Visual secret sharing by random grids revisited

Recently, the visual secret sharing (VSS) technique by random grids (RG), proposed by Kafri and Keren in 1987, has drawn attention in academia again to remove the abovementioned drawbacks. However, Kafri and Keren's scheme is a 2-out-of-2 VSS scheme but neither nn-out-of-nn nor 2-out-of-n(n>2). In this paper, novel nn-out-of-nn (Method 1) and 2-out-of-nn (Method 2) secret image sharing schemes based on RG are proposed to encrypt the secret into nn cipher-grids without pixel expansion and additional codebook required. In the decryption phase, while participants superimpose all (Method 1) or at least two (Method 2) cipher-grids without any extra computation, the secret is recognizable by the human visual system. To our best knowledge, this paper is the first attempt in the literature to develop new RG-based VSS schemes by means of extending the basic 2-out-of-2 scheme to the nn-out-of-nn as well as 2-out-of-nn ones. To demonstrate the correctness of the proposed schemes, the formal analysis is given while the experimental results show the proposed schemes do work well.