Paper 2026/1009

Constant-Online PVSS from CCA2-Secure Threshold Encryption: A Generic Framework

Abstract

Publicly Verifiable Secret Sharing (PVSS) is widely used in distributed systems. Existing schemes usually incur at least $O(n)$ online cost: the dealer encrypts, proves, and publishes $n$ shareholder-dependent objects, which public verification must process. In this work, we present a generic framework that transforms publicly verifiable CCA2-secure threshold encryption (CCATE) into \emph{constant-online} PVSS, with distribution and public- verification costs independent of the number of shareholders. The framework moves the share-generation work into a reusable setup phase: once threshold keys and public verification material are fixed, online sharing amounts to a single publicly verifiable threshold encryption. We instantiate the framework with two CCATE constructions: 1) a pairing-free instantiation using standard Threshold ElGamal encryption under a committee-based setup assumption; and 2) a silent-setup scheme leveraging non-interactive key generation via a Power-of-Tau ceremony, eliminating inter-party coordination during setup. Furthermore, we discuss epoch-based membership updates under the corresponding setup assumptions, clarifying the security boundary of reconfiguration. The resulting schemes incur higher setup costs, but the critical online distribution and public-verification phases are constant-size and constant-time. This trade-off is particularly useful when setup can be amortized over many PVSS instances, as in blockchain and distributed-system deployments.