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Card-Based Overwriting Protocol for Equality Function and Applications

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Unconventional Computation and Natural Computation (UCNC 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14776))

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Abstract

Research in the area of secure multi-party computation with an unconventional method of using a physical deck of playing cards began in 1989 when den Boer proposed a protocol to compute the logical AND function using five cards. Since then, the area has gained interest from many researchers and several card-based protocols to compute various functions have been developed. In this paper, we propose a card-based protocol called the overwriting protocol that can securely compute the k-candidate n-variable equality function \(f: \{0,1,\ldots ,k-1\}^n \rightarrow \{0,1\}\). We also apply the technique used in this protocol to compute other similar functions.

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References

  1. Abe, Y., Hayashi, Y., Mizuki, T., Sone, H.: Five-Card AND computations in committed format using only uniform cyclic shuffles. N. Gener. Comput. 39(1), 97–114 (2021)

    Article  Google Scholar 

  2. Crépeau, C., Kilian, J.: Discreet solitary games. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 319–330. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_27

    Chapter  Google Scholar 

  3. den 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. 208–217. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-46885-4_23

    Chapter  Google Scholar 

  4. Heather, J., Schneider, S., Teague, V.: Cryptographic protocols with everyday objects. Formal Aspects Comput. 26(1), 37–62 (2014)

    Article  Google Scholar 

  5. 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. 215–226. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21819-9_16

    Chapter  Google Scholar 

  6. Koch, A.: The landscape of optimal card-based protocols. Math. Cryptol. 1(2), 115–131 (2021)

    MathSciNet  Google Scholar 

  7. Koch, A., Walzer, S., Härtel, K.: Card-based cryptographic protocols using a minimal number of cards. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 783–807. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_32

    Chapter  Google Scholar 

  8. Komano, Y., Mizuki, T.: Coin-based secure computations. Int. J. Inf. Secur. 21(4), 833–846 (2022)

    Article  Google Scholar 

  9. Mizuki, T., Asiedu, I.K., Sone, H.: Voting with a logarithmic number of cards. In: Proceedings of the 12th International Conference on Unconventional Computation and Natural Computation (UCNC), pp. 162–173 (2013)

    Google Scholar 

  10. Mizuki, T., Kugimoto, Y., Sone, H.: Secure multiparty computations using a dial lock. In: Proceedings of the 4th Annual Conference on Theory and Applications of Models of Computation (TAMC), pp. 499–510 (2007)

    Google Scholar 

  11. Mizuki, T., Kumamoto, M., Sone, H.: The five-card trick can be done with four cards. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 598–606. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_36

    Chapter  Google Scholar 

  12. 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. 358–369. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02270-8_36

    Chapter  Google Scholar 

  13. Mizuki, T., Uchiike, F., Sone, H.: Securely computing XOR with 10 cards. Australas. J. Combin. 36, 279–293 (2006)

    MathSciNet  Google Scholar 

  14. Niemi, V., Renvall, A.: Secure multiparty computations without computers. Theoret. Comput. Sci. 191, 173–183 (1998)

    Article  MathSciNet  Google Scholar 

  15. Nishida, T., Hayashi, Y., Mizuki, T., Sone, H.: Card-based protocols for any boolean function. In: Jain, R., Jain, S., Stephan, F. (eds.) TAMC 2015. LNCS, vol. 9076, pp. 110–121. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-17142-5_11

    Chapter  Google Scholar 

  16. Nishida, T., Mizuki, T., Sone, H.: Securely computing the three-input majority function with eight cards. In: Dediu, A.-H., Martín-Vide, C., Truthe, B., Vega-Rodríguez, M.A. (eds.) TPNC 2013. LNCS, vol. 8273, pp. 193–204. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-45008-2_16

    Chapter  Google Scholar 

  17. Ruangwises, S.: The landscape of computing symmetric \(n\)-variable functions with \(2n\) cards. In: Proceedings of the 20th International Colloquium on Theoretical Aspects of Computing (ICTAC), pp. 74–82 (2023)

    Google Scholar 

  18. Ruangwises, S.: Using five cards to encode each integer in \(\mathbb{Z}\)/6\(\mathbb{Z}\). In: Ryan, P.Y., Toma, C. (eds.) Proceedings of the 14th International Conference on Security for Information Technology and Communications (SecITC), pp. 165–177. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-17510-7_12

  19. Ruangwises, S., Itoh, T.: AND protocols using only uniform shuffles. In: van Bevern, R., Kucherov, G. (eds.) CSR 2019. LNCS, vol. 11532, pp. 349–358. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-19955-5_30

    Chapter  Google Scholar 

  20. Ruangwises, S., Itoh, T.: Securely computing the \(n\)-variable equality function with \(2n\) cards. Theoret. Comput. Sci. 887, 99–110 (2021)

    Article  MathSciNet  Google Scholar 

  21. Shinagawa, K., Mizuki, T.: Card-based protocols using triangle cards. In: Proceedings of the 9th International Conference on Fun with Algorithms (FUN), pp. 31:1–31:13 (2018)

    Google Scholar 

  22. Shinagawa, K., Mizuki, T.: The six-card trick: secure computation of three-input equality. In: Lee, K. (ed.) ICISC 2018. LNCS, vol. 11396, pp. 123–131. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-12146-4_8

    Chapter  Google Scholar 

  23. Shinagawa, K., et al.: Card-based protocols using regular polygon cards. IEICE Trans. Fundamentals 100.A(9), 1900–1909 (2017)

    Google Scholar 

  24. Stiglic, A.: Computations with a deck of cards. Theoret. Comput. Sci. 259, 671–678 (2001)

    Article  MathSciNet  Google Scholar 

  25. Toyoda, K., Miyahara, D., Mizuki, T.: Another use of the five-card trick: card-minimal secure three-input majority function evaluation. In: Adhikari, A., Küsters, R., Preneel, B. (eds.) INDOCRYPT 2021. LNCS, vol. 13143, pp. 536–555. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92518-5_24

    Chapter  Google Scholar 

  26. Ueda, I., Miyahara, D., Nishimura, A., Hayashi, Y., Mizuki, T., Sone, H.: Secure implementations of a random bisection cut. Int. J. Inf. Secur. 19(4), 445–452 (2020)

    Article  Google Scholar 

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Authors and Affiliations

  1. The University of Electro-Communications, Tokyo, Japan

    Suthee Ruangwises, Tomoki Ono, Yoshiki Abe, Kyosuke Hatsugai & Mitsugu Iwamoto

  2. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Yoshiki Abe

Authors
  1. Suthee Ruangwises
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  2. Tomoki Ono
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  3. Yoshiki Abe
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  4. Kyosuke Hatsugai
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  5. Mitsugu Iwamoto
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Correspondence to Suthee Ruangwises .

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Editors and Affiliations

  1. Ajou University, Suwon, Korea (Republic of)

    Da-Jung Cho

  2. Pohang University of Science and Technology, Pohang, Korea (Republic of)

    Jongmin Kim

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Ruangwises, S., Ono, T., Abe, Y., Hatsugai, K., Iwamoto, M. (2024). Card-Based Overwriting Protocol for Equality Function and Applications. In: Cho, DJ., Kim, J. (eds) Unconventional Computation and Natural Computation. UCNC 2024. Lecture Notes in Computer Science, vol 14776. Springer, Cham. https://doi.org/10.1007/978-3-031-63742-1_2

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  • DOI: https://doi.org/10.1007/978-3-031-63742-1_2

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  • Print ISBN: 978-3-031-63741-4

  • Online ISBN: 978-3-031-63742-1

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