Paper 2020/1488

General Properties of Quantum Bit Commitments

Abstract

While unconditionally-secure quantum bit commitment (allowing both quantum computation and communication) is impossible, researchers turn to study the complexity-based one. A complexity-based canonical (non-interactive) quantum bit commitment scheme refers to a kind of scheme such that the commitment consists of just a single (quantum) message from the sender to the receiver that can be opened later by uncomputing the commit stage. In this work, we study general properties of complexity-based quantum bit commitments through the lens of canonical quantum bit commitments. Among other results, we in particular obtain the following two: 1. Any complexity-based quantum bit commitment scheme can be converted into the canonical (non-interactive) form (with its sum-binding property preserved). 2. Two flavors of canonical quantum bit commitments are equivalent; that is, canonical computationally-hiding statistically-binding quantum bit commitment exists if and only if the canonical statistically-hiding computationally-binding one exists. Combining this result with the first one, it immediately implies (unconditionally) that complexity-based quantum bit commitment is symmetric. Canonical quantum bit commitments can be based on quantum-secure one-way functions or pseudorandom quantum states. But in our opinion, the formulation of canonical quantum bit commitment is so clean and simple that itself can be viewed as a plausible complexity assumption as well. We propose to explore canonical quantum bit commitment from perspectives of both quantum cryptography and quantum complexity theory in the future.

Note: This version is almost the same as all versions uploaded in 2022. However, there are two significant differences between versions uploaded in 2022 and pre-2022. Specifically, versions in 2022 add a new discussion and a new result as follows. New discussion: we propose to study quantum bit commitments not only as a cryptographic primitive in the MiniQCrypt world, but also as a basic (quantum) complexity-theoretic object whose existence is an interesting open problem in its own right. In particular, two flavors of canonical quantum bit commitments can be formulated as two complexity-theoretic objects that are clean and simple to state. New result: quantum bit commitment is symmetric.