An enhanced pairing-free certificateless directed signature scheme

Directed signature is a special cryptographic technique in which only the verifier designated by the signer can verify the validity of the signature. Directed signature can effectively protect the privacy of the signer's identity, so it is very suitable for medical records, taxation, and other fields. To improve the security and performance of the directed signature scheme, Gayathri et al. proposed the first certificateless directed signature (CLDS) scheme without bilinear pairing and claimed that their CLDS scheme could withstand Type I and Type II attacks. In this article, we provide two attack methods to assess the security of their CLDS scheme. Unfortunately, our results indicate that their CLDS scheme is insecure against Type I and Type II attacks. That is, their CLDS scheme does not meet the unforgeability and cannot achieve the expected security goals. To resist these attacks, we present an improved CLDS scheme and give the security proof. Compared with similar schemes, our scheme has better performance and higher security.