In self-certified public key signature scheme, the tasks of verifying the authenticity of public key and validating the signature were carried out simultaneously. The self-certified public key signature is more efficient than the existing certificate-based signature and identitybased signature in terms of communication overheads and computation efforts. There are only a few self-certified public key signatures of which the efficiency needs to be improved. In this paper, an efficient self-certified public key signature scheme was proposed by using bilinear pairings. The analysis shows the proposed scheme is secure. Furthermore, its efficiency is also better than that of the existing ones.

A complete asymmetric public-key traitor tracing scheme was proposed by Wang Qing-long et al., which claimed that it had some advantages such as revoking unlimited traitors and higher transmission efficiency. The scheme and its obvious defect were carefully analyzed, and then a attack was given. And traitors can perform a collusion attack, but the manager can not trace the traitors by the black-box traitor tracing method. Finally, an improved scheme was proposed in which traitors still could play the above attack, but they can be traced.