ANALYSIS OF STEGANOGRAPHIC METHODS IN DCT DOMAIN

The main role of steganalysis is a successful detection of secret communication. This communication is exclusively created by steganography. Steganographic methods deals with hiding a secret information into any type of multimedia data, for example to static images. Among basic requirements to steganographic systems belongs the perceptual transparency. Inserted information is perceptually transparent if an average subject is unable to distinguish any difference between data before and after embedding process. Nevertheless, each steganographic method necessarily causes some change in some statistical parameter. It represents the basis for building a successful steganalyzer. In this article are tested the impact of four steganographic methods to the selected statistical parameters which are usually utilized in the image objective quality assessment. Specifically, peak signal-to-noise ratio, normalized cross correlation, a local histogram of DCT coefficients and sample variance. The contribution of the article consists in the usage of results in the theory of statistical vector creation in building the particular image steganalytic method.


INTRODUCTION
The aim of steganography is to establish a subliminal channel which does not arouse a suspicion [1].
Example: there are two participants (they can be denoted as A and B) who want to communicate each other securely by sending the data via an Internet.If A wants to send a message to B, utilizes encryption in order to make it potentially unreadable.The third participant C is able to monitor the channel, but they cannot read the message.Although an encryption ensures secure communication, it reveals that there is a concealed information transmitted.The steganographic methods solve this problem.For example, if sender embeds a secret message into a static image and transmits it to the receiver, it will seem like an ordinary communication to participant C.
Moreover, an important attribute of steganographic methods is a minimization of impact to image statistical parameters after an embedding process, since the greater impact a method has, the more vulnerable to detect by an attacker it is [2].In other words, the goal is to make a method more resistant to steganalysis [3].In general, steganalytic technique extracts statistical parameters from a testing image to evaluate them by the previously trained model.Result is the statement whether an image contains a secret message or not [4] [5].
The proposed article deals with an embedding of secret messages by diverse steganography algorithms in order to detect an impact to four statistical parameters.Results can be utilized to make a set of statistical parameters to build universal or targeted steganalytic system [6].

STATISTICAL PARAMETERS
In general, the basic image processing quality parameter is PSNR (Peak Signal-to-Noise Ratio).PSNR indicates the ratio between the maximum energy of signal and maximum energy of noise in an image.PSNR is obtained by equation (1) [7].
In (1), n represents bit depth of an image and MSE mean square error [8].MSE is calculated by (2).
Component f(i,j) denotes pixels of original image with spatial resolution M×N whereas g(i,j) represents stego image pixels with the same resolution.When MSE equals zero, compared images are the same.Contrarily, the higher the value is, the more different images are.
Next statistical feature utilized in the work is Normalized Cross Correlation (NCC) (3) [9] [10].It is not dependent on the image size and achieves high efficiency.
Elements X i,j represent the pixel values of the original image and Y i,j are stego image pixel values.Image dimension is M×N.
The third statistical parameter was obtained from a discrete cosine transformation domain (DCT domain).It was differential histogram of DCT coefficients between cover and stego images [11].It was sufficient to use local histogram of 11 values occurring near the maximum (4).

  Z b
The last but not less important characteristic in statistics is the sample variance [12].In general, sample ISSN 1335-8243 (print) © 2017 FEI TUKE ISSN 1338-3957 (online), www.aei.tuke.skvariance is the expectation of the squared deviation of a random variable from its mean, and it informally measures how far a set of (random) numbers are spread out from their mean.It is defined by equation ( 5), where ( 6) is a deviation from mean and n represents the number of samples.For matrices, the result is a row vector containing the variance of each column.
 

TESTING PARAMETERS
The randomly generated secret messages were embedded into 200 cover images in JPEG format using steganographic methods MB1, MB2 [13], nsF5 [14] and PQ [15] (i.e.different secret message to each image).For the methods nsF5 and PQ there were messages with payloads 0.1, 0.5 and 1 bpnz (secret message size in bits per non-zero AC DCT coefficients).On the other hand, for the methods MB1 and MB2 was chosen payload with 0.1, 0.2 and 0.3 bpnz, since the methods MB1 and MB2 have smaller maximal capacity than the previous methods [16].PQ method used a converted database of cover images into grayscale.
Statistical parameters of static images which have been observed were PSNR, local histogram, NCC and sample variance.The messages have been inserted into images with different resolutions and statistical characteristics thus the results in the tables were averaged to a single image.The objective statistical parameters were not correlated with any subjective evaluation.

EXPERIMENTAL RESULTS
As a first statistical parameter was chosen PSNR.In the following Table 1 are shown the values that represent the average impact of each steganographic method to the cover image database.It is obvious that PSNR was decreasing with increasing the payload for all steganographic algorithms.However, the PQ method caused considerably lower values of PSNR than the other methods.The reason is that the PQ operates with grey images only, thus in the calculation, there are not included two other matrices as in a color image.
Results from the normalized cross-correlation point of view are shown in the Fig. 1.There are used three different payloads for all four steganographic methods.
The payload represents percentage of each steganographic method´s maximal capacity (see the section 3).Methods nsF5, MB1 and MB2 obtained NCC higher than 0.99.It points to the fact that cover and stego images were almost the same.For the PQ method it was around 0.5.
The local histograms of DCT coefficients of the cover and stego images are illustrated in the Fig. 2 and Fig. 3.  Table 2.In more details, it is differential local histogram between cover images and stego images of the method MB1 (payload = 0.3 bpnz) and method nsF5 (payload = 1 bpnz).The result difference between the frequencies of DCT coefficients from the Table 2 is shown in the Fig. 4 and Fig. 5 in the form of histogram.
The first histogram shows that the method MB1 have not affected frequency of zero DCT coefficients.The same results were obtained for the method MB2 too.On the other hand, methods MB1 and MB2 most affected frequency of values 1, -1, 2 and -2.For the method nsF5, the frequencies of all stego DCT coefficients are smaller than in cover images except the zero value.Frequency of 0 is greater than in cover images.
The last statistical parameter utilized in the experiments was sample variance.Sizes of the secret messages were the same as in the previous simulations.The Table 3 shows that by increasing size of secret message the sample variance was increasing as well.For the method nsF5 the variance ranged from 0.35 to 11.59.The smaller value belonged to 0.1 bpnz and the second one to max.size of message (1 bpnz).Methods MB1 and MB2 achieved similar results each other, whereas the method MB1 has less impact to the observed statistic.From all method the worst results achieved technique PQ.For all message sizes was observed variance higher than 83.

CONCLUSIONS
In the article, there was observed the impact of steganographic methods to the selected statistical parameters.Specifically, Peak Signal-to-Noise Ratio, Normalized Cross Correlation, local histogram of DCT coefficients and sample variance.Obtained results show that PSNR is generally increasing with increasing the size of a secret message for the all steganographic methods.We can say that all methods, except the PQ method, satisfy the PSNR limit between the cover and stego image.It has been assessed to 40 dB.Such a difference is imperceptible to the human eye.PSNR of PQ method was around 28 dB, what is already recognizable by an average human visual system.The calculation of NCC showed similar results.The methods nsF5, MB1 and MB2 achieved a value 0.99.It shows a nearly identical consistency of cover and stego images.The PQ method had achievements around 0.5.The difference in the local histogram between cover and stego images demonstrated that each of the tested methods affected it.The methods MB1 and MB2 maintained zero frequency coefficients, whereas the method nsF5 significantly increased the frequency of zero coefficients after the insertion process.From the sample variance point of view, the methods MB1 and MB2 achieved similar results.For the method nsF5 the variance ranged from 0.35 to 11.59.The biggest impact to the sample variance achieved PQ method.

Fig. 2
Fig. 2 Local histogram of cover image DCT coefficients

Fig. 3
Fig. 3 Local histogram of stego image DCT coefficientsThe local histogram of cover images was obtained by calculation of each cover image local histogram with the subsequent averaging.The same calculation was performed for stego images of all algorithms with the three different message sizes.The result was 14 local histograms where the first belonged to cover images, second to cover images of PQ method and 12 left to the stego images of the each steganographic method and secret message size.An example of the calculation of differential local histogram between cover and stego images is shown in the

Fig. 4 Fig. 5
Fig. 4 Differential histogram between cover and stego images of method MB1 with 0.3 bpnz message size

Table 1
The average PSNR values for the sample of 200 images

Table 2
Average frequency of 11 DCT coefficients of cover images and nsF5 and MB1 stego images

Table 3
Sample variance between cover and particular stego image databases