Hypergraph Decomposition and Secret Sharing 1st edition by Giovanni Di Crescenzo, Clemente Galdi ISBN 3540206958 9783540206958

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Product details:

ISBN 10:       3540206958
ISBN 13: 978-3540206958
Author:         Giovanni Di Crescenzo, Clemente Galdi
 

Hypergraph Decomposition and Secret Sharing 1st Table of contents:

• Introduction

  • 1.1 Background and Motivation
  • 1.2 Hypergraphs and Their Importance in Secret Sharing
  • 1.3 Overview of Secret Sharing Schemes
  • 1.4 Main Contributions
  • 1.5 Structure of the Paper

• Preliminaries

  • 2.1 Graph Theory and Hypergraphs
    • 2.1.1 Definition of Hypergraphs
    • 2.1.2 Basic Properties of Hypergraphs
    • 2.1.3 Hypergraph Decomposition
  • 2.2 Secret Sharing
    • 2.2.1 Definition and Key Concepts
    • 2.2.2 Types of Secret Sharing Schemes (e.g., Threshold, Verifiable, and Others)
  • 2.3 Relations Between Hypergraphs and Secret Sharing

• Hypergraph Decomposition

  • 3.1 Decomposition Models and Techniques
    • 3.1.1 General Decomposition Problems
    • 3.1.2 Decomposition for Graphs vs. Hypergraphs
  • 3.2 Algorithms for Hypergraph Decomposition
    • 3.2.1 Greedy and Exact Algorithms
    • 3.2.2 Computational Complexity of Hypergraph Decomposition
  • 3.3 Applications of Hypergraph Decomposition in Cryptography
    • 3.3.1 Partitioning of Hypergraphs in Secret Sharing Schemes
    • 3.3.2 Analysis of Decompositions in Cryptographic Contexts

• Secret Sharing Schemes Based on Hypergraph Decomposition

  • 4.1 Classic Secret Sharing Schemes (e.g., Shamir’s Scheme)
  • 4.2 Secret Sharing with Hypergraph Structures
    • 4.2.1 Hypergraph-Based Threshold Schemes
    • 4.2.2 Applications to Generalized Secret Sharing Models
  • 4.3 Decomposing Secrets Using Hypergraphs
    • 4.3.1 Hypergraph Representations of Shares and Secrets
    • 4.3.2 Reconstruction and Security Guarantees
  • 4.4 Enhanced Security via Hypergraph Decomposition

• Properties of Secret Sharing Schemes Using Hypergraphs

  • 5.1 Security Properties and Guarantees
    • 5.1.1 Perfect Secrecy and Robustness
    • 5.1.2 Monotonicity and Coalition Resilience
  • 5.2 Efficiency of Secret Sharing Schemes
    • 5.2.1 Share Distribution Complexity
    • 5.2.2 Computational Complexity of Secret Reconstruction
  • 5.3 Verifiable Secret Sharing Using Hypergraphs
    • 5.3.1 Verifiability in Hypergraph-Based Schemes
    • 5.3.2 Applications of Verifiable Schemes

• Applications of Hypergraph-Based Secret Sharing

  • 6.1 Secure Multi-Party Computation
  • 6.2 Cloud Storage and Privacy Protection
  • 6.3 Blockchain and Decentralized Systems
  • 6.4 Privacy-Preserving Cryptographic Protocols
  • 6.5 Secret Sharing in Distributed Networks

• Challenges and Limitations

  • 7.1 Scalability of Hypergraph-Based Secret Sharing
  • 7.2 Communication Overhead in Large Systems
  • 7.3 Trade-offs Between Security and Efficiency
  • 7.4 Handling Dynamic and Evolving Participant Sets
  • 7.5 Open Problems in Hypergraph Decomposition and Secret Sharing

• Advanced Topics in Hypergraph Decomposition and Secret Sharing

  • 8.1 Dynamic Secret Sharing Schemes
  • 8.2 Quantum Secret Sharing and Hypergraph Structures
  • 8.3 Hybrid Models for Secret Sharing
  • 8.4 Multi-level Secret Sharing Using Hypergraph Decomposition
  • 8.5 Cross-layer Applications in Cryptography and Network Security

• Future Directions

  • 9.1 Improving Algorithmic Efficiency for Decomposition
  • 9.2 New Hypergraph Models for Secret Sharing
  • 9.3 Exploring Secret Sharing Beyond Threshold Schemes
  • 9.4 Interdisciplinary Applications in Machine Learning and Privacy
  • 9.5 Potential Integration with Blockchain and Smart Contracts

• Conclusion

  • 10.1 Summary of Key Findings
  • 10.2 Implications for Cryptography and Secure Systems
  • 10.3 Future Outlook on Hypergraph-Based Secret Sharing
  • 10.4 Closing Remarks

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