Quantum Bit Commitment with Application in Quantum Zero-Knowledge Proof.

Abstract

Watrous (STOC 2006) proved that plugging classical bit commitment scheme that is secure against quantum attack into the GMW-type construction of zero-knowledge gives a classical zero-knowledge proof that is secure against quantum attack. In this paper, we showed that plugging quantum bit commitment scheme (allowing quantum computation and communication) into the GMW-type construction also gives a quantum zero-knowledge proof, as one expects. However, since the binding condition of quantum bit commitment scheme is inherently different from its classical counterpart, compared with Watrous ’ security proof, here we encounter new difficulty in soundness analysis. To overcome the difficulty, we take a geometric approach, managing to reduce quantum soundness analysis to classical soundness analysis. We also propose a formalization of non-interactive quantum bit commitment scheme, which may come in handy in other places. Moreover, inspired by our formalization, we generalize Naor’s construction of bit commitment scheme to the quantum setting, achieving non-interactive commit stage. We hope quantum bit commitment scheme can find more applications in quantum cryptog-raphy. 1