Secret sharing with reusable polynomials

  • Liqun Chen
  • Dieter Gollmann
  • Chris J. Mitchell
  • Peter Wild
Authentication Codes And Secret Sharing Schemes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1270)


We present a threshold secret sharing scheme based on polynomial interpolation and the Diffie-Hellman problem. In this scheme shares can be used for the reconstruction of multiple secrets, shareholders can dynamically join or leave without distributing new shares to the existing shareholders, and shares can be individually verified during both share distribution and secret recovery.


Secret Sharing Secret Sharing Scheme Threshold Scheme Share Distribution Threshold Secret Sharing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blakley, B., Blakley, G.R., Chan, A.H., Massey, J.L.: Threshold schemes with dis-enrollment. In E.F. Brickell, editor, Lecture Notes in Computer Science 740, Advances in Cryptology — Crypto '92 (Springer-Verlag, Berlin, 1993) 540–548Google Scholar
  2. 2.
    Blakley, G.R.: Safeguarding cryptographic keys. In the Proceedings of AFIPS 1979 NCC, Vol. 48, Arlington,Va. (1979) 313–317Google Scholar
  3. 3.
    Brickell, E.F., Stinson, D.R.: The detection of cheaters in threshold schemes. In S. Goldwasser, editor, Lecture Notes in Computer Science 403, Advances in Cryptology — CRYPTO '88 (Springer-Verlag, Berlin, 1988) 564–577Google Scholar
  4. 4.
    Cachin, C.: On-line secret sharing. In C. Boyd, editor, Lecture Notes in Computer Science 1025, 5th IMA Conference on Cryptography and Coding (Springer-Verlag, Berlin, 1995) 190–198Google Scholar
  5. 5.
    Charnes, C., Pieprzyk, J., Safavi-Naini, R.: Conditionally secure secret sharing schemes with disenrollment capability. In Proceedings of the 2nd ACM Conference on Computer and Communications Security (Fairfax, Virginia, USA, 1994) 89–95Google Scholar
  6. 6.
    Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Transactions on Information Theory 22 (1976) 644–654CrossRefGoogle Scholar
  7. 7.
    Hwang, S., Chang, C.: A dynamic secret sharing scheme with cheater detection. In Lecture Notes in Computer Science 1172, ACISP '96 (Springer-Verlag, Berlin, 1996) 48–55Google Scholar
  8. 8.
    Krawczyk, H.: Secret sharing made short. In Lecture Notes in Computer Science 773, Advances in Cryptology — CRYPTO '93 (Springer-Verlag, Berlin, 1993) 136–146Google Scholar
  9. 9.
    Laih, C.S., Harn, L., Lee, J.Y., Hwang, T.: Dynamic threshold scheme based on the definition of cross-product in an n-dimensional linear space. Journal Information Science and Engineering 7 (1991) 13–23Google Scholar
  10. 10.
    Pedersen, T.P.: Distributed provers with applications to undeniable signatures. In D. W. Davies, editor, Lecture Notes in Computer Science 547, Advances in Cryptology — Eurocrypt '91 (Springer-Verlag, Berlin, 1991) 221–238Google Scholar
  11. 11.
    Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In J. Feigenbaum, editor, Lecture Notes in Computer Science 576, Advances in Cryptology — Crypto '91 (Springer-Verlag, Berlin, 1992) 129–140Google Scholar
  12. 12.
    Pinch, R.G.E.: On-line multiple secret sharing. Electronics Letters 32 (1996) 1087–1088CrossRefGoogle Scholar
  13. 13.
    Shamir, A.: How to share a secret. Communications of the ACM 22 (1979) 612–613CrossRefGoogle Scholar
  14. 14.
    Shannon, C.E.: Communication theory of secrecy systems. Bell System Technical Journal 28 (1949) 656–715Google Scholar
  15. 15.
    Sun, H.-M., Shieh, S.-P.: Construction of dynamic threshold schemes. Electronics Letters 30 (1994) 2023–2025CrossRefGoogle Scholar
  16. 16.
    Zhang, Y., Hardjono, T., Seberry, J.: Reusing shares in secret sharing schemes. The Computer Journal 37 (1994) 199–205CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Liqun Chen
    • 1
  • Dieter Gollmann
    • 1
  • Chris J. Mitchell
    • 1
  • Peter Wild
    • 1
  1. 1.Information Security Group, Royal HollowayUniversity of LondonEghamUK

Personalised recommendations