Ramp Progressive Secret Image Sharing Using Ensemble of Simple Methods

This paper reviews the limitations of traditional Secret Image Sharing (SIS) methods and recent advancements such as PSIS, RPSIS, and SSIS, and presents an optimized and practical combinatorial method for secret image sharing by ensemble of simple methods. In this approach, a color or grayscale image is divided into n shares, each of which is individually meaningless. The image is reconstructed through XOR operations between corresponding pixels in different shares. The main innovation of this method is the introduction of two thresholds, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{k}_{1}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{k}_{2}$</tex>. This scheme is characterized by parameters <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mathrm{k}_{1},\ \mathrm{k}_{2},\ \mathrm{n})$</tex>, where having fewer than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{k}_{1}$</tex> shares reveals no information about the original image, while between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{k}_{1}$</tex> and k2 shares, the image quality progressively improves and reaches near-complete reconstruction. Ultimately, with k2 or more shares, the image can be recovered in its full resolution. This method allows for customization of the image quality improvement rate between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{k}_1$</tex> and k2 and addresses the limitations of previous designs regarding the selection of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{k}_{1},\mathrm{k}_{2}$</tex>, and n values. Its flexibility in providing suitable models based on specific user needs makes this method appropriate for various applications in secret image sharing.