Advertisement

Is Information-Theoretic Topology-Hiding Computation Possible?

  • Marshall BallEmail author
  • Elette Boyle
  • Ran Cohen
  • Tal Malkin
  • Tal Moran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11891)

Abstract

Topology-hiding computation (THC) is a form of multi-party computation over an incomplete communication graph that maintains the privacy of the underlying graph topology. Existing THC protocols consider an adversary that may corrupt an arbitrary number of parties, and rely on cryptographic assumptions such as DDH.

In this paper we address the question of whether information-theoretic THC can be achieved by taking advantage of an honest majority. In contrast to the standard MPC setting, this problem has remained open in the topology-hiding realm, even for simple “privacy-free” functions like broadcast, and even when considering only semi-honest corruptions.

We uncover a rich landscape of both positive and negative answers to the above question, showing that what types of graphs are used and how they are selected is an important factor in determining the feasibility of hiding topology information-theoretically. In particular, our results include the following.

  • We show that topology-hiding broadcast (THB) on a line with four nodes, secure against a single semi-honest corruption, implies key agreement. This result extends to broader classes of graphs, e.g., THB on a cycle with two semi-honest corruptions.

  • On the other hand, we provide the first feasibility result for information-theoretic THC: for the class of cycle graphs, with a single semi-honest corruption.

Given the strong impossibilities, we put forth a weaker definition of distributional-THC, where the graph is selected from some distribution (as opposed to worst-case).

  • We present a formal separation between the definitions, by showing a distribution for which information theoretic distributional-THC is possible, but even topology-hiding broadcast is not possible information-theoretically with the standard definition.

  • We demonstrate the power of our new definition via a new connection to adaptively secure low-locality MPC, where distributional-THC enables parties to “reuse” a secret low-degree communication graph even in the face of adaptive corruptions.

Notes

Acknowledgements

We thank Mike Rosulek for his graphical support, and the anonymous reviewers of TCC’19 for useful comments.

M. Ball’s research supported by an IBM Research PhD Fellowship. Part of this work was completed while M. Ball was visiting IDC Herzliya’s FACT center. M. Ball and T. Malkin’s research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) via Contract No. 2019-1902070006. E. Boyle’s research supported by ISF grant 1861/16 and AFOSR Award FA9550-17-1-0069. R. Cohen’s research supported by the Northeastern University Cybersecurity and Privacy Institute Post-doctoral fellowship, NSF grant TWC-1664445, NSF grant 1422965, and by the NSF MACS project. This work was supported in part by the Intelligence Advanced Research Project Activity (IARPA) under contract number 2019-19-020700009. T. Moran’s research supported by the Bar-Ilan Cyber Center. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of ODNI, IARPA, DoI/NBC, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon.

References

  1. 1.
    Akavia, A., Moran, T.: Topology-hiding computation beyond logarithmic diameter. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10212, pp. 609–637. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-56617-7_21CrossRefGoogle Scholar
  2. 2.
    Akavia, A., LaVigne, R., Moran, T.: Topology-hiding computation on all graphs. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 447–467. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_15CrossRefGoogle Scholar
  3. 3.
    Ball, M., Boyle, E., Malkin, T., Moran, T.: Exploring the boundaries of topology-hiding computation. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 294–325. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78372-7_10CrossRefGoogle Scholar
  4. 4.
    Beimel, A.: On private computation in incomplete networks. Distrib. Comput. 19(3), 237–252 (2007)CrossRefGoogle Scholar
  5. 5.
    Beimel, A., Franklin, M.K.: Reliable communication over partially authenticated networks. Theor. Comput. Sci. 220(1), 185–210 (1999)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Beimel, A., Malka, L.: Efficient reliable communication over partially authenticated networks. Distrib. Comput. 18(1), 1–19 (2005)CrossRefGoogle Scholar
  7. 7.
    Beimel, A., Gabizon, A., Ishai, Y., Kushilevitz, E., Meldgaard, S., Paskin-Cherniavsky, A.: Non-interactive secure multiparty computation. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8617, pp. 387–404. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44381-1_22CrossRefGoogle Scholar
  8. 8.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: STOC, pp. 1–10 (1988)Google Scholar
  9. 9.
    Bläser, M., Jakoby, A., Liśkiewicz, M., Manthey, B.: Private computation: k-connected versus 1-connected networks. J. Cryptol. 19(3), 341–357 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Boyle, E., Goldwasser, S., Tessaro, S.: Communication locality in secure multi-party computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 356–376. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-36594-2_21CrossRefGoogle Scholar
  11. 11.
    Boyle, E., Cohen, R., Data, D., Hubáček, P.: Must the communication graph of MPC protocols be an expander? In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 243–272. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-96878-0_9CrossRefGoogle Scholar
  12. 12.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptol. 13(1), 143–202 (2000)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Chandran, N., Garay, J., Ostrovsky, R.: Edge fault tolerance on sparse networks. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012. LNCS, vol. 7392, pp. 452–463. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-31585-5_41CrossRefGoogle Scholar
  14. 14.
    Chandran, N., Chongchitmate, W., Garay, J.A., Goldwasser, S., Ostrovsky, R., Zikas, V.: The hidden graph model: communication locality and optimal resiliency with adaptive faults. In: ITCS, pp. 153–162 (2015)Google Scholar
  15. 15.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: STOC, pp. 11–19 (1988)Google Scholar
  16. 16.
    Damgård, I., Meyer, P., Tschudi, D.: Information-theoretic topology-hiding computation with setup (2019). http://perso.ens-lyon.fr/pierre.meyer/docs/m2.pierre.meyer.pdf
  17. 17.
    Dolev, D.: The Byzantine generals strike again. J. Algorithms 3(1), 14–30 (1982)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Dolev, D., Dwork, C., Waarts, O., Yung, M.: Perfectly secure message transmission. J. ACM 40(1), 17–47 (1993)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Dwork, C., Peleg, D., Pippenger, N., Upfal, E.: Fault tolerance in networks of bounded degree. SICOMP 17(5), 975–988 (1988)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Fischer, M.J., Lynch, N.A., Merritt, M.: Easy impossibility proofs for distributed consensus problems. In: PODC, pp. 59–70 (1985)Google Scholar
  21. 21.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229 (1987)Google Scholar
  22. 22.
    Gordon, S.D., Malkin, T., Rosulek, M., Wee, H.: Multi-party computation of polynomials and branching programs without simultaneous interaction. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 575–591. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38348-9_34CrossRefGoogle Scholar
  23. 23.
    Halevi, S., Lindell, Y., Pinkas, B.: Secure computation on the web: computing without simultaneous interaction. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 132–150. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22792-9_8CrossRefGoogle Scholar
  24. 24.
    Halevi, S., Ishai, Y., Jain, A., Kushilevitz, E., Rabin, T.: Secure multiparty computation with general interaction patterns. In: ITCS, pp. 157–168 (2016)Google Scholar
  25. 25.
    Hinkelmann, M., Jakoby, A.: Communications in unknown networks: preserving the secret of topology. Theor. Comput. Sci. 384(2–3), 184–200 (2007)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Hirt, M., Maurer, U., Tschudi, D., Zikas, V.: Network-hiding communication and applications to multi-party protocols. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 335–365. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53008-5_12CrossRefGoogle Scholar
  27. 27.
    King, V., Lonargan, S., Saia, J., Trehan, A.: Load balanced scalable byzantine agreement through quorum building, with full information. In: Aguilera, M.K., Yu, H., Vaidya, N.H., Srinivasan, V., Choudhury, R.R. (eds.) ICDCN 2011. LNCS, vol. 6522, pp. 203–214. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-17679-1_18CrossRefGoogle Scholar
  28. 28.
    Kumar, M.V.N.A., Goundan, P.R., Srinathan, K., Rangan, C.P.: On perfectly secure communication over arbitrary networks. In: PODC, pp. 193–202 (2002)Google Scholar
  29. 29.
    LaVigne, R., Liu-Zhang, C.-D., Maurer, U., Moran, T., Mularczyk, M., Tschudi, D.: Topology-hiding computation beyond semi-honest adversaries. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11240, pp. 3–35. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-03810-6_1CrossRefGoogle Scholar
  30. 30.
    Micali, S., Ohta, K., Reyzin, L.: Accountable-subgroup multisignatures: extended abstract. In: ACM CCS, pp. 245–254 (2001)Google Scholar
  31. 31.
    Moran, T., Orlov, I., Richelson, S.: Topology-hiding computation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9014, pp. 159–181. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46494-6_8CrossRefGoogle Scholar
  32. 32.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority (extended abstract). In: FOCS, pp. 73–85 (1989)Google Scholar
  33. 33.
    Yao, A.C.: Protocols for secure computations (extended abstract). In: FOCS, pp. 160–164 (1982)Google Scholar

Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  • Marshall Ball
    • 1
    Email author
  • Elette Boyle
    • 2
  • Ran Cohen
    • 3
    • 4
  • Tal Malkin
    • 1
  • Tal Moran
    • 2
  1. 1.Columbia UniversityNew YorkUSA
  2. 2.IDC HerzliyaHerzliyaIsrael
  3. 3.Boston UniversityBostonUSA
  4. 4.Northeastern UniversityBostonUSA

Personalised recommendations