1. Two-Image Encryption by Random Grids 1 Joy Jo-Yi Chang, Ming-Jheng Li, Yi-Chun Wang and Justie Su-Tzu Juan National Chi Nan University

2. R1R1 R2R2 R 1 ⊕ R2 000 011 101 111 BBR1R1 R1R1 R2R2 BR2R2 R1R1 R2R2 BR1R1 R2R2

3. BR2R2 R1R1 BR1R1 R2R2 random(0,1) BR1R1 R2R2 BR2R2 R1R1

4. Definition 1: f RSP (.): Y ← f RSP (X), Y is the output of the function f RSP (.) with the inputs X, where f RSP (.) is that randomly select a pixel of X. Definition 2: f RG (.)Y||Z ← f RG (X), Y and Z are the outputs of the function f RG (.) with the input X, where f RG (.) is one of the three random grids algorithm in [6] which inputs a pixel of the secret image, then outputs two cipher-pixels for two shares. X Y Z (i, j)

5. Definition 3: (.) ： Z← (X,Y): Z, Z is the output of the function f’ RG (.) with the inputs X and Y, where (.) is the function according to f RG (.): (as in Definition 2) which inputs a cipher-pixel of one share Y and a pixel of the secret image X, then outputs the other cipher-pixel. XYZ (i, j)

6. Chen et al. Step 1: S A (i, j) ← f RSP (S A ). Step 2: G 1 (i, j)||G 2 (i, j) ← f RG (S A (i, j)). Step 3: G 2 (j,(m-1)-i) ← (S B (j,,(m-1)-i), G 1 (i, j)). SASA G2G2 G1G1 SBSB G1G1 G2G2

7. Step 4: G 1 (j,(m-1)-i) ← (S A (j, (m-1)-i), G 2 (j, (m-1)-i, ). Step 5: G 2 ((m-1)-i, (m-1)-j) ← (S B (j, (m-1)-i), G 1 (j, (m-1)-i, ). SASA G2G2 G1G1 SBSB G1G1 G2G2

8. Step 6: G 1 ((m-1)-i, (m-1)-j) ← (S A (m-1)-i, (m-1)-j),G 2 ((m-1)-i, (m-1)-j) Step 7: G 2 ((m-1)-j, i) ← (S B (m-1)-i, (m-1)-j),G 1 ((m-1)-i, (m-1)-j), SBSB G1G1 G2G2 SASA G2G2 G1G1

9. Step 8: G 1 ((m-1)-j, i) ←random(0,1) random(0,1)

10. Step 1: S A (i, j) ← f RSP (S A ). Step 2: G 1 (i, j)||G 2 (i, j) ← f RG (S A (i, j)). Step 3: G 2 ((i + m/4), j) ← (S B (i, j), G 1 (i, j)). SBSB G1G1 G2G2 (3,4) S A and S B with the size of 240 ╳ 240 (3,4) (63,4) SASA G2G2 G1G1 This papper

11. Step 4: G 1 ((i + m/4), j) ← (S A ((i + m/4), j), G 2 ((i + m/4),j)). SASA G2G2 G1G1 (63,4) Step 5: G 2 ((i + m/2), j) ← (S B ((i + m/4), j), G 1 ((i + m/4),j)). SBSB G1G1 G2G2 (63,4) (123,4)

12. Step 6: G 1 ((i + m/2), j) ← (S A ((i + m/2), j), G 2 ((i + m/2),j)). SASA G2G2 G1G1 (123,4) Step 7: G 2 ((i + 3m/4), j) ← (S B ((i + m/2), j), G 1 ((i + m/2),j)). SBSB G2G2 G1G1 (183,4)(123,4)

13. Step 8: G 1 ((i + 3m/4), j) ← (S A ((i + 3m/4), j), G 2 ((i +3m/4), j)). SASA G2G2 G1G1 (183,4)

14. Simulation 1: binary secrets, moving horizontally by 1/4 width. share G 1 share G 2 Simulation 2: binary secrets, moving horizontally by 1/8 width. share G 2

15. Simulation 3: binary secrets, moving horizontally by 1/30 width. share G 1 share G 2 share G 1 Simulation 4: no constraint about the size. share G 2

16. Chen et alThe Proposed Scheme 90-degree rotation Moving by 1/4 width Moving by 1/16 width Chen et alThe Proposed Scheme 90-degree Rotation Moving by 1/4 width Moving by 1/10 width Only SquareAny Rectangle QUANTITY OF THE DISTORTION THE COMPARISON OF THE SIZE.

17. VCRandom Grids J.-L. BaiChen et alOur Scheme Pixel ExpansionYesNo Use CodebookYesNo Secret Data Quantity Wh 1.75wh2wh Adjustment Distortion ---NoYes Any Secrete Rectangle Images Yes No yes