Enhancement using chaos of a steganography method in DCT domain

Enhancement using chaos of a Steganography method in DCT domain Milia Habib, Bassem Bakhache Faculty of Engineering-Lebanese University, LaSTRe laboratory Tripoli, Lebanon Abstract—Recently, Steganography is widely used for communicating data secretly. It can be divided into two domains spatial and frequency. One of the most used frequency transformation is Discrete Cosine Transform DCT. There are many techniques based on DCT. The most common is the DCT steganography based on Least Significant Bit LSB. Many proposed methods rely on it such as the LSB-DCT randomized bit embedding based on a threshold. This method is simple and provides some security. In this paper, a secure DCT steganography method is proposed. It allows hiding a secret image in another image randomly using Chaos. The chaotic generator Peace Wise Linear Chaotic Map PWLCM with perturbation was selected, it has good chaotic properties and an easy implementation. It was used to obtain the pseudo-random series of pixels in which the secret image will be embedded in their DCT coefficients. It enhances the LSB-DCT technique with threshold. Many metrics have been evaluated such as Peak Signal to Noise Ratio (PSNR), Structural Similarity (SSIM) Index and the capacity. A supervised universal approach based on Fisher Linear Discriminator (FLD) was used to evaluate the security against the steganalysts. The obtained experimental results demonstrate that the proposed algorithm achieves higher quality and security. Keywords: Steganography, DCT, LSB-DCT, threshold, PSNR, Chaos, PWLCM, FLD

I.

INTRODUCTION

Nowadays, the need to protect digital information has become an important topic. The word steganography combines the ancient greek words steganos (hidden) and graphos (writing). It is the art of hiding secret information within another carrier as images, videos, documents and graphics to obtain the stego object so that it is not affected after insertion. In this way, only the receiver knows about the presence of the secret message and can retrieve it. Steganography is classified into two domains: spatial and frequency [1]. In the first domain, the modifications are made on the pixels of the original image. The secret image is inserted directly into these pixels. In the second domain, the carrier image is transformed from the spatial domain to the frequency domain via the techniques of domain transformation. The secret message is inserted into the transformed coefficients of the cover to form the stego image [1, 2]. The frequency domain has many advantages, it is more robust than the spatial technique, it is tolerate to cropping, shrinking, image manipulation etc. [1, 2, 3]. There are many transforms used to map a signal into the frequency domain [3]. The best known methods used in the literature are Discrete Fourier Transform

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Dalia Battikh, Safwan El Assad IREENA - Ecole polytechnique de l’Université de Nantes, Nantes, France (DFT), Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) [1, 3]. There are many metrics used to evaluate a steganography method, such as Mean Square Error (MSE), Peak Signal To Noise Ratio (PSNR), Structural Similarity (SSIM) Index, the capacity as well as the robustness and the security [1, 2]. Robustness is the ability of stego image against different kind of attacks while the security is the inability of adversary to detect hidden images accessible only by the authorized user [5]. Steganalysis is used to detect the hidden information [5]. Digital images are the most commonly and frequently transmitted via the internet among the multimedia information, Hence, the importance to protect them. Many types of images can be used as cover media such as Bitmap File Format (BMP), Joint Photographic Experts Group (JPEG), and Graphics Interchange Format (GIF) images [6]. This research is mostly concerned about BMP images. It studied the steganographic methods that embed message in the Least Significant Bit (LSB) of DCT coefficients. The embedding can be done by two ways: sequential and randomly. The problem with the first one is the vulnerability, the secret message can be detected easily. One of the proposed improvements of this technique in the literature is LSB-DCT with threshold, it hides data in random locations based on a threshold [7]. The problem with it is the limited capacity related to the taken threshold, also it can be broken easily once this threshold is discovered. Hence, the purpose of this paper is to provide a novel image DCT method with high embedding capacity and more security using a chaotic generator the Piece Wise Linear Chaotic Map (PWLCM). The rest of this paper is organized as follows Section II briefly reviews the related works in the literature. Section III presents the algorithm LSB-DCT with threshold used in the comparison of the proposed method. Section IV describes Chaos and the PWLCM generator. Section V discusses the proposed method. Section VI presents different simulation and experimental results. Finally, Section VII presents our conclusion. II.

RELATED WORKS

Steganography has gained increasing importance, and have attracted lots of researchers 'attention. Many techniques have been developed. Deshpande et al., [8] explained the Least Significant Bit (LSB) embedding technique and presented the evaluation results for 2, 4 and 6 LSBs for a .png file and a .bmp



file. The authors in [6] proposed a novel high capacity data embedding scheme that hides secret information in Discrete Cosine Transform Coefficients based on Average Covariance algorithm. The cover image covariance is computed to consider number of Most Significant Bits (MSBs) of payload to be embedded based on DCT coefficients. Kafri and Suleiman [9] have utilized the idea of the spatial steganography approach SSB-4 introduced by Rodrigues, Rios and Puech in 2003 [10] to propose a novel method which embed message bits in the 4th bit of the successive non zero DCT coefficients of the low frequency region and modify the 1st, 2nd, 3rd and/or 5th bits to minimize the difference between the cover and the stego images. The 4th bit was chosen because it is the most significant bit which provides the minimum change in the pixel values. Since this approach uses significant bit, the hidden message resides in more robust areas and provides better resistance against the steganalysis [9, 10]. The authors in [5] proposed an image steganography technique based on combination of two transforms Integer Wavelet Transform and Discrete Cosine Transform. It used an assignment algorithm to select the best embedding locations of cover image to increase the visual quality of stego image and the system security. Recently, the idea of using chaotic systems has been noticed. Many chaos based steganographic methods have been discussed. Mazhar Tayel et al., [3] proposed a new chaos steganography algorithm for hiding the confidential data based on discrete chaotic dynamic system. A logistic map chaotic generator is used to encrypt the secret message then embed the message randomly into the pixels least significant bits of the original image. [4] Presented Chaos based Spatial Domain Steganography using Most Significant Bit (MSB) that hides secret information in the spatial domain using LSB and MSB with a chaotic approach. III.

DCT STEGANOGRAPHY ALGORITHM

5.

Construct a key vector consist of the locations of potential pixels.

6.

Embed the Most Significant Bit (MSB) of the secret data vector one by one in the successive DCT coefficients of the potential pixels .

7.

Apply the inverse 2D DCT (IDCT) to get the stego image. IV.

This section presents briefly the chaos and one of the simplest chaotic generators the PWLCM as well as the perturbation applied on it which is used in the proposition. A. Chaos Recently, Chaos takes an important place in the security domain. It has many applications in the field of information security. A clear definition of the term chaos was given by Poincare [11], he had used the example of the spheres : if we place a reflective sphere on which we send a beam of light, the direction in which the beam reflects depends basically on the original position. With two spheres, the variation of a tenth of a degree in the angle of the source can lead to a difference of 180° between the two beams. This sensitivity to initial conditions is a characteristic of any chaotic system. Hence, Chaos is a nonlinear dynamical system, very sensitive to initial conditions, gives unpredictable outputs in the absence of knowledge of the inputs. There are many chaotic generators such as Logistic map, PWLCM, Frey map [11]. In this research, the PWLCM has been selected, because it is easy to implement and it has very good randomness properties. B. Piecewise Linear Chaotic Map (PWLCM) PWLCM is a map composed of multiple linear segments given by [11]:

This section describes the steganography algorithm LSBDCT with threshold [7] which is used in the comparison of the proposed algorithm. The steps are as following:

‫ݔ‬ሺ݊ሻ ൌ ‫ܨ‬ሾ‫ݔ‬ሺ݊ െ ͳሻሿ ଵ ‫ݔ ۓ‬ሺ݊ െ ͳሻ ൈ

1.

=

Select a suitable cover image to embed the secret message, the size of the cover should be at least double of the secret message size.

2.

Convert the secret data to 1D binary vector.

3.

Divide the cover of size MuN pixels into non-overlapping blocks of 8u8 and apply 2D DCT transformation using the equation (1). ேିଵ ‫ܶܥܦ‬௜௝ ൌ ߙ௜ ߙ௝ σெିଵ ௠ୀ଴ σ௡ୀ଴ ‫ܥ‬௠௡ …‘•

Ͳ ൑ ݅ ൑ ‫ ܯ‬െ ͳ

గሺଶ௠ାଵሻ௜ ଶெ

…‘•

గሺ௡ାଵሻ௝ ଶே

(1)

Ͳ ൑ ݆ ൑ ܰ െ ͳ

Where, ͳൗ ξ‫ܯ‬

ߙ௜ ൌ ൞ ටʹൗ‫ܯ‬

4.

݅ ൌ Ͳ ͳ ൑ ݅ ൑ ‫ ܯ‬െ ͳ

ͳൗ ξܰ

ߙ௝ ൌ ൞ ටʹൗܰ

݆ ൌ Ͳ ͳ ൑ ݆ ൑ ܰ െ ͳ

Determine the locations of the potential pixels whose DCT coefficient is less than a threshold t.

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CHAOS AND PWLCM

݂݅Ͳ ൑ ‫ݔ‬ሺ݊ െ ͳሻ ൏ ‫݌‬

௣

ଵ

ሾ‫ݔ‬ሺ݊ െ ͳሻ െ ‫݌‬ሿ ൈ ଴Ǥହି௣ ‫۔‬ ‫ܨە‬ሾͳ െ ‫ݔ‬ሺ݊ െ ͳሻሿ

݂݅‫ ݌‬൑ ‫ݔ‬ሺ݊ െ ͳሻ ൏ ͲǤͷ ݂݅ͲǤͷ ൑ ‫ݔ‬ሺ݊ െ ͳሻ ൏ ͳ (2)

where the positive control parameter p  (0, 0.5) and x(i)  (0, 1). It is widely used because it has many important characteristics to a chaotic system such as: 1) a uniform and invariant density; 2) an exponentially decayed correlation function; 3) a simple hardware and software realization and implementation. Even if the continuous PWLCM have provided perfect properties, its digital version will have different properties from those described by the continuous map, and some degradation will arise. C. Perturbed PWLCM Since digital chaotic generators work in a discrete finite space with 2N elements where N is the taken precision, every chaotic



orbit will eventually be periodic and will finally go to a cycle with a limited length not greater than 2N. Consequently, they will suffer from dynamical degradation that threatens the security and their statistical properties [12]. To remedy this problem, many solutions have been proposed, one of them is to apply a perturbation on the chaotic system [13] [17]. The perturbation will break any cycle loop. It uses the Linear Feedback Shift Register (LFSR) and it occurs each ∆ iterations. Considering a PWLCM map defined by [11]: x(n)= F[x(n-1)]  [0,1]

n=1,2..

(3) Here, for a computing precision N, each x can be described as xi(n)  {0,1} i=1,2…,N. x(n)= 0. x1(n)x2(n)…xi(n)…. xN(n) (4) The purpose of the perturbation is to leave any cycle. The periodic loops will be avoided. The perturbation sequence can be generated as described in Qk-1+ (n) = Qk (n) = g0Q0 (n) ْ g1Q1 (n) ْ...ْgk-1Qk-1 (n) n=0,1,... (5) where g0 g1 . . gk−1 are the tap coefficients of the primitive polynomial generator, and Q0 Q1 . . . Qk−1 are the initial values of register, of which at least one is not null. The perturbation begins with n = 0, and it occurs each ∆ iterations. (∆ is a positive integer), with n = l × ∆, l = 1, 2... The perturbed sequence is given by the following equation: ‫ܨ‬ሾ‫ݔ‬௜ ሺ݊ െ ͳሻሿ ‫ݔ‬௜ ሺ݊ሻ ൌ ൜ ‫ܨ‬ሾ‫ݔ‬௜ ሺ݊ െ ͳሻ†ܳேି௜ ሺ݊ሻ

ͳ ൑ ݅ ൑ ܰ െ ݇ ܰ െ ݇ ൅ ͳ ൑ ݅ ൑ ܰ (6) where F[xi(n)] represents the ith bit of F[x(n)]. The perturbance is applied on the last k bits of F[x(n)] when n ≠ l u ∆ there is not any perturbation, and then x(n) = F[x(n − 1)]. V.

PROPOSED CHAOTIC METHOD

This section describes the proposed chaotic steganograhic method and presents the embedding and extraction algorithms. A. Description of the proposed method The purpose of this technique is to spread out the confidential information randomly in the whole cover image, so the mission of the steganalysts will be complicated. The digital chaotic generator RFCA proposed in [11] has been used, it cascades two perturbed PWLCM. This generator that passed the empirical statistic NIST tests, has very good dynamical statistical properties such as long cycle-length, high linear complexity, balance on {0, 1}, delta-like autocorrelation, cross-correlation near to zero. For these reasons, it was selected to increase the security of the steganography. The outputs of the two digital perturbed PWLCM are combined with a XOR operation to produce a new chaotic stream with higher randomicity. The binary generated sequence is used to

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determine the positions of the DCT coefficients in which the secret data will be embedded. The pixels of secret image are concatenated in 1D binary vector. Working from left to right, each bit of this vector is inserted in one DCT coefficient. So, every LSB of the DCT coefficient will be replaced by a bit of the secret message. As a result, the number of positions needed for the embedding in the cover is equal to the size s of binary secret message (s= width u height u 8 in case of gray scale images). Each position in the cover is defined by one coordinate (X, Y) where X represents the line number and Y represents the column number. There is no restriction on the cover image dimensions, the width and height can be unequal. In this case, the binary representation of X and Y has different number of bits. For simplicity, we have worked on covers having width equal height, for example covers of 512u512 pixels, it is assumed that each of X and Y is represented with k bits . As a result, the digital chaotic system generate a binary stream having l bits where l=2ukus bits to embed the whole secret image. The maximum size of the secret image that can be embedded is 12.5 percent of the cover (widthuheight/8) due to the use of one LSB only from the DCT coefficients of the cover image. The steps of embedding process are as following: 1. Read the cover and the secret image. 2. Convert the secret image to 1-D binary vector. 3. Divide the cover into 8u8 blocks and working from left to right, top to bottom, apply the 2D DCT transformation to each block. 4. Use the described chaotic generator to provide a long sequence of l bits. 5. Extract from the generated sequence the coordinates (X,Y) that represent the locations of the transformed DCT coefficients in which the secret image will be embedded as illustrated in the example below. The first k bits represent X, the following k bits represent Y and so on. ........1010.......1110...........1101.............010.......... X Y X Y Replace the LSB of these defined coefficients with the MSB of the secret data. 7. Apply 2D Inverse DCT to get the final stego image. Sharing the initial conditions of the chaotic generator and the secret image size with the receiver, he will generate the same random sequence, and apply the extraction algorithm. 6.

B. Extraction algorithm The steps of the secret image extraction applied by the receiver are: 1. Read the stego image. 2. Divide the stego image into 8u8 blocks and apply 2D DCT on each block. 3. Generate the same random sequence from the chaotic generator and extract the positions of DCT coefficients that hide the secret data. 4. Extract the LSB of the defined coefficients.



TABLE I.

5. Construct the secret image. VI.

EXPERIMENTAL RESULTS

This section presents the simulations and the obtained results. The proposed method and the LSB-DCT steganography with threshold are implemented. The implementation and the simulation have been done by using MATLAB software installed on Windows 8 platform. In the tests, the two mentioned algorithms have been applied on several standard cover images as "Lena", "Baboon" and "Cameraman", these covers are 8 bpp gray bmp images (512u512). The embedding process was repeated with many secret images of different size. We define the embedding rate ߙ ൌ ݊Ȁܰ where ݊ is the size in bits of the secret image and ܰ is the number of pixels of the cover image. Many tests have been done with embedding rates 5%, 10% and 20%. One of the examples is shown in figure 1.

Cover Images

PSNR for 5% embedding rate LSB-DCT with threshold

Proposed method

Baboon

65.3985

70.6975

Lena

65.0017

71.5038

Cameraman

65.9383

73.8652

TABLE II. Cover Images

PSNR for 10% embedding rate LSB-DCT with threshold

Proposed method

Baboon

62.3859

64.6663

Lena

62.1113

64.8786

Cameraman

63.1865

66.9976

TABLE III. Cover Images

(a)

(b)

(c)

(d)

Figure 1. (a) Secret image. (b) Original image. (c) Stego image of LSB-DCT with threshold. (d) Stego image of LSB-DCT with chaos.

Figure 1. Shows that the stego images obtained by the two algorithms are very similar to the original image. Both methods provide a good visual quality. To measure the image quality after embedding the secret data, we used the Peak Signal to Noise Ratio (PSNR) and the Structural Similarity (SSIM) index. PSNR measures the statistical difference between the cover and stego image [14]. The below equations (7) and (8) show respectively the formulas of the MSE and PSNR in dB between ‫ ܯ‬ൈ ܰ cover image C and stego image S. ‫ ܧܵܯ‬ൌ

ͳ ‫ܰܯ‬

෍

෍ ԡሺ‹ǡ Œሻ െ ሺ‹ǡ Œሻԡଶ

଴ஸ୧ஸ୑ିଵ ଴ஸ୨ஸ୒ିଵ

‫ܺܣܯ‬௜ ‫ܺܣܯ‬௜ଶ ܴܲܵܰ ൌ ͳͲǤͳ‫݃݋‬ଵ଴ ቆ ൰ ቇ ൌ ʹͲǤͳ‫݃݋‬ଵ଴ ൬ ‫ܧܵܯ‬ ξ‫ܧܵܯ‬

(7)

(8) Where ‫ܺܣܯ‬௜ is the maximum pixel value of the image (e.g., ‫ܺܣܯ‬௜ =255 in the case of 8 bits depth grayscale images). If PSNR ratio is high then images are best of quality [14]. It is considered that PSNR greater than 35 dB gives an acceptable image quality. The Tables ,, ,, and ,,, show the PSNR values in dB for 5, 10 and 20% embedding rate.

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PSNR for 20% embedding rate LSB-DCT with threshold

Proposed method

Baboon

59.3306

59.6497

Lena

59.0324

59.6906

Cameraman

60.0097

61.1395

It seems clear that the proposed method has enhanced the image quality. It achieves better PSNR. The PSNR values decrease with the increase of the embedding rate. Another criteria, the structural similarity (SSIM) index [15] is used to measure the similarity between the cover and stego images, it is illustrated in Tables IV, V and VI. It models any distortion based on three factors: loss of correlation, luminance distortion and contrast distortion. It is calculated on various windows of common size ‫ ݔ‬for the cover and ‫ ݕ‬for the stego based on local statistics parameters as shown in: ൫ʹߤ௫ ߤ௬ ൅ ‫ܥ‬ଵ ൯൫ʹߪ௫௬ ൅ ‫ܥ‬ଶ ൯ ܵܵ‫ܯܫ‬ሺ‫ܥ‬ǡ ܵሻ ൌ ଶ ൫ߤ௫ ൅ ߤ௬ଶ ൅ ‫ܥ‬ଵ ൯൫ߪ௫ଶ ൅ ߪ௬ଶ ൅ ‫ܥ‬ଶ ൯ (9) Where ߤ௫ , ߤ௬ ,ߪ௫ଶ ,ߪ௬ଶ and ߪ௫௬ are respectively the average of ‫ ݔ‬, the average of ‫ ݕ‬, the variance of ‫ݔ‬, the variance of ‫ݕ‬and the covariance of ‫ݔ‬and ‫ ݕ‬of the two images C and S. C1, C2 are constants used to avoid division by zero. ܵܵ‫ ܯܫ‬varies in the interval [-1,1]. The best value 1 is achieved if and only if S=C. TABLE IV. Cover Images

SSIM for 5% embedding rate LSB-DCT with threshold

Proposed method

Baboon

0.9999

0.9999

Lena

0.9994

0.9999

Cameraman

0.9985

0.9999



TABLE V. Cover Images

SSIM for 10% embedding rate LSB-DCT with threshold

Proposed method

Baboon

0.9999

0.9999

Lena

0.9992

0.9998

Cameraman

0.9975

0.9976

TABLE VI. Cover Images

This procedure of the random selection, training and classification was repeated 10 times. The obtained results are shown in below Tables VIII and IX. False Positive Rate FPR (1-specificity) defines the average of false detection of clean images. True Positive Rate TPR (sensitivity) is the average of true detection of stego images. The accuracy is the true detection average of both stego and clean images [5]. For a steganalyser, when the FPR gets lower and the TPR with the Accuracy get higher, the detection gets better.

SSIM for 20% embedding rate LSB-DCT with threshold

TABLE VIII.

Proposed method

Baboon

0.9999

0.9999

Lena

0.9987

0.9992

Cameraman

0.9963

0.9974

FPR

As illustrated in the above tables, the proposed method provides slightly higher SSIM than LSB-DCT with threshold, therefore its visual quality is better. The difference is larger when the embedding rate is bigger. In term of capacity, which defines the maximum size of secret information that can be hidden in the cover image, Table VII lists for the different standard images the number of locations available to hide the secret image. TABLE VII. Cover Images

Number of pixel locations LSB-DCT with threshold

123244

262144

Lena

112473

262144

Cameraman

66176

262144

The proposed method provides better capacity. The bits of the secret data can be hidden in the whole cover, there is no restriction like as the case of the algorithm LSB-DCT with threshold. To evaluate the security of the proposed method, we used the universal steganalytic technique proposed by Moulin in [16] coupled with the classification based on Fisher Linear Discriminator (FLD) as mentioned in [5]. The technique is based on characteristics functions moments that extract statistical features from wavelet subbands of clean images (covers) and stego images. The classifier FLD was trained to distinguish between cover and stego images. A large database of 1020 gray scale BMP images of size 512u512 was used. This database was subjected to two steganographic techniques, the proposed method and the threshold LSB-DCT method with the embedding rate of 0.05 and 0.1. As a result, 1020 stego images were obtained for each category of embedding rate. Then, for testing, 200 images were randomly selected from each category, while the remaining images were dedicated for training. After that, the FLD was trained with the extracted features from the training images to classify the unseen images.

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TPR

Accuracy

LSB-DCT with threshold

45.25%

57.1%

55.93%

Proposed method

52.3%

53.5%

50.65%

TABLE IX. Steganalyser detection for 10% embedding

DCT Technique

FPR

TPR

Accuracy

LSB-DCT with threshold

41.45%

62.3%

60.43%

Proposed method

45.1%

59 %

57.2%

As seen in the above tables, the proposed method cannot be reliably detected by the steganalysis. It shows better security. The performance is improved with Chaos.

Proposed method

Baboon

Steganalyser detection for 5% embedding

DCT Technique

VII. CONCLUSION In this paper, a new DCT steganography method is presented that spread out randomly the secret image within the cover image using Chaos. A digital chaotic generator based on two perturbed PWLCM has been used to generate a binary stream. This stream was used to determine the positions of DCT coefficients in which the secret data is embedded. The introduction of the perturbation improves the randomness properties of the generator. Hence, the locations of the secret data in the cover are very random. Only the receiver having the same initial conditions of the generator can detect the secret data positions and retrieve it from the stego image. The presented method was compared to another technique in the literature LSB-DCT with threshold. According to the simulation results, the proposed technique provides a high image quality, better capacity and security against the steganalysts. In the future work, the robustness against the image manipulation (filtering, compression...) can be studied. The security can be further improved by employing encryption techniques and the capacity can be increased by embedding more than one bit in each DCT coefficient. REFERENCES [1]

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