How to Physically Verify a Rectangle in a Grid: A Physical ZKP for Shikaku
This work addresses the need for secure, physical verification methods in puzzle-solving contexts, though it is incremental as it builds on existing zero-knowledge proof concepts applied to a specific domain.
The authors tackled the problem of physically verifying a solution to the Shikaku puzzle without revealing it, by developing two card-based zero-knowledge proof protocols, with the second protocol introducing a general technique for verifying rectangle-shaped areas in grids.
Shikaku is a pencil puzzle consisting of a rectangular grid, with some cells containing a number. The player has to partition the grid into rectangles such that each rectangle contains exactly one number equal to the area of that rectangle. In this paper, we propose two physical zero-knowledge proof protocols for Shikaku using a deck of playing cards, which allow a prover to physically show that he/she knows a solution of the puzzle without revealing it. Most importantly, in our second protocol we develop a general technique to physically verify a rectangle-shaped area with a certain size in a rectangular grid, which can be used to verify other problems with similar constraints.