Color Image Encryption and Decryption Using Multiple Chaotic Maps

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY
VOLUME 5 ISSUE 2 – MAY 2015 - ISSN: 2349 - 9303
27
Color Image Encryption and Decryption Using
Multiple Chaotic Maps
V.Kumar1
1
P.A College of Engineering and Technology
Computer Science and Engineering
kumarpride@gmail.com
M.Yuvaraja2
2
P.A college of Engineering and Technology
Electronics and Communication Engineering
yuvarajmuthusamy@gmail.com
Abstract— Owing to advances in communication technology, a bulk of visual digital data is being stored and transmitted over the
internet now-a-days. Particularly millions and millions of images transfer through the network per day as per the statistics and a
result, the security of image data is an important requirement. Image encryption algorithm is used to provide this security. In this
paper, an image encryption algorithm based on confusion diffusion architecture that uses dynamic key space is proposed. An
internal key generator is used to generate the initial seeds for the overall encryption scheme is proposed. With these initial seeds
logistic map generates pseudo random numbers then these numbers are converted into permutation order for permutation. The
diffusion bits are generated in parallel using the logistic map and manipulated with pixels confused. The image pixels are
iteratively confused and diffused using permutation order and diffusion bits respectively to produce cipher image in minimum
number of rounds. This paper proposes a new kind of initial seed generation that utilizes the combo of logistic and tent maps. Even
all external seeds are same. The internal seeds will be totally different. This ensures the key sensitivity. The simulation results and
analysis confirm that the satisfactory level of security is achieved in three rounds and overall encryption time is saved.
Index Terms— Confusion Order, permutation, Diffusion, Logistic maps, tent maps
——————————  ——————————
1 INTRODUCTION
. The network technology and multimedia technology
have more advanced in development digital images are used
more widely in day to day activities. The security of the digital
images has been taken as a greater effort in protection due to the
access on the internet. In order to protect the image the
confidentiality of images encryption is necessary. The traditional
cryptographic tools such as Data Encryption Standard (DES),
Advanced Encryption Standard (AES) are used in encryption, but
they are not suitable for encrypting digital images without any
modification because of a size that is larger than that of the text.
These methods require a great deal of computation time.
The various form of cryptography has their own
approaches but the main goal of data hiding is to conceal the
hidden data by the carrier media is to transfer data without
drawing suspicion. These hiding algorithm are to maintain the
natural appearance on the data or image by keeping uninvolved
from thinking the information exists. The random number
generators have proven invaluable in simulating natural
phenomena and in sampling data. The copying a digital data is
very easy and fast too so, issues like, protection of the content
and misuse of the same, arise. Image encryption came as a
technique and a tool to overcome shortcomings of current
secured transmission of digital data. Many encryption methods
have been proposed in literature, the most common used to
protect large multimedia file is by using conventional encryption
techniques. Some of the popular techniques are DES, and AES.
Implementation of these algorithms cannot provide suitable
encryption rates while security of these algorithms relies on the
difficulty of quickly factorizing large numbers or solving the
discrete logarithm problem, topics are seriously challenged by
recent advances in number theory and distributed computing.
The encryption technique used in this paper is not a
conventional one. Chaotic cryptographic scheme is a private
encryption scheme, used here to encrypt the image. Chaotic map
presents desired cryptographic qualities such as simplicity of
implementation leads to higher encryption rates and excellent
security. In this work two maps are used to encrypt the image,
maps used are standard logistic map and tent map. The
parameters of these two maps are used as a key for encryption.
2. REQUIREMENTS OF MULTIMEDIA ENCRYPTION
Due to special characteristics of multimedia data, such as
large data volumes, high redundancy, interactive operations, and
requires real-time responses, sometimes multimedia applications
have their own requirements like security, invariance of
compression ratio, format compliance, transmission error tolerance.
For multimedia encryption, security is the requirement, thus the
usage of chaotic maps should guarantee the security of a
multimedia datum. Generally speaking, an encryption algorithm is
regarded as secure the cost for cracking is no smaller than the One
paid for the authorization of video content. For example, in
broadcasting, the news may be of no value after an hour. Thus, the
attacker cannot break the encryption algorithm during an hour, and
then the encryption algorithm may be regarded as secure in this
application Saikai et al (2014). Security of an encryption usually
consists of perceptual security, key space, key sensitivity, and the
ability against potential attacks.

28
3. GENERAL CHAOTIC SYSTEM
An important step in any digital chaotic encryption is the
selection of the map. Chaotic maps have different behavior regarding
complexity, chaotic cycle length, chaotic interval, periodic windows,
sensitivity to initial conditions and reaction to trajectory
perturbations, influence the structure or behavior of the chaotic
encryption system. In fact, some systems have been broken for not
considering the weaknesses of the chosen chaotic map and
efficiency; is desirable to provide some independency between the
cryptosystem and the chaotic map under consideration.
The encryption algorithms based on chaos offer the
advantages to be very sensitive to the initial conditions, periodicity,
randomness and simplicity. Chaotic encryption systems generally
have high speed with low cost, makes them better candidate than
conventional methods for multimedia data encryption.
The architecture of substitution diffusion type chaos image
cryptosystems is shown in Figure1. There are two stage are repeated
for n and m times. In the substitution stage the pixels are permuted is
the spatial correlation between the pixels are broken by permutation
method. In the diffusion stage the value of each pixel is changed by
adding and shifting operations. In a m rounds are performed together
with the permutation. The existing system is a modified version of
the Ravisankar et al (2006) cryptosystem.
The whole substitution-diffusion round repeats for a
number of times to achieve a satisfactory level of security, the
parameter of the chaotic maps governing the permutation and
diffusion should better be distinct in different rounds. This is
achieved around key generator with a seed secret key is input. In
this cryptosystem, the substitution process is realized by solely by
permuting gall pixels by an invertible discredited 2D standard map,
without mixing their values. As the corner pixels is not permuted at
all under the standard map, a random scan couple (rx,ry) is included
to permute this corner this pixel together with other pixels. The
modified standard map equations are given by equation (1) and (2).
Xk+1=(xk+yk+rx+ry)modN (1)
Yk+1=(yk+ry+Kcsin2xk+1/N)modN (2)
(xk,yk) and (xk+1,yk+1) is the original and permuted pixel
position of an N*N image, respectively. The standard map parameter
KC is a positive integer.
In the diffusion stage, each pixel of the 2D permuted
image is scanned sequentially; usually start form the upper left
corner. The diffusion effect in this stage is achieved by the following
equation (3) and (4). In vi the value of the ith
pixel of the permuted
image, ci-1 and ci is the value of the (i-1) th
and the ith
pixel of the
image, respectively. The seed of the diffusion function is c is
obtained from the diffusion key Kd. The nonlinear function f(ci-1) is
the logistic map is given by
equation (3).
f(ci-1)=4ci-1(1-ci-1) (3)
The quantization function q (ci-1) takes the L bits just after
the decimal points, as defined by equation (4).
q(X,L)=2L
X (4)
X=0 b1b2b3…bl.. is the binary representation of X and bi is
either 0 or 1
The new pixel value obtained by exclusive –OR (XOR) the
current pixel value vi of the permuted image with an L-bit sequence
from the logistic map taking the previous diffused pixel value ci-1 as
input. As the previous diffused pixel will affect the current one, a
tiny change in the plain image is reflected in more than one pixel in
the cipher image and so the diffusion effect is introduced in this
stage.
4. PROPOSED SCHEME FOR ENCRYPTION
The proposed schema is a modification of the one suggested
by Ravisankar et al (2006). In their cryptosystem, an explicit
diffusion function based on a logic map is used to spread out the
influence of single plain image pixels over many cipher image
elements. Although the diffusion function is executed at a fairly high
rate, it is still the higher cost, in terms computational time, of the
whole cryptosystem
The encryption speed can be accelerated substantially
fewer diffusion rounds are required. The diffusion effect is
downgrade we simply reduce the number of diffusion rounds and
keep other parts unchanged. A better way is to introduce certain
diffusion effect in the permutation stage as well. The architecture of
the proposed method is shown in Figure 1. In the permutation stage
both the permutation on pixel position and the change of are carried
out at the same time while the diffusion process remains unchanged.
As a result, the pixel value of that mixing effect of the whole
cryptosystem is contributed by two levels of diffusion operation.
The modified permutation process and the original
diffusion function. As the diffusion effect is not solely contributed
by the diffusion function, the same level of security is achieved in
fewer cipher rounds. Thus the encryption speed is that accelerated.
In this modified permutation stage, the new position of a
pixels is calculated according to equation below. Before performing
the pixel relocation, diffusion effect is injected by adding the current
pixels value of the plain image to the previous permutated and then
performs a cyclic shift. Other simple logical operation such as XOR
can be used instead of the addition operation. Simulation results
found the add and then shift combination leads to the best
performance and so it becomes the choice in our cryptosystem. The
new pixel value is then given by equation (5).

29
Figure 1 Proposed Encryption Structure
Vi=cyc[(pi+vi-1)modL,LSB3(vi-1)] (5)
pi is the current pixel value of the plain image, L is the total
number of grey levels of the image,vi-1 is the value of the (i-1) th
pixel after permutation, Cycle [s, q] is the q-bit right cyclic shift on
the binary sequences s, LSB3(s) refers to the value of the least three
significant bits of s, vi is the resultant pixel value in the permutated
image. Similar to the effect of using higher-dimensional chaotic
maps for image encryption, this modification makes the histogram of
confused image uniform in a few rounds. Take a 256*256 white
square image as an example of homogenous image.
The existing cryptosystem gives noisy cipher image and a
uniform histogram in only three permutation rounds. By the property
of pixels value mixing, the value of every single pixel is diffused
over the image. It is regarded as the first level diffusion of the
proposed system.
A key generator is proposed on the tent map as shown in
Figure 2. The advantages of the tent map over the logistic map is
calculation are simplified dramatically .In particularly, the higher
order iterates of the tent map, are involved in the study of the
asymptotic dynamics, are themselves piecewise linear maps and are
easy to compute. This form is mainly designed to increase the
sensitivity of the key as shown below. In Figure2 each tent map in
the formation is feed with the initial seed is external keys k 1, k 2 and
iterated for number of times. The final values obtained from the
iteration are feed to the next tent map. Internal keys k in1, k in2 are
obtained at the final tent maps and this kind of feeding will increase
the sensitivity of key.
A small changes in the external keys scattered through the
neighbors at each rounds and the final result will be different one is
a small change in a key dramatically change the results and thus the
structure proposed to generate the internal keys will highly resist
the brute force attack.
Figure 2 Internal Seed Generation
For example if four external keys are used then the total
number possible keys will be equal to 2212
approx 6.58*1063
. Given
today’s computer speed, it is commonly accepted a key space of a a
size smaller than 2128
is not secure enough. In the present case this
phenomena is satisfied and this structures more suitable, very
sensitive and good enough to generate the internal keys in a
unpredictable manners.
Following analysis shows the sensitivity of the proposed
key generator,
Internal key space is,
Kspace=[0.1234567891234567,0.9876543219876543,0.45
69871234569871,0.65412398745698874]
After the 200 iteration (or) at the end of level 1 the key space will be,
Kspace=[0.806566923490395,0.433024531300489,0.3268
73336834747,0.977189373512217]
At the end of 16 levels, the generated internals keys will be,
Kspace=[0.322426612184176,0.146663977532628,0.5225
39285981829,0.439739833426830].
Small change in KSpace will produce entirely different key
as shown below, number in bold show the challenge,
Kspace=[0.1234567891234567,.9876543219875543,0.456
9871234569871,0.65412398745698874]
Final key after 16 levels,
Kspace=[0.612998181420386,0.337221761924433,0.3716
54212088910,0.890801990516176]
Key sensitivity is clear from the above analysis; the
proposed structure for generating the initial seed is very sensitive to
its initial conditions. A small change in K space shown in bold is the
change made, as a result the final result is completely deviated from
the original one. Internal key will be 53 bits each.

30
Figure 3 PO and DFB Generation
In the Figure3 shows the generations of keys are used to
produce diffusion bits used for dispersing the correlation among the
pixels. Internal keys (Kin1, Kin2.., K inn) are given to the logistic
maps grouped as shown in Figure 3.Each of the map is iterated for N
time where n equal to the length of bit stream and the resulting
values are compared to produce the diffusion bits, if map-1 produces
values X and map-2 produces values-y then the random bits are
generated by the following relation.
5. EXPERIMENTAL RESULTS
The grey-level images Lena of a a size 256*256 are used as
the plain image. The corresponding cipher image is shown in the
following Figure 3 respectively. Decryption of the encrypted image
and its respective histograms with the variation in its initial secret
key shows in the results. The histogram distributions of all encrypted
images are flat. This analysis proves there is no chance for statistical
attacks on the proposed scheme.
The histogram of several original images is widely
different. Results shows the encrypted images at different rounds and
their histograms and encrypted image at initial set of key and its
histogram. Encryption and decryption for this elapsed time varying
based on the images a sizes. For this method taking image a a size is
256*256 based on this elapsed time is calculated as 1.2953.
The existing cryptosystem gives noisy cipher image and a
uniform histogram in only three permutation rounds. By the property
of pixels value mixing, the value of every single pixel is diffused
over the image. It is regarded as the first level diffusion of the
proposed system.
Figure 3 Image Encryption
6. SECURITY ANALYSIS
The proposed encryption algorithm has been tested with
several test images of differing content. The visual inspection of the
original encrypted and decrypted images of different images after
applied only one round of encryption algorithm. The first row shows
the original images there second row shows the encrypted images
and the last row shows the decrypted images. The encrypted images
are non-recognizable in appearance, unintelligible, random and
noise-like images without any leakage of the original information.
This demonstrates the proposed algorithm can be used to protect
various images for that is diverse protection. The decrypted images
are exactly same as the original images.
A. HISTOGRAM ANALYSIS
The histograms present the statistical characteristics of
images. An image histogram plots the frequency of occurrences of
each gray level. An encrypted image is expected to have no statistical
similarity with the original image to prevent the leakage of
information. The histogram of several plain images are computed
and analyzed. The histogram image is shown in Figure4. The
histogram of the encrypted image is uniformly distributed and is
completely different from of the original image, and bears no
statistical resemblance to the original image. Hence the proposed
algorithm is resistant to statistical attacks. The diffusion function is
employed to modify the gray values of the image pixels to confuse
the relationship between the plain image and the encrypted image.
The diffusion function is to almost all pixels in the whole image.
The encrypted images are non-recognizable in appearance,
unintelligible, incomprehensible, random and noise-like images
without any leakage of the original information. This demonstrates
the proposed algorithm can be used to protect various images for
diverse protection. The decrypted images are exactly same as the
original images.

31
Figure 4 Encrypted histogram analyses
B. KEY SPACE ANALYSIS
The key-space of an encryption system should be
sufficiently large enough to resist brute-force attacks. Brute-force
attack is an attack an opponent tries to break the cryptosystem by
exhaustive search with all possible keys. In our schema key space is
increased as 53 bit. It is resist against the brute force attack.
C. CORRELATION COEFFICIENT ANALYSIS
Correlation between the pixels of the image must also be to
check the robustness against the statistical attacks. The best
encryption scheme the correlation between the pixels must be zero.
This analysis shows the correlation between the randomly selected
pairs of both plain image and encrypted image. This analysis carried
out by following the procedures, Randomly 5,000 pairs are selected
and they are selected like horizontally, vertically and diagonally
adjacent.
Moreover, we have also calculated the correlation between
two vertically as well as horizontally adjacent pixels in the original
encrypted images. For this calculation, we have used the following
formula,
(6)
(7)
(8)
Where x and y are the value of two adjacent pixels in the
image and N is total number of pixels selected from the image for
the calculation. However, the two adjacent pixels in the original
image are highly correlated.
Table.1 Correlation Co-efficient Analysis
Parameters Horizontal Vertical Diagonal
Plain
image.lena
0.9311 0.9301 0.9321
Encrypted
image.lena
-0.0299 -0.0170 -0.0358
Plain
image.house
0.9532 0.9512 0.9567
Encrypted
image.house
-0.0203 -0.0154 -0.0201
Figure 5 Plain and Encrypted image plot
D. DIFFERENTIAL ATTACK
The range of NPCR is [0, 1]. When N (C1, C2)00, it
implies that all pixels in C2 remain the same values as in C1. When
N (C1, C2)01, it implies that all pixel values in C2 are changed
compared to those in C1. In other words, it is very difficult to
establish relationships between this pair of cipher-image C1 and C2.
However, N(C1, C2)01 rarely happens, because even two
independently generated true random images fail to achieve this
NPCR maximum with a high possibility, especially when the image
a size is fairly large compared to 255. The range of UACI is clearly
[0, 1] as well, but it is not obvious that what a desired.
Table.2 Differential Analysis

32
Parameters NPCR UACI NBCR
Plane 99.6038 33.7276 50.0638
Lena 99.6048 33.0178 49.8825
Baboon 99.6099 33.1335 50.0435
Pepper 99.6068 33.9751 49.7653
House 99.7078 33.4236 50.0312
Tree 99.7341 33.7634 49.9354
Jelly Beans 99.8081 33.6734 49.9675
Aerial 99.6759 33.7650 50.0312
clock 99.7856 33.5634 50.0231
Boat.512 99.8654 33.5432 50.0010
Elaine.512 99.5641 33.2318 50.0321
Fishing
Boat.512
99.9341 33.2243 49.9801
Air
plane.512
99.5674 33.5320 50.0176
Airport.1k 99.8726 33.8765 50.0129
7. CONCLUSION AND FUTURE SCOPE
The typical structure of chaos-based image encryption
schemes has been studied. In this work an efficient method for
encrypting the images using two chaotic maps have been proposed
and simulated. Permutation is applied to each pixel in the image and
its order assigns for that pixels. The proposed chaotic algorithm is
quite simple and compact. The result shows that using this algorithm
in image encryption results in accuracy and faster than traditional
algorithms. This work is also extended to color image.
The main objective of this work is to develop a secure
image encryption scheme that can provide more security in a real
time for sending and receiving the images. Simulation result shows
that the scheme performs well with number of images with reduced
time for encryption.
Chaotic technique can be use in video encryption hence in
future video encryption algorithm can be proposed. Chaotic
technique works on two steps hence reverse of these two steps can be
apply on the encryption of data where data will be converting in
image data. Hence in future a lot of work can be done in chaotic
technique like designing of algorithm for video, graphs, text any kind
of data and in reverse for design of decryption algorithms.
REFERENCES
[1] Ankit Gupta, Namrata Joshi and ChetanNagar (2012), ‘A
Review New Symmetric Image Encryption Scheme Based
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[2] Bhagwati Prasad, Kunti Mishra (2014), ‘A Combined
Encryption Compression Scheme Using Chaotic Maps’,
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[3] Pareek N.K. Vinod Patidhar and Sud K.K. (2004), ‘Image
encryption using chaotic logistic map’, Image and Vision
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[4] Ravishankar K.C. and Venkateshmurthy M.G. (2006),
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[7] Saikia M. Bora S.J and Hussain A. (2014), ‘A Review on
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