Physical Zero-Knowledge Proofs for Akari, Takuzu, Kakuro and KenKen
This provides a secure, accessible method for players to verify solutions in logic games without revealing them, though it is incremental as it extends existing physical proof techniques to new games.
The paper tackles the problem of proving knowledge of solutions to logic games (Akari, Takuzu, Kakuro, KenKen) without revealing the solutions, by developing physical zero-knowledge proofs using cards and envelopes, and formally proves their security.
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.