On the Design of Secret Image Sharing for General Access Structure

Secret image sharing (SIS) under general access structures (GAS) offers a flexible and secure way to manage distributed images. However, conventional frameworks only guarantee lossless reconstruction when all participants pool their shares. If an authorized group tries to recover the image without everyone participating, the reconstruction becomes lossy and probabilistic. To overcome this limitation, an all-selection sharing strategy is proposed. Instead of randomly selecting a single subset, this strategy encodes each secret pixel across all minimal qualified subsets. This approach enables deterministic and lossless recovery for any authorized group but inevitably results in “one-to-more projection conflicts”. These conflicts occur when participants belonging to multiple qualified subsets receive inconsistent share values from different polynomial evaluations. To resolve these conflicts, the minimal qualified subsets are organized into sectioned linked sequences (SLS), and a virtual ID mapping technique is introduced to algebraically decouple the overlapping constraints into independent Vandermonde systems. Theoretical analyses and experiments confirm that the proposed framework achieves perfect, deterministic reconstruction for all qualified subsets without requiring every member to participate. This significantly improves both security and practicality for the distributed storage of secret images.