Physically Verifying the First Nonzero Term in a Sequence: Physical ZKPs for ABC End View and Goishi Hiroi
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In this paper, we develop a physical protocol to verify the first nonzero term of a sequence using a deck of cards. This protocol enables a prover to show a verifier the value of the first nonzero term in a given sequence without revealing which term it is. Our protocol uses Θ(1) shuffles, making it simpler and more practical than a similar protocol recently developed by Fukusawa and Manabe in 2022, which uses Θ(n) shuffles, where n is the length of the sequence. We also apply our protocol to construct zero-knowledge proof protocols for two famous logic puzzles: ABC End View and Goishi Hiroi. These zero-knowledge proof protocols allow a prover to physically show that he/she know solutions of the puzzles without revealing them.
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