Consumer Behavior Models in Marketing

ISSN:2229-6093 Lakshmi Priya Tadiboyna et al ,Int.J.Computer Technology & Applications,Vol 3 (1), 416-419

Visual cryptography for color images by dithering techniques Lakshmi Priya Tadiboyna1, M. Deena Babu2 1

Pursuing M.Tech(CS), Nalanda Institute of Engineering & Technology,Siddharth Nagar, Sattenapalli, Guntur., Affiliated to JNTUK, Kakinada, A.P., India. 2

Asst. Professor, Department of Computer Science Engineering, Nalanda Institute of Engineering & Technology,Siddharth Nagar, Sattenapalli, Guntur., Affiliated to JNTUK, Kakinada, A.P., India. [email protected]

Abstract - Color visual cryptography (VC) encrypts a color secret message into n color halftone image shares. Previous methods in the literature show good results for black and white or gray scale VC schemes, however, they are not sufficient to be applied directly to color shares due to different color structures. Some methods for color visual cryptography are not satisfactory in terms of producing either meaningless shares or meaningful shares with low visual quality, leading to suspicion of encryption. The decoding process of a visual cryptography scheme, which differs from traditional secret sharing, does not need complicated cryptographic mechanisms and computations. Instead, it can be decoded directly by the human visual system. Previous efforts in this topic are almost restricted in processing binary images, which are insufficient for many applications. In this paper, a new visual cryptography scheme suitable for colorlevel images is proposed. Instead of using gray sub pixels directly to construct shares, a dithering technique is used first to convert a color-level image into an approximate binary image. Then existing visual cryptography schemes for binary images are applied to accomplish the work of creating shares. The overall effect of the proposed method is the achievement of visual encryption and decryption functions for colorlevelimages. Some comparisons with a previously proposed method are also made. Keywords - Visual cryptography; secret sharing; Watermarking; Dithering.

1. Introduction It is now common to transfer multimedia data via the Internet. With the coming era of electronic commerce, there is an urgent need to solve the problem of ensuring information safety in today’s increasingly open

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network environment. The encrypting technologies of traditional cryptography are usually used to protect information security. With such technologies, the data become disordered after being encrypted and can then be recovered by a correct key. Without the correct key, the encrypted source content can hardly be detected even though unauthorized persons steal the data. Naor and Shamir [1] proposed a new cryptography area, visual cryptography, in 1994. The most notable feature 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. The threshold scheme [1–3] makes the application of visual cryptography more Dexible. With the t out of n threshold scheme (t6n); the manager can Erst produces n copies of transparency drawn from the secret image, one for each of his members. If any t of them stacks their transparencies together, the content of the secret image will show up. If the number of transparencies is less than t, the content of the secret image will remain hidden. How to keep a secret is always an important issue in many applications. Two major approaches to this aim are information hiding and secret sharing. A common method for information hiding is to use the watermarking technique [4][5]. And a well known technique for secret sharing is the cryptography method proposed by Shamir (1979). For sharing images, Naor and Shamir proposed further the idea of visual cryptography [6][7] in 1994. Following their work, several extensions have been proposed (Droste, 1996; Hofmeister et al., 1997; De Bonis and De Santis, 2000). A (k,n) - threshold visual cryptography scheme is a method to encode a secret image into n shadow images called shares, where any k or more of them can be combined visually to recover the secret image, but any k - 1or fewer of them gain no information about it. The visual recovery process consists of Xeroxing the shares onto transparencies, and then stacking them to obtain a

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ISSN:2229-6093 Lakshmi Priya Tadiboyna et al ,Int.J.Computer Technology & Applications,Vol 3 (1), 416-419

‘‘decoded’’ image visually approximating the original secret image. This basic model has been applied to many applications, which include information hiding, general access structures, visual authentication and identification and so on.

2. Visual cryptography for color images 2.1 Basic principles of color The additive and subtractive models (Fig. 6) are commonly used to describe the constitutions of colors [8]. In the additive system, the primaries are red, green and blue (RGB), with desired colors being obtained by mixing different Fig. 6.

(a)

Additive model, and (b) Subtractive model

RGB components. By controlling the intensity of red (green or blue) component, we can modulate the amount of red (green or blue) in the compound light. The more the mixed colored-lights, the more is the brightness of the light. When mixing all red, green and blue components with equal intensity, white color will result. The computer monitor is a good example of the additive model. In the subtractive model, color is represented by applying the combinations of coloredlights reDected from the surface of an object (because most objects do not radiate by themselves). Take an apple under the natural light for example. The surface of the apple absorbs green and blue part of the natural light and reDects the red light to human eyes, so it becomes a red apple. By mixing cyan (C) with magenta (M) and yellow (Y) pigments, we can produce a wide range of colors. The more the pigment we add, the lower is the intensity of the light, and thus the darker is the light. This is why it is called the subtractive model. C, M and Y are the three primitive colors of pigment, which cannot be composed from other colors. The color printer is a typical application of the subtractive model. The above discussion illustrates that Rijmen and Preneel’s [9] approach, which uses red, green, blue, and white (transparent) colors to Ell the blocks, is not appropriate. In the additive model, any color mixed with white color is still white color. It thus seems more reasonable to use red, green, blue, and

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black colors to Ell the blocks. On the other hand, in the subtractive model, the combination of any two of R, G, and B colors results in black color. R, G or B combined with white color will not change and can only result in the same color. Consequently, it is more appropriate to Ell the blocks with cyan, magenta, yellow and white colors. In computer systems, Application Interfaces (APIs) provided by most image processing software as well as the Windows operating system are based on the RGB model. This is mainly because they use monitors as the primary output media. Monitors themselves generate color images by sending out RGB light into human’s retina. In true color systems, R, G, B are each represented by 8 bits, and therefore each single color of R, G, B can represent 0–255 variations of scale, resulting in 16.77 million possible colors. When using (R, G, B) to describe a color pixel, (0; 0; 0) represents full black and (255; 255; 255) represents full white. In visual cryptography, we use sharing images as the decryption tool; that is, the final outputs are transparencies. Because the subtractive model is more suitable for printing colors on transparencies, we will use the CMY model to represent colors in what follows. Because (R, G, B) and (C, M, Y) are complementary colors, in the true color model, (R, G, B) and (C, M, Y) possess the following relationships: C = 255−R, M = 255−G, Y = 255−B: Thus, in the (C, M, Y) representation, (0; 0; 0) represents full white and (255; 255; 255) represents full black. 2.1.1. Algorithm of color visual cryptography— method 1 1. Transform the color image into three halftone images: C, M, and Y. 2. for each pixel Pij with color components (Cij, Mij or Yij) of the composed image P, do the following: (a) Select a black mask with a size of 2×2, and assign a black pixel randomly to two of these four positions and leave the rest positions blank (transparent or white). This step will make the black mask a half black-andwhite block. (b) After selecting a mask, determine the positions of the cyan pixels in the block of the corresponding sharing images. This is done according to the positions of the black pixels in the mask and the value of Cij If Cij = 1 (the cyan component will be revealed), fill the positions corresponding to the positions of the white pixels in the mask with a cyan pixel and leave the rest positions blank.

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ISSN:2229-6093 Lakshmi Priya Tadiboyna et al ,Int.J.Computer Technology & Applications,Vol 3 (1), 416-419

If Cij = 0 (the cyan component will be hidden), fill the colors in the opposite way. That is, fill the positions corresponding to the positions of the black pixels in the mask with a cyan pixel and leave the rest positions blank. Finally, add the block to the corresponding position of Share 1. (c) In accord with (b), determine the positions of magenta pixels of the block in Share 2 with the value of Mij and those in Share 3 with the value of Yij . 3. Repeat Step 2 until every pixel of the composed image is decomposed, hence obtaining four transparencies (cyan, magenta, yellow and black) of visual cryptography to share the secret image. 4. After stacking the four sharing images, the secret image can be decrypted by human eyes.

3. Proposed scheme With the (k,n)- threshold visual cryptography scheme for binary images proposed in, the theoretical increase of size is with a factor nk-1, which is comparatively smaller than the scheme proposed by Verheul and van Tilborg (1997) in ordinary situations with c>=n. Therefore, if we can convert first a color-levelimage into an approximate binary image with the same size and then apply the scheme proposed in, we can get a smaller increase in the image size than the Verheul and van Tilborg scheme. Ordered dithering is a technique satisfying this purpose. That is, it can be employed to conduct fast and parallel transformation of a color-level image into an equal-sized binary one. For this, we adopt in this study the space-filling curve ordered dithering (SFCOD) algorithm (Zhang, 1998) that has the merit of keeping image quality by determining dither thresholds along a space-filling curve. Let I be an m x m gray image, H the corresponding half toned binary image, M(m,m) the map of a traversal-order number of the pixels of the image I along a spacefilling curve over I (a simple example using Hilbert curve to divide the pixels of a 4 _ 4 image into 16 classes is shown in Fig. 6, where the numbers in the grid are the traversal-order numbers), and B a spacefilling curve dither array (with the array contents being a permutation of 0; 1; 2; . . . ; l _ 1where l is the array length and is less than m). Then the SFCOD algorithm can be described as a procedure in the following.

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Fig. 6. Traversal order determined by a Hilbert curve. PROCEDURE SFCOD(MB, l, I, H) BEGIN FOR i = 0 TO m - 1DO FOR j = 0 TO m - 1DO IF I(I,j)/256>=(B(M(i,j) mod l)+0.5/l THEN H(i,j)=1 ELSE H(i,j)=0 END This algorithm can be regarded to divide the input image into non-overlapping blocks whose size is  l x  l and assign each pixel a value equal to the corresponding value of the traversal-order number along the space-filling curve in the block. Then the assigned value, say j, of each pixel is taken to be the index of an element of the dither array B, yielding a mapped value B(j). Finally, the mapped values are used as the thresholding values to binarize the input colorlevel image. In short, we transform an input color-level image into an approximate binary image and apply to it the visual cryptography scheme proposed in (Naor and Shamir, 1995). The overall effect is that we get a result of encrypting a color-level image, thus achieving (k,n) threshold visual cryptography.

4. Conclusion Extension of visual cryptography for binary images to one for gray-level ones is useful for wider applications. In this study, we have developed a scheme that achieves this goal. An input gray-level image is first converted into an approximate binary image with the dithering technique, and a visual cryptography method for binary images is then applied to the resulting dither image. This scheme possesses the advantages of inheriting any developed cryptographic technique for binary images and having less increase of image size in

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ISSN:2229-6093 Lakshmi Priya Tadiboyna et al ,Int.J.Computer Technology & Applications,Vol 3 (1), 416-419

ordinary situations. The decoded images can reveal most details of original images. Some experiments have been conducted to evaluate the effect of our proposed method. The experimental results prove that our approach is feasible. A possible application has also been proposed in this study. For further research, efficient visual cryptography for color images may be chosen as the next topic.

References [1] M. Naor, A. Shamir, in: A. De Santis (Ed.), Visual Cryptography, Advances in Cryptology: Eurpocrypt’94, Lecture Notes in Computer Science, Vol. 950, Springer, Berlin, 1995, pp. 1–12. [2] M. Naor, A. Shamir, in: M. Lomas (Ed.), Visual Cryptography, II: Improving the Contrast via the Cover Base, Presented at Security in Communication Networks, AmalE, Italy, September 16–17, 1996. Lecture Notes in Computer Science, Vol. 1189, Springer, Berlin, 1997, pp. 197–202. Available also at Theory of Cryptography Library, Report 96-07, http://theory.lcs.mit.edu/∼ tcryptol/1996.html.

AUTHORS PROFILE

Lakshmi Priya. T, Pursuing M.Tech(CS) from Nalanda Institute of Engineering & Technology, Siddharth Nagar, Sattenapalli, Guntur Affiliated to JNTUK, Kakinada, A.P., India. My research Interests are computer networks and image Processing.

M. Deena Babu, working as Asst. Professor, Department of Computer Science Engineering at Nalanda Institute of Engineering & Technology,Siddharth Nagar, Sattenapalli, Guntur Affiliated to JNTUK, Kakinada, A.P., India. My research Interests are Data Mining and Computer Networks. He is a Life member of AMITE.

[3] D.R. Stinson, An introduction to visual cryptography, presented at Public Key Solutions ’97, Toronto, Canada, April 28–30, 1997. http://bibd.unl.edu/∼ stinson/vcs-pus.ps. [4] Cox, I., Miller, M., Bloom, J., 2001. Digital Watermarking. Morgan Kaufmann Publishers, San Francisco. [5] Katzenbeisser, S., Petitcolas, F.A.P., 2000. Information Hiding Techniques for Steganography and Digital Watermarking. Artech House, MA. [6] Shamir, A., 1979. How to share a secret. Communications of the Association for Computing Machinery 22 (11), 612–613. [7] Naor, M., Pinkas, B., 1997. Visual authentication and identification. In: Advances in Cryptology–– CRYPTO’97 Lecture Notes in Computer Science, vol. 1294, pp. 322–336. [8] A. Shamir, Visual cryptanalysis, Proceedings of the Eurocrypt’ 98, Espoo, 1998. [9] V. Rijmen, B. Preneel, ELcient colour visual encryption for shared colors of Benetton, Eurocrypto’96, Rump Session, Berlin, 1996. Available at http://www.iacr.org/conferences/ec96/rump/preneel.ps.

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