Strong unforgeability in group signature schemes

A signature scheme is strongly unforgeable if no adversary can produce a new valid signature σ on a message M even after seeing some signatures on M. We define strong unforgeability of group signature schemes and explain why the strong unforgeability of a group signature scheme is necessary. This relatively new security concept was not considered when Bellare–Micciancio–Warinschi established their security model, what we call the BMW security model, of group signature schemes. We show that a scheme proposed at Eurocrypt'06 that was proven secure in the BMW security model is not strongly unforgeable. We also present a method to convert this scheme into a strongly unforgeable group signature scheme preserving the security in the BMW security model.