Weighted Secret Image Sharing for a $(k,n)$ Threshold Based on the Chinese Remainder Theorem

In general, in a secret image sharing (SIS) scheme with a (k, n) threshold, the participants have equal weights, and their shares have the same average light transmission. No share can reveal any information about the secret. Only when the number of participants involved in restoration is greater than or equal to k can the secret image be revealed. However, on some occasions, the participants' weights need to be set differently, and their shares have different effects on the restoration of the secret image. Therefore, there are many studies of weighted SIS, including schemes based on visual secret sharing using random grids (VSSRG). However, they can only share binary images, not grayscale images. Therefore, we propose a scheme based on the Chinese remainder theorem (CRT) for sharing grayscale images. The shares are generated with different weights. When the threshold is reached and shares with higher weights are involved in restoration, the quality of the restored image is higher. As the number of participating shares increases, the quality of the recovered secret image increases, and if all the shares are involved, lossless restoration can be achieved.