Confidential gossip

  • Chryssis GeorgiouEmail author
  • Seth Gilbert
  • Dariusz R. Kowalski


Epidemic gossip has proven a reliable and efficient technique for sharing information in a distributed network. Much of this reliability and efficiency derives from processes collaborating, sharing the work of distributing information. As a result of this collaboration, processes may receive information that was not originally intended for them. For example, some process may act as an intermediary, aggregating and forwarding messages from some set of sources to some set of destinations. But what if rumors are confidential? In that case, only processes that were originally intended to receive the rumor should be allowed to learn the rumor. This blatantly contradicts the basic premise of epidemic gossip, which assumes that processes can collaborate. In fact, if only processes in a rumor’s “destination set” participate in gossiping that rumor, we show that high message complexity is unavoidable. A natural approach is to rely on cryptography, for example, assuming that each process has a well-known public-key that can be used to encrypt the rumor. In a dynamic system, with changing sets of destinations, such a process seems potentially expensive. In this paper, we propose a scheme in which each rumor is broken into multiple fragments using a very simple coding scheme; any given fragment provides no information about the rumor, while together, the fragments can be reassembled into the original rumor. The processes collaborate in disseminating the rumor fragments in such a way that no process outside of a rumor’s destination set ever receives all the fragments of a rumor, while every process in the destination set eventually learns all the fragments. Notably, our solution operates in an environment where rumors are dynamically and continuously injected into the system and processes are subject to crashes and restarts. In addition, the presented scheme can tolerate a moderate amount of collusions among curious processes without a substantial increase in cost; curious processes are non-malicious processes that are not in a rumor’s destination set, and still want to learn the rumor (that is, collect all fragments of the rumor).


Confidentiality Collusion Randomized gossip Fault-tolerance Dynamic rumor injection Message complexity 



The authors would like to thank the anonymous reviewers that have helped them to significantly improve the presentation of the results.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Baehni, S., Eugster, P.T., Guerraoui, R.: Data-aware multicast. In: DSN 233–242 (2004)Google Scholar
  2. 2.
    Ballardie, A.J.: A New Approach to Multicast Communication in a Datagram Network. Ph.D. Thesis, University College London (1995)Google Scholar
  3. 3.
    Beimel, A., Nissim, K., Omri, E.: Distributed private data analysis. In: CRYPTO, pp. 451–468 (2008)Google Scholar
  4. 4.
    Brickell, J., Shmatikov, V.: Privacy-preserving graph algorithms in the semi-honest model. In: ASIACRYPT, pp. 236–252 (2005)zbMATHGoogle Scholar
  5. 5.
    Canetti, R., Garay, J., Itkis, G., Micciancio, D., Naor, M., Pinkas, B.: Multicast security: a taxonomy and some efficient constructions. In: INFOCOM, pp. 708–716 (1999)Google Scholar
  6. 6.
    Chlebus, B.S., Kowalski, D.R.: Time and communication efficient consensus for crash failures. In: DISC, pp. 314–328 (2006)Google Scholar
  7. 7.
    Chockler, G., Melamed, R., Tock, Y., Vitenberg, R.: SpiderCast: a scalable interest-aware overlay for topic-based pub/sub communication. In: DEBS, pp. 14–25 (2007)Google Scholar
  8. 8.
    Chockler, G., Melamed, R., Tock, Y., Vitenberg, R.: Constructing scalable overlays for pub/sub with many topics. In: PODC, pp. 109–118 (2007)Google Scholar
  9. 9.
    Delposte-Gallet, G., Fauconnier, H., Guerraoui, R., Ruppert, E.: Secretive birds: privacy in population protocols. In: OPODIS, pp. 329–342 (2007)Google Scholar
  10. 10.
    Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading: expanders, push vs pull, and robustness. In: ICALP, pp. 366–377 (2009)Google Scholar
  11. 11.
    Fernandess, Y., Malkhi, D.: On spreading recommendations via social gossip. In: SPAA, pp. 91–97 (2008)Google Scholar
  12. 12.
    Fiat, A., Naor, M.: Broadcast encryption. In: CRYPTO, pp. 480–491 (1993)Google Scholar
  13. 13.
    Georgiou, Ch., Gilbert, S., Kowalski, D.R.: Meeting the deadline: on the complexity of fault-tolerant continuous gossip. Distrib. Comput. 24(5), 223–244 (2011). (A preliminary version appears in PODC 2010, pp. 247–256)Google Scholar
  14. 14.
    Georgiou, Ch., Gilbert, S., Guerraoui, R., Kowalski, D.R.: Asynchronous gossip. J. ACM 60(2), article 11 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Goldreich, O.: Foundations of Cryptography: Volume II (Basic Applications). Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  16. 16.
    Gupta, I., Kermarrec, A.M., Ganesh, A.J.: Efficient epidemic-style protocols for reliable and scalable multicast. In: SRDS, pp. 180–189 (2002) Google Scholar
  17. 17.
    Hromkovic, J., Klasing, R., Pelc, A., Ruzika, P., Unger, W.: Dissemination of Information in Communication Networks: Broadcasting, Gossiping, Leader Election, and Fault-Tolerance. Springer, Berlin (2005)zbMATHGoogle Scholar
  18. 18.
    Johansen, H.D., Allavena, A., van Renesse, R.: Fireflies: scalable support for intrusion-tolerant network overlays. In: EuroSys, pp. 3–13 (2006)Google Scholar
  19. 19.
    Karp, R., Schindelhauer, C., Shenker, S., Vocking, B.: Randomized rumor spreading. In: FOCS, pp. 565–574 (2000)Google Scholar
  20. 20.
    Kempe, D., Kleinberg, J., Demers, A.: Spatial gossip and resource location protocols. J. ACM 51, 943–967 (2004)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Kermarrec, A., Massoulie, L., Ganesh, A.: Probabilistic reliable dissemination in large-scale systems. IEEE Trans. Parallel Distrib. Syst. 14(3), 248–258 (2003)CrossRefGoogle Scholar
  22. 22.
    Kissner, L., Song, D.: Privacy-preserving set operations. In: CRYPTO, pp. 241–257 (2005)CrossRefGoogle Scholar
  23. 23.
    Kowalski, D.R., Strojnowski, M.: On the communication surplus incurred by faulty processors. In: DISC, pp. 328–342 (2007)Google Scholar
  24. 24.
    Lindell, Y., Pinkas, B.: Privacy preserving data mining. J. Cryptol. 15(3), 177–206 (2002)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Malkhi, D., Mansour, Y., Reiter, M.K.: Diffusion without false rumors: on propagating updates in a Byzantine environment. Theor. Comput. Sci. 299, 289–306 (2003)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Micciancio, D., Panjwani, S.: Corrupting one vs. corrupting many: the case of broadcast and multicast encryption. In: ICALP, pp. 70–82 (2006)Google Scholar
  27. 27.
    Minsky, Y.M., Schneider, F.B.: Tolerating malicious gossip. Distrib. Comput. 16, 49–68 (2003)CrossRefGoogle Scholar
  28. 28.
    Mittra, S.: Iolus: a framework for scalable secure multicasting. SIGCOMM Comput. Commun. Rev. 27(4), 277–288 (1997)CrossRefGoogle Scholar
  29. 29.
    Multicast Security. Accessed 2 Aug 2019
  30. 30.
    Onus, M., Richa, A.W.: Minimum maximum degree pub/sub overlay network design. In: INFOCOM, pp. 882–890 (2009)Google Scholar
  31. 31.
    Pang, J., Zhang, C.: How to work with honest but curious judges? In: Proceedings of 7th international workshop on security issues in concurrency, pp. 31–45 (2009)Google Scholar
  32. 32.
    Panjwani, S.: Tackling adaptive corruptions in multicast encryption protocols. In: TCC, pp. 21–40 (2007)Google Scholar
  33. 33.
    Pelc, A.: Fault-tolerant broadcasting and gossiping in communication networks. Networks 28, 143–156 (1996)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Sherman, A.T., McGrew, D.A.: Key establishment in large dynamic groups using one-way function trees. IEEE Trans. Softw. Eng. 29(5), 444–458 (2003)CrossRefGoogle Scholar
  36. 36.
    Stinson, D.R.: Cryptography: Theory and Practice, 3rd edn. CRC Press, Cambridge (2005)zbMATHGoogle Scholar
  37. 37.
    Wong, C.K., Gouda, M., Lam, S.: Secure group communications using key graphs. IEEE/ACM Trans. Netw. 8(1), 16–30 (2000)CrossRefGoogle Scholar
  38. 38.
    Xu, G., Amariucai, G., Guan, Y.: Delegation of computation with verification outsourcing: curious verifiers. In: PODC, pp. 393–402 (2013)Google Scholar
  39. 39.
    Yao, A.C.: Protocols for secure computations. In: FOCS, pp. 160–164 (1982)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CyprusNicosiaCyprus
  2. 2.Department of Computer ScienceNational University of SingaporeSingaporeSingapore
  3. 3.School of Computer and Cyber SciencesAugusta UniversityAugustaUSA
  4. 4.SWPS UniversityWarsawPoland

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