STEGANO-CRYPTOGRAPHY FOR SECURED TRANSMISSION …Symmetrical hybrid based 128 bit key AES-DES algorithm for motion image transmission [5] was proposed by Vishnu, et.al. (2008). It

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International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 10, October 2018, pp. 784–798, Article ID: IJMET_09_10_082

Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=10

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

STEGANO-CRYPTOGRAPHY FOR SECURED

TRANSMISSION OF MEDICAL X-RAY

IMAGESUSING CHAOTIC MAPS

V.Praneeth Kumar Reddy, Annis Fathima A

School of Electronics Engineering, VIT University, Chennai

ABSTARCT

Recently, many fraudulent attacks towards life/health insurances by providing fake

health information are in increase. A secured transmisssion of the medical images to

avoid misrepresentation of medical report by hacking the medical image sent by the

medical practitioner to the insurance provider. In this paper, steganography and

encryption techniques are combined to protect the patient confidentiality, and increase

the security in medical images. In existing approaches, steganography or water marking

are used to secure the medical images, but these techniques cannot assure robust

security on transmission. Hence, a combined steganography to incorporate the patient’s

details and advanced encryption techniques to secure the transmission is required. An

approach for encryption and steganography using discrete non-linear system that

provides least correlation for secured transmission is proposed. Henon and Chebyshev

maps are the discrete non-linear systems adopted in the process. A database of 100 X-

ray images is considered for performance evaluation. The metrics such as entropy and

correlation coefficient for encryption and metrics such as PSNR, MSE, and elapsed time

for steganography are evaluated. It is observed that the combined Henon and

Chebyshev map gives better results for encryption and the proposed steganography

gives better results than LSB approach. The combination of steganography and

encryption will give robust security for the transmission.

Keywords: Chaotic map, Encryption, Steganography, Medical X-ray images

Cite this Article V.Praneeth Kumar Reddy and Annis Fathima A, Stegano-

Cryptography for Secured Transmission of Medical X-ray Images using Chaotic Maps..,

International Journal of Mechanical Engineering and Technology, 9(10), 2018, pp. 784–

798.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=10

STEGANO-CRYPTOGRAPHY FOR SECURED TRANSMISSION OF MEDICAL X-RAY

IMAGES USING CHAOTIC MAPS


1. INTRODUCTION

In recent times, fraud and abuse are extensive and expensive in any health care systems. For

illegal medical insurance claim, procedures like unbundling of claims, double billing,

misrepresentation etc. are done. Fraudulent submission of medical images will result in

misrepresentation deliberated to result for the uncertified benefits and false claims to get

undeserved payments [23, 24]. Illegal data attacks are wide spread in communication networks

and retaining the medical x-ray images is predominant for the precise claim. To avoid

misrepresentation of the medical images, the patient’s details can be integrated in the medical

image. To avoid any further attack, secured transmission has to be ensured.

Nowadays, there is a move to change from paper-based medical record to keep digital-based

record. In medical centres, the medical images are obtained by radiographer and stored in

Health care information system. From the information system, only the medical practitioners

will have the access to retrieve the images stored for diagonising. It needs to be transmitted

when expert opinion is required. It needs to be transmitted also in the case of insurance claim.

While on internet, the image is exposed to threat. The data can be modified by the patient or

some hacker can use the information to have false insurance claims. The modified image can

also be used as evidence for pressing false charges against medical centers. To answer the stated

concerns, the authentication of images is of highest priority.

Steganography and digital watermarking are primarily used for the security in medical

images, which will hide the patient details in the medical image, yet additionally there is a need

for security in the medical images. Hence, in addition, encryption of the medical image is

proposed. In this paper, the encrypting module is of concern and discrete non-linear systems

are used to encrypt the image.

In the traditional approach steganography techniques rely on using LSB algorithmic

technique. In this method, the message is converted to binary bits and later inserted into LSB

of the pixel values of the image. This approach is very common and hence easier to hack as

there is no key. In later stages, algorithms utilize pseudorandom generator to identify the

random pixel location and LSB is replaced with message bit [1]. The security aspects in it are,

random generator solely depends on seed value and hence key are relatively less secured. In

place of random generator, chaotic maps are conventional to generate the random numbers,

which have comparatively more key values to come up with random numbers and subsequently

also increases the security.

The widely used image encryption techniques are AES, DES and RSA. Advance Encryption

Standard (AES) algorithm which is first proposed by Danmen and Rijmen, is an iterated block

cipher. But the traditional AES algorithm have some disadvantages like singleness of the key,

deficiency of key space. These will cause the security problems. Data Encryption Standard

(DES) is a symmetric key encryption algorithm. In these algorithms, permutation process will

take more time and chances of mistakes are also high. It is computationally expensive process

and there is a chance of erroneous key, as the key length is 256 bits.

The existing AES, DES and RSA techniques exhibit low security and weak anti-attack

ability. To resist the mentioned problems and the security attacks; chaotic maps are used for

encryption and steganography of the medical X-ray images [2]. Chaotic systems improve the

security and robustness and it forms the base for efficient encryption system. Discrete non-

linear systems are used to generate sequences which are used for the encryption. In this paper,

Henon map and Chebyshev map are used for the encryption of the medical images. First, the

X-ray medical image is encrypted with 2D Henon map followed by 2D Chebyshev map. The

security analysis of the algorithm is ensured by evaluating the parameters like key sensitivity,

correlation coefficient, entropy for encryption and PSNR, MSE and elapsed times for

V.Praneeth Kumar Reddy and Annis Fathima A


steganography. For performance evaluation, database of 10 medical x-ray images are

considered.

2. RELATED WORK

The literature survey is of two parts. The first part is on the steganography how the details are

incorporated in the cover image and the steganalysis. The second part is on the encryption

techniques used in the medical images and security analysis on those techniques.

A fast approach for the image encryption [3] is proposed by Reza Moradi Rad, et.al (2013)

with scan patterns and XOR function for simple images. Scan pattern is a spatial accessing

technique to generate a means to select location. Initially blocks are rearranged and then pixels

in each block are rearranged using scan patterns and all blocks are XORed with arbitrary blocks.

This approach is fast and modest.

Zhang et.al (2009) has reviewed the usage of chaotic maps, DES and also the combination

of both for image encryption algorithm [4]. The algorithms were simulated and based on the

analysis proposed an algorithm utilizing logistic Chaotic map. Primarily the scheme generates

pseudo-random sequence from the logistic chaos sequencer for rearranging RGB of the image

chaotically. Double time encryption is done using the improved DES. It has high sensitivity and

the neighboring RGB relevance values are nearly zero.

Symmetrical hybrid based 128 bit key AES-DES algorithm for motion image transmission

[5] was proposed by Vishnu, et.al. (2008). It works on the idea of integrating the AES within

the Feistel network of DES for image encryption. The performance of Hybrid AES-DES

algorithm was better compared to current AES algorithm.

A scheme of AES where the independent round key was produced by the two dimensional

chaotic maps [6] was proposed by Jianhua and Hui (2013). With the mathematical model,

hacker can obtain cipher key by attacking one round of round key. So the generated key is

proposed to change after every round. In this algorithm, the cipher key is directly filled into

the head of round key, so cipher key can be obtained by exhaustive method when the

information of key is leaked in a certain degree. It improves the defect of the traditional AES

algorithm.

A fast and high security image encryption algorithm [7] is proposed by Salim and

Nasharuddin (2014), this approach uses BCD code based decomposition, reordering and a

simple scrambling process to shuffle binary bit planes. A shift column is applied to image which

is constructed after scrambling the bit planes to advance security. In this algorithm a new

scrambling operation was also introduced and applied on bit planes to alter the pixel values and

increasing the key space by 12!.

A fractal based image encryption system [8] is proposed by Kamla (2013), the method has

been adopted using single and multi-fractals. Encryption is based on confusion and diffusion

processes and image information is concealed in complex details of fractal images. For a

general encryption system utilizing multiple fractal images is presented to improve the

performance and to increase the key to hundreds of bits, achieved through the parameters like

multiplexing, feedback delay and independent shifts.

Jolfaei and Wu (2016) reexamined the previous works on cryptanalysis [9] of different

image encryption systems. Chandra, et.al (2015) has analysed chaotic based image encryption

techniques [10] and also reviewed the related works for each technique.

Zhang, et.al (2005) projected and enhanced the properties of confusion and diffusion in

terms of discrete exponential chaotic maps [11], and designed a key scheme to resist the static

attack, differential attack and grey code attack. Image encryption algorithm using Arnold or




Baker and Henon chaotic system is proposed by Abu Zaid et.al (2013). The process also utilizes

code books and Ciphering Feed Back for encryption [12].

Optical image encryption is proposed by Ahmed M.Elshamy (2013), based on chaotic baker

map and double random phase encoding (DRPE) [13]. Chaotic baker map is a permutation

based tool which randomizes the pixel positions based on a secret key in a square matrix.

Algorithm involves two stages to increase security, stage one is pre-processing stage in which

chaotic baker map is performed on the original image, stage two involves classical DRPE.

Singh and Kaur (2011) compared four chaotic maps and noise effects on an encrypted image

[14]. The image encryption is performed using chaotic maps and DNA. In the images with eight

bit grey level each and every pixel is indicated by the DNA sequence of length four. The result

shows that cross chaotic map gives better result but at the cost of increasing complexity.

Authentication system for medical images using steganography [15] is proposed by

Hisham, et.al (2014). Ahmad, et.al (2014) proposed method to protect the medical data using

shared secret mechanism and steganography for two and one bit LSB [16].

For image steganography, the very common approach utilised is LSB algorithm. An

improvement is made in the basic LSB based steganography [17] by Akthar, et.al (2014). Here

the bit inversion technique is organized to improve the quality of the stego-image. LSBs of

pixels or cover image are inverted only for the specified pattern so that less number of pixels

will be modified between cover image and stego-image as compared to the basic LSB

algorithm.

A revisited LSB approach is proposed by Jarno Mielikainen (2006), in this method choice

of adding bits into cover image is random [18]. The embedding process is done using a pair of

pixels as a single unit, where each pixel will carry one bit of information. The proposed method

will embed the data with only few changes in cover image.

LSB algorithm with the combination of midpoint circle approach to choose the pixel

position for hiding the message [19] is proposed by Verma, et.al (2014). With the dimensions

of the cover image found the center of the image to be used to choose the pixels that would be

used to hide the message.

Image steganography based on the DES by means of S-Box mapping and a secret key [20]

is proposed by Manoj, et.al (2012). It offers high security as extraction is impossible without

the awareness of secret key and mapping rules of the algorithm. But, this scheme not just

scrambles the data but also modifies the intensity of pixels which is not favorable.

Hisham, et.al (2014) authenticated medical images using Hilbert numbering [15]. The

authors performed watermarking using twisting style numbering which are good for embedding

but in square shape only. Later enhanced to Hilbert numbering which is appropriate to all

shapes. The capacity of the proposed algorithm is high, it will embed the data all over the image,

regardless region of interest and region of non interest.

A security technique for medical images in health systems [21] is proposed by Kester, et.al

(2015) through encryption and authentication process. The algorithm is fully recoverable

encrypted and watermarked image processing, initially authentication of the medical images

then proceeding for encryption. The entropy and mean values of the images were computed,

and it was found to be same for all ciphered and plain images.

Dagar, 2014 mentioned that, utilising an approach with two different keys to hide the

message bits at random pixels of the cover image [22] is more secured. From literature it is

learnt that the chaotic maps gives the efficient encryption results and using cross chaotic maps

will give enhanced results but increases the computational complexity. For the medical images

robustness is of more importance, hence chaotic maps are used and the complexity factor is not



considered in the work for securing the images. Similarly, for the steganography chaotic maps

are used to improve security by locating and hiding the information.

3. DISCRETE LINEAR SYSTEMS Discrete non-linear systems are complex in structure and dynamic in nature. Random numbers are generated with

the initial values and are very sensitive to the initial conditions. This is similar to butterfly effect. Butterfly effect

solely depends on the initial conditions. A small uncertainty in initial conditions may result in large difference in

the resulting map. It is unendurable to predict the succeeding reaction. Hence this sensitivity is very convenient in

the security justification.

3.1 Henon Map

Henon map was first proposed in 1976 by French astronomer Henon. Henon map is discrete-

time and dynamical system. Based on the initial values and arbitrary constants the random

sequence is generated. The Henon map is generated using the Eq. 1 and 2

Xn+1 = - a Xn2 + b Yn +1 (1)

Yn+1 = Xn (2)

In these expressions, a and b are arbitrary constants; and X0 and Y0 are initial values. The X

and Y variables will form the Henon map, H. These four values form the initial keys for the

Henon map. Henon map with a=1.4, b=0.3, X0=0.1 and Y0=0.1 is shown in the Figure 1(a). The

initial values are the main asset for the generation of the sequences. As like butterfly effect, the

map generate sequence of numbers with high sensitivity towards initial and arbitrary values.

3.2 Chebyshev map

Chebyshev map is introduced by Chebyshev. Chebyshev map has more randomness than Henon

map as shown in the Figure 1(b). The random sequence is generated using the Eq. 3 and 4.

Un+1 = Cos(c arc CosUn) (3)

Vn+1 = Cos(d arc CosVn) (4)

U0 and V0 are the initial values, c and d are the arbitrary constants. The initial values later

acts as key for the logical operation. Figure 1(b) is the chaotic Chebyshev map, C, constructed

with the initial values c=1.4, d=0.3, U0=0.1 and V0=0.1.

(a) (b)

Figure 1 (a) Henon map (b) Chebyshev map




4. PROPOSED APPRAOCH FOR SECURING IMAGES

The 2D chaotic maps namely Henon and Chebyshev are used in the proposed work i.e., for

Steganography Chebyshev map is used and for the efficient Encryption both

Figure 2 Block diagram for generating Crypto-Stego image

Henon map and Chebyshev map are used consequently. To increase the randomness and

robustness, both the maps are used consecutively.The objective of the steganography is to

incorporate the patient’s details in the medical image. In the proposed algorithm for

steganography Chebyshev chaotic map is employed for the higher security in steganography

process.

The flow diagram for obtaining the stego-crypto image is shown in Figure 2. In the

transmitting side, the message is embedded in the medical image. Figures 4 and 5 gives block

diagrams for embedding and retrieving the patient details. The medical image, patient’s details

and the key for generating the chaotic map are inputs in the transmitting side. Initially the

message to be embedded is converted using ASCII code. In the information of length N, initially

twenty one bits are allotted to provide the information about message length as given in Eq. 5

where N gives the total number of bits of information to be inserted. The initial twenty one bits

specify the number of random values to be generated for retrieving message. For selection of

the location, Chebyshev map is utilized and the information bits of the character are embedded

in the LSB of the selected pixel location.

N=21bits + message bits (5)

From the initial values, random numbers are generated by the chaotic map, these initial

values act as keys for the steganography. The generated random numbers are normalized and

standardized to fall in the range {1, mn}, where mxn is the size of the cover image.



Figure 3 Block diagram for steganography

The generated values, XN aid in identifying the pixel location iN, jN in the cover image using

the Equations 6 and 7. iN, jN gives the row and column position in the image.

iN = floor (XN/m) +1 (6)

jN = XN mod(m) (7)

The initial 21 bits for message length and the message bits are inserted in the location iN,

jN. The resultant stego image is safer as a result of the additional sensitivity of the keys for the

generation of random numbers. The algorithm for embedding is given below.

Algorithm for embedding process

Input: Cover image, Stego key, Message

Output: Stego Image

{Step1: Read the cover image.

Step2: Read the message.

Convert message to ASCII

Convert ASCII to binary

Step3: Read the key for chaotic map.

Step4: Generate chaotic map using Stego keys

Get the values, XN, in range {1, mn}.

Step5: Read the normalized values.

for N values

{

Find the pixel location using Equation 5 and 6.

Replace LSBs in cover image with message bit.

}

Step7: Write stego image.

}




At the receiver end the embedded information is retrieved from stego-image using chaotic

map keys as given in Figure 3. With the keys of Chebyshev map, initial 21 random numbers

are generated. These 21 bits give the information of the no. of message bits i.e. N-21. Then N-

21 random numbers are generated in the similar way. From the LSB of the pixel locations

obtained using Eq. 6 and 7, the message bits are derived. The 7 bits are grouped to form ASCII

code, and then converted to character. This finally gives the message and the cover image is

retrieved.

Figure 4 Block diagram for Encryption process

Figure 4 gives the steps involved in the process of the Encryption. With the initial keys,

chaotic maps are generated. The initial values and arbitrary constants act as the keys for the

encryption. Both the Henon and Chebyshev map has independent four keys making it to 8 keys

on total. With the initial keys mentioned in the previous section, random discrete values are

generated. The original image, I, is first encrypted with the generated Henon map, H, as given

in Eq. 8 giving the subsequent encrypted image, I1. Then the image is further encrypted using

Chebyshev map, C as given in Eq. 9. The final resultant image I2 is more secure as it has wide

randomness and very sensitive key.

(8)

(9)

On the other end i.e. in the receiving side, the image I2 is first decrypted with Chebyshev

map, C and later with Henon map, H, to get back the original image I.

5. RESULTS AND DISCUSSIONS

In this work of securing the medical images, 100 medical X-ray images of chest, fractured

shoulder and ankle images randomly collected from the web are used. The implementation is

done using Matlab2013a.

5.1 Performance Analysis for Steganography

The information to be embedded in the medical X-ray image, includes the patient details

and the number of binary bits required to encode the details in ASCII. As the no. of bits required

to write the patient details vary from person to person, it becomes essential to mention the

message length. Otherwise the more random numbers will be generated leading to the

∑ ∑−

=

−

=⊕=

1

0

1

01 ),(),(),(m

i

n

jjiHjiIjiI

∑ ∑−

=

−

=⊕=

1

0

1

0 12 ),(),(),(m

i

n

jjiCjiIjiI



unnecessary computation or it may also lead to difficulty in decoding the required information.

The message length is given in first 21 bits in ASCII format. The format in which the details

are encoded is given below:

{Message length (21 bits); Name; Age; Gender; Date; Clinical place; Major indication}

Each character in the message are converted to ASCII and then to 7 bit binary code. At the

receiver end excluding first 21 bits each 7 bit binary code gives one character. Figures 5(a) and

(b) gives the cover image and stego-image constructed using the Chebyshev map. Henon map

is also used for steganography but due to more randomness of Chebyshev map then Henon map,

it is more preferred than Henon map.

To evaluate the performance characteristics of proposed algorithm, took measures such as

PSNR (Peak Signal to Noise Ratio), Correlation coefficient and Evaluation time. The result is

compared with the existing Steganography approach using LSB algorithms.

5.1.1 Peak Signal to Noise Ratio

Peak Signal to Noise Ratio (PSNR) gives the noise content in an altered image compared to

source image, and in this case it is between cover image and stego image. MSE is Mean Square

Error; it gives cumulative square error between cover image and stego image. MSE and PSNR

between two images are calculated using the Eq. 10 and 11, where m and n are number of rows

and columns of an image, L is the maximum graylevel value i.e. 255.

Table 1 tabulates the evaluated PSNR value for stego-image computed using existing LSB

algorithm and the proposed approach using Chebyshev map.

(a) (b)

Figure 5(a). Cover Image and (b) Stego Image

( ) ( )[ ]

nm

jiIjiI

MSE

m

i

n

j

∗

−

=

∑∑−

=

−

=

1

0

1

0

2

21 ,,

(10)

=

MSE

LPSNR

2

10log10

(11)

TABLE 1. Comparisons of PSNR for stego-image

S.No. PSNR for LSB

algorithm(dB)

PSNR for

proposed

approach(dB)

Image 1 71.5485 77.5881

Image 2 75.2996 79.9217

Image 3 80.5193 86.4833

Image 4 71.4873 78.0099

Image 5 77.2018 82.8068

Image 6 72.9307 77.6082

Image 7 71.4592 76.4243




Image 8 82.6137 86.8169

Image 9 83.7337 89.0713

Image 10 78.7279 83.9378

5.1.2 Correlation Coefficients

Correlation coefficient is the measure of similarity between two images. The correlation

coefficient between the cover image and stego-image are very close. The results are tabulated

in Table 2 with comparison to the traditional algorithm.

TABLE 2. Comparison of correlation coefficients for stego-image

S.No.

Correlation

for LSB

algorithm

Correlation for

proposed approach

Image 1 0.999998247 0.999999471

Image 2 0.999997055 0.999999891

Image 3 0.999998980 0.999999971

Image 4 0.999998552 0.999999567

Image 5 0.999994691 0.999999830

Image 6 0.999993655 0.999999797

Image 7 0.999991853 0.999999758

Image 8 0.999993771 0.999999801

Image 9 0.999999320 0.999999790

Image 10 0.999999151 0.999999456

5.1.3Elapsed Time

Elapsed time is the time taken to obtain the stego-image using the proposed algorithm. Table 3

gives the result for elapsed time. From the table it is observed that elapsed time for the proposed

algorithm is lower than the simple LSB algorithm. In LSB algorithm initially every LSB of

pixels are made to zero and then message bits are inserted one by one in an order, but in the

proposed algorithm only at the selected random pixel locations message bits are inserted at

LSB. This results in the time conservation.

5.2 Performance analysis for Encryption

For the better encryption procedure should be robust to security attacks and statistical attacks.

To evaluate the

TABLE 3. Elapsed times in computing stego-image

S.No.

Time taken for

LSB

approach(sec)

Time taken for

proposed

approach(sec)

Image 1 0.6239 0.5579

Image 2 0.8480 0.7339

Image 3 1.2943 0.8319

Image 4 0.6426 0.6170

Image 5 0.7848 0.5529

Image 6 0.5614 0.5676

Image 7 0.5704 0.5327

Image 8 1.2212 0.6889



Image 9 1.4514 0.6730

Image 10 1.0211 0.5295

performance of the proposed algorithm, the measures such as key sensitivity, entropy and

correlation coefficient are measured.

For the comparative analysis, the encryption was done with Henon map and Chebyshev

map individually. Then it is compared with the approach combining both the maps.

5.2.1 Histogram Analysis

For an image, histogram plot gives the frequency of the intensity levels in an image. From

histogram of an image it is easy to estimate the intensity or tonal distribution Figure 6(a) shows

the histogram of the original image. Figure 6(b) shows the histogram of the encrypted image

using Henon map.

On comparison, it is clear that the encrypted image is of high contrast when compared with

that of the original image. Similarly Figure 6(c) shows the histograms of the encrypted images

using Chebyshev map. For the image encrypted with both maps, histogram is shown in Figure

6(d). From the results histogram for original image and encrypted image is different. Due to

high contrast it will be difficult to extract the information without keys. Histogram for the

original image and decrypted image is observed to be same.

The encryption of an image is initiated with the initial keys and they are required to be more

sensitive. The sensitivity of the keys is directly related to the robustness that can be achieved.

In case of Henon Map the initial key values are a=1.4, b=0.3, X0=0.1 and Y0=0.1.

(a) (b)

(c) (d)

Figure 6 Histogram of (a) Original Image (b) Encrypted with Henon map (c) Encrypted with

Chebyshev map (d) Decrypted with different keys

5.2.2 Key Sensitivity

The original and the encrypted image with H values are shown in Figure 7(a) and 7(b)

respectively. Figure 7(c) shows the decryption of the encrypted image with the same key values

except for very minor change in the value of A as X0=0.001. From the resultant image shown it

is clear that the keys are very sensitive.

Similarly, for the case of encryption with Chebyshev map. The initial keys are c=1.4, d=0.3,

U0=0.1 and V0=0.1 encrypted with these values and to get the exact image after decryption its

mandatory to use the same keys. For the analysis purpose, the initial key values are modified

as c=1.3 and d=0.33, and the result is shown in Figure 7 (e).




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

(e) (f) (g)

Figure 7 (a) Original Image (b) Encrypted Image using only Henon map (c) Decrypted using

different key in Henon map case (d) Encrypted Image using only Chebyshev map (e) Decrypted Image

Using different key in Chebyshev map (f) Encrypted Image using Henon Map and Chebyshev Map

(g) Decrypted Image with original key

On using the combination of two maps the keys are more sensitive and altering even one

key will not extract the original image after decryption. On subjective analysis, from the results

it is proven that Henon map have more sensitivity and the large key space, better key sensitivity

and robust security which is more particular in security of medical images. As it has large key

space it will be difficult to debug the key by search method.

Figure 7(f) shows the encrypted original image using the combined chaotic maps. The

decrypted image on the receiving side using 8 keys is shown in Figure 7(g).

5.2.3 Correlation and Entropy

The other performance metrics used for evaluation are correlation coefficient and entropy.

Correlation defines the relation or matching between two images, if correlation value is 0 then

there is a random relation or non-linear relation between two images and if the value is 1 then

there is linear relation between two images. For the better encryption the correlation coefficient

should be 0. Entropy is the measurement of uncertainty related with the random variable.

The results of entropy for the sample 10 medical x-ray images is given in Table 4. Table 5

gives the correlation coefficient between original and encrypted images

TABLE 4. Entropy of sample images

S.No.

Origin

al

Image

Encr

ypted

with

Heno

n

Encryp

ted

with

Chebys

hev

Encryp

ted

combo

map

Image 1 7.4771 0.0379 0.0370 0.0357

Image 2 7.5451 0.0352 0.0398 0.0409

Image 3 7.8379 0.0359 0.0284 0.0355

Image 4 7.7466 0.0391 0.0291 0.0368

Image 5 7.8612 0.0359 0.0289 0.0367

Image 6 7.3164 0.0363 0.0387 0.0365



Image 7 7.3976 0.0380 0.0453 0.0367

Image 8 7.7988 0.0340 0.0352 0.0345

Image 9 7.7367 0.0344 0.0344 0.0364

Image10 7.3454 0.0387 0.0415 0.0357

The correlation coefficient is calculated between the original image and encrypted image,

also the correlation between original image and decrypted image are evaluated. The results are

tabulated in Table 5. The value of correlation coefficient on an average of 0.025 when image is

encrypted using Henon map, the value on an average of 0.035 when encrypted with Chebyshev

map and the average value is 0.002 when encrypted with the combination of two maps. Hence

correlation coefficient is very near to zero when used the combination of two maps. The

correlation coefficient between original image and decrypted image is found to be 1.0.

TABLE 5. Correlation coefficients

S.No.

Encry

pted

with

Henon

Encrypt

ed with

Chebysh

ev

Encrypte

d with

Henon

and

Chebysh

ev

Dec

rypt

ed

ima

ge

Image1 0.028

5 0.0370 0.0004 1

Image2 0.016

5 0.0398 0.0043 1

Image

3

0.033

0 0.0284 0.0021 1

Image

4

0.033

8 0.0291 0.0023 1

Image

5

0.044

6 0.0289 0.0021 1

Image

6

0.016

8

0.0387 0.0014 1

Image

7

0.020

9

0.0453 0.0004 1

Image

8

0.030

4

0.0352 0.0006 1

Image

9

0.038

5

0.0344 0.0023 1

Image1

0 0.019

1

0.0415 0.0021 1

6. CONCLUSION

A stego-crypto methodology is proposed to avoid misrepresentation of medical X-ray images

for the fraudulent claims. In steganography it is proposed to enclose the details of patient in the

image with the reference of pixel location by random numbers generated using Chebyshev map.

The performance is evaluated in terms of PSNR, elapsed time and correlation. From the

performance characteristics the proposed algorithm gives better results and better security.

Followed by steganography, encryption is done using the chaotic systems. For comparison,

encryption is performed with three approaches, using Henon map, Chebyshev map and

combination of both maps. The performance metrics used for evaluation are histogram, entropy

and correlation. From the results, it is observed that the combination of Henon map and




Chebyshev map will give the better results and give robust security to the medical images but

at the cost of computational complexity. As robustness is more specific for insurance claims,

the combined approach is preferred.

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Documents

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