Cheating prevention in visual cryptography Author: C.M. Hu and W.G. Tzeng Source: IEEE-TIP 2007 Presenter: Yu-Chi Chen Date: /4/13 1

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

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

Introduction - (2,2)-VSS 2015/4/ Permutation from T 1 Permutation from T 0

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

T1 T2 T3 T1+T2 T2+T3 T1+T T1 T2 T3 T1+T2 T2+T3 T1+T3

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

Cheating in VC 2015/4/ T1 T2 Black T3

Cheating in VC 2015/4/ T1 T T3 P1 P2 collude T2’ 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 CJ /4/13 10

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

Review of HT scheme Proposed by Hu and Tzeng, and published in IEEE Transactions on Image Processing It is an authentication based cheating prevention (ABCP) scheme. 2015/4/13 12

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

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

Review of HT scheme Verification shares generating: If the pixel in VI is black, the sibpixels are [ ]. (which corresponds to the permutation of basic matrices) If the pixel in VI is white, the sibpixels are [ ]. Extra subpixels. 2015/4/13 15

T1, T2, T3 T1+T2, T1+T3, T2+T3 V1, V2, V3 Example: T1[ ] (white) T2[ ] (white) T1+T2[ ] (black) V2[ ] (white +) T1+V2[ ] (black) V1+T2, V1+T3, V2+T1 V2+T3, V3+T1, V3+T2 Review of HT scheme 2015/4/13 16

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

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