Lossless Recovery Scheme for Grayscale Visual Cryptography Based on Random Grids

With the advancement of digitalization, the demand for grayscale image encryption has been increasing. Previous visual cryptography schemes for grayscale images have encountered issues such as information loss during recovery, poor recovery quality, and significant pixel expansion. This study introduces novel grayscale visual cryptography schemes based on grayscale threshold segmentation, including the (n,n) and (k,n) schemes, utilizing random grids. These schemes enable lossless recovery of the secret image when all shares are involved in the decryption process. Furthermore, by incorporating the particle swarm optimization algorithm, a scheme for generating share images containing grayscale information was proposed. This method relies on the grayscale-overlay principle, allowing secret image recovery through the overlay of shares without requiring computational devices, demonstrating the applicability of the extended scheme. Theoretical analysis demonstrates the security of the proposed schemes, and experimental results further verify their effectiveness.