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 di

rected transitive binary relation is presented by combining the proposed scheme with the undirected transitive signature schemes available.