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A Combinatorial Algorithm for Sharing a Key

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Advanced Computer Systems

Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 664))

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Abstract

We propose a novel algorithm for sharing a key. This algorithm is similar to that proposed by Benaloh and Leichter, but does not require to store (or compute online) the minimal authorized subsets. The algorithm uses the representation of the access structure (that is the collection of authorized sets) by means of transversals of the set of maximal elements of the ideal dual to the access structure.

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Bibliography

  1. E. Bach and J. Shallit, Algorithmic Number Theory, MIT Press, 1996.

    Google Scholar 

  2. J. Benaloh and J. Leichter, Generalized secret sharing and monotone functions, in: Advances in cryptology — CRYPTO’88, Lecture Notes in Computer Science, vol. 403, Springer-Verlag, 1990, pp. 27–35.

    Article  MathSciNet  Google Scholar 

  3. H. Cohen, A Course in Computational Algebraic Number Theory, Springer-Verlag, 1995. (Second editon)

    Google Scholar 

  4. W. Dobrzański, A. Soroczuk, M. Srebrny and MA. Srebmy Jr, Distributed password, Technical Report, Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland, December 1999; also in this volume.

    Google Scholar 

  5. N. Koblitz, Algebraic Aspects of Cryptography, Springer-Verlag, 1998.

    Google Scholar 

  6. E. Kranakis, Primality and Cryptography, Wiley, 1986.

    Google Scholar 

  7. Z. Lonc, V.W. Marek, Filters in Boolean Lattices with Applications, submitted..

    Google Scholar 

  8. A. Menezes, P. V. Oorschot and S. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997.

    Google Scholar 

  9. M. Mignotte, How to share a secret, in: Cryptography, Lecture Notes in Computer Science, vol. 149, Springer-Verlag, 1983, pp. 371–375.

    Article  MathSciNet  Google Scholar 

  10. Ch.H. Papadimitriou, Computational complexity, Addison Wesley, 1994.

    Google Scholar 

  11. R.L. Rivest, Cryptography, In: Handbook of Theoretical Computer Science, vol. A, pp. 717–755.

    Google Scholar 

  12. R.L. Rivest, A. Shamir and L.M. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM 20(1979,), pp. 120–126.

    MathSciNet  Google Scholar 

  13. B. Schneider, Applied Cryptography, Wiley, 1996.

    Google Scholar 

  14. A. Shamir, How to share a secret, Communications of the ACM, 22(1979), p. 612–613.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  16. D. R. Stinson, On some methods for unconditionally secure key distribution and broadcast encryption, Designs, codes and cryptography 12(1997)3, pp. 215–243.

    Article  MathSciNet  MATH  Google Scholar 

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Jerzy Sołdek Jerzy Pejaś

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© 2002 Springer Science+Business Media New York

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Lonc, Z., Srebrny, M. (2002). A Combinatorial Algorithm for Sharing a Key. In: Sołdek, J., Pejaś, J. (eds) Advanced Computer Systems. The Springer International Series in Engineering and Computer Science, vol 664. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8530-9_32

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  • DOI: https://doi.org/10.1007/978-1-4419-8530-9_32

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-4635-7

  • Online ISBN: 978-1-4419-8530-9

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