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International Conference on Computer Vision and Graphics

ICCVG 2022: Computer Vision and Graphics pp 237–267Cite as

Error Analysis and Graphical Evidence of Randomness in Two Methods of Color Visual Cryptography

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Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 598))

Abstract

Analysis of errors in two methods of color visual cryptography with random shares introduced by us in previous publications was performed. In both methods the shares are random, and consequently, errors occur in the decoded image. In one of the methods, where the coding is done by unhiding the pixels, there are two types of errors: missing color errors and hiding failure errors. In the other method, where the coding is done by unhiding, only the missing color errors occur. Probabilities of the missing color errors were modelled mathematically and frequencies of two types of errors were tested experimentally for both methods. Tests demonstrate that the model is correct. The results show in which cases the considered methods exhibit more accurate decoding results. Also, the extended results of randomness tests conducted with the NIST statistical test suite on the results of coding for a set of typical benchmark images are presented in the form of histograms of p-values. These graphical results indicate that the shares are indeed truly random.

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Author information

Authors and Affiliations

  1. Institute of Information Technology, Warsaw University of Life Sciences—SGGW, Warsaw, Poland

    Leszek J. Chmielewski & Arkadiusz Orłowski

  2. Faculty of Mathematics and Informatics, University of Lodz, Łódź, Poland

    Mariusz Nieniewski

Authors
  1. Leszek J. Chmielewski
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  2. Mariusz Nieniewski
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  3. Arkadiusz Orłowski
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Corresponding author

Correspondence to Leszek J. Chmielewski .

Editor information

Editors and Affiliations

  1. Institute of Information Technology, Warsaw University of Life Sciences—SGGW, Warsaw, Poland

    Leszek J. Chmielewski

  2. Institute of Information Technology, Warsaw University of Life Sciences—SGGW, Warsaw, Poland

    Arkadiusz Orłowski

Appendix: Histograms of p-Values

Appendix: Histograms of p-Values

Here, the graphs which represent the histograms of p-values generated in the tests of the truly random method, basic version and no hiding error version, as well as those for the coordinated method ([5], for comparison with a method which is not fully random), are presented.

The notations concerning the histograms and the additional graphs were explained in Sects. 4.1 and 4.2.

The histograms of p-values for the truly random method, basic version, are shown in Figs. 7–12, and for the no hiding error version, the histograms are shown in Figs. 13–18. In the histograms for the image test100, Figs. 7 and 13, it can be seen that the preconditions for the test Universal were never met, due to that this simple testing image was too small.

Additionally, examples of histograms for images coded with the coordinated method [5], which indicate that the shares are not fully random in that method, are shown for reference in Figs. 19, 20.

Some of the histograms for the basic method as well as those for the coordinated method were shown previously in [4, 5]. For this paper they were improved by adding the subgraphs of \(r_L\) and \(r_N\) according to (5, 6), which broadens the image of randomness of the methods considered. Moreover, the histograms for images and methods which were already presented before were now generated from different random realizations of the images than those previously shown.

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Chmielewski, L.J., Nieniewski, M., Orłowski, A. (2023). Error Analysis and Graphical Evidence of Randomness in Two Methods of Color Visual Cryptography. In: Chmielewski, L.J., Orłowski, A. (eds) Computer Vision and Graphics. ICCVG 2022. Lecture Notes in Networks and Systems, vol 598. Springer, Cham. https://doi.org/10.1007/978-3-031-22025-8_17

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