Statistically-Hiding Quantum Bit Commitment from Approximable-Preimage-Size Quantum One-Way Function

We provide a quantum bit commitment scheme which has statistically-hiding and computationally-binding properties from any approximable-preimage-size quantum one-way function, which is a generalization of perfectly-hiding quantum bit commitment scheme based on quantum one-way permutation due to Dumais, Mayers and Salvail. in the classical case, statistically-hiding bit commitment scheme is constructible from any one-way function. However, it is known that the round complexity of the classical statistically-hiding bit commitment scheme is Omega(n/ log n) for the security parameter n. Our quantum scheme as well as the Dumais-Mayers-Salvail scheme is non-interactive, which is advantageous over the classical schemes.