Code-Based Cryptography

Name: Code-Based Cryptography | 11th International Workshop, CBCrypto 2023, Lyon, France, April 22-23, 2023, Revised Selected Papers
Brand: Springer
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11th International Workshop, CBCrypto 2023, Lyon, France, April 22-23, 2023, Revised Selected Papers

Andre Esser Paolo Santini(Herausgeber*in)

Springer (Verlag)

Erschienen am 27. Oktober 2023

IX, 175 Seiten

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978-3-031-46495-9 (ISBN)

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Beschreibung

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Inhalt

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
References
Fast Gao-Like Decoding of Horizontally Interleaved Linearized Reed-Solomon Codes
1 Introduction
2 Preliminaries
2.1 Skew-Polynomial Rings
2.2 The Sum-Rank Metric and the Corresponding Interleaved Channel Model
2.3 Horizontally Interleaved Linearized Reed-Solomon (HILRS) Codes
3 A Gao-Like Decoder for HILRS Codes
4 A Fast Variant of the Gao-Like Decoder for HILRS Codes
4.1 Minimal Approximant Bases
4.2 Solving the Gao-Like Key Equation via Minimal Approximant Bases
5 Conclusion
References
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
1 Introduction
1.1 Our Contributions
1.2 Related Work
2 Prerequisites
3 Key Exchange over Unreliable Networks
3.1 Modeling Noise
3.2 Noisy Matching Conversations
4 The Validity of Our Model
4.1 Secure in a Noise-Free Environment
4.2 Canonical Extension to a Noisy Environment
5 Tools for Constructing Noisy Key Exchange
5.1 Other Error-Resistant Security Notions
5.2 Error Tolerant FO-Transform
5.3 Error-Resistant KEA Construction
6 Existence of Error-Resistant PKE
A Proof of Modified FO-transform Theorem 2
References
Generic Error SDP and Generic Error CVE
1 Introduction
2 Preliminaries
3 Generic Error Sets
3.1 Error Detectability and Correctability
3.2 Generic Gilbert-Varshamov Bound
3.3 Density of Codes Correcting a Generic Error Set
4 Generic Error SDP
5 Generic Error CVE
5.1 Completeness
5.2 Soundness
5.3 Zero-Knowledge
6 On Polynomial Instances of GE-SDP
6.1 Vulnerability of R-SDP and R-CVE
7 Conclusions
References
PALOMA: Binary Separable Goppa-Based KEM
1 Introduction
1.1 Trapdoor
1.2 KEM Structure
1.3 Parameter Sets
2 Specification
2.1 Parameter Sets
2.2 Key Generation
2.3 Encryption and Decryption
2.4 Encapsulation and Decapsulation
3 Performance Analysis
3.1 Description of C Implementation
3.2 Data Size
3.3 Speed
4 Security
4.1 OW-CPA-secure PKE=(GenKey, Encrypt, Decrypt)
4.2 IND-CCA2-Secure KEM= (GenKey, Encap, Decap)
5 Conclusion
A Mathematical Background
A.1 Syndrome Decoding Problem
A.2 Binary Separable Goppa Code
A.3 Extended Patterson for Binary Separable Goppa code
B Pseudo codes for PALOMA
References
Author Index

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