Cheating Prevention in Visual Cryptography - Visual Cryptography and Secret Image Sharing - page 280

10.3 Cheating Prevention Schemes
A visual secret sharing scheme is said to be a cheating prevention scheme if the
probability of successful cheating is negligible. We will not consider cheating
prevention in computational visual cryptographic schemes [21]. We can divide
the cheating prevention schemes into two classes. One is based on share au-
thentication where another share (transparency) is used to authenticate other
shares (transparencies) and the other is based on blind authentication where
some property of the image is used to authenticate the reconstructed secret
image. For example, in [8], it is assumed that a smooth image such that its
boundary of black and white regions is clearly perceptible is regarded as au-
thentic. Due to practical reasons, most cheating prevention schemes focus on
2-out-of-n schemes. In the following subsections, we will survey 6 recent pro-
posed cheating prevention schemes: two from [8], proposed in 2006 and will
be referred to as HCT1 and HCT2, one from [15], proposed in 2007 and will
be referred to as HT, one from [18], proposed in 2007 and will be referred to
as TCH, and two from [20], proposed in 2009 and will be referred to as PS1
and PS2.
10.3.1 HCT1 and HCT2
In [8], two cheating prevention schemes are proposed: the Authentication
Based Cheating Prevention scheme, referred to as HCT1, and the 2-out-of-
(n + l) cheating prevention scheme, referred to as HCT2. HCT1, shown in
Figure 10.5, is a share-authentication-based cheating prevention scheme and
HCT2, shown in Figure 10.7, is a blind-authentication-based cheating pre-
vention scheme. Figure 10.6 shows an experiment of HCT1. In HCT1, each
participant uses an extra transparency to verify the integrity of other trans-
parencies by means of the appearance of the verification logo. A participant
adopts a verification transparency to verify the integrity of other transparen-
cies through the appearance of his own verification logo. Each verification
transparency is generated by a 2-out-of-2 VC. Therefore, each participant re-
ceives two transparencies, namely, secret share transparency and verification
transparency created by the 2-out-of-n and 2-out-of-2 VC, respectively. Figure
10.6 shows an experiment of HCT1.
HCT2 generates (n+l) transparencies but it only delivers n transparencies
to participants. The probability that cheaters can correctly guess the structure
of each block generated for a black pixel of the victim's transparency is down
to 1=(1 + l). The secret image is redesigned to consist of two complementary
parts. Two binary images are said to be complementary to each other if and
only if they have the same size and, for all corresponding pixels, one is black
and the other is white. Therefore, the probability that cheaters can correctly