For resisting the adaptive chosen message attack and improving the sign generation efficiency, a signature scheme based on the strong RSA assumption is described in this paper. The scheme uses a fixed base rather than by raising them to a fixed power, which is different from the RSA algorithm. Moreover, one can use pre-computation techniques in order to get a better efficiency. In addition, a hash function can be incorporated into the scheme in such a way that it offers a trapdoor to the sign algorithm. The merits of this amendatory scheme are that if one makes a distinction between the“off line”and the