Application of hypothesis testing theory for optimal detection of LSB matching data hiding
Highlights
► Steganalysis is addressed using hypothesis testing theory. ► The statistical performance of the proposed test is analytically calculated. ► The proposed test permits the guaranteeing of a false-alarm probability. ► This provides an upper bound on the detection performance of any detector. ► Using general statistical concept it can be applied for a wide range of media.
Section snippets
Introduction and contributions
Steganography concerns the reliable transmission of a secret message buried in a host digital medium, such as digital image or audio file. This data hiding technique has been mainly used in information security applications and has receive an increasing interest in the past decade. While a cyphered messages can easily be detected the detection of data hidden within innocuous-looking digital media remains a difficult problem. More generally, the goal of steganalysis is to obtain any information
Statistical model of media
This paper studies uncompressed digital medium and, without loss of generality, focuses on natural images, i.e. recorded with some imaging device. Hence, the column vector represents medium, of pixels for a grayscale image. The set of quantized levels is denoted as sample values are usually unsigned integers encoded with B bits. Each cover sample cn results from the quantization:where denotes the analogical sample value recorded by the
Optimal Likelihood Ratio Test for simple hypotheses
Let us start with the simplest case, when the embedding rate R and, for all n, the parameters are known. In this case, the hypothesis testing problem (9) is reduced to a test between two simple hypotheses.
In virtue of the Neyman–Pearson lemma, see [26, Theorem 3.2.1], the most powerful (MP) test over the class (10) is the LRT given by the following decision rule:where is the solution of , to insure that , and the likelihood ratio
Case of simple hypotheses, when R=2
In this section it is first proposed to study the statistical performance for the case of simple hypotheses, when R=2. The results are then extended to the general case of in Section 4.2. To calculate easily the statistical performance of the LR test (11), the asymptotic approach is of crucial interest. Indeed, even though Theorem 1 establishes that tends to be distributed as a Gamma distribution, it is not easy to explicit the distribution of the sum , see [33] for a
Practical design of LR test: dealing with nuisance parameters
In practice, the application of the test (22) is compromised because neither the expectation nor the variance of samples are known. In such a situation, an usual solution consist in replacing the unknown values by their Maximum Likelihood Estimation (MLE), denoted and , respectively, to design a Generalized Likelihood Ratio Test (GLRT).
However, accurate estimation of the parameters and is a difficult problem but necessary to obtain a high detection performance. In 5.1
Numerical simulations
One of the main motivations for this paper is to show that the hypothesis testing theory can be applied in practice to design a reliable LSB matching detector.
As previously discussed, the reliability of the proposed tests heavily depends of the possibility to theoretically predict the parameters of proposed test in practice. To verify that the proposed test performs as established by Theorem 2, Theorem 3, Theorem 4 a numerical simulation was performed on simulated data. The Monte-Carlo
Conclusion and future works
The first step to fill the gap between hypothesis testing theory and steganalysis was recently proposed in [12], [7], [48]. This paper extends this first step to the case of LSB matching. By casting the problem of LSB matching steganalysis in the framework of hypothesis testing theory, the most powerful Likelihood Ratio Test is designed. Then, a thorough statistical study permits the analytical calculation of its performance in terms of the false-alarm probability and detection power. To apply
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2015, Information SciencesCitation Excerpt :Specifically, steganographic scheme embeds secret message into innocuous looking cover data (e.g., digital images) by slightly modifying the cover content in such a way that the intended recipient can precisely extract the embedded message. Unlike digital watermarking, steganography is a fragile data hiding technique, and the most important requirement for a steganographic scheme is its security, i.e., the perceptual and statistical undetectability of the hidden message [4,30,32,41]. Generally, there are mainly two ways to improve the stego-security.
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With the financial support from the Prevention of and Fight against Crime Programme of the European Union European Commission - Directorate-General Home Affairs (2centre.eu project). Research partially funded by Troyes University of Technology (UTT) strategic program COLUMBO.