Publicly Verifiable Secret Sharing over Class Groups and Applications to DKG and YOSO

Publicly Verifiable Secret Sharing (PVSS) allows a dealer to publish encrypted shares of a secret so that parties holding the corresponding decryption keys may later reconstruct it. Both dealing and reconstruction are non-interactive and any verifier can check their validity. PVSS finds applications in randomness beacons, distributed key generation (DKG) and in YOSO MPC (Gentry et al. CRYPTO\u2721), when endowed with suitable publicly verifiable re-sharing as in YOLO YOSO (Cascudo et al. ASIACRYPT\u2722). We introduce a PVSS scheme over class groups that achieves similar efficiency to state-of-the art schemes that only allow for reconstructing a function of the secret, while our scheme allows the reconstruction of the original secret. Our construction generalizes the DDH-based scheme of YOLO YOSO to operate over class groups, which poses technical challenges in adapting the necessary NIZKs in face of the unknown group order and the fact that efficient NIZKs of knowledge are not as simple to construct in this setting. Building on our PVSS scheme\u27s ability to recover the original secret, we propose two DKG protocols for discrete logarithm key pairs: a biasable 1-round protocol, which improves on the concrete communication/computational complexities of previous works; and a 2-round unbiasable protocol, which improves on the round complexity of previous works. We also add publicly verifiable resharing towards anonymous committees to our PVSS, so that it can be used to efficiently transfer state among committees in the YOSO setting. Together with a recent construction of MPC in the YOSO model based on class groups (Braun et al. CRYPTO\u2723), this results in the most efficient full realization (i.e without assuming receiver anonymous channels) of YOSO MPC based on the CDN framework with transparent setup