Image encryption by multiple random grids

In this paper, we first give a formal definition to the visual cryptograms of n (>=2) random grids (VCRG-n) for encrypting an image. Specifically, a set of VCRG-n with respect to image P consists of n random grids printed on transparencies such that only when the n transparencies are superimposed altogether can P be recognized by human vision (without any computing device), while any group of less than n transparencies obtains no information about P. Then, we design novel VCRG-n encryption schemes for binary, gray-level and color images, validate the correctness by formal proofs and demonstrate the feasibility by computer simulations. Our schemes do not require any extra pixel expansion neither any encoding basis matrix, which are necessary and inevitable in the approaches of conventional visual cryptography. These attractive advantages make our schemes more informative in theoretical interests and much applicable in practical applications.