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We present a realization of the transitive signature scheme based on the algebraic properties of bilinear group pairs. The scheme is proven secure, i.e. transitively unforgeable under adaptive chosen message attack, assuming hardness of the computational co-Diffie-Hellman problem in bilinear group pairs and the security of the underlying standard signature scheme under known message attack. Our scheme mostly conforms to previously designed schemes of Micali-Rivest and Bellare-Neven in structure; yet there are two contributions: firstly, we take advantage of bilinear group pairs which were previously used by Boneh, Lynn, and Shacham to build short signature schemes. Secondly, we show that a slight modification in previous definitions of the transitive signature relaxes the security requirement for the underlying standard signature from being secure under chosen message attack to being secure …