Improved Efficiency for Private Stable Matching

  • Matthew Franklin
  • Mark Gondree
  • Payman Mohassel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4377)


At Financial Crypto 2006, Golle presented a novel framework for the privacy preserving computation of a stable matching (stable marriage). We show that the communication complexity of Golle’s main protocol is substantially greater than what was claimed in that paper, in part due to surprising pathological behavior of Golle’s variant of the Gale-Shapley stable matching algorithm. We also develop new protocols in Golle’s basic framework with greatly reduced communication complexity.


stable matching stable marriage Gale-Shapley privacy-preserving protocols secure multiparty computation passive adversaries 


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  1. 1.
    Algesheimer, J., Camenisch, J., Shoup, V.: Efficient computation modulo a shared secret with application to the generation of shared safe-prime products. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 417–432. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols. In: ACM Symposium on Theory of Computing, pp. 503–513 (1990)Google Scholar
  3. 3.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. Journal of Cryptology 13, 143–202 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cramer, R., Damgård, I.: Secure distributed linear algebra in a constant number of rounds. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 119–136. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Damgård, I., Fitzi, M., Nielsen, J.B., Toft, T.: How to split a shared secret into shared bits in constant-round. Cryptology ePrint Archive, Report 2005/140 (2005)Google Scholar
  6. 6.
    Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: Public Key Cryptography, pp. 119–136 (2001)Google Scholar
  7. 7.
    Fouque, P.-A., Poupard, G., Stern, J.: Sharing decryption in the context of voting or lotteries. In: Financial Crypto (2000)Google Scholar
  8. 8.
    Franklin, M., Gondree, M., Mohassel, P.: Improved efficiency for private stable matching. Cryptology ePrint Archive, Report 2006/332 (2006)Google Scholar
  9. 9.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. American Mathematical Monthly 69, 9–15 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Goldreich, O.: Foundations of Cryptography. Cambridge University Press, Cambridge (2001)zbMATHCrossRefGoogle Scholar
  11. 11.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: ACM Symposium on Theory of Computing, pp. 218–229 (1987)Google Scholar
  12. 12.
    Golle, P.: A private stable matching algorithm. In: Financial Crypto (2006)Google Scholar
  13. 13.
    Golle, P., Juels, A.: Parallel mixing. In: ACM Computer and Communications Security, pp. 220–226 (2004)Google Scholar
  14. 14.
    Gusfield, D., Irving, R.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge (1989)zbMATHGoogle Scholar
  15. 15.
    Jakobsson, M., Juels, A., Rivest, R.: Making mix nets robust for electronic voting by randomized partial checking. In: Proc. of USENIX 2002, pp. 339–353 (2002)Google Scholar
  16. 16.
    Jakobsson, M., Schnorr, C.P.: Efficient oblivious proofs of correct exponentiation. In: Communications and Multimedia Security, pp. 71–86 (1999)Google Scholar
  17. 17.
    Kiltz, E.: Unconditionally secure constant round multi-party computation for equality, comparison, bits and exponentiation. Cryptology ePrint Archive, Report 2005/066 (2005)Google Scholar
  18. 18.
    Kushilevitz, E., Ostrovsky, R.: Replication is not needed: single database, computationally-private information retrieval. In: Foundations of Computer Science, pp. 364–373 (1997)Google Scholar
  19. 19.
    Lindell, Y., Pinkas, B.: A proof of Yao’s protocol for secure two-party computation. Cryptology ePrint Archive, Report 2004/175 (2004)Google Scholar
  20. 20.
    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
  21. 21.
    Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: ACM Symposium on Theory of Computing, pp. 590–599 (2001)Google Scholar
  22. 22.
    Andrew Neff, C.: A verifiable secret shuffe and its application to e-voting. In: ACM Computer and Communications Security, pp. 116–125 (2001)Google Scholar
  23. 23.
    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)Google Scholar
  24. 24.
    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
  25. 25.
    Yao, A.C.: How to generate and exchange secrets. In: Foundations of Computer Science, pp. 162–167 (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matthew Franklin
    • 1
  • Mark Gondree
    • 1
  • Payman Mohassel
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaDavis

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