UNIVERSAL STEGANALYSIS METHOD FOR SPATIAL DOMAIN STEGANOGRAPHY TECHNIQUE BASED ON PREDICTION-ERROR HISTOGRAM FEATURE

UNIVERSAL STEGANALYSIS METHOD FOR

SPATIAL DOMAIN STEGANOGRAPHY TECHNIQUE BASED ON PREDICTION-ERROR HISTOGRAM FEATURE

Hsing-Han Liu

* Chiang-Lung Liu

1Department of Information Management National Defense University

Taipei, Taiwan 112, R.O.C.

2Department of Electrical and Electronic Engineering National Defense University

Taoyuan, Taiwan 335, R.O.C.

Key Words: universal steganalysis, steganography, prediction-error histo- gram, probabilistic neural network.

ABSTRACT

In this paper, a universal steganalysis method for spatial domain steg- anography technique in which features are extracted from prediction-error histogram is proposed. To find the relative features that alter due to em- bedding, the prediction-error histogram of images were used for analytic models. The current 12 spatial steganography methods with 100% embed- ding rate were used for testing. Through experimental analysis, it was dis- covered that the prediction-error histogram of cover images before and after embedding showed obvious differences. Therefore, the 8-D features extracted from prediction-error histogram made up the feature vector of the proposed steganalysis scheme. These features were further used for probabilistic neural network (PNN) classifier training and testing. The accuracy of the proposed steganalysis scheme was examined by using the NRCS image database. The experimental results showed the detection accuracy of the proposed universal steganalysis scheme for the 12 steganography methods reaches 98.2% at best.

The comparison with prior technology shows that the proposed universal steganalysis scheme offers superior accuracy in detecting the 12 spatial do- main steganography methods. Therefore, the proposed blind steganalysis scheme is very reliable for the detection of a spatial domain steganography method.

I. INTRODUCTION

Owing to the rapid development of internet applications and information techniques, the delivery of data has clearly moved from exchange by manpower to immediate exchange using a network. Data communication over the internet has become common in our daily lives. However, this con- venient environment is a double-edged sword. If an unau- thorized user exploits the handy network to steal confidential

information, the loss to individuals or groups will be difficult to estimate. To protect confidential information, various cryptographic methods can be used. These methods con- ceal the meaning of secret or confidential message. Encryp- tion hides the content of confidential information; however, meaningless data will catch the attention of adversaries who can intercept suspicious data. The steganography technique aims to solve this problem.

The concept behind the steganography technique is to

*Corresponding author: Hsing-Han Liu, e-mail: [email protected]

hide the very existence of the secret message. Steg- anography can conceal the secret message in an innocuous cover medium [1-3]. The purpose of steganography is to avoid arousing any suspicion against the transfer of a hidden message. The advancements in internet and information technology provide steganography with an excellent evolu- tion environment. Many different steganography techniques for images, such as spatial domain techniques and transform domain techniques, have been proposed. Spatial domain steganography techniques embed messages directly in the intensity of pixels of images. For transform domain ste- ganography, images are first transformed to another domain, and messages are then embedded in transform coefficients.

Conventional spatial domain steganography technique is based on Least Significant Bit (LSB) replacement, which hides the encrypted message by replacing the least significant bits (LSBs) of the pixels of the cover image [4]. However, sequentially flipping the LSBs can result in the Pair of Value (PoV) problem [5], which has been explored by many ste- ganalysis methods, such as x

[5] and RS [6]. To avoid an RS attack and achieve higher embedding capacity, Wu and Tsai [7] proposed a steganographic method based on pixel- value differencing (PVD), which embeds the secret messages in the difference value of two adjacent pixels. To increase the security of the original PVD, a modified PVD [8] uses variable intervals instead of fixed intervals as used in the ori- ginal PVD method. Modified PVD avoids the step effect of pixel difference histogram of a stego image and uses the original PVD embedding procedure by changing the me- thod to embed messages. To increase the embedding pay- load of the original PVD, a different embedding technique based on the PVD has been proposed. Enhanced PVD [9]

uses LSB embedding for smooth regions and PVD embedding for complicated regions. Tri-way PVD (TPVD) [10] is an- other modified version of the original PVD, which aims to increase the payload of the original PVD by embedding secret bits in all horizontal, vertical, and diagonal edge di- rections. Wang et al. [11] proposed a PVD steganography method to use modulus function, which adjusts the remain- der of two consecutive pixels to match the secret message.

This method is called modulus PVD. Modulus PVD gains high quality and capacity in comparison with the previous PVD methods. Yang et al. [12] proposed an adaptive LSB steganographic method using a PVD (adaptive PVD) that provides a larger embedding capacity and imperceptible stego images.

The above-mentioned steganographic methods belong to lossy steganography. In lossy steganography, the cover im-

age experiences some perdurable distortion due to secret message embedding and cannot be inverted back to the ori- ginal image. Some permanent distortion to the cover image occurs even after the hidden messages have been extracted.

With the requirement of protecting special cover images for military, medical, or law enforcement uses, many reversible steganography schemes have been proposed.

Unlike irreversible steganography, such as LSB re- placement and PVD-based steganography, reversible steg- anography requires not only the correct retrieval of the hidden message but also inverting the stego image back to the original cover image without any distortion. Among published reversible steganography methods, histogram shift embedding shows lower computational complexity and smaller execution time; therefore, this method has gained much attention recently. Histogram shift embedding was first proposed by Ni et al. in 2006 [13]. In Ni’s method, a histogram gap is created by shifting values of pixels between the most often occurring pixels (peak point), and nearby least often occurring pixels (zero points) by one intensity level.

The data bits, thereby, can be embedded by increasing the pixel value of the peak point by one unit if the value of the data bit is “1”. For Ni’s method, the embedding capacity usually implies the number of pixels (frequency) of the peak point in the histogram of the cover image. In general, the capacity of Ni’s method is not as large as the lossy steg- anography scheme. To improve the capacity of Ni’s me- thod, several works based on histogram shifting technique have been proposed, such as Hwang’s method [14] and Fallahpour’s method [15]. However, the improvement pro- vided by these works is limited because image histograms are rather evenly distributed.

The latest trend of reversible steganography combines histogram shift with Prediction Error (PE). PE is defined as the difference between the pixel value and its prediction value. Since the pixel values between adjacent pixels are highly correlated, PE histograms are very concentrated, which results in a high peak point. The payload of steganography based on Prediction Error Histogram Shift (PEHS) (such as Hong et al. [16], Tsai et al. [17], and Kim et al. [18]) is larger than the payload of steganography based on histogram shift.

Lately, reversible data hiding technology based on

Pixel Value Ordering (PVO) has been of extensive concern

to researchers in the field of reversible steganography me-

thod, because the incorporation of PVO based reversible

steganography reduces pixels modification, and thus it can

contribute to the high fidelity of image quality [19]. To date,

several improvements of the PVO method originated by Li et al. have been proposed [20-23].

The steganography technique, however, can be abused by criminals and terrorists. It is urgent and important to develop a steganalysis technique that aims to reveal the existence of the embedded message. The purpose of ste- ganalysis is to judge whether the suspicious image contains any embedded message. Generally, steganography is re- garded as being broken when the secret messages are dis- covered [24]. The current steganalysis methods can be broadly divided into two categories: embedding specific or universal (blind). Embedding specific steganalysis takes advantage of the details of a specific embedding algorithm to develop a detection algorithm. If the detection targets are specific stego images, the detection performance of the embedding specific steganalysis is potentially better than the universal one. An example of embedding specific ste- ganalysis is the RS attack [6], which can successfully detect the steganography of LSB flipping. The shortcoming of embedding specific steganalysis is that satisfactory detection performance is restricted to the specific steganography.

Universal steganalysis aims to overcome this weakness and attempts to detect the existence of the embedded message independent of a specific embedding algorithm; therefore, it can be used to perform any type of steganalysis. For ex- ample, the high order of statistics [25] is proven to be effec- tive for the detection of various types of embedding algorithms.

Because the development of various steganography techniques is rapid and diverse, the design of embedding specific steganalysis for the specific embedding algorithm is hardly practical and is time-consuming in practical ap- plications. While universal steganalysis can be operated for different steganography techniques; however, the detective object of current universal steganalysis is not explicit and the detection accuracy ratio needs to be improved. To overcome the above-mentioned shortcomings, this paper focuses on spatial domain steganography methods (such as k-bit LSB, PVD-based, PEHS-based, and PVO-based) and proposes effective and general features for steganalysis. Compared to the current universal steganalysis, the objective of the pro- posed steganalysis, which focuses on spatial-domain steg- anography method, is explicit and the detection accuracy of the proposed steganalysis outperforms other spatial-domain steganalysis.

There are two reasons for adopting the probabilistic neural network (PNN) in this study. First, the PNN model is applicable to classification problems and it was utilized in this study to classify the testing images into stego images

and cover images. Second, in most similar studies, support vector machine (SVM) and back propagation neural (BPN) network were commonly used, whereas the PNN was rarely used. Thus, in this study, the PNN was applied as a clas- sifier for feature-learning, training, and testing.

The rest of this paper is organized as follows. In Section II, the related works of steganalysis and probabilistic neural network are reviewed. The proposed steganalysis scheme including the feature selection and extraction of PE histogram and pixel histogram of test images and classifi- cation stages to use PNN is introduced in Section III. In Section IV, experiments and performance evaluation for the proposed steganalysis method are presented. Section V concludes this work.

II. RELATED WORKS

This section provides a review of the steganalysis scheme based on the embedding specific and universal categories.

The survey literature of current image steganalysis tech- niques can be found in [26-27].

1. Embedding Specific Steganalysis

Specific steganalysis can reveal secret messages or even

estimate the embedding ratio with the knowledge of the ste-

ganography algorithm. To date, many specific steganalysis

techniques have been proposed. For steganalysis of LSB

embedding, Westfeld and Pfitzmann [5] proposed the x

(Chi-square) attack based on statistical analysis of PoV in

the histogram of an image. The raw quick pair (RQP) me-

thod was proposed by Fridrich et al. [28]. The RQP me-

thod is based on analyzing close pairs of colors created by

LSB embedding. Fridrich et al. [6] proposed RS stega-

nalysis, which utilizes sensitive dual statistics derived from

spatial correlations in images. Dumitrescu et al. [29] in-

vestigated that the statistics of sample pairs of pixels are

highly sensitive to LSB embedding and the proposed sample

pair analysis (SPA) method. Ker [30] proposed structural

steganalysis methods for embedding in two least-significant

bits. The structural steganalysis methods may be extended

and applied to make more sensitive purpose-built detectors

for two-bit plane steganography. Zhang et al. [31] observed

that the local maxima of an image’s gray level histogram

decrease and the local minima increase after LSB matching

and the proposed specific steganalysis algorithm for LSB

matching based on the statistics of the amplitudes of local

extrema (ALE) in the gray level histogram. To reduce the

noise associated with border effects in the histogram and ex-

tend the analysis to amplitudes of local extrema in the 2D adjacency histogram, Cancelli et al. [32] proposed the im- proved ALE method to detect LSB matching.

For steganalysis of PVD-based embedding, Zhang et al.

[8] analyzed the histogram of stego image embedded by PVD and proposed a steganalysis technique that attacks the original PVD successfully by exploiting the step effect in the PVD histogram. Sabeti et al. [33] proposed the steganaly- sis method using chi-square testing to attack the enhanced PVD. To detect the modified PVD, Sabeti et al. [34] used features generated from five bins in PVD histogram and utilized a neural network to distinguish whether the suspicious image comprises any embedded message. Bui et al. [35]

introduced a steganalysis method on modified PVD using double embedding to generate steganalytic features. Joo et al. [36] proposed a steganalysis method that utilizes the changes of the PVD histogram to attack the modulus PVD.

Three features including the fluctuation around the border of the subrange, the asymmetry of the stego PVD histogram, and the abnormal increase of the histogram, are useful for steganalysis. Zaker et al. [37] presented a novel steganalysis for TPVD steganographic method based on the differences of PVD histogram. The method introduced a new stega- nalytic measure, named Growing Anomalies that its value has a linear relationship with secret message embedding rate.

For steganalysis of HS-based embedding, based on a special feature when all the pixels of the peak point are used to embed the secret message, Kuo et al. proposed two embedding specific steganalysis methods [38, 39] to detect the Ni’s method and HKC method respectively. That is, the Kuo’s method may not work properly when partial pixels of the peak point are used to embed the secret message [40]. To solve this problem, Liu et al. [41] proposed features that are independent of the embedding ratio to attack Ni’s method with a different embedding ratio.

2. Universal Steganalysis

Universal (blind) steganalysis techniques detect the ex- istence of secret messages embedded in digital images when the steganography algorithm is unknown. Avcibas et al.

[42] proposed the first universal steganalysis technique based on image quality metrics and multivariate regression analysis. Farid [43] proposed a universal steganalysis ap- proach, which uses a wavelet decomposition, to build higher- order statistical models of natural images and employed Fisher linear discriminate (FLD) analysis to discriminate between cover and stego images. A universal steganalysis, which comprises higher-order magnitude and phase statistics

x1 x2 xk xn

Input Layer

Pattern Layer

Summation Layer

Output Layer

Fig. 1 Architecture of the Probabilistic Neural Network

extracted from multi-scale, multi-orientation image decom- positions, was proposed by Lyu et al. [25]. Goljan et al.

[44] proposed a blind steganalysis method. The features for the steganalysis scheme are calculated in the wavelet domain as higher-order absolute moments of the noise re- sidue. Geetha et al. [45] presented a blind image stegana- lysis, which uses content-independent image quality metrics as the features of the steganalysis model and integrates ge- netic algorithms with the X-means model. Gul et al. [46]

introduced a universal steganalysis method that models linear dependencies of image rows/columns using singular value decomposition (SVD) and employs content indepen- dency via Wiener filtering. Pevný et al. [47] utilized the local dependences between differences of neighboring cover ele- ments and modeled as a Markov chain. The empirical pro- bability transition matrix of the Markov chain is taken as a feature vector for steganalysis. Fridrich et al. [48] propose a general methodology for steganalysis of digital images based on the concept of a rich model consisting of a large number of diverse submodels.

3. Probabilistic Neural Network

The probabilistic method for the neural network has

been developed in the frame work of statistical pattern

recognition. The probabilistic neural network (PNN) is

supervised learning network architecture with its theory

based on the Bayesian decision. Because the design of

PNN is based on the Bayesian decision, PNN is applicable

to the general classification problem. The main advantages

of the PNN are fast training process, an inherently parallel

structure, guarantee to converge to an optimal classifier as

the size of the representative training set increases, and train-

ing samples can be added or removed without extensive re-

training [49]. Fig. 1 shows the architecture of PNN [50].

x3 xn

x2

x1

xi3 xin

xi2

xi1

g(zi) = exp[(zi – 1)/σ²] zi = X ⋅ Wi

Fig. 2 Operations of the Pattern Units

The input layer is merely distribution units that supply the same input values to all of the pattern units of the pattern layer. Each pattern unit (shown in Fig. 2) forms a dot product of the input pattern vector X with a weight vector W

, which can be represented as

i i

z

 

(1)

where X = (x

, x

, , x

), W

= (w

, w

, , w

), and i represents the index of the pattern unit. A nonlinear op- eration exp[(z

 1)/ 

] is performed on z

before outputting its activation level to the summation layer. The outputs of z

are divided into m groups which correspond to the number of neurons in the summation layer and are equal to the number of the desired output classes. Each unit of the summation layer uses Eq. (2) to sum the inputs from the pattern layer, which corresponds to a category from which the training pattern was selected. That is,

 

exp[ 2 ]

j

T

j i i

i G

S



  





⁽²⁾

where S

is the output of the jth unit of the summation layer, j {1, 2, , m}. The output layer takes all the outputs of the summations layer and outputs the value of the class that has the maximum value of S

.

III. PROPOSED STEGANALYSIS SCHEME

In this section, a novel steganalysis scheme whose features are derived from the PE histogram of test images is presented. The first step was to extract the features of PE histogram of test images by using a block-sampling based predictor. Furthermore, the stego images and cover images were given diverse labels. The purpose of the different labels

Training images Class labels Test image

PE histogram extraction

PNN training

PNN model

PE histogram extraction

8-D feature vectors

PNN classification

Classification results

8-D feature vectors

Fig. 3 Flowchart of the Proposed Steganalysis Scheme

that are used in the PNN training stage was to obtain the relationship between feature sets and classification categories.

The second step was to use a more flexible classifier, PNN, which is employed to discriminate between cover images and the stego images. Finally, according to the results of clas- sification, the detection accuracy was calculated. Fig. 3 shows the flowchart of the proposed steganalysis scheme.

Details of the proposed steganalysis scheme are addressed in the following subsection.

1. Features Selection and Extraction

To find the set of image characteristics that alter due to embedding, the PE histogram of images were used for ana- lytic models. The following subsections present the de- scriptions of PE histogram.

The PE is defined as the difference between the pixel value and its prediction value. The PE histogram can be used to represent the statistics of various prediction errors.

PE histograms shown in Fig. 4 represent a shape that is sharply peaked at zero and has a two-sided exponential decay.

Such a shape is similar to Laplace distribution. A block- sampling based predictor proposed by Tsai et al. [17] was used to produce the PE histogram of Fig. 4(a). The me- dian edge detector (MED) [51], gradient-adjusted predictor (GAP) [52], and rhombus predictor [53] were used to pro- duce the PE histograms of Figs. 4(b)-(d). Tsai’s predictor was chosen as the analytic model. The major reason was that in the PE histogram produced by Tsai’s predictor com- pared with the one produced by the other predictor, the bins to locate both sides of the peak are symmetric each other.

The characteristics of Laplace distribution and symmetry belong to the PE histogram produced by Tsai’s predictor benefits steganalysis.

To compare with the PE histogram by Tsai’s predictor

Table 1 List of Spatial Domain Steganography Methods for Testing

Category Steganography Embedding Rate of

Steganography LSB-Based

PVD-Based PVD [7], Modified PVD [8], Enhanced PVD [9], Tri-way PVD [10], Modulus PVD [11], and Adaptive PVD [12]

PEHS-Based Kim’s PEHS method [16], Hong’s PEHS method [17], and Tsai’s PEHS method [18]

PVO-Based Li’s PVO [20], Chen’s PVO [23]

Maximum embedding rate

(a) (b)

(c) (d)

2

1.6

1

0.6

0-25 -20 -15 -10

Prediction Error Prediction Error

Prediction Error

FrequencyFrequency

FrequencyFrequency

Prediction Error

-5 0 5 10 15 20 25 -25 -20 -15 -10 -5 0 5 10 15 20 25

-25 -20 -15 -10 -5 0 5 10 15 20 25 -25 -20 -15 -10 -5 0 5 10 15 20 25 3

2.5 2

1 1.5

0.5 0

3.5 3 2.5 2

1 1.5

0.5 0 3 2.5 2 1.5

0.5 1

0

×10⁴ ×10⁴

×10⁴ ×10⁴

Fig. 4 PE Histogram. The test image is Lena and the predictor is (a) Tsai’s predictor (b) MED (c) GAP (d) Rhombus predictor

before and after the embedding, 12 common spatial steg- anography methods, which include k-bit LSB, PVD-based, PEHS-based, and PVO-based, were used for the test. The embedding rate of steganography for testing is the maximum embedding rate (100%). Table 1 presents a list of spatial domain steganography methods for testing. The test results reflected in Fig. 5 highlight the differences between the PE histogram of a cover image and the one of a stego image.

In Fig. 5, the solid line represents the PE histogram of a cover image and the dashed lines represent the PE histo-

grams of different stego images. Compared with the peak of the PE histogram of a cover image, the peak of PE his- togram of various stego images reduces drastically. The dis- tance from the peak to the bins located on both sides of the peak in the PE histogram of a cover image is longer than the one in a stego image embedded by a different steganography method. The results show a striking effect of the embedded process of the different steganography methods on the PE histogram of a cover image.

To understand the characteristics of PE histogram of a

(a) (b) (c)

(d) (e) (f)

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

-10 -8 -6 -4 -2 0 2 4 6 8 10

-10 -8 -6 -4 -2 0 2 4 6 8 10

-10 -8 -6 -4 -2 0 2 4 6 8 10

-10 -8 -6 -4 -2 0 2 4 6 8 10

-10 -8 -6 -4 -2 0 2 4 6 8 10

-10 -8 -6 -4 -2 0 Prediction Error

1-LSB Stage Image 2-LSBs Stage Image 3-LSBs Stage Image Cover Image

Adaptive PVD Stage Image TPVD Stage Image

PVO Stage Image

Cover Image PVOMM Stage Image

Cover Image Modulus PVD Stage Image

Cover Image

Kim’s Stage Image Hong’s Stage Image Tsai’s Stage Image Cover Image

OPVD Stage Image Modified PVD Stage Image Enhanced PVD Stage Image Cover Image

Prediction Error

Prediction Error

Prediction Error

Prediction Error

Prediction Error

FrequencyFrequency FrequencyFrequency FrequencyFrequency

2 4 6 8 10 5

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 5

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

×10⁴

×10⁴

×10⁴

×10⁴

×10⁴

×10⁴

Fig. 5 Comparison of PE Histogram of a Cover Image and Different Stego Images: (a) k-bit LSB (b) PEHS-based (c) PVD-based-1 (d) PVD-based-2 (e) Li’s PVO Method (f) Chen’s PVO Method

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

-20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0

Prediction Error

Frequency Frequency

Prediction Error

(a) (b)

5 10 15 20

0

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

×10⁴

×10⁴

Fig. 6 PE Histogram of (a) Cover Image (b) Stego Image Embedded by Original PVD

cover image that alters due to embedding, PE histograms of a cover image and a stego image embedded by original PVD were depicted in Fig. 6. A more detailed understanding of the change from PE histogram of a cover image to the one

of a stego image can be gained from Fig. 7. Fig. 8 highlights the differences between the two diverse PE histograms.

It has been observed that the PE histogram for a cover

image has a Laplace distribution. It is expected that the

Table 2 8-D Features of the Proposed Steganalysis Scheme No. Feature

1

= (H

-H

)/(H

-H

) 2

= (H

-H

)/(H

-H

) 3

= (H

-H

)/(H

-H

) 4

= (H

-H

)/(H

-H

)

5

= H

/H

6

= H

/H

7

= H

/H

8

= H

/H

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

(a) (b) (c)

Fig. 7 (a) PE Histogram of a Cover-Image (b) PE Histogram of a Cover-Image Evolved Into the PE Histogram of a Stego-Image (c) PE Histogram of a Stego-Image Embedded by PVD

-3 -2 -1 0 1 2 3

Fig. 8 PE for Feature Extraction

PE histogram for a stego image with 100% embedding would be more diverse than the one for a cover image and would have different distribution than Laplace. In other words, the distance of peak to bins located at 1 and -1 and the distance of bins located at 1 and -1 to bins located at 2 and -2 in the PE histogram of a stego image would be dif- ferent than the one in histogram of a stego image would be different than the one in the PE histogram of a cover image.

To distinguish correctly between a cover image and stego

Slego Images

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

0 500 1000 1500

Feature value

Feature value

2000 2500

0

Cover Images

Fig. 9 F

Feature Scatter Diagram of the Cover Images and TPVD Stego Images

image, the ratio of the distance of bins located at the PE histogram could be used. Fig. 6 supposes that H

, H

, H

, H

, H

, H

, and H

are respectively the values of ‘0’, ‘1’,

‘-1’, ‘2’, ‘-2’, ‘3’, and ‘-3’ in the PE histogram. The 8-D fea- tures of the proposed steganalysis scheme are presented in Table 2.

To prove the distinguishing effect of the eight feature

values (F

to F

), 2,724 cover images were retrieved from

the NRCS image database and their corresponding TPVD

images (with 100% embedding rate) were used to extract

Slego Images

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

0 500 1000 1500

Feature value

2000 2500

0

Cover Images

Feature value

Fig. 10 F

Feature Scatter Diagram of the Cover Images and TPVD Stego Images

Slego Images

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

0 500 1000 1500

Feature value

2000 2500

0

Cover Images

Feature value

Fig. 11 F

Feature Scatter Diagram of the Cover Images and TPVD Stego Images

Slego Images

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

0 500 1000 1500

Feature value

2000 2500

0

Cover Images

Feature value

Fig. 12 F

Feature Scatter Diagram of the Cover Images and TPVD Stego Images

Slego Images

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

0 500 1000 1500

Feature value

2000 2500

0

Cover Images

Feature value

Fig. 13 F

Feature Scatter Diagram of the Cover Images and TPVD Stego Images

the feature values. The results are shown in Figs. 9-16. For each figure, the horizontal axis represents the testing images, whereas the vertical axis represents the feature value ex-

Slego Images

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

0 500 1000 1500

Feature value

2000 2500

0

Cover Images

Feature value

Fig. 14 F

Feature Scatter Diagram of the Cover Images and TPVD Stego Images

Slego Images

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

0 500 1000 1500

Feature value

2000 2500

0

Cover Images

Feature value

Fig. 15 F

Feature Scatter Diagram of the Cover Images and TPVD Stego Images

Slego Images

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

0 500 1000 1500

Feature value

2000 2500

0

Cover Images

Feature value

Fig. 16 F

Feature Scatter Diagram of the Cover Images and TPVD Stego Images

tracted from the image.

Figs. 9-16 show the scatter diagram of F

to F

feature values. These figures demonstrate that the proposed F

to F

feature have distinguishing effects.

2. Classifier Training and Testing

For the use of PNN for steganalysis with different spa-

tial domain steganography methods, the required 8-D features

from the training images were extracted. Then the 8-D fea-

tures were passed to PNN for training. Finally, the required

8-D features from the test images were extracted, and the 8-D

features were passed to PNN for testing. The results to

be classified from PNN could help in judging whether the

suspicious image comprises any embedded message.

IV. EXPERIMENTS AND PERFORMANCE EVALUATION

The experiments in this section were conducted to clarify that the proposed technique can effectively detect stego im- ages, which are based on spatial-domain steganography (e.g., LSB, PVD, PEHS, and PVO) with 100% embedding rate.

The experimental results are compared with the results of the popular general detection techniques (e.g., SPAM and ALE) to illustrate the superiority of our proposed analyti- cal method. The relevant experimental environment, pro- cedures, and results are summarized in the following sections.

1. Experiments Environment

The software and hardware environments used for the experiments are as follows:

i. Hardware Environment

Notebook computers with Intel Core i5 CPUs and 16 GB RAMs.

ii. Spatial-domain Steganography

MATLAB was employed to implement spatial-domain steganography based on LSB, PVD, PEHS, and PVO, as shown in Table 1.

iii. Feature Value Extraction Program

MATLAB was used to implement a feature extraction program for deriving the eight feature values of PEH.

iv. Predictor

The block-type predictor proposed by Tsai et al. was selected for steganalysis in this study. Implementation of block-type predictor is based on MATLAB environment.

v. Secret Information

Encrypted secret information is simulated by using a uniformly-distributed binary numerical sequence. The se- quence is generated by the built-in random number genera- tor in MATLAB.

vi. PNN

The built-in neural network toolbox in MATLAB is used to construct a PNN for steganalysis.

vii. Experimental Images

For cover images, 2,724 8-bit gray-scale images of size 512  512 were randomly selected from the NRCS image database [54]. For stego images, 12 different spatial-domain steganography techniques, listed in Table 1, were used to encrypt cover images with a 100% embedding rate.

2. Experiments Steps

In this study, the stego images of 100% embedding rate (14 groups) generated by 12 different types of spatial- domain steganography methods were detected through the following steps:

Step 1

2,724 cover images and the corresponding 2,724 stego images generated by one of 12 spatial-domain steganography methods were input.

Step 2

1,362 cover images and 1,362 stego images were ran- domly selected and together constituted the training dataset.

Step 3

The feature value extraction program was used to ex- tract the feature values from the training dataset, both for cover images and stego images.

Step 4

The extracted feature set obtained in Step 3, and its cor- responding classification labels were input into the PNN classifier for model training.

Step 5

The remaining cover and stego images from Step 2 were considered the validation dataset, with a total of 2,724 im- ages. Subsequently, the feature value extraction program was applied to extract the eight feature values.

Step 6

The derived PNN model trained in Step 4 was used to classify the validation dataset. Specifically, the feature set obtained in Step 5 was input into the trained PNN model for classification. The output classification result of the vali- dation dataset and its corresponding labels were recorded.

Step 7

Step 2-Step 6 were repeated ten times and the average value of the classification results was computed.

3. Performance Evaluation

The outputs of the steganalysis can be categorized

into four types: true positive (TP), false positive (FP), true

negative (TN), and false negative (FN). True positive is

the number of the stego images that were correctly identi-

fied while false positive results are those cover images that

were identified as stego. True negative is the number of

cover images that were correctly identified while false ne-

gative results are those stego images that were identified as

Table 3 Description of Classifier Evaluation Indicators

Indicators Equation Description

Accuracy (AC) (TP TN)/(TP TN FP FN)

Accuracy is used to evaluate the performance of the pro- posed steganalysis method and is defined as the percentage of correctly identified cover and stego images.

True Positive Rate (TPR)

FN) TPR reflects the classifier’s ability to detect members of the stego images.

True Negative Rate (TNR)

FP) TNR reflects the classifier’s ability to detect members of the cover images.

Precision (Confidence)

Precision or Confidence denotes the proportion of predicted stego images that are correctly real stego images.

Recall (Sensitivity)

Recall or Sensitivity is the proportion of real stego images that are correctly predicted as stego images.

F1 Score

2

1 1

Precision

The F1 Score is the harmonic mean of precision and recall.

G-mean

 G-mean is the geometric mean of sensitivity and precision.

87.8

94.6 96.4 97.4 88.4

95.7 82.9

91.7

98.2 95.6 92.2 89.7 92.9 93.8

1-LSB 100

90 80 70 60 50 40 30 20 10 0

2-LSB 3-LSB

Steganography Method

Detection accuracy (%)

PVD

Modified PVDEnhanced PVDModulus PVDAdaptive PVD TPVD

Kim’m PEHSHong’

s PEHS Tsai’s PEHS

Li’s PVO Chen’

s PVO

Fig. 17 Average Detection Result of Proposed Steganalysis Scheme

cover. Generally, the steganalysis method requires higher values for TP and TN, and lower values for FP and FN.

We used the following indicators presented in Table 3 to evaluate the accuracy of different methods.

4. Experimental Results

To evaluate the performance of the proposed stegana- lysis scheme, the study randomly selected half of the cover images and the corresponding stego images for training and the remaining for testing. By repeating the procedure 10 times, average detection results were obtained. Fig. 17 shows the average detection accuracy of the proposed steganalysis

scheme.

As shown in Fig. 17, the proposed steganalysis scheme performed best on 2-LSBs embedding, 3-LSBs embedding, Kim’s method, original PVD, Enhanced PVD, and TPVD.

This is because the embedding capacity of the above- mentioned steganography methods is higher than the other steganography methods. The more secret message bits embedded, the higher stego images caused distortion. Dif- ference between PE histogram of a cover and stego image was obvious. The detection accuracy of Hong’s method, Tsai’s method, and Modified PVD reached at least 88%.

For Li’s PVO method and Chen’s PVO method, the detection

accuracy was 92.9% and 93.8% respectively. However, as the embedding capacity of 1-LSB embedding was less than that of other steganography; the proposed steganalysis scheme performed poorly on 1-LSB embedding. Com- pared with 1-LSB embedding, the embedding capacity of modulus PVD was higher, but the detection accuracy of the proposed steganalysis scheme for modulus PVD was poorest. The reason for poor performance was that an op- timal approach to alter the remainder was used by modulus PVD to greatly reduce the image distortion caused by the hiding of the secret message bits. Adaptive PVD was si- milar to modulus PVD, which uses a delicate readjusting procedure to remain at the same level for the difference value of two consecutive pixels before and after embedding.

Although the embedding capacity of adaptive PVD was highest among the 12 steganography methods, the detection accuracy of the proposed steganalysis for adaptive PVD was poorer than original PVD, Enhanced PVD, and TPVD.

The proposed steganalysis scheme (8 features) was com- pared with the second-order SPAM features (686 features) [47] and ALE (10 features) [32]. The SPAM features were primarily developed for blind steganalysis in the spatial do- main and source code to extract SPAM features was down- loaded in [55]. ALE features were developed for 1 LSB steganography and source code of the ALE feature extractor was downloaded in [56]. For a fair comparison, all the experiments were repeated 10 times by randomly selecting the training and testing images. Each time, the PNN was used to train and classify cover and stego images. Finally, the averaged results were used for comparison. Tables 4-7 show the average detection accuracy of the steganalyzers for the case wherein the proposed method, SPAM, and ALE are used for analysis of K-LSB, PVD-based, PEHS-based, and PVO-based steganography respectively. From the average detection results shown in Tables 4-7, the proposed stegana- lysis method outperforms SPAM or ALE for detection of the twelve steganographic methods. It means that the proposed method can use fewer features to provide higher detection accuracy for analysis of spatial-domain steganography. The dominant performance of the proposed method was quite apparent.

The proposed method, SPAM method, and ALE me- thod were thoroughly analyzed in this study. Three different types of indicators, as shown in Table 8 to Table 10, were utilized to assess the accuracy. According to the above ex- perimental procedure, each type of stego image with 100%

hiding capacity (total of 14 groups), which was generated through the spatial-domain steganography methods in Table 1,

Table 4 Average detection accuracy of proposed method, SPAM, and ALE against K-LSB steganography Steganographic Average Detection Accuracy (%)

Method 1-LSB 2-LSB 3-LSB

Proposed 87.8 94.6 96.4

SPAM 56.7 67.1 80.8

ALE 72 74.6 76.4

Table 5 Average detection accuracy of proposed method, SPAM, and ALE against PVD-based steganography Steganographic Average Detection Accuracy (%)

Method Proposed SPAM ALE PVD

Modified PVD Enhanced PVD Modulus PVD Adaptive PVD

TPVD

97.4 88.4 95.7 82.9 91.7 98.2

76.7 69.4 80.8 60.2 77.7 79.4

74.5 76.3 75.1 71.9 76.2 71.6

Table 6 Average detection accuracy of proposed method, SPAM, and ALE against PEHS-based steganography Steganographic Average Detection Accuracy (%)

Method Proposed SPAM ALE Kim’s PEHS

Hong’s PEHS Tsai’s PEHS

95.6 92.2 89.7

70.9 70.2 60.2

69.7 74.4 62

Table 7 Average detection accuracy of the proposed method, SPAM, and ALE Against PVO-based steganography Steganographic Average Detection Accuracy (%)

Method Proposed SPAM ALE

Li’s PVO 92.9 56.6 62.3

Chen’s PVO 93.8 59.2 71.8

would be classified and detected by the trained PNN mo- del ten times.

The proposed method, SPAM method, and ALE me-

thod were thoroughly analyzed in this study. Three different

types of indicators, as shown in Tables 8-10, were utilized to

assess the accuracy. According to the above experimental

procedure, each type of stego image with 100% hiding ca-

pacity (total of 14 groups), which was generated through

Table 8 Description of Evaluation Indicators of the Proposed Method

TP FN TN FP TPR TNR Precision Recall F1 Score G-mean 1-LSB 1257.2 104.8 1133.5 228.5 0.923 0.832 0.846 0.923 0.883 0.876 2-LSB 1314.4 47.6 1261.4 100.6 0.965 0.926 0.929 0.965 0.947 0.945 3-LSB 1329.2 32.8 1295.5 66.5 0.976 0.951 0.952 0.976 0.964 0.963 PVD 1344.5 17.5 1308.9 53.1 0.987 0.961 0.962 0.987 0.974 0.974 Modified PVD 1302.6 59.4 1104.3 257.7 0.956 0.811 0.835 0.956 0.891 0.881 Enhanced PVD 1334.6 27.4 1271.8 90.2 0.98 0.934 0.937 0.98 0.958 0.957 Modulus PVD 1278.4 83.6 979 383 0.939 0.719 0.769 0.939 0.846 0.822 Adaptive PVD 1310.7 51.3 1186.5 175.5 0.962 0.871 0.882 0.962 0.92 0.915

TPVD 1350 12 1325.1 36.9 0.991 0.973 0.973 0.991 0.982 0.982 Kim’s PEHS 1317.2 44.8 1287.8 74.2 0.967 0.946 0.947 0.967 0.957 0.956 Hong’s PEHS 1274.5 87.5 1238 124 0.936 0.909 0.911 0.936 0.923 0.922 Tsai’s PEHS 1243.9 118.1 1199.6 162.4 0.913 0.881 0.885 0.913 0.899 0.897 Li’s PVO 1288.6 73.4 1242.9 119.1 0.946 0.913 0.915 0.946 0.93 0.929 Chen’s PVO 1248.7 113.3 1306.3 55.7 0.917 0.959 0.957 0.917 0.937 0.938 Average 1299.61 62.39 1224.33 137.67 0.95 0.9 0.91 0.95 0.93 0.93

Table 9 Description of Evaluation Indicators of SPAM

TP FN TN FP TPR TNR Precision Recall F1 Score G-mean 1-LSB 1336.3 25.7 207.9 1154.1 0.981 0.153 0.537 0.981 0.694 0.387 2-LSB 1338.2 23.8 488.7 873.3 0.983 0.359 0.605 0.983 0.749 0.594 3-LSB 1350.9 11.1 851.1 510.9 0.992 0.625 0.726 0.992 0.838 0.787 PVD 1327.2 34.8 761.3 600.7 0.974 0.559 0.688 0.974 0.806 0.738 Modified PVD 1330.2 31.8 559.9 802.1 0.977 0.411 0.624 0.977 0.762 0.634

Enhanced PVD 1352 10 850 512 0.993 0.624 0.725 0.993 0.838 0.787 Modulus PVD 1358.5 3.5 280 1082 0.997 0.206 0.557 0.997 0.715 0.453 Adaptive PVD 1341.7 20.3 774.3 587.7 0.985 0.569 0.695 0.985 0.815 0.749

TPVD 1336.5 25.5 827 535 0.981 0.607 0.714 0.981 0.826 0.772 Kim’s PEHS 1114.9 247.1 815.5 546.5 0.819 0.599 0.671 0.819 0.738 0.7 Hong’s PEHS 1172 190 740 622 0.86 0.543 0.653 0.86 0.742 0.683

Tsai’s PEHS 1069.4 292.6 569.9 792.1 0.785 0.418 0.574 0.785 0.663 0.573 Li’s PVO 789.3 572.7 751.5 610.5 0.58 0.552 0.564 0.58 0.572 0.566 Chen’s PVO 863.2 498.8 749.5 612.5 0.634 0.55 0.585 0.634 0.609 0.591

Average 1220.02 141.98 659.04 702.96 0.9 0.48 0.64 0.9 0.74 0.64

the spatial-domain steganography methods in Table 1, would be classified and detected by the trained PNN model ten times.

The relevant results were analyzed separately for each type of assessment indicator, as shown below:

i. TPR and TNR

The average TPR values of the proposed method, SPAM, and ALE were 95%, 90%, and 96%, respectively, which showed that all the three techniques could properly identify

stego images. However, the corresponding average values of TNR were 90%, 48%, and 48%, respectively. This indi- cated that our proposed method could effectively detect cover images, whereas SPAM and ALE could not recognize cover images well, leading to significant misclassifications.

ii. Precision and Recall

The average values of precision of the proposed me-

thod, SPAM, and ALE were 91%, 64%, and 65%, respectively.

Table 10 Description of Evaluation Indicators of ALE

TP FN TN FP TPR TNR Precision Recall F1 Score G-mean 1-LSB 1286 76 675.6 686.4 0.944 0.496 0.652 0.944 0.771 0.684 2-LSB 1352.7 9.3 678.3 683.7 0.993 0.498 0.664 0.993 0.796 0.703 3-LSB 1362 0 719.5 642.5 1 0.528 0.679 1 0.809 0.727

PVD 1362 0 666.6 695.4 1 0.489 0.662 1 0.797 0.699 Modified PVD 1337.5 24.5 740.2 621.8 0.982 0.543 0.683 0.982 0.806 0.73 Enhanced PVD 1361.4 0.6 685 677 1 0.503 0.668 1 0.801 0.709

Modulus PVD 1359.1 2.9 598.7 763.3 0.998 0.44 0.64 0.998 0.78 0.663 Adaptive PVD 1360.5 1.5 714 648 0.999 0.524 0.677 0.999 0.807 0.724

TPVD 1362 0 589.6 772.4 1 0.433 0.638 1 0.779 0.658 Kim’s PEHS 1300 62 598.1 763.9 0.954 0.439 0.63 0.954 0.759 0.647 Hong’s PEHS 1353.2 8.8 673.1 688.9 0.994 0.494 0.663 0.994 0.795 0.701

Tsai’s PEHS 1226.8 135.2 462.6 899.4 0.901 0.34 0.577 0.901 0.703 0.553 Li’s PVO 1116.8 245.2 581.4 780.6 0.82 0.427 0.589 0.82 0.686 0.592 Chen’s PVO 1241.5 120.5 715.6 646.4 0.912 0.525 0.658 0.912 0.764 0.692

Average 1312.96 49.04 649.88 712.12 0.96 0.48 0.65 0.96 0.78 0.68

This proved that the proposed method detected stego images more effectively than SPAM and ALE. Moreover, the aver- age values of recall were 95%, 90%, and 96%, respectively. It demonstrated that all the three methods could show good recall values.

iii. F1 Score and G-mean

The average values of the F1 score of the proposed method, SPAM, and ALE were 93%, 74%, and 78%, re- spectively. This indicated that our proposed method had better performance in Precision and Recall than SPAM and ALE. The average values of G-means were 93%, 64%, and 68%, respectively, which also indicated that, compared with SPAM and ALE, the proposed method could provide better performance in general with regard to Precision and Recall.

V. CONCLUSIONS

Since it is hard for steganalyzers to understand what steganography scheme was used in suspicious images, ste- ganalysis for specific embedding is hardly practical. On the contrary, universal steganalysis can detect the secret mes- sage, independent of the steganography technique. How- ever, the detective target of current universal steganalysis is not explicit and detection accuracy must be improved.

To overcome shortcomings, this paper proposes a novel spatial domain steganalysis method.

To find the relative features that alter due to embedding, the PE histogram of images were used for analytic models.

The current 12 spatial steganography methods with 100%

embedding rate were used for testing. Through experimental analysis, it was discovered that the PE histogram of cover images before and after embedding showed obvious differ- ences. Therefore, the 8-D features extracted from PE his- togram made up the feature vector of the proposed steganalysis scheme. These features were further used for PNN classi- fier training and testing. The accuracy of the proposed ste- ganalysis scheme was examined by using the NRCS image database.

Experimental results showed that the detection accuracy of the proposed steganalysis scheme for the 12 stegano- graphy methods reached 98.2%, at its highest. The results were compared with spatial domain steganalysis schemes including SPAM and ALE. The experiments demonstrated that the proposed steganalysis scheme outperforms the prior technology for all 12 spatial domain steganography methods.

The dominant performance of the proposed steganalysis method is quite apparent.

The number of feature values used in the proposed

method was eight, that proposed by researchers like Pevny

was 686, and that required in ALE was ten. Although the

number of feature values used in our proposed analysis

technique was smaller than that of the above methods such

as SPAM and ALE, the detection accuracy of our technique

was higher. In addition, the computing resource require-

ments and time cost of this technique were less than those of SPAM and ALE, demonstrating the superiority of our proposed method.

In this study, the proposed steganalysis method is based on the hypothesis that stego images encrypted using spatial- domain steganography are built upon a gray-scale cover image.

Whether the proposed method is applicable to stego images that were built upon color cover images is a topic worthy of further study.

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Manuscript Received: Mar. 29, 2018 First Revision Received: Aug. 16, 2018 Second Revision Received: Sep. 21, 2018 and Accepted: Oct. 01, 2018