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
E. Bach and J. Shallit, Algorithmic Number Theory, MIT Press, 1996.
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.
H. Cohen, A Course in Computational Algebraic Number Theory, Springer-Verlag, 1995. (Second editon)
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.
N. Koblitz, Algebraic Aspects of Cryptography, Springer-Verlag, 1998.
E. Kranakis, Primality and Cryptography, Wiley, 1986.
Z. Lonc, V.W. Marek, Filters in Boolean Lattices with Applications, submitted..
A. Menezes, P. V. Oorschot and S. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997.
M. Mignotte, How to share a secret, in: Cryptography, Lecture Notes in Computer Science, vol. 149, Springer-Verlag, 1983, pp. 371–375.
Ch.H. Papadimitriou, Computational complexity, Addison Wesley, 1994.
R.L. Rivest, Cryptography, In: Handbook of Theoretical Computer Science, vol. A, pp. 717–755.
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.
B. Schneider, Applied Cryptography, Wiley, 1996.
A. Shamir, How to share a secret, Communications of the ACM, 22(1979), p. 612–613.
D. R. Stinson, Cryptography, Theory and Practice, CRC Press 1995.
D. R. Stinson, On some methods for unconditionally secure key distribution and broadcast encryption, Designs, codes and cryptography 12(1997)3, pp. 215–243.
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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
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