Insecurity of position-based quantum cryptography protocols against entanglement attacks

TL;DR

This paper demonstrates that existing position-based quantum cryptography protocols are insecure against entanglement-based attacks, and proposes a modified scheme that is more resistant, with proofs for certain quantum resources.

Contribution

The paper reveals vulnerabilities in current protocols due to entanglement attacks and introduces a modified scheme with improved security features.

Findings

Existing protocols are insecure against entanglement attacks.

A modified protocol reduces the success rate of cheating to at most 85%.

The modified scheme is proven secure with two- or three-level shared quantum resources.

Abstract

Recently, position-based quantum cryptography has been claimed to be unconditionally secure. In contrary, here we show that the existing proposals for position-based quantum cryptography are, in fact, insecure if entanglement is shared among two adversaries. Specifically, we demonstrate how the adversaries can incorporate ideas of quantum teleportation and quantum secret sharing to compromise the security with certainty. The common flaw to all current protocols is that the Pauli operators always map a codeword to a codeword (up to an irrelevant overall phase). We propose a modified scheme lacking this property in which the same cheating strategy used to undermine the previous protocols can succeed with a rate at most 85%. We conjecture that the modified protocol is unconditionally secure and prove this to be true when the shared quantum resource between the adversaries is a two- or three- level system.