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Cheating Prevention
in Visual Cryptography
IEEE TRANSACTIONS ON IMAGE PROCESSING,2007
指導老師：李南逸
報告者：黃資真
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Outline
 Introduction
 Cheating in VC
 Three cheating methods
 Generic transformation for cheating prevention.
 Conclusion
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Introduction
 Propose three cheating methods against VC or EVC schemes.
 Propose some necessary criteria for a VCS to be secure
against cheat-preventing.
 Propose a generic method that converts any VCS to another
VCS with the property cheating prevention.
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Set of n participants
A qualified set
A forbidden set
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m
m subpixels of a pixel
0
White pixel
1
black pixel
Cheating in VC
 Two types of cheaters:
• Malicious participant(MP)
• Malicious outsider(MO)
 A cheating process against a VCS:
 Fake share construction.
 Image reconstruction phase.
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Cheating in VC
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Three cheating methodsCheating a VCS by an MP
 Assume that is the cheater.
 Uses his genuine share as a template to construct a set of fake
share.
 Fake share are indistinguishable from its genuine share.
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Three cheating methodsCheating a VCS by an MP
Input: .(Assume that the cheater is )
Fake Share construction phase:
Assume: (1) Each pixel of has x black and y white subpixels.
(2) chooses a fake image and prepares r= (m/x)-1
fake shares.
For each white pixel of the fake image, copy the corresponding subpixels of the pixel in
to each fake share.
For each black pixel of the fake image, randomly assign x black and y white subpixels to
each fake share.
1)
2)
Image reconstruction phase (the fake image):
If
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,the stacking of genuine shares and fake shares reveal the fake image.
Three cheating methodsCheating a VCS by an MP
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Three cheating methodsCheating a VCS by an MO
 MO can cheat even without any genuine share at hand.
 Use the optimal (2,2)-VCS to construct the fake shares for
the fake image.
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Three cheating methodsCheating a VCS by an MO
Input : none.
Fake share construction phase:
The MO chooses a fake image.
1) Encode the fake image into two fake shares
with the optimal
(2,2)-VCS.
2) Generate enough pairs of fake shares
with various sizes and
subpixel distributions, 1≦i ≦r for some r.
Image reconstruction phase (the fake image):
Let . The stacking of
and two fake shares
image for some c, 1≦c≦r.
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shows the fake
Three cheating methodsCheating a VCS by an MO
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Three cheating methodsCheating a EVCS by an MP
 Use the fake shares to reduce the contrast between the share
images and the background.
 The fake image in the stacking of fake shares has enough
contrast against the background since the fake image is
recovered in perfect blackness.
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Three cheating methodsCheating a EVCS by an MP
 be the threshold for contrast that human eyes distinguish the image from the
background.
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Three cheating methods-
Cheating a EVCS by an MP
Input: .(Assume that the cheater is )
Fake Share construction phase:
Assume: chooses a fake image
1)
Create . The
S1' share image of is removed by changing d black subpixels into white
subpixels in each black pixel. d is the difference between the numbers of black subpixels
of a black and a white pixel.
2)
Create
temporary fake shares ,1≦i ≦r, by using according to CA-1.
m
'
'
r    1
FS
Randomly change
d
white
subpixels
into
black
subpixels
of
each
pixel
of
the
share
S
x
i
 
1image
in , 1≦i ≦r.
Construct by randomly adding black subpixels to each pixel in ,1≦i ≦r.
3)
4)
FS i'
Image reconstruction phase (the fake image):
m
FSi
Same as in CA-1FS '
i
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Three cheating methodsCheating a EVCS by an MP
a (, m)  EVCS
P  {P1 , P2 , P3 }, Q  {{P1 , P2 },{P2 , P3},{P1 , P2 , P3}}
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Generic transformation
for cheating prevention
 An cheat-preventing method should have the following
properties:
1)
2)
3)
4)
5)
6)
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It does not rely on the help of an on-line TA.
The increase to pixel expansion should be as small as possible.
Each participant verifies the shares of other participants.
The verification image of each participant is different and confidential.
The contrast of the secret image in the stacking of shares is not reduced
significantly.
A cheat-preventing method should be applicable to any VCS.
Generic transformation
for cheating prevention
Input: S 0 and S 1 of a (, m)  VCS.
Shares construction phase:
Let
1.
10

.
0
T 
 .

10
S0
10



1
 and T   .
 .



10

S1






Use T 0 and
as basis
T 1 matrices for generation share ,1≦i ≦n, of
(,and
m generate
2)  VCS
.
3.
,1≦i ≦n,Sichoose a verificationofimage
a verification
Pshare as follows:
2.
a)
b)
i
For each white pixel in the verification image, put
Vi the pixel of (m+2)dimensional[100…0] (subpixels) to .
For each black pixel in the verification image, put the pixel of (m+2)-Vi
dimensional[0100…0] (subpixels) to .
Vi
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Generic transformation
for cheating prevention
Share verification phase:
Before stacking their share, checks whether
Pi
his verification image, where is another
Vi  Sshows
j, i  j
participant.
Pj
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Generic transformation
for cheating prevention
a (, m  2)  VCS with cheating prevention
P  {P1 , P2 , P3}, Q  {{P1 , P2 },{P2 , P3},{P1 , P2 , P3}}
Verification image: P1  A, P2  B, P3  C
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Conclusion
 Proposed three cheating methods against VCS and EVCS.
 Proposed an efficient transformation of VCS for cheating
prevention.
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