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arXiv:1608.03398 · Physical Review A

Robust relativistic bit commitment

Kaushik Chakraborty, André Chailloux, Anthony Leverrier

Published Dec 12, 2016• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.94.062314

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•Mar 19, 2019•0 citations
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.
Bit commitment is a fundamental cryptographic primitive in which a party wishes to commit a secret bit to another party. Perfect security between mistrustful parties is unfortunately impossible to achieve through the asynchronous exchange of classical and quantum messages. Perfect security can nonetheless be achieved if each party splits into two agents exchanging classical information at times and locations satisfying strict relativistic constraints. A relativistic multiround protocol to achieve this was previously proposed and used to implement a 2-millisecond commitment time. Much longer durations were initially thought to be insecure, but recent theoretical progress showed that this is not so. In this Letter, we report on the implementation of a 24-hour bit commitment solely based on timed high-speed optical communication and fast data processing, with all agents located within the city of Geneva. This duration is more than 6 orders of magnitude longer than before, and we argue that it could be extended to one year and allow much more flexibility on the locations of the agents. Our implementation offers a practical and viable solution for use in applications such as digital signatures, secure voting and honesty-preserving auctions.
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.
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.
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.
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.
This thesis considers multi-prover commitment schemes whose security is based on restrictions on the communication between the provers. The results are applicable to so-called relativistic commitment schemes: schemes whose security is guaranteed by the fact that information does not travel faster than the speed of light. A commitment scheme is a cryptographic protocol solving the following problem: One party, the prover, has selected a value which he wants to keep secret at first. The prover wants to have the option to reveal it to the other party, the verifier, at a later time, but the verifier wants a guarantee that no value other than the originally selected one can be revealed. Standard commitment schemes can only be proven secure with computational hardness assumptions. This can be circumvented by splitting the prover into multiple entities and restricting their communication, e.g., no communication at all, or communication only with a delay (as in relativistic commitment schemes). This dissertation introduces new methods for analyzing and designing such multi-prover schemes. As an application, we show that the Lunghi et al. commitment scheme from 2015 has much stronger security that their original analysis indicated.