Round-Efficient Private Stable Matching from Additive Homomorphic Encryption

  • Tadanori TeruyaEmail author
  • Jun Sakuma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7807)


In the present paper, we propose private stable matching protocols to solve the stable marriage problem with the round complexity \(O(n^2)\), where n is the problem size. In the multiparty setting, the round complexity of our protocol is better than all of the existing practical protocols. We also implement our protocol on a standard personal computer, smartphones, and tablet computers for experimental performance evaluation. Our protocols are constructed by using additive homomorphic encryption only, and this construction yields improved round complexity and implementation-friendliness. To the best of our knowledge, our experiment is the first implementation report of a private stable matching protocol that has a feasible running time.



The work is supported by FIRST program and Grant-in-Aid 12913388. The authors would like to thank Jacob Schuldt, Nuttapong Attrapadung, and Naoto Yanai for the valuable discussion and comments. We also thank the members of Shin-Akarui-Angou-Benkyou-Kai and the anonymous reviewers of ISC 2013 for their valuable discussion and comments.


  1. 1.
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: Ortiz, H. (ed.) STOC, pp. 503–513. ACM (1990)Google Scholar
  2. 2.
    Damgård, I.B., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  3. 3.
    Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  4. 4.
    ECRYPT II: Yearly report on algorithms and keysize (2011–2012), September 2012.
  5. 5.
    El Gamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985) CrossRefGoogle Scholar
  6. 6.
    Fouque, P.-A., Poupard, G., Stern, J.: Sharing decryption in the context of voting or lotteries. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 90–104. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  7. 7.
    Franklin, M.K., Gondree, M., Mohassel, P.: Improved efficiency for private stable matching. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 163–177. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  8. 8.
    Franklin, M.K., Gondree, M., Mohassel, P.: Multi-party indirect indexing and applications. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 283–297. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  9. 9.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Mon. 69(1), 9–15 (1962)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. J. Crypt. 20(1), 51–83 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Golle, P.: A private stable matching algorithm. In: Di Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, pp. 65–80. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  13. 13.
    Golle, P., Juels, A.: Parallel mixing. In: Atluri, V., Pfitzmann, B., McDaniel, P.D. (eds.) ACM Conference on Computer and Communications Security, pp. 220–226. ACM (2004)Google Scholar
  14. 14.
    Google, Open Handset Alliance: Android developers.
  15. 15.
    Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. The Foundations of Computing. MIT Press, Cambridge (1989) zbMATHGoogle Scholar
  16. 16.
    Lipmaa, H.: Verifiable homomorphic oblivious transfer and private equality test. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 416–433. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  17. 17.
    Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: Vitter, J.S., Spirakis, P.G., Yannakakis, M. (eds.) STOC, pp. 590–599. ACM (2001)Google Scholar
  18. 18.
    NIST: Special publication 800–57, recommendation for key management - part 1: General (revision 3), July 2012.
  19. 19.
  20. 20.
    Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  21. 21.
    Stern, J.P.: A new and efficient all-or-nothing disclosure of secrets protocol. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 357–371. Springer, Heidelberg (1998) CrossRefGoogle Scholar
  22. 22.
    Yao, A.C.C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167. IEEE Computer Society (1986)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Information Technology Research InstituteNational Institute of Advanced Industrial Science and TechnologyTokyoJapan
  2. 2.Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan
  3. 3.JST CRESTTokyoJapan

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