A (k, n)-Threshold Progressive Visual Secret Sharing without Expansion

Abstract

Visual cryptography (VC) encrypts a secret image into n shares (transparency). As such, we cannot see any information from any one share, and the original image is decrypted by stacking all of the shares. The general (k, n)-threshold secret sharing scheme (SSS) can similarly encrypt and decrypt the original image by stacking at least k (≤ n) shares. If one stack is fewer than k shares, the secret image is unrecognizable. Another subject is progressive visual secret sharing, which means that when more shares are progressively stacked, the combined share becomes clearer. In this study, we constructed an advanced scheme for (k, n)-threshold SSS that can be encrypted in VC for any positive integers n ≥ k ≥ 2 through the method of combination, and the size of each share is the same as that of the original image. That is, no pixel expansion is required. Our scheme is novel, and the results from the theoretical analysis and simulation reveal that our scheme exhibits favorable contrast to that of other related schemes.

An Easy-to-implement Construction for $(k,n)$-threshold Progressive Visual Secret Sharing Schemes

“…Precisely, for any given positive integers k and n, the codebook of the (k, n)-threshold PVSS scheme can be obtained efficiently and directly by a formula. The general formula therein extends the (4, n)-threshold PVSS scheme by Chen and Juan [3] to the cases of large k. The authors [2] also show that the performance, including contrast, size constraint and pixel expansion, of their method is comparable with previous results [3,4,8,9,15,19,20,21,22]. However, the formula would be unsatisfied in a theoretical point of view because it seems quite complicated and cannot unify the well-known constructions of (k, n)-threshold PVSS schemes for k = 2, 3 and n by Naor and Shamir [15].…”

“…has been the focus of the study of (k, n)-threshold VSS schemes. Meanwhile, progressive visual secret sharing (PVSS) schemes have been proposed in recent years [2,3,4,7,8,9,11,14,16,17,18,19,20,21,22]; namely, the contrast of the proposed scheme is increasing progressively with more and more shares being stacked together. For a particular integer k, there are various constructions of basis matrices of a (k, n)-threshold PVSS scheme.…”

“…A recent paper by Chen, Huang and Juan [2] has revealed a simple method to design the codebooks of general (k, n)-threshold PVSS schemes. Precisely, for any given positive integers k and n, the codebook of the (k, n)-threshold PVSS scheme can be obtained efficiently and directly by a formula.…”

“…With more designs being revealed, it raises naturally an interesting question that "is there a single formula to unify all these constructions?" To this aim, Chen et al [2] made a first attempt, which helps us to see the possibility of answering such a question.…”

Two-in-One Secret Image Sharing Scheme with Higher Visual Quality of the Previewed Image

“…In recent years, researchers have proposed more SIS schemes, including schemes for color images [12,13], progressive decoding [14,15], meaningful shares [16], and minimizing pixel expansion [17,18], etc. In addition, there exist novel SIS schemes based on various theorems, like matrix theory [19], non-full rank linear model [20] and natural steganography (NS) [21].…”