“Manouchehr Zaker”

Tel:  +98 21 2290928
Fax:  +98 21 2290648

IPM Positions

Non Resident Researcher (non-resident), School of Mathematics
(2004 - 2005 )

Past IPM Positions

Associate Researcher (non-resident), 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. 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

Related Papers

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]
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