Efficient Directed Transitive Signature Scheme

Transitive signature was first introduced by Micali and Rivest in 2002 to meet the need of certain applications like signing a chain of command,a chain of certificate or transitive binary relations.Unfortunately,all the transitive signature schemes available are undirected ones and can only be used in the case of equivalence relation.The problem of finding a directed transitive signature scheme remains a very interesting open problem.In this paper,an efficient total ordering directed transitive signature scheme is proposed and its security against adaptive chosen-message attack is proved.In the proposed scheme,the part β_(uv) of signature is limited from 0 to q/2 to prevent an adversary from forging (v,u)'s signature with the knowledge of (u,v)'s signature,and thus achieve the directed property.A solution for signing any directed transitive binary relation is presented by combining the proposed scheme with the undirected transitive signature schemes available.