Improvement of a proxy multi-signature scheme without random oracles

A proxy multi-signature scheme permits two or more original singers to delegate their signing powers to the same proxy signer. Recently, Liu et al. proposed the first proxy multi-signature that be proven secure in the standard model [Liu et al. (2008) [20]], which can be viewed as a two-level hierarchical signature due to Waters. However, because of the direct employment of Waters’ signature, their scheme needs a relatively large number of public parameters and is not tightly reduced to the security assumption. In this paper, inspired by Boneh, Boyen’s technique and Waters’ technique, we propose a new proxy multi-signature scheme without random oracles, whose unforgeability can be tightly reduced to the CDH assumption in bilinear groups. The new scheme can be regarded as an improvement to overcome the weaknesses of Liu et al.’s scheme. Compared with Liu et al.’s scheme, the improvement has three merits, tighter security reduction, shorter system parameters and higher efficiency.