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.

在本文中，我们提出了一种物理协议，使用一副纸牌来验证序列的第一个非零项。该协议允许证明者向验证者显示给定序列的第一个非零项的值，而无需透露它是哪个项。我们的协议使用\(\varTheta (1)\)洗牌，这渐近低于福泽和真锅现有的使用\(\varTheta (n)\)洗牌的协议，其中n是序列的长度。我们还应用我们的协议为三个著名的逻辑难题构建零知识证明协议：ABC End View、Goishi Hiroi 和 Toichika。这些协议使证明者能够以物理方式表明他/她知道谜题的解决方案，而无需透露它们。