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DOI: 10.4230/LIPIcs.FUN.2016.8
URN: urn:nbn:de:0030-drops-58693
URL: http://drops.dagstuhl.de/opus/volltexte/2016/5869/
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Bultel, Xavier ; Dreier, Jannik ; Dumas, Jean-Guillaume ; Lafourcade, Pascal

Physical Zero-Knowledge Proofs for Akari, Takuzu, Kakuro and KenKen

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Abstract

Akari, Takuzu, Kakuro and KenKen are logic games similar to Sudoku. In Akari, a labyrinth on a grid has to be lit by placing lanterns, respecting various constraints. In Takuzu a grid has to be filled with 0's and 1's, while respecting certain constraints. In Kakuro a grid has to be filled with numbers such that the sums per row and column match given values; similarly in KenKen a grid has to be filled with numbers such that in given areas the product, sum, difference or quotient equals a given value. We give physical algorithms to realize zero-knowledge proofs for these games which allow a player to show that he knows a solution without revealing it. These interactive proofs can be realized with simple office material as they only rely on cards and envelopes. Moreover, we formalize our algorithms and prove their security.

BibTeX - Entry

@InProceedings{bultel_et_al:LIPIcs:2016:5869,
  author =	{Xavier Bultel and Jannik Dreier and Jean-Guillaume Dumas and Pascal Lafourcade},
  title =	{{Physical Zero-Knowledge Proofs for Akari, Takuzu, Kakuro and  KenKen}},
  booktitle =	{8th International Conference on Fun with Algorithms (FUN 2016)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-005-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{49},
  editor =	{Erik D. Demaine and Fabrizio Grandoni},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5869},
  URN =		{urn:nbn:de:0030-drops-58693},
  doi =		{10.4230/LIPIcs.FUN.2016.8},
  annote =	{Keywords: Physical Cryptography, ZKP, Games, Akari, Kakuro, KenKen, Takuzu}
}

Keywords: Physical Cryptography, ZKP, Games, Akari, Kakuro, KenKen, Takuzu
Seminar: 8th International Conference on Fun with Algorithms (FUN 2016)
Issue Date: 2016
Date of publication: 25.05.2016


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