Strong designated verifier signature in a multi-user setting

The security of strong designated verifier (SDV) signature schemes has thus far been analyzed only in a two-user setting. We observe that security in a two-user setting does not necessarily imply the same in a multi-user setting for SDV signatures. Moreover, we show that existing security notions do not adequately model the security of SDV signatures even in a two-user setting. We then propose revised notions of security in a multi-user setting and show that no existing scheme satisfies these notions. A new SDV signature scheme is then presented and proven secure under the revised notions in the standard model. For the purpose of constructing the SDV signature scheme, we propose a one-pass key establishment protocol in the standard model, which is of independent interest in itself.