### Position-Based Quantum Cryptography: Impossibility and Constructions

Harry Buhrman, Nishanth Chandran, Serge Fehr, Ran Gelles, Vipul Goyal, Rafail Ostrovsky, and Christian Schaffner

##### Abstract

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.

##### Metadata
Available format(s)
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
Position based cryptography
Contact author(s)
gelles @ cs ucla edu
History
2010-12-12: last of 2 revisions
2010-05-11: received
See all versions
Short URL
https://ia.cr/2010/275
License

CC BY

BibTeX

@misc{cryptoeprint:2010/275,
author = {Harry Buhrman and Nishanth Chandran and Serge Fehr and Ran Gelles and Vipul Goyal and Rafail Ostrovsky and Christian Schaffner},
title = {Position-Based Quantum Cryptography: Impossibility and Constructions},
howpublished = {Cryptology ePrint Archive, Paper 2010/275},
year = {2010},
note = {\url{https://eprint.iacr.org/2010/275}},
url = {https://eprint.iacr.org/2010/275}
}

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