Code-routing: a new attack on position verification

Abstract

The cryptographic task of position verification attempts to verify one party's location in spacetime by exploiting constraints on quantum information and relativistic causality. A popular verification scheme known as f-routing involves requiring the prover to redirect a quantum system based on the value of a Boolean function f. Cheating strategies for the f-routing scheme require the prover use pre-shared entanglement, and security of the scheme rests on assumptions about how much entanglement a prover can manipulate. Here, we give a new cheating strategy in which the quantum system is encoded into a secret-sharing scheme, and the authorization structure of the secret-sharing scheme is exploited to direct the system appropriately. This strategy completes the f-routing task using O(SPp(f)) EPR pairs, where SPp(f) is the minimal size of a span program over the field Zp computing f. This shows we can efficiently attack f-routing schemes whenever f is in the complexity class ModpL, after allowing for local pre-processing. The best earlier construction achieved the class L, which is believed to be strictly inside of ModpL. We also show that the size of a quantum secret sharing scheme with indicator function fI upper bounds entanglement cost of f-routing on the function fI.