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The Computer Journal

Quantum Bit Commitment Without Quantum Memory

Lidong Xu, Mingqiang Wang, Jing Qin

Published May 17, 2023• 5 citations
Publisher

Abstract

Abstract Commitment scheme is a fundamental cryptographic primitive that serve as building blocks for many other two-party protocols. In this paper, we propose a novel quantum bit commitment scheme, which is secure and does not require quantum memory. Our scheme processes the quantum information using coherent states and unambiguous state discrimination (USD) measurements, which can be experimentally realized by linear optics and photon detectors. We ensure the unconditionally hiding and binding property by preventing both Alice and Bob from obtaining complete information about the commitment in committing stage, and eliminate the requirement for quantum memory by performing USD measurements and phase shifts immediately after receiving the coherent states.

DOI
10.1093/comjnl/bxad049

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Abstract Commitment scheme is a fundamental cryptographic primitive that serve as building blocks for many other two-party protocols. In this paper, we propose a novel quantum bit commitment scheme, which is secure and does not require quantum memory. Our scheme processes the quantum information using coherent states and unambiguous state discrimination (USD) measurements, which can be experimentally realized by linear optics and photon detectors. We ensure the unconditionally hiding and binding property by preventing both Alice and Bob from obtaining complete information about the commitment in committing stage, and eliminate the requirement for quantum memory by performing USD measurements and phase shifts immediately after receiving the coherent states.
Bit commitment is an essential primitive in quantum cryptography. It is the basic building block of many cryptographic protocols in which it provides security over distrustful parties. This paper proposes a secured quantum two-bit commitment protocol for any two classical bits. The protocol contains two parties - a committer and a receiver - who share both quantum and classical communication channels. The main phases of this protocol are commitment and revealing phases where the concealing and binding conditions are proved in order to accept the commitment message. The proposed framework utilizes different security layers to hide specific quantum states in a superposition alongside trivial one qubit operations. The secured unitary transformations are applied by the two parties to meet the concealing and binding conditions. To verify the success of the proposed protocol, the measured output of the two parties are compared. The protocol operates under the assumption that the two parties might cheat and the possible existence of an eavesdropper.
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.
Most of the quantum voting protocols are impractical due to the currently limited quantum storage capabilities. In this article, based on the interference principle of light, we proposed a new quantum voting protocol without quantum memory. In our protocol, the ballot is a sequence of non-orthogonal coherent states, the voting information is encoded by implying different phase shifts on the coherent states, and the vote counting is carried out by performing USD measurement on the coherent states. Particularly, the design of USD measurement on coherent states eliminates the need for quantum storage. Our protocol satisfies the general security requirements of quantum voting protocols and can resist various attacks. In addition, our protocol can be implemented by only linear optics and thus can be experimentally achieved with current technology.
A new unconditionally secure multi-party quantum commitment is proposed in this paper by encoding the committed message to the phase of a quantum state. Multi-party means that there are more than one recipient in our scheme. We show that our quantum commitment scheme is unconditional hiding and binding, and hiding is perfect. Our technique is based on the interference of phase-encoded coherent states of light. Its security proof relies on the no-cloning theorem of quantum theory and the properties of quantum information.
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.
Quantum Bit Commitment (QBC) is a foundational primitive in quantum cryptography, intended to enable secure commitments with strong information-theoretic guarantees. The protocol described in ‘Unconditionally secure multi-party quantum commitment scheme’, [1] published in Quantum information processing, 2018 Springer, uses coherent-state encoding and claims statistical hiding and computational binding. In this work, we identify a fundamental vulnerability in the hiding property of the protocol. Specifically, we demonstrate that an adversarial receiver applies Hadamard transformation to the incoming states, effectively changing the basis to enhance distinguishability between the two received messages. This linear optical strategy enables partial extraction of message without the use of quantum storage or entangled resources. We formally analyze the structure of the protocol and quantify the information leakage by computing the distinguishability between quantum state ensembles associated with different commitments. Our findings indicate that the protocol fails to maintain statistical hiding under general quantum adversarial models, raising concerns about its applicability in settings requiring strong concealment guarantees.