Generic Construction of UC-Secure Oblivious Transfer

We show how to construct a completely generic UC-secure oblivious transfer scheme from a collision-resistant chameleon hash scheme (CH) and a CCA encryption scheme accepting a smooth projective hash function (SPHF). Our work is based on the work of Abdalla et al. at Asiacrypt 2013, where the authors formalize the notion of SPHF-friendly commitments, i.e. accepting an SPHF on the language of valid commitments (to allow implicit decommitment), and show how to construct from them a UC-secure oblivious transfer in a generic way. But Abdalla et al. only gave a DDH-based construction of SPHF-friendly commitment schemes, furthermore highly relying on pairings. In this work, we show how to generically construct an SPHF-friendly commitment scheme from a collision-resistant CH scheme and an SPHF-friendly CCA encryption scheme. This allows us to propose an instanciation of our schemes based on the DDH, as efficient as that of Abdalla et al., but without requiring any pairing. Interestingly, our generic framework also allows us to propose an instantiation based on the learning with errors (LWE) assumption. For the record, we finally propose a last instanciation based on the decisional composite residuosity (DCR) assumption.