An XOR-Based (k, n) Visual Fully Independent Secrets Sharing Scheme with Meaningful Shares ^†

With the rapid advancement of technology, data transmission security has become an increasingly critical issue. Visual Cryptography Scheme (VCS) provides a secure method for sharing secret images without complex computation—by stacking multiple shares, the secret image can be visually recognized. The earliest visual cryptography scheme was proposed. However, traditional VCS are limited to the encryption and decryption of a single secret. To address the evolving demands of modern information security, numerous enhanced VCS have been introduced by researchers, offering new perspectives and capabilities. This paper proposes a novel XOR-based visual cryptography scheme that supports fully independent secrets within a (k, n)-threshold framework for 2 ≤ k < n. In the proposed scheme, n shares can simultaneously encrypt C(n, k) distinct secrets. Each secret can be reconstructed by one subset of k shares out of the n, and all shares are designed to be meaningful images so as not to be identified as hiding a secret. This approach significantly enhances the flexibility of VCS, enabling its application in scenarios where different groups hold different secrets or where the reconstructed secret identifies the associated group, which can help administrators know which group has accessed the secret. As such, the proposed scheme is more suitable for a wide range of practical applications.