A more secure steganography based on adaptive pixel-value differencing scheme

Abstract

Pixel-value differencing (PVD) based steganography is one of popular approaches for secret data hiding in the spatial domain. However, based on extensive experiments, we find that some statistical artifacts will be inevitably introduced even with a low embedding capacity in most existing PVD-based algorithms. In this paper, we first analyze the common limitations of the original PVD and its modified versions, and then propose a more secure steganography based on a content adaptive scheme. In our method, a cover image is first partitioned into small squares. Each square is then rotated by a random degree of 0, 90, 180 or 270. The resulting image is then divided into non-overlapping embedding units with three consecutive pixels, and the middle one is used for data embedding. The number of embedded bits is dependent on the differences among the three pixels. To preserve the local statistical features, the sort order of the three pixel values will remain the same after data hiding. Furthermore, the new method can first use sharper edge regions for data hiding adaptively, while preserving other smoother regions by adjusting a parameter. The experimental results evaluated on a large image database show that our method achieves much better security compared with the previous PVD-based methods.

Appendix

Figure 8 illustrates the four different cases according to the pixel values g _i , g _i + 1, g _i + 2 within an embedding unit and a given threshold T. Note that g _i and g _i + 2 are fixed before and after data embedding. In this appendix, we want to show you how to determine the range of the centre pixel values $range_{g_{i+1}'}$ so that the sort order of the three consecutive pixel values and the relationships between the pixel values and T are well preserved after data embedding.

Fig. 8

Four different cases according to the values of g _i ,g _i + 1,g _i + 2

Without loss of generality, case 1.1 is considered. Other cases can be analyzed in a similar way. In case 1.1,we have the following inequations:

$$ g_{i+1}<g_i, g_{i+1}<g_{i+2}, \big|d_1\big|>T, \big|d_2\big|>T $$

Then we obtain

$$ \big|d_1\big|=\big|g_i-g_{i+1}\big|=g_i-g_{i+1}>T, \big|d_2\big|=\big|g_{i+1}-g_{i+2}\big|=g_{i+2}-g_{i+1}>T $$

Namely

$$ g_{i+1}<g_i-T, g_{i+1}<g_{i+2}-T $$

Since g _i + 1 is an integer and belongs to [0,...,255], we can obtain

$$ g_{i+1}\in \big[0, \ldots ,min\big(g_i-T-1,g_{i+2}-T-1\big)\big] $$

Therefore, if we limit the centre pixel value changing in the following range when doing data embedding

$$range_{g_{i+1}'}=[0, \ldots ,min(g_i-T-1,g_{i+2}-T-1)]$$

All the inequations in case 1.1 will hold. And this is very important to preserve some local structure features in the cover image. However, most existing PVD-based approaches will inevitably destroy such relationships and thus make it easy to detect based on the extensive experiments.

Moreover, it can be seen that the range is constrained by a threshold T. Usually, the larger the threshold T is, the narrower the range is, and thus the fewer secret bits can be embedded using our proposed method. In practice, we can change the threshold T to adjust the embedding capacity. For the short secret message, we can just use those pixels on the sharper edges (larger than T) within an image for data hiding, while keep other smooth regions (smaller than or equal to T) unchanged. If there is not enough space for the given secret message, we will decrease the threshold T to enlarge the embedding space. In such a way, our method is more adaptive with image contents. Based on our experiments and analysis, both the visual imperceptivity and security will become much better.

Please note that since all the inequations are preserved after data embedding, we can reappear the same range in the stego image, which guarantees the validity of data extraction.