Cryptography and steganography are used to protect and secure information. Encryption algorithms protect secret data by converting it into unreadable data; however, such unreadable and incomprehensible data are likely to draw the attention of criminals. Steganography can conceal data in carriers without changing the original data. Common carriers include videos, audios, texts, and images. Compared with other carriers, digital images have considerable amount of redundant space. Therefore, digital images are commonly used for steganography and are called cover images (before embedding secret messages); similarly, images with embedded messages are called stego images. Steganography techniques can be categorized into spatial and frequency domains. In terms of image quality, the embedding capacity in the spatial domain is higher than that in the frequency domain. Therefore, the spatial domain is suitable for a large number of embedded messages. In the spatial domain, the least significant bit (LSB) substitution steganography [1], proposed in 1996, is the most popular steganography technique. Here, the LSB bit of a pixel value is directly substituted by secret bitstreams. However, LSB substitution steganography can be detected using regular-singular (RS) analysis [2].
Pixel-value differencing (PVD) steganography [3] was developed based on the edge areas in an image; it can conceal more secret messages compared to those in smooth areas. Based on this principle, PVD steganography determines the amount of messages to be embedded depending on the value of the difference between adjacent pixels. Although this method provides a high embedding capacity and invisibility, it creates a step-like shape in the pixel difference histogram (PDH), and embedded messages may be detected. A modified PVD (MPVD) steganography was proposed by Zhang et al. [4], which dynamically generates the PVD interval range to improve security.
In recent years, many scholars have proposed PVD-based methods and have verified their safety via RS analysis. For instance, a hybrid method was proposed [5] using LSB steganography in smooth areas and PVD steganography in edge areas. In other studies [6,7,8,9,10,11,12,13,14,15], the combination of PVD and LSB techniques has been proposed to obtain a large embedding capacity. In addition, other hybrid methods have been proposed to offer a high embedding capacity, such as PVD combined with the side-match method [16] or exploiting modification directions [17, 18].
Because PVD steganography does not make full use of edge areas, a tri-way PVD (TPVD) steganography was proposed by Chang et al. [19], which utilizes three different directional edges to improve the embedding capacity. To achieve a higher embedding capacity, many studies [20,21,22,23,24,25] used PVD with LSB techniques in multi-directional edges. Afterward, to provide a good image quality, a PVD steganography technique using the modulus function (MFPVD) was proposed by Wang et al. [26]. This method utilizes the concept of congruence modulo to adjust the remainder of two consecutive pixels and match the message value. Many scholars have utilized this concept to formulate related studies [27,28,29,30,31,32,33,34].
With the popularity of steganography, a field of steganalysis was generated that is aimed at detecting the presence of embedding data in a stego image. Recently, most studies on steganalysis have mainly used machine learning and deep learning methods [35,36,37,38,39]. Many steganalysis techniques with multidimensional features have been proposed to improve the performance of detection; however, these techniques utilize multiple complex processes and computational resources. In addition, steganalysis schemes can be classified into universal or specific. The universal steganalysis scheme is designed to detect embedding messages regardless of the steganography technique used, such as deep learning methods. In contrast, specific steganalysis scheme aims to detect known steganography.
The steganalysis of the original PVD steganography [3] was first proposed by Zhang et al. [4], which made the step effects of the PDH and detected embedding messages. In 2019, Zhang et al. [40] proposed PVD noise steganalysis with weighted stego image (WS) steganalysis to detect the embedding capacity of the original PVD steganography, but the original steganography parameters need to be obtained. MPVD steganography [4] overcomes the step effects of the original PVD steganography, but it was detected through a one-more-time embedding [41,42,43] and revealed the features of the difference between before and after embedding messages.
In addition, the steganalysis of TPVD steganography was proposed by Zaker et al. [44], which utilized the vulnerability from the PDH of stego images under TPVD steganography. Subsequently, because the embedding process of MFPVD steganography [26] generates fluctuations and growing abnormalities, the asymmetry on the PDH is created. The steganalysis of MFPVD [26] was proposed by Joo et al. [45], which utilizes these features to detect the embedding messages.
The above PVD-based studies are extensions of the traditional PVD steganography techniques [3]. These techniques have only verified their security against RS analysis. However, RS analysis is aimed at the feature of the LSB substitution method [2], which is relatively less significant for PVD steganography [3]. In addition, the PDH method [4] and WS technique [40] are commonly used to detect the original PVD steganography [3]. In existing studies, the PDH method has been commonly used for PVD-based steganalysis; however, its effectiveness is limited in low embedding ratios.
Therefore, we propose a statistical feature-based method for steganalysis of the original PVD steganography [3]. Compared with the state-of-the-art steganalysis [40], the proposed method is more accurate and precise at low embedding ratios and can be performed without obtaining the original embedding parameters.
This article is organized as follows: Sect. 2 describes the related techniques. Section 3 details our proposed steganalysis of the original PVD steganography. Section 4 presents the experimental results and discussion. Finally, Sect. 5 shows the conclusions.