In 1999, Gennaro, Halevi and Rabin proposed a signature which achieves provable security without assuming the random oracles, and it is the first RSA-type signature whose security is proved in the standard model. Since that time, several signatures have been proposed to achieve better efficiency or useful property along with the provable security in the standard model. In this paper, we construct a trapdoor hash function, and design an efficient online/offline signature by using the trapdoor hash function. Our signature scheme requires only one non-modular multiplication of two small integers for online signing, and it provides the fastest online signing among all online/offline signatures that achieve provable security in the standard model.