Polynomial Based Progressive Secret Image Sharing Scheme With Smaller Shadow Size

Progressive secret image sharing (PSIS) scheme attracts the interests of researchers in recent years. Many approaches have been proposed to construct PSIS schemes. In most of these schemes, the size of the shadow is expanded from the original image. On the contrary, polynomial-based PSIS can reduce shadow size from the original image. Recently, Yang and Huang proposed a polynomial-based <inline-formula> <tex-math notation="LaTeX">$(k,n)$ </tex-math></inline-formula> PSIS, where the image can be progressively reconstructed from <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> shadows. However, the problem of Yang–Huang’s scheme is that the percentage of the recovered partial image from <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> shadows is extremely low when <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> is close to <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>. Later, Yang and Chu constructed another polynomial-based <inline-formula> <tex-math notation="LaTeX">$(k,n)$ </tex-math></inline-formula> PSIS with smooth property to solve this problem, but the size of the shadow is expanded greatly from Yang–Huang’ scheme. In this paper, we propose a new <inline-formula> <tex-math notation="LaTeX">$(k,n)$ </tex-math></inline-formula> PSIS based on polynomial to overcome the drawbacks of these two schemes. In our scheme, <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> shadows (<inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> is close to <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>) can recover more percentage partial image than Yang–Huang’s scheme with a little shadow size expansion; comparing with Yang–Chu’s scheme, our scheme achieves almost the same smooth property with much smaller shadow size.

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