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Hierarchical Secret Sharing Schemes Secure Against Rushing Adversary: Cheater Identification and Robustness

  • Partha Sarathi Roy
  • Sabyasachi Dutta
  • Kirill Morozov
  • Avishek Adhikari
  • Kazuhide Fukushima
  • Shinsaku Kiyomoto
  • Kouichi Sakurai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11125)

Abstract

Threshold access structures of secret sharing schemes capture a scenario in which all the participants have the same weight (or power) and their contributions are equal. However, in some situations such as gradation among officials in an organization, the participants have different weights. Hierarchical access structures capture those natural scenarios, where different levels of hierarchy are present and a participant belongs precisely to one of them. Although an extensive research addressing the issues of cheater identifiability and robustness have been done for threshold secret sharing, no such research has been carried out for hierarchical secret sharing (HSS). This paper resolves this long-standing open issue by presenting definitions and constructions of both cheater identifiable and robust HSS schemes secure against rushing adversary, in the information-theoretic setting.

Keywords

Hierarchical secret sharing Cheater identification Robustness Rushing adversary Multi-receiver authentication code Universal hash function 

References

  1. 1.
    Adhikari, A., Morozov, K., Obana, S., Roy, P.S., Sakurai, K., Xu, R.: Efficient threshold secret sharing schemes secure against rushing cheaters. IACR Cryptology ePrint Archive 2015/23 (2015)Google Scholar
  2. 2.
    Adhikari, A., Morozov, K., Obana, S., Roy, P.S., Sakurai, K., Xu, R.: Efficient threshold secret sharing schemes secure against rushing cheaters. In: Nascimento, A.C.A., Barreto, P. (eds.) ICITS 2016. LNCS, vol. 10015, pp. 3–23. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-49175-2_1CrossRefGoogle Scholar
  3. 3.
    Belenkiy, M.: Disjunctive multi-level secret sharing. IACR Cryptology ePrint Archive 2008/18 (2008)Google Scholar
  4. 4.
    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).  https://doi.org/10.1007/3-540-46885-4_45CrossRefGoogle Scholar
  5. 5.
    Carter, J.L., Wegman, M.N.: Universal classes of hash functions. J. Comput. Syst. Sci. 18(2), 143–154 (1979)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Cevallos, A., Fehr, S., Ostrovsky, R., Rabani, Y.: Unconditionally-secure robust secret sharing with compact shares. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 195–208. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29011-4_13CrossRefGoogle Scholar
  7. 7.
    Choudhury, A.: Brief announcement: optimal amortized secret sharing with cheater identification. In: Proceedings of the 2012 ACM Symposium on Principles of Distributed Computing, pp. 101–102. ACM (2012)Google Scholar
  8. 8.
    Cramer, R., Damgård, I., Fehr, S.: On the cost of reconstructing a secret, or VSS with optimal reconstruction phase. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 503–523. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44647-8_30CrossRefGoogle Scholar
  9. 9.
    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).  https://doi.org/10.1007/BFb0053748CrossRefzbMATHGoogle Scholar
  10. 10.
    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).  https://doi.org/10.1007/3-540-39568-7_19CrossRefGoogle Scholar
  11. 11.
    Kurosawa, K., Obana, S., Ogata, W.: t-Cheater identifiable (k, n) threshold secret sharing schemes. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 410–423. Springer, Heidelberg (1995).  https://doi.org/10.1007/3-540-44750-4_33CrossRefGoogle Scholar
  12. 12.
    McEliece, R.J., Sarwate, D.V.: On sharing secrets and reed-solomon codes. Commun. ACM 24(9), 583–584 (1981)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: Proceedings of the Twenty-First Annual ACM Symposium on Theory of Computing, pp. 73–85. ACM (1989)Google Scholar
  14. 14.
    Roy, P.S., Adhikari, A., Xu, R., Morozov, K., Sakurai, K.: An efficient robust secret sharing scheme with optimal cheater resiliency. In: Chakraborty, R.S., Matyas, V., Schaumont, P. (eds.) SPACE 2014. LNCS, vol. 8804, pp. 47–58. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-12060-7_4CrossRefGoogle Scholar
  15. 15.
    Roy, P.S., Adhikari, A., Xu, R., Morozov, K., Sakurai, K.: An efficient t-cheater identifiable secret sharing scheme with optimal cheater resiliency. IACR Cryptology ePrint Archive 2014/628 (2014)Google Scholar
  16. 16.
    Safavi-Naini, R., Wang, H.: New results on multi-receiver authentication codes. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 527–541. Springer, Heidelberg (1998).  https://doi.org/10.1007/BFb0054151CrossRefGoogle Scholar
  17. 17.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Simmons, G.J.: How to (really) share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, New York (1990).  https://doi.org/10.1007/0-387-34799-2_30CrossRefGoogle Scholar
  19. 19.
    Tassa, T.: Hierarchical threshold secret sharing. J. Cryptol. 20(2), 237–264 (2007)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Tentu, A.N., Paul, P., Vadlamudi, C.V.: Conjunctive hierarchical secret sharing scheme based on MDS codes. In: Lecroq, T., Mouchard, L. (eds.) IWOCA 2013. LNCS, vol. 8288, pp. 463–467. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-45278-9_44CrossRefGoogle Scholar
  21. 21.
    Traverso, G., Demirel, D., Buchmann, J.: Dynamic and verifiable hierarchical secret sharing. In: Nascimento, A.C.A., Barreto, P. (eds.) ICITS 2016. LNCS, vol. 10015, pp. 24–43. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-49175-2_2CrossRefGoogle Scholar
  22. 22.
    Wegman, M.N., Carter, J.L.: New classes and applications of hash functions. In: 20th Annual Symposium on Foundations of Computer Science, pp. 175–182. IEEE (1979)Google Scholar
  23. 23.
    Xu, R., Morozov, K., Takagi, T.: Cheater identifiable secret sharing schemes via multi-receiver authentication. In: Yoshida, M., Mouri, K. (eds.) IWSEC 2014. LNCS, vol. 8639, pp. 72–87. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-09843-2_6CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Partha Sarathi Roy
    • 1
  • Sabyasachi Dutta
    • 2
  • Kirill Morozov
    • 3
  • Avishek Adhikari
    • 4
  • Kazuhide Fukushima
    • 1
  • Shinsaku Kiyomoto
    • 1
  • Kouichi Sakurai
    • 5
  1. 1.Information Security LaboratoryKDDI Research, Inc.FujiminoJapan
  2. 2.R. C. Bose Centre for Cryptology and SecurityIndian Statistical InstituteKolkataIndia
  3. 3.Department of Computer Science and EngineeringUniversity of North TexasDentonUSA
  4. 4.Department of Pure MathematicsUniversity of CalcuttaKolkataIndia
  5. 5.Faculty of Information Science and Electrical EngineeringKyushu UniversityFukuokaJapan

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