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Color Visual Cryptography Schemes Using Linear Algebraic Techniques over Rings

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Information Systems Security (ICISS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12553))

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Abstract

The research on color Visual Cryptographic Scheme (VCS) is much more difficult than that of the black and white VCS. This is essentially because of the fact that in color VCS, the rule for superimposition of two colors is not that simple as in black and white VCS. It was a long standing open issue whether linear algebraic technique in constructing Black and White visual cryptographic schemes could also be extended for color images. It was thought that such an extension was impossible. However, we resolve this issue by providing color VCS in same color model for the threshold access structures by extending linear algebraic techniques from the binary field \(\mathbb {Z}_2\) to finite ring \(\mathbb {Z}_c\) of integers modulo c. We first give a construction method based on linear algebra to share a color image for an (n, n)-threshold access structure. Then we give constructions for (2, n)-threshold access structures and in general (k, n)-threshold access structures. Existing methodology for constructing color VCS in same color model assumes the existence of black and white VCS, whereas our construction is a direct one. Moreover, we give closed form formulas for pixel expansion which is combinatorially a difficult task. Lastly, we give experimental results and propose a method to reduce pixel expansion.

S. Dutta—is grateful to the NICT, Japan for financial support under the NICT International Exchange Program during 2018-19 when the preliminary draft was prepared.

Md K. Sardar—is thankful to the CSIR, Govt. of India for providing financial support (Award no. 09/028(0975)/2016-EMR-1).

A. Adhikari—Research of A. Adhikari is partially supported by DST-SERB Project MATRICS vide Sanction Order: MTR/2019/001573.

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Author information

Authors and Affiliations

  1. University of Calgary, Calgary, Canada

    Sabyasachi Dutta

  2. University of Calcutta, Kolkata, India

    Md Kutubuddin Sardar

  3. Presidency University, Kolkata, India

    Avishek Adhikari

  4. CSIRO, Data61, Sydney, Australia

    Sushmita Ruj

  5. Kyushu University, Fukuoka, Japan

    Kouichi Sakurai

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  1. Sabyasachi Dutta
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  3. Avishek Adhikari
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  4. Sushmita Ruj
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  5. Kouichi Sakurai
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Correspondence to Sabyasachi Dutta .

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Editors and Affiliations

  1. UNSW Sydney, Sydney, NSW, Australia

    Salil Kanhere

  2. IIT Bombay, Mumbai, India

    Vishwas T Patil

  3. IIT Kharagpur, Kharagpur, West Bengal, India

    Shamik Sural

  4. IIT Jammu, Jammu, India

    Manoj S Gaur

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Dutta, S., Sardar, M.K., Adhikari, A., Ruj, S., Sakurai, K. (2020). Color Visual Cryptography Schemes Using Linear Algebraic Techniques over Rings. In: Kanhere, S., Patil, V.T., Sural, S., Gaur, M.S. (eds) Information Systems Security. ICISS 2020. Lecture Notes in Computer Science(), vol 12553. Springer, Cham. https://doi.org/10.1007/978-3-030-65610-2_13

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  • DOI: https://doi.org/10.1007/978-3-030-65610-2_13

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