LPSIS: a lossless secret image sharing scheme based on Legendre polynomials with low-cost reconstruction

Secret image sharing is a crucial area of research to maintain the privacy of images by distributing them among multiple parties. The well-known polynomial-based image sharing faces challenges like the requirement of an expensive interpolation technique, combining shares in an ordered manner for the reconstruction of the secret image. In this article, a novel secret image sharing scheme based on Legendre polynomials has been designed with the objective of reducing the reconstruction time. Unlike other polynomial-based secret image sharing, the proposed approach facilitates an addition-based reconstruction of secret images in a lossless manner with all n shares in arbitrary order. For n participants, n distinct Legendre polynomials, each with varying degrees, have been employed to maintain the secrecy of the input image. The qualitative analysis for the proposed scheme ensures no information leakage, individually or collectively, up to \((n-1)\) $(n-1)$ shares. The efficacy of our scheme is established by quantitative results based on parameters PSNR, SSIM, MSE and correlation coefficient. We have also conducted the experimental security analysis and reconstruction time analysis in the performance analysis section.