Non Resident Researcher (non-resident), School of Mathematics
(2004 - 2005 )
Past IPM Positions
Associate Researcher (non-resident), School of Mathematics
(2002 - 2003)
Visual cryptography is a method to encrypt printed materials like pictures.
Informally a visual cryptography scheme for a set P
of n participants is a method to encode a secret image SI into n shadow images
called shares, where each participant in P
receives one share. Certain qualified subsets of participants can ``visually''
recover the secret image, but other, forbidden, sets of participants have no
information (in an information?theoretic sense) on SI . A ``visual'' recovery
for a set X ? P
consists of xeroxing the shares given to the participants in X onto
transparencies, and then stacking them. The participants in a qualified set X
will be able to see the secret image without any knowledge of cryptography and
without performing any cryptographic computation.
In this project we introduce a model for visual cryptography scheme for general access structures, based on the concept of cognitive metric. A cognitive distance among binary digitized pictures, measures how much the pictures are close to each other. We give a solution for our model, which is a modification of model given by Shamir and Naor, [M. Naor and A. Shamir, Visual Cryptography, in ?dvances in Cryptography - Eurocrypt '94", A. De Santis Ed., Vol. 950 of Lecture Notes in Computer Science, Springer - Verlag, Berlin, pp. 1-12, 1995.] . We consider access structures defined on the edges of a graph. We determine some bounds for pixel expansion and contrast for these access structures and some characterizations of graphs with given pixel expansion.
Present Research Project at IPM
|Visual Cryptography Schemes|
|1.||M. Zaker |
Maximum transversal in partial Latin squares and rainbow matchings
Discrete Appl. Math. 155 (2007), 558-565 [abstract]
|2.||M. Zaker |
Greedy defining sets of graphs
Australas. J. Combin. 23 (2001), 231-235 [abstract]
|3.||H. Hajiabolhassan, M.L. Mehrabadi, R. Tusserkani and M. Zaker |
A characterization of uniquely vertex colorable graphs using minimal defining sets
Discrete Math. 199 (1999), 233-236 [abstract]