An Efficient Group Signature Scheme without Random Oracles

In this paper, we give an efficient short constant-size group signature scheme that is secure in standard model based on strong Diffie-Hellman assumption. We achieve this result by combining a variant signature scheme of the one presented by Okamoto and non-interactive zero knowledge proof used by Boyen and Waters. Compared with the most efficient group signature scheme without random oracle, our scheme has a much shorter public key length and signature length, and needs less computation.