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IPM Positions 

Non Resident Researcher (nonresident), School of Mathematics
(2004  2005 ) 

Past IPM Positions 

Associate Researcher (nonresident), School of Mathematics
(2002  2003) 

Research Activities 

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. 112, 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  
Related Papers 
1.  M. Zaker Maximum transversal in partial Latin squares and rainbow matchings Discrete Appl. Math. 155 (2007), 558565 [abstract] 
2.  M. Zaker Greedy defining sets of graphs Australas. J. Combin. 23 (2001), 231235 [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), 233236 [abstract] 
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