VISUAL CRYPTOGRAPHY for COLOR IMAGES USING ERROR DIFFUSION AND PIXEL SYNCHRONIZATION

VISUAL CRYPTOGRAPHY for COLOR IMAGES USING ERROR DIFFUSION AND PIXEL SYNCHRONIZATION Pankaja Patil Department of Computer Science and Engineering Gogte Institute of Technology, Belgaum, Karnataka Bharati Pannyagol Department of Computer Science and Engineering Gogte Institute of Technology, Belgaum, Karnataka ABSTRACT-Visual Cryptography (VC) is not sufficient in terms of providing color meaningful shares with high visual quality. This paper produces visual cryptography encryption method for color images which use the error diffusion and visual information pixel (VIP) synchronization techniques to generate meaningful color shares with high visual quality. Low frequency differences between the input and output images are minimized in Error diffusion method and consequently it produces pleasing halftone images to human vision. Synchronization of the VIPs across the color channels improves visual contrast of shares. Comparison of Jarvis halftone with Floyd halftone shows good result of Jarvis method. Keywords Color meaningful shares, halftoning, error diffusion, visual cryptography (VC). I INTRODUCTION Visual Cryptography (VC) is a data security technique which allows visual information (pictures, text, etc.) to be encrypted in such a way that decryption operation does not require a computer. Visual Cryptography (VC) for black and white was first formally introduced by Naor and Shamir [1]. In which one secret binary image is cryptographically encoded into n shares of random binary patterns. The n shares are distributed amongst group of n participants, one for each participant. No participants can retrieve any information from his own transparency, but any k or more participants can visually reveal the secret image by polling there transparencies together. The secret cannot be decoded by any k-1 or less participants, even if higher computational power is available to them. In VC the decryption process requires only human visual system. This property makes visual cryptography especially useful for the low computation load requirement. VC scheme has been applied to many applications. Apart from the obvious applications to information hiding, there are many applications of VC [2, 3], which include general access control [4]. VC can also be used in a number of other applications such as threshold cryptography, electronic cash, private multiparty computations and digital electronics etc. Vol. 1 Issue 2 July 2012 1 ISSN: 2278-621X

Fig.1: Construction of (2, 2) VC scheme Generally, the black-and-white (2, 2) visual cryptography decomposes every pixel in a secret image into a 2 2 block in the two transparencies according to the rules in figure 1, two of them black and white. If pixel is white (black) one of the above six columns of figure 1 is chosen to generate Share1 and Share2. Then, the characteristics of two stacked pixels are: black and black is black, white and black is black, and white and white is white. Therefore, when stacking two transparencies the blocks corresponding to black pixels in the secret image are full black and those corresponding to white pixels are half-black-and-half-white. As concern to information security, one of the six columns is selected with equal probability. (a) Binary secret image. (b) Encrypted share 1. (c) Encrypted share 2. (d) Decrypted secret message. Fig.2: Example of 2-out-of-2 scheme. The secret image is encoded into two shares showing random patterns. The decoded image shows the secret image with 50% contrast loss. Figure 2 shows an example of a simple (2, 2)-VC scheme with a set of subpixels shown in figure 1. Figure 2(a) shows a secret binary message, Figure 2(b) and (c) depict encrypted shares for two participants. Stacking these two shares leads to the output secret message as shown in figure 2(d). Little research has been carried out on VC, a more general method for VC scheme is based upon general access structure [4]. The access structure is a specification of qualified and forbidden subsets of shares. The participants in a qualified subset can recover the secret image while the participants in a forbidden subset cannot. But this technique gives good result on binary images. In extended visual cryptography (EVC)[5] method, a shares contain not only the secret information but are also some meaningful binary images are developed. In this method Hypergraph colorings are used for constructing meaningful binary shares. Since, hypergraph colorings are constructed by random pixels distribution, the resultant binary shares contain strong white noise leading to insufficient results. A VCS for color images based upon an additive color Vol. 1 Issue 2 July 2012 2 ISSN: 2278-621X

mixing [6] method is introduced. In this scheme, each pixel is expanded by a factor of three, which will increase the size of encrypted shares. This paper introduces a color VC encryption method to generates meaningful shares. It based on two fundamental concepts used in the generation of shares they are error diffusion[7] and pixel synchronization[8]. Error diffusion is a procedure that produces pleasing halftone images to human vision. Synchronization of the pixels of secret image and covering images across the color channels improves visual quality of shares. Visual Information Pixel (VIP) synchronization prevents colors and contrast of original shares from degradation even with matrix permutation. This paper is organized as follows. Section II describes the proposed method which uses Error diffusion and VIP Synchronization. Section III shows experimental results of the new method and comparisons of Error diffusion methods. Finally, we conclude this paper in Section IV. II. IMPLEMENTATION System is designed into 2 phases. The first phase generates shares by using the error diffusion [11] algorithm and Pixel Synchronization. The Figure 3 explains the working of the system. N covering Secret Img Share Generation Halftoning VIP synchronization Secret image Stacking Fig.3 Block Diagram of System Design A. Halftoning Error diffusion [7],[9] produces halftone images of much higher quality than other halftone. It quantifies each pixel using a neighborhood operation. A schematic diagram of error diffusion method is given in figure 4. The error diffusion scans the image one row at a time and one pixel at a time. The current pixel is compared to a threshold (127) value. If it is above the value a white pixel is generated in the resulting image. If the pixel is below the half way value, a black pixel is generated. The generated pixel is either full bright, or full black. Fig.4: Error Diffusion Block Diagram Vol. 1 Issue 2 July 2012 3 ISSN: 2278-621X

Fig.5: Two error diffusion weight matrixes (a) Jarvis, Judice, and Ninke (b) Floyd and Steinberg Error is calculated which is the difference between original image and halftone image. The error is then added to the next pixel in the image and the process repeats. To which neighbor and how this error is pushed is decided by an error diffusion matrix. Algorithm: Jarvis error diffusion halftoning 1: procedure JARVIS ERROR DIFFUSION (g) 2: for i=1,..n do 3: for j=1,.m do (This algorithm goes through all pixels in the original image, normally starting from the pixel up to the left and then goes through all pixels from left to right and up down). 4: if f[i j ] >127 then else b[i j ]=1 b[i j ]=0 5: Since the pixel value in f, which is a real number between 0 and 255, has been replaced by 0 or 1 in b and error has been calculated. e= f - b(i,j) The error is the difference between the pixel value in f and b at that position. 6: The error occurred at the position (i, j) is weighted by 7/48 and added to the pixel value at (i+1, j). The same error is weighted by 5/48 and added to the pixel at (i+1, j+1) and so on. After the error has been diffused the pixel value of the next position is compared to the threshold and the same process continues until all pixels have been met. 7: end for 8: end for 9: end procedure Floyd and Steinberg error diffusion method follow the same algorithm except that while distributing error it uses Floyd and Steinberg matrix as shown in figure 5(b). B.VIP Synchronization Vol. 1 Issue 2 July 2012 4 ISSN: 2278-621X

Visual Information Pixel (VIP) is pixel on the encrypted shares that have color values of the original images, which make shares meaningful. In the proposed method each subpixel n carries visual information as well as message information,while other methods in [1] and [5] extra pixels are needed in addition to the pixel expansion n to produce meaningful shares. Algorithm: VIP synchronization Input: C1, C2 covering Images of size n x m, Sc secret image of size K1xK2. Output: 2 meaningful shares 1: procedure: VIP Synchronization and Matrix Distribution 2: for p=1,..k1 and for q=1, K2 do 3: for the color channel R of the secret image Sc R (p,q) do 4: if the bit Sc R (p,q)=1 then for i=1,..k1 do for j=1,.k2 do if C1(i,j)=C2(i,j) then Randomly select any one Ci and complement Ci(i,j) end if 5: end for end for 6: else if Sc R (p,q)=0 then for i=1,..k1 do for j=1,.k2 do if C1(i,j) end if end for end for end if 7: Repeat 3 to 6 for the channel G and Y. 8: end for 9: end for 10: end procedure then Randomly select any one Ci and make them equal i.e.c1(i,j)=c2(i,j) or C2(i,j)= C1(i,j) This algorithm takes the input as halftone images which are created by error diffusion method. It decomposes the color images into 3 basic colors (Red, Green, and Blue) and then it executes VIP Synchronization algorithm on each color bit. The output of this block are meaningful shares. Now each bit on share contains information regarding covering image as well as secret image without giving any clue about encryption. C. Stacking Decoding does not need any algorithm. The meaningful shares are XORed to reconstruct the secret image by simply human vision system. III RESULTS and ANALYSIS The algorithms discussed above are implemented using MATLAB 2008 and higher version on P8600 @ 2.40GHz, 2.92 GB RAM. To test the performance of these algorithms 4 color images belonging to different classes of size 128x128 are used. A. Results In this section, we provide some experimental results to illustrate the effectiveness of the proposed method. Example are composed with (2, 2) Color VC, (2,3) Color VC and (3,4) color VC. The secret message of size 128x128 pixels and covering images of size 256x256 in natural colors are provided for the share Vol. 1 Issue 2 July 2012 5 ISSN: 2278-621X

generation. Figure 6 to 10 represent the results of each step of the system. Size of images is resized to fit in the paper. (a) (b) (c) (d) (e) Fig.6 (a) (d) Covering Input Images of size 256x256 (e) secret input image of size 128x128 (a) (b) (c) (d) (e) Fig.7 Halftone shares using error diffusion method All the images are halftone before encryption process. Halftone images create a space so that we can embed secret message into covering image. A. (2, 2) Visual Cryptography (a)share 1 (b) Share 2 (c) Reconstructed secret image Fig 8 (a)-(b) result of encrypting images (a),(b) and (e) of figure 7. fig.8 (c) Result of stacking (a) and (b) of figure 8. B. (2, 3) Visual Cryptography Vol. 1 Issue 2 July 2012 6 ISSN: 2278-621X

image (a)share1 (b) Share 2 (c) Share 3 (d) Reconstructed secret Fig 9 (a)-(c) Result of encrypting images (a),(b),(c)and (e) of figure 7.fig 9 (d) Result of stacking (a),(b) and (c) of figure 9 C. (2, 4) Visual Cryptography (a) Share1 (b) Share2 (c) Share3 (d) Share4 (e) reconstructed image Fig.10 (a)-(d) Result of encrypting images (a),(b),(c),(d) and (e) of figure 7.fig.10 (e) Result of stacking (a),(b),(c)and (d) of figure 10 B.Analysis Table-I,II and III shows the result of 4 sample images of different categories for Jarvis[13] and Floyd and Steinberg[8] error diffusion algorithm for (2,2),(2,3) and (2,4) VC schemes,respectively. TABLE I: PSNR AND CORRELATION PARAMETERS USED FOR DIFFERENT IMAGES AND HALF TONE METHODS FOR 2 SHARES. Image Parameter Floyd-Steinberg method Jarvis method Letter img PSNR 84.9575 89.3672 Correlation 0.974538 0.99192 Map Img PSNR 71.7093 79.246 Correlation 0.81175 0.986 Chi Img PSNR 77.8475 82.1807 Correlation 0.960843 0.990318 Logo Img PSNR 75.4791 78.7595 Correlation 0.950232 0.981658 Fig.11 (a) Different images versus PSNR with different halftone methods Fig.11 (b) Different images versus Correlation Coefficient with different halftone methods. Vol. 1 Issue 2 July 2012 7 ISSN: 2278-621X

Figure 11 (a) shows the PSNR values for the sample images. Stacked image produced by Jarvis [13] is very good retains pictorial details as compared to Floyd and Steinberg [8] half tone method. Since, Jarvis halftone method give clearer image compared to Floyd and Steinberg halftone method. Figure 11 (b) shows the correlation values for the sample images. Reconstructed image produced by Jarvis [13] is very much similar to original image as compared to Floyd and Steinberg [8] halftone method. This means there is very small amount of data loss in Jarvis halftone method. TABLE II: PSNR AND CORRELATION PARAMETERS USED FOR DIFFERENT IMAGES AND HALF TONE METHODS FOR 3 SHARES. Image Parameter Floyd-Steinberg method Jarvis method Letter img PSNR 78.8211 76.0964 Correlation 0.891287 0.825342 Map Img PSNR 71.2261 74.2355 Correlation 0.872098 0.971221 Chi Img PSNR 73.8673 75.1725 Correlation 0.935264 0.95069 Logo Img PSNR 74.5543 74.4709 Correlation 0.929823 0.91969 Fig.12 (a): Different images versus PSNR with different halftone methods Fig.12 (b): Different images versus Correlation coefficient with different halftone methods. Figure 12 a) and b) shows the PSNR and correlation values for the sample images, respectively. Jarvis halftone method produce clearer image compared to Floyd and Steinberg halftone method. If less information is present secret image then in (2,3) VC Floyd and Steinberg provide clear picture compared to Jarvis. TABLE III: PSNR AND CORRELATION PARAMETERS USED FOR DIFFERENTIMAGES AND HALF TONE METHODS FOR 4 SHARES. Image Parameter Floyd-Steinberg Jarvis method method Letter PSNR 66.8975 74.0314 img Correlation 0.142009 0.742706 Map Img PSNR 65.4256 65.9732 Correlation 0.0236446 0.480244 Chi Img PSNR 66.1038 67.4695 Correlation 0.184984 0.701278 Logo Img PSNR 66.9184 70.5797 Correlation 0.101503 0.65802 Vol. 1 Issue 2 July 2012 8 ISSN: 2278-621X

Fig.13 (a) Different images versus PSNR with different halftone methods images Fig 13 (b) shows the correlation values for the sample Figure 13(a) and (b) shows the PSNR and correlation values for the sample images, respectively for (2,4) VC. Jarvis halftone method produce clearer image compared to Floyd and Steinberg halftone method. TABLE IV PSNR PAMETERS USED FOR DIFFERENT IMAGES AND NO.OF SHARES GENERATED Images 2 Shares 3 Shares 4 Shares Letter img 89.3672 76.0964 74.0314 Map Img 79.2460 74.2355 65.9732 Chi Img 82.1807 75.1725 67.1217 Logo Img 78.7595 74.4709 70.5797 Fig.14 Different images versus PSNR with different No. of share generation. Figure 14 shows PSNR value for different VC scheme. Stacked image of (2,2) VC scheme is very good retains pictorial details as compared to another two VC schemes. As we increase the number of covering images performance of Synchronization process is less. As the security point of view (2,2) has more security ratio compared to (2,3) and (2,4) VC. IV. CONCLUSION AND FUTURE WORK The proposed system presents an encryption method for color Visual Cryptography scheme with Error diffusion and VIP Synchronization for visual quality improvement. Jarvis and Floyd and Steinberg halftone methods are compared. Jarvis kernel gives better visual quality. For encryption VIP synchronization is used. It hold the original pixels in the actual VIP values to produce meaningful shares. The secret information is revealed by overlapping of meaningful shares. V. REFERENCES [1] M. Naor and A. Shamir, Visual cryptography, in Proc. EUROCRYPT, 1994, pp. 1 12. [2] M. S. Fu and O. C. Au, Joint visual cryptography and watermarking, in Proc. IEEE Int. Conf. Multimedia Expo, 2004, pp. 975 978. [3] M. Naor and B. Pinkas, Visual authentication and identification, Adv.Cryptol., vol. 1294, pp. 322 336, 1997. [4] G. Ateniese, C. Blundo, A. D. Santis, and D. R. Stinson, Visual cryptography for general access structures, Inf. Comput., vol. 129, no. 2, pp. 86 106, 1996. Vol. 1 Issue 2 July 2012 9 ISSN: 2278-621X

[5] G. Ateniese, C. Blundo, A. Santis, and D. R. Stinson, Extended capabilities for visual cryptography, ACM Theor. Comput. Sci., vol. 250,pp. 143 161, 2001. [6] C. N. Yang and T. S. Chen, Visual cryptography scheme based on additive color mixing, Pattern Recognit.,vol. 41, pp. 3114 3129, 2008. [7] S. Gooran, Digital Halftoning,Thesis, Linkoping University, Linkoping,Sweden. [8] InKoo Kang,Gonzalo R.Arce,heung-Kyu Lee, Color Extended Visual Cryptography Using Error Diffusion, IEE Trans. On Image processing,vol.20.no.1.2.11 [9] Sadan Ekdemir, Xunxun Wu, Digital Halftoning Improvements on the Two-by-Two Block Re-placement Method.333,jan 2011. Vol. 1 Issue 2 July 2012 10 ISSN: 2278-621X