Card-Based Zero-Knowledge Proof Protocols for Graph Problems and Their Computational Model

Daiki Miyahara, Hiromichi Haneda, Takaaki Mizuki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


Zero-Knowledge Proof (ZKP) is a cryptographic technique that enables a prover to convince a verifier that a given statement is true without revealing any information other than its truth. It is known that ZKP can be realized by physical objects such as a deck of cards; recently, many such “card-based” ZKP protocols for pencil puzzles (such as Sudoku and Numberlink) have been devised. In this paper, we shift our attention to graph theory problems from pencil puzzles: We propose card-based ZKP protocols for the graph 3-coloring problem and the graph isomorphism problem. Similar to most of the existing card-based ZKP protocols, our two protocols have no soundness error. The proposed protocols can be implemented without any technical knowledge, and the principle of zero-knowledge proof is easy to understand. In particular, our protocol for the graph isomorphism problem requires only three shuffles regardless of the sizes of a pair of given graphs. In addition, to deal with our proposed protocols more rigorously, we present a formal framework for card-based ZKP protocols which are non-interactive and have no soundness error.

Original languageEnglish
Title of host publicationProvable and Practical Security - 15th International Conference, ProvSec 2021, Proceedings
EditorsQiong Huang, Yu Yu
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages17
ISBN (Print)9783030904012
Publication statusPublished - 2021
Externally publishedYes
Event15th International Conference on Provable Security, ProvSec 2021 - Guangzhou, China
Duration: 2021 Nov 52021 Nov 8

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13059 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Conference on Provable Security, ProvSec 2021


  • Card-based cryptography
  • Graph 3-coloring problem
  • Graph isomorphism problem
  • Physical zero-knowledge proof

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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