Check Alternating Patterns: A Physical Zero-Knowledge Proof for Moon-or-Sun

Hand, Samuel; Koch, Alexander; Lafourcade, Pascal; Miyahara, Daiki; Robert, Léo

doi:10.1007/978-3-031-41326-1_14

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Cited by 6 publications

References 28 publications

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Upper Bounds on the Number of Shuffles for Two-Helping-Card Multi-Input AND Protocols

Yoshida,

Tanaka,

Nakabayashi

et al. 2023

Lecture Notes in Computer Science

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Upper Bounds on the Number of Shuffles for Two-Helping-Card Multi-Input AND Protocols

Yoshida,

Tanaka,

Nakabayashi

et al. 2023

Lecture Notes in Computer Science

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Printing Protocol: Physical ZKPs for Decomposition Puzzles

Ruangwises,

Iwamoto

2024

New Gener. Comput.

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Decomposition puzzles are pencil-and-paper logic puzzles that involve partitioning a rectangular grid into several regions to satisfy certain rules. In this paper, we construct a generic card-based protocol called printing protocol, which can be used to physically verify solutions of decompositon puzzles. We apply the printing protocol to develop card-based zero-knowledge proof protocols for two such puzzles: Five Cells and Meadows. These protocols allow a prover to physically show that he/she knows solutions of the puzzles without revealing them.

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Physical Zero-Knowledge Proof Protocols for Topswops and Botdrops

Komano,

Mizuki

2024

New Gener. Comput.

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Suppose that a sequence of $${\varvec{n}}$$ n cards, numbered 1 to $${\varvec{n}}$$ n , is placed face up in random order. Let $${\varvec{k}}$$ k be the number on the first card in the sequence. Then take the first $${\varvec{k}}$$ k cards from the sequence, rearrange that subsequence of $${\varvec{k}}$$ k cards in reverse order, and return them to the original sequence. Repeat this prefix reversal until the number on the first card in the sequence becomes 1. This is a one-player card game called Topswops. The computational complexity of Topswops has not been thoroughly investigated. For example, letting $${\varvec{f}}({\varvec{n}})$$ f ( n ) denote the maximum number of prefix reversals for Topswops with $${\varvec{n}}$$ n cards, values of $${\varvec{f}}({\varvec{n}})$$ f ( n ) for $${\varvec{n}}\ge 20$$ n ≥ 20 remain unknown. In general, there is no known efficient algorithm for finding an initial sequence of $${\varvec{n}}$$ n cards that requires exactly $$\ell $$ ℓ prefix reversals for any integers $${\varvec{n}}$$ n and $${\varvec{\ell }}$$ ℓ . In this paper, using a deck of cards, we propose a physical zero-knowledge proof protocol that allows a prover to convince a verifier that the prover knows an initial sequence of $${\varvec{n}}$$ n cards that requires $${\varvec{\ell }}$$ ℓ prefix reversals without leaking knowledge of that sequence. We also deal with Botdrops, a variant of Topswops.

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Check Alternating Patterns: A Physical Zero-Knowledge Proof for Moon-or-Sun

Cited by 6 publications

References 28 publications

Upper Bounds on the Number of Shuffles for Two-Helping-Card Multi-Input AND Protocols

Upper Bounds on the Number of Shuffles for Two-Helping-Card Multi-Input AND Protocols

Printing Protocol: Physical ZKPs for Decomposition Puzzles

Physical Zero-Knowledge Proof Protocols for Topswops and Botdrops

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