A steganalysis by adjacency pixel bits structure☆
Graphical abstract
Highlights
► We model the states of two adjacency pixels by choosing the correct modification component of adjacency pixel bits structure. ► The mechanism of state transitions in the model may explain the changes of states completely. ► The state transitions of model are used to verifying that it may improve the detection rate greatly.
Introduction
Information hiding refers to a number of disciplines where steganography and watermarking are the two main branches. Steganography mainly concerns with embedding of information in a cover files in such manner that the very existence of hidden information is not detectable. Except for the sender and the recipient of the stego files, no one should judge the presence of hidden information with a probability better than a random guess. On the contrary, steganalysis attacks try to exploit the statistical discrepancies that may exist in the stego medium and reveal the existence of the secret messages [1], [2].
Three parameters that characterize a steganographic system are hiding capacity, security and robustness. Steganographic algorithms are concerned mainly with high security and capacity, and usually robustness is not of main concern. But the main issue in digital watermarking is robustness which means the ability to resist distortion introduced by standard or malicious data processing. There is a wealth of information in the literature on data embedding to maintain robust watermarks in digital media [3], [4].
There are widespread applications for information hiding and steganography of digital images (such as JPEG), because of their inherent redundancy. There are two kinds of digital image steganographic techniques: methods based on spatial domain and transform domain. Methods based on spatial domain embed messages into the intensity of pixels of images directly. For steganographic algorithms based on transform domain, images are first transformed to another domain (such as frequency domain), and then messages are embedded in transform domain coefficients [1], [2]. The simplest and most popular paradigm for digital media steganography is LSB (least significant bits) embedded. The least significant bits of image pixels or transform coefficients having pseudorandom and noise-like characteristics and embedding messages in them cannot be visually detected. Hence, data hiding in the LSBs was among the early steganographic methods and its variations are still being considered by the researchers of this field [5], [6].
The rest of the paper is organized as follows. Section 2 reviews prior works related to information hiding. In Section 3, we describe an efficient high payload ±1 data embedding scheme, EPES. We talk about the motivation for our work and analyze the proposed scheme in Section 4. Next, Section 5 describes the detection of EPES steganogaphy. The experimental results which are from the efficiency of the algorithm comparing with that of the SPA are presented in Section 6. Finally, we conclude the paper in Section 7.
Section snippets
Related work
There are two types of LSB steganography: LSB flipping (LSB-F) and LSB matching method (LSB-M). In the LSB-F method, least significant bits of cover pixels are simply replaced by the secret message bits. It means that, in the case of difference between LSBs of the cover pixels and their corresponding message bits, the even (odd) pixel values are increased (or decreased) by one. In the LSB-M method, wherever the LSB of a cover pixel does not match with its corresponding message bit, the pixel
An efficient high payload ±1 data embedding scheme (EPES)
We define a basic two variable binary function B which maps Z2 to Z2. In other words, this function operates on two integers and produces a binary number. It is defined as follows:where bi is a single variable binary function with the following definition, which generates the (i + 1)st LSB of u:
Function B has the following basic properties which are essential in our algorithm.
- (a)
Since , one unit change in v causes B(u, v) to flip.
Proposed method
In this section, for motivating the proposed approach of steganalysis, we firstly study the effects of EPES embedded on some sets of sample pairs selected. Assuming that the digital signal is represented by the succession of samples s1, s2, … ,sN. A sample pair means a two-tuple (si,sj), 0 ⩽ i, j ⩽ N. We use sample pairs rather than individual samples as a basic unit in our steganalysis to utilize higher order statistics such as sample correlation. Let (u, v) be a set of sample pairs drawn from a
Detection of EPES steganogaphy
For each modification pattern π = (00, 01, 10,11) and any submultiset A ∈ P, let ρ(π,A) be a probability modified by the sample pairs of A under the pattern π. Let p be the ratio of the embedded messages length to the total samples number in a multimedia file. Then, the revision rate of LSB embedded is 3p/8 when n is 2. Assuming that the message bits of LSB steganography are randomly scattered in the spatial domain, we have
- (1)
ρ(00, p) = (1 − p/2)2
- (2)
ρ(01, p) = ρ(10,p) = p/2(1 − p/2)
- (3)
ρ(11, p) = (1 − p/2)2
The equations of
Experimental results
In this section, we examine the factors which influence the robustness of the steganalytic technique proposed above. We will try to find the ways of improving the accuracy of estimated hidden message length.
Given a chosen multiset p of sample pairs, the proposed LSB steganalytic technique is based on assumption (12). The accuracy of the estimated hidden message length p made by (17) or (18) primarily depends on the actual difference e.
However, a more robust estimate of
Conclusion
The SAP method is a new approach proposed to detect EPES steganography embedded in digital signals and estimate the length of the hidden message length. Experiments are conducted on a set of continuous-tone images. Empirical observations made in the simulations agree with the analysis of the results. The results of experiments show that SAP method is better than SPA method for detecting the EPES method. The accuracy of SAP detection will be improved further in the next step research content.
Acknowledgments
This work is supported by Natural Science Foundation of China (Nos. 60373109, 60272091) , the National High Technology Research, Development Program of China (Nos. 2009AA01 2403, 2009AA012435), Open-Ended Fund of Beijing Electronic Science and Technology Institute (No. KFHT200704), the focus of Scientific Research Funds Project of Xihua University (No. 2012) and the Fundamental Research Funds for the Central Universities (No. SWJ TU12BR045).
Mingwei Tang is an associate professor with the School of Mathematics and Computer Science Technology of Xihua University. He received a Ph.D. degree at the School of Computer Science and Engineering from University of Electronic Science and Technology of China in 2011. His current research interests include network security and information hiding.
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Mingwei Tang is an associate professor with the School of Mathematics and Computer Science Technology of Xihua University. He received a Ph.D. degree at the School of Computer Science and Engineering from University of Electronic Science and Technology of China in 2011. His current research interests include network security and information hiding.
Jie Hu is currently pursuing the Ph.D. degree at the School of Information Science and Technology of Southwest Jiaotong University. Her current research interests include network security and data mining.
Mingyu Fan is a professor at the School of Computer Science and Engineering from University of Electronic Science and Technology of China since 2004. She received a Ph. D. degree in Southwest Jiaotong University of China in 1996. Her main research interests are focused on computer networks and information security.
Wen Song is a professor of Xihua University since 2005. senior member of Petri net Special Commission. His main research interests are theory of Petri nets and mathematical logic.
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Reviews processed and approved for publication by Editor-in-Chief Dr. Manu Malek.