A New Cheating Prevention
Scheme For Visual
Cryptography
第十六屆全國資訊安全會議
Jun 8 2006
Du

Shiau Tsai
ab
,Tzung

her Chen
c
and Gwoboa Horng
a
a
Department of Computer Science, National Chung Hsing University
b
Department of Information Management, Hsiuping institue of Technology
c
Department of Computer Science and Information Engineering, National
Chiayi University
報告人：張淯閎
2
Conspectus
Abstract
Visual Cryptography
Cheating in Visual Cryptography
VC Cheating Protection Scheme
Simulated Results
Conclusion
3
Abstract
Naor and Shamir proposed the (k,n) Visual
Cryptography(VC for short) scheme in 1995,
and has been used in numerous applications.
In 2006, Horng et al. proposed that cheating is
possible in VC.
In this study, a new scheme used Generic
Algorithms(GA for short) is proposed to solve
the cheating problem.
4
Visual Cryptography
The nm subpixels is described as an
n
×
m boolean matrix
S=[S
ij
] such that S
ij
= 1 if and only if the j
th
subpixel of the i
th
share is black. A solution to the (k,n) VC scheme consists of
two collections of
n
×
m boolean matrices C
0
(For white) and
C
1
(For black).
The solution is considered valid if the following three
conditions are met
：
1.H(
V
)
≦
d

α
*m
in C
0
2.H(
V
)
≧
d
in C
1
3.For any subset {i
1
,i
2
,
…
,i
q
} of {1,2,
…
,n} with q < k, the two
collections of q
×
m matrices D
t
for t
ε
{0,1} obtained by
restricting each n
×
m matrix in C
t
(where t=0,1) to rows
i
1
,i
2
,
…
,i
q
are indistinguishable
in the
sense that they contain
the same matrices with the same frequencies.
5
Cheating in Visual Cryptography
Horng et al. proposed that cheating is possible
in (
k
,
n
) VC when
k
is smaller than
n
.
The key point of cheating is how to predict
and rearrange the positions of black and white
subpixels in the victim
’
s and cheater
’
s share.
Figure 1. shows the whole cheating process
and Table 1. shows the cheaters create to
change the decoded image.
Figure 1.: the cheating process
Pixel in
Secret
Image
Share
pixel in
Share S
A
Share
pixel in
Share S
B
Share
pixel in
Share S
C
Pixel in
Cheating
Image
Share
pixel in
Share S
A
’
Share
pixel in
Share S
B
’
Case1
white
[1 0 0]
[1 0 0]
[1 0 0]
white
[1 0 0]
[1 0 0]
Case2
white
[1 0 0]
[1 0 0]
[1 0 0]
black
[0 1 0]
[0 0 1]
Case3
black
[1 0 0]
[0 1 0]
[0 0 1]
white
[0 0 1]
[0 0 1]
Case4
black
[1 0 0]
[0 1 0]
[0 0 1]
black
[1 0 0]
[0 1 0]
Table 1.: The concept of cheating in VC
8
VC Cheating Protection Scheme(1)
Figure 2. shows the process to proposed scheme.
●
First, The rotation process turns SI with
different degrees of angle to generate SI.
●
Second, used GA to proposed scheme.
2
n
C
Figure 2. The sketch of proposed scheme
9
VC Cheating Protection Scheme(2)
Individual 1
Individual 2
Individual 3
...
Fitness Function
Transmutation
stop yes or no?
Reproduction
Crossover
Mutation
Population
Simulation
environment
MatingPool
New
generation
Figure 3.GA Process
10
VC Cheating Protection Scheme(3)
Figure 4. The chromosomes
11
VC Cheating Protection Scheme(4)
IF
H
(
V
j
) =
E
V
THEN
ρ
j
= 1 ELSEρ
j
= 0, where
j
= 1,2,
…
,
n
IF
H
(
g
(
i
1 ,
i
2 )
) satisfy
S
V
(
i
1 ,
i
2 )
THEN
ψ
(
i
1 ,
i
2 )
= 1 else ψ
(
i
1 ,
i
2 )
= 0, where
i
1
<
i
2
<
n
fitness value =
2
1
*
)
,
(
2
1
n
j
i
i
Fitness function algorithm
12
Simulated Results(1)
Figure 5. Decoded images in the (2, 4) cheating prevention scheme
13
Simulated Results(2)
Figure 7: Results of simulated cheating attack.
14
Conclusion
The proposed scheme does against the
cheating attack in VC.
The GA based share construction method
provides another direction for creating shares.
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