Secret Image Sharing Based on Chinese Remainder Theorem over a Polynomial Ring

Abstract

Secret image sharing denotes a technique for apportioning secret images into $n$ shadow images and preserving in $n$ participants as the extension of secret sharing on images. Compared to Shamir’s scheme-based secret image sharing, Chinese remainder theorem-based secret imaging has the advantages as lossless recovery, no further encryption, and low recovery computation complexity. However, traditional secret sharing schemes based on the Chinese remainder theorem have shortcomings including no $\left( {t, n} \right)$ threshold, lossy recovery, ignoring image features or further encryption. In this paper, a $\left( {t, n} \right)$ secret image sharing scheme is suggested based on Chinese remainder theorem over a polynomial ring realizing no further encryption and lossless recovery and making the pixel values of shadow images randomly distribute $\left[ {0, 255} \right]$. The effectiveness of the suggested scheme will be demonstrated by experiments and analyses later.