Two-Image Encryption by Random Grids
Joy Jo-Yi Chang, Ming-Jheng Li, Yi-Chun Wang and Justie Su-Tzu Juan
National Chi Nan University
R1 R2 R1 R2⊕
0 0 0
0 1 1
1 0 1
1 1 1
BB
R1
R1 R2
B R2
R1 R2
B R1 R2
B R2R1
B R1 R2
random(0,1)
B R1 R2
random(0,1)
B R2R1
• Definition 1: fRSP(.): Y ← fRSP(X), Y is the output of the function fRSP(.)
with the inputs X, where fRSP(.) is that randomly
select a pixel of X.
• Definition 2: fRG (.)Y||Z ← fRG (X), Y and Z are the outputs of the
function fRG(.) with the input X, where fRG(.) 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) (i , j) (i , j)
• 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 fRG (.): (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.
X Y Z
RGf RGfRGf
(i , j) (i , j) (i , j)
Chen et al.Step 1: SA(i, j) ← fRSP(SA).Step 2: G1(i, j)||G2(i, j) ← fRG(SA(i, j)).
Step 3: G2(j,(m-1)-i) ← (SB(j, ,(m-1)-i), G1(i, j)).
SA G2G1
SB G1 G2
RGf
RGf
Step 4: G1(j,(m-1)-i) ← (SA(j, (m-1)-i), G2(j, (m-1)-i, ).
Step 5: G2((m-1)-i, (m-1)-j) ← (SB(j, (m-1)-i), G1(j, (m-1)-i, ).
SA G2G1
SBG1 G2
RGf
RGf
Step 6: G1((m-1)-i, (m-1)-j) ← (SA(m-1)-i, (m-1)-j),G2((m-1)-i, (m-1)-j)
Step 7: G2((m-1)-j, i) ← (SB(m-1)-i, (m-1)-j),G1((m-1)-i, (m-1)-j),
SBG1 G2
SA G2G1
RGf
RGf
Step 8: G1((m-1)-j, i) ←random(0,1)
random(0,1)
• Step 1: SA(i, j) ← fRSP(SA).
• Step 2: G1(i, j)||G2(i, j) ← fRG(SA(i, j)).
• Step 3: G2((i + m/4), j) ← (SB(i, j), G1(i, j)).
SBG1 G2
(3,4)
SA and SB with the size of 240 240╳
(3,4)
(3,4)
(3,4)
(3,4) (63,4)
SA G2G1
RGf
This papper
• Step 4: G1((i + m/4), j) ← (SA((i + m/4), j), G2((i + m/4),j)).
SA G2G1
(63,4) (63,4) (63,4)
• Step 5: G2((i + m/2), j) ← (SB((i + m/4), j), G1((i + m/4),j)).
SBG1 G2
(63,4) (63,4) (123,4)
RGf
RGf
• Step 6: G1((i + m/2), j) ← (SA((i + m/2), j), G2((i + m/2),j)).
SA G2G1
(123,4)
(123,4)
(123,4)
• Step 7: G2((i + 3m/4), j) ← (SB((i + m/2), j), G1((i + m/2),j)).
SB G2G1
(183,4)
(123,4)
(123,4)
RGf
RGf
• Step 8: G1((i + 3m/4), j) ← (SA((i + 3m/4), j), G2((i +3m/4), j)).
SA G2G1
(183,4)
(183,4)
(183,4)
RGf
•
Simulation 1: binary secrets, moving horizontally by 1/4 width.
share G1
share G1
share G2
Simulation 2: binary secrets, moving horizontally by 1/8 width.
share G2
Simulation 3: binary secrets, moving horizontally by 1/30 width.
share G1
share G2
share G1
Simulation 4: no constraint about the size.
share G2
Chen et al The Proposed Scheme
90-degreerotation
Moving by 1/4width
Moving by 1/16width
Chen et al The Proposed Scheme
90-degree Rotation
Moving by 1/4 width
Moving by 1/10 width
Only Square Any Rectangle Any Rectangle
QUANTITY OF THE DISTORTION
THE COMPARISON OF THE SIZE.
VC RandomGrids
J.-L. Bai Chen et al OurScheme
Pixel Expansion Yes No No No No
Use Codebook Yes No No No No
Secret DataQuantity
Wh Wh 1.75wh 2wh 2wh
AdjustmentDistortion
- - - No Yes
Any SecreteRectangle Images
Yes Yes No No yes