{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T10:42:25Z","timestamp":1779360145445,"version":"3.51.4"},"publisher-location":"Cham","reference-count":52,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032156402","type":"print"},{"value":"9783032156419","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-15641-9_23","type":"book-chapter","created":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T11:37:09Z","timestamp":1769773029000},"page":"344-360","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Gakmoro: An Application of\u00a0Physical Secure Computation to\u00a0Card Game"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8698-1043","authenticated-orcid":false,"given":"Takaaki","family":"Mizuki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomoki","family":"Kuzuma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomoya","family":"Hirano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ririn","family":"Oshima","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-7122-5380","authenticated-orcid":false,"given":"Momofuku","family":"Yasuda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,31]]},"reference":[{"key":"23_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1007\/3-540-46885-4_23","volume-title":"Advances in Cryptology \u2014 EUROCRYPT \u201989","author":"B Boer","year":"1990","unstructured":"Boer, B.: More efficient match-making and satisfiability the five card trick. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 208\u2013217. Springer, Heidelberg (1990). https:\/\/doi.org\/10.1007\/3-540-46885-4_23"},{"key":"23_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/978-3-030-03232-6_8","volume-title":"Stabilization, Safety, and Security of Distributed Systems","author":"X Bultel","year":"2018","unstructured":"Bultel, X., et al.: Physical zero-knowledge proof for Makaro. In: Izumi, T., Kuznetsov, P. (eds.) SSS 2018. LNCS, vol. 11201, pp. 111\u2013125. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03232-6_8"},{"key":"23_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/3-540-48329-2_27","volume-title":"Advances in Cryptology \u2014 CRYPTO\u2019 93","author":"C Cr\u00e9peau","year":"1994","unstructured":"Cr\u00e9peau, C., Kilian, J.: Discreet solitary games. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 319\u2013330. Springer, Heidelberg (1994). https:\/\/doi.org\/10.1007\/3-540-48329-2_27"},{"key":"23_CR4","doi-asserted-by":"publisher","unstructured":"Doi, A., et al.: Card-based protocols for private set intersection and union. New Gener. Comput. 42, 359\u2013380 (2024). https:\/\/doi.org\/10.1007\/s00354-024-00268-z","DOI":"10.1007\/s00354-024-00268-z"},{"issue":"1","key":"23_CR5","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1111\/bjet.13482","volume":"56","author":"X Gong","year":"2025","unstructured":"Gong, X., Xu, W., Yu, S., Ma, J., Qiao, A.: Enhancing computational thinking and spatial reasoning skills in gamification programming learning: a comparative study of tangible, block and paper-and-pencil tools. Br. J. Edu. Technol. 56(1), 80\u2013102 (2025). https:\/\/doi.org\/10.1111\/bjet.13482","journal-title":"Br. J. Edu. Technol."},{"key":"23_CR6","doi-asserted-by":"publisher","unstructured":"Haga, R., Hayashi, Y., Miyahara, D., Mizuki, T.: Card-minimal protocols for three-input functions with standard playing cards. In: Batina, L., Daemen, J. (eds.) AFRICACRYPT 2022. LNCS, vol. 13503, pp. 448\u2013468. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-17433-9_19","DOI":"10.1007\/978-3-031-17433-9_19"},{"key":"23_CR7","doi-asserted-by":"publisher","unstructured":"Hand, S., Koch, A., Lafourcade, P., Miyahara, D., Robert, L.: Efficient card-based ZKP for single loop condition and its application to Moon-or-Sun. New Gener. Comput. 42, 449\u2013477 (2024). https:\/\/doi.org\/10.1007\/s00354-024-00274-1","DOI":"10.1007\/s00354-024-00274-1"},{"key":"23_CR8","doi-asserted-by":"publisher","unstructured":"Hashimoto, Y., Shinagawa, K., Nuida, K., Inamura, M., Hanaoka, G.: Secure grouping protocol using a deck of cards. IEICE Trans. Fundam. E101.A(9), 1512\u20131524 (2018). https:\/\/doi.org\/10.1587\/transfun.E101.A.1512","DOI":"10.1587\/transfun.E101.A.1512"},{"key":"23_CR9","doi-asserted-by":"publisher","unstructured":"Hatsugai, K., Ruangwises, S., Asano, K., Abe, Y.: NP-completeness and physical zero-knowledge proofs for Sumplete, a puzzle generated by ChatGPT. New Gener. Comput. 42, 429\u2013448 (2024). https:\/\/doi.org\/10.1007\/s00354-024-00267-0","DOI":"10.1007\/s00354-024-00267-0"},{"key":"23_CR10","doi-asserted-by":"publisher","unstructured":"Honda, Y., Shinagawa, K.: Efficient card-based protocols with a standard deck of playing cards using partial opening. In: Minematsu, K., Mimura, M. (eds.) Advances in Information and Computer Security. LNCS, vol. 14977, pp. 85\u2013100. Springer, Singapore (2024). https:\/\/doi.org\/10.1007\/978-981-97-7737-2_5","DOI":"10.1007\/978-981-97-7737-2_5"},{"key":"23_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/978-3-319-21819-9_16","volume-title":"Unconventional Computation and Natural Computation","author":"R Ishikawa","year":"2015","unstructured":"Ishikawa, R., Chida, E., Mizuki, T.: Efficient card-based protocols for generating a hidden random permutation without fixed points. In: Calude, C.S., Dinneen, M.J. (eds.) UCNC 2015. LNCS, vol. 9252, pp. 215\u2013226. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-21819-9_16"},{"key":"23_CR12","doi-asserted-by":"publisher","unstructured":"Isuzugawa, R., Miyahara, D., Mizuki, T.: Zero-knowledge proof protocol for Cryptarithmetic using dihedral cards. In: Kostitsyna, I., Orponen, P. (eds.) Unconventional Computation and Natural Computation. LNCS, vol. 12984, pp. 51\u201367. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-87993-8_4","DOI":"10.1007\/978-3-030-87993-8_4"},{"key":"23_CR13","doi-asserted-by":"publisher","unstructured":"Ito, Y., Shikata, H., Suganuma, T., Mizuki, T.: Card-based cryptography meets 3D printer. In: Cho, D.J., Kim, J. (eds.) Unconventional Computation and Natural Computation. LNCS, vol. 14776, pp. 74\u201388. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-63742-1_6","DOI":"10.1007\/978-3-031-63742-1_6"},{"key":"23_CR14","doi-asserted-by":"publisher","unstructured":"Iwamoto, C., Ohara, K.: Card-based zero-knowledge proof for Dosun-Fuwari. IEICE Trans. Fundam. (2025). https:\/\/doi.org\/10.1587\/transfun.2024DML0001","DOI":"10.1587\/transfun.2024DML0001"},{"key":"23_CR15","doi-asserted-by":"publisher","unstructured":"Koch, A.: The landscape of security from physical assumptions. In: IEEE Information Theory Workshop, pp.\u00a01\u20136. IEEE, NY (2021). https:\/\/doi.org\/10.1109\/ITW48936.2021.9611501","DOI":"10.1109\/ITW48936.2021.9611501"},{"key":"23_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"488","DOI":"10.1007\/978-3-030-34578-5_18","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2019","author":"A Koch","year":"2019","unstructured":"Koch, A., Schrempp, M., Kirsten, M.: Card-based cryptography meets formal verification. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 488\u2013517. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-34578-5_18"},{"key":"23_CR17","doi-asserted-by":"publisher","unstructured":"Komano, Y., Mizuki, T.: Card-based zero-knowledge proof protocol for pancake sorting. In: Bella, G., Doinea, M., Janicke, H. (eds.) Innovative Security Solutions for Information Technology and Communications. LNCS, vol. 13809, pp. 222\u2013239. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-32636-3_13","DOI":"10.1007\/978-3-031-32636-3_13"},{"key":"23_CR18","doi-asserted-by":"publisher","unstructured":"Komano, Y., Mizuki, T.: Physical zero-knowledge proof protocols for Topswops and Botdrops. New Gener. Comput. 42, 399\u2013428 (2024). https:\/\/doi.org\/10.1007\/s00354-024-00272-3","DOI":"10.1007\/s00354-024-00272-3"},{"key":"23_CR19","doi-asserted-by":"publisher","unstructured":"Koyama, H., Miyahara, D., Mizuki, T., Sone, H.: A secure three-input AND protocol with a standard deck of minimal cards. In: Santhanam, R., Musatov, D. (eds.) Computer Science \u2013 Theory and Applications. LNCS, vol. 12730, pp. 242\u2013256. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-79416-3_14","DOI":"10.1007\/978-3-030-79416-3_14"},{"key":"23_CR20","doi-asserted-by":"publisher","unstructured":"Manabe, Y., Ono, H.: Card-based cryptographic protocols with a standard deck of cards using private operations. New Gener. Comput. 42, 305\u2013329 (2024). https:\/\/doi.org\/10.1007\/s00354-024-00257-2","DOI":"10.1007\/s00354-024-00257-2"},{"key":"23_CR21","doi-asserted-by":"publisher","unstructured":"Miyahara, D., Hayashi, Y., Mizuki, T., Sone, H.: Practical card-based implementations of Yao\u2019s millionaire protocol. Theor. Comput. Sci. 803, 207\u2013221 (2020). https:\/\/doi.org\/10.1016\/j.tcs.2019.11.005","DOI":"10.1016\/j.tcs.2019.11.005"},{"key":"23_CR22","doi-asserted-by":"publisher","unstructured":"Miyahara, D., Mizuki, T.: Secure computations through checking suits of playing cards. In: Li, M., Sun, X. (eds.) Frontiers in Algorithmics. LNCS, vol. 13461, pp. 110\u2013128. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-20796-9_9","DOI":"10.1007\/978-3-031-20796-9_9"},{"key":"23_CR23","doi-asserted-by":"publisher","unstructured":"Miyahara, D., Robert, L., Lafourcade, P., Mizuki, T.: ZKP protocols for Usowan, Herugolf, and Five Cells. Tsinghua Sci. Technol. 29(6), 1651\u20131666 (2024). https:\/\/doi.org\/10.26599\/TST.2023.9010153","DOI":"10.26599\/TST.2023.9010153"},{"key":"23_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1007\/978-3-319-48965-0_29","volume-title":"Cryptology and Network Security","author":"T Mizuki","year":"2016","unstructured":"Mizuki, T.: Efficient and secure multiparty computations using a standard deck of playing cards. In: Foresti, S., Persiano, G. (eds.) CANS 2016. LNCS, vol. 10052, pp. 484\u2013499. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-48965-0_29"},{"key":"23_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/978-3-642-39074-6_16","volume-title":"Unconventional Computation and Natural Computation","author":"T Mizuki","year":"2013","unstructured":"Mizuki, T., Asiedu, I.K., Sone, H.: Voting with a logarithmic number of cards. In: Mauri, G., Dennunzio, A., Manzoni, L., Porreca, A.E. (eds.) UCNC 2013. LNCS, vol. 7956, pp. 162\u2013173. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-39074-6_16"},{"key":"23_CR26","doi-asserted-by":"publisher","unstructured":"Mizuki, T., Shizuya, H.: A formalization of card-based cryptographic protocols via abstract machine. Int. J. Inf. Secur. 13(1), 15\u201323 (2014). https:\/\/doi.org\/10.1007\/s10207-013-0219-4","DOI":"10.1007\/s10207-013-0219-4"},{"key":"23_CR27","doi-asserted-by":"publisher","unstructured":"Mizuki, T., Shizuya, H.: Computational model of card-based cryptographic protocols and its applications. IEICE Trans. Fundam. E100.A(1), 3\u201311 (2017). https:\/\/doi.org\/10.1587\/transfun.E100.A.3","DOI":"10.1587\/transfun.E100.A.3"},{"key":"23_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1007\/978-3-642-02270-8_36","volume-title":"Frontiers in Algorithmics","author":"T Mizuki","year":"2009","unstructured":"Mizuki, T., Sone, H.: Six-card secure AND and four-card secure XOR. In: Deng, X., Hopcroft, J.E., Xue, J. (eds.) FAW 2009. LNCS, vol. 5598, pp. 358\u2013369. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-02270-8_36"},{"key":"23_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/978-3-030-68211-8_7","volume-title":"WALCOM: Algorithms and Computation","author":"S Murata","year":"2021","unstructured":"Murata, S., Miyahara, D., Mizuki, T., Sone, H.: Efficient generation of a card-based uniformly distributed random derangement. In: Uehara, R., Hong, S.-H., Nandy, S.C. (eds.) WALCOM 2021. LNCS, vol. 12635, pp. 78\u201389. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-68211-8_7"},{"key":"23_CR30","doi-asserted-by":"publisher","unstructured":"Nakai, T., Iwanari, K., Ono, T., Abe, Y., Watanabe, Y., Iwamoto, M.: Card-based cryptography with a standard deck of cards, revisited: Efficient protocols in the private model. New Gener. Comput. 42, 345\u2013358 (2024). https:\/\/doi.org\/10.1007\/s00354-024-00269-y","DOI":"10.1007\/s00354-024-00269-y"},{"key":"23_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1007\/978-3-319-48965-0_30","volume-title":"Cryptology and Network Security","author":"T Nakai","year":"2016","unstructured":"Nakai, T., Tokushige, Y., Misawa, Y., Iwamoto, M., Ohta, K.: Efficient card-based cryptographic protocols for millionaires\u2019 problem utilizing private permutations. In: Foresti, S., Persiano, G. (eds.) CANS 2016. LNCS, vol. 10052, pp. 500\u2013517. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-48965-0_30"},{"key":"23_CR32","doi-asserted-by":"publisher","unstructured":"Niemi, V., Renvall, A.: Solitaire zero-knowledge. Fundam. Inf. 38(1,2), 181\u2013188 (1999). https:\/\/doi.org\/10.3233\/FI-1999-381214","DOI":"10.3233\/FI-1999-381214"},{"key":"23_CR33","doi-asserted-by":"publisher","unstructured":"Nishimura, A., Hayashi, Y., Mizuki, T., Sone, H.: Pile-shifting scramble for card-based protocols. IEICE Trans. Fundam. 101(9), 1494\u20131502 (2018). https:\/\/doi.org\/10.1587\/transfun.E101.A.1494","DOI":"10.1587\/transfun.E101.A.1494"},{"key":"23_CR34","doi-asserted-by":"publisher","unstructured":"Nuida, K.: Efficient card-based Millionaires\u2019 protocols via non-binary input encoding. In: Shikata, J., Kuzuno, H. (eds.) Advances in Information and Computer Security. LNCS, vol. 14128, pp. 237\u2013254. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-41326-1_13","DOI":"10.1007\/978-3-031-41326-1_13"},{"key":"23_CR35","doi-asserted-by":"publisher","unstructured":"Odaka, S., Komano, Y.: Card-based arithmetic operations and application to statistical data aggregation. In: Morogan, L., Roenne, P., Bica, I. (eds.) Innovative Security Solutions for Information Technology and Communications. SecITC 2024. LNCS, vol. 15595, pp. 118\u2013134. Springer, Cham (2025). https:\/\/doi.org\/10.1007\/978-3-031-87760-5_10","DOI":"10.1007\/978-3-031-87760-5_10"},{"key":"23_CR36","doi-asserted-by":"publisher","unstructured":"Robert, L., Miyahara, D., Lafourcade, P., Mizuki, T.: Physical ZKP protocols for Nurimisaki and Kurodoko. Theor. Comput. Sci. 972, 114071 (2023). https:\/\/doi.org\/10.1016\/j.tcs.2023.114071","DOI":"10.1016\/j.tcs.2023.114071"},{"key":"23_CR37","doi-asserted-by":"publisher","unstructured":"Ruangwises, S., Itoh, T.: Physical ZKP for connected spanning subgraph: Applications to Bridges puzzle and other problems. In: Kostitsyna, I., Orponen, P. (eds.) Unconventional Computation and Natural Computation, LNCS, vol. 12984, pp. 149\u2013163. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-87993-8_10","DOI":"10.1007\/978-3-030-87993-8_10"},{"key":"23_CR38","doi-asserted-by":"publisher","unstructured":"Ruangwises, S., Itoh, T.: Securely computing the n-variable equality function with 2n cards. Theor. Comput. Sci. 887, 99\u2013110 (2021). https:\/\/doi.org\/10.1016\/j.tcs.2021.07.007","DOI":"10.1016\/j.tcs.2021.07.007"},{"key":"23_CR39","doi-asserted-by":"publisher","unstructured":"Ruangwises, S., Ono, T., Abe, Y., Hatsugai, K., Iwamoto, M.: Card-based overwriting protocol for equality function and applications. In: Cho, D.J., Kim, J. (eds.) Unconventional Computation and Natural Computation. LNCS, vol. 14776, pp. 18\u201327. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-63742-1_2","DOI":"10.1007\/978-3-031-63742-1_2"},{"key":"23_CR40","doi-asserted-by":"publisher","unstructured":"Ruangwises, S., Shinagawa, K.: Simulating virtual players for UNO without computers. arXiv preprint (2025). https:\/\/doi.org\/10.48550\/arXiv.2502.05987, https:\/\/arxiv.org\/abs\/2502.05987","DOI":"10.48550\/arXiv.2502.05987"},{"key":"23_CR41","doi-asserted-by":"publisher","unstructured":"Shinagawa, K., Kanai, K., Miyamoto, K., Nuida, K.: How to covertly and uniformly scramble the 15 puzzle and Rubik\u2019s cube. In: Broder, A.Z., Tamir, T. (eds.) Fun with Algorithms. LIPIcs, vol.\u00a0291, pp. 30:1\u201330:15. Schloss Dagstuhl, Dagstuhl, Germany (2024). https:\/\/doi.org\/10.4230\/LIPIcs.FUN.2024.30","DOI":"10.4230\/LIPIcs.FUN.2024.30"},{"key":"23_CR42","doi-asserted-by":"publisher","unstructured":"Shinagawa, K., Miyahara, D., Mizuki, T.: How to play old maid with virtual players. Theory Comput. Syst. 69(1) (2025). https:\/\/doi.org\/10.1007\/s00224-024-10203-w","DOI":"10.1007\/s00224-024-10203-w"},{"key":"23_CR43","doi-asserted-by":"publisher","unstructured":"Shinagawa, K., et al.: Card-based protocols using regular polygon cards. IEICE Trans. Fundam. E100.A(9), 1900\u20131909 (2017). https:\/\/doi.org\/10.1587\/transfun.E100.A.1900","DOI":"10.1587\/transfun.E100.A.1900"},{"key":"23_CR44","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/978-3-030-69255-1_17","volume-title":"Innovative Security Solutions for Information Technology and Communications","author":"Y Shinoda","year":"2021","unstructured":"Shinoda, Y., Miyahara, D., Shinagawa, K., Mizuki, T., Sone, H.: Card-based covert lottery. In: Maimut, D., Oprina, A.-G., Sauveron, D. (eds.) SecITC 2020. LNCS, vol. 12596, pp. 257\u2013270. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-69255-1_17"},{"key":"23_CR45","doi-asserted-by":"publisher","unstructured":"Takahashi, Y., Shinagawa, K.: Extended addition protocol and efficient voting protocols using regular polygon cards. New Gener. Comput. 42, 479\u2013496 (2024). https:\/\/doi.org\/10.1007\/s00354-024-00275-0","DOI":"10.1007\/s00354-024-00275-0"},{"key":"23_CR46","doi-asserted-by":"publisher","unstructured":"Takahashi, Y., Shinagawa, K., Shikata, H., Mizuki, T.: Efficient card-based protocols for symmetric functions using four-colored decks. In: ACM ASIA Public-Key Cryptography Workshop, pp. 1\u201310. ACM, New York (2024). https:\/\/doi.org\/10.1145\/3659467.3659902","DOI":"10.1145\/3659467.3659902"},{"key":"23_CR47","doi-asserted-by":"publisher","unstructured":"Tamura, Y., Suzuki, A., Mizuki, T.: Card-based zero-knowledge proof protocols for the 15-puzzle and the token swapping problem. In: ACM ASIA Public-Key Cryptography Workshop, pp. 11\u201322. ACM, New York (2024). https:\/\/doi.org\/10.1145\/3659467.3659905","DOI":"10.1145\/3659467.3659905"},{"key":"23_CR48","doi-asserted-by":"publisher","unstructured":"Tanaka, K., Sasaki, S., Shinagawa, K., Mizuki, T.: Only two shuffles perform card-based zero-knowledge proof for Sudoku of any size. In: 2025 Symposium on Simplicity in Algorithms (SOSA), pp. 94\u2013107. SIAM (2025). https:\/\/doi.org\/10.1137\/1.9781611978315.7","DOI":"10.1137\/1.9781611978315.7"},{"key":"23_CR49","doi-asserted-by":"publisher","unstructured":"Tozawa, K., Morita, H., Mizuki, T.: Single-shuffle card-based protocol with eight cards per gate. In: Genova, D., Kari, J. (eds.) Unconventional Computation and Natural Computation. LNCS, vol. 14003, pp. 171\u2013185. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-34034-5_12","DOI":"10.1007\/978-3-031-34034-5_12"},{"key":"23_CR50","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1007\/978-3-319-49001-4_5","volume-title":"Theory and Practice of Natural Computing","author":"I Ueda","year":"2016","unstructured":"Ueda, I., Nishimura, A., Hayashi, Y., Mizuki, T., Sone, H.: How to implement a random bisection cut. In: Mart\u00edn-Vide, C., Mizuki, T., Vega-Rodr\u00edguez, M.A. (eds.) TPNC 2016. LNCS, vol. 10071, pp. 58\u201369. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-49001-4_5"},{"key":"23_CR51","doi-asserted-by":"publisher","unstructured":"Yao, A.C.: Protocols for secure computations. In: Foundations of Computer Science, pp. 160\u2013164. IEEE Computer Society, Washington, DC, USA (1982). https:\/\/doi.org\/10.1109\/SFCS.1982.88","DOI":"10.1109\/SFCS.1982.88"},{"key":"23_CR52","doi-asserted-by":"publisher","unstructured":"Yoshida, T., Tanaka, K., Nakabayashi, K., Chida, E., Mizuki, T.: Upper bounds on the number of shuffles for two-helping-card multi-input AND protocols. In: Deng, J., Kolesnikov, V., Schwarzmann, A.A. (eds.) Cryptology and Network Security. LNCS, vol. 14342, pp. 211\u2013231. Springer, Singapore (2023). https:\/\/doi.org\/10.1007\/978-981-99-7563-1_10","DOI":"10.1007\/978-981-99-7563-1_10"}],"container-title":["Lecture Notes in Computer Science","Unconventional Computation and Natural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-15641-9_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T11:37:11Z","timestamp":1769773031000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-15641-9_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032156402","9783032156419"],"references-count":52,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-15641-9_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"31 January 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"UCNC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Unconventional Computation and Natural Computation","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Nice","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"uc2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/webusers.i3s.univ-cotedazur.fr\/UCNC2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}