Secure Network Coding for Multiple Unicast: On the Case of Single Source

  • Gaurav Kumar AgarwalEmail author
  • Martina Cardone
  • Christina Fragouli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10681)


This paper considers multiple unicast wireline noiseless networks where a single source wishes to transmit independent messages to a set of legitimate destinations. The primal goal is to characterize the secure capacity region, where the exchanged messages have to be secured from a passive external eavesdropper that has unbounded computational capabilities, but limited network presence. The secure capacity region for the case of two destinations is characterized and it is shown to be a function of only the min-cut capacities and the number of edges the eavesdropper wiretaps. A polynomial-time two-phase scheme is then designed for a general number of destinations and its achievable secure rate region is derived. It is shown that the secure capacity result for the two destinations case is not reversible, that is, by switching the role of the source and destinations and by reversing the directions of the edges, the secure capacity region changes.


  1. 1.
    Cai, N., Yeung, R.W.: Secure network coding. In: Proceedings IEEE International Symposium on Information Theory (ISIT), p. 323, July 2002Google Scholar
  2. 2.
    Koetter, R., Effros, M., Ho, T.: Network codes as codes on graphs. In: Conference on Information Sciences and Systems (CISS) (2004)Google Scholar
  3. 3.
    Riis, S.: Reversible and irreversible information networks. IEEE Trans. Inf. Theor. 53(11), 4339–4349 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ahlswede, R., Cai, N., Li, S.Y.R., Yeung, R.W.: Network information flow. IEEE Trans. Inf. Theor. 46(4), 1204–1216 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Li, S.Y.R., Yeung, R.W., Cai, N.: Linear network coding. IEEE Trans. Inf. Theor. 49(2), 371–381 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Jaggi, S., Sanders, P., Chou, P.A., Effros, M., Egner, S., Jain, K., Tolhuizen, L.M.G.M.: Polynomial time algorithms for multicast network code construction. IEEE Trans. Inf. Theor. 51(6), 1973–1982 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Koetter, R., Medard, M.: An algebraic approach to network coding. IEEE/ACM Trans. Netw. 11(5), 782–795 (2003)CrossRefGoogle Scholar
  8. 8.
    Kamath, S.U., Tse, D.N.C., Anantharam, V.: Generalized network sharing outer bound and the two-unicast problem. In: International Symposium on Networking Coding (NetCod), pp. 1–6, July 2011Google Scholar
  9. 9.
    Kamath, S., Tse, D.N.C., Wang, C.C.: Two-unicast is hard. In: IEEE International Symposium on Information Theory (ISIT), pp. 2147–2151, June 2014Google Scholar
  10. 10.
    Ramamoorthy, A., Wesel, R.D.: The single source two terminal network with network coding. arXiv:0908.2847, August 2009
  11. 11.
    Cui, T., Ho, T., Kliewer, J.: On secure network coding with nonuniform or restricted wiretap sets. IEEE Trans. Inf. Theor. 59(1), 166–176 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Agarwal, G.K., Cardone, M., Fragouli, C.: On secure network coding for two unicast sessions: studying butterflies. In: IEEE Globecom Workshops (GC Wkshps), pp. 1–6, December 2016Google Scholar
  13. 13.
    Agarwal, G.K., Cardone, M., Fragouli, C.: Coding across unicast sessions can increase the secure message capacity. In: IEEE International Symposium on Information Theory (ISIT), pp. 2134–2138, July 2016Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Gaurav Kumar Agarwal
    • 1
    Email author
  • Martina Cardone
    • 1
  • Christina Fragouli
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of California Los AngelesLos AngelesUSA

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