Generalized Random Grid and Its Applications in Visual Cryptography

Random grid (RG) is a method to implement visual cryptography (VC) without pixel expansion. However, a reconstructed secret with lower visual quality reveals in RG-based VC due to the fact that average light transmission of a share is fixed at 1/2. In this work, we introduce the concept of generalized RG, where the light transmission of a share becomes adjustable, and adopt generalized RG to implement different VC schemes. First, a basic algorithm, a (2,2) generalized RG-based VC, is devised. Based on the (2,2) scheme, two VC schemes including a (2,n) generalized RG-based VC and a (n,n) xor-based meaningful VC are constructed. The two derived algorithms are designed to solve different problems in VC. In the (2,n) scheme, recovered image quality is further improved. In the (n,n) method, meaningful shares are constructed so that the management of shadows becomes more efficient, and the chance of suspicion on secret image encryption is reduced. Moreover, superior visual quality of both the shares and recovered secret image is achieved. Theoretical analysis and experimental results are provided as well, demonstrating the effectiveness and advantages of the proposed algorithms.