Paper 2026/813

Practical Post-Quantum Secure Publicly Verifiable Secret Sharing and Applications

Abstract

We present a new framework for constructing practically efficient publicly verifiable secret sharing(PVSS) with non-interactive dealers, in that the dealer may go offline after sending a single message, and is not involved in the share verification process. We use identity-based encryption (IBE) and commitments as the main ingredients and avoid expensive zero-knowledge proofs. Instantiating them with post-quantum secure schemes, a lattice-based IBE and a hash-based commitment, we obtain our first construction - a post-quantum secure PVSS with non-interactive dealers that outperform the prior lattice-based practical construction, Gentry et al. [Eurocrypt 2022] by two orders of magnitude. However, to enable the aggregation of PVSS transcripts (which facilitates many additional applications such as secure voting), we propose our second construction by replacing hash-based commitments with Pedersen's homomorphic commitments. While this does not achieve full-fledged post-quantum security (as Pedersen's scheme is not quantum safe), it still provides privacy against a post-quantum adversary. We prove the security of this construction in a new model, which we call long-lasting security. This model guarantees that the protocol is secure in the present (pre-quantum era) while maintaining privacy in the long term (post-quantum era). This new model is of independent interest for constructing efficient schemes that are resilient to harvest-now-decrypt-later line of attacks. In this model, we propose a blockchain-compatible secure voting scheme using our PVSS scheme. Our PVSS schemes demonstrate practical efficiency: our post-quantum PVSS shares a secret among $1024$ receivers in $692$~ms and verifies the dealing in $128$ ms, and communicates $4$MB, overall yielding a two orders of magnitude improvement over the state of the art [Gentry et al., Eurocrypt 2022].

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