Elsevier

Signal Processing

Volume 87, Issue 6, June 2007, Pages 1251-1263
Signal Processing

A DCT-based Mod4 steganographic method

https://doi.org/10.1016/j.sigpro.2006.10.014Get rights and content

Abstract

This paper presents a novel Mod4 steganographic method in discrete cosine transform (DCT) domain. Mod4 is a blind steganographic method. A group of 2×2 spatially adjacent quantized DCT coefficients (GQC) is selected as the valid message carrier. The modulus 4 arithmetic operation is then applied to the valid GQC to embed a pair of bits. When modification is required for data embedding, the shortest route modification scheme is applied to reduce distortion as compared to the ordinary direct modification scheme. Mod4 is capable in embedding information into both uncompressed and JPEG-compressed image. To compare Mod4 with other existing methods, carrier capacity, stego image quality, and results of blind steganalysis for 500 various images are shown. Visual comparison of three additional metrics is also presented to show the relative performance of Mod4 among other existing methods.

Introduction

Steganography is a data hiding technique that has been mainly used in information security applications. It is similar to watermarking and cryptography techniques, but these three techniques are different in some aspects. Firstly, watermarking mainly tracks illegal copies or claims of the ownership of digital media. It is not geared for communication. Secondly, cryptography scrambles the data with the mixture of permutation(s) and substitution(s) so that unintended receivers cannot perceive the processed information. However, the fact that information has been embedded into a medium (i.e., watermarking) and communication has been carried out (i.e., cryptography) is known to everyone, or at least it is acceptable to reveal such a fact. Finally, steganography transmits information by embedding messages into innocuous-looking cover objects, such as digital images, to conceal the very existence of communication. As a result, steganography is the art and science of data smuggling since its goal is to hide the presence of communication [1].

Despite the fact that steganography has been notoriously used in spying and evil plots, there are many friendly applications of steganography. For instance, a photographer may record the aperture size, shuttle speed, and other settings for future references when capturing a picture. A person may want to embed a file containing private information into a multimedia file to save storage space. Other applications include signature, authentication, history recording and so on.

For such reasons, many imagery steganographic methods have been invented. Here we briefly review research carried out particularly in the DCT domain. Upham invented JSteg that hides information sequentially in LSBs of the quantized DCT coefficients (qDCTCs) while skipping 0's and 1's [2]. Provos developed OutGuess to scatter information into the LSB of qDCTCs [3]. Embedding is followed by a correction procedure to ensure that the distributions of any related pair of the qDCTCs are unchanged. Westfeld employs the technique of matrix encoding to hold secret information using LSB of qDCTCs in F5 [4]. Whenever a modification is needed, the magnitude of a coefficient is decremented.

Sallee proposed a model-based steganographic scheme that treats a cover medium as a random variable that obeys some parametric distribution such as Cauchy or Gaussian [5]. The medium is divided into two parts, i.e., the deterministic, and the indeterministic part where the secret message is embedded. Miyake et al. define diagonal bands for each 8×8 DCT block, and the number of zeros (in a zero sequence) in each band are modified to embed exactly one bit [6]. If the frequency of zeros within a zero sequence in a band is odd, that band stores the message bit 1, and vice versa. Seki et al. apply modulus arithmetic on the sum of all 64 qDCTCs from a block to embed information [7]. The coefficient(s) is (are) modified by exploiting the quantization errors so that the sum yields the desired remainder when divided by a fixed number d.

On the other hand, along with the evolution of steganographic methods, many steganalysis methods are invented. Westfeld and Pfitzmann invented the χ2-statistical test to detect the message embedded sequentially into a cover medium by LSB flipping methods [8]. Fridrich et al. employ a macroscopic measure, i.e., increment of blockiness, to determine the length of the embedded message [9]. This measure detects the stego of OutGuess [3]. However, this macroscopic measure is limited to LSB flipping approaches. Extending their work to non-LSB flipping methods, Fridrich et al. successfully detect the message embedded using F5 [4] by exploiting the awkward concentration of zero coefficients in the distribution of qDCTCs [10].

While the above steganalysis methods target at some specific steganographic methods, Farid invented a blind steganalysis method that detects stegos regardless of the embedding algorithm in use [11]. This steganalyzer employs features extracted from the image after a series of filterings, and the errors collected from an optimal linear predictor. This method is recently extended to non-linear support vector machine to classify a given image with higher accuracies [12]. Avcibas et al. invented a blind steganalysis method utilizing various image quality metrics as the features [13]. This method is based on the observation that an embedded and filtered image differs statistically from a non-embedded but simply filtered image. Recently, Fridrich proposed an effective feature-based steganalysis method for JPEG images [14]. This classifier uses 23 features that are possibilly altered during data embedding. It detects the stego generated by JP Hide & Seek [15], OutGuess [3], F5 [4] and model-based steganography [5]. This method is further extended to include the ability to associate a detected stego with a known steganographic method [16].

In this paper, we propose a novel DCT-based Mod4 steganographic method for still images. It extends our previous work [17], which presents preliminary results, by adding more flexible constraints on a set of parameters and comparing with existing methods using six metrics and the state-of-the-art blind steganalysis method [14]. Our work is presented with the passive warden scenario [1] and assumes that there is no channel noise during data transmission. The remainder of the paper is organized as follows. Section 2 presents the Mod4 steganographic method. Section 3 discusses the features of the proposed method. Section 4 shows the experimental results to compare Mod4 with some selected existing steganographic methods in DCT domain. Visual comparison is presented in Section 5 to show the relative performance of Mod4 among other existing methods. Finally, conclusions are given in Section 6.

Section snippets

The embedding scheme

The block diagram of the proposed method is shown in Fig. 1, where we consider the JPEG compressed image for presentation purpose. In the following subsections, we discuss each block in detail.

Coefficient distribution and migration

Since Mod4 is a non-LSB flipping-based steganographic method, it can withstand χ2-statistical-based tests [8]. With the construction of SRM, it is obvious that the magnitude of a coefficient is incremented when modification is required. Thus the Laplacian distribution property of the AC-components is preserved. Also, coefficients in [-φ2,φ1] are left unmodified, hence leading to the undetectability by histogram-based steganalysis that seeks for awkward concentration of coefficients at low value

Preparation

To compare Mod4 with the existing methods in terms of embedding capacity, image quality, and robustness against blind steganalysis, a database of 500 images is generated with Sony DSC-828 digital camera. Each image is converted to grayscale, and resized to 800×600 pixels using bicubic interpolation. These images are used as uncompressed original cover images. The considered methods are OutGuess [3], F5 [4], model-based steganography [5], and ZeroSequence [6], respectively referred as OG,F5,MB,

Visual comparison

Three additional evaluation metrics are computed to further compare the proposed Mod4 method with other existing methods. These three metrics are filesize ratio (FSR), histogram product (HP), and embedding efficiency (EE). Specifically, FSR measures the difference between the filesizes of original image A (i.e., unmodified JPEG) and its stego image A that contains a certain message. It is computed asFSR(Ak,Ak)=1-8×|FS(Ak)-FS(Ak)|bpc×(k0hk)×2,where hk represents the count (from global

Conclusions

A DCT-based steganographic method called Mod4 is proposed. A pair of message bits is hidden among qDCTCs in a vGQC. SRM is employed to ensure the expected number of modifications is minimal. Also, adjustable parameters (i.e., φ1,φ2,τ1, and τ2) are utilized to select message carriers adaptively. We have conducted experiments to compare Mod4 with other existing steganographic methods in terms of carrier capacity (bpc), image quality (PSNR and Q-metric), and detectability for blind steganalysis.

Acknowledgments

The authors are grateful to the anonymous reviewers for their invaluable comments and recommendations to improve our paper. Special thanks to Prof. Jessica Fridrich for generously providing the execution code for feature-based steganalysis.

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