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

Abstract

We provide a non-interactive quantum bit commitment scheme which has statisticallyhiding 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.Keyword: quantum bit commitment, quantum one-way function, non-interactive

Can relativistic bit commitment lead to secure quantum oblivious transfer?

“…It covers relativistic BC [39][40][41][42], as well as many practically secure QBC [50][51][52], conditionally secure QBC [53], computationally secure QBC [54][55][56], cheat-sensitive QBC [57][58][59][60][61][62], and some other types of protocols [45,[63][64][65]. Nevertheless, when Bob is limited to bounded or noisy quantum storages, secure QOT can be made possible in practice with two approaches.…”

Quantum commitments and signatures without one-way functions

“…Unfortunately, it is already known that both binding and hiding cannot be statistical at the same time even in the quantum world [20,21]. In fact, all known constructions of quantum commitments require at least (quantum-secure) one-way functions [22][23][24][25][26][27][28].…”

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

“…This protocol was later extended by Tanaka [14] to quantum string commitment using an additional technique of quantum fingerprinting to reduce the communication cost between Alice and Bob. Recently, Koshiba and Odaira [12] reduced this assumption to the existence of quantum one-way functions.…”