Lossless (k, n)-Threshold Image Secret Sharing Based on the Chinese Remainder Theorem Without Auxiliary Encryption

A typical Chinese remainder theorem (CRT)-based secret sharing (SS) scheme has been proposed by Asmuth and Bloom for several decades, with lower computation complexity compared to Shamir's original polynomial-based SS. But when applied to images, CRT-based image secret sharing (CRTISS) shows many problems, such as lossy recovery, auxiliary encryption, and extra parameters requirement. We analyze the characteristics of images and ISS and propose a (k, n)-threshold CRTISS based on the Asmuth and Bloom's scheme by sharing the high 7 bits of a grayscale secret pixel and embedding the least significant bit (LSB) into the random integer. The pixel values of a grayscale image are divided into two parts, which make it possible to share all the secret pixels with no expansion. Our method has the advantages of (k, n) threshold, lossless recovery, and no auxiliary encryption. The parameters requirement is the same as that in the Asmuth and Bloom's original method. Analysis and experiments are provided to validate the effectiveness of the proposed method.