Research on Pairing-Based Batch Verification

Batch verification is used in cases of verifying many signatures at the same time, for it can speedup the verification of signature significantly. It is well known that if the verifier uses batch verification to verify n different signatures, he needs to pick n exponents at random. Through the study on batch verification, we find that picking n-1 random exponents is enough, and the last one is chosen by the n-1 exponents picked earlier. We prove that using the new exponents choosing method in the probabilistic Batch is still batch verification. This new technology can be used in the signatures whose verification equation contains pairings independent of the user´s parameters. It can speedup the verification by reducing the 1024 bits exponential computation. Finally, we modified a hierarchical ID-based signature algorithm without changing the security properties or increasing the computations of the scheme, in order to achieve efficiently verification where the pairing operation is independent of the number of signatures to verify.