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.
Highlights
The security definitions for relativistic bit commitment are the ones we presented in the section above
We presented a cheating strategy for the FQ relativistic bit commitment protocol, which has recently become the most widely studied relativistic bit commitment protocol
We show that the security analysis presented in [21,22] is essentially tight, at least when Q is an even power of a prime
Summary
The goal of relativistic cryptography is to exploit the no superluminal signaling (NSS) principle in order to perform various cryptographic tasks. NSS is more precise since it gives an upper bound on the speed at which such an influence can propagate Apart from this physical principle, we want to ensure information-theoretic security meaning that the proposed schemes cannot be attacked by any classical (nor quantum) computer, even with infinite computing power. Lunghi et al devised a multi-round bit commitment protocol involving only four agents, two for Alice and two for Bob [20] They managed to prove that this protocol, which we call the “FQ protocol” on, remains secure for several rounds, against classical attacks. No cheating strategy has been proposed for this scheme
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