Advertisement

Efficient, XOR-Based, Ideal \((t,n)-\)threshold Schemes

  • Liqun Chen
  • Thalia M. Laing
  • Keith M. Martin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10052)

Abstract

We propose a new, lightweight \((t,n)-\)threshold secret sharing scheme that can be implemented using only XOR operations. Our scheme is based on an idea extracted from a patent application by Hewlett Packard that utilises error correction codes. Our scheme improves on the patent by requiring fewer randomly generated bits and by reducing the size of shares given to each player, thereby making the scheme ideal. We provide a security proof and efficiency analysis. We compare our scheme to existing schemes in the literature and show that our scheme is more efficient than other schemes, especially when t is large.

Keywords

Threshold Secret sharing Perfect Efficient Ideal Error correction 

References

  1. 1.
    Chen, L., Camble, P.T., Watkins, M.R., Henry, I.J.: Utilizing error correction (ECC) for secure secret sharing. Hewlett Packard Enterprise Development LP, World Intellectual Property Organisation. Patent Number WO2016048297 (2016). https://www.google.com/patents/WO2016048297A1?cl=en
  2. 2.
    Blakely, G.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, vol. 48, pp. 313–317 (1979)Google Scholar
  3. 3.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979). ACMMathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Kurihara, J., Kiyomoto, S., Fukushima, K., Tanaka, T.: A fast (3, n)-threshold secret sharing scheme using exclusive-or operations. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 91(1), 127–138 (2008). IEICECrossRefGoogle Scholar
  5. 5.
    Kurihara, J., Kiyomoto, S., Fukushima, K., Tanaka, T.: A new (k,n)-threshold secret sharing scheme and its extension. In: Wu, T.-C., Lei, C.-L., Rijmen, V., Lee, D.-T. (eds.) ISC 2008. LNCS, vol. 5222, pp. 455–470. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-85886-7_31 CrossRefGoogle Scholar
  6. 6.
    Lv, C., Jia, X., Tian, L., Jing, J., Sun, M.: Efficient ideal threshold secret sharing schemes based on exclusive-or operations. In: 4th International Conference on Network and System Security (NSS), pp. 136–143. IEEE (2010)Google Scholar
  7. 7.
    Lv, C., Jia, X., Lin, J., Jing, J., Tian, L., Sun, M.: Efficient secret sharing schemes. In: Park, J.J., Lopez, J., Yeo, S.-S., Shon, T., Taniar, D. (eds.) Secure and Trust Computing, Data Management, and Application. Communications in Computer and Information Science, vol. 186, pp. 114–121. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Wang, Y., Desmedt, Y.: Efficient secret sharing schemes achieving optimal information rate. In: Information Theory Workshop (ITW), pp. 516–520. IEEE (2014)Google Scholar
  9. 9.
    Beimel, A.: Secret-sharing schemes: a survey. In: Chee, Y.M., Guo, Z., Ling, S., Shao, F., Tang, Y., Wang, H., Xing, C. (eds.) IWCC 2011. LNCS, vol. 6639, pp. 11–46. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Jackson, W., Martin, K.M.: A combinatorial interpretation of ramp schemes. Australas. J. Comb. 14, 52–60 (1996). Centre for CombinatoricsMathSciNetzbMATHGoogle Scholar
  11. 11.
    MacWilliams, F., Sloane, N.: The Theory of Error Correcting Codes. Elsevier, Amsterdam (1977)zbMATHGoogle Scholar
  12. 12.
    Reed, I., Solomon, G.: Polynomial codes over certain finite fields. J. Soc. Ind. Appl. Math. 8(2), 300–304 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Karnin, E.D., Greene, J.W., Hellman, M.E.: On secret sharing systems. IEEE Trans. Inf. Theor. 29(1), 35–41 (1983). IEEEMathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Chen, H., Cramer, R.: Algebraic geometric secret sharing schemes and secure multi-party computations over small fields. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 521–536. Springer, Heidelberg (2006). doi: 10.1007/11818175_31 CrossRefGoogle Scholar
  15. 15.
    Krawczyk, H.: Distributed fingerprints and secure information dispersal. In: Proceedings of the Twelfth Annual ACM Symposium on Principles of Distributed Computing, pp. 207–218. ACM (1993)Google Scholar
  16. 16.
    Rabin, M.: Efficient dispersal of information for security, load balancing, and fault tolerance. J. ACM (JACM) 36(2), 335–348 (1989). ACMMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Resch, J.K., Plank, J.S.: AONT-RS: blending security and performance in dispersed storage systems. In: FAST-2011: 9th USENIX Conference on File and Storage Technologie, pp. 191–202. USENIX Association (2011)Google Scholar
  18. 18.
    Blaum, M., Roth, R.: New array codes for multiple phased burst correction. IEEE Trans. Inf. Theor. 39(1), 66–77 (1993). IEEEMathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Blundo, C., De Santis, A., Vaccaro, U.: Randomness in distribution protocols. Inf. Comput. 131(2), 111–139 (1996). ElsevierMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Liqun Chen
    • 1
    • 2
  • Thalia M. Laing
    • 3
  • Keith M. Martin
    • 3
  1. 1.Hewlett-Packard EnterpriseBristolUK
  2. 2.University of SurreyGuildfordUK
  3. 3.Information Security GroupRoyal Holloway, University of LondonEghamUK

Personalised recommendations