A CDH-based ordered multisignature scheme in the standard model with better efficiency

An ordered multisignature scheme is a digital signature scheme which guarantees the signing order among a group of signers in addition to an improvement of efficiency provided by an ordinary multisignature scheme. In this primitive, Yanai et al. proposed an efficient scheme under only standard assumptions, i.e., the CDH assumption without random oracles, and their scheme is the first one whose number of bilinear maps and number of elements of public keys are independent of both the security level and the number of the signers. However, their scheme utilizes the Waters hash function and so its size of a system parameter shared between signers is quite large. In this work, we propose a more efficient CDH-based scheme without the random oracles by adopting a stateful signature. The size of a system parameter of our scheme is seven elements in bilinear groups while that of the previous works using stateless signatures is at least 160 elements. We show that in practical applications, the security is not downgraded by our stateful setting.