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Size of Broadcast in Threshold Schemes with Disenrollment

  • S. G. Barwick
  • W. -A. Jackson
  • Keith M. Martin
  • Peter R. Wild
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2384)

Abstract

Threshold schemes are well-studied cryptographic primitives for distributing information among a number of entities in such a way that the information can only be recovered if a threshold of entities cooperate. Establishment of a threshold scheme involves an initialisation overhead. Threshold schemes with disenrollment capability are threshold schemes that enable entities to be removed from the initial threshold scheme at less communication cost than that of establishing a new scheme. We prove a revised version of a conjecture of Blakley, Blakley, Chan and Massey by establishing a bound on the size of the broadcast information necessary in a threshold scheme with disenrollment capability that has minimal entity information storage requirements. We also investigate the characterisation of threshold schemes with disenrollment that meet this bound.

Keywords

Distinct Element Access Structure Secret Data Secret Sharing Scheme Secure Channel 
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.

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References

  1. 1.
    G. R. Blakley. Safeguarding cryptographic keys. Proceedings of AFIPS 1979 National Computer Conference, 48 (1979) 313–317.Google Scholar
  2. 2.
    B. Blakley, G.R. Blakley, A.H. Chan and J.L. Massey. Threshold schemes with disenrollment. In Advances in Cryptology-CRYPTO’92, LNCS 740 Springer-Verlag, Berlin (1993) 540–548.Google Scholar
  3. 3.
    C. Blundo, A. Cresti, A. De Santis and U. Vaccaro. Fully dynamic secret sharing schemes. In Advances in Cryptology-CRYPTO’ 93, LNCS 773, Springer, Berlin (1993) 110–125.Google Scholar
  4. 4.
    T.M. Cover and J.A. Thomas. Elements of Information Theory, John Wiley & Sons, New York (1991).zbMATHGoogle Scholar
  5. 5.
    Y. Desmedt and S. Jajodia. Redistributing secret shares to new access structures and its applications. Preprint (1997).Google Scholar
  6. 6.
    E.D. Karnin, J.W. Greene and M.E. Hellman. On secret sharing systems. IEEE Trans. on Inf. Th., 29 (1983) 35–41.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    K.M. Martin. Untrustworthy participants in perfect secret sharing schemes. In Cryptography and Coding III, (M.J. Ganley, Ed.) Clarendon Press, Oxford (1993) 255–264.Google Scholar
  8. 8.
    K.M. Martin, J. Pieprzyk, R. Safavi-Naini and H. Wang. Changing thresholds in the absence of secure channels. In Information Security and Privacy-ACISP’99, LNCS 1587, Springer, Berlin (1999) 177–191.CrossRefGoogle Scholar
  9. 9.
    K.M. Martin, R. Safavi-Naini and H. Wang. Bounds and techniques for efficient redistribution of secret shares to new access structures. The Computer Journal, 42, No. 8 (1999) 638–649.zbMATHCrossRefGoogle Scholar
  10. 10.
    A. Shamir. How to share a secret. Communications of the ACM, 22 (1979) 612–613.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    C.E. Shannon. Communication theory of secrecy systems. Bell System Tech. Journal, 28 (1949) 656–715.MathSciNetGoogle Scholar
  12. 12.
    G. J. Simmons. An introduction to shared secret and/or shared control schemes and their application. In Contemporary Cryptology, 441–497. IEEE Press, (1991).Google Scholar
  13. 13.
    D.R. Stinson. An explication of secret sharing schemes. Des. Codes Cryptogr., 2 (1992) 357–390.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Y. Tamura, M. Tada and E. Okamoto. Update of access structure in Shamir’s (k, n)-threshold scheme. Proceedings of The 1999 Symposium on Cryptography and Information Security, Kobe, Japan, January 26–29, (1999).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • S. G. Barwick
    • 1
  • W. -A. Jackson
    • 1
  • Keith M. Martin
    • 2
  • Peter R. Wild
    • 2
  1. 1.Department of Pure MathematicsUniversity of AdelaideAdelaideAustralia
  2. 2.Information Security Group, Royal HollowayUniversity of LondonEgham, SurreyUK

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