(1) Image sharing method for gray-level images, Wei-Kuei Chen, The Journal of Systems and Software 86 (2013) 581– 585

(2) Random grid-based visual secret sharing with abilities of OR and XOR decryptions, Xiaotian Wu, Wei Sun , The Journal of Vis. Commun. Image R. 24 (2013) 48–62.

(1) Image sharing method for gray-level images Wei-Kuei Chen

Uses linear equations of Hill cipher to divide an image into several sub-images

Then the random grid is applied to the sub-images to construct the shared images

Motivation

Naor and Shamir(1994) proposed a VSSusing a codebook to encode a binary image into sharesno computational effort for decryptionproblem of pixel expansion and lossy recovery

Lukac and Plataniotis (2005) proposed a bit-level based VSSA gray-level image decomposed into 8 bit-planes(binary image)every binary image is encoded into two shared images by the codebookShares decomposed to bit-planes to recover the original imageLossless recovery but still the problem of pixel expansion

Motivation….

Shyu (2007) proposed a random grid method based on Kafri and Keren algorithmrandomly generates a image consisting of 0 and 1create shares using random grid and secret imageremoves the problem of pixel expansion but distortion still be a problem

Chen & Tsao(2009) proposed RG based VSSWhen more shared images are collected, the secret image can be clearly recoveredhow to completely obtain the original image is an unsolved issue.

Proposed Method

Use linear equations of Hill cipher to divide a secret image (n x m) into sub images(size <n x m)

Apply random grid to the sub-images and construct the share imagesNo one can obtain the original image unless the authorized personCollecting all shared images can completely recover the original secret image

without distortion

Hill Cipher

• Polygraphic substitution cipher based on linear algebra• ‘m’ cipher text letters to substitute ‘m’ successive plaintext letters, where m

belongs to positive integer• For m=2 ,the cipher text can be obtained by C = KP mod 26

• Key matrix K must be invertible • P = K-1 C mod 26

Random Grid

Random grids was proposed by Kafri and Keren (1987) Construct a master grid M1 consisting of 0 and 1 randomly, where M1 has the same size

with the secret image Use the master grid M1 and secret image S1 to construct an encoded grid E1

the secret image can be recovered by superimposing the two grids together

The method of the random grid can solve the problem of pixel expansion

Proposed scheme(2 Stages)

Fig. Sharing Stage

1. Divide a gray-level image G with size M × N into blocks consisting of two pixels by raster-scan order

2. Take two pixels of first block. Compute I1 and I2 as

3. Repeat step 2 for the rest of the pixels of the block and construct the two sub-images I1 and

I2 with size MxN/2

4. Construct Master Grid M1 with size MxN/2, whereM1[i,j] ξ [0,255]

Stage-1 The Sharing stage

• Sharing Stage……

5. Transform M1, I1 and I2 from decimal value to binary value

6. Use the master grid M1 and sub-images I1 and I2 to construct two encoded grids E1 and E2 with size M×N/2 by

7. Transform E1 and E2 from binary value to decimal value and transmit to different

participant

Stage-2 The recovering stage

1. Collect the two encoded grids (E1 and E2) and master grid M1.

2. Transform M1, E1 and E2 from decimal value to binary value

3. Use the master grid M1, encoded grids E1 and E2 to construct the sub-images I1 and I2

4. Transform I1 and I2 from binary value to decimal value

5. Take first pixel of sub-images I1 and I2 by raster-scan order into the following equation and obtain two values

6. Successively take the pixels and recover the original secret image without distortion

Results

(a) The secret image Lena with size 256×256, (b) and (c) the sub-images I1 and I2 with size 256×128,(d) the master grid M1 with size 256×128, (e) and (f) the two encoded grids E1 and E2 with size 256x128

Recovering stage

a b c

(a) Recovered image with correct key(b) & (c) Recovered image with incorrect key

Implementation

a b c d e

a,b : Sub images (I1,I2) c,d : Encoded Grids E1, E2e : Master Grid

Recovered Image

Conclusion

The proposed method has the following advantages

(1) Sub images reducing in size, so saving in storage space

(2) Master and encoded grid alone will not reveal any secret information, increased security

(3) Original secret image is recovered (Lossless)

Scope for improvement

1. K-1 for Hill Cipher does not always exist

2. How to send multiple secret images?

3. How to generate n shares?

4. Can be extended for Color images?

5. Is there any way to repair hill cipher to prevent from known-plaintext attack?

Image Encryption Using Advanced Hill Cipher Algorithm , Acharya et. al., International Journal of Recent Trends in Engineering -2009; Proposed a solution for key inverse, involutory matrix generation To generate key A=

1. Select any arbitrary n/2 , n/2 matrix A22

2. A11= - A22

3. Take A12 = k( I - A11), k is a scalar

4. A21 = 1/k( I - A11)

5. Form the matrix completely

Use involutory key matrix for encryption, so that we need not compute K-1 as K=K-1

2221

1211

AA

AA

How to send mult iple secret images?For 2 Secret sharing

a. Secret1 b. Secret2

c. Master Grid

d. EncodedGrid1 e. EncodedGrid2

a. Sub Image1 b. Sub Image2

Recovered Image1 Recovered Image2

To compute n-sharesSharing Stage1. Apply Hill cipher on secret image I (hxw) and get I’(hxw)

2. Generate n-1 random matrices B(hxw) ( B[i,j]=0-255

3. Encoded Gridsa) E1 = B1

b) Ek=Bk exor Bk-1 for k=2 to n-1

c) En=Bn-1 exor I’

Recovering stage1. R=E1 exor E2 exor …..exor En

(2).Random grid-based visual secret sharing with abilities of OR and XOR decryptions

Xiaotian Wu, Wei Sun

RG-based VSS is proposed Secret image can be recovered in two situations:

(1) when computational devices are not available, the secret image can be reconstructed by stacking the shares directly

(2) when some light-weight computational devices are available, the secret image can be decrypted by XOR operation

(3) Better visual quality is achieved by XOR The proposed method employs the (2,n) and (k, n) RG-based VSS scheme

Diagram of share construction

Decryption

reconstruction by stacking k or more shares (or)applying XOR operation on k or more shares (xor)

Conclusion

no code book required and no pixel expansion improved contrast

larger contrast is obtained by the proposed method when XOR decryption is applied

Scope for improvementContrast can still be improved

In reconstructed image, black and white pixels may group together as they are generated randomly