(Hierarchical Identity-Based) Threshold Ring Signatures without Random Oracles

We construct the first several efficient threshold ring signatures (TRS) without random oracles. Specializing to a threshold of one, they are the first several efficient ring signatures without random oracles after the only earlier instantiation of Chow, Liu, Wei, and Yuen [22]. Further specializing to a ring of just one user, they are the short (ordinary) signatures without random oracles summarized in Wei and Yuen [41]. We also construct the first hierarchical identity-based threshold ring signature without random oracles. The signature size is O(nλs) bits, where λs is the security parameter and n is the number of users in the ring. Specializing to a threshold of one, it is the first hierarchical identity-based ring signature without random oracles. Further specializing to a ring of one user, it is the constant-size hierarchical identity-based signature (HIBS) without random oracles in [44] the signature size is O(λs) bits which is independent of the number of levels in the hierarchy.