ICETACS 2013

978-1-4673-5250-5/13/$31.00 ©2013 IEEE

A Colour Image Encryption Based On DNA Coding and Chaotic Sequences

Sukalyan Som

Department of Computer Science,

Barrackpore Rastraguru

Surendranath College

85, Middle Road & 6, Riverside

Road, Barrackpore, Kolkata – 120,

West Bengal, India

sukalyan.s@gmail.com

Atanu Kotal

Department of Computer Science

and Engineering, Techno India

College of Technology

New Town Mega City, Rajarhat,

Kolkata – 156, West Bengal, India

atanukotal@gmail.com

Ayantika Chatterjee

Department of Computer Science,

Barrackpore Rastraguru

Surendranath College

85, Middle Road & 6, Riverside

Road, Barrackpore, Kolkata – 120,

West Bengal, India

ayantipinki@gmail.com

Soumista Dey

Department of Computer Science, Barrackpore Rastraguru

Surendranath College

85, Middle Road & 6, Riverside Road, Barrackpore,

Kolkata – 120, West Bengal, India

soumistad@gmail.com

Sarbani Palit

Computer Vision and Pattern Recognition Unit, Indian

Statistical Institute

203 Barrackpore Trunk Road, Kolkata - 108, West Bengal,

India

palitsarbani@gmail.com

Abstract— in this communication, a Chaos Based Symmetric

Key Encryption of RGB Color Images with DNA Coding and a

Chaos based Pseudorandom Binary Number Generator

(PRBNG) has been proposed. In the proposed algorithm, the

plain image is first scrambled using generalized Arnold Cat Map to achieve confusion. The scrambled image pixel are converted

to DNA codes and again reconverted to integers where the

choice of DNA coding rule is made pseudorandom based on the

binary sequences generated by chaos based pseudorandom

binary number generator. The integers thus obtained are diffused by performing exclusive OR operation with the integer

sequences generated by 1D Logistic map producing the cipher

image. The experimental results depicts that the proposed

algorithm can successfully encrypt and decrypt RGB color

images with secret keys. The simulation analysis also exhibit that the proposed method is loss-less, secure and efficient measured

in terms of statistical tests(like histogram analysis, correlation

coefficient analysis, measures of central tendency and

dispersion), key sensitivity test, key space analysis, information

entropy test, encryption quality by MSE, PSNR, NPCR and

UACI.

Keywords— Color image, DNA Coding, Pseudorandom Binary

Number Generator, 1D Logistic Map, Information Entropy,

Histogram, Correlation Coefficient, Mean Square Error, Peak

Signal to Noise Ratio

I. INTRODUCTION

With the rapid growth of Internet and mobile phone

networks, the limits and possibilit ies of information

transmission, including images have tremendously increased.

Therefore, secure transmission of image data, has become

inevitable. Due to some intrinsic features of images such as

bulk data capacity and high redundancy, traditional encryption

schemes appear not to be idle for images. Chaos based

cryptosystems, first proposed in1989, achieve a good level of

image encryption. In general, the term ‗chaos‘ refers to a

situation or place of great disorder and unpredictability or

according to the Merriam-Webster dictionary ―A state of utter

confusion‖ [1]. Chaos theory describes the behaviour of

certain nonlinear dynamic system, that under specific

conditions, exhibit dynamics that are sensitive to initial

conditions. Since 1990s, many researchers have discovered an

interesting relationship between chaos and cryptography

which include several properties of chaotic systems having

their corresponding counterparts in cryptographic systems as

shown in Table I.

TABLE I. RELATIONSHIP BETWEEN CHAOTIC AND CRYPTOGRAPHIC

PROPERTIES

Chaotic property Cryptographic property

Explanation

Ergodicity Confusion For any input, the output has the same distribution.

Sensitivity to initial

conditions/control parameter

Diffusion with a small

change in plain text/secret key

Producing a small

deviation in the input can generate a huge change at the output.

Mixing property Diffusion with a small change in one plain

block of the whole plain-text

Producing a small deviation in a local

area can generate a huge change in the entire space.

Deterministic dynamics

Deterministic pseudo-randomness

A deterministic process can cause a

random behavior. Structural

Complexity

Algorithmic complexity A simple process has

a very high complexity

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Due to the close relationship between chaos theory and

cryptography, chaos-based cryptosystems have gained huge

attention since 1990s. However, researches have proved that

encryption algorithms based only on chaotic maps, such as one

dimensional chaotic map, multi-dimensional chaotic maps and

ultra-dimensional chaotic maps have lower Key space and are

susceptible to be interpreted.

A new technique has evolved called DNA computing,

which makes use of recombinant DNA techniques for

performing computation. DNA cryptography is a newly

evolved technique in which DNA is used as an information

carrier. The vast parallelis m, exceptional energy efficiency and

extraord inary information density inherent in DNA molecules

are used in cryptography such as encryption, authentication,

signature, etc. [2]. DNA based chaotic cryptosystems is

extensively researched on cryptographic grounds.

In recent years, many DNA based chaotic encryption

techniques have been put forward. Wang [3] had proposed an

algorithm based on index-based symmetric DNA encryption

which adopts the methods of Block-Cipher and Index of

string; the algorithm encrypts the DNA sequence based

plaintext. Zhang [4] had proposed an algorithm based on DNA

coding combined with chaotic maps on RGB images. The

algorithm first computes the DNA coding for each component

R, G, B and then performs addition on them by DNA addition

and carries out complement operation by using DNA sequence

matrix controlled by Logistic Map. Finally the encrypted RGB

image is obtained. Liu [5] had proposed a RGB image

encryption algorithm based on DNA encoding combined with

chaotic map, aiming at characteristics of RGB image.

In this communication, , instead of using only DNA

coding or only chaotic maps, their combination has been used

so that better confusion and diffusion can be achieved. The

plain image is first scrambled using generalized Arnold Cat

Map to achieve confusion. Further, the scrambled image is

encrypted with DNA coding using chaotic sequences

generated by multiple one-dimensional chaotic maps where

the selection of map is made pseudorandom based on the

binary sequences generated by chaos based pseudorandom

binary number generator. The experimental results depict that

the proposed algorithm can successfully encrypt and decrypt

RGB co lour images with secret keys. The simulat ion analysis

also exh ibit that the proposed method is loss-less, secure and

efficient measured in terms of statistical tests(like histogram

analysis, correlation coefficient analysis, measures of central

tendency and dispersion), key sensitivity test, key space

analysis, information entropy test, encryption quality by MSE,

PSNR, NPCR and UACI.

In section II a brief overview of chaotic maps, chaos

based pseudo random bit generator and DNA coding used in

the communication is presented. The proposed encryption and

decryption algorithms are presented in section III with the

security analysis and tests being stated in section IV. To prove

the novelty of the work comparison with existing algorithms

are done section V. Conclusions are drawn in section V.

II. BACKGROUND

A. DNA Coding

DNA computation comes into existence after the release

of Dr Adleman‘s ―Molecular Computation of Solutions to

Combinatorial Problems" in 1994 [6]. Dr Adleman solved a

problem on Directed Hamilton Path by DNA coding. DNA

computation includes DNA, biochemistry and molecular

biology, i.e. it uses the biological molecule DNA as a medium

of computation and biochemical reaction as a tool of

computation. Now a days, due to the rapid development of

DNA computation, which is more generally known as ‗Bio

molecular Computing (BMC)‘, the researchers have developed

many algebraic operations and biological operations based on

DNA sequence [7]. DNA coding uses the double helix

structure of DNA. The basic element of DNA is nucleotide;

for the different chemical structure it is divided into four parts:

Adenine (A), Guanine (G), Cytosine (C) and Thymine (T).The

DNA sequence is based on these four bases A, C, G and T

where A and T are complement to each other and so are C and

G. In DNA coding, information is expressed by this DNA

sequence. Here, each base is represented by a two digit binary

number. As in b inary number system, 0 and 1 are complement

to each other, we can use 00 and its complement 11 and 10

and 11 to express the 4 bases. Thus the total number of coding

combinations is 4!=24. But out of these 24 combinations, only

8 combinations can be used because of the complementary

relationship between the bases. Table II shows the 8 possible

combinations of DNA-Binary Coding.

T ABLE II. DIFFERENT KINDS OF DNA-BINARY CODING

000 001 010 011 100 101 110 111

00–A 00 –A 00 –C 00–C 00–G 00–G 00–T 00–T

01–C 01 –G 01–A 01–T 01–A 01–T 01–C 01–G

10–G 10 –C 10 –T 10–A 10–T 01–T 10–G 10–C

11–T 11 –T 11–G 11–G 11–C 11–C 11–A 11–A

B. 1D Logistic Map

The one-dimensional Logistic map was proposed first

by R. M. May in 1976 [8]. It is one of the simplest nonlinear

chaotic discrete systems that exh ibit chaotic behaviour,

defined as

(1)

Where, is init ial condition with , is the

system parameter with and n is the number of

iterations.

C. Arnold’s Cat Map

Arnold's cat map is a chaotic map which was discovered

by Vladimir Arnold in 1960 [9].

Let X = where X is a vector, then the

Mod N (2)

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Where ( , ) is the pixel position of an N N image, p,

q are the parameters which are positive integers and

( , ) is the new position of the original pixel position

( , ) when Arnold Cat Map is performed once.

D. Pseudorandom Binary Number Generator

A Pseudo Random Bit Generator (PRBG) based on two

one-dimensional logistic maps proposed by K. K. Sud et al.

[10] running side-by-side and starting from random

independent initial conditions has been used in the literature.

The pseudo random bit sequence is generated by comparing

the outputs of the sequences generated by two the chaotic

logistic maps.

The PRBG is based on two logistic maps,

(3)

starting from random independent initial conditions (x0,

y0 (0, 1), and x0 0), generates bit sequences

by comparing the outputs of both the logistic maps as

(4)

The set of init ial conditions (x0, y0 (0, 1) and x0 y0)

serves as the seed for the PRBG, if we supply the exact ly

same seed to the PRBG, it will produce the same bit sequence

due to the above deterministic procedure.

III. PROPOSED SCHEME

A. Method of Encryption.

Step 1: The original image,

is decomposed into its RGB components

Step 2: Scramble each component of the plain image using

the generalized Arnold Cat Map stated in equation (2) with

given values of p, q and n. Consider the scrambled image at

nth iteration to be .

Step 3: Consider and convert each of its pixels into

their 8-bit binary equivalent.

Step 4: A pseudorandom binary sequence of size

is generated with chosen value of the triplet by the

PRBNG stated in equations (3) and (4) from which 3-b it

disjoint and consecutive binary sequences are extracted to

choose DNA coding rule, as stated in Table II, and thus each

8-bit b inary pixels are converted to their corresponding DNA

codes producing DNA coded image . This

generates the first level of diffusion for the image component.

Step 5 : Now use every third pair generated in Step 4

by the PRBG to decode the DNA coded image b inary codes

and then into pixel value . It is 2nd level of

diffusion.

Step 6: Keys for encryption, are generated by the 1D

logistic map with chosen value of as

Step 7: Each decoded image pixel of is

encrypted with the key generated in Step 6 to get the

encrypted pixel at the coordinate (x, y) where

as

Mod ( where

denotes the exclusive-OR operation.

Step 8: Continue Step 3 to 6 fo r the other components

of the original image.

Step 9: The final cipher image is generated by

recombining the cipher R, G and B components ,

and

B. Method of Decryption

The orig inal image can successfully be recovered by

applying the encryption algorithm in reverse order with the

parameters p, q and n for generalised Arnold Cat Map for

scrambling the original image or descrambling the cipher

image, the initial condition and system parameter for

1D Logistic map for key generation and the triplet

for pseudorandom binary number generation would be used

during both encryption and decryption which has to be

transmitted through secure channel.

IV. EXPERIMENTAL RESULTS

An extensive study of the proposed algorithm has been

performed using the USC-SIPI [11] and CSIQ [12] image

databases which are co llect ions of digitized images availab le

and maintained by University of Southern Californ ia and

School of electrical and computer engineering, Oklahoma

State University respectively primarily to support research in

image processing, image analysis and machine v ision.

Currently, four volumes availab le at USC-SIPI site are—

textures, aerials, miscellaneous and sequences. We have

chosen miscellaneous volume of USC-SIPI image database.

The miscellaneous volume consists of 44 images out of which

16 are colored and 28 monochrome. CSIQ database consists

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of 30 color images on Animals, Landscape, People, Plants

and Urban. The experiments have been performed using

Matlab 10 on a system with Intel Pent ium i3 Processor with

4GB DDR3 Ram and 500GB of hard disk Capacity.

A. Statistical test and analysis

1) Visual test through Histogram analysis

In statistics, a histogram is a graphical representation

showing a visual impression of the distribution of data. It is

an estimate of the probability distribution of a continuous

variable and was first introduced by Karl Pearson. An

histogram of an image illustrates how pixels in an image are

distributed by graphing the number of pixels at each color

intensity level.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig 1. (a) Original Image Baboon (b) Cipher Image baboon (c) – (e) Histogram of Red, Green and Blue components of (a), (f) – (h) Histograms of

Red, Green and Blue components of (b)

We can find that histogram of encrypted image appears

more uniformly d istributed, which means most of values of

image elements are changed, and then encryption algorithm

has good confusing property.

2) Correlation coefficient analysis

In most of the plain images, there exists high correlation

among adjacent p ixels whereas poor correlation between the

neighbouring pixels of corresponding cipher image is

observed. Karl Pearson‘s Product Moment correlation

coefficient, stated as follows, is used as a measure to find the

correlation of horizontally, vert ically and diagonally adjacent

pixels of both the plain and cipher image and the correlation

between the plain image and cipher image pixels.

(5)

(6)

(7)

The results of the correlation coefficients for horizontal,

vertical adjacent pixels for the p lain image and its cipher

image are given in Table 3-4.

T ABLE III. CORRELATION COEFFICIENTS OF HORIZONTALLY ADJACENT

PIXELS IN ORIGINAL IMAGE AND CIPHER IMAGE

Image name

O riginal Image Cipher Image

R G B R G B Tiffany 0.9270 0.9241 0.9133 -0.0036 0.0017 -0.0032

Baboon 0.8624 0.7591 0.8782 0.0004 0.0004 -0.0004

Lena 0.8624 0.7591 0.8782 0.0004 0.0004 -0.0004 Airplane 0.9507 0.9665 0.9162 0.0002 0.0002 0.0001

Peppers 0.9640 0.9771 0.9619 0.0032 -0.0014 -0.0020

T ABLE IV. CORRELATION COEFFICIENTS OF VERTICALLY ADJACENT PIXELS IN

ORIGINAL IMAGE AND CIPHER IMAGE

Image name

O riginal Image Cipher Image R G B R G B

Tiffany 0.9585 0.8588 0.8995 -0.0027 -0.0004 0.0017

Baboon 0.9218 0.8643 0.9071 0.0013 -0.0017 -0.0033

Lena 0.9775 0.9662 0.9304 -0.0015 -0.0016 -0.0007

Airplane 0.9726 0.9425 0.9633 -0.0026 -0.0004 0.0045

Peppers 0.9618 0.9777 0.9628 -0.0004 -0.0002 0.0010

From the Table IV, it is clearly seen that the values of

correlation coefficient, be it horizontal or vert ical, is almost

equal to 1(h igh correlat ion) in case of RGB components of

original p lain image and is almost equal to zero (no

correlation or low correlation) [13] in case of cipher images

of RGB components of that image. Thus, the obtained cipher

images are almost uncorrelated. Therefore, we can conclude

that the proposed algorithm is guarded against pixel

correlation statistical attacks.

3) Measures of central tendency and dispersion

A measure of central tendency attempts to describe a

whole set of data with a single value that represents the

middle or centre of its distribution. Here, as a measure of

homogeneity, central tendency is calculated in terms of mean

[14]. Mean is the sum of the values of all the pixels divided

by the total number of pixels. The expression for mean is

given as follows:

(8)

Where n = total number of p ixels in the image; = pixel

element.

T ABLE V. MEASURE OF CENTRAL TENDENCY OF PIXELS IN ORIGINAL IMAGE

AND CIPHER IMAGE IN TERMS OF MEAN

Image

name

O riginal Image Cipher Image

R G B R G B Tiffany 253.3 213.0 157.0 127.0 127.0 128.0

Baboon 132.0 129.0 100.0 128.0 128.0 128.0

Lena 197.0 97.0 100.0 128.0 128.0 128.0

Airplane 197.0 202.0 203.0 127.0 128.0 127.0

Peppers 154.0 129.0 61.0 128.0 128.0 128.0

Comparative study of the Table V depicts that values of

mean of RGB components of any original plain image varies

extensively from image to image, while in case of RGB

components of cipher image, the values of mean is uniform,

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or in other words, homogeneous irrespective of that of the

original image.

Dispersion gives an idea of how the pixel values are

spread with respect to a specific value. Here, dispersion is

measured in terms of Standard Deviation. Standard deviation

is equal to the square root of the variance which in turn is

equal to the arithmetic mean of the squared differences

between each value of the pixel and the mean value [15]. The

expression is given as follows:

(9)

Where N= total number of pixel; = pixel element; =

Mean value.

T ABLE VI. MEASURE OF DISPERSION OF PIXELS IN ORIGINAL IMAGE AND

CIPHER IMAGE

Image name

O riginal Image Cipher Image

R G B R G B Tiffany 253.3 213.0 157.0 127.0 127.0 128.0

Baboon 132.0 129.0 100.0 128.0 128.0 128.0

Lena 197.0 97.0 100.0 128.0 128.0 128.0

Airplane 197.0 202.0 203.0 127.0 128.0 127.0

Peppers 154.0 129.0 61.0 128.0 128.0 128.0

Comparative study of plain image and cipher image

from the Table VI shows that the value of standard deviation

varies widely in case of p lain o rig inal images and is

homogeneous in case of cipher images.

B. Information entropy test

In information theory, entropy is the most significant

feature of d isorder, or more preciselyUnpredictability. To

calculate the entropy H(s) of a source s, we have:

(10)

Where (si) represents the probability of symbol si and

the entropy is expressed in bits. Let us suppose that the source

emits 28 symbols with equal probability, i.e.,

. For a t ruly random source emitting

2N symbols, the entropy is H(m) = N. therefore, fo r a

Ciphered image with 256 gray levels, the entropy should

ideally be H(m) = 8. If the output of a cipher emits symbols

with entropy less than 8, there exists certain degree of

predictability, which threatens its security. Information

entropy for a few images is shown in Tab le VII to conclude

that a high permutation and substitution is achieved by the

proposed algorithm and has a robust performance against the

entropy attack.

T ABLE VII. INFORMATION ENTROPY OF ORIGINAL IMAGE AND CIPHER IMAGE

Image name

O riginal Image

Cipher Image

Tiffany 6.4165 7.9998

Baboon 7.7624 7.9997

Lena 7.7502 7.9998

Airplane 6.6639 7.9998

Peppers 7.6698 7.9998

C. Key sensitivity test

One of the significant characteristics of chaotic

sequence is having a large key space and high sensitivity to

initial conditions. A small change in one or more than one of

the values of the input parameters will cause a huge change at

the output. In order to test the sensitivity of secret key, the

original in itial conditions of and

is slightly changed to

keeping other values constant; and, in the other cipher image,

the value of is changed to keeping other values

constant.

From Fig 2 we can depict that only when the secret keys

are consistent, we can extract the original image. Having a

slight change in any one of the keys results in a different

cipher image and thus, we obtain an incorrect decrypted

image that does not reflect the true informat ion of the original

plain image. Thus, we can see that the proposed algorithm has

secret key sensitivity, and can resist exhaustive attack

efficiently.

(a)

(b)

(c)

(d)

Fig 2 Key sensitivity test (a) Original Image (b) Cipher Image with chosen

key tuple ( ) (c) Cipher Image with chosen key

tuple ( ) (d) Cipher Image with chosen key

tuple ( )

D. Encryption quality test through MSE, PSNR, NPCR,

UACI

In general, a desirable p roperty for an encrypted image

is being sensitive to the small changes in plain -image (e.g.,

modifying only one pixel). Opponent can create a small

change in the input image to observe changes in the result. By

this method, the meaningfu l relationship between original

image and encrypted image can be found. If one s mall change

in the plain-image can cause a significant change in the

cipher-image, with respect to diffusion and confusion, then

the differential attack actually loses its efficiency and

becomes practically useless. To test the influence of one-pixel

change on the whole image encrypted by the proposed

algorithm, three common measures were used NPCR and

UACI [16][17]. NPCR means the number of p ixels change

rate of ciphered image while one pixel of plain-image is

changed. UACI which is the unified average changing

intensity, measures the average intensity of the differences

between the plain-image and ciphered image.The d iffusion

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performance is commonly measured by means of two criteria,

namely, the number of pixel change rate (NPCR) and the

unified average changing intensity (UACI). The NPCR is

used to measure the percentage of different pixel numbers

between two images. UACI which is the unified average

changing intensity, measures the average intensity of the

differences between the plain-image and ciphered image.

Consider two cipher-images, C1 and C2, whose

corresponding plain-images have only one pixel difference.

The NPCR of these two images is defined in

(11)

Where W and H are the width and height of C1 or C2

and D (i, j) is defined as

(12)

The NPCR value for two random images, which is an

expected estimate for a good image Cryptosystem, is given by

(13)

Where L is the gray levels of the image. For instance,

the expected NPCR for two random images with 256 gray

levels is 99.609% [18].

The second criterion, UACI is used to measure the

average intensity of differences between the two images.

UACI, is defined by the following formula

(14)

The UACI value for two random images is given by

(15)

For a 256 gray levels image, the expected UACI value is

33.464%. Tests have been performed on the proposed scheme; about the one-pixel change influence on five sample images is presented in Table VIII.

T ABLE VIII. MEASUREMENT OF ENCRYPTION QUALITY- MSE, PSNR, NPCR

AND UACI

Image name

MSE PSNR NPCR UACI

Tiffany 1.2780e+004 7.0993 0.99231 33.2349%

Baboon 8.6263e+003 8.8066 0.99324 32.6762%

Lena 8.9428e+003 8.6501 0.99122 33.1298%

Airplane 1.0354e+004 8.0139 0.99298 32.6645%

Peppers 1.0146e+004 8.1020 0.99987 33.4567%

V. COMPARISON WITH EXISTING TECHNIQUES

In order to compare our proposed algorithm with

existing chaos based encryption algorithms we focused on the

security considerations. The proposed method is loss -less,

secure and efficient measured in terms of statistical tests(viz.

histogram analysis, correlation coefficient analysis, measures

of central tendency and dispersion), key sensitivity test,

informat ion entropy test, encryption quality by MSE, PSNR,

NPCR and UACI. The comparison results are given in Table

IX.

TABLE IX. COMPARISON WITH SOME EXISTING T ECHNIQUES

Comparison on Proposed method

Zhang’s Method [4]

Liu’s method [5]

Homogeneity test Yes No No

Key sensitivity Yes Yes No

Information

entropy 7.9998 7.9976 7.9890

VI. CONCLUSION

This paper puts forward an RGB image encryption

algorithm based on DNA coding and a chaos based ps eudo

random binary number generator. The proposed algorithm

effectively eliminates the pixels correlation of the RGB image

in the spatial domain by using generalized Arnold Cat map,

and in order to increase security, we combine DNA coding to

disturb the value of the p ixels where the choice of DNA

coding rule is made pseudo random by the b inary stream

generated by chaos based PRBNG. The integers obtained

after DNA coding and re-coding are diffused by performing

exclusive OR operation with the integer sequences generated

by 1D Logistic map producing the cipher image. The

simulation experiment and results show that the encryption

algorithm is effective, simple to implement, its secret key

space is large and can effectively resists exhaustive attack,

statistical attack and so on, thus it is suitable for RGB image

encryption. To prove the superiority of the proposed scheme

comparisons with exiting algorithms are made. In addit ion,

the algorithm also has certain reference value for encryption

of video, audio and other multimedia data. The speed

performance of the proposed algorithm is not ideal, instead of

encrypting all the bit planes of the R, G and B components

the significant bit planes can be detected to facilitate partial

image encryption to reduce encryption time. This aspect

would be of future concern.

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