Modification and Improvement on Group Signature Scheme without Random Oracles

Group signature can provide anonymity for signers, and in CIS´2007, Wang et.al. presented an efficient group signature schemes secure in the standard model by combining the HSDH variant signature scheme of Okamoto scheme and NIZK proof techniques used by Boyen and Waters. In this paper, we point out that the scheme in CIS´07 is not unforgeable because of the wrong construction of the HSDH variant signature scheme. We correct the mistake and give the corresponding group signature scheme without random oracle using the same method in CIS´07, and the efficiency is decreased a little. In addition, we improve the new scheme to present a new group signature scheme in the standard model, and the new scheme has a relatively shorter public key, secret key length, and needs less computation.