Digital Signature is a basic cryptographic primitive. Security of signature scheme has been studied for decades. How to build an efficient signature scheme based on simple and standard assumptions without relying on random oracle heuristic has been an interesting problem. In this paper we provide a solution to this problem from another angle. We present a generic construction of digital signature schemes existentially unforgeable under chosen message attacks from adaptive trapdoor function, which has shown its power in building other important cryptographic primitives. Furthermore, we extend the generic construction and present a construction of secure digital signature schemes from tag-based adaptive trapdoor function. Since there are many instantiations of (tag-based) adaptive trapdoor function, our constructions could be instantiated based on simple assumptions like CDH and RSA in the standard model.