Abstract: To design a signature scheme which are efficient and provably secure in the standard model is suitable for applications.Two signature schemes based on Paterson's and Waters's signature schemes are proposed.A(t,n) threshold signature scheme is presented at first and is provable secure in the standard model under CDH assumption.The other contribution in this paper is to construct a new hierarchical identity based signature scheme.It has a highly efficient signing algorithm which requires only two exponentiation operations and is provably secure under CDH assumption in the standard model.