Secure Computation with Preprocessing via Function Secret Sharing

  • Elette BoyleEmail author
  • Niv Gilboa
  • Yuval Ishai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11891)


We propose a simple and powerful new approach for secure computation with input-independent preprocessing, building on the general tool of function secret sharing (FSS) and its efficient instantiations. Using this approach, we can make efficient use of correlated randomness to compute any type of gate, as long as a function class naturally corresponding to this gate admits an efficient FSS scheme. Our approach can be viewed as a generalization of the “TinyTable” protocol of Damgård et al. (Crypto 2017), where our generalized variant uses FSS to achieve exponential efficiency improvement for useful types of gates.

By instantiating this general approach with efficient PRG-based FSS schemes of Boyle et al. (Eurocrypt 2015, CCS 2016), we can implement useful nonlinear gates for equality tests, integer comparison, bit-decomposition and more with optimal online communication and with a relatively small amount of correlated randomness. We also provide a unified and simplified view of several existing protocols in the preprocessing model via the FSS framework.

Our positive results provide a useful tool for secure computation tasks that involve secure integer comparisons or conversions between arithmetic and binary representations. These arise in the contexts of approximating real-valued functions, machine-learning classification, and more. Finally, we study the necessity of the FSS machinery that we employ, in the simple context of secure string equality testing. First, we show that any “online-optimal” secure equality protocol implies an FSS scheme for point functions, which in turn implies one-way functions. Then, we show that information-theoretic secure equality protocols with relaxed optimality requirements would follow from the existence of big families of “matching vectors.” This suggests that proving strong lower bounds on the efficiency of such protocols would be difficult.



Research supported by ERC Project NTSC (742754). E. Boyle additionally supported by ISF grant 1861/16 and AFOSR Award FA9550-17-1-0069. N. Gilboa additionally supported by ISF grant 1638/15, ERC grant 876110, and a grant by the BGU Cyber Center. Y. Ishai additionally supported by ISF grant 1709/14, NSF-BSF grant 2015782, and a grant from the Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India.


  1. 1.
    Bauer, B., Vihrovs, J., Wee, H.: On the inner product predicate and a generalization of matching vector families. In: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2018, 11–13 December 2018, Ahmedabad, India, pp. 41:1–41:13 (2018)Google Scholar
  2. 2.
    Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992). Scholar
  3. 3.
    Ben-Efraim, A., Nielsen, M., Omri, E.: Turbospeedz: double your online SPDZ! Improving SPDZ using function dependent preprocessing. In: Deng, R.H., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 530–549. Springer, Cham (2019). Scholar
  4. 4.
    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). Scholar
  5. 5.
    Bhowmick, A., Dvir, Z., Lovett, S.: New bounds for matching vector families. SIAM J. Comput. 43(5), 1654–1683 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Scholl, P.: Efficient pseudorandom correlation generators: silent OT extension and more. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 489–518. Springer, Cham (2019). Scholar
  7. 7.
    Boyle, E., Gilboa, N., Ishai, Y.: Function secret sharing. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 337–367. Springer, Heidelberg (2015). Scholar
  8. 8.
    Boyle, E., Gilboa, N., Ishai, Y.: Function secret sharing: improvements and extensions. In: Proceedings of the ACM Conference on Computer and Communications Security, pp. 1292–1303 (2016). Full version: ePrint report 2018/707Google Scholar
  9. 9.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptol., 143–202 (2000)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Couteau, G.: New protocols for secure equality test and comparison. In: Preneel, B., Vercauteren, F. (eds.) ACNS 2018. LNCS, vol. 10892, pp. 303–320. Springer, Cham (2018). Scholar
  11. 11.
    Couteau, G.: A note on the communication complexity of multiparty computation in the correlated randomness model. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11477, pp. 473–503. Springer, Cham (2019). Scholar
  12. 12.
    Damgård, I., 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). Scholar
  13. 13.
    Damgård, I., Nielsen, J.B., Nielsen, M., Ranellucci, S.: The TinyTable protocol for 2-party secure computation, or: gate-scrambling revisited. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 167–187. Springer, Cham (2017). Scholar
  14. 14.
    Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). Scholar
  15. 15.
    Demmler, D., Schneider, T., Zohner, M.: ABY - a framework for efficient mixed-protocol secure two-party computation. In: NDSS 2015 (2015)Google Scholar
  16. 16.
    Doerner, J., Shelat, A.: Scaling ORAM for secure computation. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, CCS 2017, Dallas, TX, USA, 30 October–03 November, pp. 523–535 (2017)Google Scholar
  17. 17.
    Dvir, Z., Gopalan, P., Yekhanin, S.: Matching vector codes. SIAM J. Comput. 40(4), 1154–1178 (2011)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Efremenko, K.: 3-query locally decodable codes of subexponential length. SIAM J. Comput. 41(6), 1694–1703 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Gilboa, N., Ishai, Y.: Distributed point functions and their applications. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 640–658. Springer, Heidelberg (2014). Scholar
  20. 20.
    Goldreich, O.: Foundations of Cryptography - Basic Applications. Cambridge University Press, New York (2004)CrossRefGoogle Scholar
  21. 21.
    Grolmusz, V.: On set systems with restricted intersections modulo a composite number. In: Jiang, T., Lee, D.T. (eds.) COCOON 1997. LNCS, vol. 1276, pp. 82–90. Springer, Heidelberg (1997). Scholar
  22. 22.
    Ishai, Y., Kushilevitz, E., Meldgaard, S., Orlandi, C., Paskin-Cherniavsky, A.: On the power of correlated randomness in secure computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 600–620. Springer, Heidelberg (2013). Scholar
  23. 23.
    Katz, J., Kolesnikov, V., Wang, X.: Improved non-interactive zero knowledge with applications to post-quantum signatures. In: Proceedings of the ACM Conference on Computer and Communications Security, pp. 525–537 (2018)Google Scholar
  24. 24.
    Katz, J., Ranellucci, S., Rosulek, M., Wang, X.: Optimizing authenticated garbling for faster secure two-party computation. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 365–391. Springer, Cham (2018). Scholar
  25. 25.
    Mohassel, P., Rindal, P.: ABY\({}^{\text{3}}\): a mixed protocol framework for machine learning. In: Proceedings of the ACM Conference on Computer and Communications Security, pp. 35–52 (2018)Google Scholar

Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.IDCHerzliyaIsrael
  2. 2.Ben Gurion UniversityBeershebaIsrael
  3. 3.TechnionHaifaIsrael

Personalised recommendations