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arXiv:1404.6925

Unconditionally secure bit commitment by causally independent encryptions

Chi-Yee Cheung

Published Apr 28, 2014• 0 citations
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Abstract

We propose a new classical bit commitment protocol using the relativistic constraint that signals cannot travel faster than the speed of light $c$. 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 $d$, 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 $Δt=d/2c$. This protocol requires only limited communication resources and is readily implementable with current technologies.

DOI
10.48550/arxiv.1404.6925

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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.
If mistrustful parties A and B control two or more appropriately located sites, special relativity can be used to guarantee that a pair of messages exchanged by A and B are independent. Using this fact, an unconditionally secure relativistic bit commitment protocol, RBC1, was recently defined. Security is maintained in RBC1 by exchanging a sequence of messages whose transmission rate increases exponentially in time. We define here a variant, RBC2, which requires a constant transmission rate and can in practice be securely maintained for long periods. We also introduce a zero-knowledge proof protocol which allows A to convince B of the value of any function of NNN relativistic bit commitments without giving any further information. Applying this to the XOR of two bit commitments made by RBC1 or RBC2, we define two further relativistic bit commitment protocols, RBC3 and RBC4. These two protocols are permanently unconditionally secure against classical attack and require only a constant transmission rate. We conjecture that they are also unconditionally secure against quantum attack.
Bit commitment is a fundamental cryptographic primitive in which Alice wishes to commit a secret bit to Bob. Perfectly secure bit commitment between two mistrustful parties is impossible through an asynchronous exchange of quantum information. Perfect security is, however, possible when Alice and Bob each split into several agents exchanging classical information at times and locations suitably chosen to satisfy specific relativistic constraints. In this Letter we first revisit a previously proposed scheme [C. Crépeau et al., Lect. Notes Comput. Sci. 7073, 407 (2011)] that realizes bit commitment using only classical communication. We prove that the protocol is secure against quantum adversaries for a duration limited by the light-speed communication time between the locations of the agents. We then propose a novel multiround scheme based on finite-field arithmetic that extends the commitment time beyond this limit, and we prove its security against classical attacks. Finally, we present an implementation of these protocols using dedicated hardware and we demonstrate a 2 ms-long bit commitment over a distance of 131 km. By positioning the agents on antipodal points on the surface of Earth, the commitment time could possibly be extended to 212 ms.
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.
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.
Bit commitment is a fundamental cryptographic primitive in which Bob wishes to commit a secret bit to Alice. Perfectly secure bit commitment between two mistrustful parties is impossible through asynchronous exchange of quantum information. Perfect security is however possible when Alice and Bob split into several agents exchanging classical and quantum information at times and locations suitably chosen to satisfy specific relativistic constraints. Here we report on an implementation of a bit commitment protocol using quantum communication and special relativity. Our protocol is based on [A. Kent, Phys. Rev. Lett. 109, 130501 (2012)] and has the advantage that it is practically feasible with arbitrary large separations between the agents in order to maximize the commitment time. By positioning agents in Geneva and Singapore, we obtain a commitment time of 15 ms. A security analysis considering experimental imperfections and finite statistics is presented.