Efficient and Lossless Polynomial-Based Secret Image Sharing for Color Images

In today's era of developed network, it is particularly important to ensure the security of information. Secret image sharing is a kind of secret information protection technology with loss tolerance by sharing a secret image to a number of shadow images. Most of the researches on secret image sharing focus on grayscale images, but the images we use in our daily life are mostly in color, so the research on the secret image sharing for color image is very meaningful and has great application value. The traditional color image sharing scheme is to share and recover R, G, and B color planes separately, which cause that the time of sharing and recovering one color image is at least triple that of sharing and recovering one grayscale image with the same size as the color image. In this paper, we propose an efficient and lossless secret image sharing scheme for color images. We concatenate the R, G, and B values of every color pixel into a long integer and share it by the polynomial-based secret image sharing, thus the sharing efficiency of color images is greatly improved by reducing the number of sharing operations to 1/3 of the traditional scheme. And we achieve lossless recovery by taking GF(16777259) as the finite field of polynomial operations. 16777259 is the smallest prime number greater than 2
²⁴
- 1, so we intend to screen the random numbers to drop the invalid share values. Theoretical analyses and experiments are used to prove the effectiveness of the proposed scheme.