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A General Decomposition Construction for Incomplete Secret Sharing Schemes

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Abstract

A secret sharing scheme for an incomplete access structure (Γ,Δ) is a method of distributing information about a secret among a group of participants in such a way that sets of participants in Γ can reconstruct the secret and sets of participants in Δ can not obtain any new information about the secret. In this paper we present a more precise definition of secret sharing schemes in terms of information theory, and a new decomposition theorem. This theorem generalizes previous decomposition theorems and also works for a more general class of access structures. We demonstrate some applications of the theorem.

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References

  1. P. Beguin and A. Cresti, General short computational secret sharing schemes, Adv. in Cryptology: EUROCRYPT' 95, Lecture Notes in Comput. Sci., 921 (1995) pp. 194-208.

  2. A. Beutelspacher, How to say no, Advances in Cryptology: Proceedings of EUROCRYPT' 89, Lecture Notes in Comput. Sci., 434 (1990) pp. 491-496.

  3. G. R. Blakley and G. A. Kabatianski, On general perfect secret sharing schemes, Adv. in Cryptology: CRYPTO'95, Lecture Notes in Comput. Sci., 963 (1995) pp. 367-371.

  4. G. R. Blakley and C. Meadows, Security of ramp schemes, Adv. in Cryptology: CRYPTO' 84, Lecture Notes in Comput. Sci., 196 (1985) pp. 242-268.

  5. C. Blundo, Secret sharing schemes for access structures based on graphs, Tesi di Laurea, 1991. (in Italian).

  6. C. Blundo, A. De Santis, A. Herzberg, S. Kutten, U. Vaccaro, and M. Yung, Perfectly-secure key distribution for dynamic conferences, Adv. in Cryptology: CRYPTO'92, Lecture Notes in Comput. Sci., 740 (1993) pp. 471-481.

  7. C. Blundo, A. De Santis, D.R. Stinson, and U. Vaccaro, Graph decompositions and secret sharing schemes, J. Cryptology, Vol. 8 (1995) pp. 39-64.

    Google Scholar 

  8. E. F. Brickell and D. M. Davenport, On the classification of ideal secret sharing schemes, J. Cryptology, Vol. 4 (1991) pp. 123-134.

    Google Scholar 

  9. E. F. Brickell and D. R. Stinson, Some improved bounds on the information rate of perfect secret sharing schemes, J. Cryptology, Vol. 5 (1992) pp. 153-166.

    Google Scholar 

  10. R. M. Capocelli, A. De Santis, L. Gargano, and U. Vaccaro, A note on secret sharing schemes, Sequences II: Methods in Communications, Security and Computer Science, Springer Verlag (1993) pp. 335-344.

  11. R. M. Capocelli, A. De Santis, L. Gargano, and U. Vaccaro, On the size of shares for secret sharing schemes, J. Cryptology, Vol. 6 (1993) pp. 157-167.

    Google Scholar 

  12. T. M. Cover and J. A. Thomas, Elements of Information Theory, John Wiley and Sons, Inc. (1991).

  13. M. van Dijk, On the information rate of perfect secret sharing schemes, Designs, Codes, and Cryptography, Vol. 6 (1995) pp. 143-169.

    Google Scholar 

  14. M. van Dijk, A linear construction of secret sharing schemes, Designs, Codes and Cryptography., Vol. 12 (1997) pp. 161-201.

    Google Scholar 

  15. R. G. Gallager. Information Theory and Reliable Communications, John Wiley, New York (1968).

    Google Scholar 

  16. W.-A. Jackson and K. M. Martin, Combinatorial models for perfect secret sharing schemes, to appear in Journal of Combin. Math. and Combin. Comput.

  17. W.-A. Jackson and K. M. Martin, Perfect secret sharing schemes on five participants, Designs, Codes and Cryptography, Vol. 9 (1996) pp. 267-286.

    Google Scholar 

  18. W.-A. Jackson, K. M. Martin, and C. M. O'Keefe, Efficient secret sharing without a mutually trusted authority, Adv. in Cryptology: EUROCRYPT' 95, Lecture Notes in Comput. Sci., 921 (1995) pp. 183-193.

  19. W.-A. Jackson and K. M. Martin, An algorithm for efficient geometric secret sharing schemes, to appear in Utilitas Mathematica.

  20. K. Kurosawa, K. Okada, K. Sakano, W. Ogata, and S. Tsujii, Nonperfect secret sharing schemes and matroids, Adv. in Cryptology: EUROCRYPT' 93, Lecture Notes in Comput. Sci., 765 (1994) pp. 126-141.

  21. K. M. Martin, Discrete structures in the theory of secret sharing, PhD thesis, Royal Holloway and Bedford New College, University of London (1991).

  22. K. M. Martin, New secret sharing schemes from old, Journal of Combin. Math. and Combin. Comput., Vol. 14 (1993) pp. 65-77.

    Google Scholar 

  23. W. Ogata, K. Kurosawa, and S. Tsujii, Nonperfect secret sharing schemes, Adv. in Cryptology: AUSCRYPT' 92, Lecture Notes in Comput. Sci., 718 (1993) pp. 56-66.

  24. K. Okada and K. Kurosawa, Lower bound on the size of shares of nonperfect secret sharing schemes, Proceedings of ASIACRYPT' 94, Lecture Notes in Comput. Sci., (1995) pp. 33-41.

  25. A. Shamir, How to share a secret, Commun. of the ACM, Vol. 22 (1979) pp. 612-613.

    Google Scholar 

  26. G. J. Simmons, An introduction to shared secret and/or shared control schemes and their application, Contemporary Cryptology, The Science of Information Integrity, (G. J. Simmons, ed.), IEEE Press (1992).

  27. D. R. Stinson, Bibliography on secret sharing schemes, available online. http://bibd.unl.edu/~stinson/ssbib.html.

  28. D. R. Stinson, An explication of secret sharing schemes, Designs, Codes and Cryptography, Vol. 2 (1992) pp. 357-390.

    Google Scholar 

  29. D. R. Stinson. New general lower bounds on the information rate of secret sharing schemes, Advances in Cryptology: CRYPTO' 92, Lecture Notes in Comput. Sci., 740 (1993) pp. 168-182.

    Google Scholar 

  30. D. R. Stinson, Decomposition constructions for secret sharing schemes, IEEE Trans. Inform. Theory, Vol. IT-40 (1994) pp. 118-125.

    Google Scholar 

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Authors and Affiliations

  1. Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA, Eindhoven, The Netherlands

    Marten van Dijk

  2. Department of Pure Mathematics, The University of Adelaide, Adelaide, SA, 5005, Australia

    Wen-Ai Jackson

  3. ESAT-COSIC, Katholieke Universiteit Leuven, Kard. Mercierlaan 94, B-3001, Heverlee, Belgium

    Keith M. Martin

Authors
  1. Marten van Dijk
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  2. Wen-Ai Jackson
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  3. Keith M. Martin
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Dijk, M.v., Jackson, WA. & Martin, K.M. A General Decomposition Construction for Incomplete Secret Sharing Schemes. Designs, Codes and Cryptography 15, 301–321 (1998). https://doi.org/10.1023/A:1008381427667

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