\({\Pi }\) : A Unified Framework for Computational Verifiable Secret Sharing
摘要
An (n, t)-Verifiable Secret Sharing (VSS) scheme allows a dealer to share a secret among n parties, s.t. all the parties can verify the validity of their shares and only a set of them, i.e., more than t, can access the secret. In this paper, we present \(\mathbf {\Pi }\) , as a unified framework for constructing computational VSS schemes in the honest-majority setting, based on Shamir secret sharing. Notably, \(\mathbf {\Pi }\) does not rely on homomorphic commitments; instead requires a random oracle and any commitment scheme that extra to its core attributes hiding and binding, it might be homomorphic and/or Post-Quantum (PQ) secure. We believe \(\mathbf {\Pi }\) is general enough to be employed in various contexts such as lattices, isogenies, and an extensive array of practical use cases.