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

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 \(\varTheta (1)\) shuffles, which is asymptotically lower than that of an existing protocol of Fukusawa and Manabe which uses \(\varTheta (n)\) 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.