Secure Multi-party Computation: Information Flow of Outputs and Game Theory

  • Patrick Ah-Fat
  • Michael HuthEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10204)


Secure multiparty computation enables protocol participants to compute the output of a public function of their private inputs whilst protecting the confidentiality of their inputs. But such an output, as a function of its inputs, inevitably leaks some information about input values regardless of the protocol used to compute it. We introduce foundations for quantifying and understanding how such leakage may influence input behaviour of deceitful protocol participants as well as that of participants they target. Our model captures the beliefs and knowledge that participants have about what input values other participants may choose. In this model, measures of information flow that may arise between protocol participants are introduced, formally investigated, and experimentally evaluated. These information-theoretic measures not only suggest advantageous input behaviour to deceitful participants for optimal updates of their beliefs about chosen inputs of targeted participants. They also allow targets to quantify the information-flow risk of their input choices. We show that this approach supports a game-theoretic formulation in which deceitful attackers wish to maximise the information that they gain on inputs of targets once the computation output is known, whereas the targets wish to protect the privacy of their inputs.


Information Flow Shannon Entropy Public Output Oblivious Transfer Input Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by the UK EPSRC with Fees Award and grants EP/N023242/1 and EP/N020030/1. We thank Geoffrey Smith and anonymous reviewers for their constructive comments and suggestions.


  1. 1.
    Asharov, G., Lindell, Y.: A full proof of the BGW protocol for perfectly secure multiparty computation. Cryptology ePrint Archive, Report 2011/136 (2011)Google Scholar
  2. 2.
    Avis, D., Rosenberg, G.D., Savani, R., Von Stengel, B.: Enumeration of Nash equilibria for two-player games. Econ. Theor. 42(1), 9–37 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Baum, C., Damgård, I., Toft, T., Zakarias, R.: Better preprocessing for secure multiparty computation. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 327–345. Springer, Cham (2016). doi: 10.1007/978-3-319-39555-5_18 Google Scholar
  4. 4.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of STOC, pp. 1–10. ACM (1988)Google Scholar
  5. 5.
    Bogetoft, P., et al.: Secure multiparty computation goes live. In: Dingledine, R., Golle, P. (eds.) Financial Cryptography and Data Security. LNCS, vol. 5628. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Cachin, C.: Entropy measures and unconditional security in cryptography. Ph. D thesis, Diss. Techn. Wiss. ETH Zürich, Nr. 12187 (1997). Ref.: Maurer, U., Korref, Massey, J.L. (1997)Google Scholar
  7. 7.
    Chaum, D., Crépeau, C., Damgard, I.: Multiparty unconditionally secure protocols. In: Proceedings of STOC, pp. 11–19. ACM (1988)Google Scholar
  8. 8.
    Clark, D., Hunt, S., Malacaria, P.: A static analysis for quantifying information flow in a simple imperative language. J. Comput. Secur. 15(3), 321–371 (2007)CrossRefGoogle Scholar
  9. 9.
    Michael, M.R., Myers, A.C., Schneider, F.B.: Quantifying information flow with beliefs. J. Comput. Secur. 17(5), 655–701 (2009)CrossRefGoogle Scholar
  10. 10.
    Cramer, R., Damgård, I., Nielsen, J.B.: Secure Multiparty Computation and Secret Sharing. Cambridge University Press, Cambridge (2015)CrossRefzbMATHGoogle Scholar
  11. 11.
    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). doi: 10.1007/978-3-642-32009-5_38 CrossRefGoogle Scholar
  12. 12.
    Dorothy, D.E.: A lattice model of secure information flow. Commun. ACM 19(5), 236–243 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Dima, C., Enea, C., Gramatovici, R.: Nondeterministic noninterference and deducible information flow. Technical report, Citeseer (2006)Google Scholar
  14. 14.
    Wenliang, D., Atallah, M.J.: Secure multi-party computation problems, their applications: a review and open problems. In: Proceedings of the Workshop on New Security Paradigms, pp. 13–22. ACM (2001)Google Scholar
  15. 15.
    Goldreich, O., Micali, S., Wigderson, A.: How to play ANY mental game. In: Proceedings of STOC 1987, pp. 218–229. ACM (1987)Google Scholar
  16. 16.
    Joshi, R., Leino, K.R.M.: A semantic approach to secure information flow. Sci. Comput. Program. 37(1), 113–138 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Kolesnikov, V., Schneider, T.: Improved garbled circuit: free XOR gates and applications. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5126, pp. 486–498. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-70583-3_40 CrossRefGoogle Scholar
  18. 18.
    Lindell, Y., Pinkas, B.: A proof of security of yao’s protocol for two-party computation. J. Cryptology 22(2), 161–188 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Lindell, Y., Pinkas, B.: Secure multiparty computation for privacy-preserving data mining. J. Priv. Confidentiality 1(1), 5 (2009)Google Scholar
  20. 20.
    Malacaria, P.: Algebraic foundations for quantitative information flow. Math. Struct. Comput. Sci. 25(02), 404–428 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Malone, D., Sullivan, W.: Guesswork is not a substitute for entropy. Slides (2005)Google Scholar
  22. 22.
    Mardziel, P., Magill, S., Hicks, M., Srivatsa, M.: Dynamic enforcement of knowledge-based security policies. In: IEEE 24th Computer Security Foundations Symposium, pp. 114–128. IEEE (2011)Google Scholar
  23. 23.
    Massey, J.L.: Guessing and entropy. In: Proceedings of the IEEE International Symposium on Information Theory, p. 204. IEEE (1994)Google Scholar
  24. 24.
    McIver, A., Morgan, C.: A probabilistic approach to information hiding. Programming Methodology. Monographs in Computer Science, pp. 441–460. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  25. 25.
    Alvim, M.S., Chatzikokolakis, K., Palamidessi, C., Smith, G.: Measuring information leakage using generalized gain functions. In: IEEE 25th Computer Security Foundations Symposium, pp. 265–279. IEEE (2012)Google Scholar
  26. 26.
    Nair, D.G., Binu, V.P., Kumar, G.S.: An improved e-voting scheme using secret sharing based secure multi-party computation. arXiv preprint arXiv:1502.07469 (2015)
  27. 27.
    Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681–700. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-32009-5_40 CrossRefGoogle Scholar
  28. 28.
    Phan, Q-S., Malacaria, P., Păsăreanu, C.S., d’Amorim, M.: Quantifying information leaks using reliability analysis. In: Proceedings of the International SPIN Symposium on Model Checking of Software, pp. 105–108. ACM (2014)Google Scholar
  29. 29.
    Shamir, A.: How to share a secret. CACM 22(11), 612–613 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press, Urbana (1949)zbMATHGoogle Scholar
  31. 31.
    Smart, N.P.: Cryptography Made Simple. Springer, Heidelberg (2016)CrossRefzbMATHGoogle Scholar
  32. 32.
    Smith, G.: Principles of secure information flow analysis. In: Christodorescu, M., Jha, S., Maughan, D., Song, D., Wang, C. (eds.) Malware Detection. Advances in Information Security, vol. 27, pp. 291–307. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  33. 33.
    Smith, G.: On the foundations of quantitative information flow. In: Alfaro, L. (ed.) FoSSaCS 2009. LNCS, vol. 5504, pp. 288–302. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-00596-1_21 CrossRefGoogle Scholar
  34. 34.
    Smith, G.: Quantifying information flow using min-entropy. In: Eighth International Conference on Quantitative Evaluation of Systems, pp. 159–167. IEEE (2011)Google Scholar
  35. 35.
    Smith, G.: Recent developments in quantitative information flow (invited tutorial). In: Proceedings of the 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pp. 23–31. IEEE Computer Society (2015)Google Scholar
  36. 36.
    Volpano, D., Irvine, C., Smith, G.: A sound type system for secure flow analysis. J. Comput. Secur. 4(2–3), 167–187 (1996)CrossRefGoogle Scholar
  37. 37.
    Yasuoka, H., Terauchi, T.: Quantitative information flow as safety and liveness hyperproperties. Theor. Comput. Sci. 538, 167–182 (2014)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of ComputingImperial College LondonLondonUK

Personalised recommendations