Waves interference for perfect output VES in spite of swarm Byzantine participants

Visual Encryption Schemes (VES) encode the pixels of a secret image into $n$ subpixel maps (shares), each of size $m\times m$, where $m$ is a scheme parameter. The encoding relies on a visual property such as transparency, and the resulting shares appear as random patterns of black and white subpixels. Each individual share reveals no information about the original image.

To reconstruct the secret image, at least $k$ out of $n$ shares must be stacked, where $k$ is a predefined threshold. This structure poses a challenge in swarm-based applications – such as Unmanned Aerial Vehicle (UAV) swarms – where each UAV holds only a single share and collaborates to identify a target image.

In this work, we propose an optical VES solution that leverages wave interference as a physical encoding mechanism. The reconstructed image contains only pure black and white pixels, thus overcoming the grayscale degradation associated with traditional VES methods. Furthermore, the proposed scheme retains the computational efficiency of classical approaches while offering an improved security model: it achieves statistical information-theoretic security against honest-but-curious adversaries and is also resilient to active Byzantine adversaries.