Scheme For Visual

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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.