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

Xavier Bultel (1) , Jannik Dreier (2) , Jean-Guillaume Dumas (3) , Pascal Lafourcade (1)

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

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.

Keywords: logic games; zero knowledge

Domains: Cryptography and Security [cs.CR]

Xavier Bultel, Jannik Dreier, Jean-Guillaume Dumas, Pascal Lafourcade. Physical Zero-Knowledge Proofs for Akari, Takuzu, Kakuro and KenKen. 8th International Conference on Fun with Algorithms, Jun 2016, La Maddalena, Italy. pp.8:1-8:20, ⟨10.4230/LIPIcs.FUN.2016.8⟩. ⟨hal-01326059⟩