Linear algebraic techniques to construct monochrome visual cryptographic schemes for general access structure and its applications to color images

Though the monochrome (black and white) visual cryptography has a very rich literature, a very few papers have been published for the construction of general access structure. In this paper we put forward a method of construction of a strong monochrome visual cryptographic scheme (VCS) for general access structure using linear algebra. As a particular case of general access structure, $$(k,n)$$(k,n)-VCS for $$2 \le k \le n$$2≤k≤n is obtained. The $$(n,n)$$(n,n)-VCS obtained from the scheme attains the optimal pixel expansion as well as optimal relative contrast. We provide an efficient construction of $$(n-1,n)$$(n−1,n)-VCS. We further extend our monochrome VCS to color VCS for restricted access structures. Finally, we provide some interesting examples that will lead to some future research directions in the area of VCS.

[1]  Shyong Jian Shyu,et al.  Efficient visual secret sharing scheme for color images , 2006, Pattern Recognit..

[2]  Edward M. Reingold,et al.  Efficient generation of the binary reflected gray code and its applications , 1976, CACM.

[3]  Hiroki Koga,et al.  A general method for construction of (t, n)-threshold visual secret sharing schemes for color images , 2011, Des. Codes Cryptogr..

[4]  Shyong Jian Shyu,et al.  Image encryption by multiple random grids , 2009, Pattern Recognit..

[5]  Moni Naor,et al.  Visual Cryptography , 1994, Encyclopedia of Multimedia.

[6]  Alfredo De Santis,et al.  On the Contrast in Visual Cryptography Schemes , 1999, Journal of Cryptology.

[7]  Chin-Chen Chang,et al.  Safeguarding Visual Information using (t, n) Verifiable Secret Shares , 2011 .

[8]  Jim Hefferon,et al.  Linear Algebra , 2012 .

[9]  Ching-Nung Yang,et al.  $k$ Out of $n$ Region Incrementing Scheme in Visual Cryptography , 2012, IEEE Trans. Circuits Syst. Video Technol..

[10]  Eric R. Verheul,et al.  Constructions and Properties of k out of n Visual Secret Sharing Schemes , 1997, Des. Codes Cryptogr..

[11]  Ching-Nung Yang,et al.  New Colored Visual Secret Sharing Schemes , 2000, Des. Codes Cryptogr..

[12]  Hiroki Koga,et al.  New Constructions of the Lattice-Based Visual Secret Sharing Scheme Using Mixture of Colors , 2002, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[13]  Shyong Jian Shyu,et al.  Image encryption by random grids , 2007, Pattern Recognit..

[14]  Hirosuke Yamamoto,et al.  Proposal of a lattice-based visual secret sharing scheme for color and gray-scale images , 1998 .

[15]  Hirosuke Yamamoto,et al.  An Analytic Construction of the Visual Secret Sharing Scheme for Color Images , 2001 .

[16]  Duncan S. Wong,et al.  On the security of a visual cryptography scheme for color images , 2009, Pattern Recognit..

[17]  Bimal K. Roy,et al.  A New Black and White Visual Cryptographic Scheme for General Access Structures , 2004, INDOCRYPT.

[18]  Somnath Sikdar,et al.  A New (2, n)-Visual Threshold Scheme for Color Images , 2003, INDOCRYPT.

[19]  Bimal K. Roy,et al.  Applications of Partially Balanced Incomplete Block Designs in Developing (2, n) Visual Cryptographic Schemes , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[20]  Annalisa De Bonis,et al.  Improved Schemes for Visual Cryptography , 2001, Des. Codes Cryptogr..

[21]  Stelvio Cimato,et al.  Colored visual cryptography without color darkening , 2004, Theor. Comput. Sci..

[22]  Stefan Droste,et al.  New Results on Visual Cryptography , 1996, CRYPTO.

[23]  Mitsugu Iwamoto.  A Weak Security Notion for Visual Secret Sharing Schemes , 2012, IEEE Transactions on Information Forensics and Security.

[24]  Alfredo De Santis,et al.  Constructions and Bounds for Visual Cryptography , 1996, ICALP.

[25]  Alfredo De Santis,et al.  Contrast Optimal Threshold Visual Cryptography Schemes , 2003, SIAM J. Discret. Math..

[26]  Stelvio Cimato,et al.  Optimal Colored Threshold Visual Cryptography Schemes , 2005, Des. Codes Cryptogr..

[27]  Xiaobo Li,et al.  Probabilistic visual secret sharing schemes for grey-scale images and color images , 2007, Inf. Sci..

[28]  Avishek Adhikari,et al.  A New Visual Cryptographic Scheme Using Latin Squares , 2004 .

[29]  Alfredo De Santis,et al.  Visual Cryptography for General Access Structures , 1996, Inf. Comput..

[30]  Xiaobo Li,et al.  On general construction for extended visual cryptography schemes , 2009, Pattern Recognit..

[31]  W. Greub.  Linear Algebra , 1981 .

[32]  Ching-Nung Yang,et al.  Colored visual cryptography scheme based on additive color mixing , 2008, Pattern Recognit..

[33]  Ching-Nung Yang,et al.  $k$ Out of $n$ Region Incrementing Scheme in Visual Cryptography , 2012, IEEE Transactions on Circuits and Systems for Video Technology.