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966 Z Khan and A B Mansoor,Fig 1 A general steganography model. Steganography and cryptography are closely related data hiding methods The. purpose of cryptography is to scramble a message so that it cannot be under. stood while that of steganography is to hide the message so that it cannot be. seen In general a message in cipher text might arouse suspicion on an observer. while an invisible message created with steganographic methods will not Some. times steganography and cryptography are combined in a way that the message. may be encrypted before hiding to provide additional security Those who conceal. communications through steganography are countered by those who wish to un. veil such communications The eld devoted to counter steganography is known as. steganalysis The rst and foremost goal of a steganalyst is to detect the presence. of steganography so that the secret message may be stopped before it is received. Then the second goal is to identify the steganography tool so that the secret mes. sage may be spoofed and or corrupted or even extracted from the stego le. Generally two approaches are followed for steganalysis one is to come up. with a steganalysis method speci c to a particular steganographic algorithm. The other is to develop universal steganalysis techniques which are independent. of the steganographic algorithm Both approaches have their own strengths and. weaknesses A steganalysis technique speci c to an embedding method would. give very good results when tested only on that embedding method but might. fail on all other steganographic algorithms as in 4 5 6 and 7 On the other. hand a steganalysis technique which is independent of the embedding algorithm. might perform less accurately overall but still shows its e ectiveness against new. and unseen embedding algorithms as in 8 9 10 and 11 Our research work. is concentrated on the second approach due to its wide applicability. In this paper we propose a steganalysis technique by extracting features from. two transform domains the discrete wavelet transform and the discrete cosine. transform The features are investigated individually and combinatorially The. rest of the paper is organized as follows In Section 2 we discuss the previous. research work related to steganalysis In Section 3 we present our proposed. approach Experimental results are presented in Section 4 Finally the paper is. concluded in Section 5, Steganalysis of JPEG Images with Joint Transform Features 967. 2 Related Work, Due to the increasing availability of new steganography tools over the internet. there has been an increasing interest in the research for new and improved ste. ganalysis techniques which are able to detect both previously seen and unseen. embedding algorithms A good survey of benchmarking of steganography and. steganalysis techniques is given by Kharrazi et al 3. Fridrich et al presented a steganalysis method which can reliably detect mes. sages hidden in JPEG images using the steganography algorithm F5 and also. estimate their lengths 4 This method was further improved by Aboalsamh. et al 5 by determining the optimal value of the message length estimation. parameter Westfeld and P tzmann presented visual and statistical attacks. on various steganographic systems including EzStego v2 0b3 Jsteg v4 Steganos. v1 5 and S Tools v4 0 by using an embedding lter and the 2 statistic 6 A. steganalysis scheme speci c to the embedding algorithm Outguess is proposed. in 7 by making use of the assumption that the embedding of a message in a. stego image will be di erent than embedding the same into a cover image. Avcibas et al proposed that the correlation between the bit planes as well. as the binary texture characteristics within the bit planes will di er between a. stego image and a cover image thus facilitating steganalysis 8 Farid suggested. that embedding of a message alters the higher order statistics calculated from. a multi scale wavelet decomposition 9 Particularly he calculated the rst four. statistical moments mean variance skewness and kurtosis of the distribution of. wavelet coe cients at di erent scales and subbands These features moments. calculated from both cover and stego images were then used to train a linear clas. si er which could distinguish them with a certain success rate Fridrich showed. that a functional obtained from marginal and joint statistics of DCT coe cients. will vary between stego and cover images In particular a functional such as. the global DCT coe cient histogram was calculated for an image and its de. compressed cropped and recompressed versions Finally the resulting features. were obtained as the L1 norm of the di erence between the two The classi er. built with features extracted from both cover and stego images could reliably. detect F5 Outguess and Model based steganography techniques 10 Avcibas. et al used various image quality metrics to compute the distance between a. test image and its lowpass ltered versions Then a classi er built using linear. regression showed detection of LSB steganography and various watermarking. techniques with a reasonable accuracy 11,3 Proposed Approach. 3 1 Feature Extraction, Since the dimensionality of image data is huge it is not feasible to use the.

complete image data directly for steganalysis A better option is to extract a. certain amount of useful data and use it to represent the image instead of the. image itself for steganalysis This useful set of data points are called features. 968 Z Khan and A B Mansoor, The addition of a message to a cover image does not a ect the visual appearance. of the image but may a ect some statistics The features required for the task. of steganalysis should be able to catch these minor statistical disorders that are. created during the data hiding process, In our approach we rst extract features in the discrete wavelet transform. domain followed by the discrete cosine transform domain and nally combine. both extracted features to make a joint feature set. DWT Based Features For extraction of features in the Discrete Wavelet. Transform domain we chose three scale decomposition as proposed by Wang. and Moulin 12 Figure 2 shows the levels and selection of subbands for this. decomposition Using Haar wavelet lter we obtained nine detail subbands. Horizontal Hi Vertical Vi and Diagonal Di i 1 2 3 and three approxima. tion subbands Lowpass Li i 1 2 3 We further decomposed the rst scale. diagonal subband D1 to improve the performance of the features 12 As D1 is. the nest detail subband and each of its coe cients involves diagonal di erences. in a four pixel block So H 1 V 1 and D 1 will contain more information about. the di erence of di erences between neighboring pixels. Various statistical measures are used in our analysis Particularly the rst. three normalized moments of the characteristic function are computed The K. point discrete Characteristic Function CF is de ned as. where h m M 1, m 0 is the M bin histogram which is an estimate of the PDF p x. of the wavelet coe cients distribution The nth absolute moment of discrete CF. is de ned as,MnA k sinn 2,Fig 2 A three scale wavelet decomposition. Steganalysis of JPEG Images with Joint Transform Features 969. Finally the normalized CF moment is de ned as, where M0A is the zeroth order moment We calculated the rst three normalized.

CF moments for each of the 16 subbands giving a 48 D feature vector. DCT Based Features The DCT based feature set is constructed following. the approach of Fridrich 10 A vector functional F is applied to the JPEG. image J1 This image is then decompressed to the spatial domain cropped by 4. pixels in each direction and recompressed with the same quantization table as. J1 to obtain J2 The vector functional F is then applied to J2 The nal feature. f is obtained as the L1 norm of the di erence of the functional applied to J1. f F J1 F J2 L1 4, The rational behind this procedure is that the recompression after cropping by. 4 pixels does not see the previous JPEG compression s 8 8 block boundary and. thus it is not a ected by the previous quantization and hence embedding in the. DCT domain So J2 can be thought of as an approximation to its cover image. We calculated the global individual and dual histograms of the DCT coef. cient array d k i j as the rst order functionals The symbol d k i j de. notes the i j th quantized DCT coe cient i j 1 2 8 in the k th block. k 1 2 B The global histogram of all 64B DCT coe cients is given as. H m R m L where L mink i j d k i j and R maxk i j d k i j We com. puted H H L1 the normalized global histogram of DCT coe cients as the. rst functional, Steganographic techniques that preserve global DCT coe cients histogram. may not necessarily, preserve the histogram of individual DCT modes So we. calculated hij hij L the normalized individual histograms h m R m L of 5 low. frequency DCT modes i j 2 1 3 1 1 2 2 2 1 3 as the next ve. functionals, The dual histogram is an 8 8 matrix which indicates the number of how. many times the value d occurs as the i j DCT coe cient over all blocks B. in the image We computed gij gij L the normalized dual histograms where. gij d d k i j for 11 values of d 5 4 4 5, Inter block dependency is captured by the second order features variation and.

blockiness Most steganographic techniques add entropy to the DCT coe cients. which is captured by the variation V,dIr k i j dIr k 1 i j dIc k i j dIc k 1 i j. i j 1 k 1 i j 1 k 1,970 Z Khan and A B Mansoor, where Ir and Ic denote the vectors of block indices while scanning the image by. rows and by columns respectively, Blockiness is calculated from the decompressed JPEG image and is a measure. of discontinuity along the block boundaries over all DCT modes over the whole. image The L1 and L2 blockiness B 1 2 is de ned as,x8i j x8i 1 j xi 8j xi 8j 1. i 1 j 1 j 1 i 1,N M 1 8 M N 1 8, where xi j are the grayscale intensity values of an image with dimensions M N.

The nal DCT based feature vector is 20 D Histograms 1 global 5 individ. ual 11 dual Variation 1 Blockiness 2, Joint Features After extracting the features in the discrete cosine transform. and the discrete wavelet transform domain we nally combine the extracted. feature sets into one joint feature set giving a 68 D feature vector 48 DWT. 3 2 Classi er, We used the two class Fisher Linear Discriminant FLD classi er 19 Let. xi i 1 Nx and yj j 1 Ny represent the samples from each of the. two classes of the training set The within class means are given by. mx xi my yj 7,Nx i 1 Ny j 1,The between class mean is. Nx Ny i 1 j 1,The within class scatter matrix is,Sw Mx MxT My MyT 9. where Mx xi mx My yj my are the matrices containing the zero. meaned ith and j th samples respectively The between class scatter matrix is. Sb Nx mx m mx m T Ny my m my m T 10, The maximal generalized eigenvalue eigenvector e is related to Sb and Sw by.

Sb e Sw e 11, Steganalysis of JPEG Images with Joint Transform Features 971. By projecting the training samples xi and yj onto one dimensional linear sub. space e xp xT T, i e yp yj e the within class scatter is minimized and the. between class scatter is maximized In any classi cation problem this e ect is. highly desirable as it maintains the discriminability while simultaneously reduces. the dimensions of data An unknown sample z can now be tested for its class by. projecting it onto the same subspace e zp z T e and its class determined on. the basis of a threshold Th,4 Experimental Results. 4 1 Image Datasets, Cover Image Dataset For our experiments we used 1338 grayscale images of. size 512x384 obtained from the Uncompressed Colour Image Database UCID. constructed by Schaefer and Stich 13 available at 14 These images contain. a wide range of indoor outdoor daylight night scenes providing a real and. challenging environment for a steganalysis problem All images were converted. to JPEG at 80 quality for our experiments, F5 Stego Image Dataset Our rst stego image dataset is generated by the.

steganography software F5 15 proposed by Andreas Westfeld F5 steganogra. phy algorithm embeds information bits by incrementing and decrementing the. values of quantized DCT coe cients from compressed JPEG images 16 F5. also uses an operation known as matrix embedding in which it minimizes the. amount of changes made to the DCT coe cients necessary to embed a message. of certain length Matrix embedding has three parameters c n k where c is the. number of changes per group of n coe cients and k is the number of embedded. bits These parameter values are determined by the embedding algorithm. F5 algorithm rst compresses the input image with a user de ned quality. factor before embedding the message We chose a quality factor of 80 for stego. images Messages were successfully embedded at rates of 0 05 0 10 0 20 0 3. 0 40 and 0 60 bpc bits per non zero DCT coe cients We chose F5 because. recent results in 8 9 12 have shown that F5 is harder to detect than other. commercially available steganography algorithms, MB Stego Image Dataset Our second stego image dataset is generated. by the Model Based steganography method 17 proposed by Phil Sallee 18. The algorithm rst breaks down the quantized DCT coe cients of a JPEG im. age into two parts and then replaces the perceptually insigni cant component. with the coded message signal The algorithm has two types MB1 is normal. steganography and MB2 is steganography with deblocking The deblocking al. gorithm adjusts the unused coe cients to reduce the blockiness of the resulting. image to the original blockiness Unlike F5 the Model Based steganography al. gorithm does not recompress the cover image before embedding We embed at. rates of 0 05 0 10 0 20 0 3 0 40 0 60 and 0 80 bpc The model based steganog. raphy algorithm has also shown high resistance against steganalysis techniques. 972 Z Khan and A B Mansoor, Table 1 The number of images in the stego image datasets given the message length. F5 with matrix embedding turned o 1 1 1 and turned on c n k Model based. steganography without deblocking MB1 and with deblocking MB2 U unachiev. Embedding F5 F5 MB1 MB2,Rate bpc 1 1 1 c n k,0 05 1338 1338 1338 1338. 0 10 1338 1338 1338 1338,0 20 1338 1337 1338 1334,0 30 1337 1295 1338 1320. 0 40 1332 5 1338 1119,0 60 5 U 1332 117,0 80 U U 60 U.

The reason for choosing the message length proportional to the number of. non zero DCT coe cients was to create a stego image database for which the. steganalysis is roughly of the same level of di culty We further carried out em. bedding at di erent rates to observe the steganalysis performance for messages. of varying length It can be seen in Table 1 that the Model based steganography. is more e cient in embedding as compared to F5 since longer messages can be. accommodated in images using Model based steganography. 4 2 Evaluation of Results, The Fisher Linear Discriminant classi er described in Section 3 2 was utilized. for our experiments Each steganographic algorithm was analyzed separately for. the evaluation of the steganalytic classi er For a xed relative message length. we created a database of training images comprising 669 cover and 669 stego im. ages Both DWT based features DWT and DCT based features DCT were. extracted from the training set and were combined to form a Joint feature set. JNT according to the procedure explained in Section 3 1 The FLD classi er. was then tested on the features extracted from a di erent database of test images. comprising 669 cover and 669 stego images The Receiver Operating Character. istics ROC curves which give the variation of the Detection Probability Pd. the fraction of correctly classi ed stego images with the False Alarm Proba. bility Pf the fraction of stego images wrongly classi ed as cover image were. computed for each steganographic algorithm and embedding rate The area un. der the ROC curve AUC was measured to determine the overall classi cation. Figures 3 5 give the obtained ROC curves for the steganographic techniques. under test for di erent embedding rates Note that due to the space limitation. these gures are displayed in small size However readers are encouraged to take. a look by using zoom to 400 We observe that the DCT based features out. perform the DWT based features for all embedding rates As could be expected. the detection of F5 without matrix embedding is better than F5 with matrix. Steganalysis of JPEG Images with Joint Transform Features 973. 0 9 0 9 0 9 0 9,0 8 0 8 0 8 0 8,Test Detection Probability. Test Detection Probability,Test Detection Probability. Test Detection Probability,0 7 0 7 0 7 0 7,0 6 0 6 0 6 0 6. 0 5 0 5 0 5 0 5,0 4 0 4 0 4 0 4,0 3 0 3 0 3 0 6 0 3.

0 4 0 4 0 4,0 2 0 3 0 2 0 3 0 2 0 3 0 2 0 3,0 2 0 2 0 2 0 2. 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1,0 05 0 05 0 05 0 05. 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1. Test False Alarm Probability Test False Alarm Probability Test False Alarm Probability Test False Alarm Probability. Fig 3 ROC curves using DCT based features a F5 without matrix embedding b. F5 with matrix embedding c MB1 without deblocking d MB2 with deblocking. 0 9 0 9 0 9 0 9,0 8 0 8 0 8 0 8,Test Detection Probability. Test Detection Probability,Test Detection Probability. Test Detection Probability,0 7 0 7 0 7 0 7,0 6 0 6 0 6 0 6.

0 5 0 5 0 5 0 5,0 4 0 4 0 4 0 4,0 3 0 3 0 3 0 6 0 3. 0 4 0 4 0 4,0 2 0 3 0 2 0 3 0 2 0 3 0 2 0 3,0 2 0 2 0 2 0 2. 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1,0 05 0 05 0 05 0 05. 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1. Test False Alarm Probability Test False Alarm Probability Test False Alarm Probability Test False Alarm Probability. Fig 4 ROC curves using DWT based features a F5 without matrix embedding b. F5 with matrix embedding c MB1 without deblocking d MB2 with deblocking. 0 9 0 9 0 9 0 9,0 8 0 8 0 8 0 8,Test Detection Probability. Test Detection Probability,Test Detection Probability.

Test Detection Probability,0 7 0 7 0 7 0 7,0 6 0 6 0 6 0 6. 0 5 0 5 0 5 0 5,0 4 0 4 0 4 0 4,0 3 0 3 0 3 0 6 0 3. 0 4 0 4 0 4,0 2 0 3 0 2 0 3 0 2 0 3 0 2 0 3,0 2 0 2 0 2 0 2. 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1,0 05 0 05 0 05 0 05. 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1. Test False Alarm Probability Test False Alarm Probability Test False Alarm Probability Test False Alarm Probability. Fig 5 ROC curves using Joint features a F5 without matrix embedding b F5. with matrix embedding c MB1 without deblocking d MB2 with deblocking. embedding as the matrix embedding operation signi cantly reduces detectabil. ity at the expense of message capacity, Table 2 summarizes the classi cation results For F5 without matrix embed.

ding the proposed Joint transform features dominate both DCT and DWT. based features for embedding rates till 0 20 bpc For higher embedding rates the. DCT based features perform better For F5 with matrix embedding both the. proposed joint features and the DCT based features are close competitors. For MB1 algorithm without deblocking the proposed joint features outper. form both the DCT and DWT based features for all embedding rates For MB2. algorithm with deblocking the joint features perform close to the DCT based. features It is observed that the detection of MB1 is better than MB2 as the. deblocking algorithm in MB2 reduces the blockiness of the stego image to match. the original image,974 Z Khan and A B Mansoor, Table 2 Classi cation results AUC using FLD for all embedding rates F5 with ma. trix embedding turned o 1 1 1 and turned on c n k Model based steganography. without deblocking MB1 and with deblocking MB2 U unachievable rate. Embedding F5 F5 MB1 MB2,Rate bpc 1 1 1 c n k,0 05 0 767 0 640 0 622 0 598 DCT. 0 05 0 531 0 491 0 498 0 492 DWT,0 05 0 770 0 636 0 614 0 588 JNT. 0 10 0 932 0 794 0 732 0 692 DCT,0 10 0 562 0 528 0 535 0 520 DWT. 0 10 0 943 0 796 0 729 0 686 JNT,0 20 0 993 0 971 0 872 0 841 DCT.

0 20 0 624 0 592 0 581 0 580 DWT,0 20 0 993 0 966 0 890 0 849 JNT. 0 30 0 998 0 998 0 942 0 924 DCT,0 30 0 689 0 653 0 654 0 639 DWT. 0 30 0 993 0 996 0 954 0 931 JNT,0 40 0 999 U 0 972 0 965 DCT. 0 40 0 735 U 0 667 0 666 DWT,0 40 0 997 U 0 980 0 978 JNT. 0 60 U U 0 984 U DCT,0 60 U U 0 693 U DWT,0 60 U U 0 991 U JNT.

5 Conclusion, This paper presents a new DCT and DWT based joint features approach for. universal steganalysis DCT and DWT based statistical features are investi. gated individually followed by research on combined features The Fisher Linear. Discriminant classi er is employed for classi cation The experiments were per. formed on image datasets with di erent embedding rates for F5 and Model based. steganography algorithms Experiments revealed that for JPEG images the DCT. is a better choice for extraction of features as compared to the DWT The ex. periments with joint transform features reveal that the extraction of features in. more than one transform domain improves the steganalysis performance. Acknowledgments The work on this paper was supported by the National. University of Sciences and Technology Pakistan,References. 1 Johnson N F Jajodia S Exploring Steganography Seeing the Unseen IEEE. Computer 31 2 26 34 1998, 2 Simmons G J Prisoners Problem and the Subliminal Channel In CRYPTO. 1983 Advances in Cryptology pp 51 67 1999, Steganalysis of JPEG Images with Joint Transform Features 975. 3 Kharrazi M Sencar T H Memon N Benchmarking Steganographic and Ste. ganalysis Techniques In Proc of SPIE Electronic Imaging Security Steganog. raphy and Watermarking of Multimedia Contents VII San Jose California USA. 4 Fridrich J Goljan M Hogea D Steganalysis of JPEG images Breaking the F5. Algorithm In Proc 5th International Workshop on Information Hiding Noord. wijkerhout The Netherlands pp 310 323 October 2002. 5 Aboalsamh H A Dokheekh S A Mathkour H I Assassa G M Breaking the. F5 Algorithm An Improved Approach Egyptian Computer Science Journal 29 1. 6 Westfeld A P tzmann A Attacks on Steganographic Systems In Proc 3rd. Information Hiding Workshop Dresden Germany pp 61 76 1999. 7 Fridrich J Goljan M Hogea D Attacking the OutGuess In Proc ACM Work. shop on Multimedia and Security 2002 ACM Press Juan les Pins December 2002. 8 Avcibas I Memon N Sankur B Image Steganalysis with Binary Similarity. Measures In Proc of the IEEE International Conference on Image Processing. Rochester New York September 2002, 9 Farid H Detecting Hidden Messages Using Higher order Statistical Models In.

Proc of the IEEE International Conference on Image Processing vol 2 pp 905. 10 Fridrich J Feature Based Steganalysis for JPEG Images and its Implications for. Future Design of Steganographic Schemes In Moskowitz I S ed Information. Hiding 2004 LNCS vol 2137 pp 67 81 Springer Heidelberg 2005. 11 Avcibas I Memon N Sankur B Steganalysis Using Image Quality Metrics. IEEE Transactions on Image Processing 12 2 221 229 2003. 12 Wang Y Moulin P Optimized Feature Extraction for Learning Based Image. Steganalysis IEEE Transactions on Information Forensics and Security 2 1 2007. 13 Schaefer G Stich M UCID An Uncompressed Colour Image Database In. Proc SPIE Storage and Retrieval Methods and Applications for Multimedia San. Jose USA pp 472 480 2004, 14 UCID Uncompressed Colour Image Database visited on 02 08 08. http vision cs aston ac uk datasets UCID ucid html. 15 Steganography Software F5 visited on 02 08 08,http wwwrn inf tu dresden de westfeld f5 html. 16 Westfeld A F5 A Steganographic Algorithm High capacity despite better ste. ganalysis In Moskowitz I S ed 4th International Workshop Information Hiding. LNCS pp 289 302 Springer Heidelberg April 2001, 17 Model Based JPEG Steganography Demo visited on 02 08 08. http www philsallee com mbsteg index html, 18 Sallee P Model Based Steganography In International Workshop on Digital Wa. termarking Seoul Korea pp 174 188 October 2003, 19 Duda R O Hart P E Stork D G Pattern Classi cation 2nd edn John Wiley.

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