cheating prevention in visual cryptography

IEEE TRANSACTIONS ON IMAGE PROCESSING,2007指導老師：李南逸報告者：黃資真

Cheating Prevention in Visual Cryptography

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OutlineIntroductionCheating in VCThree cheating methodsGeneric transformation for cheating

prevention.Conclusion

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IntroductionPropose 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

m m subpixels of a pixel

0 White pixel

1 black pixel

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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 methods- Cheating a VCS by an MPAssume 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 methods- Cheating 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.

1) For each white pixel of the fake image, copy the corresponding subpixels of the pixel in to each fake share.

2) For each black pixel of the fake image, randomly assign x black and y white subpixels to each fake share.

Image reconstruction phase (the fake image): If ,the stacking of genuine shares and fake shares reveal the

fake image.

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Three cheating methods- Cheating a VCS by an MP

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Three cheating methods- Cheating a VCS by an MOMO 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 methods- Cheating 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 shows the fake image for some c, 1≦c≦r.

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Three cheating methods- Cheating a VCS by an MO

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Three cheating methods- Cheating a EVCS by an MPUse 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 methods- Cheating 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 MPInput: .(Assume that the cheater is ) Fake Share construction phase: Assume: chooses a fake image

1) Create . The 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.

3) Randomly change d white subpixels into black subpixels of each pixel of the share image in , 1≦i ≦r.

4) Construct by randomly adding black subpixels to each pixel in ,1≦i ≦r.

Image reconstruction phase (the fake image): Same as in CA-1

'1S

1m

rx

'iFS '

1S

'iFS

iFS m'iFS

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Three cheating methods- Cheating a EVCS by an MP

1 2 3 1 2 2 3 1 2 3

( , )

{ , , }, {{ , },{ , },{ , , }}

a m EVCS

P P P P Q P P P P P P P

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Generic transformation for cheating preventionAn cheat-preventing method should have

the following properties:1) It does not rely on the help of an on-line TA.2) The increase to pixel expansion should be as small

as possible.3) Each participant verifies the shares of other

participants.4) The verification image of each participant is

different and confidential.5) The contrast of the secret image in the stacking of

shares is not reduced significantly.6) A cheat-preventing method should be applicable to

any VCS.17

Generic transformation for cheating preventionInput:Shares construction phase:

1. Let

2. Use as basis matrices for generation share ,1≦i ≦n, of

3. ,1≦i ≦n, choose a verification image and generate a verification share as follows:

a) For each white pixel in the verification image, put the pixel of (m+2)-dimensional[100…0] (subpixels) to .

b) For each black pixel in the verification image, put the pixel of (m+2)-dimensional[0100…0] (subpixels) to .

0 1 ( , ) .S and S of a m VCS

0 0 1 1

10 10

. .

. .

10 10

T S and T S

0 1 T and T

iS ( , 2) .of m VCS

iPiV

iV

iV18

Generic transformation for cheating prevention

Share verification phase:Before stacking their share, checks whether

shows his verification image, where is another participant.

iP, i jV S i j

jP

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Generic transformation for cheating prevention

1 2 3 1 2 2 3 1 2 3

1 2 3

( , 2)

{ , , }, {{ , },{ , },{ , , }}

: , ,

a m VCS with cheating prevention

P P P P Q P P P P P P P

Verification image P A P B P C

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ConclusionProposed three cheating methods against

VCS and EVCS.

Proposed an efficient transformation of VCS for cheating prevention.

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