Non-Interactive Statistically-Hiding Quantum Bit Commitment from Any   Quantum One-Way Function
  We provide a non-interactive quantum bit commitment scheme which has statistically-hiding and computationally-binding properties from any quantum one-way function. Our protocol is basically a parallel composition of the previous non-interactive quantum bit commitment schemes (based on quantum one-way permutations, due to Dumais, Mayers and Salvail (EUROCRYPT 2000)) with pairwise independent hash functions. To construct our non-interactive quantum bit commitment scheme from any quantum one-way function, we follow the procedure below: (i) from Dumais-Mayers-Salvail scheme to a weakly-hiding and 1-out-of-2 binding commitment (of a parallel variant); (ii) from the weakly-hiding and 1-out-of-2 binding commitment to a strongly-hiding and 1-out-of-2 binding commitment; (iii) from the strongly-hiding and 1-out-of-2 binding commitment to a normal statistically-hiding commitment. In the classical case, statistically-hiding bit commitment scheme (by Haitner, Nguyen, Ong, Reingold and Vadhan (SIAM J. Comput., Vol.39, 2009)) is also constructible from any one-way function. While the classical statistically-hiding bit commitment has large round complexity, our quantum scheme is non-interactive, which is advantageous over the classical schemes. A main technical contribution is to provide a quantum analogue of the new interactive hashing theorem, due to Haitner and Reingold (CCC 2007). Moreover, the parallel composition enables us to simplify the security analysis drastically. 
Takeshi Koshiba and Takanori Odaira
quant-ph