Optimal XOR Based (2,n)-Visual Cryptography Schemes

Abstract

A (2, )-Visual Cryptography Scheme (VCS) is a kind of secret sharing scheme, where participants share a secret image, and any two of them can recover the secret image visually without any cryptographic knowledge and computation devices, but any one of them cannot get any information about the secret image other than the size of the secret image. This paper studies the (2, )− , and shows the smallest (optimal) pixel expansion of such schemes, and the largest possible contrast for the (2, ) − given its optimal pixel expansion. It also shows the largest (optimal) contrast of the (2, ) − , and the smallest possible pixel expansion of such schemes given their optimal contrast. The results of this paper show that the (2, ) − can achieve smaller pixel expansion and larger contrast than that of (2, ) − . It also shows that the construction of the basis matrix of optimal contrast (2, )− is equivalent to the construction of binary codes when they reach the maximum capability, and the construction of a specific class of optimal contrast (2, ) − for = 2 − 1 is given.

Non-expansible XOR-based visual cryptography scheme with meaningful shares

“…Hence, their computational complexity is Oð1Þ. Indeed, the computation complexity of the proposed scheme and other XORbased VC schemes [26,28,27] is relatively high as that of the OR-based VC schemes. However, the XOR-based VC schemes can achieve superior visual quality and solve the pixel alignment problem of OR-based VC schemes.…”

“…Let n be the number of shares, the computation complexity is O(n). Table 3 summarises the comparisons of computational complexity for the decryption among the proposed scheme and other related schemes [26,28,27,21,12,[35][36][37]. As compared to some reported schemes [36,37] based on Shamir's method [38] which involves the polynomial evaluation and interpolation, the computational complexity of the proposed scheme requires less time.…”

“…Moveover, the generated shares are meaningless which may impose difficulty in managing the shares. Liu et al [27] presented an optimal XOR-based VC scheme for improving the contrast, but the drawbacks such as meaningless share, codebook required and pixel expansion remain in their scheme. To address the above-mentioned problems, Wu and Sun [26] introduced a (n,n) XOR-based meaningful VC scheme by utilizing generalized random grid.…”

“…Due to the decryption of XOR operation, better visual quality can be achieved and the alignment problem is solved as well. Recently, many works on XOR-based VC scheme [24,25,19,[26][27][28] have been investigated. In [28], Tuyls et al gave some valid constructions for the XORbased VC scheme, but codebooks are still required.…”

Password-oriented Image Encryption with multiple dependent factors

“…The (2,n) Visual Cryptography technique [1] can also be broken by few of the sharing parties and their shares can be changed in order to create an entirely different secret message.…”