Steganography Based on Adaptive Pixel-Value Differencing Scheme Revisited

Abstract

The adaptive pixel-value differencing (APVD) based steganography proposed by Luo et al. is a state-of-the-art steganographic approach in spatial domain. It can resist blind steganalysis but is vulnerable to the targeted attack proposed by Tan et al. In this paper, we introduce an improved version of APVD. Like APVD, we also first divide an image into some non-overlapping squares and then rotate each of them by a random degree of 0, 90, 180 or 270. For an embedding unit constructed with three consecutive pixels of the resulting image, we randomly select one pixel of it for data embedding. Furthermore, the local statistical features are well preserved by exploiting neighborhood information of pixels. The experimental results evaluated on a large image database reveal that our method makes a significant improvement against the APVD-specific steganalytic attack, and has an impressive performance on resisting blind steganalysis compared with previous PVD-based steganographic methods.

Appendix

The appendix will show how to derive the range of the modified pixel in an embedding unit so that the secret message can be embedded and extracted properly.

Without loss of generality, consider Case 3.2 of Step 3 in data embedding. That is to say, given the condition that |d ₁| > T, |d ₂| > T, p _i+3 ≤ p _i+1, p _i+3 < p _i+2, so p _i+3 is supposed to be modified according to the embedding algorithm and denote the modified p _i+3 as $p_{i + 3}^{'}$. The goal is to derive the range of $p_{i + 3}^{'}$, a new pixel value of which is able to preserve the inequations as follows:

$$ \left| {d_{1} } \right| = \left| {p_{i + 2} - p_{i + 1} } \right| > T $$

$$ \left| {d_{2} } \right| = \left| {p_{i + 3} - p_{i + 2} } \right| = p_{i + 2} - p_{i + 3} > T $$

$$ p_{i + 3} \le p_{i + 1} $$

$$ p_{i + 3} < p_{i + 2} $$

Consequently, the range of $p_{i + 3}^{'}$, denoted by $range_{{p_{i + 3}^{'} }}$, can be finally derived as

$$ range_{{p_{i + 3}^{'} }} = [0,1, \ldots , { \hbox{min} }(p_{i + 1} , p_{i + 2} - T - 1)]. $$

Notice that the range of the modified pixel depends on at least one of the two others which keep their own pixel values unchanged. When the same embedding unit is dealt with during data extraction, the receiver will depend on those inequations which can reappear to ensure the secret message extracted properly.

Other cases of Step 3 in data embedding can be considered in a similar way.