Coding and Cryptology

Name: Coding and Cryptology | Third International Workshop, IWCC 2011, Qingdao, China, May 30-June 3, 2011. Proceedings
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Third International Workshop, IWCC 2011, Qingdao, China, May 30-June 3, 2011. Proceedings

Yeow Meng Chee Zhenbo Guo San Ling Fengjing Shao Yuansheng Tang Huaxiong Wang Chaoping Xing(Editor)

Springer (Publisher)

Published on 5. June 2011

VIII, 295 pages

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978-3-642-20901-7 (ISBN)

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Content

Title Page
Preface
Third International Workshop on Coding and Cryptology (IWCC 2011)
Table of Contents
A Signature Scheme with Efficient Proof of Validity
Introduction
Background
Boneh-Boyen Signature Scheme
Our Contribution
Preliminaries
Syntax and Security Notions
Proof of Validity with Committed Key
The Scheme
Security
Comparison
Conclusion
References
Secret-Sharing Schemes: A Survey
Introduction
Organization
Definitions
Constructions of Secret-Sharing Schemes
Shamir's Threshold Secret-Sharing Scheme
Undirected s-t-Connectivity
Ito, Saito, and Nishizeki's Constructions [45]
The Monotone Formulae Construction [14]
The Monotone Span Programs Construction [21,46]
Multi-Linear Secret-Sharing Schemes [16,32]
Other Constructions
Secret Sharing and Secure Multi-party Computation
Computing the Sum of Two Shared Numbers
Computing the Product of Two Shared Numbers
Computing an Arithmetic Circuit
Extensions to Other Models
Lower Bounds on the Size of the Shares
A Simple Lower Bound
Stronger Lower Bounds
Csirmaz's Lower Bound
Limitations of Known Techniques for Lower Bounds
Lower Bounds for Linear Secret Sharing
Secret-Sharing, Cryptomania, and NP =coNP
Impossibility of Secret-Sharing with Efficient Sharing
Oblivious-Transfer Protocols from Secret-Sharing
Summary and Open Problems
Open Problems
References
Lattice Codes for the Gaussian Wiretap Channel
Introduction
Notations and Previous Results
Notations and System Model
Theta Series of a Lattice
Minimization of the Theta Series
The Secrecy Gain
Definitions
The Secrecy Gain of Unimodular Lattices
Higher Dimension Unimodular Extremal Lattices
Asymptotic Analysis
A Siegel-Weil Formula for Theta Series of Even Unimodular Lattices
Limit of $E_k$
Consequences
Integral Lattices
Level of a Lattice ($resp.$ a Quadratic Form)
Dirichlet Character
Theta Series as a Modular Form
Properties of $Mk (G0(N), ?)$
Example in Dimension 4
Asymptotic Analysis
Conclusion
References
List Decoding for Binary Goppa Codes
Introduction
Review of Divisors in Arithmetic Progressions
Linear Combinations as Divisors
Review of Classical Irreducible Binary Goppa Codes
Review of Patterson's Algorithm
Extracting More Information from Patterson's Algorithm
List Decoding via Divisors
References
Faster 2-Regular Information-Set Decoding
Introduction
Low-Weight Information-Set Decoding
The Augot-Finiasz-Sendrier Algorithm for 2-Regular Decoding
A New Algorithm for 2-Regular Decoding
Applications to Hash Functions
References
Ideal Secret Sharing Schemes for Useful Multipartite Access Structures
Introduction
Shamir's Threshold Secret Sharing Scheme
First Generalizations of Threshold Secret Sharing
Brickell's Ideal Secret Sharing Schemes
Constructing and Characterizing
A New Tool: Integer Polymatroids
Open Problems and Directions for Future Work
References
Loiss: A Byte-Oriented Stream Cipher
Introduction
Description of Loiss
The LFSR
The Nonlinear Function $F$
The BOMM Structure
Initialization of Loiss
Key Stream Generation
Some Basic Properties of the Components in Loiss
Properties of the LFSR
Properties of $F$
Properties of the BOMM
Key Entropy Preservation in the Initialization
Security Analysis
Guess and Determine Attack
Linear Distinguishing Attack
Algebraic Attacks
Time-Memory-and-Data Attack
Evaluations on Software and Hardware Implementations
On Software Implementation
On Hardware Implementation
Conclusions
References
Secure Message Transmission by Public Discussion: A Brief Survey
Introduction and Motivation
Model and Problem Definition
The First Solutions
Round Complexity
SMT-PD with Optimal Private Communication
Reducing Public Communication
Amortized SMT-PD
Summary and Future Work
References
Variations on Encoding Circuits for Stabilizer Quantum Codes
Introduction
Stabilizer Quantum Codes
Qudit Systems
Clifford Operations
Stabilizer Codes and Classical Codes
Encoding Circuits from a Standard Form
Standard Form of Stabilizers
Example
Encoding Circuits Related to Graphs
Stabilizer Codes and Graphs
Example
Conclusions
References
Algorithms for the Shortest and Closest Lattice Vector Problems
Introduction
Some Background on Euclidean Lattices
An SVP/CVP Solver Relying on the Voronoi Cell
The Voronoi Cell Suffices for Solving SVP and CVP
Computing the Relevant Vectors
Saturating the Space
The AKS Algorithm
The ListSieve Algorithm
Solving CVP
Enumeration-Based Solvers
The Enum Algorithm
Reducing before Enumerating
Practical Improvements
Open Problems
References
An Experiment of Number Field Sieve over GF($p$) of Low Hamming Weight Characteristic
Introduction
Number Field Sieve
DLP over GF($p$)
Polynomial Selection
Searching Relations
Linear Algebra and Individual Logarithm
Joux-Lercier's NFS and Low Weight NFS
Joux-Lercier's NFS (JL03-NFS)
Low Weight NFS (Sch06-NFS)
Running Time
An Experiment on JL03-NFS and Sch06-NFS
Experimental Environments
Parameters for JL03-NFS and Sch06-NFS
Comparison between JL03-NFS and Sch06-NFS
Conclusion
References
The Minimum Distance of Graph Codes
Introduction
Basic Parameters and Bounds
General $n$-Regular Graphs
Bipartite Graphs
Bounds on the Minimum Distance
Improved Lower Bounds on the Minimum Distance
Expander Graphs from Geometries
Minimum Distances of Codes from Geometries
Conclusion
References
Local Duality and the Discrete Logarithm Problem
Introduction
The Multiplicative Case
The Case of Jacobians of Curves
Proof of Theorem 1 - The Multiplicative Case
Proof of Theorem 2 - The Case of Jacobians of Curves
The Case when $k$ Does not Contain $m$-Roots of Unity
The Multiplicative Case
The Case of Jacobians of Curves
References
On the Effects of Pirate Evolution on the Design of Digital Content Distribution Systems
Introduction
Trace and Revoke Schemes
Tracing Traitors in the Subset Cover Framework
Pirate Evolution
Pirate Evolution and the AACS
Pirate Evolution for the Subset Difference Method
Protecting against Pirate Evolution for the SD Method
Epilogue: The Effects of Pirate Evolution
References
Arithmetic of Split Kummer Surfaces: Montgomery Endomorphism of Edwards Products
Introduction
Projective Embeddings of a Kummer Variety $K$
Edwards Model and Projective Embeddings of $K_1$
Segre Embedings and Projective Products
Edwards Model and Projective Embeddings of $K_2$
Endomorphisms of Kummer Surfaces $K_2$
Conclusion
References
A New Family of Quadriphase Sequences with Low Correlation
Introduction
Preliminaries
Correlation Function
Galois Ring
Z4-Valued Quadratic Form
Basic Lemmas
A New Family of Quadriphase Sequences and Their Correlation Distribution
Correlation Distribution of the Family $S$ for Odd $n$
Correlation Distribution of the Family $S$ for Even $n$
Conclusion
References
On the Link of Some Semi-bent Functions with Kloosterman Sums
Introduction
Notation and Preliminaries
Some Technical Results
Some Semi-bent Functions in Univariate Forms
Conclusion
References
Locally Decodable Codes: A Brief Survey
Introduction
Preliminaries
Reed Muller Codes
Summary of the Parameters
Multiplicity Codes
Summary of the Parameters
Matching Vector Codes
Summary of the Parameters
Conclusions
References
On Relationship of Computational Diffie-Hellman Problem and Computational Square-Root Exponent Problem
Introduction
Some Notations and the Computational Square-Root Exponent Problem
Relation between CSREP and CDHP
Algorithm
Conclusion
References
Author Index

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Coding and Cryptology

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