An ordered multisignature scheme under the CDH assumption without random oracles

Abstract

Ordered multisignatures are digital signatures which allow multiple signers to guarantee the signing order as well as the validity of a message, and thus are useful for constructing secure routing protocols. Although one of approaches to constructing the ordered multisignatures is to utilize aggregate signatures, there is no known scheme which is provably secure without using aggregate signatures under a reasonable complexity assumption in the standard model. In this paper we propose a provably secure ordered multisignature scheme under the CDH assumption in the standard model from scratch. Our proposed scheme has a positive property that the data size of signatures and the number of computations of bilinear maps are fixed with respect to the number of signers and the message length.