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

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.