Position-Based Quantum Cryptography: Impossibility and Constructions
In this work, we study position-based 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 position-verification 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 position-verification 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 position-verification is
achievable. Jointly, these results suggest the interesting question whether
secure position-verification 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 pre-shared 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 position-verification is
achievable, other position-based cryptographic schemes are possible as well,
such as secure position-based authentication and position-based key agreement.
http://arxiv.org/abs/1009.2490
