Summary: In this paper, we first propose a new and more generic paradigm (than Boneh’s one) which modularly transforms any weakly unforgeable signature scheme into a strongly unforgeable one. Then, by applying the paradigm to the Waters signature scheme, we construct a new strongly unforgeable signature scheme which is provably secure under the CDH assumption over bilinear groups in the standard model. In our signature scheme, the major computation can be performed off-line, and the on-line computation is very fast.