Position-based quantum cryptography over untrusted networks

In this paper, we propose quantum position-verification schemes where all the channels are untrusted except the position of the prover and distant reference stations of verifiers. We review and analyze the existing QPV schemes containing some pre-shared data between the prover and verifiers. Most of these schemes are based on non-cryptographic assumptions, that is, quantum/classical channels between the verifiers are secure. It seems impractical in the environment fully controlled by adversaries and would lead to security compromise in practical implementations. However, our proposed formulism for quantum position-verification is more robust, secure and according to the standard assumptions of cryptography. Furthermore, once the position of the prover is verified, our schemes establish secret keys in parallel and can be used for authentication and secret communication between the prover and verifiers.