Generalized Robust Combiners for Oblivious Transfer

A robust combiner for a cryptographic primitive gives a secure implementation of the primitive when at least some of the input candidates are secure. Such constructions provide robustness against insecure implementations and incorrect assumptions underlying the candidate schemes. Robust combiners are useful tools for ensuring better security in applied cryptography. Combiners from the perspective of threshold schemes have been previously studied. However, such threshold schemes typically fail to capture all possible scenarios. In this paper, we characterize the possibility of a transparent black-box combiner for oblivious transfer (OT), given an access structure over the candidate implementations. We also propose a circuit-based framework for the construction of such combiners, and hence reduce the problem of optimal OT combiners to circuit optimization.