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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Random Chaotic Number Generation based Clustered Image Encryption

Fadhil Hanoon Abbood Computer Science Dept.

Education College. Al-Mustansiriyah University

Rana Saad Mohammed Computer Science Dept.

Education College., Al-Mustansiriyah University.

Intisar Abid Yousif Computer Science Dept.

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: 푥 = 푥 + c sin 푦 mod 2π …….(1.a) 푦 = 푦 + 푥 mod 2π ………(1.b)

A modified Standard map as key generation as in equation (2): 푥 = (푎 + (푏 − 푎)(푥 + csin푦 mod2π))푚표푑푎푣… (2.a) 푦 = (푎+ (푏 − 푎)(푦 + 푥 mod2π))푚표푑푎푣 …. (2.b)

A modified Standard map as multiple key generation as in equation (3):

푥 = (푎 +(푏 -푎 )(푥 + k sin 푦 mod 2π))mod 푎푣 … (3.a) 푦 = (푎 +(푏 -푎 )(푦 + 푥 mod 2π))mod 푎푣 … (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).




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




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 푥 and 푦 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 푥 . 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 푥 and 푦 each with size Q. 7. XORing between 1D (A) and round of 푦 values. And then permuted by sorting 푥 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 푥 and 푦 each with size Q’.




3. Inverse the permutation of B’ using 푥 to sort the index (1… Q’). And then XOR the result with round 푦 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 푥 and 푦 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 푥 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

Mea

n Sq

uare

Er

ror

Peak

Sig

nal t

o N

oise

Rat

io

MN

orm

aliz

ed

Cro

ss-

Cor

rela

tion

Ave

rage

D

iffer

ence

Stru

ctur

al

Con

tent

Max

imum

D

iffer

ence

Nor

mal

ized

A

bsol

ute

Erro

r

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




Fig. 6. Sample 2 clusters and its permutations

TABLE 2 MEASUREMENTS RESULT OF SAMPLE 2

Mea

n Sq

uare

Er

ror

Peak

Sig

nal t

o N

oise

Rat

io

MN

orm

aliz

ed

Cro

ss-

Cor

rela

tion

Ave

rage

D

iffer

ence

Stru

ctur

al

Con

tent

Max

imum

D

iffer

ence

Nor

mal

ized

A

bsol

ute

Erro

r

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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