1. Step Construction of Visual Cryptography Schemes IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 5, NO. 1, MARCH 2010 Feng Liu, Chuankun Wu, Senior Member, IEEE, and Xijun Lin Reporter:Bibitana

2. Introduction propose a step construction to construct General access structure – VCS OR – VCS XOR their scheme applies a technique to simplify the access structure – multiple share images – reduce the average pixel expansion (APE) Applying a (2, 2) VCS recursively 2

3. Preliminaries (1/2) 3 V ={1, 2, …, n },  Qual   Forb =  and  Qual   Forb =2 V

4. Preliminaries (2/2) (2, 2)-VCS OR (2, 2)-VCS XOR 4

5. STEP CONSTRUCTION OF VCS FOR GENERAL ACCESS STRUCTURE (1/4) They propose 3 constructions of the step construction of general access structure VCS. Each of the participants may take multiple share images with different pixel expansions. 5

6. Example (3, 3) OR : 6 STEP CONSTRUCTION OF VCS FOR GENERAL ACCESS STRUCTURE (2/4) APE OR =(2+4+4)/3=10/3,  OR =1/4

7. 7 Example (3, 3) XOR : STEP CONSTRUCTION OF VCS FOR GENERAL ACCESS STRUCTURE (3/4) APE XOR =1,  XOR =1

8. ( n, n )-VCS can achieve by applying (2, 2)-VCS for n -1 times 8 APE OR =(3*2 n -1 -2)/ n  OR =2 -( n -1) optimal pixel expansion and contrast STEP CONSTRUCTION OF VCS FOR GENERAL ACCESS STRUCTURE (4/4)

9. Simplifying the Access Structure by Using Equivalent Participants (1/3) Participant i is equivalent to j – they can be assigned to identical shares without affecting the access structure 9

10. 10 Simplifying the Access Structure by Using Equivalent Participants (2/3)

11. Example of construction 1: 11 Simplifying the Access Structure by Using Equivalent Participants (3/3) (2, 2)-VCS, first share assing {1, 4} and another assing to {2, 3}

12. Thank You!! Next Week will present: – Construction 2, – Construction 3 – The rest session of the paper. 12