Linked e-resources
Details
Table of Contents
Intro
Preface
Organization
Contents
An Analysis of the RankSign Signature Scheme with Rank Multipliers
1 Introduction
2 Rank Metric Properties and Bounds
2.1 The Rank Metric
2.2 Bounds in the Rank Metric
2.3 A Difficult Problem in the Rank Metric
3 LRPC Codes
3.1 Erasure Decoder for LRPC Codes
4 The RankSign Signature Scheme
4.1 KeyGen
4.2 Sign
4.3 Verify
5 Attack by Debris-Alazard and Tillich
6 Repairing RankSign
6.1 KeyGen
6.2 Sign
6.3 Verify
6.4 Key and Signature Size
6.5 Discussion of Parameters
7 Conclusion
Theoretical Analysis of Decoding Failure Rate of Non-binary QC-MDPC Codes
1 Introduction
2 Analysis of Guaranteed Error-correction Capability of Non-binary QC-MDPC Codes
2.1 One-Step Majority Logic Decoding
3 Plausibility Analysis of 1-iteration Parallel Symbol Flipping Decoder
3.1 Distribution of Counters
3.2 Analysis of Parallel Symbol-Flipping Decoder
4 Choice of Cryptosystem Parameters
5 Conclusion
References
FuLeeca: A Lee-Based Signature Scheme
1 Introduction
2 Preliminaries
2.1 Notation
2.2 Basic Cryptographic Tools
2.3 Lee-Metric Codes
3 System Description
3.1 Key Generation
3.2 Signature Generation
3.3 Signature Verification
3.4 Encoding and Decoding
4 Security Analysis
4.1 Hardness of Underlying Problem and Generic Solvers
4.2 Analysis of the Algorithm with Respect to Known Attacks
4.3 Lattice-Based Attacks
5 Efficiency and Performance
5.1 Parameters
5.2 Reason for Choice of Parameters
5.3 Detailed Performance Analysis
6 Preliminary Attack on FuLeeca
7 Conclusion
References
Algebraic Algorithm for the Alternating Trilinear Form Equivalence Problem
1 Introduction
2 Preliminaries
3 Previous Algorithms for Solving ATFE
3.1 Graph-Theoretic Algorithm of Bouillaguet et al. ch5BFV12
3.2 Graph-Theoretic Algorithm of Beullens ch5Beu22
4 A Coding Theory Perspective of ATFE
5 Algebraic Algorithms for Solving ATFE
5.1 Direct Modelling
5.2 Improved Matrix-Code Modelling
5.3 Removing Invalid Solutions
6 Complexity Analysis
6.1 Non-trivial Syzygies
6.2 Hilbert Series and the Solving Degree
7 Experimental Results
7.1 Computing Syzygies
7.2 Running Gröbner Basis Computations
References
Modeling Noise-Accepting Key Exchange
Preface
Organization
Contents
An Analysis of the RankSign Signature Scheme with Rank Multipliers
1 Introduction
2 Rank Metric Properties and Bounds
2.1 The Rank Metric
2.2 Bounds in the Rank Metric
2.3 A Difficult Problem in the Rank Metric
3 LRPC Codes
3.1 Erasure Decoder for LRPC Codes
4 The RankSign Signature Scheme
4.1 KeyGen
4.2 Sign
4.3 Verify
5 Attack by Debris-Alazard and Tillich
6 Repairing RankSign
6.1 KeyGen
6.2 Sign
6.3 Verify
6.4 Key and Signature Size
6.5 Discussion of Parameters
7 Conclusion
Theoretical Analysis of Decoding Failure Rate of Non-binary QC-MDPC Codes
1 Introduction
2 Analysis of Guaranteed Error-correction Capability of Non-binary QC-MDPC Codes
2.1 One-Step Majority Logic Decoding
3 Plausibility Analysis of 1-iteration Parallel Symbol Flipping Decoder
3.1 Distribution of Counters
3.2 Analysis of Parallel Symbol-Flipping Decoder
4 Choice of Cryptosystem Parameters
5 Conclusion
References
FuLeeca: A Lee-Based Signature Scheme
1 Introduction
2 Preliminaries
2.1 Notation
2.2 Basic Cryptographic Tools
2.3 Lee-Metric Codes
3 System Description
3.1 Key Generation
3.2 Signature Generation
3.3 Signature Verification
3.4 Encoding and Decoding
4 Security Analysis
4.1 Hardness of Underlying Problem and Generic Solvers
4.2 Analysis of the Algorithm with Respect to Known Attacks
4.3 Lattice-Based Attacks
5 Efficiency and Performance
5.1 Parameters
5.2 Reason for Choice of Parameters
5.3 Detailed Performance Analysis
6 Preliminary Attack on FuLeeca
7 Conclusion
References
Algebraic Algorithm for the Alternating Trilinear Form Equivalence Problem
1 Introduction
2 Preliminaries
3 Previous Algorithms for Solving ATFE
3.1 Graph-Theoretic Algorithm of Bouillaguet et al. ch5BFV12
3.2 Graph-Theoretic Algorithm of Beullens ch5Beu22
4 A Coding Theory Perspective of ATFE
5 Algebraic Algorithms for Solving ATFE
5.1 Direct Modelling
5.2 Improved Matrix-Code Modelling
5.3 Removing Invalid Solutions
6 Complexity Analysis
6.1 Non-trivial Syzygies
6.2 Hilbert Series and the Solving Degree
7 Experimental Results
7.1 Computing Syzygies
7.2 Running Gröbner Basis Computations
References
Modeling Noise-Accepting Key Exchange