Lattice-Based Group Encryption with Full Dynamicity and Message Filtering Policy 📺
Group encryption (GE) is a fundamental privacy-preserving primitive analog of group signatures, which allows users to decrypt speciﬁc ciphertexts while hiding themselves within a crowd. Since its ﬁrst birth, numerous constructions have been proposed, among which the schemes separately constructed by Libert et al. (Asiacrypt 2016) over lattices and by Nguyen et al. (PKC 2021) over coding theory are postquantum secure. Though the last scheme, at the ﬁrst time, achieved the full dynamicity (allowing group users to join or leave the group in their ease) and message ﬁltering policy, which greatly improved the state-of-aﬀairs of GE systems, its practical applications are still limited due to the rather complicated design, ineﬃciency and the weaker security (secure in the random oracles). In return, the Libert et al.’s scheme possesses a solid security (secure in the standard model), but it lacks the previous functions and still suﬀers from ineﬃciency because of extremely using lattice trapdoors. In this work, we re-formalize the model and security deﬁnitions of fully dynamic group encryption (FDGE) that are essentially equivalent to but more succinct than Nguyen et al.’s; Then, we provide a generic and eﬃcient zero-knowledge proof method for proving that a binary vector is non-zero over lattices, on which a proof for the Prohibitive message ﬁltering policy in the lattice setting is ﬁrst achieved (yet in a simple manner); Finally, by combining appropriate cryptographic materials and our presented zero-knowledge proofs, we achieve the ﬁrst latticebased FDGE schemes in a simpler manner, which needs no any lattice trapdoor and is proved secure in the standard model (assuming interaction during the proof phase), outweighing the existing post-quantum secure GE systems in terms of functions, eﬃciency and security.