Zhang Lina, Zhang Jing, Sun Jiaqi, Chen Qingpeng
College of Computer Science and Technology, Xi'an University of Science and Technology, Xi'an 710600, China.
Math Biosci Eng. 2024 Jan;21(1):1286-1304. doi: 10.3934/mbe.2024055. Epub 2022 Dec 26.
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.
与传统的秘密共享方案不同，群组秘密共享方案能够通过群组之间的协作努力来恢复秘密信息。现有方案很少考虑不同群组之间图像信息保密级别的问题。因此，我们提出了一种多群组联合管理下的全局渐进式图像秘密共享方案。对于组间关系，采用比特极性分解的方法构建具有不同优先级别的多个群组。在这种安排下，较高级别的群组获得更清晰的秘密图像信息。对于组内关系，基于中国剩余定理和伯克霍夫插值构建了一种参与者加权秘密共享方案，其中参与者的秘密子份额是可重复使用的。在恢复过程中，子图像可以在组内以相应级别进行恢复。群组通过轻量级叠加操作进行协作以获得不同层的秘密图像，实现全局渐进效果。分析结果表明，该方案对于群组秘密共享既安全又实用。
