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Practical Relativistic Zero-Knowledge for NP

Authors Claude Crépeau, Arnaud Y. Massenet, Louis Salvail, Lucas Shigeru Stinchcombe, Nan Yang

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Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum information theory
Keywords
  • Multi-Prover Interactive Proofs
  • Relativistic Commitments
  • 3-COLorability
  • Quantum Entanglement
  • Non-Locality

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Abstract

In a Multi-Prover environment, how little spatial separation is sufficient to assert the validity of an NP statement in Perfect Zero-Knowledge ? We exhibit a set of two novel Zero-Knowledge protocols for the 3-COLorability problem that use two (local) provers or three (entangled) provers and only require exchanging one edge and two bits with two trits per prover. This greatly improves the ability to prove Zero-Knowledge statements on very short distances with very basic communication gear.

Cite As Get BibTex

Claude Crépeau, Arnaud Y. Massenet, Louis Salvail, Lucas Shigeru Stinchcombe, and Nan Yang. Practical Relativistic Zero-Knowledge for NP. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ITC.2020.4

Author Details

Claude Crépeau
  • School of Computer Science, McGill University, Montréal, Québec, Canada
Arnaud Y. Massenet
  • École Normale Supérieure Paris-Saclay, Gif-sur-Yvette, France
Louis Salvail
  • Département d'Informatique et de R.O., Université de Montréal, Montréal, Québec, Canada
Lucas Shigeru Stinchcombe
  • Bloomberg L.P., Tokyo, Japan
Nan Yang
  • Canadian Centre for Cyber Security, Ottawa, Ontario, Canada
  • Concordia University, Montréal, Québec, Canada

Funding

  • Crépeau, Claude: Supported in part by Québec’s FRQNT (INTRIQ) and Canada’s NSERC.
  • Salvail, Louis: Supported in part by an NSERC discovery grant and acceleration to discovery grant.
  • Yang, Nan: This work was completed at Concordia University and supported in part by Professors Jeremy Clark, and Claude Crépeau.

Acknowledgements

We would like to thank P. Alikhani, N. Brunner, A. Chailloux, S. Designolle, A. Leverrier, W. Shi, T. Vidick, and H. Zbinden for various discussions about earlier versions of this work. We would also like to thank Jeremy Clark for his insightful comments. We are grateful to ITC’s reviewers for several useful comments and corrections. Most of these have been implemented.

References

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