Zero-knowledge Group Identification and Hidden Group Signature for Smart Cards Using Bilinear Pairings

In this paper, we propose a new blind group identification protocol and a hidden group signature protocol as its application. These protocols involve many provers and one verifier such that (1) the statement of all the provers are proved simultaneously, (2) and also all the provers using computationally limited devices (e.g. smart cards) have no need of computing the bilinear pairings, (3) but only the verifier uses the bilinear pairings. A. Saxena et al. proposed a two-round blind (group) identification protocol in 2005 using the bilinear pairings. But it reveals weakness in the activeintruder attack, and all the provers as well as the verifier must have devices computing bilinear pairings. Comparing their results, our protocol is secure from the activeintruder attack and has more fit for smart cards. In particular, it is secure under only the assumption of the hardness of the DiscreteLogarithm Problem in bilinear groups.