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A Comprehensive Survey of Threshold Signatures: NIST Standards, Post-Quantum Cryptography, Exotic Techniques, and Real-World Applications

Kiarash Sedghighadikolaei, Attila Altay Yavuz

TL;DR

This paper provides a comprehensive and systematic survey of threshold and distributed signatures with advanced features and examines both generic and custom thresholding techniques for a myriad of signature families while investigating exotic signatures, real-life applications, and potential future research direction.

Abstract

Threshold digital signatures enable a distributed execution of signature functionalities and will play a crucial role in the security of emerging decentralized next-generation networked systems and applications. In this paper, we provide a comprehensive and systematic survey of threshold and distributed signatures with advanced features. Our survey encompasses threshold signatures in conventional and post-quantum cryptography (PQC) settings and captures custom-design and standard signatures (e.g., conventional NIST and NIST-PQC). We examine both generic (via secure multi-party computation) and custom thresholding techniques for a myriad of signature families while investigating exotic signatures, real-life applications, and potential future research direction.

A Comprehensive Survey of Threshold Signatures: NIST Standards, Post-Quantum Cryptography, Exotic Techniques, and Real-World Applications

TL;DR

This paper provides a comprehensive and systematic survey of threshold and distributed signatures with advanced features and examines both generic and custom thresholding techniques for a myriad of signature families while investigating exotic signatures, real-life applications, and potential future research direction.

Abstract

Threshold digital signatures enable a distributed execution of signature functionalities and will play a crucial role in the security of emerging decentralized next-generation networked systems and applications. In this paper, we provide a comprehensive and systematic survey of threshold and distributed signatures with advanced features. Our survey encompasses threshold signatures in conventional and post-quantum cryptography (PQC) settings and captures custom-design and standard signatures (e.g., conventional NIST and NIST-PQC). We examine both generic (via secure multi-party computation) and custom thresholding techniques for a myriad of signature families while investigating exotic signatures, real-life applications, and potential future research direction.
Paper Structure (41 sections, 5 figures, 9 tables)

This paper contains 41 sections, 5 figures, 9 tables.

Table of Contents

  1. Introduction
  2. The state-of-the-art Surveys and Limitations
  3. Limited Coverage on Thresholding Approaches and Their Comparison
  4. Narrow/Selective Focus on Conventional-custom and Exotic Distributed Signatures
  5. Limited Attention to Broad Applications and Future Directions
  6. Our Contribution
  7. Extensive Coverage of Custom and Generic Thresholding with a Vast Range of Digital Signatures
  8. Comprehensive Examination of Threshold Conventional/PQ-secure Signatures and Standards
  9. Investigation of Exotic Features and Real-life Applications
  10. Preliminaries
  11. Notations
  12. Intractability Assumptions and Mathematical Backgrounds
  13. Digital Signatures
  14. Security Models of Digital Signatures
  15. Threshold Digital Signatures
  16. ...and 26 more sections

Figures (5)

  • Figure 1: High-level Taxonomy of Our Survey.
  • Figure 3: Threshold CRYSTALS-Dilithium Digital Signature (Level-3 security parameters)
  • Figure 4: Threshold FALCON Digital Signature (Level-3 security parameters)
  • Figure 5: Applications of Distributed Digital Signatures
  • Figure : (a) (DLP and ECDLP)-based Schnorr Signature Comparison brandao2023notes

Theorems & Definitions (17)

  • Definition 2.2.1: Integer Factorization
  • Definition 2.2.2: Discrete Logarithm Problem (DLP)
  • Definition 2.2.3: Elliptic Curve Discrete Logarithm Problem (ECDLP)
  • Definition 2.2.4: Decisional Diffie–Hellman Problem (DDH)
  • Definition 2.2.5: Lattice
  • Definition 2.2.6: Short Integer Solution Problem (SIS)
  • Definition 2.2.7: Learning With Errors Problem (LWE)
  • Definition 2.2.8: Module Learning With Errors Problem (M-LWE)
  • Definition 2.2.9: Module Short Integer Solution Problem (M-SIS)
  • Definition 2.2.10: Shamir's secret sharing (SSS)
  • ...and 7 more