Abstract
A ( k , n ) visual cryptography (VC) scheme encodes a secret image into n shadows that are printed on transparencies distributed among a group of n participants secretly, and reveal the secret image by stacking no less than k of them. Its decryption requires no computation and attracts much attention in image security applications. The pixel expansion and contrast are two important characteristics to evaluate the visual quality of the revealed secret image for a ( k , n ) -VC scheme. The ( k , n ) XOR-based VC (XVC) schemes can greatly improve the visual quality including both pixel expansion and contrast. Previous methods require complex computation and result in high pixel expansion when they are used to construct such schemes. In this paper, we propose a pixel expansion adjustable ( k , n ) -XVC scheme, which allows pixel expansion to be changed among 2 k - 1 - 1 different values. It can ensure each pixel being exactly recovered with the same average contrast no matter it takes any pixel expansion value. The least pixel expansion is much smaller than previous schemes. Our scheme can be easily implemented based on any conventional OR-based ( k , n ) -VC (OVC) scheme.
Highlights
Visual cryptography (VC) was firstly designed by Naor and Shamir in 1994 to share an image secret in visual pattern instead of computational pattern as the traditional secret sharing [1]
To solve the problem of pixel expansion in a (k, n)-XOR-based VC (XVC) scheme, we can allow the difference of the gray levels of recovered white and black pixels to be changed among the interval [1, 2k−1 ]
We propose a (k, n)-XVC scheme with adjustable pixel expansion being m0, which is built on any (k, n)-OVC scheme with pixel expansion m denoted as (k, n)m -OVC scheme
Summary
Visual cryptography (VC) was firstly designed by Naor and Shamir in 1994 to share an image secret in visual pattern instead of computational pattern as the traditional secret sharing [1]. We propose to use part columns of the basis matrices of (k, n)-OVC scheme to construct a (k, n)-XVC scheme with flexible pixel expansion, and it can reduce the pixel expansion from the least 1 pixel to the largest 2k−1 − 1 pixels at the same time it can keep the same average contrast with the corresponding (k, n)-XVC scheme. It is a deterministic scheme suitable for any secret image.
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