Classical and Quantum Strategies for Two-Prover Bit Commitments

First we show that the assumption behind the Two-Prover Zero-knowledge Interactive proof of BenOr, Goldwasser, Kilian and Wigderson [5] is too weak and need be made more precise to preserve soundness of their construction. Secondly, we introduce a Two-Prover Zero-knowledge Interactive proof similar to theirs and demonstrate that classically it is equally secure as the original but however, we later show that if the provers are allowed to share quantum entanglement, they are able to successfully prove false statements to the verifier with probability nearly one. Then we show that another variation of the original scheme of BGKW is secure against quantum provers. Finally we investigate the possibility of using this two-prover bit commitment scheme in order to achieve three applications : zero-knowledge proofs, quantum Oblivious Transfer and mutual identification.

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