A certificateless signature scheme with strong unforgeability in the random oracle model

Certificateless public key cryptography (CL-PKC) was introduced to solve two important problems in public key cryptography. One was the presence of certificates in traditional public-key cryptography (TPKC), the other was the key escrow problem in ID-based public-key cryptography (ID-PKC). In recent years, several certificateless signature schemes (CLS) have been proposed in the random oracle model (ROM) and the standard model. However, many implementations of the random oracle may result in insecure schemes. Some CLS schemes in the standard model were insecure against key replacement attack and were not strongly unforgeable. In order to solve these problems, we construct a CLS scheme in the ROM in this paper. Based on the Computational Diffie-Hellman (CDH) assumption and collision-resistant hash (CRH) assumption and partially depending on the ROM, we prove that the scheme has strong unforgeability. In addition, we show that the proposed scheme enjoys higher computational efficiency.