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 $\Theta (1)$ shuffles, which is asymptotically lower than that of an existing protocol of Fukusawa and Manabe which uses $\Theta (n)$ 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 enables a prover to physically show that he/she know solutions of the puzzles without revealing them.

A preliminary version of this paper has appeared at FAW 2023

References in corpus (6)

• Two Standard Decks of Playing Cards are Sufficient for a ZKP for Sudoku
• Physical ZKP for Connected Spanning Subgraph: Applications to Bridges Puzzle and Other Problems
• Physical Zero-Knowledge Proof for Ripple Effect
• Physical ZKP for Makaro Using a Standard Deck of Cards
• An Improved Physical ZKP for Nonogram and Nonogram Color
• Physical Zero-Knowledge Proof for Ball Sort Puzzle

Cited by in corpus (2)

• NP-Completeness and Physical Zero-Knowledge Proofs for Zeiger
• Tatami Printer: Physical ZKPs for Tatami Puzzles