Extended Visual Cryptography for Photograph Images - Visual Cryptography and Secret Image Sharing - page 94

4.1 Introduction
Visual cryptography is a kind of cryptography that can be decoded directly by
the human visual system without any computation for decryption. It usually
prints certain images on transparencies and the secret image is reconstructed
by simply stacking the transparencies together. Extended visual cryptogra-
phy allows the printing of meaningful images on transparencies so that it
can conceal the very existence of "secret" in the transparencies. There have
been a lot of studies to incorporate photograph images into extended visual
cryptography. This chapter attempts to survey the studies on extended visual
cryptography for photograph images.
4.2 Basic Visual Cryptography Schemes
In order to determine basic terminology in this chapter, this section explains
basic concepts of visual cryptography, namely, k out of n Visual Secret Sharing
Scheme ((k;n) VSSS), an Extended Visual Cryptography Scheme (EVCS), and
Random Grids.
4.2.1 (k;n) Visual Secret Sharing Schemes
This scheme was proposed by Naor and Shamir in 1994 [31]. It generates n
transparencies from an original secret image. The transparencies are usually
shared by n participants so that each participant is expected to keep one
transparency. Thus, a secret image is sometimes called a shared image. The
secret image can be observed if any k or more of them are stacked together.
However, the secret image is totally invisible if fewer than k transparencies
are stacked. The images on transparencies are called shadow images.
Each pixel of a shadow image is generated separately in the conventional
VSSS. An original secret pixel will be transformed to n patterns of pixels
for shadow images. These pixels on shadow images are called shares. A share
consists of m black and white subpixels. The human visual system observes
the average of subpixels, because they exist in close proximity. This structure
is usually described by an nm Boolean matrix M = [m ij ]. Here m ij = 0
or 1 if the jth subpixel in the ith shadow is white or black, respectively. If
transparencies of r shadows i 1 ;i 2 ; ;i r out of n are stacked in a way that
properly aligns the subpixels, each combined share can be represented by the
Boolean "OR" of the corresponding rows i 1 ;i 2 ; ;i r in the Boolean matrix