Cheating Prevention in Visual Cryptography - Visual Cryptography and Secret Image Sharing - page 275

original secret image. Since the invention of VC, many researchers have de-
voted themselves to enhancing the contrast and resolution of the reconstructed
images [1, 3] and to extending it to general access structures [7]. Moreover,
many schemes to visually share nonbinary secret images, such as gray-level
secret images [2, 5] and color secret images [12, 13], were also proposed. There
are lots of applications based on VC, for example, visual authentication and
identification [10], steganography [4, 6, 8], and image encryption [14].
In 2006, Horng et al. showed that cheating is possible in the k-out-of-n VC
[8]. The cheating activity could cause unpredictable damage to victims be-
cause they will accept a forged image different from the actual secret image as
authentic. In this chapter, we survey some recently proposed cheating preven-
tion schemes in VC and provide a comparative evaluation of their advantages
and disadvantages.
The rest of this chapter is organized as follows. Section 10.2 provides pre-
liminary background on VC and the cheating activities. Section 10.3 surveys
some cheating prevention schemes. Their comparative analyses are in Section
10.4. Finally, conclusions and some research issues are given in Section 10.5.
10.2 Preliminaries
10.2.1 Visual Cryptography
A visual secret sharing scheme is a special variant of a k-out-of-n secret sharing
scheme where the shares given to participants are xeroxed onto transparencies.
Therefore, a share is also called a transparency. If X is a qualified subset, then
the participants in X can visually recover the secret image by stacking their
transparencies without performing any cryptographic computation. Usually,
the secret is an image. To create the transparencies, each black and white
pixel of the secret image is handled separately. It appears as a collection of m
black and white subpixels in each of the n transparencies. We will call these
m subpixels a block. Therefore, a pixel of the secret image corresponds to nm
subpixels. We can describe the nm subpixels by an nm Boolean matrix,
called a base matrix, S = [S ij ] such that S ij = 1 if and only if the j th subpixel
of the i th share is black and S ij = 0 if and only if the j th subpixel of the if th
share is white. The gray level of the stack of k shared blocks is determined by
the Hamming weight H(V ) of the "OR"ed m-vector V of the corresponding
k rows in S. This gray level is interpreted by the visual system of the users as
black if H(V ) d and as white if H(V ) dm for some xed threshold
d and relative dierence . We would like m to be as small as possible and
to be as large as possible.
More formally, a solution to the k-out-of-n VC consists of two collections
C 0 and C 1 of nm base matrices. To share a white pixel, the dealer randomly