A novel ID-based group signature

Group signatures, first introduced by Chaum and Heyst at Eurocrypt'91, allow individual members of a group to make signatures on behalf of the group while providing the signer's anonymity. Most of the previously proposed group signature schemes are based on the discrete logarithm problem, the public keys of users are not identity information, except for the ID-based scheme proposed by Park et al. in 1997. However, Park et al.'s scheme has a serious problem, which is that all of the previous group signatures signed by other members will be no longer valid if the group is changed. Moreover, the length of the group signature grows linearly with the number of group members, which makes their proposed scheme inefficient. In this paper, the authors propose a novel ID-based group signature scheme which can solve the problem raised by the inclusion of a new group member or the exclusion of an old group member. Meanwhile, compared to Park et al.'s scheme, our scheme requires less computing time for generating the group signature and verifying the group signature. The security of the proposed ID-based group signature scheme is based on the difficulty of computing the discrete logarithm modulo for a composite number.