IEEE SIGNAL PROCESSING LETTERS, VOL. 14, NO. 3, MARCH 2007 205 Steganalytic Features for JPEG Compression-Based Perturbed Quantization Gökhan Gül, Ahmet Emir Dirik, and ˙ Ismail Avcıbas ¸, Member, IEEE Abstract—Perturbed quantization (PQ) data hiding is almost un- detectable with the current steganalysis methods. We briefly de- scribe PQ and propose singular value decomposition (SVD)-based features for the steganalysis of JPEG-based PQ data hiding in im- ages. We show that JPEG-based PQ data hiding distorts linear de- pendencies of rows/columns of pixel values, and proposed features can be exploited within a simple classifier for the steganalysis of PQ. The proposed steganalyzer detects PQ embedding on relatively smooth stego images with 70% detection accuracy on average for different embedding rates. Index Terms—Singular value decomposition (SVD), steganal- ysis, steganography. I. INTRODUCTION S TEGANOGRAPHY hides information in a manner that the existence of the message is unknown. The goal of steganography is to communicate as many bits as possible without creating any detectable artifacts in the cover-object. If any suspicion about the secret communication is raised, then the goal is defeated. Steganalysis is the art of detecting the presence of covert communication between sender and receiver. A steganographic scheme is considered secure if no existing steganalysis method distinguishes cover and stego-images with a success better than random guessing. The embedding process on an object, while being perceptually transparent, leaves statistical artifacts that can be used to distinguish stego and cover-objects. The argument that data hiding methods leave telltale effects is common to all steganalysis methods [1]–[4]. Recently pro- posed perturbed quantization (PQ) steganography [5] is a quite successful data hiding approach for which current steganalysis methods fail to work [6]. In other words, PQ does not leave any traces in the form that the current steganalysis methods can catch. However, linear dependency between image rows and/or columns in the spatial domain is affected by PQ embedding due to random modifications on discrete cosine transform (DCT) co- efficients’ parities during data hiding. In this letter, the change in linear dependency is analyzed by singular value decomposition (SVD), and several features are derived from SVD. By a statis- tical hypothesis test, we justify the effectiveness of the features and then use these features to build a classifier to differentiate Manuscript received April 10, 2006; revised July 19, 2006. This work was supported in part by TÜB ˙ ITAK under Project 104E056. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Fernando Perez-Gonzalez. G. Gül and A. E. Dirik and are with the Electronics Engineering Depart- ment, Uludag University, 16059 Bursa, Turkey (e-mail: gokhan@uludag.edu.tr; emirdirik@yahoo.com). I. Avcıbas ¸ is with the Electrical-Electronics Engineering Department, Baskent University, 06530 Ankara, Turkey (e-mail: avcibas@baskent.edu.tr). Digital Object Identifier 10.1109/LSP.2006.884010 cover and stego-images embedded with the JPEG-based PQ steganography method. The rest of this letter is organized as follows: In Section II, we briefly describe PQ, SVD, and the features derived from SVD. We show the effectiveness of the features in discriminating cover and stego-images via analysis of variance (ANOVA) and scatter diagrams. Data set and experimental results are given in Section III. Conclusions are drawn in Section IV. II. PQ AND SVD-BASED FEATURES In PQ steganography, the cover-object is applied an infor- mation-reducing operation that involves quantization such as lossy compression, resizing, or A/D conversion before data em- bedding. The quantization is perturbed according to a random key for data embedding, therefore called “perturbed quantiza- tion.” PQ steganography, which uses JPEG compression for in- formation reducing operation, is different from their DCT-based counterparts. Since message bits are encoded by changing DCT parities after quantization, the cover image can be thought of just as a recompressed input image. To achieve high embedding rates, recompression is realized by doubling the input quanti- zation table with the assumption that recompression of cover JPEG images does not draw any suspicion because of its wide usage in digital photography [5]. Since the original cover image is recompressed via embedding operation, its compressed ver- sion should be considered as “cover” instead of original image. While we answer “if any message bits are hidden” for any other steganographic method, we answer “if quantization steps are perturbed” for PQ to make steganalysis possible. As a result of permuting of slight perturbations and altering the quantiza- tion steps of nonzero DCT coefficients, statistical properties of an image change in different regions in such a way that these changes balance each other as a whole. The permutation of DCT coefficients makes it impossible to predict which sections of an image are affected by data embedding. Unlike statistical proper- ties, the inherent linear dependency cannot be preserved because any little change made on rows in any region yields a linear de- pendency modification, regardless of being negative or positive. Since PQ steganography changes DCT coefficients randomly, the linear dependencies between columns and rows of a cover image, especially in smooth regions, decrease according to em- bedding noise in the DCT domain. The decrease of linear depen- dencies between rows and columns can be detected by checking singular values resulting from SVD over a given image. A. Singular Value Decomposition and Derived Features SVD is an extremely powerful tool in linear algebra. SVD decomposes a matrix into the product of two or- 1070-9908/$25.00 © 2007 IEEE