On the Relation of Random Grid and Deterministic Visual Cryptography

Visual cryptography is a special type of secret sharing. Two models of visual cryptography have been independently studied: 1) deterministic visual cryptography, introduced by Naor and Shamir, and 2) random grid visual cryptography, introduced by Kafri and Keren. In this paper, we show that there is a strict relation between these two models. In particular, we show that to any random grid scheme corresponds a deterministic scheme and vice versa. This allows us to use results known in a model also in the other model. By exploiting the (many) results known in the deterministic model, we are able to improve several schemes and to provide many upper bounds for the random grid model and by exploiting some results known for the random grid model, we are also able to provide new schemes for the deterministic model. A side effect of this paper is that future new results for any one of the two models should not ignore, and in fact be compared with, the results known in the other model.

[1]  Tzung-Her Chen,et al.  Threshold visual secret sharing by random grids , 2011, J. Syst. Softw..

[2]  Douglas R. Stinson,et al.  Threshold Visual Cryptography Schemes with Specified Whiteness Levels of Reconstructed Pixels , 2002, Des. Codes Cryptogr..

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

[4]  Hans Ulrich Simon Perfect Reconstruction of Black Pixels Revisited , 2005, FCT.

[5]  Chin-Chen Chang,et al.  Self-Verifying Visual Secret Sharing Using Error Diffusion and Interpolation Techniques , 2009, IEEE Transactions on Information Forensics and Security.

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

[7]  Hans Ulrich Simon,et al.  Determining The Optimal Contrast For Secret Sharing Schemes In Visual Cryptography , 2003, Comb. Probab. Comput..

[8]  Alfredo De Santis,et al.  Using Colors to Improve Visual Cryptography for Black and White Images , 2011, ICITS.

[9]  Shyong Jian Shyu,et al.  General Constructions for Threshold Multiple-Secret Visual Cryptographic Schemes , 2013, IEEE Transactions on Information Forensics and Security.

[10]  Pei-Ling Chiu,et al.  An Extended Visual Cryptography Algorithm for General Access Structures , 2012, IEEE Transactions on Information Forensics and Security.

[11]  Feng Liu,et al.  Step Construction of Visual Cryptography Schemes , 2010, IEEE Transactions on Information Forensics and Security.

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

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

[14]  Tzung-Her Chen,et al.  Visual secret sharing by random grids revisited , 2009, Pattern Recognit..

[15]  Wei Sun,et al.  Generalized Random Grid and Its Applications in Visual Cryptography , 2013, IEEE Transactions on Information Forensics and Security.

[16]  Wei Sun,et al.  Random grid-based visual secret sharing with abilities of OR and XOR decryptions , 2013, J. Vis. Commun. Image Represent..

[17]  Ching-Nung Yang,et al.  Aspect ratio invariant visual secret sharing schemes with minimum pixel expansion , 2005, Pattern Recognit. Lett..

[18]  Ran-Zan Wang,et al.  Incrementing visual cryptography using random grids , 2010 .

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

[20]  Alfredo De Santis,et al.  Visual cryptography schemes with perfect reconstruction of black pixels , 1998, Comput. Graph..

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

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

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

[24]  Stelvio Cimato,et al.  Probabilistic Visual Cryptography Schemes , 2006, Comput. J..

[25]  Alfredo De Santis,et al.  Extended capabilities for visual cryptography , 2001, Theor. Comput. Sci..

[26]  Sian-Jheng Lin,et al.  Optimal (2, n) and (2, infinity) visual secret sharing by generalized random grids , 2012, J. Vis. Commun. Image Represent..

[27]  Rafail Ostrovsky,et al.  Visual cryptography on graphs , 2008, J. Comb. Optim..

[28]  Wei-Ho Chung,et al.  A Probabilistic Model of $(t,n)$ Visual Cryptography Scheme With Dynamic Group , 2012, IEEE Transactions on Information Forensics and Security.

[29]  Xiaobo Li,et al.  Towards Shift Tolerant Visual Secret Sharing Schemes , 2010, IEEE Transactions on Information Forensics and Security.

[30]  Ching-Nung Yang,et al.  Optimal Contrast Grayscale Visual Cryptography Schemes With Reversing , 2013, IEEE Transactions on Information Forensics and Security.

[31]  Bin Yu,et al.  Visual Cryptography and Random Grids Schemes , 2013, IWDW.

[32]  Young-Chang Hou,et al.  Visual cryptography for color images , 2003, Pattern Recognit..

[33]  E. Keren,et al.  Encryption of pictures and shapes by random grids. , 1987, Optics letters.

[34]  Stelvio Cimato,et al.  Visual cryptography schemes with optimal pixel expansion , 2006, Theor. Comput. Sci..

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

[36]  Hans Ulrich Simon,et al.  Contrast-optimal k out of n secret sharing schemes in visual cryptography , 2000, Theor. Comput. Sci..

[37]  Ching-Nung Yang,et al.  Size-Adjustable Visual Secret Sharing Schemes , 2005, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

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

[39]  Paolo D'Arco,et al.  Secure Two-Party Computation: A Visual Way , 2013, ICITS.

[40]  Chuankun Wu,et al.  Embedded Extended Visual Cryptography Schemes , 2011, IEEE Transactions on Information Forensics and Security.

[41]  Alfredo De Santis,et al.  Color visual cryptography schemes for black and white secret images , 2013, Theor. Comput. Sci..

[42]  Alfredo De Santis,et al.  Measure-Independent Characterization of Contrast Optimal Visual Cryptography Schemes , 2013, ICITS.

[43]  Feng Liu,et al.  A new definition of the contrast of visual cryptography scheme , 2010, Inf. Process. Lett..

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

[45]  Ching-Nung Yang,et al.  New visual secret sharing schemes using probabilistic method , 2004, Pattern Recognit. Lett..