An enhanced image protection framework: polynomial-based secret sharing meets information hiding

The security of modern communication requires not only the confidentiality of communication content but also the concealment of communication behavior. Secret image sharing has emerged as a prominent research topic in recent years, aiming to transfer meaningful shares while ensuring that covert communication activities remain hidden from potential attackers' monitoring and analysis. In this paper, we propose a novel polynomial-based secret image sharing scheme with meaningful shares. It utilizes the mathematical construction of polynomial coefficients, along with the secret pixel values and the pixel values of the cover images, to determine the coefficients of the polynomial. Subsequently, we propose two algorithms to compute the pixel values of the n-th cover image for each respective image by minimizing their discrepancy with the corresponding cover image's pixel values. As a result, this scheme achieves both image sharing and hiding simultaneously, allowing for dynamic adjustment of share and recovered image quality in different application scenarios. Experimental results and analysis demonstrate that the proposed scheme is secure, reliable, easy to implement. Specifically, when the fluctuation value b = 3, both the shares and the recovered images demonstrate excellent visual quality, achieving an average PSNR of over 40 dB.