General Properties of Quantum Bit Commitments (Extended Abstract)

Abstract

AbstractWhile unconditionally-secure quantum bit commitment (allowing both quantum computation and communication) is impossible, researchers turn to study the complexity-based one, a.k.a. computational quantum bit commitment. A computational canonical (non-interactive) quantum bit commitment scheme refers to a kind of schemes such that the commitment consists of just a single (quantum) message from the sender to the receiver that later can be opened by uncomputing the commit stage. In this work, we study general properties of computational quantum bit commitments through the lens of canonical quantum bit commitments. Among other results, we in particular obtain the following two: 1. Any computational 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 computational 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.KeywordsQuantum bit commitmentQuantum bindingRound complexityParallel composition