Cheating prevention in visual Cheating prevention in visual cryptographycryptography

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

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10

01

01

01

1

0

T

T

1 0 0 1

1 1 1 1

0 1 1 0

1 0 0 1

1 0 0 1

1 0 0 1

10

10

01

01

01

10

10

01

Permutation from T1

Permutation from T0

Introduction - (2,3)-VSS

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100

010

001

001

001

001

1

0

T

T

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1 0 0 0 1 0

1 0 0 0 1 0

1 0 0 0 1 0

1 0 0 0 1 0

1 0 0 0 1 0

1 0 0 0 1 0

T1

T2

T3

T1+T2

T2+T3

T1+T3

1 0 0 0 1 0

0 1 0 1 0 0

0 0 1 0 0 1

1 1 0 1 1 0

0 1 1 1 0 1

1 0 1 0 1 1

T1

T2

T3

T1+T2

T2+T3

T1+T3

010

010

010

001

001

001

100

001

010

100

010

001

Outline

• Introduction

• Cheating in VC

• Review HT scheme

• Conclusions

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Cheating in VC

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1 0 0 0 1 0

0 1 0 1 0 0

T1

T2

001

010

010

001

Black

100

001

010

100

010

001

0 0 1 0 0 1T3

Cheating in VC

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1 0 0 0 1 0

0 1 0 1 0 0

T1

T2

001

010

010

001

100

001

010

100

010

001

0 0 1 0 0 1T3

P1 P2

collude

0 0 1 0 0 1T2’

0 0 1 0 0 1

Succeed to cheat T3.Replace Black into White

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):

• BW=

• BB=

001

001

001

0

0

0

1

1

1

100

010

001

0

0

0

1

1

1

Extra subpixels (verifying).

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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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T1, T2, T3

T1+T2, T1+T3, T2+T3

V1, V2, V3

Example:

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)V1+T2, V1+T3, V2+T1

V2+T3, V3+T1, V3+T2

Review of HT scheme

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Review of Horng et al.’s scheme

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Stacking VC and SA, LC is shown on the left-top corner

Stacking VC and SB, LC is shown on the right-top corner

Verification logo LC

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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