1. IEEE TRANSACTIONS ON IMAGE PROCESSING,2007 指導老師：李南逸 報告者：黃資真 Cheating Prevention in Visual Cryptography 1

2. Outline Introduction Cheating in VC Three cheating methods Generic transformation for cheating prevention. Conclusion 2

3. 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. 3

4. Set of n participants A qualified set A forbidden set mm subpixels of a pixel 0White pixel 1black pixel 4

5. 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. 5

6. Cheating in VC 6

7. Three cheating methods- Cheating 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. 7

8. 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. 8

9. Three cheating methods- Cheating a VCS by an MP 9

10. Three cheating methods- Cheating 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. 10

11. 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. 11

12. Three cheating methods- Cheating a VCS by an MO 12

13. Three cheating methods- Cheating 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. 13

14. Three cheating methods- Cheating a EVCS by an MP be the threshold for contrast that human eyes distinguish the image from the background. 14

15. 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 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 15

16. Three cheating methods- Cheating a EVCS by an MP 16

17. Generic transformation for cheating prevention An 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

18. Generic transformation for cheating prevention Input: 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. 18

19. Generic transformation for cheating prevention Share verification phase: Before stacking their share, checks whether shows his verification image, where is another participant. 19

20. Generic transformation for cheating prevention 20

21. Conclusion Proposed three cheating methods against VCS and EVCS. Proposed an efficient transformation of VCS for cheating prevention. 21