Journal of Information Security, 2011, 2, 139150 doi:10.4236/jis.2011.24014 Published Online October 2011 (http://www.SciRP.org/journal/jis) Copyright © 2011 SciRes. JIS 139 New Approach for Fast Color Image Encryption Using Chaotic Map Kamlesh Gupta1*, Sanjay Silakari2 1Department of Com p ut er Sci ence, Jaypee University of Engineering and Technology, Guna, India 2Department of Com p ut er Sci ence, Rajiv Gandhi Technical University, Bhopal, I ndia Email: {*Kamlesh_rjitbsf, ssilakari}@yahoo.com Received June 6, 2011; revised July 5, 2011; accepted July 16, 2011 Abstract Image encryption using chaotic maps has been established a great way. The study shows that a number of functional architecture has already been proposed that utilize the process of diffusion and confusion. How ever, permutation and diffusion are considered as two separate stages, both requiring imagescanning to ob tain pixel values. If these two stages are mutual, the duplicate scanning effort can be minimized and the en cryption can be accelerated. This paper presents a technique which replaces the traditional preprocessing complex system and utilizes the basic operations like confusion, diffusion which provide same or better en cryption using cascading of 3D standard and 3D cat map. We generate diffusion template using 3D standard map and rotate image by using vertically and horizontally red and green plane of the input image. We then shuffle the red, green, and blue plane by using 3D Cat map and standard map. Finally the Image is encrypted by performing XOR operation on the shuffled image and diffusion template. Theoretical analyses and com puter simulations on the basis of Key space Analysis, statistical analysis, histogram analysis, Information entropy analysis, Correlation Analysis and Differential Analysis confirm that the new algorithm that mini mizes the possibility of brute force attack for decryption and very fast for practical image encryption. Keywords: Chaotic Map, 3D Cat Map, Standard Map, Confusion and Diffusion 1. Introduction With the fast development of image transmission through computer networks especially the Internet, medical im aging and military message communication, the security of digital images has become a most important concern. Image encryption, is urgently needed but it is a chal lenging task because it is quite different from text en cryption due to some intrinsic properties of images such as huge data capacity and high redundancy, which are generally difficult to handle by using conventional tech niques. Nevertheless, many new image encryption sche mes have been suggested in current years, among which the chaosbased approach appears to be a hopeful direc tion. General permutationdiffusion architecture for chaos based image encryption was employed in [1,2] as illus trated in Figure 1. In the permutation stage, the image pixels are relocated but their values stay unchanged. In the diffusion stage, the pixel values are modified so that a minute change in onepixel spreads out to as many pix els as possible. Permutation and diffusion are two dif ferent and iterative stages, and they both require scan ning the image in order to gain the pixel values. Thus, in the encryption process, each round of the permutation diffusion operation requires at least twice scanning the same image. In this paper, we generate diffusion template using 3D standard map and rotated image by using vertically and horizontally red and green plane of the input image. We then shuffle the red, green, and blue plane by using 3D Figure 1. Permutation and diffusion based image crypto system.
K. GUPTA ET AL. 140 Cat map and standard map. Finally the Image is en crypted by performing XOR operation on the shuffled image and diffusion template. The objectives of this new design includes: 1) to efficiently extract good pseudo random sequences from a cascading of 3D cat and stan dard map for color image and 2) to simultaneously per form permutation and diffusion operations for fast en cryption. The rest of this paper is organized as follows: Section 2 focuses on the efficient generation of pseudorandom sequences. In Section 3, proposed algorithm is described in detail. Section 4 presents simulation results and per formance analyses. In Section 5, conclusions and future work. 2. Efficient Generation of Pseudorandom Sequences The generation of pseudorandom is based on two cas caded chaotic maps behave as a single chaotic map in present case. The 3D cat map & 3D standard map are taken for encryption. The pseudorandom matrix gener ated by this method is given below. (The explanation for pseudorandom sequences generation is given in Section 3). 3. Proposed Algorithm The proposed algorithm are divided into several stages Table 1. Generation of pseudorandom values by proposed method. and explained below. 3.1. Diffusion Template According to the proposal the diffusion template must have the same size as main image. Let the main image have m number of rows n number of columns then the diffusion template is created as follows 255 , ,roundijk j n (1) where 1im , 1jn and . 13k Equation (1) form the matrix with all rows filled with linearly spaced number in between 0 to 255. The se quence is randomized by 3D standard map in discrete form as given below. The 3D standard map randomizes the pixels by real locating it in new position by utilizing its property of one to one mapping. Figure 2 shows the final diffusion tem plate by using 3D standard map. modiij m (2) 1sin mod 2 c jjkKi pi n (3) 1 sin2sinmod 22 pp kkK iKjp pi pi (4) where the K1, K2 are the integers, p = 3 for the case of color image and i′, j′, k′ shoes the transformed location of i, j, k. diff diff ,, ,, ijkI ijk . 3.2. Image Encryption Step 1. The main image is divided into three separate images IR, IG and IB as follows ,, R,1 xyIxy ,, G ,2 xyIxy ,,,3 B xyIxy where 1 m and 1 n. Step 2. The Red and Green image are transform verti Figure 2. Diffusion template. Copyright © 2011 SciRes. JIS
K. GUPTA ET AL. 141 cally and horilue image rezontally respectively. The b mains same and reconstructs the new image. ,m 2 RR mod, xy Ixmy ,m 2 GR nod xyIx yn ,, BB xyIxy new ,,1 , R xyI xy new ,,2, G xyI xy new ,,3 , B xyI xy . Step 3. Perform the first level confusion by usin2D ca w where j′ and k′ are obtained by 2D cat map and p q are erate Final confusion stage by two cascade 3D g t map. Slice the plane normal to R, G, B Planes by I′new(i, j, k) = I′SRGB(j′, k′) = Inew(i, j, k) here 1im , 1jn and 13k. k and mo dm 1modk n xy rrp rpq jj y kqj integer > 0 and rx, ry are offset integer such that 0 ≤ rx ≤ m, 0 ≤ ry ≤ n. Step 4. Gen maps first by cat map then by standard map. So the transformation of location (i, j, k) into (i″, j″, k″) is per formed by following equations. 1 iaabiaj mod xzy z yxzxyzy aaaaaabkm + 1mod zxyxzyz zz 1 zxyzyzxz yy ibabaabbiab jaa aaabbaa abk n 1 m xxy yx xyxyxx yy kabbbibj aabbababk modiik m y b od p 1sin mod 2 n jijK in pi 1sin 2 2sinmod 2 p kkKipi p jp pi con ,, ,, fi jkIijk where a, a, a, b, b, b and 1 , 2 are n step is followed by diffusion obtained by .3. Key Generation Process he proposed method has a large number of variables fling Ds = 8 bits. 8 ion template variables Dk1Dk2 = 8 + 8 = 16 . Sliced RGB plane Shuffling = Ss = 8 bits. ts. bi p 7. Final Confusion shuffling Cs = 8 bits. 8 + 8 + 2 onfusion cat map variables CaCb = 8 + 8 = 16 0. Confusion offset of standard map Cx′Cy′Cz′ = dard map variables Ck1Ck2 = 8 + ructure k1Dk2SsSxSySpSq C To s. .4. Image Decryption tep 1. Generate the diffusion template in same way as mation of location is done by two ca e retransformation of location (i″, j″, k″) into (i, j, k) integers >0. Each confusio EXOR operations performed between each pixels of Iconf and diffusion Idiff. The proposed image encryption architecture is given in Figure 3. = II I encpconfdiff. 3 T which can be used as key parameters but to avoid the exceptionally large key and decreased key sensitivity, the parameter which does not having great affects on en cryption are avoid or scaled. The selected key parameters and their length are given below Step 1. Diffusion template shuf Step 2. Diffusion template offset value DxDyDz = 8 + + 2 = 18 bits. Step 3. Diffus bits. Step 4 Step 5. Sliced RGB plane offset values SxSy = 8 bi Step 6. Sliced RGB Plane Variables SpSq = 8 + 8 = 16 ts. Ste Step 8. Confusion offset of cat map CxCyCz = = 18 bits. Step 9. C bits. Step 1 8 + 8 + 2 = 18 bits. Step 11. Confusion stan 8 = 16 bits. Final key st DsDxDyDzD sCxCyCzCaCbCx’Cy’Cz’Ck1Ck2 tal bits = 8 + 18 + 16 + 8 + 8 +16 + 8 + 16 + 16 + 18 + 16 = 148 bit 3 S in encryption section. Step 2. Retransfor scaded 3D maps firstly by standard map then by cat map. So th is performed by following equations modiik m 1sin mod 2 jijkin pi n Copyright © 2011 SciRes. JIS
K. GUPTA ET AL. Copyright © 2011 SciRes. JIS 142 Figuer 3. Image encryption by using confusion and diffusion.
K. GUPTA ET AL. 143 1sin2 mod 22 nn kkkjk j pi pi 1 mod xzy z yxzxyzy iaabiaj aaaaaab km 1 mod zxyxzyz zz p zxyzyzxyy x ibabaabbiab j aaaaabbaab ak n 1mod xxy yx xyxyxxyy kabbbibj aabbababkp Iretransf (i, j, k) = Iencp (i, j, k) where a, a, a, b, b, b and , are integers > 0. Each confusion step is followed by diffusion obtained by EXOR operations performed between each pixels of Iretrnsf and diffusion Idiff 1K2K dencp retrnsfdiff II . Step 3. Performing inverse of First level confusion. Slicing the plane normal to R, G, B Planes , SRGB dencp ,, jkIijk for each value of i, j changed from 0 to m, k changed from 0 to 3. Deshuffling the sliced plane DRGB SRGB ,, jk Ijk where j′ and k′ are obtained by 2D cat map given below m n where p and q are integers > 0, and rx, ry are offset inte gers such that 0 ≤ rx ≤ m and 0 ≤ ry ≤ n. Recombining the planes for forming 3D matrix for next operation mod xy jjrrpk 1m y kqjrpq k od DRGB ,, , ijk Ijk . Step 4. Rerotating the image planes Dividing main image into three separate images IR, IG and IB as follows ,, R ,1 xyIxy ,, g ,2 xyIxy ,,,3 B xy I xy where 1 m and 1 n. d plane verticallyScro lling the re ,m 2 RR mod, xy Ixmy . Scrolling the green plane horizontally ,m 2 GR nod xyIx yn . Blue plane remain intact. ,, BB xyIxy. Step 5. Next recombination of planes are performed to form final decrypted image ,,1 , final R xyI xy ,,2, final G xyI xy 3 , B ,, final xyI xy 4. Performance Analysis 4.1. Key Space Analysis The strong point of the proposed algorithm is the genera tion of the permutation sequence with the chaos se quence. The key space should also be suitably large to make bruteforce attack not feasible. In the proposed algorithm, we use 148 bit key (37 Hex number) is used. It has been observed in Figures 4(a) and (b) that with slightly varying the initial condition of the chaotic se quence. It has been almost impossible to decrypt the im age. 4.2. Statistical Analysis It is well known that passing the statistical analysis on ciphertext is of crucial importance for a cryptosystem actually, an ideal cipher should be strong against any statistical attack. In order to prove the security of the proposed image encryption scheme, the following Statis tical tests are performed. 4.2.1. Histogram Analysis To prevent the access of information to attackers, it is important to ensure that encrypted and original images do not have any statistical similarities. The histogram analysis clarifies that, how the pixel values of image are distributed. A number of images are encrypted by the encryption schemes under study and visual test is per formed. An example is shown in Figure 5. In Figure 5 shows histogram analysis on test image using proposed algo rithm. The histogram of original image contains great sharp rises followed by sharp declines as shown in Fig ure 5 and the histograms of the encrypted images for different round as shown in Figures 5(a)(f) have uni form distribution which is significantly different from original image and has no statistical similarity in ap Copyright © 2011 SciRes. JIS
K. GUPTA ET AL. 144 (a) 1010110D2833020202 and Decrypted by 0304002030402030 03040020304020301011010110D2833040404 and Decrypted (b) Figure 4. (a) Input image encrypted with 0304002030402 030101 with pe tistical attack. The encrypted image histogram, approximated by a uniform distribution, quite different fr very good correlaon among adjacent piels in the digital image [3]. Equation (5) is used to study the djacent pixels in horizontal, 1011010110D2833020203; (b) Input lenna image encrypted by 03040020304020301011010110D2833040405. arance. So, the surveyed algorithms do not provide any clue for sta is om plainimage histogram. 4.2.2. Correlation Analysis There is a ti x Correlation between two a vertical and diagonal orientations. This is shown in Fig ure 6. x and y are intensity values of two neighboring pixels in the image and N is the number of adjacent pixels se lected from the image to calculate the correlation. 1000 pairs of two adjacent pixels are selected randomly from image to test correlation. The correlation coefficient be 111 2 2 11 j NN j j jj NN j jj x y Ny y (5) 2 2 11 j N jj j NN j jj Nxy Nx x r c Copyright © 2011 SciRes. JIS
145 K. GUPTA ET AL. (a) (b) (c) (d) Copyright © 2011 SciRes. JIS
K. GUPTA ET AL. 146 (e) (f) Figure 5. (a) Histogram for red, green and blue plane of original and encrypted image for R = 1; (b) Histogram for red, green and blue plane of encrypted image for R = 2; (c) Histogram for red, green and blue plane of encrypted image for R = 4; (d) Histogram for red, green and blue plane of encrypted image for R = 8; (e) Histogram for red, green and blue plane of en crypted image for R = 16; (f) Histogram for red, green and blue plane of encrypted image for R = 32. Figure 6. Correlation for horizontal, vertical and diagonal. tween original and cipher image is calculate in Table 6. 4.3. Key Space Analysis Key space size is the total number of different keys that can be used in the cryptography. Cryptosystem is totally sensitive to all secret keys. A good encryption algorithm should not only be sensitive to the cipher key, but also the key space should be large enough to make bruteforce at tack infeasible. The key space size for initial conditions and control parameters is over than 2148. Apparently, the key space is sufficient for reliable practical use. 4.4. Differential Analysis In general, a desirable characteristic for an encrypted image is being sensitive to the little changes in plain image (e.g. modifying only one pixel). Adversary can create a small change in the input image to observe changes in the result. By this method, the meaningful relationship between original image and cipher image can be found. If one little change in the plainimage can Copyright © 2011 SciRes. JIS
K. GUPTA ET AL. 147 cause a significant change in the cipherimage, with re spect to diffusion and confusion, then the differential attack actually loses its efficiency and becomes almost useless. There are three common measures were used for differential analysis: MAE, NPCR and UACI. Mean Ab solute Error (MAE). The bigger the MAE value, the bet ter the encryption security. NPCR means the Number of Pixels Change Rate of encrypted image while one pixel of plainimage is changed. UACI which is the Unified Average Changing Intensity, measures the average in tensity of the differences between the plainimage and Encrypted image. Let C(i, j) and P(i, j) be the color level of the pixels at the ith row and jth column of a W × H cipher and plain image, respectively. The MAE between these two images is defined in 11 1 MAE, , WH ji cij pij WH . er two cipherimages, C1 and C2, wh (6) Consid ose cor responding plainimages have only one pixel difference. The NPCR of these two images is defined in ,, PCR 100% ij Dij WH (7) where W and H are the width and height of the image and D(i, j) is defined as 0,if 1,2, ,. 1,if 1,2, CijC ij Dij CijCij Another measure, UACI, is defined by the following formula: , 1, 2, 1 UACI 100% 255 ij cijc ij WH . (8) Tests have been performed on the encryption schemes on a 256level color image of size 256 × 256 shown in Figures 5(a)(f). The MAE, NPCR and UACI experi ment result is shown in Tables 4 and 2. The Tables 3 and 5 compare the result of Yo based on chaotic map and our. Results obtained from to ttle changes in the input image is under 0.01%. Ac ation result, the rate influ nce due to one pixel change is very low. The results demonstrate that a swiftly change in the original image will result in a negligible change in the ciphered image. 4.5. Information Entropy Analysis It is well known that the entropy H(m) of a message source m can be measured by ng previous related work NPCR show that the encryption scheme’s sensitivity li cording to the UACI estim e 1 0 1 log m i ii Hmpm pm (9 where M is the total number of symbols mi ∈ m; p(mi) represents the probability of occurrence of symbol mi and log denotes the base 2 logarithm so that the entropy is expressed in bits. For a random source emitting 256 symbols, its entropy is H(m) = 8 bits. This means that the cipherimages are close to a random source and the pro posed algorithm is secure against the entropy attack. The test result on different image for different round is de fined in Table 7. 4.6. Speed Analysis cesses. In general, en cryption speed is highly dependent on the CPU/MPU structure, RAM size, Operating System platform, the programming language and also on the compiler options. So, it is senseless to compare the encryption speeds of two ciphers image. Without using the same developing atmosphere and optimization techniques. Inspire of the mentioned diffi culty, in order to show the effectiveness of the proposed image encryption scheme over existing algorithms. We Table 2. NPCR, UACI and Entropy for key sensitivity test. Lenna Error Image R = 2 R = 3 R = 4 ) Apart from the security consideration, some other issues on image encryption are also important. This includes the encryption speed for realtime pro NPCR 99.5966593424998836263 99.651082356 .609 UACI 52.539481368751.6816741344 50.603535970 Entropy 7.999130689807.99912231127 7.9991865161 NPCR 99.610392252699.5905558268 99.599711100 8581327550 48.719709807 Entropy 7.999010789687.99905756543 7.9991734549 Baboon Error Image UACI 46.999834846047. Table 3. Comparison of NPCR Name of image R = 1 and UACI with Yong Wong et al. R = 2 R = 3 Our Yong Wang et. alOur Yong Wang et. alOur Yong Wang et al. NPCR 99.62 97.621 Airplane UACI 33.19 32.909 99.60 99.637 99.62 99.634 33.10 33.575 33.35 33.580 Copyright © 2011 SciRes. JIS
K. GUPTA ET AL. 148 eren = 4 R = 8 R = 10 R = 16 R = 32 Table 4. NPCR and UACI for diff Image R = 1 R = 2 R = 3 t round on different color image. R NPCR 99.55 99.57 99.59 99.59 99.61 99.60 99.60 99.61 Baboon UACI 37.17 38.68 39.00 MAE 71.65 74.52 75.29 NPCR 99.63 99.64 99.59 Lenna UACI 28.87 27.51 27.33 38.78 38.69 38.88 39.03 38.89 75.18 75.23 75.37 75.34 75.50 99.62 99.62 99.61 99.62 UACI 38.05 38.26 37.99 MAE 75.20 74.68 99.61 99.59 99.60 33.28 33.32 33.31 99.59 27.42 27.43 27.64 27.51 27.37 77.58 77.76 77.84 77.67 77.54 99.58 99.63 99.62 99.62 99.62 38.03 38.34 38.20 38.33 38.11 74.48 74.89 74.62 74.62 74.61 9.62 99.63 MAE 80.84 77.24 77.46 NPCR 99.62 99.62 99.58 Pepper 74.27 NPCR 99.62 99.60 99.59 Airplane 33.35 9 UACI 33.19 33.10 33.27 33.329 Table 5. The round number of scanningimag tion and diffusion to achieve NPCR > 0.996 a NPCR UACI No. of Round for Confusion and Diffusion e, permuta nd UACI > 0.287. Our >0.996 >0.287 1 Ref. [3] >0.996 >0.333 2 Ref. [4] >0.996 >0.333 18 Ref. [5] >0.996 5 Ref. [6] >0.996 >0.333 6 Ref. [7] >0.996 >0.333 6 evaluated the performance of encryption schemes with an unoptimized MATLAB 7.0 code. Performance was measured on a machine with Intel core 2 Duo 2.00 GHz CPU with 2 GB of RAM running on Windows XP. The time for encryption and decryption is measured for dif ferent round is shown in Tables 8 and 9. 4.7. FIPS 140 Testing We also sr proposed algorithm pass the FIPS 14ss testsThere are four tesonobit, Poker, Runs tests and Lng run tesach was to test the randomness of a sam quence length of 20,0 as follo how that ou 02 randomne. ts: M ots. E of the tests designedple se 00 bitsws: 4.7.1. The Monobit Test 1) Calculate x which is the number of ones in the 20,000 bit stream. 2) The test is passed if 9725 < x < 10,275. 4.7.2. The Poker Test 1) Divide the 20,000 bit stream into 5000 contiguous 4 bit segments. Count and store the number of occurrences of each of the 16 possible 4 bit values. Denote g(i) as the number of each 4 bit value i where 0  15. 2) Calculate x by 15 2 0 5000 5000 i Xgi (10) 16 t is if 2.16 < 6.17. 4.7e R un mc tivf aeenf all lengths in the sld be counted and sto teifof runs is each cind e . 4.7.4. The Lg Run Test 1) Findngest run in the 20,000 e ngen in f 20bothnd z smaller , the test is passed. 3) The tespassedx < 4 .3. Thuns Test 1) A rrepresents a aximal sequene of consecu e bits oll ones or all zros. The incidces of runs o ample stream shou red. 2) Thest is passed the number w 10 ithin theorresponding terval specifie below Tabl on the lobits. 2) If th length of the lost ruthe bit stream o ,000 bit ( of one aero) isthan 26 Copyright © 2011 SciRes. JIS
K. GUPTA ET AL. 149 Correlation coefof plae orrelatiicient ofimage Table 6. Correlation coefficient for plain and cipher image. ficient in imagCon coeff Cipher Images Horizontal Vertical Diagonal Horizontal Vertical Diagonal Baboon 8646 0.810.007 0. .9156 0.8603 0.006 0.091 Pepper 0.9376 0.890.006 0. 0.0.829314 0.004 037 Lena 00.8808 0.9364 0.001 0.005 35 023 Table 7. Entropy test for different color image. Im R = 1 R = 2 R = 3 R = 4 R = 8 R = 10 R = 16 R = 32 Yong Wang et al. [7]age Our Scheme Baboon 7.9988 7.9990 7.9991 7.9992 7.9990 7.9990 7.9990 7.9991  Lenna 7.9981 7.9991 7.9991 7.9992 7.9991 7.9990 7.9990 7.9990 7.9990 Pepper 7.9987 7.9991 7.9991 7.9989 7.9989 7.9992 7.9992 7.9992 7.9990 Air7.9989 7.9989 7.9991 7.9991 7.9991 7.9991 7.9991 7.9992 Boat 7.9986 7.9992 7.9991 7.9990 7.9990 7.9990 7.9991 7.9991 plan   Table 8.ptioin seor difround. Image R3 R = 4 R =R =R Encryn time cond fferent = 1 R = 2 R = 8 10 = 16 R = 32 Our Scheme Baboon 0.510 0.87 1.20 1.56 2.94 3.65 5.73 11.24 5615.697 11.225 per 0.521 0.87 1.197 1.561 Airplan 0.521 0.87 1.197 1.561 11.225 Bat 21 0.81.5615.697 11.225 Lenna 0.521 0.87 1.197 1. Pep 2.933 3.662 2.933 3.662 5.697 11.225 2.933 3.662 5.697 o0.57 1.197 2.933 3.662 Table 9. Deption time in se Im× 25 = 1 R = 2 R = crycond for different round. 4 R = 8 R = 10 R = 16 R = 32 age 256 6 R R = 3 Our Scheme Baboon .43 0.77 1.12 1.470 2.85 3.55 5.62 11.17 429 0.77 137 1.471 2.869 3.548 5.618 r 430 0.78 139 1.472 2.11.22 Airplan 0.429 0.77 1.137 1.471 2.11.20 41.523 5.594 11.15 0 Lenna0.1.11.20 Peppe0.1.869 3.549 5.619 869 3.548 5.618 Boat 0.434 0.722 1.065 1.4 2.807 3 We need to change the testing algorithm to suit to im age data so we randomly chose 100 streams of 20,000 consecutive bits from the ciphered images of image A. Then we find statistics of the randomly chosen 100 reams for each test and compared them to the accep ow the numbers of the samples mong 100 randomly chosen samples, which passed the places the tradi better encryption using cascading of 3D standard an orizontally red and green plane of the input image. e then shuffle the red, green, and blue plane by using ap. Finally the Image is en crthe shuffled im ut, both confirming that the new cipher st tance ranges. Table 11 sh a Monobit, Poker, Long run tests and run tests. 5. Conclusions This paper presents a technique which re tional preprocessing complex system and utilizes the basic operations like confusion, diffusion which provide same or d 3D cat map. We generate diffusion template using 3D standard map and rotate image by using vertically and h W 3D Cat map and standard m ypted by performing XOR operation on age and diffusion template. Completion of the design, both theoretical analyses and experimental tests have een carried ob Copyright © 2011 SciRes. JIS
K. GUPTA ET AL. 150 Length of the run 3 ≥6 Table 10. FIPS140 test range. 1 2 4 5 Reerval 5 86 3 1quired int2315  2681114  13527  72240  384 03  209 103  209 Table 11. FIPS140 pass, F = f Name of image R = 1 R = 2 R = 3 R = 4 R = 8 R = 10 R = 16 R = 32 test P =ail. runs 10P, 10P 12P, 12P 16P, 12P 17P, 14P 11P, 12P 13P, 15P 12P, 14P 15P, 11P pocke mono 1008 r 374.4P 3P 13.644P 678P 556P 1P 9913P P , 12P , 13PP, 20P P, 12P P 0P 856P1.558P 2P P P 38P 054P 900P 2P P 3P , 13P , 13PP, 11P P, 14P P 7P 454P0.227P .929P r mono 10085P 9982P 10001P 9967P 10048P 9994P 9913P 10036P runs 12P, 10P 5P, 12P 12P, 13P 12P, 11P pocker 880.25F 30.016P 13.504P 12.134P 16.761P 20.108P 12.800P 9.568P Airplan m10030P 10075P9975P 40P 1P P 7F 2P 9.894 9975P 15.44 12.985P 9952P 8.12.12.556P 2P Baboon 9969P 5P 9990P 10031003 runs 10P, 11P13P, 1513P, 117P, 13P12P13P 1512 pocker 317.4F 24.30P14.0228.99218.227P 21. 118.75 Lenna mono 9956P 10025P10103996799 1091011 runs 12P, 16P13P, 1512P, 112P, 14P12P13P 1314 pocker138.41F 13.196P12.05713.3318.227P 20. 127Peppe 14P, 13P 17P, 23P 12P, 14P 14P, 13P 1 ono 9996P99100799469973P poshigh sy and fast encryptioeed. In conclusion, therefore, the new cipher indeed has excel lent potential for practical imagption applications. 6. References [1] hen, Y. d C. K., “A Syc Image Encryption Scheme Based on 3D Chaotic Cat Maps,” Chaos Solitons & Fractals, Vol. 21 [4] Z. ang and W. Guan, “ChaosBased Image Encrrithm,” Physics Letters A, Vol. . 13. 153 sesses ecuritn sp e encry G. CMao an Chuimmetri , No. 3, 2004, pp. 749761. doi:10.1016/j.chaos.2003.12.022 [2] D. Xiao, X Guan, F. Hu yption Algo346, No , 2005, pp157. doi:10.1016/j.physleta.2005.08.006 S. Lian, J. Sun and Z. Wang, “A Cipher Based on a Suise of thotic Staap,” C oli tons & Fractals, Vol. 26, No. 1, 2005, pp. 117129. [5] Block table Ue Chandard Mhaos S doi:10.1016/j.chaos.2004.11.096 [6] K. W. Wong, B. S. Kwok and W. S. Law, “A Fast Image ased on Chaotic Standard Map,” Physics Letters A, Vol. 372, No. 15, 2008, pp. 26452652. Encryption Scheme B . LiaP. Wei, “Analysis andvement of a ChaosBased Image Encryption Algorithm,” Chaos Solitons & Fractals, Vol. 40, No. 5, December 2007. [3] ga, K.Wong, X. Fo and G.en, “A haosBast Imacryptionrithm,” o ng, Vol. 12. o and Impro Y. Wan. W. Lia R. Ch New Cased Fge En Algo Applied Soft Cmputi1, No. 1, 2011, pp. 51452 doi:10. doi:10.1016/j.phy07.12.0sleta.20 26 [7] Y. Mao, G. Chen and S. Lian, “A Novel Fast Image En crypcheme B 3D C Baker Maps,” In ternational Journal of Bifurcation and Chaos, Vol. 14, No. 10, 2004, pp. 36133624. tion Sased onhaotic doi:10.1142/S0218 40115112740X 1016/j.asoc.2009.12.011 Copyright © 2011 SciRes. JIS
