A New Steganography Algorithm against Chi Square Attack

INTRODUCTION

The motto behind stegnography is hiding one message in other clean images such that they should not give any clue to the third party about even the presence of a secret, thus, is the form of security through obscurity (Amirtharajan et al., 2012; Cheddad et al., 2010). A Carrier which carries the surreptitious message is labeled cover (image) whereas one obtained after hiding the message is labeled stego (image). During this process of hiding the data, the eminence of the former gets sullied. In most stegnography techniques the bits that belong to the secret unswervingly substitute the LSBs pixels in covers. High capacity can be achieved by using these LSB substitution techniques (Amirtharajan and Rayappan, 2012a-d).

An LSB substitution data hiding technique along with OPAP would maximize images’s SNR drastically (Chan and Cheng, 2004). OPAP reduces Worst Mean Square Error to less than half which is gained through simple LSB routine. Experimental results show that with little computational complexity OPAP can improve the image quality in a remarkable way.

The most commonly known stegnographic algorithms in the field of data hiding are the simple LSBs substitutions. In this method, fixed length of secret gets rooted in fixed length right most LSBs of cover pixels. Though this seems simple, it causes some visual distortion when more LSBs are replaced by the secret data (Amirtharajan and Rayappan, 2012a-c). One of the most important parameters in stegnography is PSNR indicating efficiency of the embedding algorithm. It is a appraisal of image revival quality in lossy compression codecs. Signal, here, is nothing but original data; also, noise-blunder initiated through hiding data in the images mainly in LSB substitution. The higher the PSNR, better the visual quality.

Chi square test: Chi-square test is one of the algorithms to test the detectability of any secret data embedding algorithm (Zanganeh and Ibrahim, 2011). It is a numerical assail intending to determine embedding in pixels unswervingly. Based on frequency with which pixel values appear, the chi square value is calculated. There is no need of a authoritative line linking stochasticity in the stego upshot and non-uniformity that is sufficient enough for clean image. Here, this chi-square run comes to play which is widely accepted as an apt thing to test this dissimilarity, there by providing quantifiable result.

The next section is the proposal of an algorithm to improve PSNR of the stego-image.

IPMCS

As mentioned earlier in the paper OPAP increases the image eminence by increasing PSNR. There be some cases where PSNR can be still increased by applying our algorithm. IPMCS basically stands for increased probability of matching between cover and secret files. Apart from increasing PSNR of stego output, it also converts the data into an unintelligible form so that it makes difficult for the hacker to retrieve the information. The key generated after applying this algorithm is also transmitted so that the receiver at the receiving point can again restore the original information.

In this study, an embedding algorithm is proposed which escapes chi square test to detect the hidden information. LSB substitution is used along with proposed method. IPMCS algorithm is also used to progress the image quality in terms of PSNR. The proposed algorithms are implemented with a step by step procedure and the simulation results are included which can be used to analyze the parameters like PSNR, chi-square values.

RELATED WORK

Steganography grabs its attention world wide, which forces the research community in scheming algorithms to improve robustness (Al-Frajat et al., 2010; Hansen, 2007; Provos and Honeyman, 2003; Wang et al., 2001; Stefan and Fabin, 2000; Thenmozhi et al., 2012; Zhu et al., 2011).

Cheddad et al. (2010) in their paper discussed on chief practices in steganography which are exploited in digital images additionally associated with their processing. Robustness and payload capacity is discussed for various methods.

Chan and Cheng (2004) explained the data infixing strategy via simple LSB in images with OPAP by which visual presence and PSNR of stego images are deeply enhanced. Extensive experiments show that the effectiveness of this method.

Amirtharajan et al. (2010) in his study has given a comparative analysis of different stegnography methods. The paper includes computed values of MSE, PSNR of all methods and discussed on major emerging stegnographic techniques such as LSB based, Inverted pattern based LSB using MSE, OPAP and relative entropy in substitution and a string of 1 and 0 and mod based (Padmaa et al., 2011).

Hansen (2007) considered the embedding of data in images by making use of singular value decomposition. He asserted that chi-square test measures the matching level between the given trial with the theoretically random one. It acts very well in studying the divergence, given quantitative and numerical end result.

Provos and Honeyman (2003) discussed about the existing stegnographic strategies and steganalysis. Their paper includes an introduction to stegnography and explains the basics of embedding.

PROPOSED METHOD

Algorithm for chi square test on stego-images: The Chi-square test detects presence of furtive message in cover using some statistical properties of the images. It is unusual in case where pixel value’s frequency 2k is almost same as that of 2k+1 indistinctive image having no embedded data. This property is exploited in detecting secret message in cover image. The Algorithm is given below:

n_i^* = (|pixels with gray value 2i|+|pixels with gray value 2i+1|)/2

Algorithm which escapes from chi square test: This algorithm uses the loop holes in the chi square test to screen secret in cover file. Here rows get embedded in such a way that the chi square value is controlled wherein the probability function which uses chi square value gives nearly zero as the probability of embedding. As the algorithm is mainly image dependent, that is, the embedding capacity varies from image to image. This is the major disadvantage but the advantage is that the security is increased where the hacker cannot predict the information using chi square test. Algorithm and experimental results are included.

Embedding procedure: Following are the steps involved in embedding procedure:

Extraction procedure: Following are the steps involved in embedding procedure:

Algorithm of IPMCS: The basic idea behind IPMCS algorithm has been discussed earlier in this paper and step by step procedure is included in this section.

Let M represent the n-bit secret message:

As in simple LSB substitution, assume that n-bit secret message has to be embedded into k-rightmost LSBs of the carrier i.e. Cover image:

Where n' is the number of packets formed after discretizing the secret message, m ' is i the variable which holds the packet value

Algorithm for variable length bit embedding: In this section, a data hiding method called alternate variable length bit embedding is discussed.

Let k represent the rightmost LSBs that are substituted by the secret message

Let C represent the 8-bit grayscale cover-image of size M_cxN_c pixels

C = {x_ij|0 = i<Mc, 0 = j<Nc, x_ij ε{0, 1,…, 255}}

In a constant bit embedding k is constant for all the pixels that are modified whereas in variable length coding k value is varied alternatively between 2 and 3 from pixel to pixel.

Total binary secret message is divided alternatively as 2 bits and 3bits and are represented as packet1 and packet2.This can be explained clearly in much simpler way as first 2’bits in message as packet1 and next 3’bits in message as packet2 and next 2’bits as packet3 and so on. After performing this operation we get a total of 2*n/5 discrete messages and the value of each such packet range from 0 to 2^k-1. We get 2^k different values called as symbols.‘n’ represents the size of the secret message in bits.

EXPERIMENTAL RESULTS

Here, discussed the analytical results observed for four cover files. It contains four standard gray scale covers, ‘Cameraman’, ‘Lena’, ‘Penguin’ along with ‘Peppers’, of dimension 256x256, are given in Fig. 1a-e, respectively. There are three sets of covert information. First set of secret data is the erratically formed data of 256x256xk bits; here k represents bits that get replaced. Here, first set of secret message, the value of k = 2 and for second set of secret message, the value of k = 3. For example, suppose that two bits of data is placed in last 2 LSBs of every cover pixel, then, secret information should be of size 256x256x2 = 131072 bits and suppose that three bits of data is placed in the last three LSBs, then the secret data should have the size 256x256x3 = 196608 bits. The number of pixels in an 256x256 gray scale image is 256x256 = 65536 pixels and for a third set of secret message, our proposed method alternate 2 and 3’bit LSB substitution consists of randomly generated message of (((256x256)/2)x2)+(((256x256)/2)x3) bits. In which half of the number of pixels are embedded with 2’b LSB substitution and another half is done so by 3’bit LSB substitution.

The second set consists of gray scale stego-images obtained by 2’ bit replacement. For this LSB substitution the value of k is 2, so the length of the message is 131072 bits and the stegoimages of cameraman, Lena, penguin and peppers are given in Fig. 2-d, respectively. Third set consists of stego images is obtained by 3’ bit swapping. For this LSB substitution the value of k is 3 and the length of the message is 196608 bits. The fourth set consists of gray scale stego-images for cameraman, Lena, peppers and penguin as shown in Fig. 3-d, respectively, obtained by variable length bit embedding (alternatively 2 and 3’bit) for this the value of k is 2 and 3. In this case the length of the message is 163840 bits and the stegoimages of cameraman, Lena, penguin and peppers are given in Fig. 4-d, respectively.

The stegnographic parameter (PSNR) after embedding the first, second and third secret data sets into first group of covers and are represented as second, third and fourth set of grayscale stego images, respectively.

After OPAP to subsequent second, third and fourth set of gray scale stego-images the resultant images are shown and analysed. Generally by applying OPAP, the PSNR value gets increased. Through applying our advised routine IPMCS before embedding, the PSNR value is further increased to a small extent, but the constraint is that the PSNR value after obtaining OPAP should be less than some threshold value for any particular type of simple LSB substitution. IPMCS algorithm for the stego images Camera man, Circuit Obama, Rice and Peppers are shown in Fig. 5a-e, respectively The results show that IPMCS method outperforms OPAP as in Table 1.

The chi-square value of the full image for 2’bit embedding is greater than 1’bit, 3’bit and 4’bit embedding unless for some exceptional images. Generally, the chi-square value is increased for 2’bit and then decreased for 3’bit and it is further decreased for 4’bit embedding and is given in Table 2.

Table 1:	PSNR and capacity values of the proposed method for various images

Fig. 1(a-d):	Cover images (a) Camera man (b) Lena (c) Penguin and (d) Peppers

Fig. 2(a-d):	Stego-images for 2’bit LSB embedding (a) Camera man (b) Lena (c) Penguin and (d) Peppers

Fig. 3(a-d):	Stego-images for 3’bit LSB embedding (a) Camera man (b) Lena (c) Penguin and (d) Peppers

Fig. 4(a-d):	Stego-images for variable length embedding (a) Camera man (b) Lena (c) Penguin and (d) Peppers

Fig. 5(a-e):	Stego-image obtained for proposed algorithm (escape chi square test) (a) Cameraman (b) Circuit (c) Obama (d) Rice and (e) Peppers

Fig. 6(a-e):	Comparison of chisquare test output of the stego image (a) Camera man (b) Circuit (c) obama (d) Rice and (e) Peppers, with the other embedding techniques

Table 2:	PSNR analysis for various bit embedding

Table 3:	PSNR analysis of IPMCS algorithm

Figure 3 shows all the stego-images obtained after applying the algorithm. All the images are 256x256 gray scale images. Fig. 6a-e shows the output of Chi square test corresponds to stegoimages of camera man, circuit, obama, rice and peppers respectively. In almost all the images probability of embedding is approximately one for single bit LSB substitution. For 2’bit and 3’bit LSB substitution chi square test gives a clue of the presence of secret data. For the proposed algorithm it drastically reduces the probability of embedding (nearly equal to zero). Hence this method is superior to other methods that are there in the literature. With the proposed algorithm the hacker finds it difficult to trace the data using chi square test. The only disadvantage of this method is embedding capacity depends on the image. Table 3 gives the information of PSNR and capacity for the stego images obtained after using proposed algorithm.