PositionBased Quantum Cryptography: Impossibility and Constructions
Abstract
In this work, we study positionbased cryptography in the quantum setting. The aim is to use the geographical position of a party as its only credential. On the negative side, we show that if adversaries are allowed to share an arbitrarily large entangled quantum state, no secure positionverification is possible at all. We show a distributed protocol for computing any unitary operation on a state shared between the different users, using local operations and one round of classical communication. Using this surprising result, we break any positionverification scheme of a very general form. On the positive side, we show that if adversaries do not share any entangled quantum state but can compute arbitrary quantum operations, secure positionverification is achievable. Jointly, these results suggest the interesting question whether secure positionverification is possible in case of a bounded amount of entanglement. Our positive result can be interpreted as resolving this question in the simplest case, where the bound is set to zero. In models where secure positioning is achievable, it has a number of interesting applications. For example, it enables secure communication over an insecure channel without having any preshared key, with the guarantee that only a party at a specific location can learn the content of the conversation. More generally, we show that in settings where secure positionverification is achievable, other positionbased cryptographic schemes are possible as well, such as secure positionbased authentication and positionbased key agreement.
 Publication:

arXiv eprints
 Pub Date:
 September 2010
 arXiv:
 arXiv:1009.2490
 Bibcode:
 2010arXiv1009.2490B
 Keywords:

 Quantum Physics;
 Computer Science  Cryptography and Security
 EPrint:
 27 pages, 5 figures. v4: improved proofs for the impossibility theorem and for the instantaneous computation theorem