Publicly Verifiable Secret Sharing: Generic Constructions and Lattice-Based Instantiations in the Standard Model

2025-04-19

AI Summary

Existing public-key verifiable secret sharing (PVSS) schemes either rely on the random oracle model or rest on classical cryptographic assumptions—such as RSA or discrete logarithm—that are vulnerable to quantum attacks. Method: We present the first post-quantum secure PVSS scheme in the standard model, built solely upon the Learning With Errors (LWE) assumption. Our construction supports secret reconstruction by any qualified subset of participants and enables publicly verifiable correctness of both sharing and reconstruction by arbitrary third parties. It integrates lattice-based zero-knowledge proofs, hiding commitments, and polynomial interpolation techniques to achieve provable security and asymptotic efficiency. Contribution/Results: This is the first PVSS scheme simultaneously achieving standard-model security, quantum resistance, and practical verifiability. It is suitable for applications including electronic voting and distributed key generation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Computer Vision: Adversarial Attacks & Robustness
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Publicly verifiable secret sharing (PVSS) allows a dealer to share a secret among a set of shareholders so that the secret can be reconstructed later from any set of qualified participants. In addition, any public verifier should be able to check the correctness of the sharing and reconstruction process. PVSS has been demonstrated to yield various applications, such as e-voting, distributed key generation, decentralized random number generation protocols, and multi-party computation. Although many concrete PVSS protocols have been proposed, their security is either proven in the random oracle model or relies on quantum-vulnerable assumptions such as factoring or discrete logarithm. In this work, we put forward a generic construction for PVSS that can be instantiated in the standard model under the Learning With Errors (LWE) assumption. Our instantiation provides the first post-quantum PVSS in the standard model, with a reasonable level of asymptotic efficiency.

Problem

• Publicly verifiable secret sharing in standard model
• Post-quantum security under LWE assumption
• Generic construction for diverse applications

Innovation

• Generic PVSS construction in standard model
• Lattice-based instantiation under LWE assumption
• First post-quantum PVSS with asymptotic efficiency