Unfair Noisy Channels and Oblivious Transfer

In a paper from EuroCrypt’99, Damg̊ard, Kilian and Salvail show various positive and negative results on constructing Bit Commitment (BC) and Oblivious Transfer (OT) from Unfair Noisy Channels (UNC), i.e., binary symmetric channels where the error rate is only known to be in a certain interval [γ..δ] and can be chosen adversarily. They also introduce a related primitive called PassiveUNC. We prove in this paper that any OT protocol that can be constructed based on a PassiveUNC and is secure against a passive adversary can be transformed using a generic “compiler” into an OT protocol based on a UNC which is secure against an active adversary. Apart from making positive results easier to prove in general, this also allows correcting a problem in the EuroCrypt’99 paper: There, a positive result was claimed on constructing from UNC an OT that is secure against active cheating. We point out that the proof sketch given for this was incomplete, and we show that a correct proof of a much stronger result follows from our general compilation result and a new technique for transforming between weaker versions of OT with different parameters.