A global progressive image secret sharing scheme under multi-group joint management

Lina Zhang; Jing Zhang; Jiaqi Sun; Qingpeng Chen; Lina Zhang; Jing Zhang; Jiaqi Sun; Qingpeng Chen

doi:10.3934/mbe.2024055

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 1286-1304. doi: 10.3934/mbe.2024055

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Research article

A global progressive image secret sharing scheme under multi-group joint management

College of Computer Science and Technology, Xi'an University of Science and Technology, Xi'an 710600, China

Academic Editor: Yang Kuang

Received: 17 September 2023 Revised: 10 December 2023 Accepted: 21 December 2023 Published: 26 December 2023

Diverging from traditional secret sharing schemes, group secret sharing schemes enable the recovery of secret information through collaborative efforts among groups. Existing schemes seldom consider the issue of the secrecy level of image information between different groups. Therefore, we propose a global progressive image secret sharing scheme under multi-group joint management. For inter-group relations, multiple groups with different priority levels are constructed using the approach of bit-polar decomposition. In this arrangement, higher-level groups obtain clearer secret image information. For intra-group relations, a participant-weighted secret sharing scheme is constructed based on Chinese Remainder Theorem and Birkhoff interpolation, in which the participants' secret sub-shares are reusable. During the recovery process, the sub-images can be recovered within the intragroup with the corresponding level. Groups collaborate through lightweight overlay operations to obtain different layers of secret images, achieving a global progressive effect. Analysis results show that the scheme is both secure and practical for group secret sharing.
- group secret sharing,
- priority,
- Chinese Remainder Theorem,
- Birkhoff interpolation,
- global progressive
Citation: Lina Zhang, Jing Zhang, Jiaqi Sun, Qingpeng Chen. A global progressive image secret sharing scheme under multi-group joint management[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 1286-1304. doi: 10.3934/mbe.2024055

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Abstract

Diverging from traditional secret sharing schemes, group secret sharing schemes enable the recovery of secret information through collaborative efforts among groups. Existing schemes seldom consider the issue of the secrecy level of image information between different groups. Therefore, we propose a global progressive image secret sharing scheme under multi-group joint management. For inter-group relations, multiple groups with different priority levels are constructed using the approach of bit-polar decomposition. In this arrangement, higher-level groups obtain clearer secret image information. For intra-group relations, a participant-weighted secret sharing scheme is constructed based on Chinese Remainder Theorem and Birkhoff interpolation, in which the participants' secret sub-shares are reusable. During the recovery process, the sub-images can be recovered within the intragroup with the corresponding level. Groups collaborate through lightweight overlay operations to obtain different layers of secret images, achieving a global progressive effect. Analysis results show that the scheme is both secure and practical for group secret sharing.

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