scholarly journals Lossless and Efficient Secret Image Sharing Based on Matrix Theory Modulo 256

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1018
Author(s):  
Long Yu ◽  
Lintao Liu ◽  
Zhe Xia ◽  
Xuehu Yan ◽  
Yuliang Lu
Keyword(s):  
Matrix Theory ◽  
Matrix Multiplication ◽  
Recovery Phase ◽  
Secret Image Sharing ◽  
Computational Costs ◽  
Secret Image ◽  
Image Sharing ◽  
Lossless Recovery ◽  
Filter Operation ◽  
Theoretical Analyses

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.

scholarly journals An Image Secret Sharing Method Based on Matrix Theory

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 530 ◽  
Author(s):  
Wanmeng Ding ◽  
Kesheng Liu ◽  
Xuehu Yan ◽  
Huaixi Wang ◽  
Lintao Liu ◽  
...  
Keyword(s):  
Secret Sharing ◽  
Matrix Theory ◽  
Secret Image Sharing ◽  
Secret Image ◽  
Image Sharing ◽  
Lossless Recovery ◽  
Sharing Scheme ◽  
Image Secret Sharing ◽  
Special Case ◽  
Secret Image Sharing Scheme

Most of today’s secret image sharing technologies are based on the polynomial-based secret sharing scheme proposed by shamir. At present, researchers mostly focus on the development of properties such as small shadow size and lossless recovery, instead of the principle of Shamir’s polynomial-based SS scheme. In this paper, matrix theory is used to analyze Shamir’s polynomial-based scheme, and a general (k, n) threshold secret image sharing scheme based on matrix theory is proposed. The effectiveness of the proposed scheme is proved by theoretical and experimental results. Moreover, it has been proved that the Shamir’s polynomial-based SS scheme is a special case of our proposed scheme.

scholarly journals Robust Secret Image Sharing Resistant to Noise in Shares

2021 ◽  
Vol 17 (1) ◽  
pp. 1-22
Author(s):  
Xuehu Yan ◽  
Lintao Liu ◽  
Longlong Li ◽  
Yuliang Lu
Keyword(s):  
Chinese Remainder Theorem ◽  
Recovery Phase ◽  
Error Correcting Codes ◽  
Secret Image Sharing ◽  
Data Loss ◽  
Least Significant Bit ◽  
Recovery Method ◽  
Secret Image ◽  
Image Sharing ◽  
Salt And Pepper

A secret image is split into   shares in the generation phase of secret image sharing (SIS) for a  threshold. In the recovery phase, the secret image is recovered when any   or more shares are collected, and each collected share is generally assumed to be lossless in conventional SIS during storage and transmission. However, noise will arise during real-world storage and transmission; thus, shares will experience data loss, which will also lead to data loss in the secret image being recovered. Secret image recovery in the case of lossy shares is an important issue that must be addressed in practice, which is the overall subject of this article. An SIS scheme that can recover the secret image from lossy shares is proposed in this article. First, robust SIS and its definition are introduced. Next, a robust SIS scheme for a  threshold without pixel expansion is proposed based on the Chinese remainder theorem (CRT) and error-correcting codes (ECC). By screening the random numbers, the share generation phase of the proposed robust SIS is designed to implement the error correction capability without increasing the share size. Particularly in the case of collecting noisy shares, our recovery method is to some degree robust to some noise types, such as least significant bit (LSB) noise, JPEG compression, and salt-and-pepper noise. A theoretical proof is presented, and experimental results are examined to evaluate the effectiveness of our proposed method.

scholarly journals Meaningful Secret Image Sharing Scheme with High Visual Quality Based on Natural Steganography

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1452
Author(s):  
Yuyuan Sun ◽  
Yuliang Lu ◽  
Jinrui Chen ◽  
Weiming Zhang ◽  
Xuehu Yan
Keyword(s):  
Visual Quality ◽  
Secret Image Sharing ◽  
Secret Image ◽  
Image Sharing ◽  
Lossless Recovery ◽  
Sharing Scheme ◽  
Image Protection ◽  
Embedding Rate ◽  
Secret Image Sharing Scheme

The (k,n)-threshold Secret Image Sharing scheme (SISS) is a solution to image protection. However, the shadow images generated by traditional SISS are noise-like, easily arousing deep suspicions, so that it is significant to generate meaningful shadow images. One solution is to embed the shadow images into meaningful natural images and visual quality should be considered first. Limited by embedding rate, the existing schemes have made concessions in size and visual quality of shadow images, and few of them take the ability of anti-steganalysis into consideration. In this paper, a meaningful SISS that is based on Natural Steganography (MSISS-NS) is proposed. The secret image is firstly divided into n small-sized shadow images with Chinese Reminder Theorem, which are then embedded into RAW images to simulate the images with higher ISO parameters with NS. In MSISS-NS, the visual quality of shadow images is improved significantly. Additionally, as the payload of cover images with NS is larger than the size of small-sized shadow images, the scheme performs well not only in visual camouflage, but also in other aspects, like lossless recovery, no pixel expansion, and resisting steganalysis.

A Novel Progressive Secret Image Sharing Scheme Based on Arithmetic Mean

2017 ◽  
Vol 9 (3) ◽  
pp. 28-37
Author(s):  
Lintao Liu ◽  
Yuliang Lu ◽  
Xuehu Yan ◽  
Song Wan
Keyword(s):  
Visual Quality ◽  
Recovery Process ◽  
Arithmetic Mean ◽  
Secret Image Sharing ◽  
Binary Images ◽  
Secret Image ◽  
Image Sharing ◽  
Lossless Recovery ◽  
Sharing Scheme ◽  
Grayscale Images

The current researches in secret sharing techniques have limitations of lossy recovery for binary images, complex computation for grayscale images, and “All-or-Nothing”. In this paper, we propose a novel progressive secret image sharing (PSS) scheme based on arithmetic mean. In the proposed scheme, the more shares are collected, the better recovered visual quality will be. Furthermore, it can realize lossless recovery with all the shares. It can be directly used to share grayscale images and can be easily extended to deal with binary and color images. In the recovery process, it only needs simple computing (arithmetic mean). Simulations show the advantages and effectiveness of the proposed scheme.

Polynomial-Based Secret Image Sharing Scheme with Fully Lossless Recovery

2018 ◽  
Vol 10 (2) ◽  
pp. 120-136 ◽  
Author(s):  
Wanmeng Ding ◽  
Kesheng Liu ◽  
Xuehu Yan ◽  
Lintao Liu
Keyword(s):  
Storage Capacity ◽  
Image Data ◽  
Secret Sharing Scheme ◽  
Secret Image Sharing ◽  
Secret Image ◽  
Image Sharing ◽  
Lossless Recovery ◽  
Sharing Scheme ◽  
And Storage ◽  
Secret Image Sharing Scheme

Lossless recovery is important for the transmission and storage of image data. In polynomial-based secret image sharing, despite many previous researchers attempted to achieve lossless recovery, none of the proposed work can simultaneously satisfy an efficiency execution and at no cost of some storage capacity. This article proposes a secret sharing scheme with fully lossless recovery based on polynomial-based scheme and modular algebraic recovery. The major difference between the proposed method and polynomial-based scheme is that, instead of only using the first coefficient of sharing polynomial, this article uses the first two coefficients of sharing polynomial to embed the pixels as well as guarantee security. Both theoretical proof and experimental results are given to demonstrate the effectiveness of the proposed scheme.

scholarly journals Chinese Remainder Theorem-Based Secret Image Sharing with Small-Sized Shadow Images

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 340 ◽  
Author(s):  
Jinrui Chen ◽  
Kesheng Liu ◽  
Xuehu Yan ◽  
Lintao Liu ◽  
Xuan Zhou ◽  
...  
Keyword(s):  
Information Hiding ◽  
Chinese Remainder Theorem ◽  
Transmission Time ◽  
Storage Space ◽  
Secret Image Sharing ◽  
Computation Complexity ◽  
Secret Image ◽  
Image Sharing ◽  
Lossless Recovery ◽  
Adjacent Pixel

Secret image sharing (SIS) with small-sized shadow images has many benefits, such as saving storage space, improving transmission time, and achieving information hiding. When adjacent pixel values in an image are similar to each other, the secret image will be leaked when all random factors of an SIS scheme are utilized for achieving small sizes of shadow images. Most of the studies in this area suffer from an inevitable problem: auxiliary encryption is crucial in ensuring the security of those schemes. In this paper, an SIS scheme with small-sized shadow images based on the Chinese remainder theorem (CRT) is proposed. The size of shadow images can be reduced to nearly 1 / k of the original secret image. By adding random bits to binary representations of the random factors in the CRT, auxiliary encryption is not necessary for this scheme. Additionally, reasonable modifications of the random factors make it possible to incorporate all advantages of the CRT as well, including a ( k , n ) threshold, lossless recovery, and low computation complexity. Analyses and experiments are provided to demonstrate the effectiveness of the proposed scheme.

scholarly journals Weighted Polynomial-Based Secret Image Sharing Scheme with Lossless Recovery

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yongjie Wang ◽  
Jia Chen ◽  
Qinghong Gong ◽  
Xuehu Yan ◽  
Yuyuan Sun
Keyword(s):  
Light Transmission ◽  
Chinese Remainder Theorem ◽  
Secret Image Sharing ◽  
Visual Secret Sharing ◽  
Theoretical Derivation ◽  
Secret Image ◽  
Image Sharing ◽  
Lossless Recovery ◽  
Sharing Scheme

In some particular scenes, the shadows need to be given different weights to represent the participants’ status or importance. And during the reconstruction, participants with different weights obtain various quality reconstructed images. However, the existing schemes based on visual secret sharing (VSS) and the Chinese remainder theorem (CRT) have some disadvantages. In this paper, we propose a weighted polynomial-based SIS scheme in the field of GF (257). We use k , k threshold polynomial-based secret image sharing (SIS) to generate k shares and assign them corresponding weights. Then, the remaining n − k shares are randomly filled with invalid value 0 or 255. When the threshold is satisfied, the number and weight of share can affect the reconstructed image’s quality. Our proposed scheme has the property of lossless recovery. And the average light transmission of shares in our scheme is identical. Experiments and theoretical analysis show that the proposed scheme is practical and feasible. Besides, the quality of the reconstructed image is consistent with the theoretical derivation.

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