## “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. Maximum transversal in partial Latin squares and rainbow matchingsDiscrete Appl. Math. 155 (2007), 558-565  [abstract]
 2. M. Zaker Greedy defining sets of graphsAustralas. 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 setsDiscrete Math. 199 (1999), 233-236  [abstract]
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