Welcome to the resource topic for 2022/1323
Title:
On Constructing One-Way Quantum State Generators, and More
Authors: Shujiao Cao, Rui Xue
Abstract:As a quantum analogue of one-way function, the notion of one-way quantum state generator is recently proposed by Morimae and Yamakawa (CRYPTO’22), which is proved to be implied by the pseudorandom state, and can be used to devise a construction of one-time secure digital signature. Due to Kretschmer’s result (TQC’20), it’s believed that pseudorandom state generator requires less than post-quantum secure one-way function. Unfortunately, it remains to be unknown how to achieve the one-way quantum state generator without the existence of post-quantum secure one-way function. In this paper, we mainly study that problem and obtain the following results:
We propose two variants of one-way quantum state generator, which we call them the weak one-way quantum state generator and distributionally one-way quantum state generator, and show the equivalence among these three primitives.
The distributionally one-way quantum state generator from average-case hardness assumption of a promise problem belongs to \textsf{QSZK} is obtained, and hence a construction of one-way quantum state generator.
A direct construction of quantum bit commitment with statistical binding (sum-binding) and computational hiding from the average-case hardness of a complete problem of \textsf{QSZK}.
To show the non-triviality of the constructions above, a quantum oracle \mathcal{U} is devised relative to which such promise problem in \textsf{QSZK} doesn’t belong to \mathsf{QMA}^{\mathcal{U}}.
Our results present the first non-trivial construction of one-way quantum state generator from the hardness assumption of complexity class, and give another evidence that one-way quantum state generator probably requires less than post-quantum secure one-way function.
ePrint: https://eprint.iacr.org/2022/1323
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