In this paper, two new signature schemes whose security is based on both discrete logarithms and factorization are proposed to enhance the security of the OSS signature scheme. The major benefit of these new signature schemes is that the signer dose not need to know how to factor p-1, thus it is possible for every user to employ the same modulus p, where p is the modulus commonly used in the system. Furthermore, two identification schemes based on this advantage are also developed in this paper.