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.
@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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