The digital equivalent of a handwritten signature or stamped seal, but offering far more inherent security, a digital signature is intended to solve the problem of tampering and impersonation in digital communications. Digital signatures can provide the added assurances of evidence to origin, identity and status of an electronic document, transaction or message, as well as acknowledging informed consent by the signer. Even though, some signature schemes have already been proposed to address all the requirements of a digital signature scheme. However, they are unable to accomplish forward or backward unforgeability in arbitrated signature scheme, where if the signature key used in the scheme is compromised then an attacker will be able to forge any previous/future signature. In order to resolve this issue, in this article, we propose secure digital signature schemes, which can ensure the security requirements including forward and backward unforgeability supports.