Arithmetic of Finite Fields
4th International Workshop, WAIFI 2012, Bochum, Germany, July 16-19, 2012, Proceedings
Published on 2. July 2012
XII, 247 pages
978-3-642-31662-3 (ISBN)
Description
This book constitutes the refereed proceedings of the 4th International Workshop on the Arithmetic of Finite Field, WAIFI 2012, held in Bochum, Germany, in July 2012. The 13 revised full papers and 4 invited talks presented were carefully reviewed and selected from 29 submissions. The papers are organized in topical sections on coding theory and code-based cryptography, Boolean functions, finite field arithmetic, equations and functions, and polynomial factorization and permutation polynomial.
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Ferruh Özbudak | Francisco Rodriguez-Henriquez
Arithmetic of Finite Fields
4th International Workshop, WAIFI 2012, Bochum, Germany, July 16-19, 2012, Proceedings
Book
07/2012
Springer
€49.22
Shipment within 7-9 days
Content
- Title
- Preface
- Table of Contents
- Generalised Jacobians in Cryptography and Coding Theory
- Introduction and Summary
- Preliminaries
- Pairings on Generalised Jacobians
- A Generalised Tate-Lichtenbaum Pairing
- Variations - New Bilinear and Multilinear Pairings
- Weak Discrete Logarithm Problem in the Domain
- Lower Complexity Bounds for Codes
- Generalised Algebraic Geometric Codes
- Reduction of the Discrete Logarithm Problem to Code Based Computational Problems
- Efficient Generating Sets of Generalised Jacobians
- Examples
- References
- The Weight Distribution of a Family of Reducible Cyclic Codes
- Introduction
- Definitions, Notations, Preliminaries and Main Assumption
- Some General Results
- The Weight Distribution of a Family of Non-irreducible Cyclic Codes
- Conclusion
- References
- A New Method for Constructing Small-Bias Spaces from Hermitian Codes
- Introduction
- The AG-Bound
- The New Small-Bias Spaces
- Time Complexity Considerations
- Small-Bias Spaces from Norm-Trace Codes
- References
- An Improved Threshold Ring Signature Schem eBased on Error Correcting Codes
- Introduction
- Preliminaries
- Definitions
- The q-SD Identification Scheme
- Description of the q-SD Identification Scheme
- Signature Schemes from Identification Schemes
- Code-Based Threshold Ring Signature Schemes
- Description of Our Threshold Identification Protocol
- Security
- Performance and Implementation
- Practical Results
- Conclusion
- References
- Sequences and Functions Derived from Projective Planes and Their Difference Sets
- Introduction
- Difference Sets and Incidence Structures
- Equivalence of Difference Sets and Isomorphism of Incidence Structures
- Projections of Generalized Difference Sets and a Lifting Problem
- The Prime Power Conjecture for Projective Planes
- Difference Sets and Affine Difference Sets
- Difference Sets and Semifields
- The n Even Case
- The n Odd Case
- Direct Product Difference Sets
- Generalized Difference Sets Relative to Three Subgroups
- Conclusion
- References
- On Formally Self-dual Boolean Functions in 2,4 and 6 Variables
- Introduction
- Notation and Definitions
- Classification of Formally Self-dual Boolean Functions
- Conclusion
- References
- On the Algebraic Normal Form and Walsh Spectrum of Symmetric Functions over Finite Rings
- Introduction
- Symmetric Functions over Finite Rings
- Functions over Finite Rings
- Partitions
- Symmetric Functions over Finite Rings
- Algebraic Normal Form
- Definition
- Computing the Simplified Value Vector of m
- Link between Simplified ANF and Simplified Value Vector
- Walsh Spectrum
- Definition
- Computing the Matrix Wq,r,n
- Computing Wr,r,n
- Computing the Walsh Spectrum of a Symmetric Function
- Using These Algorithms to Test Large Set of Symmetric Functions
- Conclusion
- References
- Verification of Restricted EA-Equivalence for Vectorial Boolean Functions
- Introduction
- Preliminaries
- Verification of Restricted EA-Equivalence
- Conclusions
- References
- Software Implementation of Modular Exponentiation, Using Advanced Vector Instructions Architectures
- Introduction
- Preliminaries
- The RSA Context
- The Non Reduced Montgomery Multiplication
- The Relevant AVX2 Instructions
- Modular Exponentiation with Vector Instructions
- Redundant Representation
- NRMM
- Modular Exponentiation Using VNRMM
- Implementation, Choice of Parameters and Optimizations
- Choice of Parameters
- Why Is the AVX2 Architecture Sufficient for an Efficient Vectorized Implementation?
- Optimizing the Implementation
- Vectorized Redundant Montgomery Square
- Results
- Conclusion
- References
- Efficient Multiplication over Extension Fields
- Introduction
- AMNS
- Definition of an AMNS Representation
- Arithmetic in AMNS Representation
- Efficient Multiplication in Fqm Using AMNS
- Theory
- Some Theory about Lattices
- Construction When We Can Choose q
- Construction When We Cannot Choose q
- Implementation and Results
- Conclusion
- References
- GF(2m) Finite-Field Multipliers with Reduced Activity Variations
- Introduction
- Activity in Hardware Arithmetic Operators
- GF(2m) Finite-Field Multiplication Operators
- Classic Two-Step Multiplication Algorithm
- Montgomery Multiplication Multiplier
- Mastrovito Multiplication Algorithm
- Useful Activity Analysis for Multiplication Algorithms
- Modifications on Multiplication Algorithms for Reducing Useful Activity Variations
- Conclusion
- References
- Finding Optimal Formulae for Bilinear Maps
- Introduction
- Some Instances of the Bilinear Rank Problem
- From Bilinear Applications to Linear Algebra
- Solving the Linear Algebra Problem
- Naive Algorithm
- Improved Algorithm
- Implementation Issues
- From Solution Subspaces back to Formulae
- Complexity Analysis
- Special Case of Symmetric Bilinear Maps
- Experimental Results
- Conclusion
- References
- Solving Binary Linear Equation Systems over the Rationals and Binaries
- Introduction
- Background
- Deriving a Solution over F2
- Discussion
- Conclusion
- References
- Hashing with Elliptic Curve L-Functions
- Introduction
- Elliptic Curve L-Function
- ECOH
- Hashing with L-Functions
- One Way Function
- Hashing and MAC's Protocol
- MAC's Elliptic Curve L-Function against ECOH
- Implementations:
- Security
- Conclusion
- References
- Square Root Algorithms for the Number Field Sieve
- The Direct (lifting) Approach
- Working p-Adically
- Bound on the Square Root Coefficients
- Complexity
- Couveignes' Algorithm
- Montgomery's Algorithm
- Iterative Reduction
- Complexity
- A New CRT-Based Lifting Approach
- CRT-Based Reconstruction
- Determining Signs
- Strategies for Fast Computation
- Complexity
- Implementation and Experimental Data
- A Variant Using a Large Number of Primes
- References
- Improving the Berlekamp Algorithm for Binomials xn - a
- Introduction
- Binomials
- Berlekamp Algorithm
- Our Algorithm
- Complexity
- Conclusion and Future Works
- References
- On Some Permutation Binomials of the Form x2n-1k +1 + ax over F2n : Existence and Count
- Introduction
- Existence of Permutation Binomial x2n-13+1 + ax
- Permutation Polynomials of the Form x2n + 2+ax over F22n
- Cryptographic Relevance of Permutation Polynomials
- Boolean Functions from Permutation Polynomials
- Conclusions
- References
- Author Index
