A Physical Zero-Knowledge Proof for Sumplete, a Puzzle Generated by ChatGPT

Hatsugai, Kyosuke; Asano, Kyoichi; Abe, Yoshiki

doi:10.1007/978-3-031-49190-0_29

Cited by 4 publications

References 25 publications

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NP-Completeness and Physical Zero-Knowledge Proofs for Sumplete, a Puzzle Generated by ChatGPT

Hatsugai,

Ruangwises,

Asano

et al. 2024

New Gener. Comput.

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Sumplete is a logic puzzle generated by ChatGPT in March 2023. The puzzle consists of a rectangular grid, with each cell containing an integer. Each row and column also has an integer called target value assigned to it. The objective of this puzzle is to cross out some numbers in the grid such that the sum of uncrossed numbers in each row and column is equal to the corresponding target value. In this paper, we prove that Sumplete is NP-complete. We also propose a physical zero-knowledge proof protocol for the puzzle using physical cards.

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NP-Completeness and Physical Zero-Knowledge Proofs for Sumplete, a Puzzle Generated by ChatGPT

Hatsugai,

Ruangwises,

Asano

et al. 2024

New Gener. Comput.

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Efficient Card-Based ZKP for Single Loop Condition and Its Application to Moon-or-Sun

Hand,

Koch,

Lafourcade

et al. 2024

New Gener. Comput.

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A zero-knowledge proof (ZKP) allows a prover to prove to a verifier that it knows some secret, such as a solution to a difficult puzzle, without revealing any information about it. In recent years, ZKP protocols using only a deck of playing cards for solutions to various pencil puzzles have been proposed. The previous work of Lafourcade et al. deals with a famous puzzle called Slitherlink. Their proposed protocol can verify that a solution forms a single loop without revealing anything about the solution, except this fact. Their protocol guarantees that the solution satisfies the single-loop condition, by interactively constructing a solution starting from a state that holds a simple single loop, and proceeding via steps that preserve the invariant of encoding a single loop, until the proper solution is reached. A drawback of their protocol is that it requires additional verifications to guarantee a single loop. In this study, we propose a more efficient ZKP protocol for such a puzzle with fewer additional verifications. For this, we employ the previous work of Robert et al., which addressed the connectivity property in a puzzle. That is, we verify that a solution is connected but not split, to be a single loop. Applying our proposal, we construct a card-based ZKP protocol for Moon-or-Sun, which has its specific rule of alternating pattern in addition to the single-loop condition.

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Verifying the first nonzero term: physical ZKPs for ABC End View, Goishi Hiroi, and Toichika

Ruangwises

2024

J Comb Optim

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A Physical Zero-Knowledge Proof for Sumplete, a Puzzle Generated by ChatGPT

Cited by 4 publications

References 25 publications

NP-Completeness and Physical Zero-Knowledge Proofs for Sumplete, a Puzzle Generated by ChatGPT

NP-Completeness and Physical Zero-Knowledge Proofs for Sumplete, a Puzzle Generated by ChatGPT

Efficient Card-Based ZKP for Single Loop Condition and Its Application to Moon-or-Sun

Verifying the first nonzero term: physical ZKPs for ABC End View, Goishi Hiroi, and Toichika

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