Non-interactive statistically-hiding quantum bit commitment from any quantum one-way function

Takeshi Koshiba, Waseda University

We show how to construct a non-interactive quantum bit commitment scheme which has statistically-hiding and computationally-sum-binding properties from any quantum one-way function, where sum-binding is a weak binding property. Our protocol is ba- sically a parallel composition of the previous non-interactive quantum bit commitment schemes (based on quantum one-way permutations, due to Dumais, Mayers and Sal- vail (EUROCRYPT 2000)) with pairwise independent hash functions. Our construction of non-interactive quantum bit commitment scheme from any quantum one-way func- tion has the following steps: (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 com- mitment; (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 commit- ment 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 and non-interactive analogue of the new interac- tive hashing theorem, due to Haitner and Reingold (CCC 2007). Moreover, the parallel composition enables us to simplify the security analysis drastically.