Polynomial-based extended secret image sharing scheme with reversible and unexpanded covers

In comparison with traditional secret image sharing (SIS), extended secret image sharing (ESIS) can encrypt the secret image into several meaningful shadow images rather than noise-like shares, which both decrease enemies' suspects and make them more manageable for participants. However, a majority of current ESISs are based on a combination between SIS and steganography, which result in the limited performance such as the small capacity of secret information and the large cost for decryption. In this paper, we propose a (k, n) threshold extended polynomial-based ESIS, namely EPSIS, completely based on Shamir's classic PSIS without the help of steganography. Firstly, novel concepts, such as the sharing map and sharing pool, are defined to reconstruct the sharing and recovery phases of PSIS; secondly, the secret image and halftone binary cover images act on the sharing phase to generate meaningful grayscale shares from the novel view of PSIS based on the sharing map; finally, in order to achieve the same effects but without the huge sharing map, a filtering procedure for appropriate shared values is added into the sharing phase of natural PSIS, which aims to make the most significant bit of pixel in each share equal to bit in corresponding binary cover. In comparison with current ESISs, the proposed EPSIS not only has advantages in the traditional properties, such (k, n) threshold, capacity, visual quality and computational cost, but also owns two unique properties about covers, including no restrictive requirements on the selection of covers and reversible recovery of cover with the single related share. These significant properties are beneficial for searchable encryption in the area of cloud storage. Furthermore, the security condition of the proposed EPSIS is discussed in detail, and then simulations are provided to verify the security and effectiveness.