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Title |
ON HOMOGENEOUS IDEAL SECRET SHARING SCHEMES AND
MATROIDS CORANK THREE |
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Authors |
MEDVEDEV Nikita, senior lecturer of the
department «Information Technologies and Information
Security» Ural State University of Railway Transport,
Ph.D. Bld. 66, Kolmogorova Str., Ekaterinburg,
620075. E-mail: itcrypt@gmail.com
TITOV Sergey, professor of department «Higher
and Applied Mathematics» Ural State University of
Railway Transport, Prof. Bld. 66, Kolmogorova Str.,
Ekaterinburg, 620075. E-mail: sergey.titov@usaaa.ru |
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Section |
MATHEMATICAL METHODS IN INFORMATION SECURITY |
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Issue |
18 |
Page |
21–26 |
index UDC |
519.151 + 519.725 |
index LBC |
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Abstract |
The work is dedicated to questions relating to the
delimitation of access by the ideal perfect secret
sharing schemes and matroids. The problem of
describing homogeneous secret sharing schemes, with
qualified coalition of the same capacity.
Accordingly, for the matroid corresponding to the
ideal scheme, proposed the term homogeneous matroid
if all its circuits have the same capacity. It is
proved that homogeneous separating matroid with
capacity of co-hyperplanes m 3 is either an affine
plane of order m, or a projective plane of order (m
– 1) with straight lines as co-hyperplanes. |
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Keywords |
homogeneous access structure, secret
sharing schemes, matroids, cycles. |
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