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arXiv:1608.03820 · Cryptography

Recursive Cheating Strategies for the Relativistic FQ Bit Commitment Protocol

Rémi Bricout, André Chailloux

Published Aug 24, 2017• 0 citations
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Abstract

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.

DOI
10.3390/cryptography1020014

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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.
Recursive cheating strategies for the relativistic FQ\mathbb F_QFQ​ bit commitment protocol
In this paper, we study relativistic bit commitment, which uses timing and location constraints to achieve information theoretic security. We consider the FQ multi-round bit commitment scheme introduced by Lunghi et al. [LKB + 15]. This protocol was shown secure against classical adversaries as long as the number of rounds m is small compared to √ Q where Q is the size of the used field in the protocol [CCL15, FF16]. In this work, we study classical attacks on this scheme. We use classical strategies for the CHSHQ game described in [BS15] to derive cheating strategies for this protocol. In particular, our cheating strategy shows that if Q is an even power of any prime, then the protocol is not secure when the number of rounds m is of the order of √ Q. For those values of Q, this means that the upper bound of [CCL15, FF16] is essentially optimal.
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 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.
In this thesis we have studied how to exploit relativistic constraints such as the non-superluminal signalling principle to design secure cryptographic primitives like position-verification and bit commitment. According to non-superluminal signalling principle, no physical carrier of information can travel faster than the speed of light. This put a constraint on the communication time between two distant stations. One can consider this delay in information transfer as a temporal non-communication constraint. Cryptographic primitives like bit-commitment, oblivious transfer can be implemented with perfect secrecy under such non-communication assumption between the agents. The first part of this thesis has studied how non-signalling constraints can be used for secure position verification. Here, we have discussed about a strategy which can attack any position verification scheme. In the next part of this thesis we have discussed about the nonlocal games, relevant for studying relativistic bit commitment protocols. We have established an upper bound on the classical value of such family of games. The last part of this thesis discusses about two relativistic bit commitment protocols and their security against classical adversaries. We conclude this thesis by giving a brief summary of the content of each chapter and mentioning interesting open problems. These open problems can be very useful for better understanding of the role of spacetime constraints such as non-superluminal signalling in designing perfectly secure cryptographic primitives.
In this thesis we explore the benefits of relativistic constraints for cryptography. We first revisit non-communicating models and its applications in the context of interactive proofs and cryptography. We propose bit commitment protocols whose security hinges on communication constraints and investigate its limitations. We explain how some non-communicating models can be justified by special relativity and study the limitations of such models. In particular, we present a framework for analysing security of multiround relativistic protocols. The second part of the thesis is dedicated to analysing specific protocols. We start by considering a recently proposed two-round quantum bit commitment protocol. We propose a fault-tolerant variant of the protocol, present a complete security analysis and report on an experimental implementation performed in collaboration with an experimental group at the University of Geneva. We also propose a new, multiround classical bit commitment protocol and prove its security against classical adversaries. This demonstrates that in the classical world an arbitrarily long commitment can be achieved even if the agents are restricted to occupy a finite region of space. Moreover, the protocol is easy to implement and we report on an experiment performed in collaboration with the Geneva group.
We examine the possibility of device-independent relativistic quantum bit commitment, introducing three relativistic quantum bit commitment schemes that offer device-independent security against hypothetical postquantum adversaries subject only to the no-signaling principle. We discuss the potential threat of location attacks, in which the behavior of untrusted devices used in relativistic quantum cryptography depends on their space-time location and show that our protocols are secure against both location attacks and memory attacks. The protocols are compared to a relativistic classical bit commitment scheme with similar features and we note some advantages for the quantum schemes.