In the electronic commerce and e-government era, digital signature has become more and more important recently. Digital signature algorithms can be categorized based on one of security suppositions, discrete logarithm and factorization hard-problems, which are currently believed to be unsolvable in a reasonable time-period. In other words, if the discrete logarithm or factorization problem can be broken, the corresponding digital signature scheme will become insecure any more. Therefore, to enhance the system security, the adoption of a digital signature algorithm based on both assumptions is a possible choice. In this paper, by referring to Laih and Kuo's architecture , we propose a new digital signature algorithm based on both discrete logarithm and factorization problems. We also propose another digital signature scheme. After analyses, the proposed scheme used less key length can achieve the similar security purposes. We also prove that the security of the proposed scheme is based on both discrete logarithm and factoring problems.