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Efficient Proactive Secret Sharing for Large Data via Concise Vector Commitments

  • Matthias GeihsEmail author
  • Lucas Schabhüser
  • Johannes Buchmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11445)

Abstract

Proactive secret sharing has been proposed by Herzberg, Jarecki, Krawczyk, and Yung (CRYPTO’95) and is a powerful tool for storing highly confidential data. However, their scheme is not designed for storing large data and communication and computation costs scale linearly with the data size. In this paper we propose a variant of their scheme that uses concise vector commitments. We show that our new scheme, when instantiated with a variant of the Pedersen commitment scheme (CRYPTO’92), reduces computation costs by up to \(50\%\) and broadcast communication costs by a factor of L, where L is the length of the commitment message vectors.

Notes

Acknowledgments

This work has been co-funded by the DFG as part of project S6 within the CRC 1119 CROSSING.

References

  1. 1.
    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, Cham (2015).  https://doi.org/10.1007/978-3-319-28166-7_2CrossRefGoogle Scholar
  2. 2.
    Baron, J., El Defrawy, K., Lampkins, J., Ostrovsky, R.: How to withstand mobile virus attacks, revisited. In: Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing, PODC 2014, pp. 293–302. ACM, New York (2014).  https://doi.org/10.1145/2611462.2611474. http://doi.acm.org/10.1145/2611462.2611474
  3. 3.
    Bellare, M., Rogaway, P.: Code-based game-playing proofs and the security of triple encryption. Cryptology ePrint Archive, Report 2004/331 (2004). https://eprint.iacr.org/2004/331
  4. 4.
    Bellare, M., Rogaway, P.: The security of triple encryption and a framework for code-based game-playing proofs. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 409–426. Springer, Heidelberg (2006).  https://doi.org/10.1007/11761679_25CrossRefGoogle Scholar
  5. 5.
    Blakley, G.R.: Safeguarding cryptographic keys. In: International Workshop on Managing Requirements Knowledge (AFIPS), December 1979.  https://doi.org/10.1109/AFIPS.1979.98. doi.ieeecomputersociety.org/10.1109/AFIPS.1979.98
  6. 6.
    Brands, S.A.: Rethinking Public Key Infrastructures and Digital Certificates: Building in Privacy. MIT Press, Cambridge (2000)CrossRefGoogle Scholar
  7. 7.
    Cachin, C., Kursawe, K., Lysyanskaya, A., Strobl, R.: Asynchronous verifiable secret sharing and proactive cryptosystems. In: Proceedings of the 9th ACM Conference on Computer and Communications Security, CCS 2002, pp. 88–97. ACM, New York (2002).  https://doi.org/10.1145/586110.586124. http://doi.acm.org/10.1145/586110.586124
  8. 8.
    Catalano, D., Fiore, D.: Vector commitments and their applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 55–72. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-36362-7_5CrossRefGoogle Scholar
  9. 9.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984).  https://doi.org/10.1016/0022-0000(84)90070-9. http://www.sciencedirect.com/science/article/pii/0022000084900709MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Groth, J.: Linear algebra with sub-linear zero-knowledge arguments. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 192–208. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-03356-8_12CrossRefGoogle Scholar
  11. 11.
    Gupta, V.H., Gopinath, K.: \(g_{its}^2\) VSR: an information theoretical secure verifiable secret redistribution protocol for long-term archival storage. In: Fourth International IEEE Security in Storage Workshop, pp. 22–33, September 2007.  https://doi.org/10.1109/SISW.2007.11
  12. 12.
    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).  https://doi.org/10.1007/3-540-44750-4_27CrossRefGoogle Scholar
  13. 13.
    Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-size commitments to polynomials and their applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177–194. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-17373-8_11CrossRefGoogle Scholar
  14. 14.
    Nikov, V., Nikova, S.: On proactive secret sharing schemes. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 308–325. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-30564-4_22CrossRefGoogle Scholar
  15. 15.
    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).  https://doi.org/10.1007/3-540-46766-1_9CrossRefGoogle Scholar
  16. 16.
    Sadeghi, A.-R., Steiner, M.: Assumptions related to discrete logarithms: why subtleties make a real difference. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 244–261. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44987-6_16CrossRefGoogle Scholar
  17. 17.
    Schultz, D., Liskov, B., Liskov, M.: MPSS: mobile proactive secret sharing. ACM Trans. Inf. Syst. Secur. 13(4), 341–3432 (2010).  https://doi.org/10.1145/1880022.1880028. http://doi.acm.org/10.1145/1880022.1880028CrossRefGoogle Scholar
  18. 18.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979).  https://doi.org/10.1145/359168.359176. http://doi.acm.org/10.1145/359168.359176MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Wong, T.M., Wang, C., Wing, J.M.: Verifiable secret redistribution for archive systems. In: Proceedings of the First International IEEE Security in Storage Workshop, pp. 94–105, December 2002.  https://doi.org/10.1109/SISW.2002.1183515
  20. 20.
    Zhou, L., Schneider, F.B., Van Renesse, R.: APSS: proactive secret sharing in asynchronous systems. ACM Trans. Inf. Syst. Secur. 8(3), 259–286 (2005).  https://doi.org/10.1145/1085126.1085127. http://doi.acm.org/10.1145/1085126.1085127CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Matthias Geihs
    • 1
    Email author
  • Lucas Schabhüser
    • 1
  • Johannes Buchmann
    • 1
  1. 1.Technische Universität DarmstadtDarmstadtGermany

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