A (k, n)-threshold secret image sharing scheme is any method of distributing a secret image amongst n participants in such a way that any k participants are able to use their shares collectively to reconstruct the secret image, while fewer than k shares do not reveal any information about the secret image. In this work, we propose a lossless linear algebraic (k, n)-threshold secret image sharing scheme. The scheme associates a vector vi to the ith participant in the vector space F k 2α , where the vectors vi satisfy some admissibility conditions. The ith share is simply a linear combination of the vectors vi with coefficients from the secret image. Simulation results demonstrate the effectiveness and robustness of the proposed scheme compared to standard statistical attacks on secret image sharing schemes. Furthermore, the proposed scheme has a high level of security, errorresilient capability, and the size of each share is 1/k the size of the secret image. In comparison with existing work, the scheme is shown to be very competitive.

中文翻译：

---

一种无损线性代数秘密图像共享方案

(k, n)-阈值秘密图像共享方案是在 n 个参与者之间分发秘密图像的任何方法，其中任何 k 个参与者都能够共同使用他们的份额来重建秘密图像，而少于 k 个份额不透露有关秘密图像的任何信息。在这项工作中，我们提出了一种无损线性代数 (k, n) 阈值秘密图像共享方案。该方案将向量 vi 与向量空间 F k 2α 中的第 i 个参与者相关联，其中向量 vi 满足一些可接受条件。第 i 个份额只是向量 vi 与来自秘密图像的系数的线性组合。与对秘密图像共享方案的标准统计攻击相比，仿真结果证明了所提出方案的有效性和鲁棒性。此外，所提出的方案具有较高的安全性和容错能力，每个共享的大小为秘密图像大小的1/k。与现有工作相比，该方案显示出非常有竞争力。