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A crucial task for secure communication networks is to determine the minimumof physical requirements to certify a cryptographic protocol. A widely acceptedcandidate for certification is the principle of relativistic causality which isequivalent to the disallowance of causal loops. Contrary to expectations, wedemonstrate how correlations allowed by relativistic causality could beexploited to break security for a broad class of multi-party protocols (allmodern protocols belong to this class). As we show, deep roots of this dramaticlack of security lies in the fact that unlike in previous (quantum orno-signaling) scenarios the new theory "decouples" the property of extremalityand that of statistical independence on environment variables. Finally, we findout, that the lack of security is accompanied by some advantage: the newcorrelations can reduce communication complexity better than the no-signalingones. As a tool for analysis of this advantage, we characterize relativisticcausal polytope by its extremal points in the simplest multi-party scenariothat goes beyond the no-signaling paradigm.

A No-go theorem for device-independent security in relativistic causal theories