Paper 2025/1964

Generic PVSS Framework with $O(1)$ Complexity Using CCA2-Secure Threshold Encryption

Abstract

Existing PVSS schemes suffer from at least $O(n)$ online complexity due to the need to individually encrypt and prove/ verify each of the $n$ shares. In this work, we present a generic framework for constructing PVSS schemes with $O(1)$ complexity for share distribution and (the expected to be repeated numerous times) public verification. Our key insight lies in establishing a novel connection between PVSS and CCA2-Secure threshold encryption (CCATE), which enables public verifiability enforced by Non-Interactive Zero-Knowledge (NIZK) proofs. We show that a CCATE scheme can be generically transformed into a secure PVSS scheme, eliminating the $O(n)$ bottleneck per on-line operations. We instantiate the framework by presenting two CCATE constructions: 1) A pairing-free scheme based on a committee-based Distributed Key Generation (DKG) protocol and Threshold ElGamal encryption. 2) A silent setup scheme leveraging a non-interactive distributed key generation, relying on Power-of-Tau ceremony. Furthermore, we introduce solutions for dynamic membership updates in both DKG constructions, demonstrating their practicality and adaptability for real-world applications. The scheme is based on an off-line setup stage (before a specific value to share is given) where the $O(n)$ complexity is dealt with. Although our schemes incur higher setup costs, they drastically reduce the complexity of the critical distribution and verification stages to constant time. This trade-off marks a significant advancement in the scalability of PVSS-based systems, especially in the context of blockchain modern transactions. Conceptually, the work points out how variants of the notion of Threshold Encryption can potentially serve as a ``compression mechanism'' for information sharing schemes.