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Unconditionally Secure Qubit Commitment Scheme Using Quantum Maskers

Seok Hyung Lie, Hyukjoon Kwon, Myung-Gun Kim, Hyunseok Jeong

Published Mar 29, 2019• 9 citations
OpenAlex

Abstract

A commitment scheme allows one to commit to hidden information while keeping its value recoverable when needed. Despite considerable efforts, an unconditionally and perfectly secure bit commitment has been proven impossible both classically and quantum-mechanically. The situation is similar when committing to qubits instead of classical bits as implied in the no-masking theorem [K. Modi et al., Phys. Rev. Lett. {\bf 120}, 230501 (2018)]. In this Letter, we find that circumvention of the no-masking theorem is possible with the aid of classical randomness. Based on this, we construct an unconditionally secure quit-commitment scheme that utilises any kind of universal quantum maskers with optimal randomness consumption, which is distributed by a trusted initializer. This shows that randomness, which is normally considered only to obscure the information, can benefit a quantum secure communication scheme. This result can be generalised to an arbitrary dimensional system.

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Standard quantum bit commitment - an indefinite commitment time.

Muhammad Nadeem

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•Jan 1, 2016•0 citations
A commitment scheme allows one to commit to hidden information while keeping its value recoverable when needed. Despite considerable efforts, an unconditionally and perfectly secure bit commitment has been proven impossible both classically and quantum-mechanically. The situation is similar when committing to qubits instead of classical bits as implied in the no-masking theorem [K. Modi et al., Phys. Rev. Lett. {\bf 120}, 230501 (2018)]. In this Letter, we find that circumvention of the no-masking theorem is possible with the aid of classical randomness. Based on this, we construct an unconditionally secure quit-commitment scheme that utilises any kind of universal quantum maskers with optimal randomness consumption, which is distributed by a trusted initializer. This shows that randomness, which is normally considered only to obscure the information, can benefit a quantum secure communication scheme. This result can be generalised to an arbitrary dimensional system.
The no-masking theorem for quantum information proves that it is impossible to encode an arbitrary input state into a larger bipartite entangled state such that the full information is stored in the correlation but the individual subsystems have no information about the input state. Here, we ask the question: Is it possible to mask an observable such that the information about the observable is available in the joint system, but individual subsystems reveal nothing about the imprints of the observable? This generalizes the notion of masking to observables. We show that a universal unitary that can mask an arbitrary observable in any dimension does not exist. For a qubit system, we show that the masking operation for a given observable is locally unitarily connected to the swap operation. This suggests a conservation law for information content of observables that goes beyond the conservation laws under symmetry operations. Furthermore, we prove that the unconditional no-bit commitment result follows from the no-masking theorem for observables. Our results can have important applications in quantum information and quantum communication where we encode information not in states but in observables.
Bit commitment is a fundamental cryptographic primitive and a cornerstone for numerous two-party cryptographic protocols, including zero-knowledge proofs. However, it has been proven that unconditionally secure bit commitment, both classical and quantum, is impossible. In this work, we demonstrate that imposing a restriction on the committing party to perform only separable operations enables secure quantum bit-commitment schemes. Specifically, we prove that in any perfectly hiding bit-commitment protocol, an honestly committing party limited to separable operations will be detected with high probability if they attempt to alter their commitment. To illustrate our findings, we present an example protocol.
It is well known, due to the no-go theorems, that perfectly secure bit commitment is impossible. For that reason, there exist many proposals for bit commitment protocols that are secure under certain assumptions (such as the existence of a trusted party, computational hardness, or noisy memories). In this paper, we investigate the minimal assumptions required to obtain a secure bit commitment protocol. We show that it is possible to construct a bit commitment scheme with two parties Alice and Bob as long as there is a third party that is willing to broadcast either entangled qubits for the parties or to produce classical strings that are xor-correlated. We also show that the bit commitment scheme proposed is universally composable.
Classical information encoded in composite quantum states can be completely hidden from the reduced subsystems and may be found only in the correlations. Can the same be true for quantum information? If quantum information is hidden from subsystems and spread over quantum correlation, we call it masking of quantum information. We show that while this may still be true for some restricted sets of nonorthogonal quantum states, it is not possible for arbitrary quantum states. This result suggests that quantum qubit commitment-a stronger version of the quantum bit commitment-is not possible in general. Our findings may have potential applications in secret sharing and future quantum communication protocols.
Bit commitment (BC) is an important cryptographic primitive for an agent to convince a mutually mistrustful party that she has already made a binding choice of 0 or 1 but only to reveal her choice at a later time. Ideally, a BC protocol should be simple, reliable, easy to implement using existing technologies, and most importantly unconditionally secure in the sense that its security is based on an information-theoretic proof rather than computational complexity assumption or the existence of a trustworthy arbitrator. Here we report such a provably secure scheme involving only one-way classical communications whose unconditional security is based on no superluminal signaling (NSS). Our scheme is inspired by the earlier works by Kent, who proposed two impractical relativistic protocols whose unconditional securities are yet to be established as well as several provably unconditionally secure protocols which rely on both quantum mechanics and NSS. Our scheme is conceptually simple and shows for the first time that quantum communication is not needed to achieve unconditional security for BC. Moreover, with purely classical communications, our scheme is practical and easy to implement with existing telecom technologies. This completes the cycle of study of unconditionally secure bit commitment based on known physical laws.
Currently, it is believed in the literature that unconditionally secure bit commitment is impossible in non-relativistic quantum cryptography while only a weaker notion of bit commitment with finite commitment time is achievable in relativistic quantum setting. Moreover, relativistic classical bit commitment protocols allow arbitrary long commitment time but such protocols are not practically feasible; either because of multiple rounds of communication that result in exponential increase in communication complexity or due to asymptotic nature of security argument. The impossibility of practically feasible standard bit commitment leaves an obvious skepticism on the completeness of Hilbert space quantum cryptography and its claims of unconditional security. Contrary to the previously proposed results, we demonstrate here that an information-theoretic standard bit commitment scheme can be devised by using rules of purely non-relativistic quantum mechanics only; neither additional resources from theory of relativity nor multiple rounds of communications are required. The proposed bit commitment scheme can be applied efficiently with existing quantum technologies without long term quantum memory; quantum entanglement is required only for time t+δ where t is the communication time between the committer and receiver while δ << t is the processing time at laboratory.