1. 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 2015/4/13 1

2. Outline Introduction Cheating in VC Review HT scheme Conclusions 2015/4/13 2

3. Visual Cryptography a variant of secret sharing (Noar and Shamir) 2015/4/13 3

4. Introduction - (2,2)-VSS 2015/4/13 4 1001 1111 0110 1001 1001 1001 Permutation from T 1 Permutation from T 0

5. Introduction - (2,3)-VSS 2015/4/13 5

6. 6 100010 100010 100010 100010 100010 100010 T1 T2 T3 T1+T2 T2+T3 T1+T3 100010 010100 001001 110110 011101 101011 T1 T2 T3 T1+T2 T2+T3 T1+T3

7. Outline Introduction Cheating in VC Review HT scheme Conclusions 2015/4/13 7

8. Cheating in VC 2015/4/13 8 100010 010100 T1 T2 Black 001001 T3

9. Cheating in VC 2015/4/13 9 100010 010100 T1 T2 001001 T3 P1 P2 collude 001001 T2’ 001001 Succeed to cheat T3. Replace Black into White

10. 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 2015/4/13 10

11. Outline Introduction Cheating in VC Review HT scheme Conclusions 2015/4/13 11

12. 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. 2015/4/13 12

13. 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. 2015/4/13 13

14. Review of HT scheme Shares generating (basic matrices in HT): B W = B B = Extra subpixels (verifying). 2015/4/13 14

15. 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. 2015/4/13 15

16. 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 2015/4/13 16

17. Review of Horng et al.’s scheme 2015/4/13 17 Stacking V C and S A, L C is shown on the left-top corner Stacking V C and S B, L C is shown on the right-top corner Verification logo L C

18. 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. 2015/4/13 18