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Dynamic and Verifiable Hierarchical Secret Sharing

  • Giulia TraversoEmail author
  • Denise Demirel
  • Johannes Buchmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10015)

Abstract

In this work we provide a framework for dynamic secret sharing and present the first dynamic and verifiable hierarchical secret sharing scheme based on Birkhoff interpolation. Since the scheme is dynamic it allows, without reconstructing the message distributed, to add and remove shareholders, to renew shares, and to modify the conditions for accessing the message. Furthermore, each shareholder can verify its share received during these algorithms protecting itself against malicious dealers and shareholders. While these algorithms were already available for classical Lagrange interpolation based secret sharing, corresponding techniques for Birkhoff interpolation based schemes were missing. Note that Birkhoff interpolation is currently the only technique available that allows to construct hierarchical secret sharing schemes that are efficient and allow to provide shares of equal size for all shareholder in the hierarchy. Thus, our scheme is an important contribution to hierarchical secret sharing.

Keywords

Hierarchical secret sharing Distributed storage Cloud computing Long-term security Birkhoff interpolation Proactive secret sharing 

References

  1. 1.
    Agarwal, M., Mehr, R.: Review of matrix decomposition techniques for signal processing applications. Int. J. Eng. Res. Appl. 4(1), 90–93 (2014). www.ijera.com Google Scholar
  2. 2.
    Backes, M., Kate, A., Patra, A.: Computational verifiable secret sharing revisited. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 590–609. Springer, Heidelberg (2011). http://dx.doi.org/10.1007/978-3-642-25385-0_32 CrossRefGoogle Scholar
  3. 3.
    Baron, J., Defrawy, K.E., Lampkins, J., Ostrovsky, R.: Communication-optimal proactive secret sharing for dynamic groups. In: Malkin, T., Kolesnikov, V., Lewko, A.B., Polychronakis, M. (eds.) ACNS 2015. LNCS, vol. 9092, pp. 23–41. Springer, Heidelberg (2015). http://dx.doi.org/10.1007/978-3-319-28166-7_2 CrossRefGoogle Scholar
  4. 4.
    Blundo, C., Cresti, A., Santis, A., Vaccaro, U.: Fully dynamic secret sharing schemes. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 110–125. Springer, Heidelberg (1994). http://dx.doi.org/10.1007/3-540-48329-2_10 Google Scholar
  5. 5.
    Brickell, E.F.: Some ideal secret sharing schemes. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 468–475. Springer, Heidelberg (1990). doi: 10.1007/3-540-46885-4_45 Google Scholar
  6. 6.
    Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults (extended abstract). In: 26th Annual Symposium on Foundations of Computer Science, Portland, Oregon, USA, 21–23 October 1985, pp. 383–395 (1985). http://dx.doi.org/10.1109/SFCS.1985.64
  7. 7.
    Doganay, M.C., Pedersen, T.B., Saygin, Y., Savaş, E., Levi, A.: Distributed privacy preserving k-means clustering with additive secret sharing. In: Proceedings of 2008 International Workshop on Privacy and Anonymity in Information Society, pp. 3–11. ACM (2008)Google Scholar
  8. 8.
    Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: 28th Annual Symposium on Foundations of Computer Science, pp. 427–438. IEEE (1987)Google Scholar
  9. 9.
    Fitzi, M., Garay, J.A., Gollakota, S., Rangan, C.P., Srinathan, K.: Round-optimal and efficient verifiable secret sharing. In: Proceedings of 3rd Theory of Cryptography Conference Theory of Cryptography, TCC 2006, New York, NY, USA, 4–7 March 2006, pp. 329–342 (2006). http://dx.doi.org/10.1007/11681878_17
  10. 10.
    Gennaro, R., Ishai, Y., Kushilevitz, E., Rabin, T.: The round complexity of verifiable secret sharing and secure multicast. In: Proceedings on 33rd Annual ACM Symposium on Theory of Computing, 6–8 July 2001, Heraklion, Crete, Greece, pp. 580–589 (2001). http://doi.acm.org/10.1145/380752.380853
  11. 11.
    Ghodosi, H., Pieprzyk, J., Safavi-Naini, R.: Secret sharing in multilevel and compartmented groups. In: Boyd, C., Dawson, E. (eds.) ACISP 1998. LNCS, vol. 1438, pp. 367–378. Springer, Heidelberg (1998). doi: 10.1007/BFb0053748 CrossRefGoogle Scholar
  12. 12.
    Gupta, V., Gopinath, K.: \(\text{G}_{{\rm its}}^{{2}}\) VSR: : an information theoretical secure verifiable secret redistribution protocol for long-term archival storage. In: 4th International IEEE Security in Storage Workshop, SISW 2007, pp. 22–33. IEEE (2007)Google Scholar
  13. 13.
    Herzberg, A., Jarecki, S., Krawczyk, H., Yung, M.: Proactive secret sharing or: how to cope with perpetual leakage. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 339–352. Springer, Heidelberg (1995). doi: 10.1007/3-540-44750-4_27 Google Scholar
  14. 14.
    Katz, J., Koo, C., Kumaresan, R.: Improving the round complexity of VSS in point-to-point networks. Inf. Comput. 207(8), 889–899 (2009). http://dx.doi.org/10.1016/j.ic.2009.03.007 MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Kothari, S.C.: Generalized linear threshold scheme. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 231–241. Springer, Heidelberg (1985). doi: 10.1007/3-540-39568-7_19 CrossRefGoogle Scholar
  16. 16.
    Nojoumian, M., Stinson, D.R., Grainger, M.: Unconditionally secure social secret sharing scheme. Inf. Secur. IET 4(4), 202–211 (2010)CrossRefGoogle Scholar
  17. 17.
    Pakniat, N., Eslami, Z., Nojoumian, M.: Ideal social secret sharing using Birkhoff interpolation method. IACR Cryptology ePrint Archive 2014, 515 (2014). http://eprint.iacr.org/2014/515
  18. 18.
    Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992). doi: 10.1007/3-540-46766-1_9 Google Scholar
  19. 19.
    Schultz, D.A., Liskov, B., Liskov, M.: MPSS: mobile proactive secret sharing. ACM Trans. Inf. Syst. Secur. 13(4), 34 (2010). http://doi.acm.org/10.1145/1880022.1880028 CrossRefGoogle Scholar
  20. 20.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979). http://doi.acm.org/10.1145/359168.359176 MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Simmons, G.J.: How to (really) share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, Heidelberg (1990). doi: 10.1007/0-387-34799-2_30 Google Scholar
  22. 22.
    Tassa, T.: Hierarchical threshold secret sharing. J. Cryptol. 20(2), 237–264 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Giulia Traverso
    • 1
    Email author
  • Denise Demirel
    • 1
  • Johannes Buchmann
    • 1
  1. 1.Technische Universität DarmstadtDarmstadtGermany

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