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International Journal of Electrical and Computer Engineering (IJECE)

Vol. 10, No. 1, February 2020, pp. 935~946

ISSN: 2088-8708, DOI: 10.11591/ijece.v10i1.pp935-946 935

Journal homepage: http://ijece.iaescore.com/index.php/IJECE

Image steganography using least significant bit and

secret map techniques

Ashwak ALabaichi1, Maisa'a Abid Ali K. Al-Dabbas2, Adnan Salih3

1Department of Biomedical Engineering, Engineering College, University of Kerbala, Iraq

2Department of Computer Science, University of Technology, Iraq

3Department of Computer Science, Science College, University of Kirkuk, Iraq

Article Info

ABSTRACT

Article history:

Received Aug 6, 2019

Revised Oct 2, 2019

Accepted Oct 11, 2019

In steganography, secret data are invisible in cover media, such as text,

audio, video and image. Hence, attackers have no knowledge of the original

message contained in the media or which algorithm is used to embed or

extract such message. Image steganography is a branch of steganography in

which secret data are hidden in host images. In this study, image

steganography using least significant bit and secret map techniques is

performed by applying 3D chaotic maps, namely, 3D Chebyshev and 3D

logistic maps, to obtain high security. This technique is based on the concept

of performing random insertion and selecting a pixel from a host image.

The proposed algorithm is comprehensively evaluated on the basis of

different criteria, such as correlation coefficient, information entropy,

homogeneity, contrast, image, histogram, key sensitivity, hiding capacity,

quality index, mean square error (MSE), peak signal-to-noise ratio (PSNR)

and image fidelity. Results show that the proposed algorithm satisfies all

the aforementioned criteria and is superior to other previous methods. Hence,

it is efficient in hiding secret data and preserving the good visual quality of

stego images. The proposed algorithm is resistant to different attacks, such as

differential and statistical attacks, and yields good results in terms of key

sensitivity, hiding capacity, quality index, MSE, PSNR and image fidelity.

Keywords:

3D Chebyshev

3D logistic map

LSB

Secret message

Steganography

Copyright © 2020Institute of Advanced Engineering and Science.

All rights reserved.

Corresponding Author:

Ashwak ALabaichi,

Department of Biomedical Engineering,

Engineering College,

University of Kerbala, Iraq.

Email: ashwaq.alabaichi@gmail.com

1. INTRODUCTION

The Communication is vital in the modern world. During communication, information is transmitted

through different data channels. This process is prone to serious security problems. Increasing attention has

thus been paid to the discovery of ways to protect valuable information during its transmission. Cryptography

is a technique used to secure communication secrecy, and several methods have been proposed to encrypt

and decrypt data and thereby ensure message secrecy. However, maintaining the secrecy of message contents

is not always sufficient, hence the use of ciphertext. Ciphertext is easy to notice, but it informs others when

communication channels are monitored. Thus, the delivery of secret messages by exchanging plaintext has

been widely investigated in the past two decades. Maintaining message secrecy is required and is realised

through steganography. Steganography involves hiding information in a way that no information appears to

be hidden, whereas cryptography involves encrypting information by using a key and sending this

information through a specific channel. A user or process can observe the communication process, but they

cannot steal the relevant information unless they possess the key. In steganography, the person or process is

unaware of the transmission of secret information. Therefore, no attempt is made to extract information [1-7].

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The term steganography is derived from the Greek words stegos, which means cover, and grapha,

which means writing. It is defined as covered writing that hides the existence of the actual message.

Steganography is used to hide information inside other media. Its two main steps are embedding a secret

message inside a cover using a stego key and extracting the secret message from the cover using the stego

key. The combination of embedded message and cover creates stego media. Stego keys are utilised to hide

and extract secret messages. Only the holders of stego keys can correctly retrieve hidden secret messages.

Steganography can be described with the following formula: stego media = cover media + embedded

message + stego key.

Steganography is classified into linguistic steganography and technical steganography.

Linguistic steganography involves the use of natural language as a carrier for hiding secret data.

Technical steganography employs a multimedia carrier. Most digital file formats are characterised by a high

degree of redundancy that benefits steganographic techniques. Common steganographic techniques are

steganography in texts, images, audio and videos. Among these varieties of file formats, digital images are

the most popular because of their frequency on the internet and high capacity for data transmission while

minimising image quality degradation [6-10]. Steganographic methods may be in the form of spatial domain

embedding or frequency domain embedding. Frequency domain embedding involves the transformation of

images into frequency components through discrete cosine transform, fast Fourier transform and discrete

wavelet transform (DWT). Messages are embedded at the bit or block level. In spatial domain embedding,

information is directly hidden depending on the intensity of pixels. Frequency domain procedures are robust

and are commonly used for watermarking, whereas spatial domain methods provide high capacity and are

widely used in steganography. Steganography and its usefulness are influenced by three aspects, namely,

1) capacity, which refers to the number of data bits that can be hidden in cover media; 2) visual quality of

stego images, which must remain unchanged (imperceptibility); and 3) robustness, which refers to

the resistance to modification or destruction [3, 9, 11].

A widely used spatial domain method is the least significant bit (LSB) substitution in which lower

order image bits (those that do not possess useful image information) are replaced with secret message

bits [9,12]. The use of LSB substitution preserves image quality without entailing complex operations. In this

method, the bits of secret data are hidden in the K-LSB plane in each pixel of a cover image. The most

widely known LSB methods are LSB matching (LSBM), LSBM revised (LSBMR) and edge adaptive-based

LSBMR steganography. However, most of these techniques are most of these techniques are probably easy to

be broken. Therefore these methods have undergone improvements in various aspects [1, 2, 7, 8, 10, 13].

In particular, researchers have used chaos theory. Unlike traditional methods, chaotic methods are sensitive

to primary conditions and nonperiodic, nonconvergence and controlling parameters. Hence, they have been

utilised by many researchers as a vital solution in their work [9]. Although a 1D chaotic system is highly

efficient, it has some inherent disadvantages, such as small key assignment and inadequate security that

reduces its efficiency and performance.

Numerous systems encompassing one-, two- or higher-dimensional systems with chaotic maps have

been introduced in recent years. 3D maps provide higher security and randomness than 1D and 2D

maps [14-17]. Chaos-based steganography algorithms have attracted much attention in existing studies

because of their efficiency and applicability to steganography for providing secure communication.

Bandyopadhyay, Dasgupta, Mandal and Dutta [2] put forward a new approach secure data are built into

digital images by using a 1D logistic map. This logistic map is used to encrypt secret messages before

embedding. Rajendran and Doraipandian [5] put forward a novel method for hiding secret images using 1D

logistic maps. These 1D logistic maps are utilised to generate pseudo random keys. These keys are used to

randomly select the pixel positions of cover images for hiding secret images. Sharif, Mollaeefar and

Nazari [6] also proposed a novel algorithm for image steganography based on chaos theory. The proposed

algorithm involves a novel 3D chaotic map (LCA map) with a maximum Lyapunov exponent of 20.58, which

is adopted to generate three chaotic sequences. Mishra, Routray and Kumar [9] proposed the embedding of

secret information in a digital image in the spatial domain through LSB and Arnold’s transform. Arnold’s

transform is applied two times in two different phases. Thenmozhi and Chandrasekaran [13] presented

a novel technique for image steganography by using a DWT chaotic system. In this method, Henon mapping

is applied to secret images, and 2D DWT is performed on cover images. Ghebleh and Kanso [18] developed

a new robust chaotic method for digital image steganography, in which a 3D chaotic cat map is used to

embed secret messages, lifted DWT is adopted to provide robustness, and Sweldens’ lifting is used to ensure

integer-to-integer transformation. Bilal, Imtiaz, Abdul, Ghouzali and Asif [19] introduced a zero-

steganography algorithm based on chaos theory which embeds data according to the relationship between

cover images, chaotic sequences and payloads rather than directly embedding data in cover images. Alam,

Kumar, Siddiqui and Ahmad [20] improved a method for image steganography by utilising edge detection

and logistic maps as a random generator of secret keys for random LSB substitution. Sabery and

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Image steganography using least significant bit and secret map techniques (Ashwak ALabaichi)

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Yaghoobi [21] proposed the use of a simple logistic map to hide secret images in host images. Embedding

was performed in the logistic map to determine the blocks of pixels. Roy, Sarkar and Changder [22]

presented chaos-based adaptive image steganography, in which the efficiencies of matrix encoding and

LSBM are combined for embedding data and chaos is utilised to provide enhanced security. Kanso and

Own [23] introduced a digital image steganography method based on Arnold’s cat map. Anees, Siddiqui,

Ahmed and Hussain [24] proposed a steganographic method in the spatial domain in which chaotic maps are

used to resolve pixel positions. Raghava, Kumar, Deep and Chahal [25] proposed the new use of Henon

chaotic maps to boost the conventional LSB technique for image steganography.

The current study mainly focuses on made image steganography using LSB techniques is complex

and the hidden information is controlled by the secret keys and cannot be retrieved without the same secret

keys. A new approach to LSB-based image steganography that uses secret maps is introduced. A secret map

is controlled by using secret keys to secure hidden information. Hidden information may be inserted

sequentially or randomly. In this study, the hidden information is randomly distributed before hiding it in

a cover image to provide better security than sequential methods. The hidden information is permuted by

using a 3D Chebyshev map. Insertion is performed through the chaotic sequence generated by the chaotic

map. The cover image pixels are randomly selected on the basis of the secret map. The secret map is created

by using secret keys that are generated through a 3D logistic map. The hidden information is controlled by

the secret keys and cannot be retrieved without the same secret keys. Thus, using secret keys enhances

the security of hidden information in LSB-based image steganography.

The rest of the paper is organised as follows. Section 2 presents the chaotic map, its properties and

the types used in this study. Section 3 describes the proposed algorithm. Section 4 provides the experimental

results of the proposed algorithm. Section 5 discusses the analysis of the proposed algorithm based on several

factors. Section 6 presents the conclusions and recommendations for future work.

2. CHAOTIC MAP

Chaos refers to a state of disorder. In the field of mathematics, chaotic behaviour is revealed by

maps serving an evolution function. Discrete-time dynamical systems are also referred to as maps.

Chaos theory is used to encrypt information, and DWT is used to hide information [5, 13]. This theory

centres on system behaviour that is characterised by deterministic laws but shows randomness and

unpredictability. That is, a dynamical system depends on its initial conditions with high sensitivity that any

slight variation in the initial parameters results in a different chaotic sequence. Chaos is difficult to define

comprehensively [2, 15]. The sensitivity of dynamical system is fractal in nature and thus benefits the search

for solutions to nonlinear equations. Chaos theory boosts the confidentiality, nonperiodicity, randomness and

easy implementation are the main properties that lead to benefit of them in steganography techniques.

Chaotic systems have been used in several fields, including nonlinear dynamics that is man-made and

natural real systems. Numerous steganographic methods based on chaos theory have been proposed and

discussed in the past few decades [2]. In these methods, secret keys are generated using 3D logistic and 3D

Chebyshev maps.

2.1. 3D logistic map

A logistic map is a simple chaotic map which belongs to the family of first-order difference

equations. It can be mathematically represented as follows:

Xn+1 =RXn(1− Xn),

(1)

where the system parameter is μ [0,4] and the initial condition is X0(0,1). A logistic map chaotically

behaves with R (3.5699456,4] [19, 20]. A 1D logistic map can be extended to the 3D, as defined

in (2) to (4).

Xn+1= RXn(1−Xn)+β

Xn+α

,

(2)

Yn+1= RYn(1−Yn)+β

Yn+α

,

(3)

Zn+1 = RZn(1− Zn) +β

Zn+α

.

(4)

The parameters of a nonlinear system are valued in the range of 0.53 <R< 3.81, 0 <β< 0.022, 0 <α< 0.015,

where X0, Y0 and Z0 are defined in [1, 16, 17, 26].

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2.2. 3D chebyshev map

Chebyshev polynomials are utilised to generate the secret keys required to hide information.

Chebyshev polynomials are characterised as Fn (x) of the first type which is a polynomial of x with degree n.

They comprise the prototype of a chaotic map and are defined as Fn(x) = cosnθ, where x = cosθ. By letting n

= 0, 1, 2, 3, 4, we can obtain cos0θ = 1, cos1θ = cosθ, cos2θ = 2cos2θ − 1, cos3θ = 4cos3θ − 3cosθ and cos4θ

= 8cos4θ − 8cos2θ + 1. With cosθ = x, we obtain F0(x) = 1, F1(x) = x, F2(x) = 2x2 − 1, F3(x) = 4x3 −3x and

F4(x) = 8x4 −8x2 + 1. The transformations are expressed as

F2(x) = 2x2 – 1,

(5)

F3(y) = 4y3−3y,

(6)

F4(z) = 8z4 −8z2 +1.

(7)

The Chebyshev polynomial map is Fp: [−1, 1][−1, 1] of degree p, when p> 1 [16, 17]. The (5) to (7) are

used to generate secret keys which are then used as a secret map of image pixels in the hiding process.

3. PROPOSED ALGORITHM

This section is composed of two phases (embedding and extracting phases) that are explained in

the following subsections.

3.1. Embedding phase

The embedding phase includes several steps, including the following:

1. Select the secret message and host image.

2. Set the length of the secret message in the first two pixels of the host image.

3. Convert the secret message to ASCII values and then to binary numbers. For example, S = 83,

01010 011.

4. Initialise the secret parameters of the 3D Chebyshev map to generate secret keys X, Y and Z.

= (* 104 the length of the binary secret message),

(8)

Y = (Y* 104od 3),

(9)

Z = (Z* 1043).

(10)

5. Permute the secret message on the basis of the secret keys generated from (8) before hiding it in the host

image. For example, let the secret message be 01010011 with a length of 8. Suppose that the secret keys

of X are expressed as 1, 5, 6, 4, 0, 2, 3, 7. Then, the secret message is labelled as 10100011.

6. Decompose the binary numbers into three separate groups as follows: 10, 100, 011 (0, 1, 2).

7. Select the group that will be hidden first on the basis of the secret keys generated from (9). For example,

let the generated secret keys be {1, 2, 0}. In this case, select 100 first, followed by 011 and 10.

8. Break down the red (R), green (G) and blue (B) components of the image. Store the components in

three N×M arrays, where N and M are the number of array rows and columns, respectively.

9. Label the components as follows:

RGB

0 12

10. Select which component (R, G or B) will be hidden first on the basis of the secret keys generated

from (10). For example, let the generated secret keys be {2, 0, 1}. In this case, the secret message 100 is

hidden in the B component, followed by 011 in the R component and 10 in the G component.

11. Decompose each component (array) into nonoverlapping blocks by dividing N and M by 8. The result

represents the number of blocks in each component. For example, the result is 128 blocks of 4×4 whenN

and M are 512.

12. Initialise the secret parameters of the 3D logistic map.

13. Generate the secret keys for each block into R, G and B components.

14. Convert the secret keys into decimal numbers by using the following equations:

= or(*104d16),

(11)

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Y = (Y*10416),

(12)

Z = or(Z*10416),

(13)

Where X, Y and Z represent the secret keys for blocks R, G and B, respectively.

15. Store these secret keys in an 8×8 array with a range of 0–63. The values in the array should satisfy

the condition without repeating the values in the rows and columns.

16. Map the values of the blocks with the values in Step 14 and hide their information. Hence, the host

image pixels are randomly selected on the basis of the generated secret keys in each block in Step 14.

For simplification, we take the following:

Secret keys (X)

Secret keys (Y)

Secret keys (Z)

5

6

3

2

4

0

1

7

8

2

5

6

3

4

1

0

8

7

3

1

0

6

5

8

4

7

2

Host image (R)

Host image (G)

Host image (B)

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

We choose the sixth (5) pixel in the block of host image (R) and convert it into binary form to embed

011 into 3LSB. Then, we choose the third (2) pixel in the block of host image (G) and convert it into binary

form to embed 10 into 2LSB. Subsequently, we choose the fourth (3) pixel in the block of host image (B) and

convert it into binary form to embed 100 into 3LSB.

17. Convert the binary values to decimal values.

18. Repeat Steps 13 to 16 to embed all bytes of the secret message in all components of the host image.

19. Obtain the stego image. Figure 1 presents the diagram of the embedding phase.

Figure 1. Diagram of embedding phase

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3.2. Extraction phase

In this phase, the secret message is retrieved from the stego image. This procedure is the opposite of

the embedding process. In the extraction phase, the receiving party must be aware of the initial values of

the 3D, Chebyshev and 3D logistic maps to produce secret keys X, Y and Z. The stego image is used as input

in this phase. Subsequently, the stego image is blocked into nonoverlapping 4×4 blocks, and the image pixels

are selected in the blocks on the basis of the secret keys for each block of the 3D logistic map, which are X

for R, Y for G and Z for B. The procedure implemented in the embedding phase is then run. Z of the 3D

Chebyshev map is obtained by using chaotic sequences. The order of the components is selected in

the embedding process, whereas the chaotic sequences of Y determine the order of the groups of bits that are

hidden. The original order of characters in the secret message is known through the X values.

4. EXPERIMENTAL RESULTS

The embedding and extraction phases of more than 30 images were run on MATLAB R2018a on

a computer with Windows 10 64 bit, Intel Core i7-7500U processor, 8 GB CPU and 2400 MHz RAM. In this

section, four standard well-known images, namely, Lena, Pepper, Baboon and Barbara, are presented.

Figure 2(a–d) illustrates the host and stego images. As shown in the figure, the host and stego images do not

present significant differences. Hence, the proposed algorithm can successfully hide secret messages in host

images without any distortion. The correct secret messages can be easily and correctly extracted from stego

images with valid stego keys when stego images are transmitted to authorised receivers, as explained in

the next section. The following initial values were used in the 3D logistic and 3D Chebyshev maps in

all experiments:

For the 3D logistic map, x0 = 0.976, y0 = 0.677, z0 = 0.973, R = 3.79, β = 0.020, α = 0.014, where x denotes

R, y denotes G and z denotes B.

For the 3D Chebyshev map, x0 = 0.234, y0 = −0.398, z0 = −0.88.

Figure 2. (A) host images, (B) stego images

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5. SECURITY ANALYSIS

In this section, several statistical analyses are presented to verify the effectiveness and efficiency of

the proposed algorithm against statistical attacks.

5.1. Correlation coefficient

Correlation coefficient r is used to measure the extent and direction of the linear correlation of two

random variables. A correlation coefficient close to 1 indicates that two random variables are closely related;

the opposite is true when the correlation coefficient is close to 0. Coefficient r can be calculated as

follows [18]:

r=

,

(14)

Where Xi is the pixel intensity of the original image, Xm is the mean value of the original image intensity, Yi is

the pixel intensity of the stego image and Ym is the mean value of the stego image intensity. The results of

this test are shown in Table 1. All values in Table 1 are close to 1, indicating that the host and stego images

are closely related.

Table 1 Correlation coefficient results

Image

Correlation coefficients

R G B

Baboon

0.9998

0.9998

0.9997

Lena

0.9983

0.9986

0.9965

Peppers

0.9995

0.9998

0.9994

Barbara

0.9998

0.9998

0.9998

5.2. Information entropy

The security of a steganographic system is measured in terms of entropy. Let, ,..., be m

possible elements with probabilities P(), P(), ..., P(). The entropy is given as

.

(15)

This equation yields an estimate of the average minimum number of bits that is needed to encode

a string of bits on the basis of the frequency of the symbol [27].

5.3. Homogeneity

The value returned in homogeneity analysis is used to determine how close the element distribution

in the grey-level co-occurrence matrix(GLCM) is to the GLCM diagonal. Image homogeneity is calculated as

Hom=

,

(16)

where p(i, j) denote the pixel values at the ith row and jth column and (i, j) represent the indices of row and

column numbers, respectively [6].

5.4. Contrast

Contrast analysis produces a measure of the intensity contrast between a pixel and its neighbour in

an entire image. For viewers, contrast analysis helps them recognise objects in the texture of an image.

Contrast analysis is written as [6]

C=

.

(17)

Table 2 presents the results of the tests on the four standard images.

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Table 2. Statistical analysis of four images

Statistical

Analysis

Images

Host image

Stego image

R

G

B

R

G

B

Entropy

Baboon

7.8457

7.7842

7.5144

7.8457

7.7852

7.5146

Lena

7.2477

7.5883

6.9232

7.2477

7.5884

6.9232

Peppers

7.3857

7.6658

7.1687

7.3859

7.6658

7.1687

Barbara

7.4892

7.4859

7.2022

7.4892

7.4859

7.2022

Homogeneity

Baboon

2.3501e+03

2.3054e+03

1.9043e+03

2.3491e+03

2.3031e+03

1.9025e+03

Lena

1.4164e+03

752.1079

796.8155

1.4137e+03

749.4450

794.8281

Peppers

2.6881e+03

2.2229e+03

1.2909e+03

2.6864e+03

2.2209e+03

1.2899e+03

Barbara

2.7576e+03

3.0292e+03

1.9838e+03

2.7561e+03

3.0281e+03

1.9827e+03

Contrast

Baboon

2.7475e+09

2.5673e+09

2.1547e+09

2.7475e+09

2.5672e+09

2.1546e+09

Lena

1.1391e+08

6.2484e+07

6.4222e+07

1.1367e+08

6.2307e+07

6.3999e+07

Peppers

1.6035e+09

1.6052e+09

9.1440e+08

1.6034e+09

1.6052e+09

9.1437e+08

Barbara

8.4412e+09

7.2760e+09

6.5267e+09

8.4399e+09

7.2773e+09

6.5267e+09

5.5. Image histogram

A histogram shows the exact occurrence of each pixel in the image. The high similarity between

the host and stego image histograms indicates the occurrence of minimal distortion after embedding

the secret image into the host image [5,10]. This test is performed on many images. The histogram of

the Lena image is presented. Figure 3 shows the histogram of the host and stego images of three components.

From Figure 3 can be shown that the histogram of the proposed algorithm highlights slight changes between

the host and stego images.

Figure 3. Histogram of host and stego images of three components

5.6. Key sensitivity

Chaotic maps are extremely sensitive to initial conditions and system control parameters.

The slightest change can cause difficulties in the extraction of hidden messages from stego images [6, 18].

The key sensitivity test conducted in this work is aimed at establishing the sensitivity of the proposed

algorithm to slight modifications in secret keys. 3D logistic and Chebyshev maps are used in the proposed

algorithm and are rigorously evaluated. The sensitivity of the proposed algorithm towards initial state

conditions is shown accordingly. The Pepper image is used as the host image in this test. The first change is

applied to the initial values of the 3D logistic map. The subsequent change is applied to the initial values of

the 3D Chebyshev map. Suppose that the selected keys for the 3D logistic map are α = 0.014, β = 0.020 and

R = 3.79 while the slightly different keys are α = 0.01400001, β = 0.020 and R = 3.79; α = 0.014,

β = 0.02000001 and R = 3.79; and α = 0.014, β = 0.020 and R = 3.7900001. Figure 4 shows that the hidden

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message cannot be extracted from the stego image. Suppose that the selected keys for the 3D Chebyshev map

are x0 = 0.234, y0 = −0.398 and z0 = −0.88 while the slightly different keys are x0 = 0.23400001,

y0 = −0.398 and z0 = −0.88; x0 = 0.234, y0 = −0.39800001 and z0 = −0.88; and x0 = 0.234, y0 = −0.398 and

z0 = −0.8800001. Briefly, we present only the case of α = 0.014, β = 0.020 and R = 3.79 and the slight

changes of α = 0.01400001, β = 0.020 and R = 3.79.

(a)

(b)

(c)

Figure 4. (a) Hidden message, (b) text extraction using the right key, (c) text extraction using the wrong key

5.7. Hiding capacity

Hiding capacity refers to the maximum number of bits that can be hidden in a host image while

ensuring the acceptable quality of the resultant stego image. A large hiding capacity boosts the performance

of steganographic schemes [7]. In the proposed algorithm, one byte is embedded in each pixel of the true

image. Each pixel contains three components, namely, R, G and B. Each component contains one byte.

Therefore, the capacity of the proposed algorithm is equal to 8/24.

5.8. Quality index

We measure the quality of the stego image by using a quality index as shown in Table 3 [20]

calculated as

,

,

=

,

(18)

where n is the number of pixels in the image, H is the host image and T is the stego image. Q falls in

the range of 1 and −1. The host and stego images are dissimilar when the calculated value is −1, whereas

the two images are identical when the calculated value is 1 [6]. This test is applied to the Barbara image for

the three components R, G and B after hiding the secret message with 50,000 letters. The results are

presented in Table 3. Some of the results are 1, and others are close to 1. Thus, the proposed algorithm has

good image quality, and the stego image has high similarity with the host image. Therefore, statistical

analysis cannot be used to extract secret messages and overcome the steganography algorithm.

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Table 3. Results of quality index

Images

Quality Index

R

G

B

Baboon

0.9992

1.0000

1.0000

Lena

1.0000

1.0000

1.0000

Peppers

1.0000

0.9960

0.9910

Barbara

1.0000

1.0000

0.9997

5.9. Mean square error

The mean square error (MSE) is calculated by comparing the bytes of two images. A pixel

comprises 8 bits, and thus, 256 levels are available to represent various grey levels. MSEs are valuable when

the bytes of an image are compared with the corresponding bytes of another image. Let h and s be the host

and stego images, respectively. MSE can be computed as

MSE=

(19)

where H and W respectively denote the numbers of rows and columns of the host image, P (i, j) represents

the pixel of the host image at the (i, j) position and S(i, j) represents the pixel of the stego image at the (i, j)

position. The best value of MSE is the value that minimises it [7, 11]. This test is applied to four images for

three components R, G and B after hiding the secret message with 50,000 letters. The results are shown in

Table 4. The small values in Table 4 indicate that the proposed algorithm passes the test.

Table 4. Results of MSE

Images

MSE

R

G

B

Baboon

1.5877

1.8215

1.6841

Lena

2.9967

2.0188

1.8811

Peppers

2.0621

2.2507

2.0776

Barbara

1.1518

1.0852

1.1426

5.10. Peaksignal-to-noise ratio

The peak signal-to-noise ratio (PSNR) is a parameter used to measure the amount of

imperceptibility in decibels. It measures the quality between the host and stego images. A large PSNR value

indicates that a small difference exists between the host and stego images. By contrast, a small PSNR value

indicates a huge distortion between the host and stego images. The steganographic algorithm aims to provide

a large PSNR value. PSNR is defined on the basis of the MSE as follows:

PSNR=

=20.

(20)

where L denotes a greyscale image’s peak signal level and is equal to 255 [5, 7, 28]. The PSNR test is applied

to four images for three components R, G and B after hiding the secret message with 50,000 letters.

The results are shown in Table 5. The proposed algorithm obviously generates large PSNR values, which

indicate strong resistance against statistical attacks.

Table 5. Results of the peak signal-to-noise ratio (PSNR)

Images

PSNR

R

G

B

Baboon

45.9012

45.5605

46.1571

Lena

39.1357

39.1237

39.1989

Peppers

45.0216

44.6416

44.9892

Barbara

47.5509

47.8098

47.5859

5.11. Image fidelity

Image fidelity is another metric used to show the robustness of the proposed scheme. Image fidelity

is calculated as follows [6]:

IF = 1-

.

(21)

Int J Elec & Comp Eng ISSN: 2088-8708

Image steganography using least significant bit and secret map techniques (Ashwak ALabaichi)

945

This test is applied to four images for three components R, G and B after hiding the secret message with

50,000 letters. The results are shown in Table 6.

Table 6. Results of image fidelity

Image

Image Fidelity

R

G

B

Baboon

0.9999

0.9999

0.9998

Lena

0.9994

0.9994

0.9994

Peppers

0.9999

0.9999

0.9997

Barbara

0.9999

0.9999

0.9999

5.12. Comparison of the proposed scheme with other methods

The results of the proposed algorithm for the Baboon image with a size of 256×256 in three tests are

compared with those of other methods as shown in Table 7. The proposed algorithm is clearly superior to all

methods in terms of PSNR, quality index and image fidelity

Table 7. Results of comparison between the proposed scheme and other methods

Methods

PSNR

Quality Index

Image Fidelity

Proposed method

45.8661

0.9998

0.9999

Sharif, Mollaeefar and Nazari [6]

38.7540

0.99967

0.99940

Ghebleh and Kanso [14]

36.5437

0.99905

0.99900

Bandyopadhyay, Dasgupta, Mandal and Dutta [2]

33.5467

0.99865

0.99100

5.13. Knownhost attack

The adversary in a known host attack holds information about the host image. This adversary then

compares the host image with the stego image through statistical analysis to identify any pattern differences.

This type of attack can be avoided by determining host pixel positions using high-level chaotic maps.

Such process depends greatly on Equations 11–13, the results of which prevent the adversary holding

the host and stego images (without the secret message) from determining critical information through

statistical analysis. As indicated by these facts and the experimental analysis (Sections 5.1 to 5.5),

the proposed algorithm hides secret data such that only the most crucial change between the host and the

stego image is exist. Therefore, the adversary cannot gain anything except similar patterns. The proposed

algorithm can has good statistical analysis, which in turn enhances its robustness against known host attacks.

5.14. Known message attack

The adversary in a known message attack is aware of the original message. Any adversary holding

the original message and host image cannot obtain hidden information because the proposed algorithm

depends heavily on secret keys and host images. Even the slightest change in secret keys or host images can

change the position of the embedded secret data. Thus, the proposed algorithm is robust against known

message attacks.

6. CONCLUSION AND FUTURE WORK

Image steganography using LSB and secret map techniques is proposed in this study. The secret

maps are primarily based on 3D chaotic maps, which are 3D Chebyshev and 3D logistic maps. The random

concept focuses on the insertion and selection of host image pixels. This process provides high level of

security and resistance to different types of attacks. Empirical results, such as correlation coefficient,

information entropy, homogeneity, contrast, image histogram, hiding capacity, quality index, MSE, PSNR

and image fidelity, prove the satisfactory performance of the proposed algorithm and its superiority to other

algorithms. The proposed algorithm also has high sensitivity to its secret keys. Future work should

investigate image steganography with secret map bioinformatics, such as immune system, swarm and ant

colony algorithms.

ISSN: 2088-8708

Int J Elec & Comp Eng, Vol. 10, No. 1, February 2020 : 935 - 946

946

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