New Approach for Fast Color Image Encryption Using Chaotic Map

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. However , permutation and diffusion are considered as two separate stages, both requiring image-scanning to obtain 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 computer 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 minimizes the possibility of brute force attack for decryption and very fast for practical image encryption


Introduction
With the fast development of image transmission through computer networks especially the Internet, medical imaging and military message communication, the security of digital images has become a most important concern.Image encryption, is urgently needed but it is a challenging task because it is quite different from text encryption due to some intrinsic properties of images such as huge data capacity and high redundancy, which are generally difficult to handle by using conventional techniques.Nevertheless, many new image encryption schemes have been suggested in current years, among which the chaos-based approach appears to be a hopeful direction.
General permutation-diffusion architecture for chaosbased image encryption was employed in [1,2] as illustrated 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 one-pixel spreads out to as many pix-els as possible.Permutation and diffusion are two different and iterative stages, and they both require scanning the image in order to gain the pixel values.Thus, in the encryption process, each round of the permutationdiffusion 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 Cat map and standard map.Finally the Image is encrypted by performing XOR operation on the shuffled image and diffusion template.The objectives of this new design includes: 1) to efficiently extract good pseudorandom sequences from a cascading of 3D cat and standard map for color image and 2) to simultaneously perform permutation and diffusion operations for fast encryption.
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 performance analyses.In Section 5, conclusions and future work.

Efficient Generation of Pseudorandom Sequences
The generation of pseudorandom is based on two cascaded 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 generated by this method is given below.(The explanation for pseudorandom sequences generation is given in Section 3).

Proposed Algorithm
The proposed algorithm are divided into several stages and explained below.

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 where 1) form the matrix with all rows filled with linearly spaced number in between 0 to 255.The sequence is randomized by 3D standard map in discrete form as given below.
The 3D standard map randomizes the pixels by reallocating it in new position by utilizing its property of one to one mapping.Figure 2 shows the final diffusion template by using 3D standard map.

 mod
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.

Image Encryption
Step 1.The main image is divided into three separate images I R , I G and I B as follows Step 2. The Red and Green image are transform verti- cally and hori lue image re-zontally respectively.The b mains same and reconstructs the new image.

 
Step integer > 0 and r x , r y are offset integer such that 0 ≤ r x ≤ m, 0 ≤ r y ≤ 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 performed by following equations.
 

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 encryption 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 D x D y D z = 8 + + 2 = 18 bits.
Step 4 Step 5. Sliced RGB plane offset values S x S y = 8 bi Step 6. Sliced RGB Plane Variables S p S q = 8 + 8 = 16 ts.

Ste
Step 8. Confusion offset of cat map C x C y C z = = 18 bits.
Final key st Step 2. Re-transfor scaded 3D maps firstly by standard map then by cat map.
So th is performed by following equations Copyright © 2011 SciRes.JIS Figuer 3. Image encryption by using confusion and diffusion.
Each confusion step is followed by diffusion obtained by EXOR operations performed between each pixels of I retrnsf and diffusion Step 3. Performing inverse of First level confusion.
for each value of i, j changed from 0 to m, k changed from 0 to 3.
De-shuffling the sliced plane where j′ and k′ are obtained by 2D cat map given below m n where p and q are integers > 0, and r x , r y are offset integers such that 0 ≤ r x ≤ m and 0 ≤ r y ≤ n.
Recombining the planes for forming 3D matrix for next operation Step 4. Re-rotating the image planes Dividing main image into three separate images I R , I G and I B as follows Scrolling the green plane horizontally Blue plane remain intact.

  
, , Step 5. Next recombination of planes are performed to form final decrypted image

Key Space Analysis
The strong point of the proposed algorithm is the generation of the permutation sequence with the chaos sequence.The key space should also be suitably large to make brute-force 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 sequence.It has been almost impossible to decrypt the image.

Statistical Analysis
It is well known that passing the statistical analysis on cipher-text 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 Statistical tests are performed.

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 performed.
An example is shown in  arance.So, the surveyed algorithms do not provide any clue for sta is om plain-image histogram.

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 selected 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- Copyright © 2011 SciRes.JIS  tween original and cipher image is calculate in Table 6.

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 brute-force attack infeasible.The key space size for initial conditions and control parameters is over than 2 148 .Apparently, the key space is sufficient for reliable practical use.

Differential Analysis
In general, a desirable characteristic for an encrypted image is being sensitive to the little changes in plainimage (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 plain-image can Copyright © 2011 SciRes.JIS cause a significant change in the cipher-image, with respect 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 Absolute Error (MAE).The bigger the MAE value, the better the encryption security.NPCR means the Number of Pixels Change Rate of encrypted image while one pixel of plain-image is changed.UACI which is the Unified Average Changing Intensity, measures the average intensity of the differences between the plain-image 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 plainimage, respectively.The MAE between these two images is defined in . er two cipher-images, C1 and C2, wh Consid ose corresponding plain-images have only one pixel difference.
The NPCR of these two images is defined in where W and H are the width and height of the image and D(i, j) is defined as


Another measure, UACI, is defined by the following formula: Tests have been performed on the encryption schemes on a 256-level color image of size 256 × 256 shown in Figures 5(a)-(f).The MAE, NPCR and UACI experiment 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%.Acation result, the rate influnce 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.

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 where M is the total number of symbols m i ∈ m; p(m i ) 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 cipher-images are close to a random source and the proposed algorithm is secure against the entropy attack.The test result on different image for different round is defined in Table 7.

Speed Analysis
cesses.In general, encryption 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 difficulty, in order to show the effectiveness of the proposed image encryption scheme over existing algorithms.We    evaluated the performance of encryption schemes with an un-optimized 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 different round is shown in Tables 8 and 9.

FIPS 140 Testing
We also s r proposed algorithm pass the FIPS  We need to change the testing algorithm to suit to image 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 accepow 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 encr the shuffled im ut, both confirming that the new cipher st tance ranges.Bifurcation and Chaos, Vol. 14, No. 10, 2004, pp. 3613-3624
Generate the diffusion template in same way as mation of location is done by two ca e re-transformation of location (i″, j″, k″) into (i, j, k) integers >0.Each confusio EXOR operations performed between each pixels of I conf and diffusion I diff .The proposed image encryption architecture is given in Figure 3.

Figure 5 .
In Figure 5 shows histogram analysis on test image using proposed algorithm.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 uniform distribution which is significantly different from original image and has no statistical similarity in ap- Figure 4. (a) Input image encrypted with 0304002030402 030101 with

Figure 5 .
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 encrypted image for R = 16; (f) Histogram for red, green and blue plane of encrypted image for R = 32.