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Cheating Prevention in Linear Secret Sharing

  • Josef Pieprzyk
  • Xian-Mo Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2384)

Abstract

Cheating detection in linear secret sharing is considered. The model of cheating extends the Tompa-Woll attack and includes cheating during multiple (unsuccessful) recovery of the secret. It is shown that shares in most linear schemes can be split into subshares. Subshares can be used by participants to trade perfectness of the scheme with cheating prevention. Evaluation of cheating prevention is given in the context of different strategies applied by cheaters.

Keywords

Cryptography Secret Sharing Linear Secret Sharing Schemes Cheating Detection Cheating Identification 

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References

  1. 1.
    C. Asmuth and J. Bloom. A modular approach to key safeguarding. IEEE Transactions on Information Theory, IT-29 No. 2:208–211, 1983.CrossRefMathSciNetGoogle Scholar
  2. 2.
    J. Benaloh and J. Leichter. Generalised secret sharing and monotone functions. In S. Goldwasser, editor, Advances in Cryptology-CRYPTO’88, LNCS No. 403, pages 27–36. Springer-Verlag, 1988.Google Scholar
  3. 3.
    G. R. Blakley. Safeguarding cryptographic keys. In Proc. AFIPS 1979 National Computer Conference, pages 313–317. AFIPS, 1979.Google Scholar
  4. 4.
    E.F. Brickell and D.R. Stinson. The detection of cheaters in threshold schemes. In S. Goldwasser, editor, Advances in Cryptology-CRYPTO’88, LNCS No. 403, pages 564–577. Springer-Verlag, 1988.Google Scholar
  5. 5.
    M. Carpentieri. A perfect threshold secret sharing scheme to identify cheaters. Designs, Codes and Cryptography, 5(3):183–187, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    M. Carpentieri, A. De Santis, and U. Vaccaro. Size of shares and probability of cheating in threshold schemes. In T. Helleseth, editor, Advances in Cryptology-EUROCRYPT’93, LNCS No. 765, pages 118–125. Springer, 1993.Google Scholar
  7. 7.
    H. Ghodosi, J. Pieprzyk, R. Safavi-Naini, and H. Wang. On construction of cumulative secret sharing. In C. Boyd and E. Dawson, editor, In Proceedings of the Third Australasian Conference on Information Security and Privacy (ACISP’98), LNCS No. 1438, pages 379–390. Springer-Verlag, 1998.Google Scholar
  8. 8.
    H. Lin, and L. Haen. A generalised secret sharing scheme with cheater detection. In H. Imai, R. Rivest, and T. Matsumoto, editor, In Proceedings of ASIACRYPT’91, LNCS No. 739, pages 149–158. Springer-Verlag, 1993.Google Scholar
  9. 9.
    M. Ito, A. Saito, and T. Nishizeki. Secret sharing scheme realizing general access structure. In Proceedings IEEE Globecom’ 87, pages 99–102. IEEE, 1987.Google Scholar
  10. 10.
    E.D. Karnin, J.W. Greene, and M.E. Hellman. On secret sharing systems. IEEE Transactions on Information Theory, IT-29:35–41, 1983.CrossRefMathSciNetGoogle Scholar
  11. 11.
    K. Martin, J. Pieprzyk, R. Safavi-Naini, and H. Wang. Changing thresholds in the absence of secure channels. In Proceedings of the Fourth Australasian Conference on Information Security and Privacy (ACISP’99), LNCS No. 1587, pages 177–191. Springer-Verlag, 1999.Google Scholar
  12. 12.
    W. Ogata and K. Krurosawa. Optimum secret shares scheme secure against cheating. In U. Maurer, editor, Advances in Cryptology-EUROCRYPT’96, LNCS No. 1070, pages 200–211.Google Scholar
  13. 13.
    T. Rabin and M. Ben-Or. Verifiable secret sharing and multiparty protocols with honest majority. In Proceedings of 21st ACM Symposium on Theory of Computing, pages 73–85, 1989.Google Scholar
  14. 14.
    A. Shamir. How to share a secret. Communications of the ACM, 22:612–613, November 1979.Google Scholar
  15. 15.
    G. J. Simmons, W. Jackson, and K. Martin. The geometry of shared secret schemes. Bulletin of the ICA, 1:71–88, 1991.zbMATHMathSciNetGoogle Scholar
  16. 16.
    M. Tompa and H. Woll. How to share a secret with cheaters. Journal of Cryptology, 1(2):133–138, 1988.zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Josef Pieprzyk
    • 1
  • Xian-Mo Zhang
    • 1
  1. 1.Centre for Advanced Computing — Algorithms and Cryptography Department of ComputingMacquarie UniversitySydneyAustralia

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