Position-Based Quantum Cryptography
In this work, we initiate the study of position-based cryptography in the quantum setting. The aim of position-based cryptography is to use the geographical position of a party as its only credential. This has interesting applications, e.g., it enables two military bases to talk to each other over insecure (i.e. neither private nor authenticated) channels and without having any pre-shared key, with the guarantee that only parties within the bases learn the content of the conversation. We present schemes for several important position-based cryptographic tasks: positioning, authentication, and key exchange, and we prove them unconditionally secure, i.e., without assuming any restriction on the adversaries (beyond the laws of quantum mechanics). At the core of our security proofs lies the strong complementary information tradeoff recently introduced by Renes and Boileau. An attractive feature of all our schemes is that they only involve ``simple'' quantum operations, namely to prepare, communicate and measure-upon-arrival individual qubits. We stress that the above position-based tasks are impossible in the classical setting without limiting the adversary. Therefore, our work shows that position-based quantum cryptography is one of the rare examples besides QKD for which there is such a strong separation between classical and quantum cryptography. Besides the schemes for which we give rigorous security proofs, we also present a couple of significantly more efficient schemes for which we can merely conjecture security; proving them secure remains an interesting challenge. Our results open a fascinating new direction for position-based security in cryptography where security of protocols is solely based on the laws of physics and proofs of security do not require any pre-existing infrastructure.