Certificateless directed signature scheme without bilinear pairing

In Eurocrypt’96, the concept of Designated Verifier Signature was proposed. Such signatures can only be verified by a single designated verifier specified during signature creation. However, there exist situations in which the signer, as well as the designated verifier, should be equipped with the ability to check the validity of the signature. At the same time, either of them should be able to help third parties to verify the signature. This is achieved by Directed Signature Schemes. In this paper, we consider directed signatures in the certificateless cryptography setting and propose an efficient pairing-free certificateless directed signature (CLDS) scheme. Then, we prove that the proposed CLDS scheme meets the needed security requirements in the random oracle model and under the assumption of the hardness of discrete logarithm and Gap Diffie-Hellman problems. We also compare the proposed scheme with the related ones to indicate the overall superiority of the proposed CLDS scheme.