Two Provers in Isolation

We revisit the Two-Prover Bit Commitment Scheme of BenOr, Goldwasser, Kilian and Wigderson [BGKW88]. First, we introduce Two-Prover Bit Commitment Schemes similar to theirs and demonstrate that although they are classically secure using their proof technique, we also show that if the provers are allowed to share quantum entanglement, they are able to successfully break the binding condition. Secondly, we translate this result in a purely classical setting and investigate the possibility of using this Bit Commitment scheme in applications. We observe that the security claim of [BGKW88] based on the assumption that the provers cannot communicate is not a sufficient criteria to obtain soundness. We develop a set of conditions, called isolation, that must be satisfied by any third party interacting with the provers to guarantee the binding property of the Bit Commitment.