Abstract
In reversible image secret sharing (RISS), the cover image can be recovered to some degree, and a share can be comprehensible rather than noise-like. Reversible cover images play an important role in law enforcement and medical diagnosis. The comprehensible share can not only reduce the suspicion of attackers but also improve the management efficiency of shares. In this paper, we first provide a formal definition of RISS. Then, we propose an RISS algorithm for a $(k,n)$ -threshold based on the principle of the Chinese remainder theorem-based ISS (CRTISS). In the proposed RISS, the secret image is losslessly decoded by a modular operation, and the original cover image is recovered by a binarization operation, both of which are just simple operations. Theoretical analyses and experiments are provided to validate the proposed definition and algorithm.
Highlights
I MAGE secret sharing (ISS) divides a secret image into multiple shares, known as shadows or shadow images, which are sent to participants. (k, n)-threshold ISS has a loss-tolerant property, i.e., the dealer can reconstruct the secret with at most n − k shares lost
We propose one reversible image secret sharing (RISS) algorithm for a general (k, n)-threshold based on the principle of Chinese remainder theorem (CRT) and random elements in Chinese remainder theorem-based ISS (CRTISS). n different binary cover images are input in our method to output n different grayscale shares
The experimental binary cover images and grayscale secret images with a size of 256 × 256 used in this paper are illustrated in Fig. 2, which are scaled to the proper size in some experiments
Summary
I MAGE secret sharing (ISS) divides a secret image into multiple shares, known as shadows or shadow images, which are sent to participants. (k, n)-threshold ISS has a loss-tolerant property, i.e., the dealer can reconstruct the secret with at most n − k shares lost. Lin and Chan [35] in 2010 introduced a polynomial-based RISS scheme with high visual quality of shares and the recovered secret image following previous work [36]. Their method represents the secret image pixel values in the G F(P) finite field and embeds them into the first (k−1)-th coefficients of the constructed polynomial, in which their optical parameter is P = 7. High visual quality of the shares as well as a reversible share are achieved Their method is only applicable for (k, n) thresholds with k equal to or greater than 3, with pixel expansion occurring with respect to the secret image.
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