An improved color image encryption algorithm with pixel permutation and bit substitution

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 333
AN IMPROVED COLOR IMAGE ENCRYPTION ALGORITHM WITH
PIXEL PERMUTATION AND BIT SUBSTITUTION
Lini Abraham1
, Neenu Daniel2
1
M Tech Student, Computer Science and Engineering (CSE), Viswajyothi College of Engineering and Technology,
Vazhakulam, Kerala, India, linirt33@gmail.com
2
Assistant Professor, Computer Science and Engineering (CSE), Viswajyothi College of Engineering and Technology,
Vazhakulam, Kerala, India, neenudaniel@email.com
Abstract
Today the transmission of multimedia data including image and video is growing in telecommunications. Security is one of the
main issues in transferring such sensitive information. Powerful image encryption algorithm is the solution for this problem. This
paper is an implementation of a color image encryption algorithm based on Rubik’s cube technique. The Rubik’s cube technique
is used for pixel permutation and a bit substitution method based on DNA sequences are used to change the value of each pixel on
the image. Then the time-stamp is appended with encrypted image, which can be used to identify the replay attack. For evaluating
the performance of the algorithm a series of tests are performed. These tests include information entropy analysis, correlation
analysis, analysis of NPCR and UACI values etc.
Index Terms: Cryptography, encryption, decryption, timestamp, replay attack, plaintext, cipher-text, algorithm,
chaos.
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1. INTRODUCTION
Information security plays a significant role in all fields,
especially those related to confidential business or military
affairs. Keeping data from being accessed by unauthorized
users and from being corrupted is called data security.
Encryption is a very important security mechanism. It works
by scrambling the information into unreadable information
and then uses a key to unscramble it for reading. Encryption
on image or video objects has its own requirements due to
the intrinsic characters of images such as bulk data capacity
and high redundancy. Traditional symmetric encryption
algorithms are generally not suitable for image encryption
due to their slow speed in real-time processing and some
other issues such as in handling various data formatting. A
variety of chaos-based digital image encryption algorithms
have been suggested. Usually chaos based encryption
algorithms uses small key spaces. The theory of chaos has
been widely used for image encryption because of its
excellent cryptography characteristics and intrinsic features
of image. Various algorithms provide different degrees of
security and it is based on how hard they are to break. If the
cost required to break an algorithm is greater than the value
of the encrypted data then the algorithm probably
considered to be safe. Modern high quality image encryption
methods have several flaws and are subjected to extensive
attacks by expert cryptanalyst. Thorough study and analysis
between these techniques are needed to measure the
performance and to choose the better one for the intended
application. For certain applications speed of encryption
may be the prime concern and for some other cases the
security will be important.
There are three kinds of encryption techniques namely
substitution, transposition or permutation and techniques
that include both transposition and substitution. Substitution
schemes change the pixel values while permutation schemes
just shuffle the pixel values based on the algorithm. In some
cases both the methods are combined to improve security.
[3] Is an introduction about chaos based image encryption.
Chaos theory has proved to be an excellent alternative to
provide a fast, simple, and reliable image encryption scheme
that has a high enough degree of security. The method in [8]
is chaos based using bit level permutation. Permutation at
the bit level not only changes the position of the pixel but
also alters its value. In [9] a novel image encryption method
based on total shuffling scheme is illustrated. In [10]
combinations of two logistic maps are used for improving
the security of encryption. Encryption in [11] uses multiple
chaotic systems. But each of these methods has some
security issues. The algorithm in [12] combines the diffusion
and confusion operations and uses the spatial-temporal
chaotic system for generating the key. But this is time
consuming. As the key space increases the security of the
algorithm also get improved. Here this proposed scheme is
applied on a chaos based secure image encryption algorithm
based on Rubik’s cube principle in [1]. It is an image
encryption algorithm based on Rubik’s cube principle. From
[2] it is evident that this algorithm performs well as
compared to the technique in [12] in time period and other
results are also comparable.
Differential and cryptographic attacks are major concerns in
data transmission. Even thorough some of the chaos based
image encryption techniques resist these types of attacks to

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some extent; more protecting solutions are needed for further improvement. Replay attack is one of the major
security outbreaks. It can be defined as a network attack in
which a genuine data transmission is maliciously repeated or
delayed. It can be done by the originator or by an advisory.
The common measures for this type of attacks are session
tokens, one time passwords, combination of nonce and
MAC and timestamps. The content in [4] describes the
replay attack. [5] and [6] proposes some methods to prevent
such attacks. In [7], Denning proposed a method for
preventing replay attack with the help of timestamps. These
methods are usually used for preventing replay attack in
normal data transmission. The proposed system is all about
to prevent the replay attack on digital image transmission
with the help of timestamps. The technique based on grey
scale images is proposed in [14]. In [14] only permutation
mechanism is used for encrypting the grey scale image. But
the proposed system improves the security of that algorithm
by adding a bit substitution technique in [15] for encrypting
color images.
The remaining of this paper is organized as follows. Section
2 describes the proposed system. The overview of the
algorithm is presented and detailed explanation of DNA bit
substitution technique is also given. In section 3 the new
image encryption technique is compared with the Rubik’s
cube technique and the result for the same is also presented.
The results of images with distinct and various sizes are
evaluated and discussed. The last section describes the
conclusions and further discussions.
Fig -1 Overview of the proposed system
2. PROPOSED SYSTEM
The proposed system is an enhancement to the Rubik’s cube
based technique in color image. The overview of the system
is given in Fig -1. First the timestamp is taken and added
with the shared key value. Then two random keys are
generated for permuting the pixel values of the image using
Rubik’s cube principle in [1]. Then a substitution technique
based on DNA sequences are employed which is described
in [15]. Then KBRP (Key Based Random Permutation) [13]
is used to hide the time-stamp in the encrypted image. That
will form the cipher image.
During decryption, first the time-stamp is extracted from the
encrypted image by using the shared secret key. The
difference between the extracted time and the current time is
taken. If that difference is within the threshold then the
decryption is performed otherwise it is rejected. For
performing the decryption, the time-stamp is appended with
the key and the two random numbers are generated. The
decryption is then performed to get the original image.
Before performing these operations the system time should
be synchronized.
Every module except the DNA substitution is already
explained in [14]. In that proposal only permutation of
pixels in the image was used. But if we are adding a
substitution along with that image the security will get
improved. In this paper a bit substitution method based on
DNA sequences is proposed based on [15]. The detailed
explanation about DNA sequence substitution is given
below.
Appending key and timestamp
Key
Generating two random keys for
encryption with the modified key
Encryption of the image using Rubik’s
cube principle and DNA substitution
Hiding the timestamp on the encrypted
image
Extracting the timestamp from
encrypted image and checking replay
attack
Appending key and the timestamp
Decrypting the image using Rubik’s
cube principle and DNA reverse
substitution
Generating two random keys for
decryption with the help of modified
key
Key

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2.1 Chaotic DNA Substitution
The proposed substitution method is a chaotic DNA
transformation. Here two rules or steps are involved. They
are: -
 Binary coding rule
 Complementary rule
The binary coding rule transforms letters A, C, G and T into
binary codes and vice versa. In this particular method the
following binary encoding is adopted. A=00, C=01, G=10,
T=11. That means A is coded as "00", C as "01" etc. Then
each pixel value in the encryption is transformed to binary
using the DNA encoding.
In complementary rule, each letter x is assigned to a
complement denoted C(x). Here the C(x) represents the
complement of x. For getting a clear picture, consider an
example, for the following complementary transformation:
(AT)(TC)(CG)(GA), the conclusion is that C(A) = T, C(T) =
C, C(C) = G and C(G) = A. There are six allowable
complementary transformations, they are: -
(AT)(TC)(CG)(GA)
(AT)(TG)(GC)(CA)
(AC)(CT)(TG)(GA)
(AC)(CG)(GT)(TA)
(AG)(GT)(TC)(CA)
(AG)(GC)(CT)(TA).
The perturbed chaotic value used to control the substitution
process is transformed to binary format (8 bits). Each pixel
is represented by 8 bits (4 pairs). For example consider the
pixel value "222" which is represented as 11 01 11 10. A
random value is generated for each pixel on the image using
PWLCM (Piecewise Linear Chaotic Map). The equation for
PWLCM is given by: -
Where p is the positive control parameter and the chaotic
values x(i),i = 1,2,...,n, are real values and belong to the
intervals (0, 0.5) and (0, 1) respectively. The initial values p
and x(0) are calculated from the modified key value. The
output from the chaotic map is represented in 8 bits. For
each pixel in the plain image a random value in 8 bits is
generated and the pixel value is represented in 4 pairs as
explained above.
From the random value generated for a pixel, the most
significant 3 bits are used to select one of the six
transformations given above. And that transformation rule is
used for that particular pixel value. The transformation
number can be calculated by the following equation: -
Remaining 5 bits are used to compute the number of
iterations the complementary transformation is to be applied
on each pair of bits. Here the complementary rule is applied
only on 3 pairs, the right most pair is not used because of the
chances of changes during the time-stamp hiding. In other
words the fourth and fifth bits of the random number are
used to generate how many times it(1), the complementary
transformation is applied to the first two bits of the pixel
value in process. The fifth and sixth random bits are used to
determine number of the complementary rounds of it(2) for
the second pair of bits. The sixth and seventh bits are used
for the third pair of the value in process. The extraction of
this number of iterations on 1st
, 2nd
and 3rd
pair of pixel
values are given by: -
For example, consider the previous example "222" as the
pixel value. It can be represented as 11 01 11 10. Now take
the first pair of bits "11". The binary coding rule is given as
A=00, C=01, G=10, T=11. From the generated chaotic value
the most significant 3 bits can be used to find out the
sequence number. Suppose that the sequence number for
that particular pixel is 5. So the 5th complementary rule is
(AG)(GT)(TC)(CA).
If it(1) = 2, then the number of iterations for the first pair is
2. Here the first pair "11" means T from the binary coding
rule. In first iteration C(T) = C( from fifth sequence). The
value of C is "01" as per the binary coding rule. First T
("11") is replaced with C ("01"). In the second iteration
C(C) = A. So "01" is replaced by "00". This is performed for
the remaining two pairs and again they are combined
together to get the cipher value. For each pixel this is
repeated. So for each one the sequence selected and the
number of iterations is different.
3. RESULTS AND DISCUSSIONS
The Fig -2 shows an example for the encryption and
decryption using the proposed method. The test image
selected is AIR plane. The experiments are done on

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256×256 images with 128 bit key. We can see that the
original and the decrypted images are same and the
encrypted image is random. For performing the analysis the
parameters like NPCR (Number of pixel change
rate), UACI (Unified average changing intensity), entropy,
correlation coefficient and PSNR (Pixel to noise ratio) are
evaluated. The definitions and detailed explanations of these
parameters are given in [16].
Fig -2 Example using improved scheme
Some of the evaluation results for the improved scheme are
given in Table -1. The NPCR is 99.6246 and the UACI is
34.7988 for a 256×256 AIR plane color image. The NPCR
should be high as possible for an enhanced technique. The
UACI should be around 33%. We can see that the
correlation coefficients are also low. The time for encryption
and decryption will vary from system to system. The time
required for overall process is below one minute. The PSNR
value between original and decrypted image is infinity. This
means that the pixel values in original and the encrypted
images are distinct.
Table -1 Results of simulation on color image
Parameter Improved technique
NPCR
99.6246
UACI
34.7988
Entropy
7.9970
Horizontal correlation
-0.0347
Vertical correlation
0.0015
Diagonal correlation
-0.0022
PSNR
Infinity
Now the results by the application of the new scheme in
different 256×256 color images are given in Table -2. Here
the test images are Lena, Baboon and Pepper. As it includes
the effect of the time-stamp which varies by time, a little
variation in the results is possible. It is because of the reason
that on each times the timestamp varies. From the table we
can see optimal results.
Table -2 Results for different images having same size
Parameter AIR
plane
Lena Baboon Pepper
NPCR 99.6038 99.6048 99.6099 99.6068
UACI 34.7276 31.0178 29.1335 31.9751
Entropy 7.9973 7.9975 7.9973 7.9971
Horizontal
correlation
-0.0057 -0.1290 0.0013 -0.0030
Vertical
correlation
0.0037 -0.0026 0.3152 0.7563
Diagonal
correlation
0.1035 0.0041 -0.0016 0.2527
PSNR Infinity Infinity Infinity Infinity
Next the Rubik’s cube technique and the improved scheme
is applied on variable sized test images. The results of this
comparison are plotted as graphs in Fig -3 and Fig -4.
In Fig -3 the NPCR values are compared. Higher NPCR
values are desired for ideal encryption schemes. This will
indicate the percentage of different pixels between two

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images. The red line shows the improved scheme and the
blue line is the Rubik’s cube based technique.
The Fig -4 shows the comparison of entropy values. It is an
important concept for analyzing an encryption scheme.
Entropy gives an idea about self-information. From the
results it is evident that the improved method is comparable
with the Rubik’s cube technique and provides more security.
Fig -3 Comparison of NPCR values
Fig -4 Comparison of UACI values
CONCLUSIONS
Chaos based encryption algorithms are employed nowadays
because of their better security and performance aspects.
Each of the image encryption techniques has its own
advantages. Identification of the suitable algorithm for a
particular application depends on the prerequisites of that
application. The technique using Rubik’s cube principle has
a large key space and its implementation is quite simple.
Later the security of the Rubik’s cube technique has
improved by adding time-stamp and chaotic DNA
substitution. The time-stamp is appended with the original
key. So the time-stamp is specially added to produce
different cipher texts by applying same key on same plain
text. Also it can be used to check the replay attack. But it is
under the assumption that the system time is synchronized.
In basic Rubik’s cube based approach bit substitution is not
used. So a chaotic bit substitution method based on DNA
sequences is added for improving the security. The
comparison results and assessments have done and
presented. From that the efficiency of the improved
approach is evident. The experimental result shows that the
improved scheme performs well in color images. New
techniques and modifications can be added on to the
proposed system for making excellent multimedia
applications.
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