IEEE Trans Image Process. 2017 Dec;26(12):5618-5631. doi: 10.1109/TIP.2017.2738561. Epub 2017 Aug 10.
This paper first introduces a (k,n) -sharing matrix S and its generation algorithm. Mathematical analysis is provided to show its potential for secret image sharing. Combining sharing matrix with image encryption, we further propose a lossless (k,n) -secret image sharing scheme (SMIE-SIS). Only with no less than k shares, all the ciphertext information and security key can be reconstructed, which results in a lossless recovery of original information. This can be proved by the correctness and security analysis. Performance evaluation and security analysis demonstrate that the proposed SMIE-SIS with arbitrary settings of k and n has at least five advantages: 1) it is able to fully recover the original image without any distortion; 2) it has much lower pixel expansion than many existing methods; 3) its computation cost is much lower than the polynomial-based secret image sharing methods; 4) it is able to verify and detect a fake share; and 5) even using the same original image with the same initial settings of parameters, every execution of SMIE-SIS is able to generate completely different secret shares that are unpredictable and non-repetitive. This property offers SMIE-SIS a high level of security to withstand many different attacks.
本文首先介绍了一种 (k, n) -共享矩阵 S 及其生成算法。通过数学分析，展示了其在秘密图像共享中的潜在应用。结合共享矩阵和图像加密，我们进一步提出了一种无损 (k, n) -秘密图像共享方案 (SMIE-SIS)。只有不少于 k 个份额，才能重建所有的密文信息和安全密钥，从而实现原始信息的无损恢复。这可以通过正确性和安全性分析来证明。性能评估和安全性分析表明，所提出的 SMIE-SIS 具有任意设置的 k 和 n，至少具有五个优点：1）能够完全恢复原始图像而无任何失真；2）与许多现有方法相比，它的像素扩展要低得多；3）其计算成本远低于基于多项式的秘密图像共享方法；4）能够验证和检测伪造的份额；5）即使使用相同的原始图像和相同的初始参数设置，SMIE-SIS 的每次执行都能够生成完全不同的、不可预测和非重复的秘密份额。这种特性为 SMIE-SIS 提供了抵御多种不同攻击的高安全性。
