Yet Another Compiler for Active Security or: Efficient MPC Over Arbitrary Rings

  • Ivan Damgård
  • Claudio Orlandi
  • Mark SimkinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10992)


We present a very simple yet very powerful idea for turning any passively secure MPC protocol into an actively secure one, at the price of reducing the threshold of tolerated corruptions.

Our compiler leads to a very efficient MPC protocols for the important case of secure evaluation of arithmetic circuits over arbitrary rings (e.g., the natural case of \({\mathbb {Z}}_{2^{\ell }}\!\)) for a small number of parties. We show this by giving a concrete protocol in the preprocessing model for the popular setting with three parties and one corruption. This is the first protocol for secure computation over rings that achieves active security with constant overhead.



We thank the anonymous reviewers for their useful feedback. This project has received funding from: the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme (grant agreement No 669255); the Danish Independent Research Council under Grant-ID DFF-6108-00169 (FoCC); the European Union’s Horizon 2020 research and innovation programme under grant agreement No 731583 (SODA).


  1. 1.
    Asharov, G., Jain, A., López-Alt, A., Tromer, E., Vaikuntanathan, V., Wichs, D.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 483–501. Springer, Heidelberg (2012). 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-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, 2–4 May 1988, Chicago, Illinois, USA, pp. 1–10 (1988)Google 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.
    Bogdanov, D., Laur, S., Willemson, J.: Sharemind: a framework for fast privacy-preserving computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008). Scholar
  6. 6.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: 20th ACM STOC, pp. 11–19. ACM Press, May 1988Google Scholar
  7. 7.
    Cohen, G., et al.: Efficient multiparty protocols via log-depth threshold formulae. Electronic Colloquium on Computational Complexity (ECCC), 20:107 (2013)Google Scholar
  8. 8.
    Cohen, R., Lindell, Y.: Fairness versus guaranteed output delivery in secure multiparty computation. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 466–485. Springer, Heidelberg (2014). Scholar
  9. 9.
    Cramer, R., Damgård, I., Nielsen, J.B.: Secure Multiparty Computation and Secret Sharing. Cambridge University Press, New York (2015)CrossRefGoogle Scholar
  10. 10.
    Cramer, R., Damgrd, I., Escudero, D., Scholl, P., Xing, C.: SPDZ2k: efficient MPC mod \(2^k\) for dishonest majority. CRYPTO (2018).
  11. 11.
    Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013). Scholar
  12. 12.
    Damgård, I., Orlandi, C.: Multiparty computation for dishonest majority: from passive to active security at low cost. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 558–576. Springer, Heidelberg (2010). Scholar
  13. 13.
    Damgård, I., Pastro, V., Smart, N.P., 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
  14. 14.
    Desmedt, Y., Kurosawa, K.: How to break a practical MIX and design a new one. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 557–572. Springer, Heidelberg (2000). Scholar
  15. 15.
    Fitzi, M., Gisin, N., Maurer, U.M., von Rotz, O.: Unconditional Byzantine agreement and multi-party computation secure against dishonest minorities from scratch. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 482–501. Springer, Heidelberg (2002). Scholar
  16. 16.
    Fitzi, M., Gottesman, D., Hirt, M., Holenstein, T., Smith, A.: Detectable Byzantine agreement secure against faulty majorities. In: Ricciardi, A. (ed.) 21st ACM PODC, pp. 118–126. ACM, July 2002Google Scholar
  17. 17.
    Furukawa, J., Lindell, Y., Nof, A., Weinstein, O.: High-throughput secure three-party computation for malicious adversaries and an honest majority. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part II. LNCS, vol. 10211, pp. 225–255. Springer, Cham (2017). Scholar
  18. 18.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Aho, A. (ed.) 19th ACM STOC, pp. 218–229. ACM Press, May 1987Google Scholar
  19. 19.
    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
  20. 20.
    Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008). Scholar
  21. 21.
    Lindell, Y., Oxman, E., Pinkas, B.: The IPS compiler: optimizations, variants and concrete efficiency. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 259–276. Springer, Heidelberg (2011). Scholar
  22. 22.
    Maurer, U.M.: Secure multi-party computation made simple. In: Cimato, S., Persiano, G., Galdi, C. (eds.) SCN 2002. LNCS, vol. 2576, pp. 14–28. Springer, Heidelberg (2003). Scholar
  23. 23.
    Mohassel, P., Rosulek, M., Zhang, Y.: Fast and secure three-party computation: the garbled circuit approach. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, Denver, CO, USA, 12–16 October 2015, pp. 591–602 (2015)Google Scholar
  24. 24.
    Mukherjee, P., Wichs, D.: Two round multiparty computation via multi-key FHE. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 735–763. Springer, Heidelberg (2016). Scholar
  25. 25.
    Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. J. ACM (JACM) 27(2), 228–234 (1980)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: 27th FOCS, pp. 162–167. IEEE Computer Society Press, October 1986Google Scholar

Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.Aarhus UniversityAarhusDenmark

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