Generic Adoption of Spatial Steganalysis to Transformed Domain

There are several powerful steganalytic methods for images in the spatial domain, which are based on higher order statistics. We propose a generic methodology to prepare higher order steganalytic methods from spatial domain for application in the transformed domain. This paper presents 72 new systematically designed methods that are derived from the spatial domain. Their reliability and the precision of their length estimation is evaluated based on 1700 million attacks. We present the contribution of the proposed methods in terms of detection power and precision compared to prior art and determine how properties like image size and JPEG quality influence the ranking of the proposed attacks. 1 Steganography in JPEG Files Steganography is the art and science of invisible communication. Its aim is the transmission of information embedded invisibly into carrier data. The goal of steganalysis is to discover steganographic alterations to carrier data. We can distinguish targeted attacks, which are fine-tuned to one particular embedding method, and blind (or universal) attacks, which detect steganographic changes using a classifier that is trained with features from known steganograms and carrier media. Targeted methods are often used to extract features for the training. The distinction of blind and targeted attacks is blurred in this respect. The most simple embedding methods are at the same time the most widely used. Common carrier data include digitised images or audio files. In many cases the image data are stored in the spatial domain (e.g., in BMP or PNM format). The message is embedded by replacing the least significant bits of the colour or brightness values by the (encrypted) message bits. The human eye will usually not notice the changes that are caused by the embedding in the image. Sometimes, however, the embedding can still be detected by statistical means. One of the first steganalytic attacks was based on the global histogram of the colour or brightness values and is also applicable to DCT values in JPEG files [1]. JPEG files are more common as e-mail attachments than spatial domain images. As such, they are a more important carrier medium for steganography. K. Solanki, K. Sullivan, and U. Madhow (Eds.): IH 2008, LNCS 5284, pp. 161–177, 2008. c © Springer-Verlag Berlin Heidelberg 2008 162 A. Westfeld All previous targeted attacks to Jsteg embedding [2] only evaluated global frequencies of DCT values. They ignored the location of these values and the spatial frequency in the context in which they occurred. This is also calledmarginal distributions or first order statistics. Part of this concept are, e.g., the attack by Zhang and Ping [3] (ZP, cf. Sect. 3.1), the attack by Yu et al. [4] (Yu, cf. Sect. 3.2), and the category attack by Lee et al. [5] (CA, cf. Sect. 3.3) together with its generalisation (GCA) [6]. Blind attacks also employ higher order statistics, however, unlike the aforementioned attacks, they are rarely used to estimate the length of the embedded message [7,8,9]. A recent evaluation concluded that blind attacks to JPEG images are less reliable than the CA, at least for heterogeneous sources of images [6]. There are several steganalytic techniques for the spatial domain that use higher order statistics, e.g., RS [10], WS [11], SPA [12,13], and Pairs [14]. To our knowledge, they have never been applied directly to coefficients of the frequency domain before, while this was done from the beginning with the histogram based chi-square attack. It seems not very obvious how to extract the sample sequences from the DCT frequency domain to use them with spatial domain higher order statistical attacks. It is even doubtful because the goal of the JPEG compression is to remove irrelevance, i.e., to reduce the local dependency that is inherent to images and exploited by the higher order attacks. We tried it, though, contributing partly considerable improvements in terms of reliability and precision. Although we think the proposedmethodology is applicable in general to exploit local dependencies in JPEG files, there is essentially only one steganographic algorithm used for both, spatial and DCT domain: LSB replacement. At the same time this is the most completely analysed algorithm in the spatial domain, which offers a wide range of different steganalytical approaches for testing our methodology.While we apply these approaches to Jsteg [2] in our evaluation, an adaption to JPhide [15] is easy, however, the ranking of attacks could be different. This paper is organised as follows: Section 2 looks at several scanpaths (intra block and inter block) to exploit local dependencies in the DCT domain. Section 3 briefly describes histogram-based attacks to JPEG files. In Sect. 4 we derive 72 new attacks for JPEG media (6 fundamental attacks × 6 scanpaths × with and without DC coefficients) from the spatial domain attacks mentioned at the beginning (RS, WS, SPA, and Pairs). The new attacks are evaluated in Sect.5. All in all we produced 1700 million length estimations for a variety of different messages of several lengths in a set of images with different quality and size to pick the best scanpath and the most suitable attack from the spatial domain. The paper is concluded in Sect. 6. 2 Methods 2.1 Local Correlation A well-known feature of spatial domain images is the dependency between neighbouring pixels. This has been exploited for steganalysis using fractal scanpaths [16]. Generic Adoption of Spatial Steganalysis to Transformed Domain 163 Correlations of DCT coefficients have been studied in the context of entropy coding in JPEG images. Tu and Tran distinguish three kinds of correlations [17]: Intrablock or intersubband correlation. The magnitudes of (unquantised) AC coefficients decrease as the frequency increases. This results in a dependency between neighbouring coefficients. However, the intrablock dependency is limited to a small block of 8×8 pixels only. It is also weak, since the coefficients of one block belong to different, (nearly) orthogonal subbands. Most coefficients are quantised to zero and do not carry much information. Interblock or intrasubband correlation. Low frequency coefficients and their neighbours are mutually dependent on each other within the same subband. Generally, the interblock dependency is much stronger than the intrablock dependency. However, it is limited especially for higher frequencies because, compared to the raster of pixels, their distance is increased to the block raster (e.g., factor 8). Sign correlation. Deever and Hemami analysed the sign behaviour of wavelet coefficients [18]. A similar intrasubband dependency can be found for low frequency coefficients in JPEG images. Fridrich uses co-occurrence matrices of neighbouring coefficients in the same subband in her blind attack using 23 DCT features [7]. Even individual cooccurrence features very reliably detect F5, Outguess, and MB1 [19,20,21] for full embedding rate. Fu et al. rearrange the DCT coefficients to exploit both, intrablock and interblock dependency for their blind attack based on Markov empirical transition matrices [22]. They apply a zigzag scan for intrablock dependency as well as a slalom scan for interblock dependency. 2.2 Scanning Orders for DCT Coefficients The JPEG compression reorders the DCT coefficients of one 8 × 8 block from their natural order to zigzag order (cf. Fig. 1) to take advantage of the intrablock dependency. We scan DCT coefficients in natural and zigzag order to exploit intrablock dependency by our attacks. The dependency in different subbands may have different orientation. From spatial domain we know that recursive scanning paths increase the dependency between pixel values [16]. This is also valid for DC coefficients. AC coefficients might favour the interblock dependency in vertical or horizontal lines. We apply recursive and linear scanning paths (cf. Fig. 2) to evaluate the interblock dependency by the attacks that we propose in the sequel. 3 Prior Attacks to Jsteg-Like Embedding Jsteg is probably the first algorithm that was developed for JPEG images [2]. It overwrites the least significant bits of the quantised DCT coefficients with secret message bits. Jsteg is detectable by the chi-square attack [1]. However, the attack