An Image Secret Sharing Method Based on Matrix Theory

Ding, Wanmeng; Liu, Kesheng; Yan, Xuehu; Wang, Huaixi; Liu, Lintao; Gong, Qinghong

doi:10.3390/sym10100530

Cited by 13 publications

(7 citation statements)

References 18 publications

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“…In a secret image sharing setting, shares are often referred to as shadow images. A number of (t, n)-threshold secret image sharing schemes based on different techniques such as polynomial interpolation, hyperplane geometry, the Chinese remainder theorem, and matrix theory have been published by researchers [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Since these schemes do not possess the essentiality condition, all participants have the same importance in the reconstruction phase.…”

Section: Introductionmentioning

confidence: 99%

A Linear Algebraic Threshold Essential Secret Image Sharing Scheme

2022

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A secret sharing scheme allocates to each participant a share of a secret in such a way that authorized subsets of participants can reconstruct the secret, while shares of unauthorized subsets of participants provide no useful information about the secret. For positive integers r,s,t,n with r⩽s⩽t⩽n, an (r,s,t,n)–threshold essential secret sharing scheme is an algorithm that decomposes a secret S into n shares, s of which are essential, in a way that authorized subsets are precisely those with at least t members, at least r of whom are essential. This work proposes a lossless linear algebraic (r,s,t,n)–threshold essential secret image sharing scheme that decomposes the secret, S, into equally-sized shares, each of size 1/t the size of S. For each block, B, of S, the scheme assigns to the n participants distinct signature vectors v1,v2,…,vn in the vector space F2αt, where α is a suitable positive integer, typically between 2 and 5, inclusive. These signature vectors must adhere to some admissibility conditions in order to satisfy the secret sharing threshold properties. The decomposition of B into n shares is obtained by partitioning B into t vectors, then computing the share yj of the jth participant (1≤j≤n), as a linear combination of these parts with coefficients from the signature vj. The presented simulations showcase the effectiveness and robustness of the proposed scheme against standard statistical and security attacks. They further demonstrate its superiority with respect to existing schemes.

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Section: Introductionmentioning

confidence: 99%

A Linear Algebraic Threshold Essential Secret Image Sharing Scheme

2022

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“…However, 256 is not a prime number, and there is no guarantee that all elements in MS(256) have inverses, so Lagrange interpolation cannot be used in the recovery phase. Ding et al [23] proved that Shamir's sharing polynomial constructed by the Vandermonde matrix is only a special case of constructing a sharing polynomial satisfying (k, n) threshold, therefore, we design our method from a broader perspective based on matrix theory. In the sharing phase, a sharing matrix is generated by a filter operation, which is used to encrypt the secret image into n shadows.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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.

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“…Thus, the ISS technique has been applied to distributed storage in the cloud, block chain, digital watermarking, and access control [1][2][3][4]. Now the widely studied principles of ISS techniques include visual secret sharing (VSS), also known as, visual cryptography (VC) [4,5] and polynomial [6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Partial Image Secret Sharing

Yan

Sun

et al. 2020

Symmetry

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In contrast to encrypting the full secret image in classic image secret sharing (ISS), partial image secret sharing (PISS) only encrypts part of the secret image due to the situation that, in general, only part of the secret image is sensitive or secretive. However, the target part needs to be selected manually in traditional PISS, which is human-exhausted and not suitable for batch processing. In this paper, we introduce an adaptive PISS (APISS) scheme based on salience detection, linear congruence, and image inpainting. First, the salient part is automatically and adaptively detected as the secret target part. Then, the target part is encrypted into n meaningful shares by using linear congruence in the processing of inpainting the target part. The target part is decrypted progressively by only addition operation when more shares are collected. It is losslessly decrypted when all the n shares are collected. Experiments are performed to verify the efficiency of the introduced scheme.

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An Image Secret Sharing Method Based on Matrix Theory

Cited by 13 publications

References 18 publications

A Linear Algebraic Threshold Essential Secret Image Sharing Scheme

A Linear Algebraic Threshold Essential Secret Image Sharing Scheme

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

Adaptive Partial Image Secret Sharing

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