Efficient card-based zero-knowledge proof for Sudoku

Tatsuya Sasaki, Daiki Miyahara, Takaaki Mizuki, Hideaki Sone

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


In 2009, Gradwohl, Naor, Pinkas, and Rothblum proposed physical zero-knowledge proof protocols for Sudoku. That is, for a puzzle instance of Sudoku, their excellent protocols allow a prover to convince a verifier that there is a solution to the Sudoku puzzle and the prover knows it, without revealing any information about the solution. The possible drawback is that the existing protocols have an extractability error with a non-zero probability, or need special cards (such as scratch-off cards). Thus, in this study, we propose new protocols to perform zero-knowledge proof of knowledge for Sudoku using a normal deck of playing cards with no extractability error. Our protocols can be easily implemented by humans with a reasonable number of playing cards.

Original languageEnglish
Pages (from-to)135-142
Number of pages8
JournalTheoretical Computer Science
Publication statusPublished - 2020 Nov 2


  • Card-based cryptography
  • Sudoku
  • Zero-knowledge proof


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