Batch Verification for Certificateless Signature Schemes

Batch verification is a practical and significant technique which is very useful for greatly reducing the computational cost of verifying many signatures simultaneously. This technique is very attractive for authentications in computation-limited applications such as sensor network and banking service. In this paper, we study batch verification for certificateless signature (CLS) schemes for the first time. The security model of batch verification for CLS schemes is introduced. We show that an existing CLS scheme ZZ-CLS supports batch verification of Type 2. Furthermore, we modify the original ZZ-CLS to result in an efficient CLS scheme with batch verification of Type 3 (and Type 1). The modified ZZ-CLS scheme with batch verification of Type 3 is proven existentially unforgeable against adaptive chosen-message attacks under the standard computational Diffile-Hellman assumption. With respect to efficiency, only two and three bilinear maps are involved in the verification of the CLS schemes with batch verification of Type 2 and 3 respectively no matter how many signatures are to be verified at the same time.