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arXiv:1507.00239 · Physical Review Letters

Arbitrarily Long Relativistic Bit Commitment

Kaushik Chakraborty, André Chailloux, Anthony Leverrier

Published Dec 17, 2015• 25 citations
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Abstract

We consider the recent relativistic bit commitment protocol introduced by Lunghi et al. [Phys. Rev. Lett. 115, 030502 (2015)] and present a new security analysis against classical attacks. In particular, while the initial complexity of the protocol scales double exponentially with the commitment time, our analysis shows that the correct dependence is only linear. This has dramatic implications in terms of implementation: in particular, the commitment time can easily be made arbitrarily long, by only requiring both parties to communicate classically and perform efficient classical computation.

DOI
10.1103/physrevlett.115.250501

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We consider the recent relativistic bit commitment protocol introduced by Lunghi et al. [Phys. Rev. Lett. 115, 030502 (2015)] and present a new security analysis against classical attacks. In particular, while the initial complexity of the protocol scales double exponentially with the commitment time, our analysis shows that the correct dependence is only linear. This has dramatic implications in terms of implementation: in particular, the commitment time can easily be made arbitrarily long, by only requiring both parties to communicate classically and perform efficient classical computation.
Relativistic cryptography exploits the fact that no information can travel faster than the speed of light in order to obtain security guarantees that cannot be achieved from the laws of quantum mechanics alone. Recently, Lunghi et al. [Phys. Rev. Lett. 115, 030502 (2015)] presented a bit-commitment scheme where each party uses two agents that exchange classical information in a synchronized fashion, and that is both hiding and binding. A caveat is that the commitment time is intrinsically limited by the spatial configuration of the players, and increasing this time requires the agents to exchange messages during the whole duration of the protocol. While such a solution remains computationally attractive, its practicality is severely limited in realistic settings since all communication must remain perfectly synchronized at all times. In this work, we introduce a robust protocol for relativistic bit commitment that tolerates failures of the classical communication network. This is done by adding a third agent to both parties. Our scheme provides a quadratic improvement in terms of expected sustain time compared with the original protocol, while retaining the same level of security.
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.
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.
In this paper, we study relativistic bit commitment, which uses timing and location constraints to achieve information theoretic security. Using those constraints, we consider a relativistic bit commitment scheme introduced by Lunghi et al. This protocol was shown secure against classical adversaries as long as the number of rounds performed in the protocol is not too large. In this work, we study classical attacks on this scheme. We use the correspondence between this protocol and the CHSHQ game—which is a variant of the CHSH game—to derive cheating strategies for this protocol. Our attack matches the existing security bound for some range of parameters and shows that the scaling of the security in the number of rounds is essentially optimal.
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.