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

TL;DR

This paper proves a no-go theorem showing that relativistic causality alone cannot guarantee security in multi-party cryptographic protocols, as such correlations can be exploited to break security and reduce communication complexity.

Contribution

It introduces a no-go theorem demonstrating the insecurity of protocols under relativistic causality and characterizes the relativistic causal polytope's extremal points.

Findings

Relativistic causality correlations can break security in multi-party protocols.

These correlations can reduce communication complexity.

The security gap is linked to the decoupling of extremality and independence properties.

Abstract

A crucial task for secure communication networks is to determine the minimum of physical requirements to certify a cryptographic protocol. A widely accepted candidate for certification is the principle of relativistic causality which is equivalent to the disallowance of causal loops. Contrary to expectations, we demonstrate how correlations allowed by relativistic causality could be exploited to break security for a broad class of multi-party protocols (all modern protocols belong to this class). As we show, deep roots of this dramatic lack of security lies in the fact that unlike in previous (quantum or no-signaling) scenarios the new theory "decouples" the property of extremality and that of statistical independence on environment variables. Finally, we find out, that the lack of security is accompanied by some advantage: the new correlations can reduce communication complexity better than the no-signaling ones. As a tool for analysis of this advantage, we characterize relativistic causal polytope by its extremal points in the simplest multi-party scenario that goes beyond the no-signaling paradigm.