Karim Baghery, Noah Knapen, Georgio Nicolas, Mahdi Rahimi
ePrint Report
Conventional Publicly Verifiable Secret Sharing (PVSS) protocols allow a dealer to share a secret among $n$ parties without interaction, ensuring that any $t + 1$ parties (where $t+1 \le n$) can recover the secret, while anyone can publicly verify the validity of both the individual shares and the reconstructed secret. PVSS schemes are shown to be a key tool in a wide range of practical applications. In this paper, we introduce Pre-constructed PVSS (PPVSS), an extension of standard PVSS schemes, highlighting its enhanced utility and efficiency in various protocols. Unlike standard PVSS, PPVSS requires the dealer to publish a commitment or encryption of the main secret and incorporates a novel secret reconstruction method. We show that these refinements make PPVSS more practical and versatile than conventional PVSS schemes.
To build a PPVSS scheme, we first point out that the well-known PVSS scheme by Schoenmakers (CRYPTO’99) and its pairing-based variant presented by Heidarvand and Villar (SAC’08) can be seen as special cases of PPVSS, where the dealer also publishes a commitment to the main secret. However, these protocols are not practical for many applications due to efficiency limitations and are less flexible compared to a standard PPVSS scheme. To address this, we propose a general strategy for transforming a Shamir-based PVSS scheme into a PPVSS scheme. Using this strategy, we construct two practical PPVSS schemes in both the Random Oracle (RO) and plain models, grounded in state-of-the-art PVSS designs. Leveraging the new RO-based PPVSS scheme, we revisit some applications and present more efficient variants. Notably, we propose a new universally verifiable e-voting protocol that improves on the alternative scheme by Schoenmakers (CRYPTO’99), reducing the verification complexity with $m$ voters from $O(n^2m)$ to $O(nm)$ exponentiations–a previously unattainable goal with standard PVSS schemes. Our implementation results demonstrate that both our proposed PPVSS schemes and the new universally verifiable e-voting protocol significantly outperform existing alternatives in terms of efficiency.
