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  Partial Image Encryptionusing Peter De Jong Chaotic Map based Bit-Plane Permutation and it’s Performance Analysis Monjul Saikia1 , Nitumoni Hazarika2 and Margaret Kathing3 1 Assistant Professor, Department of CSE, NERIST, Nirjuli, Arunachal Pradesh Email: [email protected] 2 PG Scholar, Department of CSE, NERIST, Nirjuli, Arunachal Pradesh Email: [email protected] 3 Assistant Professor, Department of CSE, NERIST, Nirjuli, Arunachal Pradesh Email: [email protected] Abstract— Today among various medium of data transmission or storage our sensitive data are not secured with a third-party, that we used to take help of. Cryptography plays an important role in securing our data from malicious attack. This paper present a partial image encryption based on bit-planes permutation using Peter De Jong chaotic map for secure image transmission and storage. The proposed partial image encryption is a raw data encryption method where bits of some bit-planes are shuffled among other bit-planes based on chaotic maps proposed by Peter De Jong. By using the chaotic behavior of the Peter De Jong map the position of all the bit-planes are permuted. The result of the several experimental, correlation analysis and sensitivity test shows that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and decryption. Index Terms— Chaos; Peter De Jong Map; Partial Encryption; Stream Cipher; Bit-plane. I. INTRODUCTION In the recent years, secure transmission of digital image has become essential to protect it from leakages. Application like video conferencing, TV broadcasting, medical image system etc [5,9]. need secure reliable, fast system to store and transmit images. Image encryption can be done for secure transmission and storing our sensitive data. The process of encryption is classified as full encryption and partial encryption [5,7]. In full encryption algorithm which encrypts complete data where as in partial encryption algorithm which encrypts only some data instead of complete data thereby less computation overhead. For image encryption, the raw data can be partitioned with respect to bit-planes, that is from the most significant bit to least significant bit. Thus, the most significant bit-planes are encrypted, while the others are left unencrypted [6,10]. Chaotic system has many properties which are suitable for image encryption process; one of the most important properties is that the chaotic systems are extremely sensitive to initial conditions and also to control parameters. This property is effective in the field of cryptography [4]. During the past few years a large number of chaos [3] based image encryption have been proposed. Some chaos based image encryptions DOI: 02.ITC.2014.5.5 © Association of Computer Electronics and Electrical Engineers, 2014 Proc. of Int. Conf. on Recent Trends in Information, Telecommunication and Computing, ITC
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  2 are based onone-dimensional chaotic maps which are used for the generation of the encryption key. The pixels of an image are then permuted and modified according to this key. Other encryption algorithms use two-dimensional maps because an image is represented as 2D matrix. Most of those encryption schemes belong to the block ciphers; only a few of them were designed as stream ciphers which can provide efficient way for the real-time image encryption. In this paper, bit-plane image encryption scheme is proposed based on Peter De Jong chaotic map in order to meet the requirement of the secure image transfer [8,9]. This is a lossless encryption process. Here the input is converted into 8 bit-planes and using the Peter De Jong chaotic map each bit is swapped within the plane or among the planes. This process can be done for number times to increase the security. The remainder of this paper is organized as follows. Section II provides previous work done using Peter De Jong chaotic map. Section III provides chaos and strange attractor theory. Section IV provides theory of bit- plane. Section V presents the proposed algorithm for encryption and decryption of an image. Section VI presents experimental results and some security analysis. And finally in section VII conclusion and future enhancements are discussed. II. PREVIOUS WORK N.K. Pareek, Vinod Patidhar and K.K. Sud proposed an image encryption based on chaotic logistic map [1]. Another chaotic based encryption technique proposed by Jiri Giesl, Tomas Podoba and Karel Vleek [2] presents an algorithm which utilizes Peter De Jong chaotic map. To encrypt the pixels of an image it is converted into three dimensional bit-plane matrixes. They have done full encryption where all bit-planes are used for encryption. In the above techniques, the entire image is encrypted and decrypted each time, which is a big overhead in case of storage and retrieval of large set of images, in an image database or transmission of images over large an insecure channel. Also the loss of even a small part of the encrypted images results in greater distortion in the decrypted image. This is due to the fact that the part of the encrypted image which is distorted constitutes pixels that will be scattered in the decrypted image. III. CHAOS AND STRANGE ATTRACTOR Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions. Small change in initial conditions yields widely diverging outcomes for such dynamical systems. Their future behavior is fully determined by their initial conditions. Chaos theory belongs to the fields of deterministic dynamical systems. The deterministic nature of these systems does not make them predictable. The behavior of the chaotic dynamical system takes place to a set of states, which is called an attractor [11]. There are several types of an attractor – a point, a curve, a manifold or a complicated set with a fractal structure which is known as strange attractor. The fixed points of strange attractor are locally unstable but the system is globally stable. Strange attractors can be generated in several ways such as by quadratic (eq.1) or trigonometric (eq.2) maps. ‫ݔ‬௡ାଵ = ܽ + ܾ. ‫ݔ‬௡ + ܿ. ‫ݔ‬௡ ଶ + ݀. ‫ݔ‬௡‫ݕ‬௡ + ݁. ‫ݕ‬௡ + ݂. ‫ݕ‬௡ ଶ (1) ‫ݕ‬௡ାଵ = ݃ + ℎ. ‫ݔ‬௡ + ݅. ‫ݔ‬௡ ଶ + ݆. ‫ݔ‬௡‫ݕ‬௡ + ݇. ‫ݕ‬௡ + ݈. ‫ݕ‬௡ ଶ Or ‫ݔ‬௡ାଵ = ‫݊݅ݏ‬(ܽ. ‫ݕ‬௡) − ܿ‫ݏ݋‬(ܾ. ‫ݔ‬௡) ‫ݕ‬௡ାଵ = ‫݊݅ݏ‬(ܿ. ‫ݕ‬௡) − ܿ‫ݏ݋‬(݀. ‫ݔ‬௡) (2) Where ‫ݔ‬௡ାଵ and ‫ݕ‬௡ାଵ represents the chaotic sequence which lies between ±2. The initial conditions of the map are the coordinates of components of bit-planes. The control parameters a, b, c and d are positive or negative real numbers. Necessary condition of the chaotic behavior of the strange attractor is that the value of Lyapunov exponent [2, 11], should be positive, indicating chaos and if the value of Lyapunov exponent is negative, indicating regular motion. The positive exponent corresponds to the expansion; the negative exponent corresponds to the contraction of the system [12]. Strange attractors resulting in a pattern of trajectories that seem to be appear randomly within the system. One of the strange attractors with predefined control parameters is shown in Fig 1. These attractors
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  3 were found byPeter de Jong and these dynamical systems are used for the encryption purposes. Fig 1(a) is used for encryption purpose in our algorithms. Fig 1(a): Example of Peter De Jong with a=1.4, b=-2.3, c=-2.4, d=-2.1 Fig 1(b): Example of Peter De Jong with a=2.033372,b=-0.78980076, c=0.5964786,d=1.7829015 Fig 1(c): Example of Peter De Jong with a= 0.089567065, b=1.5909586, c=1.8515863, d= -2.1974306 Little change in control parameters of a, b, c and d different strange attractor can be obtain as shown in fig1. IV. BIT-PLANES Split an image into different planes plays an important role in image processing. A certain amount of data is stored at each pixel. This amount is determined by the number of bit-planes in the frame buffer. The image is partitioned into bit-planes, i.e. from the most significant one to the least significant one. The more significant bit-planes contain highest sensitive information as compared to the lower significant bit-planes. Thus, more significant bit-planes can be encrypted, while the others are left unencrypted. A bit-plane contains one bit of data for each pixel. If there are eight bit-planes, then there are 8 bits per pixel, and hence 2^8 = 256 different values that can be stored at the pixel. The partial image encryption scheme is shown in the fig 2. Here N represents total number of bit-planes, L most significant bit-planes are encrypted and N-L ones are left
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  4 unencrypted. It isseen from experimental result that to obtain high security more than 4 bit-planes should be encrypted. Fig 2: Bit-plane encryption V. OUR PROPOSED ALGORITHM In this section, the step by step procedure of the partial image encryption as well as decryption process by using Peter De Jong Chaotic map is discussed. Suppose the three-dimensional matrix S which contains the bit values sx,y,z ∈ S of an image, where x ∈ (1,2,3,...R) and y ∈ (1,2,3,...C) , here R and C represents the row and the column of the matrix/image and z ∈ (1,2, …) represents the plane number. Components sx,y,z of the bit planes are the input data for the encryption algorithm. The bit-planes 5 to 8 are not used for encryption. 1. Original chaotic system consists of two maps, which can be used for the positions permutation. But in this paper matrix/image should have three-dimensional character; hence the chaotic system has to be extended to 3D version. Third map can be used for the positions permutation among bit planes or within the bit-plane. ‫ݔ‬௡ାଵ = sin(ܽ. ‫ݕ‬௡) − cos(ܾ. ‫ݔ‬௡) ‫ݕ‬௡ାଵ = sin(ܿ. ‫ݕ‬௡) − cos(݀. ‫ݔ‬௡) (3) ‫ݖ‬௡ାଵ = sin(݁. ‫ݖ‬௡) − cos(݂. ‫ݕ‬௡) Using the equation (3), the chaotic system can be extended to three dimensional matrix. The control parameters a, b, c, d, e, f determines its action. 2. Since the idea of the encryption process is to encrypt each bit component separately. Suppose bA define as the bit component of the coordinates (xx,yy,zz), where xx , yy , zz indicates the row number, column number and plane number respectively. Putting the values of (xx,yy,zz) in equation (3) in place of (xn,yn,zn), (xn+1,yn+1,zn+1) are obtained. 3. The (xn+1,yn+1,zn+1) obtained in step 3 is quantized to get (xk+1,yk+1,zk+1) a new position within the range of image dimension. 4. Then the bit component bA at coordinate (xx,yy,zz), is swapped with bit component (say bB) at coordinate (xk+1,yk+1,zk+1) as shown in the fig 3. 5. This process repeated number of times to swap the components among bit-planes 1 to 8. 6. Thereafter these bit-planes are reconstructed to get the encrypted image. Decryption is the reverse process of encryption where encrypted image is taken as input. For decryption row number, column number and plane number are taken in the reverse order of the encryption process. Then the decrypted image is reconstructed from the bit-planes. Figure 3 and 5 shows the encryption and decryption process respectively. VI. EXPERIMENTAL RESULT AND SECURITY ANALYSIS In this section we have shown the encryption/decryption results using different keys as well as different number of iterations. Here experiment is done for different image size; one experiment is done on image size of 256x256 and another experiment on image size of 512x512. N-1 N-L-1 N-L Encrypt Key N-1 N-L N-L-1 0 . . . . 0 . . . .
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  5 Fig 3: Flowchart from original image to encrypted image a) 8th bitplane b)7th bitplane c) 6th bitplane d) 5th bitplane e) 4th bitplane f) 3rd bitplane g) 2nd bitplane h) 1st bitplane Fig 4: Different bit planes of camaraman.tif (256x256) We have also studied the correlation between the original images and encrypted images, original images and decrypted images and also between original and incorrectly decrypted using the equation (4). Higher the correlation coefficient indicates high similarities between the images and lower the correlation coefficient indicates low similarities between the images. Original image should have low correlation coefficients with the encrypted images and high correlation coefficients with the decrypted images. Figure 4 and 6 shows different bit planes of images of size 256x256 (camaraman) and 512x512 (lenna) respectively. Fig 6 and 9 shows original, encrypted, decrypted and incorrectly decrypted images of size 256x256 and 512x512 respectively. Table 1 and 4 represents the various experimental results such as correlation, encryption/decryption time for an image size of 256x256 and 512x512 respectively. Fig 7 and 11 shows the correlation of original and encrypted for cameraman and correlation of original and incorrectly decrypted for
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  6 Fig 5: Flowchart decryption of image from encrypted image lenna respectively. Fig 9 and 11 represents the time analysis for image size 256x256 and 512x512 respectively. Table 2 and 5 represents image description for cameraman and lenna respectively. Table 3 represents computer and platform description. The correlation coefficients can be calculated as follows ‫ݎ‬ = ∑ ∑ ൫஺೘೙ି஺൯(஻೘೙ି஻ത)೙೘ ට൫∑ ∑ ൫஺೘೙ି஺൯೙೘ ൯ మ (∑ ∑ (஻೘೙ି஻ത)೙೘ )మ (4) Here A and B are two images, where Aഥ=mean2(A) and Bഥ =mean2(B). Figure 8 shows the correlation of encrypted image with original, which shows number of iteration in the range 10 to 20 gives very good result. Let key value change in 'a' by little amount, other key values of b,c,d,e,f keeping same a=1.4001, b=-2.3, c=-2.4, d=-2.1, e=1.2, f=1.6. Then try to decrypt, which gives much distorted image with very less correlation coefficients.
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  7 Fig 6: Differentbit planes of lenna.bmp(512x512) Fig 7: (a),(b),(c) and (d) are original, encrypted, decrypted and wrongly decrypted image with 1 iteration, (e),(f),(g) and (h) are original, encrypted, decrypted and wrongly decrypted image with 3 iterations and (i),(j),(k) and (l) are original, encrypted, decrypted and wrongly decrypted image with 5 iterations Fig 8: Plot of Correlation of Original and Encrypted (cameraman) TABLE I: EXPERIMENTAL RESULT OF IMAGE SIZE 256X256 No of Iteration No of planes MSB onwards Correlation between Original and Encrypted Correlation between Original and Decrypted Correlation between Original and Incorrectly Decrypted Encryption Time (in sec) Decryption Time (in sec) 1 4 0.0376 1 0.1395 59.2357 57.2814 3 4 -0.0046 1 -0.0025 58.7784 57.7699 5 4 -2.42E-04 1 0.0064 59.0639 58.8885 10 4 -7.72E-04 1 0.0022 60.7062 57.1058 15 4 -0.0036 1 -0.0059 61.6548 59.4176 20 4 0.0084 1 0.0018 61.8862 59.311 40 4 -0.0012 1 0.0078 64.8964 63.6016 50 4 -0.0046 1 2.71E-04 64.2301 63.6283 100 4 0.0033 1 0.0028 74.8765 73.4961 200 4 0.0098 1 -0.0038 91.371 90.0426
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  8 TABLE II: IMAGEDESCRIPTION Image Name Cameraman Size 256x256 Type Grey level Key Values a=1.4, b=-2.3, c=-2.4, d=-2.1, e=1.2, f=1.6 TABLE III: COMPUTER AND PLATFORM DESCRIPTION Processor i3 Processor Speed 2.2GH Memory 4GB DDR RAM OS Windows 7 Fig 9: Time analysis for ‘cameraman.tif’ (256x256) Fig 10: (a),(b),(c) and (d) are original, encrypted, decrypted and wrongly decrypted image with 1 iteration, (e),(f),(g) and (h) are original, encrypted, decrypted and wrongly decrypted image with 3 iterations and (i),(j),(k) and (l) are original, encrypted, decrypted and wrongly decrypted image with 5 iterations Fig 11: Plot of Correlation of Original and Incorrectly decrypted (Lenna)
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  9 TABLE IV: EXPERIMENTALRESULTS OF IMAGE SIZE 512X512 TABLE V: IMAGE DESCRIPTION Image Name Lena Size 512x512 Type Grey level Key Values a=1.4, b=-2.3, c=-2.4, d=-2.1, e=1.2, f=1.6 Table 1 & 4 gives correlations among encrypted, decrypted and incorrectly decrypted images whose image properties are described in table 2 and 5 respectively. Figure 12 shows plot of computation times for a image (lenna) as described in table 5. Fig 12: Time analysis for ‘Lenna.bmp’(512x512) VII. CONCLUSION This paper presents an image encryption scheme which decomposes an image into bit-planes and performs partial bit-plane encryption. These bit-planes are encrypted using Peter De Jong chaotic map. Coordinates of components of bit-planes become initial input for the chaotic map. After several iteration coordinates are permuted, but bits in the bit-plane are not modified directly. Modifications of bits are done by permutation of bit-planes and hence pixel values of an image are changed. Correlation analysis shows that no loss of information and it also reduces the computation time as encrypting is performed over the partial bit-planes. This encryption scheme seems to be independent of dimension the image. However computation time increases with increase in image dimension. This technique can equally be used in other of images encryption classes. No of Itaration No of MSB onwards Correlation between Original and Encrypted Correlation between Original and Decrypted Correlation between Original and Incorrectly Decrypted Encryption Time (in sec) Decryption Time (in sec) 1 4 0.0572 1 0.1345 220.0706 222.5666 3 4 0.0023 1 7.01E-04 234.2511 221.0066 5 4 9.42E-04 1 0.0028 223.4558 225.3591 10 4 0.0018 1 0.0018 234.2979 227.6991 15 4 -0.0021 1 -0.0026 231.7551 232.1607 20 4 -3.23E-04 1 -0.0041 242.9092 235.7331 40 4 -0.0026 1 0.0015 250.3348 248.9308 50 4 0.0014 1 7.12E-04 269.6945 253.6421 100 4 -0.004 1 0.002 291.9091 287.5254 200 4 0.0031 1 -0.0014 360.9239 351.7199
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  10 REFERENCES [1] N.K. Pareek,Vinod Patidhar and K.K. Sud “Image encryption using chaotic logistic map”, Image and Vision Computing 24(2006) 926-934, August 2005 [2] Jiri Giesl, Tomas Podoba and Karel Vlcek “Chaos-Based Bit Planes Image Encryption”, Inovations in Computing Sciences and Software Engineering, 2010 ,pp 349-353, SBN 978-90-481-9112-3. [3] Zhaopin Su, Guofu Zhang and Jianguo Jiang (2012) "Multimedia Security: A Survey of Chaos-Based Encryption Technology, Multimedia - A Multidisciplinary Approach to Complex Issues", Dr. Ioannis Karydis (Ed.), ISBN: 978- 953-51-0216-8, InTech, DOI: 10.5772/36036. [4] Atul Kahate “Cryptography and Network Security” TATA McGRAW HILL, Second Edition.2009, ISBN 10:0-07- 064823-9, Pg 38-77. [5] Shiguo Lian “Multimedia Content Encryption: Techniques and Application”, CRC Press 2008, ISBN 987-1-4200- 6527-5, Pg 43-85. [6] Shiguo Lian, Jinsheng Sun, Dengfeng Zhang and Zhiquan Wang “A Selective Image Encryption Scheme Based on JPEG2000 Codec” in Multimedia Information Processing - PCM 2004, Lecture Notes in Computer Science Volume 3332, 2005, pp 65-72. [7] K.C.Ravishankar and M.G.Venkateshmurthy “Region Based Selective Image Encryption”, International Conference on Computing & Informatics, 2006. ICOCI '06, DOI:10/1109/ICOCI.2006.5276550,pg:1-6. [8] M Saikia, S Majumder "Spread Spectrum Embedding of Colluder Traceable Codeword in Multimedia," Emerging Applications of Information Technology (EAIT), 2011 Second International Conference on , vol., no., pp.190,193, 19-20 Feb. 2011doi: 10.1109/EAIT.2011.11 [9] M. Saikia, S.J. Bora and Md. A. Hussain “A Review on Applications of Multimedia Encryption” in ISBN: 987-81- 8487-088-6 in national conference on Network Security- issues 2010, challenges and Techniques, at Tezpur University. [10] Nidhi S Kulkarni, Balasubramanian Raman, and Indra Gupta “Selective Encryption Of Multimedia Images”, XXXII National Systems Conference, NSC 2008, December 17-19, 2008. [11] Mridula Budhraja, Narender Kumar and L. M. Saha “The 0-1 Test Applied To Peter-De-Jong Map”, International Journal of Engineering and Innovative Technology (IJEIT), Volume 2, Issue 6, December 2012, ISSN: 2277- 3754,ISO 9001:2008 Certified. [12] Jiri Giesl, Ladislav Behal and Karel Vlcek “Improving Chaos Image Encryption Speed”, International Journal of Future Generation Communication and Networking Vol. 2, No. 3, September, 2009