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

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  • Suthee Ruangwises

    (The University of Electro-Communications)

Abstract

In this paper, we propose a physical protocol to verify the first nonzero term of a sequence using a deck of cards. The protocol lets a prover show the value of the first nonzero term of a given sequence to a verifier without revealing which term it is. Our protocol uses $$\varTheta (1)$$ Θ ( 1 ) shuffles, which is asymptotically lower than that of an existing protocol of Fukusawa and Manabe which uses $$\varTheta (n)$$ Θ ( n ) shuffles, where n is the length of the sequence. We also apply our protocol to construct zero-knowledge proof protocols for three well-known logic puzzles: ABC End View, Goishi Hiroi, and Toichika. These protocols enable a prover to physically show that he/she know solutions of the puzzles without revealing them.

Suggested Citation

  • Suthee Ruangwises, 2024. "Verifying the first nonzero term: physical ZKPs for ABC End View, Goishi Hiroi, and Toichika," Journal of Combinatorial Optimization, Springer, vol. 47(4), pages 1-18, May.
    • Handle: RePEc:spr:jcomop:v:47:y:2024:i:4:d:10.1007_s10878-024-01170-6
    DOI: 10.1007/s10878-024-01170-6
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