Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Conjunctive Hierarchical Multi-Secret Sharing Scheme using Elliptic Curves

  • Original Research
  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

A method in which a secret is distributed among the users and a predefined number of users collaborate to reconstruct the secret is known as a secret sharing scheme. In this article, we have proposed a conjunctive hierarchical multi-secret sharing scheme using elliptic curves and bilinear pairings. The motivation for utilizing bilinear pairing of elliptic curves is to provide a similar level of security as in many existing schemes while employing a smaller key size. The proposed scheme is efficient and verifiable. The computational cost of the scheme is determined. We have also given an explicit example of the proposed scheme.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R.K.K. Ajeena and K. Hailiza, The computational complexity of elliptic curve integer sub-decomposition (ISD) method, AIP Conference Proceedings, 1605 (2014) 557-562.

    Article  Google Scholar 

  2. M. Bahramian and K. Eslami, A new verifiable multi-secret sharing scheme based on elliptic curves and pairings, Italian Journal of Pure and Applied Mathematics, n 41 (2019) 456-468.

    MATH  Google Scholar 

  3. M. Belenkiy, Disjunctive multi-level secret sharing, IACR Cryptology ePrint Archive 18 (2008).

  4. V.P. Binu and A. Sreekumar, Threshold Multi Secret Sharing Using Elliptic Curve and Pairing, International Journal of Information Processing, 9(4) (2015) 100-112.

    Google Scholar 

  5. J. Coron, Resistance against differential power analysis for elliptic curve cryptosystems, in Proceedings of the 1st International Workshop on Cryptographic Hardware and Embedded Systems (CHES ’99), vol. 1717 of Lecture Notes in Computer Science, pp. 292-302 Springer, (1999).

  6. O. Farras and C. Padro, Ideal Hierarchical Secret Sharing Schemes, IEEE Transactions on Information Theory, 58 (2012) 3273-3286.

    Article  MathSciNet  MATH  Google Scholar 

  7. G. Frey, M. M\(\ddot{u}\)ller and H.-G. R\(\ddot{u}\)ck, The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems, IEEE Transactions on Information Theory, 45 (1999) 1717-1718.

  8. S.D. Galbraith and N.P. Smart, Evaluation report for CRYPTREC: security level of cryptography-ECDLP mathematical problem. https://www.cryptrec.go.jp/exreport/cryptrec-ex-1029-2001.pdf (2001).

  9. S.D. Galbraith, F. Hess, and F. Vercauteren, Aspects of Pairing Inversion, IEEE Transactions on Information Theory, Vol. 54 (12) (2008) 5719-5728.

    Article  MathSciNet  MATH  Google Scholar 

  10. H. Ghodosi, J. Pieprzyk and R. Safavi-Naini, Secret sharing in multilevel and compartmented groups, Proc. ACISP \(1998\), Lecture Notes in Comput. Sci., 1438 (1998) 367-378.

  11. W.C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press (2012).

  12. S. Ionica and A. Joux, Pairing Computation on Elliptic Curves with Efficiently Computable Endomorphism and Small Embedding Degree, In: Joye, M., Miyaji, A., Otsuka, A. (eds) Pairing-Based Cryptography - Pairing 2010. Pairing 2010. Lecture Notes in Computer Science, vol 6487. Springer, Berlin, Heidelberg, (2010).

  13. D. Liu, D. Huang, P. Luo and Y. Da, New schemes for sharing points on an elliptic curve, Computers and Mathematics with Applications, 56 (2008) 1556-1561.

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Menezes, An introduction to pairing-based cryptography, Recent trends in Cryptography, Contemp. Math., 477 (2009) 47-65, Amer. Math. Soc., Providence, RI, 2009.

  15. V. Miller, The Weil pairing, and its efficient calculation, J. Cryptology, 17 (2004) 235-261.

    Article  MathSciNet  MATH  Google Scholar 

  16. A.R. Rao and P. Bhimasankaram, Linear Algebra, 2nd Ed., Texts and Readings in Mathematics (TRIM) 19, Hindustan Book Agency (2000).

  17. A. Shamir, How to share a secret, Comm. ACM, 22 (1979) 612-613.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, Springer, (1986).

  19. G. Simmons, How to (really) share a secret, in Advances in Cryptology - Proceedings of CRYPTO-88 (S. Goldwasser, ed.) Lecture Notes in Comput. Sci., 403 (1990) 390-448.

  20. T. Tassa, Hierarchical threshold secret sharing, Journal of Cryptology 20 (2007) 237-264.

    Article  MathSciNet  MATH  Google Scholar 

  21. A.N. Tentu, P. Paul and V.Ch. Venkaiah, Conjunctive hierarchical secret sharing scheme based on MDS codes, Combinatorial Algorithms, Lecture Notes in Comput. Sci., 8288, Springer (2013) 463-467.

  22. S.J. Wang, Y.R. Tsai and C.C. Shen, Verifiable threshold scheme in multi-secret sharing distributions upon extensions of ecc, Wireless Personal communications, 56 (2011) 173-182.

    Article  Google Scholar 

  23. J. Yuan, J. Yang, C. Wang, X. Jia, F.-W. Fu and G. Xu, A New efficient hierarchical multi-secret sharing scheme based on linear homogeneous recurrence relations, Information Sciences 592 (2022) 36-49.

    Article  Google Scholar 

Download references

Acknowledgements

The authors are thankful to the anonymous referees for their valuable comments and suggestions. The third author was supported in part by the Council of Scientific and Industrial Research, India, under award letter 09/414(1146)/2017-EMR-I.

Funding

The authors declare no special funding for the research work for this article.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohan Chintamani.

Additional information

Communicated by Sanoli Gun.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chintamani, M., Paul, P. & Sa, L. Conjunctive Hierarchical Multi-Secret Sharing Scheme using Elliptic Curves. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00450-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13226-023-00450-x

Keywords

Mathematics Subject Classification