Security analysis of batch verification on identity-based signature schemes

Batch verification can improve efficiency when the verifier has to verify a great deal of signatures. With the rising interests on pairing-based cryptography, many researches on identity-based signatures have been proposed. Furthermore, some new researches on enhancing performance of verifying identity-based signatures by a batch verification have also been reported. Another possible weaker but faster batch checking of signatures, named as the batch screening, has been considered in the literature. This paper considers the security of recent batch verification schemes, and a new attack on one identity-based signature scheme with batch screening is proposed. Then, we point, out that a previous attack on another identity-based signature scheme with batch screening is inappropriate due to the misunderstanding of the difference between batch screening and verification.