The transition of visual secret sharing from a black &amp; white secret image to a color image is not straight-forward. There are several models of color superposition principle. In this paper we present color visual cryptographic scheme realizing monotone access structure. We first give a generic construction method to share a color image in same color model. In particular, our construction achieves maximal contrast. We also give a direct and efficient construction of visual secret sharing for (k, n) ∗-access structure. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

AVISHEK ADHIKARI

Pure Mathematics

S DUTTA

S RUJ

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Designs, Codes, and Cryptography

OR-based Visual Cryptographic Schemes (OVCS) suffer from poor visual quality of the reconstructed image. XOR-based visual secret sharing (XVCS) can be thought of as an alternative where the relative contrast of the reconstructed image is much better. Moreover, it is possible to achieve optimum relative contrast equal to 1 in XVCS which is an impossibility in case of OVCS. Although there are examples of XVCSs where optimum relative contrast is achieved but to the best of our knowledge, this is the first theoretical work to find a necessary and sufficient condition for a XOR-based VCS to achieve optimum relative contrast equal to 1 in terms of the underlying access structure. © Springer International Publishing AG. 2017.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Contrast Optimal XOR Based Visual Cryptographic Schemes

In this paper we put forward an efficient construction, based on linear algebraic technique, of a t-(k, n) ∗-visual cryptographic scheme (VCS) for monochrome images in which t participants are essential in a (k, n) -VCS. The scheme is efficient in the sense that it only requires solving a system of linear equations to construct the required initial basis matrices. To make the scheme more efficient, we apply the technique of deletion of common columns from the initial basis matrices to obtain the reduced basis matrices. However finding exact number of common columns in the initial basis matrices is a challenging problem. In this paper we deal with this problem. We first provide a construction and analysis of t-(k, n) ∗-VCS. We completely characterize the case of t-(n- 1 , n) ∗-VCS, 0 ≤ t≤ n- 1 , by finding a closed form of the exact number of common columns in the initial basis matrices and thereby deleting the common columns to get the exact value of the reduced pixel expansion and relative contrast of the efficient and simple scheme. Our proposed closed form for reduced pixel expansion of (n- 1 , n) -VCS matches with the numerical values of the optimal pixel expansions for every possible values of n that exist in the literature. We further deal with the (n- 2 , n) -VCS and resolve an open issue by providing an efficient algorithm for grouping the system of linear equations and thereby show that our proposed algorithm works better than the existing scheme based on the linear algebraic technique. Finally we provide a bound for reduced pixel expansion for (n- 2 , n) -VCS and numerical evidence shows it achieves almost optimal pixel expansion. © 2015, Springer Science+Business Media New York.

Constructions and analysis of some efficient t - (k, n) âˆ— -visual cryptographic schemes using linear algebraic techniques

XOR-based visual cryptographic schemes for non-monotonic (k, n)-threshold access structures deviate from the fact that the superset of any collection of k+1 or more participants may not get the secret back while providing their shares together. In this paper, we generalize this access structure to non-monotonic t-(k, n)∗-access structure in which tessential participants along with any other (k −t) participants can reveal the secret, 0 ≤ t ≤ k and 2 ≤ k ≤ n. This notion is a generalization of the non-monotonic (k, n)-threshold access structure in the sense that if we take t = 0, we get the non-monotonic (k, n)-threshold access structure. Visual cryptographic schemes for t-(k, n)∗-threshold access structure based on Boolean “OR” operations are available in the literature. However the contrast of the reconstructed image is very poor, resulting a very bad recovery of the secret image visually. In this paper we study the same scenario for the “XOR” basedmodel which providesmuch better relative contrast for the reconstructed secret image. We provide an efficient technique, based on simple linear algebra, to construct the basis matrices realizing the XOR-based non-monotone (k, n)-VCS with t many essential parties. The contrast of the scheme is significantly better than the existing OR-based schemes. Finally, for some restricted t-(k, n)∗ non-monotonic access structures, we provide a scheme which not only achieves the optimal relative contrast but also achieves the optimal pixel expansion. © Springer International Publishing Switzerland 2015.

Xor based non-monotone t-(K, n)âˆ—-visual cryptographic schemes using linear algebra

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) -VCS for 2 ≤ k ≤ n is obtained. The (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) -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. © 2013 Springer Science+Business Media New York.

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

The aim of our paper is to show how Partially Balanced Incomplete Block Designs (PBIBD) may be used to construct (2, n) visual cryptographic schemes for black and white images with small pixel expansion. In situations where uniformity of the participants with respect to the relative contrast is not important, our schemes work well since by allowing the relative contrast to vary depending on which two participants are recovering the image, they can keep the pixel expansion quite small. Thus our schemes have considerably smaller pixel expansion than many of the existing schemes. For some n and some pairs of participants recovering the image, our schemes have larger relative contrast than some existing schemes. Copyright © 2007 The Institute of Electronics, Information and Communication Engineers.

Journal	Data powered by TypesetDesigns, Codes, and Cryptography
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ISSN	0925-1022