One-round strong oblivious signature-based envelope

Oblivious Signature-Based Envelope (OSBE) has been widely employed for anonymity-orient and privacy-preserving applications. The conventional OSBE execution relies on a secure communication channel to protect against eavesdroppers. In TCC 2012, Blazy, Pointcheval and Vergnaud proposed a framework of OSBE (BPV-OSBE) without requiring any secure channel by clarifying and enhancing the OSBE security notions. They showed how to generically build an OSBE scheme satisfying the new strong security in the standard model with a common-reference string. Their framework requires 2-round interactions and relies on the smooth projective hash function (SPHF) over special languages, i.e., languages from encryption of signatures. In this work, we investigate the study on the strong OSBE and make the following contributions. First, we propose a generic construction of one-round yet strong OSBE system. Compared to the 2-round BPV-OSBE, our one-round construction is more appealing, as its noninteractive setting accommodates more application scenarios in the real word. Moreover, our framework relies on the regular (identity-based) SPHF, which can be instantiated from extensive languages and hence is more general. Second, we also present an efficient instantiation, which is secure under the standard model from classical assumptions, DDH and DBDH, to illustrate the feasibility of our one-round framework. We remark that our construction is the first one-round OSBE with strong security