Security analysis of two certificateless short signature schemes

Certificateless public key cryptography (CL-PKC) combines the advantage of both traditional PKC and identity-based cryptography (IBC) as it eliminates the certificate management problem in traditional PKC and resolves the key escrow problem in IBC. Recently, Choi et al. and Tso et al. proposed two different efficient CL short signature schemes and claimed that the two schemes are secure against super adversaries and satisfy the strongest security. In this study, the authors show that both Choi et al.'s scheme and Tso et al.'s scheme are insecure against the strong adversaries who can replace users' public keys and have access to the signing oracle under the replaced public keys.