Paper 2025/664

Publicly Verifiable Generalized Secret Sharing Schemes and Their Applications

Abstract

Secret sharing under expressive access structures and public verifiability have largely been developed in separate lines of work. Generalized secret sharing (GSS) supports arbitrary monotone access structures, but relies on private channels and gives no public evidence that the dealer distributed a consistent sharing. Publicly verifiable secret sharing (PVSS), in contrast, supports public verification over insecure channels, but is fundamentally tailored to threshold policies. We introduce publicly verifiable generalized secret sharing (PVGSS), a primitive that combines arbitrary monotone access structures with non-interactive public verification of both encrypted shares and decrypted reconstruction shares. Our construction encrypts only the leaf shares of an underlying GSS instance and proves, via Schnorr-type NIZK proofs, that all ciphertexts are globally consistent with a single secret. The key technical ingredient is a GSS testing procedure that checks this global consistency from proof responses, without revealing the shares. We instantiate PVGSS from recursive Shamir secret sharing and from linear secret sharing schemes, obtaining verification complexity linear in the number of leaves of the access structure. We formalize correctness, encrypted-share verifiability, share-decryption verifiability, and IND1-secrecy, and prove security in the random oracle model under DDH, knowledge soundness of the proof systems, and privacy of the underlying GSS-on-group sharing. As an application, we show how PVGSS enables publicly accountable secret release in a decentralized exchange protocol.