Abstract
Secure multi-party computation using a deck of playing cards has been a subject of research since the “five-card trick” introduced by den Boer in 1989. One of the main problems in card-based cryptography is to design committed-format protocols to compute a Boolean AND operation subject to different runtime and shuffle restrictions by using as few cards as possible. In this paper, we introduce two AND protocols that use only uniform shuffles. The first one requires four cards and is a restart-free Las Vegas protocol with finite expected runtime. The second one requires five cards and always terminates in finite time.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abe, Y., Hayashi, Y., Mizuki, T., Sone, H.: Five-card AND protocol in committed format using only practical shuffles. In: Proceedings of the 5th ACM on ASIA Public-Key Cryptography Workshop (APKC 2018), pp. 3–8 (2018)
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
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
Kastner, J., et al.: The minimum number of cards in practical card-based protocols. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10626, pp. 126–155. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_5
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
Koch, A.: The Landscape of Optimal Card-based Protocols. Cryptology ePrint Archive (2018). https://eprint.iacr.org/2018/951/20181009:160322
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
Mizuki, T., Shizuya, H.: A formalization of card-based crypto-graphic protocols via abstract machine. Int. J. Inf. Secur. 13, 15–23 (2014)
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
Niemi, V., Renvall, A.: Secure multiparty computations without computers. Theor. Comput. Sci. 191, 173–183 (1998)
Stiglic, A.: Computations with a deck of cards. Theor. Comput. Sci. 259, 671–678 (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Ruangwises, S., Itoh, T. (2019). AND Protocols Using only Uniform Shuffles. In: van Bevern, R., Kucherov, G. (eds) Computer Science – Theory and Applications. CSR 2019. Lecture Notes in Computer Science(), vol 11532. Springer, Cham. https://doi.org/10.1007/978-3-030-19955-5_30
Download citation
DOI: https://doi.org/10.1007/978-3-030-19955-5_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-19954-8
Online ISBN: 978-3-030-19955-5
eBook Packages: Computer ScienceComputer Science (R0)