Threshold Ring Signatures in the Random Oracle Model

We improve on the Bresson–Stern–Szydlo threshold ring signature scheme which uses Shamir secret sharing scheme [6] by showing that the security can be proved under a strictly weaker assumption, that is the random oracle model rather than the ideal cipher model. Then we propose an efficient (n− t)-out-of-n threshold ring signature scheme which is efficient when t is small compared with n. Our scheme has a kind of dual structure of the Bresson–Stern–Szydlo threshold ring signature scheme [2], which is infeasible when t is small compared with n. In particular, we modify the trap-door one-way permutations in the ring signature scheme, and use a combinatorial notion called fair partition. Our scheme is provably secure in the random oracle model.