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DOI: 10.4230/LIPIcs.ITCS.2022.100

Beating Classical Impossibility of Position Verification

Authors: Jiahui Liu, Qipeng Liu, and Luowen Qian

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract

Chandran et al. (SIAM J. Comput. '14) formally introduced the cryptographic task of position verification, where they also showed that it cannot be achieved by classical protocols. In this work, we initiate the study of position verification protocols with classical verifiers. We identify that proofs of quantumness (and thus computational assumptions) are necessary for such position verification protocols. For the other direction, we adapt the proof of quantumness protocol by Brakerski et al. (FOCS '18) to instantiate such a position verification protocol. As a result, we achieve classically verifiable position verification assuming the quantum hardness of Learning with Errors. Along the way, we develop the notion of 1-of-2 non-local soundness for a natural non-local game for 1-of-2 puzzles, first introduced by Radian and Sattath (AFT '19), which can be viewed as a computational unclonability property. We show that 1-of-2 non-local soundness follows from the standard 2-of-2 soundness (and therefore the adaptive hardcore bit property), which could be of independent interest.

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Jiahui Liu, Qipeng Liu, and Luowen Qian. Beating Classical Impossibility of Position Verification. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 100:1-100:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{liu_et_al:LIPIcs.ITCS.2022.100,
  author =	{Liu, Jiahui and Liu, Qipeng and Qian, Luowen},
  title =	{{Beating Classical Impossibility of Position Verification}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{100:1--100:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.100},
  URN =		{urn:nbn:de:0030-drops-156963},
  doi =		{10.4230/LIPIcs.ITCS.2022.100},
  annote =	{Keywords: cryptographic protocol, position verification, quantum cryptography, proof of quantumness, non-locality}
}

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Beating Classical Impossibility of Position Verification

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