More short signatures without random oracles

We construct three new signatures and prove their securities without random oracles. They are motivated, respectively, by Boneh and Boyen [9]’s, Zhang, et al. [45]’s, and Camenisch and Lysyanskaya [14]’s signatures without random oracles. The first two of our signatures are as short as [9, 45]’s state-of-the-art short signatures, and are 17% shorter if the pairings in use admits a Verheul homomorphism or an algebraic tori attack. Our third signature is reducible to a modified LRSW Assumption [31] but without the LRSW Assumption’s hypothesized external signing oracle. New and interesting variants of the q-SDH Assumption, the q-SR (Square Root) Assumption are also presented. New and independently interesting proof techniques extending the two-mode technique of [9] are used, including a combined three-mode simulation and rewinding in the standard model.