Security analysis of choi et al.'s certificateless short signature scheme

Certificateless public key cryptography, first introduced by Al-Riyami and Paterson in 2003, is aimed to simplify the certificate management in PKI-based public key cryptography and to solve the key escrow problem of identity-based cryptography. On the other hand, Boneh et al. introduced the notion of short signatures in 2001, which are useful for systems with low bandwidth and/or low computation power. Inheriting the advantages of both certificateless cryptography and short signatures, certificateless short signatures have come into limelight in recent years. However, security and performance are always a trade-off. In 2007, Huang et al. showed security models of certificateless signature to simulate possible adversaries with their attack abilities. Recently, Choi et al. proposed a certificateless short signature scheme and showed that their scheme achieves the strongest security level. However, we have found that Choi et al.'s scheme is not as secure as they claimed. In this paper, we give comments on Choi et al. scheme including the cryptanalysis of their protocol and the weakness of their security proof.