Security Analysis of Visual based Share Authentication and Algorithms for Invalid Shares Generation in Malicious Model

Several (k, n) Secret Image Sharing (SIS) schemes supporting authentication of reconstructed secret image and that of shares are proposed in the past. In these existing schemes, two similar state-of-the-art SIS schemes performing visual based share authentication have following merits compared to other schemes: no restriction on values of k and n to be 2, linear time complexity of share authentication, lossless secret image reconstruction, no pixel expansion, and support for share authentication in both dealer participatory and non-participatory environments. In this paper, we show that respective share authentication in these two similar state-of-the-art SIS schemes is computationally insecure in malicious model. We first identify the vulnerabilities in their respective share authentication through security analysis. Then, we propose two linear time algorithms for generating invalid shares from original shares by exploiting the identified vulnerabilities. These generated invalid shares are capable of passing respective authentication in the two analyzed SIS schemes. In addition, usage of a generated invalid share in place of original share during secret image reconstruction results in distorted secret image. Finally, we provide experimental results that accord with inferences of security analysis and linear time complexity of the proposed algorithms for invalid shares generation.