Secure Network Coding over the Integers

  • Rosario Gennaro
  • Jonathan Katz
  • Hugo Krawczyk
  • Tal Rabin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6056)

Abstract

Network coding offers the potential to increase throughput and improve robustness without any centralized control. Unfortunately, network coding is highly susceptible to “pollution attacks” in which malicious nodes modify packets improperly so as to prevent message recovery at the recipient(s); such attacks cannot be prevented using standard end-to-end cryptographic authentication because network coding mandates that intermediate nodes modify data packets in transit.

Specialized “network coding signatures” addressing this problem have been developed in recent years using homomorphic hashing and homomorphic signatures. We contribute to this area in several ways:

  • We show the first homomorphic signature scheme based on the RSA assumption (in the random oracle model).

  • We give a homomorphic hashing scheme that is more efficient than existing schemes, and which leads to network coding signatures based on the hardness of factoring (in the standard model).

  • We describe variants of existing schemes that reduce the communication overhead for moderate-size networks, and improve computational efficiency (in some cases quite dramatically – e.g., we achieve a 20-fold speedup in signature generation at intermediate nodes).

Underlying our techniques is a modified approach to random linear network coding where instead of working in a vector space over a field, we work in a module over the integers (with small coefficients).

References

  1. 1.
    Agrawal, S., Boneh, D.: Homomorphic MACs: MAC-based integrity for network coding. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Ahlswede, R., Cai, N., Li, S., Yeung, R.: Network information flow. IEEE Transactions on Information Theory 46(4), 1204–1216 (2000)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ateniese, G., Burns, R.C., Curtmola, R., Herring, J., Kissner, L., Peterson, Z.N.J., Song, D.X.: Provable data possession at untrusted stores. In: ACM Conference on Computer and Communications Security, pp. 598–609 (2007)Google Scholar
  4. 4.
    Ateniese, G., Kamara, S., Katz, J.: Proofs of storage from homomorphic identification protocols. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 319–333. Springer, Heidelberg (2009)Google Scholar
  5. 5.
    Bellare, M., Garay, J., Rabin, T.: Fast batch verification for modular exponentiation and digital signatures. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 236–250. Springer, Heidelberg (1998)Google Scholar
  6. 6.
    Boneh, D., Freeman, D., Katz, J., Waters, B.: Signing a linear subspace: Signature schemes for network coding. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 68–87. Springer, Heidelberg (2009)Google Scholar
  7. 7.
    Charles, D., Jain, K., Lauter, K.: Signatures for network coding. In: 40th Annual Conference on Information Sciences and Systems, CISS 2006 (2006); To appear in International Journal of Information and Coding TheoryGoogle Scholar
  8. 8.
    Chou, P.A., Wu, Y., Jain, K.: Practical network coding. In: 41st Allerton Conference on Communication, Control, and Computing (2003)Google Scholar
  9. 9.
    Gkantsidis, C., Rodriguez, P.: Cooperative security for network coding file distribution. In: Proc. of IEEE INFOCOM 2006, pp. 1–13 (2006)Google Scholar
  10. 10.
    Ho, T., Koetter, R., Médard, M., Karger, D., Effros, M.: The benefits of coding over routing in a randomized setting. In: Proc. of International Symposium on Information Theory, ISIT (2003)Google Scholar
  11. 11.
    Ho, T., Leong, B., Koetter, R., Médard, M., Effros, M., Karger, D.: Byzantine modification detection in multicast networks using randomized network coding. In: Proc. Intl. Symposium on Information Theory (ISIT), pp. 144–152 (2004)Google Scholar
  12. 12.
    Ho, T., Lun, D.: Network Coding: An Introduction. Cambridge University Press, Cambridge (2008)MATHGoogle Scholar
  13. 13.
    Ho, T., Médard, M., Koetter, R., Karger, D.R., Effros, M., Shi, J., Leong, B.: A random linear network coding approach to multicast. IEEE Trans. Inform. Theory 52(10), 4413–4430 (2006)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Jaggi, S.: Design and Analysis of Network Codes. PhD thesis, California Institute of Technology (2006)Google Scholar
  15. 15.
    Jaggi, S., Langberg, M., Katti, S., Ho, T., Katabi, D., Médard, M., Effros, M.: Resilient network coding in the presence of Byzantine adversaries. IEEE Trans. on Information Theory 54(6), 2596–2603 (2008)CrossRefGoogle Scholar
  16. 16.
    Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    Krohn, M., Freedman, M., Mazieres, D.: On the-fly verification of rateless erasure codes for efficient content distribution. In: Proc. IEEE Symposium on Security & Privacy, pp. 226–240 (2004)Google Scholar
  18. 18.
    Li, S.-Y.R., Yeung, R.W., Cai, N.: Linear network coding. IEEE Trans. Inform. Theory 49(2), 371–381 (2003)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Shacham, H., Waters, B.: Compact proofs of retrievability. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 90–107. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Yu, Z., Wei, Y., Ramkumar, B., Guan, Y.: An efficient signature-based scheme for securing network coding against pollution attacks. In: INFOCOM (2008)Google Scholar
  21. 21.
    Zhao, F., Kalker, T., Médard, M., Han, K.: Signatures for content distribution with network coding. In: Proc. Intl. Symp. on Information Theory ISIT (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rosario Gennaro
    • 1
  • Jonathan Katz
    • 2
  • Hugo Krawczyk
    • 1
  • Tal Rabin
    • 1
  1. 1.IBM T.J. Watson Research CenterHawthorne
  2. 2.Department of Computer ScienceUniversity of Maryland 

Personalised recommendations