Abstract
This paper presents an adaptive image steganography technique that integrates linear hash functions with chessboard-partitioned image blocks to achieve high-capacity data embedding while preserving visual quality. The proposed method operates on 8×8 pixel blocks, which are classified based on local variance into three categories: smooth, moderately complex, and highly textured. Depending on the category, the algorithm adaptively determines the number of least significant bits (LSBs) used for embedding, allowing for a balance between payload and imperceptibility. A key innovation of the approach is the use of staggered partitioning within each block, where one subset of pixels is used for embedding, and the other remains unchanged to enable blind estimation of variance during extraction. This enables the decoder to reconstruct the embedding conditions without requiring access to the original image or auxiliary metadata. The embedding process utilizes a linear hash function based on primitive polynomial division in the Galois Field GF(2). This allows an m-bit message to be embedded into an $\hat D = \left\{ {{s_1}, \ldots {s_N}} \right\}$ bit sequence with only a single-bit modification, ensuring minimal statistical disruption to the cover image. Experimental validation was conducted using the BOSSBase v1.01 dataset, where the method achieved embedding rates ranging from 0.3 to 0.9 bits per pixel (bpp), with Peak Signal-to-Noise Ratio (PSNR) values consistently exceeding 44 dB. In addition to high fidelity and capacity, the algorithm is computationally efficient, relying on simple binary operations such as XOR and polynomial transformations in GF(2), which makes it suitable for implementation in low-resource environments such as embedded and mobile systems.