A high quality steganographic method with pixel-value differencing and modulus function

https://doi.org/10.1016/j.jss.2007.01.049Get rights and content

Abstract

In this paper, we shall propose a new image steganographic technique capable of producing a secret-embedded image that is totally indistinguishable from the original image by the human eye. In addition, our new method avoids the falling-off-boundary problem by using pixel-value differencing and the modulus function. First, we derive a difference value from two consecutive pixels by utilizing the pixel-value differencing technique (PVD). The hiding capacity of the two consecutive pixels depends on the difference value. In other words, the smoother area is, the less secret data can be hidden; on the contrary, the more edges an area has, the more secret data can be embedded. This way, the stego-image quality degradation is more imperceptible to the human eye. Second, the remainder of the two consecutive pixels can be computed by using the modulus operation, and then secret data can be embedded into the two pixels by modifying their remainder. In our scheme, there is an optimal approach to alter the remainder so as to greatly reduce the image distortion caused by the hiding of the secret data. The values of the two consecutive pixels are scarcely changed after the embedding of the secret message by the proposed optimal alteration algorithm. Experimental results have also demonstrated that the proposed scheme is secure against the RS detection attack.

Introduction

In recent years, enormous research efforts have been invested in the development of digital image steganographic techniques. The major goal of steganography is to enhance communication security by inserting secret message into the digital image, modifying the nonessential pixels of the image (Feng et al., 2006, Petitcolas et al., 1999). The image after the embedding of the secret message, so-called stego-image, is then sent to the receiver through a public channel.

In the transmission process, the public channel may be intentionally monitored by some opponent who tries to prevent the message from being successfully sent and received. The opponent may randomly attack the stego-image if he/she doubts the stego-image carries any secret message because the appearance of the stego-image shows obvious artifacts of hiding effect (Liao et al., 2007, Simmons, 1984). For this reason, an ideal steganography scheme, to keep the stego-image from drawing attention from the opponent, should maintain an imperceptible stego-image quality. That is to say, if there are more similarities between the cover image and the stego-image, it will be harder for an attacker to find out that the stego-image has important secret data hidden inside it (Wu and Hwang, 2007). This way, the secret data is more likely to travel from the sender to the receiver safe and sound.

For the past decade, many steganographic techniques for still images have been presented. A simple and well-known approach is directly hiding secret data into the least-significant bit (LSB) of each pixel in an image. Then, based on the LSB technique, a genetic algorithm of optimal LSB substitution is now also available to improve the stego-image quality of the simple LSB method (Wang et al., 2001). In addition, Chang et al. (2003) have also presented a fast and efficient optimal LSB method based on the dynamic programming strategy that improves the computation time of Wang et al.’s scheme (Wang et al., 2001). A novel simple LSB technique based on optimal pixel adjustment was presented to achieve the goal of improving the stego-image quality (Chan and Cheng, 2004). Besides, Thien and Lin also presented a simple LSB scheme based on the modulus function to improve the stego-image quality (Thien and Lin, 2003). In order to gain a higher payload than when the 4-LSBs method is used, Wang has proposed two new schemes based on the modulo operator (Wang, 2005). Wu et al. have also presented a combination scheme on the basis of pixel-value differencing and LSB replacement with a view to improving the hiding capacity while maintaining acceptable stego-image quality (Wu et al., 2005). In order to enhance the security, on the other hand, Lin and Tsai have proposed a new approach that integrates the concept of secret image sharing and steganographic techniques with the additional capability of image authentication (Lin and Tsai, 2004). Lou and Liu (2002) proposed a LSB-based steganographic method that can resist the common-cover-carrier attack by embedding variable-size secret data and redundant Gaussion noise.

There are many steganographic schemes have also been proposed for binary images. For example, Tseng et al. (2002) designed a binary matrix and an integer weight matrix so as to increase the payload of each sub-image. It can hide ⌊log2(m × n + 1)⌋ into a sub-image with m × n pixels by manipulating at most two bits of the original content. In addition, Tseng and Pan (2002) further proposed a high quality data hiding scheme based on (Tseng et al., 2002) that searches for the more undetectable pixels of the cover image as targets of modification. Wu and Liu (2004) used the shuffling method to equalize the uneven embedding capacity of each image block for the purpose of providing a greater hiding capacity and higher security. The hidden message of their scheme can be used to serve various purposes such as authentication, annotation, and verification. In addition, aside from regular digital images, some other multimedia forms such as 3D models and PDF texts can also serve as the cover media. The first steganographic method built on point-sampled geometry has been presented by Wang and Wang (2006), and the first steganographic system that works on PDF English texts has been created by Zhong et al. (2007). Recently, various kinds of steganalysis detectors have been under steady development, and some have been presented in an attempt to help detect the existence of messages hidden in images in place of visual inspection. For example, the well-known RS steganalytic algorithm by Fridrich et al. (2001) is able to detect the existence of LSB steganography. Basically, the detection capability of the RS steganalytic algorithm depends on the capacity of the hidden message. Specifically, the algorithm can detect the existence of the LSB scheme with high precision when the hidden capacity is more than 0.005 bits per pixel. However, when the hidden capacity is less than 0.005 bits per pixel, the RS steganalytic algorithm is completely ineffective (Fridrich et al., 2001, Ker, 2004).

The LSB-based methods mentioned above, directly embed the secret data into the spatial domain in an unreasonable way without taking into consideration the difference in hiding capacity between edge and smooth areas. In general, the alteration tolerance of an edge area is higher than that of a smooth area. That is to say, an edge area can conceal more secret data than a smooth area. With this concept in mind, Wu and Tsai presented steganographic scheme that offers high imperceptibility to the stego-image by selecting two consecutive pixels as the object of embedding. The payload of Wu and Tsai’s scheme is determined by the difference value between the pixels (Wu and Tsai, 2003). In Wu and Tsai’s method, they determine whether the two consecutive pixels belong to an edge or smooth area by checking out the difference value between the two consecutive pixels. If the difference value is large, that means the two pixels are located in an edge areas, and more secret data can be hidden here. On the contrary, if the difference value is small, that means the two pixels are located in a smooth area, and less secret data can be embedded. Therefore, their scheme produces stego-images that are more similar to the original images than those produced by LSB substitution schemes, which directly embed secret data into the cover image without considering the differences between adjacent pixels. Furthermore, Chang and Tseng have proposed a new method based on side match where the users can consult more than two neighboring pixels to determine the payload of each pixel (Chang and Tseng, 2004).

In this paper, in order to provide a better stego-image quality than Wu and Tsai’s scheme (Wu and Tsai, 2003), we shall propose a novel technique based on pixel-value difference and modulus function. In Wu and Tsai’s scheme, which is also known as the PVD method, the difference value between two consecutive pixels is regarded as a feature for recording the secret message. When the original difference value is unequal to the secret message, the two consecutive pixels will be directly adjusted so that their difference value can stand for the secret data. However, considerable stego-image distortion can happen when the PVD method adjusts the two consecutive pixels to hide the secret data in the difference value. To make a difference, with our new method, we shall improve the stego-image quality by adjusting the remainder of the two consecutive pixels instead of the difference value. Besides that, the falling-off-boundary problem may probably worsen the situation when the PVD method alone is used, especially either when the two consecutive pixels are located in an extreme edge or smooth area, or when the values of the two consecutive pixels form a contrast. To overcome the falling-off-boundary problem, our new method re-revises the remainder of the two consecutive pixels.

The rest of this paper is organized as follows. We will briefly review Wu and Tsai’s scheme in Section 2. In Section 3, the embedding and extracting algorithms of the proposed method based on the modulus operation will be presented respectively. The experimental results and analyzes will be in Section 4, followed by some concluding remarks in Section 5.

Section snippets

Review of Wu and Tsai’s scheme

Let us begin with the background on which the embedding algorithm of method (Wu and Tsai, 2003) is build up. Given a cover image F sized M × N. Fi is a sub-block of F that has two consecutive pixels broken down by partitioning F in raster scan order such that F=Fi|i=1,2,,M×N2. By definition each Fi has two elements P(i,L) and P(i,R). The pixel values of P(i,L) and P(i,R) are P(i,x) and P(i,y), respectively. The difference value di of P(i,x) and P(i,y) can be derived by Eq. (1).di=|P(i,x)-P(i,y)|.

The proposed method

Instead of the difference value, the proposed scheme modifies the remainder of two consecutive pixels P(i,x) and P(i,y) for better stego-image quality. The proposed embedding and extracting algorithms are presented in the subsections below.

Experimental results

In this section, we shall present our experimental results to demonstrate the proposed algorithm can perform better than Wu and Tsai’s scheme. We designed a range table R consisting of 6 sub-ranges Rj, for j = 1, 2,  , 6, where their widths were 8, 8, 16, 32, 64, and 128 respectively. The range of each Rj was R1 = [0, 7], R2 = [8, 15], R3 = [16, 31], R4 = [32, 63], R5 = [64, 127] and R6 = [128, 255]. Twelve cover images “Lena”, “Baboon”, “Peppers”, “Jet”, “Tank”, “Airplane”, “Truck”, “Elaine”, “Couple”, “Boat”,

Conclusions

In this paper, we propose a novel scheme to greatly reduce the visibility of the hiding effect present in the PVD method. The proposed scheme utilizes the remainder of the two consecutive pixels to record the information of the secret data which gains more flexibility, capable of deriving the optimal remainder of the two pixels at the least distortion. The hiding effect that appears in the stego-image when Wu and Tsai’s scheme is used to hide the secret data can be significantly decreased by

Acknowledgements

We thank many anonymous referees for their suggestions to improve this paper. This work is supported in part by National Science Council and Taiwan Information Security Center at NCTU, Taiwan, ROC.

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