A Non-Interactive Quantum Bit Commitment Scheme that Exploits the Computational Hardness of Quantum State Distinction

Abstract

We propose an efficient quantum protocol performing quantum bit commitment, which is a simple cryptographic primitive involved with two parties, called a committer and a verifier. Our protocol is non-interactive, uses no supplemental shared information, and achieves computational concealing and statistical binding under a natural complexity-theoretical assumption. An earlier protocol in the literature relies on the existence of an efficient quantum one-way function. Our protocol, on the contrary, exploits a seemingly weaker assumption on computational difficulty of distinguishing two specific ensembles of reduced quantum states. This assumption is guaranteed by, for example, computational hardness of solving the graph automorphism problem efficiently on a quantum computer.