Abstract
Relativistic protocols have been proposed to overcome certain impossibility results in classical and quantum cryptography. In such a setting, one takes the location of honest players into account, and uses the signalling limit given by the speed of light to constraint the abilities of dishonest agents. However, composing such protocols with each other to construct new cryptographic resources is known to be insecure in some cases. To make general statements about such constructions, a composable framework for modelling cryptographic security in Minkowski space is required. Here, we introduce a framework for performing such a modular security analysis of classical and quantum cryptographic schemes in Minkowski space. As an application, we show that (1) fair and unbiased coin flipping can be constructed from a simple resource called channel with delay; (2) biased coin flipping, bit commitment and channel with delay through any classical, quantum or post-quantum relativistic protocols are all impossible without further setup assumptions; (3) it is impossible to securely increase the delay of a channel, given several short-delay channels as ingredients. Results (1) and (3) imply in particular the non-composability of existing relativistic bit commitment and coin flipping protocols.
Highlights
IntroductionThe player will lose one of the games and win the other (or tie in both games), but given that the Elo system favours lower-rated players, the attacker ends up with a net gain of points, independently of the result
Abstract cryptography views cryptography as a resource theory: a protocol constructs a resource from some other resource, e.g. Blum’s protocol [12] constructs a coin flipping resource from a bit commitment resource
Constructing It was shown in [23] that a 1/2-biased coin flipping resource can be perfectly constructed from a bit commitment resource, by using Blum’s protocol [12]
Summary
The player will lose one of the games and win the other (or tie in both games), but given that the Elo system favours lower-rated players, the attacker ends up with a net gain of points, independently of the result. Such a vulnerability could not be detected by a standalone security analysis (which checks what happens if the games are considered individually), but only by a composable security analysis, which considers the possibility of games being used in a modular fashion, as part of a larger strategy. Several known proposals for quantum cryptographic protocols that exploit relativistic constraints are proven insecure by our paper
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