Random Chaotic Number Generation based Clustered Image Encryption

International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2763
Issue 03, Volume 3 (March 2016) www.ijirae.com
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IJIRAE: Impact Factor Value – SJIF: Innospace, Morocco (2015): 3.361 | PIF: 2.469 | Jour Info: 4.085 |
Index Copernicus 2014 = 6.57
© 2014- 16, IJIRAE- All Rights Reserved Page -103
Random Chaotic Number Generation based Clustered Image
Encryption
Fadhil Hanoon Abbood
Computer Science Dept.
Education College.
Al-Mustansiriyah University
Rana Saad Mohammed
Education College.,
Al-Mustansiriyah University.
Intisar Abid Yousif
Education College.,
Al-Mustansiriyah University.
Abstract— Image encryption process is one of secure communication techniques to get confidentiality and authority
of reading data. Encryption techniques should be improved with technological progress to overcome the security
problems like the existence of penetration of the network. This paper develop an image encryption technique by
encrypt the clusters of image using the generated keys from propose a modified of standard map. In decryption
process, a recover image can be obtained by reverse the encryption process and utilize adding instead of clustering.
Exploratory results check and demonstrate that the proposed procedure is secure and quick.
Keywords— Image encryption, decryption, cluster, standard map.
I. INTRODUCTION
Image data must be remain protected with the rapid growth of information technology from illegal users over unsecured
channels of network. Image security is an application layer to get a safely transfer of the image data. Traditional
cryptosystems have a long time to encrypt the image data since the size of image is larger than text size. The main
methods to protect a data from unauthorized users are cryptography, steganography, and watermarking. Cryptography is
one of the main tools to provide security. It deals with the improvement of techniques for converting data forms between
intelligible and unintelligible. There are two main techniques of cryptography: private key cryptography and public key
cryptography. In the private key technique, the sender and receiver use a same secret key for encryption and decryption
processes. In the public key technique, they use different keys for encryption and decryption processes [1].
The existing algorithms can be divided into three categories: Permutation of position [2,3], transformation of value
[4,5], and the combination form [6,7]. An image encryption and compression using prediction error clustering technique
is study in [8,9].
This paper focuses on the improvement of private key image encryption algorithm. The proposed algorithm based on
preprocessing process that give clusters of image and modify a standard map. The organization of this paper is as follows:
proposed image encryption and decryption technique in the first section, Experimental analysis in the second section, and
conclusion in the third section.
II. PROPOSED IMAGE ENCRYPTION AND DECRYPTION TECHNIQUE
Fig. (1) and (2) show a block diagram of encryption and decryption respectively. A technique of image encryption is
based on image clustering as preprocessing and random standard map. A standard map in equation (1) is modified into
two sub equations to generate a series of keys as a tool for image clusters encryption using a technique in [10]. Standard
map can be as follow equations:
= + c sin mod 2π …….(1.a)
= + mod 2π ………(1.b)
A modified Standard map as key generation as in equation (2):
= ( + ( − )( + c sin mod 2π)) … (2.a)
= ( + ( − )( + mod 2π)) …. (2.b)
A modified Standard map as multiple key generation as in equation (3):
= ( +( - )( + k sin mod 2π))mod … (3.a)
= ( +( - )( + mod 2π))mod … (3.b)
Where i is number of clusters.
By using a test for random dynamics was proposed by Saida in [11] that use a Lambda measurement which is the
dominant Lyapunov Exponent. A Lambda of proposed equation is decreased that indicate increased the presence of
random dynamics compared with equation (1).

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Image decryption technique uses reverse processes of image encryption and use adding process to recover an image.
Fig 1. Proposed image encryption block diagram
Fig. 2. Proposed image decryption block diagram
This paper takes “baboon image” and “peppers image” samples as example. See fig. (3) and (4) respectively.
fig. 3. Sample 1 and its histograms

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fig. 4. Sample 2 and its histograms
In the following sections show the steps of proposed technique:
 Preprocessing step
Input: An original color image with size n x n x 3.
Output: Clusters of image each with size qxqx3.
1. Read a color image with size n x n x 3 (e.g. 256x256x3).
2. Split the original image into (m) clusters (e.g. 5 clusters). See fig. (5).
 Encryption algorithm
Input: Clusters of image each with size qxqx3.
Key agreement: n, a, b, k
Output: An encryption image with size qxqx3.
1. Convert each cluster into 1D with size L such that L=n*n*3 (e.g L=256*256*3=196608).
2. Use proposed multiple key generations as eq. (3) to generate and each with size L and where i
=1…m and (e.g a=10, b=50, k=10).
3. Permute the color positions of each cluster by sorting the generated random series .
4. Concatenate these permuted clusters to get 1D array (A) with size P such that P= L * m (e.g. 196608 * 5=
983040).
5. Suppose j= 2,…, m and check if j*j = m , then compute q= n*j. Else if j*j > m , then
 Compute q= n*j (e.g. q= 256*3=768).
 Padding (A) with zero to get a new 1D array with size Q such that Q=q*q*3(e.g.Q=768*768*3=1769472).
6. Use proposed key generation as eq. (2) to generate and each with size Q.
7. XORing between 1D (A) and round of values. And then permuted by sorting to get a new 1D array (B)
with size Q.
8. Convert 1D array (B) into 2D array as encryption image with size qxqx3 (e.g 768x768x3).
 Decryption Algorithm
Input: An encryption image with size qxqx3.
Key agreement: n, a, b, k
Output: A recover color image with size n x n x 3.
1. Convert 2D encryption image into 1D (B’) with size Q’ such that Q’=q*q*3(e.g. Q’=768*768*3=1769472).
2. Use proposed key generation as eq. (2) to generate and each with size Q’.

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3. Inverse the permutation of B’ using to sort the index (1… Q’). And then XOR the result with round to
get a recover 1D array (A’) with size Q’.
4. Compute m’ such that (m’= Q’/ (n*n*3)) is number of clusters as 1D array each with size L’ such that (L’=Q’/
m’). e.g. m’= 1769472/(256*256*3)= 9 and L’= 1769472/9=196608.
5. Use multiple key generations as eq. (3) to generate and each with size L’ and where i=1…m’. And the
secret parameters a, b, and k must are similar to a parameters at the sender side (e.g a=10, b=50, k=10).
6. Inverse the permutation of each 1D array of recover cluster using to sort the index (1… L’).
7. Reshape each 1D array of a sorted recover cluster into 2D each with size nxnx3 (e.g. 256x256x3).
8. Adding between these recover 2D of clusters to get a recover image with size nxnx3.
IV. EXPERIMENTAL ANALYSIS
This paper uses 7 analysis measurements between clusters and its permutation, and also between original image and its
recover. Tables (1) and (2) show the experimental results of sample 1 and sample 2 respectively.
Fig. 5. Sample 1 clusters and its permutations
TABLE 1
MEASUREMENTS RESULT OF SAMPLE 1
MeanSquare
Error
PeakSignalto
NoiseRatio
MNormalized
Cross-
Correlation
Average
Difference
Structural
Content
Maximum
Difference
Normalized
AbsoluteError
Cluster0
&PCluster0
6.6607e+03 9.8956 0.2167 1.6202 1.8719 235 1.5203
Cluster1
&PCluster1
4.1651e+03 11.9346 0.2743 -
19.4314
0.6393 181 2.6720
Cluster2
&PCluster2
3.6135e+03 12.5515 0.2504 1.4649 1.8150 151 1.4471
Cluster3
&PCluster3
7.4634e+03 9.4014 0.1959 -0.8359 1.6779 240 1.6318
Cluster4
&PCluster4
963.8319 18.2908 0.1666 0.5398 1.9772 103 1.6081
Original &
Recover
0.8894 48.6397 1.0001 -0.0081 0.9998 0 6.2969e-05

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Fig. 6. Sample 2 clusters and its permutations
TABLE 2
MEASUREMENTS RESULT OF SAMPLE 2
MeanSquare
Error
PeakSignalto
NoiseRatio
MNormalized
Cross-
Correlation
Average
Difference
Structural
Content
Maximum
Difference
Normalized
Absolute
Error
Cluster0
&PCluster0
2.7507e+03 13.7364 0.1064 2.4257 2.4321 181 1.6443
Cluster1
&PCluster1
1.1246e+03 17.6210 0.0775 0.8819 2.2604 204 1.7413
Cluster2
&PCluster2
3.9018e+03 12.2181 0.0671 0.5641 2.1928 236 1.8264
Cluster3
&PCluster3
110.0240 27.7159 0.0824 -0.1556 0.8806 204 1.9268
Cluster4
&PCluster4
631.7205 20.1256 0.1021 -0.3624 1.1012 204 1.8759
Cluster5
&PCluster5
4.4143e+03 11.6822 0.1295 3.1517 2.3559 204 1.6076
Cluster6
&PCluster6
5.8999e+03 10.4224 0.1349 3.6626 2.2995 211 1.5987
Cluster7
&PCluster7
2.7339e+03 13.7629 0.2209 -0.5712 1.1938 204 1.6245
Original &
Recover
2.1904 44.7256 1.0001 -0.0220 0.9996 0 1.8350e-04
In the following Table (4) show an encryption and decryption speed results of Sample 1 and Sample2 respectively
using processor Intel(R) Core(TM) i7-3537U CPU @ 2.00GHz 2.50 GHz.
TABLE 4
ENCRYPTION AND DECRYPTION SPEED RESULTS OF SAMPLE 1 & SAMPLE2
Sample 1
No. cluster= 5
Sample 2
No. cluster= 8
Encryption
speed
3.3978 Sec. 3.9046 Sec.
Decryption
speed
4.2337 Sec. 4.2020 Sec.
V. CONCLUSIONS
A proposed system is used to design a technique of image encryption based on image clustering as preprocessing and
random standard map. From experimental results show the proposed method has encryption speed and secure. It gives a
different size of encrypted image compared with original image size. This cause confuses the attacker who tries getting
information about an original image. Decryption process has adding process at last step rather than re-clustering
technique. From this point the receiver cannot decrypt image unless he knows the right series of key for each image
cluster to recover an original image.

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REFERENCES
[1]. N. K. Pareek. “Design and Analysis of A Novel Digital Image Encryption”. International Journal of Network
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Communication in Nonlinear Science and Numerical Simulation, Vol. 15, No. 12, 2010. pp. 3998-4006.
[3].C. K. Nayak, A. K. Acharya and S. Das, “Image encryption using an enhanced block based transformation algorithm”,
International Journal of Research and Review in Computer Science, Vol. 2, No. 2, (2011) . pp. 275-279.
[4].I. A. Ismail, M. Amin and H. Diab, “A digital image encryption algorithm based a composition of two chaotic logistic
map”, International Journal of Network Security, Vol. 11, No. 1, (2010) , pp. 1-10.
[5].D. Chen and Y. Chang, “A novel image encryption algorithm based on logistic maps”, Advances in Information
Science and Service Sciences, Vol. 3, No. 7, (2011) .pp. 364-372.
[6].S. P. Indrakanti and P.S. Avadhani, “Permutation based image encryption technique”, International Journal of
Computer Applications, Vol. 28, No. 8, (2011) . pp. 45-47.
[7].V. Patidar, N.K. Pareek, G. Purohit and K.K. Sud, “A robust and secure chaotic standard map based pseudorandom
permutation-substitution scheme for image encryption”, Optics Communications, Vol. 284, (2011). pp. 4331-4339.
[8]. J. Zhou, X. Liu, O. C. Au, and Y. Y. Tang, “Designing an Efficient Image Encryption-Then-Compression System via
Prediction Error Clustering and Random Permutation”. IEEE transactions on information forensics and security, vol.
9, no. 1, January 2014, pp. 39-50.
[9]. H. P. Kaur, R. Kaur, “REVIEW: Improve Image Encryption-Then-Compression System using Prediction Error
Clustering with HAAR Wavelet Transform”, International Journal of Research Development & Innovation (IJRDI).
Vol. 1, Issue 6, August 2015, pp. 254-257.
[10]. S. B. Sadkhan and R. S. Mohammed, “Proposed random unified chaotic map as PRBG for voice encryption in
wireless communication”, Procedia Computer Science journal (2015) ELSEVIER pp. 314-323.
[11]. A. BenSa¨ıda, “A practical test for noisy chaotic dynamics”, ELSEVIER, 2015.

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