Voting with a Logarithmic Number of Cards

  • Takaaki Mizuki
  • Isaac Kobina Asiedu
  • Hideaki Sone
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7956)

Abstract

Consider an election where there are two candidates and several voters. Such an election usually requires the same number of ballot papers as the number of voters. In this paper, we show that such an election can be conducted using only a logarithmic number of cards with two suits—black and red—with identical backs. That is, we can securely compute the summation of a number of inputs (0s and 1s) using a logarithmic number of cards with respect to the number of inputs.

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References

  1. 1.
    Balogh, J., Csirik, J.A., Ishai, Y., Kushilevitz, E.: Private computation using a PEZ dispenser. Theoretical Computer Science 306, 69–84 (2003)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Fagin, R., Naor, M., Winkler, P.: Comparing information without leaking it. Communications of the ACM 39(5), 77–85 (1996)CrossRefGoogle Scholar
  4. 4.
    Crépeau, C., Kilian, J.: Discreet solitary games. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 319–330. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  5. 5.
    Goldreich, O.: Foundations of Cryptography II: Basic Applications. Cambridge University Press, Cambridge (2004)MATHCrossRefGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Mizuki, T., Uchiike, F., Sone, H.: Securely computing XOR with 10 cards. Australasian Journal of Combinatorics 36, 279–293 (2006)MathSciNetMATHGoogle Scholar
  9. 9.
    Moran, T., Naor, M.: Polling with physical envelopes: A rigorous analysis of a human-centric protocol. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 88–108. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Niemi, V., Renvall, A.: Secure multiparty computations without computers. Theoretical Computer Science 191, 173–183 (1998)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Schneider, T.: Engineering Secure Two-Party Computation Protocols. Springer, Heidelberg (2012)MATHCrossRefGoogle Scholar
  12. 12.
    Stiglic, A.: Computations with a deck of cards. Theoretical Computer Science 259, 671–678 (2001)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Yao, A.: Protocols for secure computations. In: Proceedings of the 23th IEEE Symposium on Foundations of Computer Science, FOCS 1982, pp. 160–164 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Takaaki Mizuki
    • 1
  • Isaac Kobina Asiedu
    • 1
  • Hideaki Sone
    • 1
  1. 1.Cyberscience CenterTohoku UniversityAobaJapan

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