Advertisement

Actively Secure Private Function Evaluation

  • Payman Mohassel
  • Saeed Sadeghian
  • Nigel P. Smart
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8874)

Abstract

We propose the first general framework for designing actively secure private function evaluation (PFE), not based on universal circuits. Our framework is naturally divided into pre-processing and online stages and can be instantiated using any generic actively secure multiparty computation (MPC) protocol.

Our framework helps address the main open questions about efficiency of actively secure PFE. On the theoretical side, our framework yields the first actively secure PFE with linear complexity in the circuit size. On the practical side, we obtain the first actively secure PFE for arithmetic circuits with O(g ·logg) complexity where g is the circuit size. The best previous construction (of practical interest) is based on an arithmetic universal circuit and has complexity O(g 5).

We also introduce the first linear Zero-Knowledge proof of correctness of “extended permutation” of ciphertexts (a generalization of ZK proof of correct shuffles) which maybe of independent interest.

Keywords

Secure Multi-Party Computation Private Function Evaluation Malicious Adversary Zero-Knowledge Proof of Shuffle 

References

  1. 1.
    Abadi, M., Feigenbaum, J.: Secure circuit evaluation. J. Cryptology 2(1), 1–12 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Barni, M., Failla, P., Kolesnikov, V., Lazzeretti, R., Sadeghi, A.-R., Schneider, T.: Secure evaluation of private linear branching programs with medical applications. In: Backes, M., Ning, P. (eds.) ESORICS 2009. LNCS, vol. 5789, pp. 424–439. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Brickell, J., Porter, D.E., Shmatikov, V., Witchel, E.: Privacy-preserving remote diagnostics. In: Ning, P., di Vimercati, S.D.C., Syverson, P.F. (eds.) ACM Conference on Computer and Communications Security, pp. 498–507. ACM (2007)Google Scholar
  5. 5.
    Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  6. 6.
    Cramer, R., Damgård, I., Schoenmakers, B.: Proof of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)Google Scholar
  7. 7.
    Damgård, I., Geisler, M., Krøigaard, M., Nielsen, J.B.: Asynchronous multiparty computation: Theory and implementation. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 160–179. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Damgård, I., Pastro, V., Smart, N.P., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, Canetti (eds.) [25], pp. 643–662.Google Scholar
  9. 9.
    Damgård, I., Zakarias, S.: Constant-overhead secure computation of boolean circuits using preprocessing. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 621–641. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Furukawa, J.: Efficient and verifiable shuffling and shuffle-decryption. IEICE Transactions 88-A(1), 172–188 (2005)CrossRefGoogle Scholar
  11. 11.
    Furukawa, J., Sako, K.: An efficient scheme for proving a shuffle. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 368–387. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Gennaro, R., Hazay, C., Sorensen, J.S.: Text search protocols with simulation based security. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 332–350. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Hazay, C., Nissim, K.: Efficient set operations in the presence of malicious adversaries. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 312–331. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Ishai, Y., Paskin, A.: Evaluating branching programs on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Katz, J., Malka, L.: Constant-round private function evaluation with linear complexity. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 556–571. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    Kolesnikov, V., Schneider, T.: A practical universal circuit construction and secure evaluation of private functions. In: Tsudik, G. (ed.) FC 2008. LNCS, vol. 5143, pp. 83–97. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Mohassel, P., Sadeghian, S.: How to hide circuits in MPC an efficient framework for private function evaluation. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 557–574. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  18. 18.
    Mohassel, P., Sadeghian, S., Smart, N.P.: Actively secure private function evaluation. Cryptology ePrint Archive, Report 2014/102 (2014), http://eprint.iacr.org/
  19. 19.
    Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, Canetti (eds.) [25], pp. 681–700Google Scholar
  20. 20.
    Niksefat, S., Sadeghiyan, B., Mohassel, P., Sadeghian, S.: Zids: A privacy-preserving intrusion detection system using secure two-party computation protocols. The Computer Journal (2013)Google Scholar
  21. 21.
    Ostrovsky, R., Paskin-Cherniavsky, A., Paskin-Cherniavsky, B.: Maliciously circuit-private fhe. Cryptology ePrint Archive, Report 2013/307 (2013), http://eprint.iacr.org/
  22. 22.
    Paus, A., Sadeghi, A.-R., Schneider, T.: Practical secure evaluation of semi-private functions. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 89–106. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  23. 23.
    Raz, R.: Elusive functions and lower bounds for arithmetic circuits. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, STOC 2008, pp. 711–720. ACM, New York (2008)CrossRefGoogle Scholar
  24. 24.
    Sadeghi, A.-R., Schneider, T.: Generalized universal circuits for secure evaluation of private functions with application to data classification. In: Lee, P.J., Cheon, J.H. (eds.) ICISC 2008. LNCS, vol. 5461, pp. 336–353. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  25. 25.
    Safavi-Naini, R., Canetti, R. (eds.): CRYPTO 2012. LNCS, vol. 7417. Springer, Heidelberg (2012)zbMATHGoogle Scholar
  26. 26.
    Valiant, L.: Universal circuits (preliminary report). In: Proceedings of the Eighth Annual ACM Symposium on Theory of Computing, pp. 196–203. ACM (1976)Google Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Payman Mohassel
    • 1
    • 2
  • Saeed Sadeghian
    • 1
  • Nigel P. Smart
    • 3
  1. 1.Dept. Computer ScienceUniversity of CalgaryCanada
  2. 2.Yahoo LabsCanada
  3. 3.Dept. Computer ScienceUniversity of BristolUK

Personalised recommendations