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arXiv:1108.2879 · Physical Review Letters

Unconditionally Secure Bit Commitment by Transmitting Measurement Outcomes

Adrian Kent

Published Sep 27, 2012• 123 citations
arXivHTMLPDF

Abstract

We propose a new unconditionally secure bit commitment scheme based on Minkowski causality and the properties of quantum information. The receiving party sends a number of randomly chosen Bennett-Brassard 1984 (BB84) qubits to the committer at a given point in space-time. The committer carries out measurements in one of the two BB84 bases, depending on the committed bit value, and transmits the outcomes securely at (or near) light speed in opposite directions to remote agents. These agents unveil the bit by returning the outcomes to adjacent agents of the receiver. The protocol's security relies only on simple properties of quantum information and the impossibility of superluminal signalling.

DOI
10.1103/physrevlett.109.130501

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We propose a new unconditionally secure bit commitment scheme based on Minkowski causality and the properties of quantum information. The receiving party sends a number of randomly chosen Bennett-Brassard 1984 (BB84) qubits to the committer at a given point in space-time. The committer carries out measurements in one of the two BB84 bases, depending on the committed bit value, and transmits the outcomes securely at (or near) light speed in opposite directions to remote agents. These agents unveil the bit by returning the outcomes to adjacent agents of the receiver. The protocol's security relies only on simple properties of quantum information and the impossibility of superluminal signalling.
We describe new unconditionally secure bit commitment schemes whose security is based on Minkowski causality and the monogamy of quantum entanglement. We first describe an ideal scheme that is purely deterministic, in the sense that neither party needs to generate any secret randomness at any stage. We also describe a variant that allows the committer to proceed deterministically, requires only local randomness generation from the receiver, and allows the commitment to be verified in the neighborhood of the unveiling point. We show that these schemes still offer near-perfect security in the presence of losses and errors, which can be made perfect if the committer uses an extra single random secret bit. We discuss scenarios where these advantages are significant.
We propose a new classical bit commitment protocol using the relativistic constraint that signals cannot travel faster than the speed of light ccc. This protocol is unconditionally secure against both classical or quantum attacks. The sender (Alice) and the receiver (Bob) each controls two secure stations separated by a large distance ddd, and they communicate by exchanging classical information only. Alice commits by sending from her stations two causally independent encrypted messages to the neighboring Bob's stations, after that the protocol is out of her control and she plays no role in the unveiling phase. The commitment remains concealed for a period of Δt=d/2cΔt=d/2cΔt=d/2c. This protocol requires only limited communication resources and is readily implementable with current technologies.
Quantum physics allows for unconditionally secure communication between parties that trust each other. However, when the parties do not trust each other such as in the bit commitment scenario, quantum physics is not enough to guarantee security unless extra assumptions are made. Unconditionally secure bit commitment only becomes feasible when quantum physics is combined with relativistic causality constraints. Here we experimentally implement a quantum bit commitment protocol with relativistic constraints that offers unconditional security. The commitment is made through quantum measurements in two quantum key distribution systems in which the results are transmitted via free-space optical communication to two agents separated with more than 20 km. The security of the protocol relies on the properties of quantum information and relativity theory. In each run of the experiment, a bit is successfully committed with less than 5.68×10(-2) cheating probability. This demonstrates the experimental feasibility of quantum communication with relativistic constraints.
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.
In the task cryptographers call bit commitment, one party encrypts a prediction in a way that cannot be decrypted until they supply a key, but has only one valid key. Bit commitment has many applications, and has been much studied, but completely and provably secure schemes have remained elusive. Here we report a new development in physics-based cryptography which gives a completely new way of implementing bit commitment that is perfectly secure. The technique involves sending a quantum state (for instance one or more photons) at light speed in one of two or more directions, either along a secure channel or by quantum teleportation. Its security proof relies on the no-cloning theorem of quantum theory and the no-superluminal-signalling principle of special relativity.
By using local quantum teleportation of a fixed state to one qubit of an entangled pair sent from the other party, it is shown how one party can commit a bit with only classical information as evidence that results in an unconditionally secure protocol. The well-known ``impossibility proof'' does not cover such protocols due to its different commitment and opening prescriptions, which necessitate actual quantum measurements among different possible systems that cannot be entangled as a consequence.