | 103 |
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Common terms and phrases
affine algebraic degree arithmetic binary field bitwise rotations Boolean functions CCZ-equivalence coefficients complexity computation coordinates coset cryptosystems cyclic codes Dedekind sums defined denote Dickson polynomials differential digit digit-serial SPB multiplier EA-equivalence efficient Elliptic Curve Cryptography elliptic curves equation equivalence finite fields formulas frequency domain Gathen genus 2 curves GF(p GF(pm graph hyperelliptic curves IEEE Transactions implementation input inversion irreducible polynomial Itoh-Tsujii Jacobian Koç Eds Kummer surface Lemma linear network coding LNCS lower bound matrix Maxima method mod F(x modular multiplication modulo monomial Montgomery ladder Montgomery reduction multiplication algorithm normalised one-weight cyclic codes polynomial basis pre-computational prime primitive element Proof Proposition q-ary functions quadratic representation result S-box scalar multiplication Section shifted polynomial basis Springer subquadratic success probability symmetric functions t-transitive Theorem transversal two-weight cyclic codes variables WAIFI