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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 A Generalization of the PVD Steganographic Method M.B. Ould MEDENI and El Mamoun SOUIDI Laboratory of Mathematic Informatics and Applications University Mohammed V-Agdal, Faculty of Sciences Rabat ,BP 1014, Morocco Email : sbaimedeni@yahoo.fr, souidi@fsr.ac.ma Abstract—In this work we propose a novel Steganographic equal amount of changes without causing noticeable distortion. method for hiding information within the spatial domain of the Hence, to improve the quality of stego images, several adaptive gray scale image. The proposed approach works by dividing the methods have been proposed in which the amount of bits to cover into blocks of equal sizes and then embeds the message in the edge of the block depending on the number of ones in left be embedded in each pixel is variable. Wu and Tsai proposed four bits of the pixel. The purpose of this work is to generalize a novel steganographic method that uses the difference value the PVD method [7] With four-pixel differencing instead of two- between two neighboring pixels to determine how many secret pixel differencing and use the LSB Substitution to hide the secret bits should be embedded [7]. message in the cover image In contrary : Steganalysis methods attempt to detect Stego- Keywords: Steganography, Watermarking, Least Signiﬁ- image and extract it. Inserting secret bits in image changes cant Bit(LSB), PVD method, Digital Images, Information some statistics of image, this opens some roads to detect Stego- Hiding,Pixel-value differencing. image. So the changes made by Steganographic are a key performance metric ; lower change : more robust algorithm. I. I NTRODUCTION It is evident that the changes in cover image are related to the Steganography is the art of stealth communication. Its pur- volume of inserted bit, so Stego-images with higher insertion pose is to make communication undetectable. The steganogra- rate are detected more easily. phy problem is also known as the prisoners’ dilemma formu- Stegananalysis methods generally are divided in two main lated by Simmons [4]. Alice and Bob are imprisoned and want groups: active and passive methods. In passive methods only to hatch an escape plan. They are allowed to communicate via presence or absence of hidden data is considered, while in a channel monitored by a warden. If the warden ﬁnds out that active methods a inserted data is extracted [8]. Furthermore, they are communicating secretly, he throws them into solitary different steganalysis methods, depending on steganography conﬁnement. Thus, the prisoners need to design a method to algorithms they target, can be classiﬁed in two groups : Model- exchange messages without raising the warden’s suspicion. based (Speciﬁc) and Universal Steganalysis. The prisoners hide their messages in innocuous-looking cover The aim of this work is to generalize the PVD method [7] With objects by slightly modifying them (obtaining stego objects). four-pixel differencing instead of two-pixel differencing and The embedding process is usually driven by a stego key, which LSB Substitution. The remainder of the paper is organized as is a secret shared between Alice and Bob. It is typically used follows. Section 2 gives a brief introduction to Steganography to select a subset of the cover object and the order in which the and Data Hiding Methods.We construct our approach and cover object elements are visited during embedding. The most report on experimental results in section 3 and 4. Section 5 important property of any steganographic communication is gives a conclusion. statistical undetectability. In other words, the warden should II. D IGITAL I MAGES IN S TEGANOGRAPHY not be able to distinguish between cover and stego objects. Formal description of this requirement in information-theoretic A. Digital Images terms was given by Cachin [5]. If the communication channel A digital image at the most abstract level is a two- that Alice and Bob use is distortion-free, we speak about the dimensional array of colored pixels or dots. When these pixels passive warden scenario. are displayed on a high-resolution monitor and viewed at The most common and well-known steganographic method is an appropriate distance, they appear to be a continuously called least signiﬁcant bit (LSB) substitution, which embeds colored image. Each pixel is a certain color which is typically secret data by replacing k LSBs of a pixel with k secret bits di- deﬁned, using the redgreen- blue (RGB) color model, as rectly [1]. Many optimized LSB methods have been proposed a combination of varying amounts of red, green, and blue to improve this work [2], [3]. The human perceptibility has light. A color image is therefore said to contain three bands, a property that it is sensitive to some changes in the pixels each of which represents the amount of red, green, or blue of the smooth areas, while it is not sensitive to changes in light in the image. Whereas a color image contains color the edge areas. Not all pixels in a cover image can tolerate and intensity information, a gray-scale image is composed of 156 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 pixels that vary only in intensity, not color. Gray-scale images The difference is that steganography conceals a message therefore have only a single band. Without loss of generality, so that this hidden message is the object of the communi- the remaining discussion will focus on gray-scale images. The cation where in watermarking; the hidden message provides discussion is easily extended to cover color images by noting important information about the cover media, such as au- that a color image is the composition of three individual gray- thentication or copyright. Steganography, in the simplest case, scale images representing the red, green and blue bands. The capitalizes on this overabundance of information by replacing typical gray-scale image has an 8-bit depth which is sufﬁcient the noise channels (i.e. the least signiﬁcant bit channels) to represent 256 unique intensity values ranging from black with an arbitrary secret message. Figure 1 gives an overview to white [9]. A brief review of binary representation will be of a steganographic process ﬂow. A source image, hereafter instructive when interpreting bit-level pixel data in the context referred to as a cover, is viewed as 8 information carrying of a digital image. An 8-bit binary numeral has the general channels. A secret message is spread over the least signiﬁcant form channels (in this case the three least signiﬁcant channels) A7 27 + A6 26 + ... + A1 21 + A0 20 with the modiﬁed channels re-combined to obtain an output, hereafter referred to as the stego image, that visually resembles where An represents a single binary digit. In a digital image the cover image and contains the injected message. it is clear that A7 is the most signiﬁcant bit and indicates whether the pixel value is greater than 127. A common means III. PVD M ETHOD FOR G RAY-L EVEL I MAGE of converting a grayscale image to a binary (i.e. black-and- The pixel-value differencing (PVD) method [7] segments white) image is to extract the A7 bit from each pixel. By the cover image into nonoverlapping blocks containing two contrast, A0 embodies relatively little information and, in the connecting pixels and modiﬁes the pixel difference in each context of a digital image, can generally be understood as a block (pair) for data embedding. A larger difference in the noise channel. original pixel values allows a greater modiﬁcation. The hiding algorithm is described as follows: B. Overview of Steganograhy 1) Calculate the difference value di for each block of two Steganography hides secret messages under the cover of consecutive pixels Pi and Pi+1 , di = Pi+1 − Pi a carrier signal so it cannot be seen or detected [6], [8], 2) Find the optimal Ri of the di such that Ri = min(ui − [11]. Steganography technique should generally possess two k), where ui ≥ k, k = |di | and Ri ∈ [li , ui ] important properties: good visual/statistical imperceptibility 3) Decide t bits of secret data which are hidden with each and a sufﬁcient payload. The ﬁrst is essential for the security di , i.e. each block of two consecutive pixels is deﬁned of hidden communication and the second ensures that a large as t = log2 (wi ) where wi is the width of the Ri quantity of data can be conveyed [10]. Two levels of protection 4) Read t bits binary secret data one by one according to can be done if the message is encrypted before hiding it, so Step 3, and then transform t into decimal value b. For it must be decrypted before reading it. Invisible watermarking instance, assume a binary secret data is 101, then b = 5. is treated as a subset of steganography [10]. 5) Calculate the new difference value di using: di = li + b, for di ≥ 0 or di = −(li + b), for di < 0 6) Pi and Pi+1 are modiﬁed to hide t secret data by the fol- lowing formula: (Pi , Pi+1 ) = (Pi − m , Pi+1 + m ) 2 2 : di ∈ odd or (Pi , Pi+1 ) = (Pi − m , Pi+1 + m ) : 2 2 di ∈ even where m = di − di . Finally, we compute the values of (Pi , Pi+1 ) which represent the secret data. 7) Repeat Steps 1-6, until all secret data are hidden into the cover image and the stego-image is obtained. In the extraction phase, the original range table is necessary. It is used to partition the stego-image by the same method as used to the cover image. The extraction phase is implemented as follows: 1) Calculate the difference value di between each two successive pixels for each block (Pi , Pi+1 ) from the following formula : di = |Pi+1 − Pi | 2) Find the optimum Ri of the di just as in Step 2 in the hiding phase. 3) Obtain b by subtracting li from di . The b value repre- sents the value of the secret data in decimal. Fig. 1. Embedding of a secret message into the three least signiﬁcant channels 4) Convert b into binary then ﬁnd number of bits t from of a cover image the secret data, where t = log2 (wi ) [7] 157 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 IV. P ROPOSED S TEGANOGRAPHY S CHEME V. E XPERIMENTAL RESULTS In this section we discuss the proposed approach for hiding Several experiments are preformed to evaluate our proposed information within the spatial domain of the gray scale image. method. Ten gray-scale images with size 512×512 are used in The proposed approach works by dividing the cover into the experiments as cover images, and three of them are shown blocks of equal sizes (8 × 8). Our proposed method adaptively in Fig. 3. A series of pseudo-random numbers as the secret bit embeds messages using two levels (lower-level and higher- streams are embedded into the cover images. The peak signal level), and the square of median value M is used to partition to noise ratio (PSNR) is utilized to evaluate the quality of the the average difference D into two levels. If D < M , D stego image. For an M ×N gray-scale image, the PSNR value belongs to ”lower-level” (i.e., the block belongs to a smooth is deﬁned as follows: area). Otherwise, D belongs to ”higher-level” (i.e., the block 255 × 255 × M × N P SN R = 10 × log10 M (dB) belongs to an edge area). N 2 i=1 j=1 (Pij − Qij ) A. Determine The Place of Embedding in The Image where Pij and Qij denote the pixel values in row i and column All the pixels in the cover image are 256 gray values. j of the cover image and the stego image, respectively. In this The cover image is partitioned into non-overlapping four-pixel section we present the experimental results of stego-image on blocks. For each block, there are four neighboring pixels pi,j , three will known images: Lena, Pepper, and Baboon images. pi,j+1 , pi+1,j , pi+1,j+1 , and their corresponding gray values These images are shown in Figs 3. The quality of stego-image are y1 , y2 , y3 and y4 , respectively. created by our proposed method are shown in Figs.4. As the ﬁgures show, distortions resulted from embedding are 1) Divide the cover into blocks of equal sizes 8 × 8 imperceptible to human vision. We present also a comparative 2) Calculate the square root of median for each block. M = study of the proposed methods with PVD method. (median) 3) Calculate the average difference value D, which is given 1 3 We have analyzed our results according to PVD method for by D = 3 i=0 (yi+1 − yi ) each of the tested images. We also analyzed our results by 4) IF D ≥ M , then embed Message in pi,j , pi,j+1 , pi+1,j , computing Payload, and peak signal-to noise ratio (PSNR). pi+1,j+1 , (go to The embedding algorithm) B. The embedding algorithm 1) Split each pixel into two equal parts (see Figure 2). 2) Count number of 1 in the most part and embed a secret message in the least part according to the corresponding number of bits in Table 1. Fig. 3. Three cover images with size 512 × 512: (a) Lena (b) Peppers (c) Baboon. Payload: the size of date that could be imbedded within the cover-image is shown in Table 2 Image Image size Data size Data size Fig. 2. Split Process. (PVD) (Proposed Method) Lena 128 × 128 2048 2493 255 × 255 8192 10007 number of 1 in number of Bits 512 × 512 32768 40017 the most part to be embedded 1024 × 1024 131072 160604 4 or 3 3 bits Peppers 128 × 128 2048 2560 2 2 bits 255 × 255 8192 10211 1 or 0 1 512 × 512 32768 40990 1024 × 1024 131072 163724 Baboon 128 × 128 2048 2443 The recipient uses the extraction algorithm in order to 255 × 255 8192 9767 extract the secret message from the stego-image. Extracting 512 × 512 32768 39034 secret message is done in the same way as in the embedded 1024 × 1024 131072 156308 operation, depending on the value of the median: M = (median). If the average difference value D is more than Figure. 4 shows the amount of messages hidden in the 3 the value of M then extract the message depending on the cover images. Three stego images (a) Lena (embedded 40017 rule in Table 1. bits, P SN R = 42.68dB) (b) Peppers (embedded 40990 158 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 bits, P SN R = 43.23dB) (c) Baboon (embedded 39034 bits, P SN R = 37.71dB). Fig. 4. Three stego images : (a) Lena (b) Peppers (c) Baboon. VI. C ONCLUSION In this paper, we have proposed a novel steganographic method based on four-pixel differencing and LSB substitution. Secret data are hidden into each pixel by the k-bit LSB substitution method, where k is decided by the number of 1 in the most part for pixel. Experimental results showed that the proposed method gave best values for the PSNR measure, which means that there is no difference between the original, and the stegano-images. R EFERENCES [1] D.W. Bender, N.M. Gruhl, A. Lu, : Techniques for data hiding, IBM Syst. J. 35 (1996) 313-316 [2] R.Z. Wang, C.F. Lin, J.C. Lin, Image hiding by optimal LSB substitution and genetic algorithm, Pattern Recognit. 34 (3) (2001) 671-683. [3] I.C. Lin, Y.B. Lin, C.M. Wang,: , Hiding data in spatial domain images with distortion tolerance, Comput. Stand. Inter. 31 (2) (2009) 458-464. [4] G. J. Simmons : The prisoners problem and the subliminal channel, in Advances in Cryptology, pp. 5167, Plenum Press, New York, NY, USA, 1984. [5] C. Cachin : An information-theoretic model for steganography, in D. 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