Strongly Secure Certificateless Signature: Cryptanalysis and Improvement of Two Schemes

Certificateless cryptography is a well-known system to avoid the key escrow problem of identity-based cryptography. Since it was introduced by Al-Riyami and Paterson in 2003, plenty of schemes and security models had been presented and discussed. Particularly, certificateless signature (CLS) is the most lightened to attract research attention. In the literature works, Hu et al. introduced generic construction and security model that can satisfy non-repudiation. On the other hand, Huang et al. simulated possible attacks and defined more complete security models of CLS for existential unforgeability, and they sorted adversaries into normal, strong, and super adversaries (ordered by their attack powers). In this paper, we consider the security of CLS schemes regarding both of existential unforgeability and non-repudiation. We not only show the weaknesses of two CLS schemes of Fan et al. [5] and Xiong et al. [13], but also point out the loopholes of their security proofs. Hence, we improve the weaknesses and loopholes by proposing a new certificateless short signature with low bandwidth. The proposed scheme is provably secure against the super adversaries and reaches the highest security level.