Skipping the q in group signatures

The notion of group signatures was introduced to allow group members to sign anonymously on behalf of a group. A group manager allows a user to join a group, and another will be able to open a signature to revoke its anonymity. Several schemes have already been proposed to fulfil these properties, however very few of them are proven in the standard model. Of those proven in the standard model, most schemes rely on a so-called q-assumptions. The underlying idea of a q-assumptions is that to prove the security of the scheme, we are given a challenge long enough to allow the simulator to answer queries. Another common solution is to rely on an interactive hypothesis. We provide one of the first schemes proven in the standard model, requiring a constant-size non-interactive hypothesis. We then compare its efficiency to existing schemes, and show that this trade-off is acceptable as most schemes with better efficiency rely on either an interactive or a q-hypothesis. The exception to this is the recent independent work Libert, Peters and Yung (CRYPTO 2015), who presented an efficient group signature scheme in the standard model relying on standard assumptions.