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DOI: 10.4230/LIPIcs.ITC.2020.4

Practical Relativistic Zero-Knowledge for NP

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

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

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.

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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)

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@InProceedings{crepeau_et_al:LIPIcs.ITC.2020.4,
  author =	{Cr\'{e}peau, Claude and Massenet, Arnaud Y. and Salvail, Louis and Stinchcombe, Lucas Shigeru and Yang, Nan},
  title =	{{Practical Relativistic Zero-Knowledge for NP}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.4},
  URN =		{urn:nbn:de:0030-drops-121091},
  doi =		{10.4230/LIPIcs.ITC.2020.4},
  annote =	{Keywords: Multi-Prover Interactive Proofs, Relativistic Commitments, 3-COLorability, Quantum Entanglement, Non-Locality}
}

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DOI: 10.4230/LIPIcs.TQC.2019.4

The RGB No-Signalling Game

Authors: Xavier Coiteux-Roy and Claude Crépeau

Published in: LIPIcs, Volume 135, 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)

Abstract

Introducing the simplest of all No-Signalling Games: the RGB Game where two verifiers interrogate two provers, Alice and Bob, far enough from each other that communication between them is too slow to be possible. Each prover may be independently queried one of three possible colours: Red, Green or Blue. Let a be the colour announced to Alice and b be announced to Bob. To win the game they must reply colours x (resp. y) such that a != x != y != b. This work focuses on this new game mainly as a pedagogical tool for its simplicity but also because it triggered us to introduce a new set of definitions for reductions among multi-party probability distributions and related non-locality classes. We show that a particular winning strategy for the RGB Game is equivalent to the PR-Box of Popescu-Rohrlich and thus No-Signalling. Moreover, we use this example to define No-Signalling in a new useful way, as the intersection of two natural classes of multi-party probability distributions called one-way signalling. We exhibit a quantum strategy able to beat the classical local maximum winning probability of 8/9 shifting it up to 11/12. Optimality of this quantum strategy is demonstrated using the standard tool of semidefinite programming.

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Xavier Coiteux-Roy and Claude Crépeau. The RGB No-Signalling Game. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{coiteuxroy_et_al:LIPIcs.TQC.2019.4,
  author =	{Coiteux-Roy, Xavier and Cr\'{e}peau, Claude},
  title =	{{The RGB No-Signalling Game}},
  booktitle =	{14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)},
  pages =	{4:1--4:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-112-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{135},
  editor =	{van Dam, Wim and Man\v{c}inska, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2019.4},
  URN =		{urn:nbn:de:0030-drops-103965},
  doi =		{10.4230/LIPIcs.TQC.2019.4},
  annote =	{Keywords: No-Signalling, Quantum Entanglement, Non-Locality, Bell inequality, Semidefinite Programming, Non-locality Hierarchy}
}

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Documents authored by Crépeau, Claude

Practical Relativistic Zero-Knowledge for NP

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The RGB No-Signalling Game

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