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Volume 8
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Article

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

by
Long Yu
1,2,
Lintao Liu
1,2,
Zhe Xia
3,
Xuehu Yan
1,2 and
Yuliang Lu
1,2,*
1
College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China
2
Anhui Key Laboratory of Cyberspace Security Situation Awareness and Evaluation, Hefei 230037, China
3
Department of Computing, Wuhan University of Technology, Wuhan 430070, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(6), 1018; https://doi.org/10.3390/math8061018
Submission received: 26 April 2020 / Revised: 17 June 2020 / Accepted: 18 June 2020 / Published: 22 June 2020
(This article belongs to the Special Issue Computing Methods in Steganography and Multimedia Security)
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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.
Keywords: secret image sharing; matrix theory; lossless recovery; (k, n) threshold secret image sharing; matrix theory; lossless recovery; (k, n) threshold

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MDPI and ACS Style

Yu, L.; Liu, L.; Xia, Z.; Yan, X.; Lu, Y. Lossless and Efficient Secret Image Sharing Based on Matrix Theory Modulo 256. Mathematics 2020, 8, 1018. https://doi.org/10.3390/math8061018

AMA Style

Yu L, Liu L, Xia Z, Yan X, Lu Y. Lossless and Efficient Secret Image Sharing Based on Matrix Theory Modulo 256. Mathematics. 2020; 8(6):1018. https://doi.org/10.3390/math8061018

Chicago/Turabian Style

Yu, Long, Lintao Liu, Zhe Xia, Xuehu Yan, and Yuliang Lu. 2020. "Lossless and Efficient Secret Image Sharing Based on Matrix Theory Modulo 256" Mathematics 8, no. 6: 1018. https://doi.org/10.3390/math8061018

APA Style

Yu, L., Liu, L., Xia, Z., Yan, X., & Lu, Y. (2020). Lossless and Efficient Secret Image Sharing Based on Matrix Theory Modulo 256. Mathematics, 8(6), 1018. https://doi.org/10.3390/math8061018

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