Recursive cheating strategies for the relativistic $\mathbb F_Q$ bit commitment protocol

Abstract : 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.
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Rémi Bricout, André Chailloux. Recursive cheating strategies for the relativistic $\mathbb F_Q$ bit commitment protocol. Cryptography, MDPI, 2017, ⟨10.3390/cryptography1020014⟩. ⟨hal-01409563⟩

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