Efficient card-based zero-knowledge proof for Sudoku
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 revealin...
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| Published in | Theoretical computer science Vol. 839; pp. 135 - 142 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
02.11.2020
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Sone, Hideaki Mizuki, Takaaki Sasaki, Tatsuya Miyahara, Daiki |
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| Cites_doi | 10.1007/s00224-008-9119-9 10.1137/0218012 10.1145/116825.116852 |
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| References | Yato, Seta (br0100) 2003; 86-A Goldreich, Micali, Wigderson (br0090) 1991; 38 Chien, Hon (br0040) 2010; vol. 6099 Goldwasser, Micali, Rackoff (br0020) 1989; 18 Ibaraki, Manabe (br0080) 2016 Ishikawa, Chida, Mizuki (br0110) 2015; vol. 9252 Bultel, Dreier, Dumas, Lafourcade, Miyahara, Mizuki, Nagao, Sasaki, Shinagawa, Sone (br0120) 2018; vol. 11201 Bultel, Dreier, Dumas, Lafourcade (br0030) 2016; vol. 49 Gradwohl, Naor, Pinkas, Rothblum (br0050) 2009; 44 Hashimoto, Shinagawa, Nuida, Inamura, Hanaoka (br0060) 2017; vol. 10681 Mizuki, Shizuya (br0070) 2014; vol. 8496 Sasaki, Mizuki, Sone (br0010) 2018; vol. 100 Chien (10.1016/j.tcs.2020.05.036_br0040) 2010; vol. 6099 Ibaraki (10.1016/j.tcs.2020.05.036_br0080) 2016 Bultel (10.1016/j.tcs.2020.05.036_br0120) 2018; vol. 11201 Gradwohl (10.1016/j.tcs.2020.05.036_br0050) 2009; 44 Goldreich (10.1016/j.tcs.2020.05.036_br0090) 1991; 38 Sasaki (10.1016/j.tcs.2020.05.036_br0010) 2018; vol. 100 Bultel (10.1016/j.tcs.2020.05.036_br0030) 2016; vol. 49 Yato (10.1016/j.tcs.2020.05.036_br0100) 2003; 86-A Goldwasser (10.1016/j.tcs.2020.05.036_br0020) 1989; 18 Hashimoto (10.1016/j.tcs.2020.05.036_br0060) 2017; vol. 10681 Mizuki (10.1016/j.tcs.2020.05.036_br0070) 2014; vol. 8496 Ishikawa (10.1016/j.tcs.2020.05.036_br0110) 2015; vol. 9252 |
| References_xml | – volume: vol. 9252 start-page: 215 year: 2015 end-page: 226 ident: br0110 article-title: Efficient card-based protocols for generating a hidden random permutation without fixed points publication-title: Unconventional Computation and Natural Computation - 14th International Conference, UCNC 2015, Auckland, New Zealand, August 30 - September 3, 2015, Proceedings – volume: 44 start-page: 245 year: 2009 end-page: 268 ident: br0050 article-title: Cryptographic and physical zero-knowledge proof systems for solutions of Sudoku puzzles publication-title: Theory Comput. Syst. – volume: vol. 10681 start-page: 135 year: 2017 end-page: 152 ident: br0060 article-title: Secure grouping protocol using a deck of cards publication-title: Information Theoretic Security - 10th International Conference, ICITS 2017, Hong Kong, China, November 29 - December 2, 2017, Proceedings – volume: vol. 8496 start-page: 313 year: 2014 end-page: 324 ident: br0070 article-title: Practical card-based cryptography publication-title: Fun with Algorithms - 7th International Conference, FUN 2014, Lipari Island, Sicily, Italy, July 1-3, 2014, Proceedings – volume: vol. 11201 start-page: 111 year: 2018 end-page: 125 ident: br0120 article-title: Physical zero-knowledge proof for Makaro publication-title: Stabilization, Safety, and Security of Distributed Systems - 20th International Symposium, SSS 2018, Tokyo, Japan, November 4-7, 2018, Proceedings – volume: 86-A start-page: 1052 year: 2003 end-page: 1060 ident: br0100 article-title: Complexity and completeness of finding another solution and its application to puzzles publication-title: IEICE Trans. – start-page: 252 year: 2016 end-page: 257 ident: br0080 article-title: A more efficient card-based protocol for generating a random permutation without fixed points publication-title: 2016 Third International Conference on Mathematics and Computers in Sciences and in Industry (MCSI) – volume: 18 start-page: 186 year: 1989 end-page: 208 ident: br0020 article-title: The knowledge complexity of interactive proof systems publication-title: SIAM J. Comput. – volume: vol. 49 start-page: 8:1 year: 2016 end-page: 8:20 ident: br0030 article-title: Physical zero-knowledge proofs for Akari, Takuzu, Kakuro and KenKen publication-title: 8th International Conference on Fun with Algorithms – volume: vol. 6099 start-page: 102 year: 2010 end-page: 112 ident: br0040 article-title: Cryptographic and physical zero-knowledge proof: from Sudoku to nonogram publication-title: Fun with Algorithms, 5th International Conference, FUN 2010, Ischia, Italy, June 2-4, 2010, Proceedings – volume: 38 start-page: 691 year: 1991 end-page: 729 ident: br0090 article-title: Proofs that yield nothing but their validity for all languages in NP have zero-knowledge proof systems publication-title: J. ACM – volume: vol. 100 start-page: 29:1 year: 2018 end-page: 29:10 ident: br0010 article-title: Card-based zero-knowledge proof for Sudoku publication-title: 9th International Conference on Fun with Algorithms – volume: vol. 49 start-page: 8:1 year: 2016 ident: 10.1016/j.tcs.2020.05.036_br0030 article-title: Physical zero-knowledge proofs for Akari, Takuzu, Kakuro and KenKen – volume: vol. 11201 start-page: 111 year: 2018 ident: 10.1016/j.tcs.2020.05.036_br0120 article-title: Physical zero-knowledge proof for Makaro – volume: 86-A start-page: 1052 issue: 5 year: 2003 ident: 10.1016/j.tcs.2020.05.036_br0100 article-title: Complexity and completeness of finding another solution and its application to puzzles publication-title: IEICE Trans. – volume: vol. 100 start-page: 29:1 year: 2018 ident: 10.1016/j.tcs.2020.05.036_br0010 article-title: Card-based zero-knowledge proof for Sudoku – volume: 44 start-page: 245 issue: 2 year: 2009 ident: 10.1016/j.tcs.2020.05.036_br0050 article-title: Cryptographic and physical zero-knowledge proof systems for solutions of Sudoku puzzles publication-title: Theory Comput. Syst. doi: 10.1007/s00224-008-9119-9 – volume: vol. 8496 start-page: 313 year: 2014 ident: 10.1016/j.tcs.2020.05.036_br0070 article-title: Practical card-based cryptography – volume: 18 start-page: 186 issue: 1 year: 1989 ident: 10.1016/j.tcs.2020.05.036_br0020 article-title: The knowledge complexity of interactive proof systems publication-title: SIAM J. Comput. doi: 10.1137/0218012 – volume: vol. 6099 start-page: 102 year: 2010 ident: 10.1016/j.tcs.2020.05.036_br0040 article-title: Cryptographic and physical zero-knowledge proof: from Sudoku to nonogram – volume: vol. 9252 start-page: 215 year: 2015 ident: 10.1016/j.tcs.2020.05.036_br0110 article-title: Efficient card-based protocols for generating a hidden random permutation without fixed points – volume: vol. 10681 start-page: 135 year: 2017 ident: 10.1016/j.tcs.2020.05.036_br0060 article-title: Secure grouping protocol using a deck of cards – start-page: 252 year: 2016 ident: 10.1016/j.tcs.2020.05.036_br0080 article-title: A more efficient card-based protocol for generating a random permutation without fixed points – volume: 38 start-page: 691 issue: 3 year: 1991 ident: 10.1016/j.tcs.2020.05.036_br0090 article-title: Proofs that yield nothing but their validity for all languages in NP have zero-knowledge proof systems publication-title: J. ACM doi: 10.1145/116825.116852 |
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| Title | Efficient card-based zero-knowledge proof for Sudoku |
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