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