New efficient batch verification for an identity-based signature scheme

Batch verification is a method to verify multiple digital signatures at a batch in time less than total individual verification time. Batch verification for an identity-based signature scheme (IBS) is attractive because a short public identity such as an e-mail address can be used as a verification key. In this paper, we first review the recent IBS scheme proposed by Shim and its batch verifier to show that the batch verifier is vulnerable to a forgery attack. In order to resist to the attack, we propose a new efficient batch verifier for the IBS scheme. The proposed batch verifier can deal with arbitrary number of signatures as a batch. We prove formally that the proposed batch verifier is secure. Then, we analyze the computation cost of the proposed batch verifier using concrete parameters and compare it with well-known batch verifiers. The comparison shows that our batch verifier can significantly outperform the existing batch verifiers in computation. We finally present a one-round three-party identity-based key agreement protocol as an application of our batch verifier, which requires only three pairing operations in verification.