Multi-Image Encryption Technique Based on Permutation …ijens.org/Vol_16_I_01/160801-3939-IJVIPNS-IJENS.pdf · algorithm is encryption of original image by using KSI ... Due to its

International Journal of Video&Image Processing and Network Security IJVIPNS-IJENS Vol:16 No:01 9

160801-3939-IJVIPNS-IJENS February 2016 IJENS

I J E N S

Multi-Image Encryption Technique Based on

Permutation of Chaotic System Noora Shihab Ahmed

Collage of Science, Department of Computer Science,

Halabja University

Halabja, Kurdistan, Iraq

[email protected]

Abstract-- The key stream generator is the key design issue of an encryption system. In this work presents an n-array three key

stream generators (KSI, KSII and KSIII), Based on permutation

of three chaotic maps (Logistic map, Kent map and tent map).

This work reviews of some image encryption algorithm and

finally investigate three methods for image encryption. First

algorithm is encryption of original image by using KSI system.

Second algorithm relies on KSII system to randomly generate

two sequences of numbers by means of selecting proper factors

along with seed value. Afterwards, the randomly produced

numbers are employed to permute the image by means of

shuffling its rows, columns and pixels sequentially in a manner

by which first sequence is utilized to shuffle rows while second

sequence is utilized to shuffle columns. Afterwards masking

process is achieved by means of basic XOR processes between

neighboring rows and columns. This technique employs the

values of the two sequences together to shuffle the pixels. Third

algorithm relies on KSIII system when the same procedures

returned on image encryption. The results shows that the

proposed algorithm has a high security, speed and gives perfect

reconstruction of the decrypted image

Index Term-- Chaotic maps, Image encryption, Key stream generation, Security.

1. INTRODUCTION In the last decays, the very quick evolution in the dispatch of

digitized images through the World Wide Web and wireless

networks came as a sequence to the interesting progress in

network communication and the processing of digital images

as well. Protecting the data of the transmitted images from any

sort of unauthorized access takes the much concern of those

who seek for security systems characterized by being trust

worthy, rapid and robust in order to safe keep and send

important confidential database images like military images,

online personal photo album, medical-purposes images, video

conferenceetc. there are substantial characteristics of digital

images among those, huge information capacity and intense

correlation amongst neighboring pixels. Consequently most

common ciphering techniques such as AES (Advanced

Encryption Standard), IDEA (International Data Encryption

Algorithm), DES (Data Encryption Standard) and so on are

not descent for encrypting digital images in traditional ways

because of the lack of low-level effectiveness when ciphering

images [1].

Chaotic algorithms have proven effectiveness and enhanced

performance in image encryption [2-3]. Chaotic algorithms

possess attributes such as ergodicity, responsiveness to initial

states, pseudo-random action in addition to control factors.

Which are similar to those of cryptography such as diffusion

and confusion as well. Due to its attributes, chaotic systems

have become a prospective selection when establishing

cryptographical systems. In general, any chaotic schema to

encrypt images involves two phases, one for permutation and

another for diffusion. The reason behind permutation

operation is to lessen the correlation among pixels of an

image. In the other hand, the aim of diffusion process is to

alter gray values of a pixel consecutively with diffusion

actions. Therefor a very little alteration for any pixel can

extend to nearly whole pixels all-over the image. A proper

permutation operation should come up with superior shuffling

result. Moreover, a proper diffusion operation should make

significant amendments over the encrypted image no matter

whether being minor alteration for only single pixel in the

encrypted image.

In 1989 Mathews was the first who employed chaotic system

to construct a cryptographical algorithm [4]. The literature has

suggested a large number of schemas to encrypt digital images

based on chaos. The one-dimensional chaotic system in

addition to two-dimensional have emerged amongst those

schemas to encrypt image. The commonly used one-

dimensional and two-dimensional chaotic systems due to

being simple are Arnold map, Logistic map, standard map,

skew tent map and baker map [5-6]. Recently, several image

encryption techniques which are based on chaotic algorithms

show lack of security and are prone to penetration because

their key spaces and not sufficiently large [7-8] to make them

hold out against cipher attack such as brute force attack in

contrast to proper encryption schemas which are very

responsive to cipher keys;

it is necessary that both operations, permutation and diffusion

be characterized with perfect statistical attributes to defeat any

kind of onslaught such as differential cryptanalysis attack,

chosen-plaintext attack (CPA), known-plaintext attack

(KPA)etcetera. To overpower obstacles like little key space

in addition to lack of security in the construction of both

processes, permutation and diffusion in chaotic systems of



I J E N S

both one and two dimensions, numerous efforts have been

made to enhance cryptosystems based on chaos with taking

into consideration larger key spaces in addition to perfect

diffusion methods. Among these efforts, an algorithm

suggested by Behnia et al. aims to improve security known as

of chaotic encryption based on piecewise nonlinear algorithm

[9]. Lately, Zhang et al. suggested a method to encrypt image

on basis of skew tent algorithm and permutation-diffusion

construction [10] in which a P-box is generated with identical

size of the original image besides shuffling whole locations of

pixels in the image. This method utilizes various key streams

based on the original image in the diffusion operation.

Therefore this method achieved better security in terms of

repelling chosen-plan attack (CPA).

Zhu et al. [11] suggested a novel permutation technique

concerning bit-level. This method able to perform image

confusion simultaneously. Later Liu and Wang [12] presented

a novel permutation technique concerning bit-level. This

method able to perform image diffusion and confusion

simultaneously. Later, Liu and Wang [12] enhanced the

schema reviewed in [11] in order to achieve color image

encryption. Changing the bits order of image took the much

interest of the authors. In this method all green, blue and red

color bits of all components are mixed together. During

permutation process, the authors used PWLCM chaotic

algorithm in replacement for Arnold cat algorithm. Additional

enhancements have been made. For instance using hyper

chaotic systems, coupled map lattice systems (CML) and

multiple chaotic systems based image encryption [13-14].

2. DYNAMIC CHAOTIC SYSTEMS

Chaos can be fined as an obvious fact that appears in nonlinear known systems responsive to initial states along

with having pseudo random activity. In condition that chaotic

dynamical systems encounter Lyapunov exponential function

they will continue stabilized in chaos mode. Pseudo random

conduct draw the attention of several cryptographic systems to

this discernible fact. Pseudo random character helps to make

the clear data of a system appear random to attacker sight.

However, it appears observable to the intended recipient and

possibly be decrypted up to now a number of chaos algorithms

which based on cryptography are proposed. Actually many of

them are utilized in one way or another to encrypt image and

text as well. It is necessary for an encryption system to have

proper speed to be able to cipher an image of enormous data.

As a matter of fact it is improper to use text encryption

techniques when encrypting an image. Practically, to transfer a

reasonable amount of data, it demands a wide range sample.

Afterwards this implicates a vast number of keys. As a

consequence, serious management problems would be at keys

delivery stage. Therefore chaotic system came with solutions.

Amongst its pros is the tactic of simplified key management.

For the reason that, this just demand to guard and assure the

security of the private key transmission in which parameters

and initial states of chaotic system are included. The private

key has moderate size. As a consequence, a little memory is

required to keep the private key as well as more insurance is

available during key transmission. Above of that, the

unauthorized access to keys of short length is remarkably less

probable as compared with keys of long length throughout

data transmission over the unsecured medium.

2.1 The Logistic mapping

Logistic mapping is a paradigmatic exemplification of

chaotic mapping. In spite of the fact that logistic mapping is

one dimensional, however the control reaction is quite perfect.

The following equation represents the logistic formula:

( ) (

) ( )

In the equation, an is denoted to the variable, also is a

denotation to system parameter whereas (0,4], an [0,1]. In case that 1 < 3 the system takes the act of 'fixed point'. If

= 3 the system startes the transmission phase. When =

3.5699456, the system undertakes a chaotic condition. In case

= 3.9 the starting value of an is 0.6. In logistic mapping

extent, repeating the process for 200 times with chaotic

ordered collection (sequence values) comes up with the

products shown in figure 1.

Fig. 1. Iterative Sequence Value of Logistic Mapping

2.2 Kent mapping

Another type of logistic mapping is Kent mapping. This

map is characterized by short-term anticipated and long-term

unexpected, meanwhile Kent map is very responsive to initial

state. The formula bellow shows Kent equation.

{

( ) ( ) ( )



I J E N S

Where bn is denoted to the variable, also a is a denotation to

system parameter whereas (0,4], bn [0,1]. In case that a =

0.6 , the starting value of bn is 0.6. In logistic mapping extent,

repeating the process for 200 times with chaotic ordered

collection (sequence values) comes up with the products

shown in figure 2.

Fig. 2. Iterative Sequence Value of Kent Mapping

2.3 The tent map

Mathematically, the tent map is real-valued formula based on

parameter, and is denoted be f. Tent map equation can be

expressed by:

{ }

The reason behind its naming is the likeness of its graph to

tent shape. By setting the parameter with values from 0 up

to 2, f charts the

( ) {

( )

(3)

Where is a positive real invariable (constant). Setting for

example the parameter =2, the outcome of the function f is

possibly be discernible as the product of the process of

bending the unit duration in twin, thereafter extending the

product duration [0,1/2] to get back the duration [0,1].

Repeating the process, each point proposes the new upcoming

locations as mentioned above, making a sequence cn.

The =2 state of tent mapping is a non-linear transmission of

bit shift mapping and state r=4 of logistic mapping as well.

Fig. 3. Orbits of unit-height tent map



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3. THE PROPOSED ALGORITHM

The proposed multi-image encryption algorithm consists of

two stages iterative (multi-level) block permutation and

nonlinear keystream chipper

3.1 The Proposed Non Linear keystream

In the first stage, stream cipher based on permutation

chaotic maps process was depended. Three kinds of generators

processes called keystream I (KSI), keystream II (KSII)

and keystream III (KSIII) are used in proposed system in

shown in the figure 5 and its equivalent description is as

follows:

Step 1

In this step we show a method in construct a system

depending on three chaotic maps: Logistic map (eq1), Kent

map (eq2), and Tent map (eq3). The system producing m-

sequences ai , bi , and ci , keystream bit xi is generated using

the Boolean function

xi = (ai . bi) + (bi . ci)

This means that xi = ai if bi = 1, xi = ci otherwise, For an

illustration of the system, see figure 4

Fig. 4. Chaotic system

Step 2 We take the permutations of chaotic maps for building the

systems KSI, KSII, and KSIII

(a) KSI System



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(b) KSII System

(c) KSIII System

Fig. 5. (a) KSI System (b) KSII System (c) KSIII System



I J E N S

3.2 Encryption process

The proposed multi-image encryption algorithm can be

summarized in the following steps:

Step 1 Image Encryption Using KSII system

This technique relies on KSII system to randomly generate

two sequences of numbers by means of selecting proper

factors along with seed value. Afterwards, the randomly

produced numbers are employed to permute the image by

means of shuffling its rows, columns and pixels sequentially

in a manner by which first sequence is utilized to shuffle rows

while second sequence is utilized to shuffle columns.

Afterwards masking process is achieved by means of basic

XOR processes between neighboring rows and columns. This

technique employs the values of the two sequences together to

shuffle the pixels. The overall procedure can be expressed by

the following formula:

Cimg = Epixel (Ecolumn (Erow (plainim)))

Whereas: Erow is denoted to encryption as a consequence to

shuffle and mask the rows. Whilst Ecolumn refers to

encryption resulted from column shuffling and masking.

Epixel is denoted to the encryption of shuffling the pixels.

Step 2 Image Encryption Using KSIII system.

This technique relies on KSIII system to randomly generate

two sequences of numbers. One of the sequences is utilized to

shuffle row while the other is utilized to shuffle column. Same

as illustrated in technique step 1, pixel shuffling is achieved

by employing the two sequences. After accomplishment of

row and column shuffle process, masking procedure is

achieved by doing basic XOR processes between neighboring

rows and columns. The overall process can be expressed by

the following formula:

Cimg = Epixel (Ecolumn (Erow (plainim)))

Whereas: Erow is denoted to encryption as a consequence to

shuffle the rows in addition to masking. Whilst Ecolumn

refers to encryption resulted from column shuffling and

masking. Epixel is denoted to the encryption of shuffling the

pixels.

Flowchart of multi-image encryption algorithm is shows in

figure 6

Fig. 6. multi-image encryption process



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4. EXPERIMENTAL RESULTS AND SECURITY ANALYSIS

Simulation results and performance analysis of the proposed

multi-image encryption scheme as provided in this section.

The original image Lina_color is shown below in part (a) of

figure 7. This RGB image is encrypted by our proposed

algorithm. The encrypted result of proposed algorithm is

shown in the part (b) of figure given below. The encryption is

done using KSI. Part (c) of the figure is the output of reverse

encryption using KSII. Part (d) in the same figure encrypted

using KSIII

(a) (b) (c) (d)

Fig. 7 (a). Original image of picture Lina_color (b) Encrypted image by KSI system (c) Encrypted image by using KSII system (d) Encrypted image by using

KSIII system

Figure 8(a) Original image and 8(b) shows histogram of original image, 8(c) shows encryption image using the proposed KSII

system, 8(d) shows the histogram of encryption image, 8(e) shows the Multi-image encryption using KSIII and 8(f) shows

histogram of the Multi-image encryption.

(a) (b) (c) (d)

(e) (f)

Fig. 8. (a) Original image of picture (b) Histogram of original image (c) encryption image using KSII system (d) Histogram of encryption image using KSII

system (e) encryption image using KSIII system (f) Histogram of encryption image using KSIII system

From analysis of figure 8, it is clearly reflected that histogram

of original image, encrypted image and Multi-encryption

image are entirely different. Statistical analysis of histogram

cannot give any information about original image.

Entropy Analysis

The entropy H of a symbol source S can be calculated by

following equation.

Where p(si) represents the probability of symbol si and the

entropy is expressed in bits. If the source S emits 28 symbols

with equal probability, i.e. S = { s1, s2, . . . , s256}, then the

result of entropy is H(S) = 8, which corresponds to a true

random source and represents the ideal value of entropy for

message source S. Information entropy of an encrypted image

can show the distribution of color value.



I J E N S

Table I

Entropy of original image and image encryption

Original

image

Level One

Encryption

Level Two

Encryption

Mulita level

encrypted image

Using KSI Using KSII

Using KSIII Row Column

Entropy 7.2718 7.2712 7.2596 7.29159 7.2915

Correlation

Table 2 shows the correlation coefficient in the horizontal direction and vertical direction to Level 1, Level 2 and Level 3 image

encryption after testing by Visual Basic. The experimental results show that the correlation of neighboring points are very small.

At the same time the chart of the pixels correlation of plaintext and cipher text plaintext shows, encryption adjacent pixel gray has

no relevance after encryption. The secrecy of cipher text is very good.

Table II

Correlation coefficient of Multi-Image Encryption

Level One

Encryption Level Two Encryption

Mulita level

Encryption

Using KSI Using KSII

Using KSIII Row Column

Vertical 0.9637 0.8795 0.8761 0.8389

Horizontal 0.9735 0.9882 0.8921 0.8604

Fig. 9. Correlations of Adjacent Pixels in (a) the Plain Image; (b) the one level image encryption.

0

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050100150200250

0

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0100200300

Pix

el g

ray

valu

e lo

cati

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(x+1

,y)

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el g

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,y)

a. Pixel gray value location(x,y) b. Pixel gray value location(x,y)



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Fig. 10. Correlations of Adjacent Pixels in (a) the second level encryption (Row); (b) the second level encryption (Column)

Fig. 11. Correlations of Adjacent Pixels of the third level encryption.

5. CONCLUSION

In this work, a multi-image encryption scheme based on

permutation at chaotic maps is proposed. The chaotic

systems principle has a large key space and its

implementation is quite simple. The algorithm is based on

the concept of shuffling the pixels in the image. The

experiments results and analysis show that the proposed

multi-image encryption system has a very large key space,

high sensitivity to secret keys has low correlation

coefficients close to ideal value 0, good entropy value.

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[3] Chen, G. R., Mao, Y. B., Chui, C. K., A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos,

Solitons & Fractals, 2004, 21: 749-761.

[4] Matthews, R., On the derivation of a chaotic encryption algorithm, Cryptologia, 1989, 8: 29-41.

[5] Guan, Z.-H., Huang, F., Guan, W., Chaos-based image encryption algorithm, Physics Letters A, 2005, 346: 153-157.

[6] Kocarev, L., Chaos-based cryptography: a brief overview, IEEE Circuits and Systems Magazine, 2001, 1: 6-21.

[7] Li, S., Zheng, X., Cryptanalysis of a chaotic image encryption method, in: Proc. IEEE Int. Symposium on Circuits and

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0

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0501001502002503000

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100

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050100150200250

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100

150

200

250

300

050100150200250300

Pix

el g

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valu

e lo

cati

on

(x,y

+1)

Pix

el g

ray

valu

e lo

cati

on

(x,y

+1)

a. Pixel gray value location(x,y) b. Pixel gray value location(x,y)

Pix

el g

ray

valu

e lo

cati

on

(x+1

,y+

1)

Pixel gray value location(x,y)



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[9] Behnia, S., Akhshani, A., Ahadpour, S., Mahmodi H., Akhavan A., A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps, Physics Letters A, 2007, 366: 391-396.

[10] Zhang, G. J., Liu, Q., A novel image encryption method based on total shuffling scheme. Opt. Commun. 2011, 284: 2775-2780.

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[14] Ye, R., Zhou W., A Chaos-based Image Encryption Scheme Using 3D Skew Tent Map and Coupled Map Lattice, I. J.

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