Robust Secret Image Sharing Resistant to JPEG Recompression Based on Stable Block Condition

$(k,n)$ Threshold secret image sharing (SIS) hides a secret image within $n$ shadows, and at least $k$ shadows are needed for recovery. Due to the popularity and frequency of JPEG recompression, there is a need for robust secret image sharing (ROSIS) designed for JPEG images that is resilient to recompression for practical SIS applications. The current state-of-the-art ROSIS, which relies on error-correcting codes (ECC), is effective only for JPEG compression with quality factors (QFs) of 99 and 100. However, it generates noise-like shadow images that are confined to the spatial domain. In this paper, we present SBC-ROSIS (Robust Secret Image Sharing Scheme Resistant to JPEG Recompression Based on Stable Block Condition), a novel ROSIS scheme that utilizes a stable block condition to guarantee the invariance of discrete cosine transform (DCT) coefficients during JPEG recompression, significantly enhancing the robustness of the scheme. By employing a polynomial-based secret sharing (SS) algorithm, we construct DCT blocks that adhere to stable block condition either directly or through strategic global regulation. Additionally, we carefully consider the similarity between the generated DCT blocks and the original cover DCT blocks. Furthermore, we devised a tailored evaluation methodology specifically for ROSIS. Extensive experimental results indicate that SBC-ROSIS can effectively process JPEG images, achieving a balance among security, robustness, concealment, and adherence to the $(k, n)$ threshold, without relying on steganography, ECC, or pixel expansion, and demonstrating robust performance in realistic recompression scenarios.