Applying LR Cube Analysis to JSteg Detection

JSteg is a steganographic method for JPEG images that can be viewed as LSB steganography. Recently, we proposed a new principle to detect the use of LSB steganography in digitized vector signals and showed how to apply it to gray-scale images. In this paper, we discuss how to apply it to JPEG images and show some experimental results for the JSteg-like algorithm. Introduction: JSteg-like algorithm [1] is a steganographic method for JPEG images. It works by replacing the LSBs (least significant bits) of quantized DCT (discrete cosine transform) coefficients excepting the values of ’0’ and ’1’ with message bits. Thus, the JSteg-like algorithm can be viewed as the LSB steganography with an exception for usable DCT coefficients. Recently, we proposed the LR cube analysis to detect the use of LSB steganography in RGB color images [2]. It used RGB vectors as basic units and took advantage of the local correlation of these vectors. In [3], we described its general framework to use n-dimensional vectors as basic units for the applications to various types of digital signals and showed how to apply it to gray-scale images. So far, we have been working on the task whether the LR cube analysis can be applied to detect the JSteg-like algorithm for JPEG images; the answer is yes. This paper shows the method of how to apply the LR cube analysis for detecting the usage of JSteg-like algorithm. Method Description and Experimental Results: Fig. 1 and Fig. 2 show the two basic ideas of the LR cube analysis. Fig. 1 represents the two types of comparable sets in Z under the LSB embedding, where the δ is a positive odd integer and the two-sided arrows represent the possible changes of the vectors by LSB embedding. Given a vector signal, the sets can be classified into their complexities as shown in Fig. 2, where the complexity of a set means the number of different vectors contained in the set. We observed that the left and right δcubes are similarly distributed on their complexities before the LSB embedding, but the left (or right) δ-cubes’ complexities tend to decrease (or increase) after the LSB embedding, respectively. The LR cube analysis measures a dissimilarity between their complexities by a well-known hypothesis test: the χ-test. For the application of the LR cube analysis to JPEG format, we have investigated various kinds of vector samplings from the DCT coefficients. As a result, we developed the (x, y; i, j) sampling; x and y indicate the numbers of joint blocks in x and y directions,and also, i and j indicate the numbers of joint