ESIS-SSI: Efficient (n, n) Secret Image Sharing with Shrinking Shadow Images

The problem of secret image sharing has been extensively studied, and the size of the shadow images is a critical factor for applying these schemes in resource-limited environments. Most existing schemes generate shadow images that are approximately the same size as the original secret image. This work addresses the issue of reducing shadow image size. A <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(n,n)$</tex> threshold scheme that produces smaller shadow images is proposed. The new method for sharing the secret image results in shadow images of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lceil\frac{h}{n}\rceil\times w$</tex>, as opposed to the standard <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$h\times w$</tex> size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{in}$</tex> most existing schemes. The secret key is not needed at the Combiner while reconstructing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$I$</tex>. The proposed scheme has been rigorously validated and implemented, demonstrating both efficiency and security, with shadow images not disclosing any information about the original secret image. Compared to existing methods, our scheme is shown to generate the shadow images with the reduced size and is efficient.