Ramp secret image sharing

Xuehu Yan; Longlong Li; Lintao Liu; Yuliang Lu; Xianhua Song; Xuehu Yan; Longlong Li; Lintao Liu; Yuliang Lu; Xianhua Song

doi:10.3934/mbe.2019221

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4433-4455. doi: 10.3934/mbe.2019221

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Research article Special Issues

Ramp secret image sharing

1.
National University of Defense Technology, Hefei 230037, China
2.
Harbin University of Science and Technology, Harbin 150080, China

Received: 09 January 2019 Accepted: 25 April 2019 Published: 20 May 2019

Secret image sharing (SIS) belongs to but differs from secret sharing. In general, conventional (k, n) threshold SIS has the shortcoming of pall-or-nothingq. In this article, first we introduce ramp SIS definition. Then we propose a $(k_1, k_2, n)$ ramp SIS based on the Chinese remainder theorem (CRT). In the proposed scheme, on the one hand, when we collect any $k_1$ or more and less than $k_2$ shadows, the secret image will be disclosed in a progressive way. On the other hand, when we collect any $k_2$ or more shadows, the secret image will be disclosed losslessly. Furthermore, the disclosing method is only modular arithmetic, which can be used in some real-time applications. We give theoretical analyses and experiments to show the effectiveness of the proposed scheme.
- secret image sharing,
- ramp secret image sharing,
- Chinese remainder theorem,
- progressiveness,
- lossless recovery
Citation: Xuehu Yan, Longlong Li, Lintao Liu, Yuliang Lu, Xianhua Song. Ramp secret image sharing[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4433-4455. doi: 10.3934/mbe.2019221

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Abstract

Secret image sharing (SIS) belongs to but differs from secret sharing. In general, conventional (k, n) threshold SIS has the shortcoming of pall-or-nothingq. In this article, first we introduce ramp SIS definition. Then we propose a $(k_1, k_2, n)$ ramp SIS based on the Chinese remainder theorem (CRT). In the proposed scheme, on the one hand, when we collect any $k_1$ or more and less than $k_2$ shadows, the secret image will be disclosed in a progressive way. On the other hand, when we collect any $k_2$ or more shadows, the secret image will be disclosed losslessly. Furthermore, the disclosing method is only modular arithmetic, which can be used in some real-time applications. We give theoretical analyses and experiments to show the effectiveness of the proposed scheme.

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