Cheating prevention in visual
cryptography
Author: C.M. Hu and W.G. Tzeng
Source: IEEE-TIP 2007
Presenter: Yu-Chi Chen
Date: 2010.9.21
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Outline
•
•
•
•
Introduction
Cheating in VC
Review HT scheme
Conclusions
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Visual Cryptography
• a variant of secret sharing (Noar and Shamir)
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Introduction - (2,2)-VSS
1 0
0
T 

1
0


1 0 
1
T 

0
1


1
0
0
1
1
0
0
1
1 0 0 1
1 0 0 1



Permutation from T0
1
0
0
1
1
0
0
1
0
1
1
0
1 0 0 1
0 1 1 0



Permutation from T1
1
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1
1
1
Introduction - (2,3)-VSS
1 0 0
T 0  1 0 0
1 0 0
1 0 0
T 1  0 1 0
0 0 1
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1 0 0 0 1 0
1 0 0 0 1 0



1 0 0 0 1 0
T1
1
0
0
0
1
0
T1+T2 1
0
0
0
1
0
T2
1
0
0
0
1
0
T2+T3 1
0
0
0
1
0
T3
1
0
0
0
1
0
T1+T3 1
0
0
0
1
0
1 0 0   0 1 0 
 0 1 0  1 0 0 



0 0 1 0 0 1
T1
1
0
0
0
1
0
T1+T2 1
1
0
1
1
0
T2
0
1
0
1
0
0
T2+T3 0
1
1
1
0
1
T3
0
0
1
0
0
1
T1+T3 1
0
1
0
1
1
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Outline
•
•
•
•
Introduction
Cheating in VC
Review HT scheme
Conclusions
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Cheating in VC
1 0 0  0 1 0 
0 1 0  1 0 0 



       
T1
1
0
0
0
1
0
T2
0
1
0
1
0
0
Black
1 0 0   0 1 0 
 0 1 0  1 0 0 



0 0 1 0 0 1
T3
0
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0
1
0
0
1
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Cheating in VC
P1
collude
1 0 0  0 1 0 
0 1 0  1 0 0 



       
T1
1
0
0
0
1
0
T2
0
1
0
1
0
0
1 0 0   0 1 0 
 0 1 0  1 0 0 



0 0 1 0 0 1
T3
0
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0
1
0
0
P2
T2’ 0
0
1
0
0
1
0
0
1
0
0
1
Succeed to cheat T3.
Replace Black into White
1
9
Cheating in VC
• Cheating prevention scheme (also called
“cheating immune scheme”)
– Authentication based
• Horng et al.’s scheme 1 DCC06
• Hu and Tzeng’s scheme IEEE TIP07
– Guessing probability based (provably secure)
• Horng et al.’s scheme 2 DCC06
• Tsai et al.’s scheme PR07
• De Prisco and De Santis’s scheme CJ09
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Outline
•
•
•
•
Introduction
Cheating in VC
Review HT scheme
Conclusions
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Review of HT scheme
• Proposed by Hu and Tzeng, and published in
IEEE Transactions on Image Processing 2007.
• It is an authentication based cheating
prevention (ABCP) scheme.
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Review of HT scheme
• Participants decide verification images
respectively.
• The dealer will share the secret image and the
verification images (VI).
• Finally, a participant gets a share from the
other one, and then recover the secret.
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Review of HT scheme
• Shares generating (basic matrices in HT):
10 1 0 0


• BW= 10 1 0 0
10 1 0 0
Extra subpixels (verifying).
1 0 1 0 0


• BB= 10 0 1 0
1 0 0 0 1
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Review of HT scheme
• Verification shares generating:
• If the pixel in VI is black, the sibpixels are
[0 1 0 0 0]. (which corresponds to the
permutation of basic matrices)
• If the pixel in VI is white, the sibpixels are
[1 0 0 0 0].
Extra subpixels.
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Review of HT scheme
Example:
T1, T2, T3
T1+T2, T1+T3, T2+T3
V1, V2, V3
V1+T2, V1+T3, V2+T1
V2+T3, V3+T1, V3+T2
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T1[1 0 1 0 0] (white)
T2[1 0 0 1 0] (white)
T1+T2[1 0 1 1 0] (black)
V2[0 1 0 0 0] (white +)
T1+V2[1 1 1 0 0] (black)
Review of Horng et al.’s scheme
Verification logo LC
Stacking VC and SA, LC is
shown on the left-top corner
Stacking VC and SB, LC is
shown on the right-top corner
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Conclusions
• HT scheme is a cheating immune VSS scheme.
• In this paper, three kinds of cheating are
proposed by Hu and Tzeng.
• They also analyze Horng et al.’s ABCP scheme
is not cheating immune.
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