Physical Zero-Knowledge Proof for Makaro

Xavier Bultel (1) , Jannik Dreier (2) , Jean-Guillaume Dumas (3) , Pascal Lafourcade (4) , Daiki Miyahara (5, 6) , Takaaki Mizuki (5) , Atsuki Nagao (7) , Tatsuya Sasaki (5) , Kazumasa Shinagawa (6, 8) , Hideaki Sone (5)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes
2 PESTO - Proof techniques for security protocols
3 CASYS - Calculs Algébriques et Systèmes Dynamiques
4 VERIMAG - IMAG - VERIMAG
5 Tohoku University [Sendai]
6 AIST - National Institute of Advanced Industrial Science and Technology
7 Ochanomizu University
8 TITECH - Tokyo Institute of Technology [Tokyo]

Makaro is a logic game similar to Sudoku. In Makaro, a grid has to be filled with numbers such that: given areas contain all the numbers up to the number of cells in the area, no adjacent numbers are equal and some cells provide restrictions on the largest adjacent number. We propose a proven secure physical algorithm, only relying on cards, to realize a zero-knowledge proof of knowledge for Makaro. It allows a player to show that he knows a solution without revealing it.

Mots clés: Puzzle; Card-based secure two-party protocols; Zero-knowledge proofs; Privacy; Makaro

Domaines: Cryptographie et sécurité [cs.CR]

Xavier Bultel, Jannik Dreier, Jean-Guillaume Dumas, Pascal Lafourcade, Daiki Miyahara, et al.. Physical Zero-Knowledge Proof for Makaro. SSS 2018 - 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems, Nov 2018, Tokyo, Japan. pp.111-125, ⟨10.1007/978-3-030-03232-6_8⟩. ⟨hal-01898048⟩