Abstract
Ripple Effect is a logic puzzle with an objective to fill numbers into a rectangular grid divided into rooms. Each room must contain consecutive integers starting from 1 to its size. Also, if two cells in the same row or column have the same number x, the space separating the two cells must be at least x cells. In this paper, we propose a physical protocol of zero-knowledge proof for Ripple Effect puzzle using a deck of cards, which allows a prover to physically show that he/she knows a solution without revealing it. In particular, we develop a physical protocol that, given a secret number x and a list of numbers, verifies that x does not appear among the first x numbers in the list without revealing x or any number in the list.
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Notes
- 1.
Actually, some protocols from previous work can verify a function that uses the mathematical meaning of numbers, but still not in the sense of cardinality. For example, a subprotocol in [12] verifies that the sum of all numbers in a list is equal to a given number; for this function, we can still replace every number x with f(x) for any linear function \(f: \mathbb {Z}^+ \rightarrow \mathbb {Z}^+\).
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Ruangwises, S., Itoh, T. (2021). Physical Zero-Knowledge Proof for Ripple Effect. In: Uehara, R., Hong, SH., Nandy, S.C. (eds) WALCOM: Algorithms and Computation. WALCOM 2021. Lecture Notes in Computer Science(), vol 12635. Springer, Cham. https://doi.org/10.1007/978-3-030-68211-8_24
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