Skip to main content
SpringerLink
Log in

A pairing-based publicly verifiable secret sharing scheme

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

A publicly verifiable secret sharing (PVSS) scheme is a verifiable secret sharing scheme with the special property that anyone is able to verify the shares whether they are correctly distributed by a dealer. PVSS plays an important role in many applications such as electronic voting, payment systems with revocable anonymity, and key escrow. Up to now, all PVSS schemes are based on the traditional public-key systems. Recently, the pairing-based cryptography has received much attention from cryptographic researchers. Many pairing-based schemes and protocols have been proposed. However, no PVSS scheme using bilinear pairings is proposed. This paper presents the first pairing-based PVSS scheme. In the random oracle model and under the bilinear Diffie-Hellman assumption, the authors prove that the proposed scheme is a secure PVSS scheme.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Shamir, How to share a secret, Communications of the ACM, 1979, 22(11): 612–613.

    Article  MATH  MathSciNet  Google Scholar 

  2. G. R. Blakey, Safeguarding cryptographic keys, AFIPS National Computer Conference, 1979: 313–317.

  3. P. Feldman, A practical scheme for non-interactive verifiable secret sharing, 28th Annual Symposium on Foundations of Computer Science, 1987: 427–437.

  4. M. Stadler, Public verifiable secret sharing, EUROCRYPT, LNCS, 1996, 1070: 190–199.

    Google Scholar 

  5. J. Cohen and M. Fischer, A robust and verifiable cryptographically secure election scheme, 26th Annual Symposium on Foundations of Computer Science, 1985: 372–382.

  6. J. Benaloh and M. Yung, Distributing the power of a government to enhance the privacy of voters, 5th annual ACM symposium on Principles of Distributed Computing, 1986: 52–62.

  7. J. Benaloh, Verifiable secret-ballot elections, PhD Thesis, Yale University, 1987.

  8. S. Micali, Fair cryptosystems, Technical Report TR-579.b, MIT, 1993.

  9. E. Brickell, P. Gemmell, and D. Kravitz, Trustee-based tracing extensions to anonymous cash and the making of anonymous change, 6th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, 1995: 457–466.

  10. M. Stadler, J. M. Piveteau, and J. Camenisch, Fair blind signatures, EUROCRYPT, LNCS, 1995, 921: 209–219.

    Google Scholar 

  11. M. Jakobsson and M. Yung, Revkcable and versatile electronic money, 3rd ACM Conference on Computer and Communications Security, New Delhi, 1996: 76–87.

  12. J. Camenisch, J. M. Piveteau, and M. Stadler, An efficient fair payment system, 3rd ACM Conference on Computer and Communications Security, New Delhi, 1996: 88–94.

  13. B. Schoenmakers, A simple publicly verifiable secret sharing scheme and its application to electronic voting, CRYPTO, LNCS, 1999, 1666: 148–164.

    MathSciNet  Google Scholar 

  14. H. Y. Chien, J. K. Jan, and Y. M. Tseng, A practical (t, n) multi-secret sharing scheme, IEICE Trans. on Fundamentals of Electronics, Communications of Computer Sciences, 2000, E83-A(12): 2762–2765.

    Google Scholar 

  15. H. Y. Chien, J. K. Jan, and Y. M. Tseng, An unified approach to secret sharing schemes with low distribution cost, Journal of the Chinese Institute of Engineers, 2002, 25(6): 723–733.

    Google Scholar 

  16. T. P. Pedersen, Non-interactive and information-theoretic secure verifiable secret sharing, CRYPTO, LNCS, 1991, 576: 129–140.

    Google Scholar 

  17. E. Fujisaki and T. Okamoto, A practical and provably secure scheme for publicly verifiable secret sharing and its applications, EUROCRYPT, LNCS, 1998, 1403: 72–84.

    MathSciNet  Google Scholar 

  18. J. Yu, F. Kong, and R. Hao, Publicly verifiable secret sharing with enrollment ability, 8th ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing, Qingdao, 2007: 194–199.

  19. A. Menezes, T. Okamoto, and S. Vanstone, Reducing elliptic curve logarithms to logarithms in a finite field, IEEE Trans. Info. Theory, 1993, 39: 1639–1646.

    Article  MATH  MathSciNet  Google Scholar 

  20. P. S. L. M. Barreto, H. Y. Kim, B. Lynn, and M. Scott, Efficient algorithms for pairing-based cryptosystems, CRYPTO, LNCS, 2002, 2442: 354–369.

    MathSciNet  Google Scholar 

  21. A. Joux, A one round protocol for tripartite Diffie-Hellman, ANTS, LNCS, 2000, 1838: 385–394.

    MathSciNet  Google Scholar 

  22. D. Boneh and M. Franklin, Identity-based encryption from the Weil pairing, CRYPTO, LNCS, 2001, 2139: 213–229.

    MathSciNet  Google Scholar 

  23. D. Boneh and M. Franklin, Identity-based encryption from theWeil pairing, SIAM J. of Computing, 2003, 32(3): 586–615.

    Article  MATH  MathSciNet  Google Scholar 

  24. D. Boneh, B. Lynn, and H. Shacham, Short signature from the Weil pairing, ASIACRYPT, LNCS, 2001, 2248: 514–532.

    MathSciNet  Google Scholar 

  25. S. D. Galbraith, Supersingular curves in cryptography, ASIACRYPT, LNCS, 2001, 2248: 495–513.

    MathSciNet  Google Scholar 

  26. K. Rubin and A. Silverberg, Supersingular abelian varieties in cryptology, CRYPTO, LNCS, 2002, 2442: 336–353.

    MathSciNet  Google Scholar 

  27. K. Paterson, ID-based signatures from pairings on elliptic curves, Electronics Letters, 2002, 38(18): 1025–1026.

    Article  Google Scholar 

  28. J. C. Cha and J. H. Cheon, An identity-based signature from gap Diffie-Hellman groups, PKC, LNCS, 2003, 2567: 18–30.

    MathSciNet  Google Scholar 

  29. Y. M. Tseng, T. Y. Wu, and J. D. Wu, Forgery attacks on an ID-based partially blind signature scheme, International Journal of Computer Science, 2008, 35(3): 301–304.

    Google Scholar 

  30. H. J. Yoon, J. H. Cheon, and Y. Kim, Batch verifications with ID-based signatures, ICISC, LNCS, 2004, 3506: 233–248.

    MathSciNet  Google Scholar 

  31. S. Cui, P. Duan, and C. W. Chan, An efficient identity-based signature scheme with batch verifications, 1st International Conference on Scalable Information Systems, ACM International Conference Proceeding Series, 2006, 152: 22.

    Google Scholar 

  32. P. S. L. M. Barreto, B. Libert, N. McCullagh, and J. J. Quisquater, Efficient and provably-secure identity-based signatures and signcryption from bilinear maps, ASIACRYPT, LNCS, 2005, 3788: 515–532.

    MathSciNet  Google Scholar 

  33. L. Chen, Z. Cheng, and N. Smart, Identity-based key agreement protocols from pairings, International Journal of Information Security, 2007, 6(4): 213–241.

    Article  Google Scholar 

  34. K. Y. Choi, J. Y. Hwang, and D. H. Lee, Efficient ID-based group key agreement with bilinear maps, PKC, LNCS, 2004, 2947: 130–144.

    MathSciNet  Google Scholar 

  35. N. P. Smart, An identity based authenticated key agreement protocol based on the Weil pairing, Electronics Letters, 2002, 38(13): 630–632.

    Article  MATH  Google Scholar 

  36. K. Shim, Efficient ID-based authenticated key agreement protocol based on the Weil pairing, Electronics Letters, 2003, 39(8): 653–654.

    Article  Google Scholar 

  37. Y. J. Choie, E. Jeong, and E. Lee, Efficient identity-based authenticated key agreement protocol from pairings, Applied Mathematics and Computation, 2005, 162(1): 179–188.

    Article  MATH  MathSciNet  Google Scholar 

  38. Y. M. Tseng, T. Y. Wu, and J. D. Wu, A pairing-based user authentication scheme for wireless clients with smart cards, Informatica, 2008, 19(2): 285–302.

    Google Scholar 

  39. L. Chen and J. Malone-Lee, Improved identity-based signcryption, PKC, LNCS, 2005, 3386: 362–379.

    MathSciNet  Google Scholar 

  40. M. Bellare and P. Rogaway, Random oracles are practical: A paradigm for designing efficient protocols, 1st ACM Conference on Computer and Communications Security, Chicago, 1993: 62–73.

  41. R. Canetti, O. Goldreich, and S. Halevi, The random oracle methodology, revisited, JACM, 2004, 51(4): 557–594.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Changhua University of Education, Jin-De Campus, Chang-Hua, 500, Taiwan

    Tsu-Yang Wu & Yuh-Min Tseng

Authors
  1. Tsu-Yang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuh-Min Tseng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuh-Min Tseng.

Additional information

This research was partially supported by National Science Council, Taiwan, under Grant No. NSC97-2221-E-018-010-MY3.

This paper was recommended for publication by Editor Xiaoshan GAO.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, TY., Tseng, YM. A pairing-based publicly verifiable secret sharing scheme. J Syst Sci Complex 24, 186–194 (2011). https://doi.org/10.1007/s11424-011-8408-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-011-8408-6

Key words

Search

Navigation