An Efficient Solution to the Millionaires’ Problem Based on Homomorphic Encryption

  • Hsiao-Ying Lin
  • Wen-Guey Tzeng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3531)


We proposed a two-round protocol for solving the Millionaires’ Problem in the setting of semi-honest parties. Our protocol uses either multiplicative or additive homomorphic encryptions. Previously proposed protocols used additive or XOR homomorphic encryption schemes only. The computation and communication costs of our protocol are in the same asymptotic order as those of the other efficient protocols. Nevertheless, since multiplicative homomorphic encryption scheme is more efficient than an additive one practically, our construction saves computation time and communication bandwidth in practicality.


secure computation the greater than problem the socialist millionaires’ problem homomorphic encryption 


  1. [BK04]
    Blake, I.F., Kolesnikov, V.: Strong conditional oblivious transfer and computing on intervals. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 515–529. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. [Cac99]
    Cachin, C.: Efficient private bidding and auctions with an oblivious third party. In: Proceedings of the 6th ACM conference on Computer and communications security - CCS 1999, pp. 120–127. ACM Press, New York (1999)CrossRefGoogle Scholar
  3. [Fis01]
    Fischlin, M.: A Cost-Effective Pay-Per-Multiplication Comparison Method for Millionaires. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 457–472. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. [FNP04]
    Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. [GMW87]
    Goldreich, O., Micali, S., Wigderson, A.: How to play and mental game. In: Proceedings of the 16th Annual ACM Symposium on the Theory of Computing (STOC 1987), pp. 218–229. ACM, New York (1987)Google Scholar
  6. [IG03]
    Ioannidis, I., Grama, A.: An efficient protocol for yao’s millionaires’ problem. In: Proceedings of the 36th Hawaii Internatinal Conference on System Sciences 2003 (2003)Google Scholar
  7. [ST04]
    Schoenmakers, B., Tuyls, P.: Practical Two-Party Computation Based on the Conditional Gate. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 119–136. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. [Yao82]
    Yao, A.C.: Protocols for secure computations. In: Proceedings of 23th Annual Symposium on Foundations of Computer Science (FOCS 1982), pp. 160–164. IEEE, Los Alamitos (1982)CrossRefGoogle Scholar
  9. [Yao86]
    Yao, A.C.: How to generate and exchange secrets. In: Proceedings of 27th Annual Symposium on Foundations of Computer Science (FOCS 1986), pp. 162–167. IEEE, Los Alamitos (1986)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hsiao-Ying Lin
    • 1
  • Wen-Guey Tzeng
    • 1
  1. 1.Department of Computer and Information ScienceNational Chiao Tung UniversityHsinchuTaiwan

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