Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Cryptology and Network Security (CANS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10052))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  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. Blakely, G.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, vol. 48, pp. 313–317 (1979)

    Google Scholar 

  3. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979). ACM

    Article  MathSciNet  MATH  Google Scholar 

  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). IEICE

    Article  Google Scholar 

  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

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  10. Jackson, W., Martin, K.M.: A combinatorial interpretation of ramp schemes. Australas. J. Comb. 14, 52–60 (1996). Centre for Combinatorics

    MathSciNet  MATH  Google Scholar 

  11. MacWilliams, F., Sloane, N.: The Theory of Error Correcting Codes. Elsevier, Amsterdam (1977)

    MATH  Google Scholar 

  12. Reed, I., Solomon, G.: Polynomial codes over certain finite fields. J. Soc. Ind. Appl. Math. 8(2), 300–304 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  13. Karnin, E.D., Greene, J.W., Hellman, M.E.: On secret sharing systems. IEEE Trans. Inf. Theor. 29(1), 35–41 (1983). IEEE

    Article  MathSciNet  MATH  Google Scholar 

  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

    Chapter  Google Scholar 

  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. Rabin, M.: Efficient dispersal of information for security, load balancing, and fault tolerance. J. ACM (JACM) 36(2), 335–348 (1989). ACM

    Article  MathSciNet  MATH  Google Scholar 

  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. Blaum, M., Roth, R.: New array codes for multiple phased burst correction. IEEE Trans. Inf. Theor. 39(1), 66–77 (1993). IEEE

    Article  MathSciNet  MATH  Google Scholar 

  19. Blundo, C., De Santis, A., Vaccaro, U.: Randomness in distribution protocols. Inf. Comput. 131(2), 111–139 (1996). Elsevier

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hewlett-Packard Enterprise, Bristol, UK

    Liqun Chen

  2. University of Surrey, Guildford, UK

    Liqun Chen

  3. Information Security Group, Royal Holloway, University of London, Egham, UK

    Thalia M. Laing & Keith M. Martin

Authors
  1. Liqun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thalia M. Laing
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Keith M. Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thalia M. Laing .

Editor information

Editors and Affiliations

  1. Università degli Studi di Milano, Crema, Italy

    Sara Foresti

  2. Università degli Studi di Salerno, Fisciano, Italy

    Giuseppe Persiano

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Chen, L., Laing, T.M., Martin, K.M. (2016). Efficient, XOR-Based, Ideal \((t,n)-\)threshold Schemes. In: Foresti, S., Persiano, G. (eds) Cryptology and Network Security. CANS 2016. Lecture Notes in Computer Science(), vol 10052. Springer, Cham. https://doi.org/10.1007/978-3-319-48965-0_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48965-0_28

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48964-3

  • Online ISBN: 978-3-319-48965-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation