Abstract
Most of today’s secret image sharing (SIS) schemes are based on Shamir’s polynomial-based secret sharing (SS), which cannot recover pixels larger than 250. Many exiting methods of lossless recovery are not perfect, because several problems arise, such as large computational costs, pixel expansion and uneven pixel distribution of shadow image. In order to solve these problems and achieve perfect lossless recovery and efficiency, we propose a scheme based on matrix theory modulo 256, which satisfies ( k , k ) and ( k , k + 1 ) thresholds. Firstly, a sharing matrix is generated by the filter operation, which is used to encrypt the secret image into n shadow images, and then the secret image can be obtained by matrix inverse and matrix multiplication with k or more shadows in the recovery phase. Both theoretical analyses and experiments are conducted to demonstrate the effectiveness of the proposed scheme.
Highlights
Shamir [1] and Blakley [2] proposed secret sharing (SS) in 1979, respectively
A (k, n) threshold secret image sharing (SIS) encrypts a secret image into n shadows and distributes them among n participants, where any k or more shadows can reconstruct the secret while less than k shadows can obtain nothing of the secret
There are a large number of pixels in an image, every pixel of the secret image needs to be shared once, and every pixel of the shadow image needs to be decoded once, so time is spent on iterative operation
Summary
Shamir [1] and Blakley [2] proposed secret sharing (SS) in 1979, respectively. Due to the characteristics of the image, SS is applied to the image to achieve secret image sharing (SIS). The secret image can be obtained by k or more shadows modulo 251 based on Lagrange interpolation. Because the adjacent pixels of the image are correlated, encryption must be performed before sharing to ensure that there is no information leakage in the shadow image, so this method permuted the pixels of the secret image before the sharing phase There is another disadvantage in their scheme that it cannot achieve lossless recovery, because the grayscale pixel value range is [0,255] and modulo 251 cannot cover it. Using matrix multiplication can reduce the computational complexity of the recovery phase compared with Lagrange interpolation Both theoretical analyses and experiments are conducted to demonstrate the effectiveness of the proposed scheme.
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