# Information Hiding In Gray Scale Computer Science Essay

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Security has become an inseparable issue since information technology is ruling the world at present. Cryptography is the study of mathematical techniques and related aspects of Information Security such as data confidentiality, data Integrity, and of data authentication. Visual cryptography (VC) is a secret sharing scheme where a secret image is encrypted into the shares which independently disclose no information about the original secret image. The beauty of the visual secret sharing scheme is its decryption process i.e. to decrypt the secret image using human visual system without any computation. Naor and Shamir proposed the basic model of visual cryptography for natural images. This paper presents a new algorithm for halftone image and by stacking the shares; the resultant image achieved in same size with original secret image. A new approach is proposed in visual information hiding using pseudo randomization and pixel reversal approach in all methods.

Keywords-Information Security, Information hiding, Halftone image, Visual cryptography, Secret share.

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INTRODUCTION

With the coming era of electronic commerce applications, there is an urgent need to solve the problem of ensuring information security in today's increasing open network environment. The encrypting methods of traditional cryptography are usually used to protect information security. In traditional cryptography techniques, the data become rearranged/ permutated after being encrypted and can then be decrypted by a correct key. So, there is computational overhead in decryption process. The new and emerging concept of visual cryptography (VC) was introduced by Naor and Shamir in 1994 [1], which requires no computation except the human visual system to process decryption. They proposed a basic (2, 2) visual cryptography scheme which encodes a given secret image into 2 shares, and reveals the secret image by stacking the shares. The main advantage of this approach is that it can recover a secret image without any computation. It exploits the human visual system to read the secret message from some overlapping shares, thus overcoming the disadvantage of complex computation required in the traditional cryptography.

RELATED WORK

The model for visual cryptography is given by Naor & Shamir as follows [2]:

A printed page of cipher text and a printed transparency, which serves as a secret key. The original clear text is revealed by placing the transparency with the key over the page with the cipher, even though each one of them is indistinguishable from random noise. The model for visual secret sharing is as follows [3]. There is a secret picture to be shared among n participants. The picture is divided into n transparencies (shares) such that if any m transparencies are placed together, the picture becomes visible. If fewer than m transparencies are placed together, nothing can be seen. Such a scheme is constructed by viewing the secret picture as a set of black and white pixels and handling each pixel separately.

Visual cryptography is a popular solution for image encryption. Using secret sharing concepts, the encryption procedure encrypts a secret image into the shares which are noise-like secure images which can be transmitted or distributed over an entrusted communication channel. Using the properties of the HVS to force the recognition of a secret message from overlapping shares, the secret image is decrypted without additional computations and any knowledge of cryptography.

Basic (2, 2) VC scheme

In the (2, 2) VC scheme each secret image is divided into two shares such that no information can be reconstructed from any single share. Each share is printed in transparencies. In Figure 1. the decryption process is performed by stacking the two shares and the secret image can be visualized by naked eye without any complex cryptographic computations.

Figure 1. Construction of (2,2) VC Scheme

There is a secret picture to be shared among n participants. The picture is divided into n transparencies (shares) such that if any m transparencies are placed together, the picture becomes visible. If fewer than m transparencies are placed together, nothing can be seen. Such a scheme is constructed by viewing the secret picture as a set of black and white pixels and handling each pixel separately.

Generalization of (k, n) VC scheme

Naor-Shamir [2] generalized their results by using the following theorem/lemma.

Lemma: There is a (k, k) scheme with m=2 k-1, Î±=2 1-k and

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r= (2 k-1!).

We can construct a (5, 5) sharing, with 16 sub pixels per secret pixel and 1 pixel contrast, using the permutations of 16 sharing matrices. In (k, n) secret sharing scheme: "an N-bits secret shared among n participants, using m sub pixels per secret bit (n strings of mN), so that any k can decrypt the secret".

Contrast: There are d<m and 0<Î±<1:

If pixel=1 at least d of the corresponding m sub pixels are dark ("1").

If pixel=0 no more than (d - Î±m) of the m sub pixels are dark

Security: Any subset of less than k shares does not provide

any information about the secret.

Proposed Work:

In (2, 2) visual cryptography which was implemented Naor & Shamir in [6], where the decoded image is twice that of original secret image because the pixel p expanded into two sub pixels where the effect is called pixel expansion. That affects the contrast of the resulting image. The problem for the pixel expansion and contrast was majorly discussed in literature. The previous work on pixel expansion and contrast optimization shows that researcher did efforts to reduce the expansion and optimize the contrast of the secret picture. Further they portrait the process of creating the shares using mathematical representations and mainly they focus the security and contrast condition [1].

Pseudo - Randomized Visual Cryptography Scheme

In (2, 2) visual cryptography scheme we have one secret halftone (gray scale) image (SI) as input to the algorithm. Where SI is consider as a matrix Sij where i and j shows pixel positions and i, j= 1, 2, 3â€¦ n. All steps of algorithm in this scheme are shown in Figure 2.

Input: Secret Gray scale image (SI)

Output: Valid Shares Share1, Share2

Method:

Step1:- Pixel Sij with position i and j is the input called original pixel.

Step2:- Apply pixel reversal i.e SijÂ´ = 255 - Sij .

Step3:- Use pseudo - random number generator (0.1 to 0.9)

to reduce Si jÂ´ randomly.

Step4:- Take the difference of SijÂ´ with original pixel Sij.

Step5:- Use pseudo-random number generator to reduce

reversed value of SijÂ´ randomly.

Step6:- Apply pixel reversal i.e SijÂ´Â´ = 255 - SijÂ´.

Step7:- Store in matrix as image called share 1.

Step8:- Take the difference of two random number generators with original pixel Si j.

Step9:- Apply pixel reversal i.e SijÂ´Â´Â´ = 255 - SijÂ´ .

Step10:- Store SijÂ´Â´Â´ in matrix as image called share 2.

Step11:- Repeat point 1 to 10 for all pixels from original image (i.e. matrix of original image)

Figure 2. Psuedo - Randomized Visual Cryptography

In our scheme the decoded image is same in size of original secret message as there is no pixel expansion effect found. However the nature of the algorithm is as general as with many other schemes of the decrypted image which is darker and contains a number of visual impairments. Our decoded secret image is darker than the original. The decoded secret image has increase the spatial resolution however, mostly of visual cryptography scheme has shown the same effect in their decoded image [6].

After testing many different images from light to dark in resolution it was observed that the proposed algorithm could not take dark true image significantly with high contrast and then generate the meaningless share. Majorly it was found that the shares reveal the information. However on light contrast we have seen that algorithm generates the perfect meaningless shares as shown in Figure 3.

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(b)

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Figure 3. Pseudo-Randomized visual Cryptography results (a) Secret Image (b) Share1 (c) Share 2 (d) Stacking of Share 1 and Share 2

Improvement

Based on our observation that proposed algorithm could not give perfect meaningless shares in case of the dark or high contrast secret image, we have added preprocessing elements to change the dark or high level of gray image into lighter one (called preprocessed image or halftone image). This is to be done before giving input secret image to proposed algorithm.

We change the pixel values to white (255) on the basis of the position of the pixel. We use odd and even combination of the pixel values in the matrix as follows:

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Examples of our workMethod 1: If i=j=odd and i=j=even

pixel (i, j) = 255

Method 2: If i=odd & j=even OR i=even & j=odd

pixel (i, j) = 255

This preprocessing convert the secret image into lighter one in contrast and then give to the proposed algorithm for processing. The result of these added elements with both type of preprocessing is shown in Figure 4.

(a)

(b)

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Figure 4. Improved Pseudo-Randomized visual Cryptography results

(a) Secret Image (b) Share1 (c) Share 2 (d) Stacking of Share 1 and Share 2

Simulation and Results

We have implemented our algorithm in java technology. To see the performance of our algorithm on different secret images. The simulation results are shown in Figure 5. It is shown in Figure 4 that after giving the true gray scale picture as secret image has better results in comparison of algorithm without preprocessing. Because of secret image (true gray scale image) which reveals the secret completely in shares in case of without preprocessing. However using preprocessing (half toning) the shares shows some information about the secret. This can be improving to further by using extended preprocessing on the same processed image. The purpose of preprocessing is to preparing the image on a certain level that the algorithm must not reveal the secret words from the image. Figure 4 shows the perfect meaningless shares and after stacking, we get the secret. The input which is observed as the preprocessed secret image. The result from stacking of share is so perfect in case of the preprocessing which is shown in the Figure 4.

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Figure 5. Visual Cryptography results (a) Smile (b) Monalisa

CONCLUSION AND FUTURE WORK

We have shown that the (2, 2) pseudo - randomized visual cryptography in practice where the shares are generated based on pixel reversal, random reduction in original pixel and subtractions of the original pixel with previous shares pixel. The original secret image is divided in such a way that after OR operation of qualified shares we reveal the secret image. Our scheme has shown less pixel expansion which is desirable and good for the final retrieval of the secret image. Some contrast is change and impairments are still visible in the results of these schemes. However, by dividing the pixels into two or more sub pixel retrieve the secret picture with more impairments and bad resolutions.

In our scheme the results are better than and the size of the retrieve image is the same as the original. However, size of pixel increase provides more easiness for alignment of the shares. This is still a researchable area to reduce this effect and also our proposed schemes have shown high level of security because of randomness. The future work is to improve the contrast and reduce the pixel expansion in the resultant secret image. Further extend this work to use this technique with color images and also consider 3D images for creating the shares that have partial secret which reveals the secret stacking to each other.

ACKNOWLEDGEMENTS

We thank immensely our management for extending their support in providing us infrastructure allowing us to utilize them in the successful completion of our research paper.