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Constructions of Cheating Immune Secret Sharing

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Information Security and Cryptology — ICISC 2001 (ICISC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2288))

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Abstract

The work addresses the problem of cheating prevention in secret sharing. Two cheating scenarios are considered. In the first one, the cheaters always submit invalid shares to the combiner. In the second one, the cheaters collectively decide which shares are to be modified so the combiner gets a mixture of valid and invalid shares from the cheaters. The secret scheme is said to be k-cheating immune if any group of k cheaters has no advantage over honest participants. The paper investigates cryptographic properties of the defining function of secret sharing so the scheme is k-cheating immune. Constructions of secret sharing immune against k cheaters are given.

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References

  1. M. Carpentieri. A perfect threshold secret sharing scheme to identify cheaters. Designs, Codes and Cryptography, 5(3):183–187, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  2. 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-Verlag, 1993.

    Google Scholar 

  3. C. Ding, D. Pei and A Salomaa. Chinese remainder theorem: applications in computing, coding and cryptography. World Scientific, Singapore, 1996

    Google Scholar 

  4. P. Feldman. A practical scheme for non-interactive verifiable secret sharing. In Proceedings of the 28th IEEE Symposium on Foundations of Computer Science, pages 427–437. IEEE, 1987.

    Google Scholar 

  5. F.J. MacWilliams and N.J.A. Sloane. The theory of error-correcting codes. North-Holland, Amsterdam, 1977.

    Google Scholar 

  6. K. Nyberg. On the construction of highly nonlinear permutations. In Advances in Cryptology-EUROCRYPT’92, LNCS No 658, pages 92–98. Springer-Verlag, 1993.

    Google Scholar 

  7. K. Nyberg and L. R. Knudsen. Provable security against differential cryptanalysis. In Advances in Cryptology-CRYPTO’92, LNCS No 740, pages 566–574. Springer-Verlag, 1993.

    Google Scholar 

  8. T.P. Pedersen. Non-interactive and information-theoretic secure verifiable secret sharing. In J. Feigenbaum, editor, Advances in Cryptology-CRYPTO’91, LNCS No 576, pages 129–140. Springer-Verlag, 1992.

    Google Scholar 

  9. J. Pieprzyk and X. M. Zhang. Cheating prevention in secret sharing over GF(p t). to appear in Indocrypt 2001.

    Google Scholar 

  10. B. Preneel, W. V. Leekwijck, L. V. Linden, R. Govaerts, and J. Vandewalle. Propagation characteristics of boolean functions. In Advances in Cryptology-EUROCRYPT’90, LNCS No 437, pages 155–165. Springer-Verlag, 1991.

    Google Scholar 

  11. 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 

  12. O. S. Rothaus. On “bent” functions. Journal of Combinatorial Theory (A), 20:300–305, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  13. B. Schoenmakers. A simple publicly verifiable secret sharing scheme and its application to electronic voting. In M. Wiener, editor, Advances in Cryptology-CRYPTO’99, LNCS No 1666, pages 148–164. Springer-Verlag, 1999.

    Google Scholar 

  14. J. Seberry, X. M. Zhang, and Y. Zheng. On constructions and nonlinearity of correlation immune functions. In Advances in Cryptology-EUROCRYPT’93, LNCS No 765, pages 181–199. Springer-Verlag, 1994.

    Google Scholar 

  15. J. Seberry, X. M. Zhang, and Y. Zheng. Nonlinearity and propagation characteristics of balanced boolean functions. Information and Computation, 119(1):1–13, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  16. T. Siegenthaler. Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Transactions on Information Theory, IT-30 No. 5:776–779, 1984.

    Article  MathSciNet  Google Scholar 

  17. M. Stadler. Publicly verifiable secret sharing. In U. Maurer, editor, Advances in Cryptology-EUROCRYPT’96, LNCS No 1070, pages 190–199. Springer-Verlag, 1996.

    Google Scholar 

  18. D.R. Stinson. Cryptography: Theory and Practice. CRC Press, 1995.

    Google Scholar 

  19. A. F. Webster and S. E. Tavares. On the design of S-boxes. In Advances in Cryptology-CRYPTO’85, LNCS No 219, pages 523–534. Springer-Verlag, 1986.

    Google Scholar 

  20. Martin Tompa and Heather Woll. How to share a secret with cheaters. In A.M. Odlyzko, editor, Advances in Cryptology-CRYPTO’86, LNCS No 263, pages 261–265. Springer-Verlag, 1987.

    Google Scholar 

  21. X. M. Zhang and J. Pieprzyk, Cheating immune secret sharing. to appear in The Third International Conference on Information and Communication Security (ICICS) 2001.

    Google Scholar 

  22. X. M. Zhang and Y. Zheng. Cryptographically resilient functions. IEEE Transactions on Information Theory, 43(5):1740–1747, 1997.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computing, Macquarie University, 2109, Sydney, NSW, Australia

    Josef Pieprzyk

  2. School of IT and CS, University of Wollongong, 2522, Wollongong, NSW, Australia

    Zhang Xian-Mo

Authors
  1. Josef Pieprzyk
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  2. Zhang Xian-Mo
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Editor information

Editors and Affiliations

  1. International Research center for Information Security (IRIS), Information and Communications University (ICU), 58-4, Hwaam-dong-Yusong-gu, 305-732, Daejeon, Korea

    Kwangjo Kim

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© 2002 Springer-Verlag Berlin Heidelberg

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Pieprzyk, J., Xian-Mo, Z. (2002). Constructions of Cheating Immune Secret Sharing. In: Kim, K. (eds) Information Security and Cryptology — ICISC 2001. ICISC 2001. Lecture Notes in Computer Science, vol 2288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45861-1_18

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  • DOI: https://doi.org/10.1007/3-540-45861-1_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43319-4

  • Online ISBN: 978-3-540-45861-6

  • eBook Packages: Springer Book Archive

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