The main goal of introducing an identity-based cryptosystem and certificateless cryptosystem was avoiding certificates' management costs. In turn, the goal of introducing a certificate-based cryptosystem was to solve the certificate revocation problem. In this paper, we propose a new digital Implicit and Explicit Certificates-Based Hess's Signature (IE-CBHS) scheme that combines the features of a standard public key infrastructure (PKI) and certificate-based cryptosystem. Our IE-CBHS scheme is an efficient certificates-based signature. The security analysis proves that the scheme is secure against two game attacks in the random oracle model. The security is closely related to the difficulty of solving the computational Diffie-Hellman and discrete logarithm problems. The IE-CBHS scheme, when compared with other signature schemes, has similar efficiency and is both more flexible and more useful in practice. It is possible to revoke the explicit certificate and use that fact during digital signature verification. Thus, our scheme is useful in applications where typical mechanisms of standard PKI are used. One of many important security features is resistance to denial of signature verification attack. Also, it is impossible for a trusted authority to recreate a partial private key, even with cooperation with the signer.