1 This research work takes place in the field of information hiding, considerably developed for the last two decades. The proposed method for
2 steganography considers digital images as covers.
3 It belongs to the well-known large category
4 of spatial least significant bits (LSBs) replacement schemes.
5 Let us recall that, in this LSB replacement category, a subset of all the LSBs of the cover image is modified
6 with a secret bit stream depending on: a secret key, the cover, and the message to embed.
7 In this well-studied steganographic approach,
8 if we consider that a LSB is the last bit of each pixel value,
9 pixels with an even value (resp. an odd value)
10 are never decreased (resp. increased),
11 thus such schemes may break the
12 structural symmetry of the host images.
13 And these structural alterations can be detected by
14 well-designed statistical investigations, leading to well
15 known steganalysis methods~\cite{DBLP:journals/tsp/DumitrescuWW03,DBLP:conf/mmsec/FridrichGD01,Dumitrescu:2005:LSB:1073170.1073176}.
17 Let us recall too that this drawback
18 can be corrected considering the LSB matching (LSBM) subcategory, in which
19 the $+1$ or $-1$ is randomly added to the cover pixel LSB value
20 only if this one does not correspond to the secret bit.
22 By considering well-encrypted hidden messages, the probabilities of increasing or decreasing the alue of pixels are equal. Then usual statistical approaches
23 cannot be applied here to discover stego-contents in LSBM.
24 The most accurate detectors for this matching are universal steganalysers such as~\cite{LHS08,DBLP:conf/ih/Ker05,FK12},
25 which classify images according to extracted features from neighboring elements of residual noise.
28 Finally, LSB matching revisited (LSBMR) has recently been introduced in~\cite{Mielikainen06}.
29 It works as follows: for a given pair of pixels, the LSB
30 of the first pixel carries a first bit of the secret message, while the parity relationship
31 (odd/even combination) of the two pixel values carries
32 a second bit of the message.
33 By doing so, the modification
34 rate of pixels can decrease from 0.5 to 0.375 bits/pixel
35 (bpp) in the case of a maximum embedding rate, meaning fewer
36 changes in the cover image at the same payload compared to both
37 LSBR and LSBM. It is also shown in~\cite{Mielikainen06} that such a new
38 scheme can avoid the LSB replacement style asymmetry, and
39 thus it should make the detection slightly more difficult than in the
40 LSBM approach. % based on our experiments
46 Instead of (efficiently) modifying LSBs, there is also a need to select pixels whose value
47 modification minimizes a distortion function.
48 This distortion may be computed thanks to feature vectors that are embedded for instance in the steganalysers
50 The Highly Undetectable steGO (HUGO) method~\cite{DBLP:conf/ih/PevnyFB10} is one of the most efficient instance of such a scheme.
51 It takes into account so-called SPAM features
52 %(whose size is larger than $10^7$)
53 to avoid overfitting a particular
54 steganalyser. Thus a distortion measure for each pixel is individually determined as the sum of the differences between
55 the features of the SPAM computed from the cover and from the stego images.
56 Thanks to this features set, HUGO allows to embed messages that are $7\times$ longer than the former ones with the same level of
57 indetectability as LSB matching.
58 However, this improvement is time consuming, mainly due to the distortion function
62 There remains a large place between random selection of LSB and feature based modification of pixel values.
63 We argue that modifying edge pixels is an acceptable compromise.
64 Edges form the outline of an object: they are the boundaries between overlapping objects or between an object
65 and its background. When producing the stego-image, a small modification of some pixel values in such edges should not impact the image quality, which is a requirement when
66 attempting to be undetectable. Indeed,
67 in a cover image, edges already break the continuity of pixels' intensity map and thus already present large variations with their neighboring
68 pixels. In other words, minor changes in regular areas are more dramatic than larger modifications in edge ones.
69 Our first proposal is thus to embed message bits into edge shapes while preserving other smooth regions.
71 Edge based steganographic schemes have already been studied,
73 approaches being detailed in~\cite{Luo:2010:EAI:1824719.1824720} and
74 in~\cite{DBLP:journals/eswa/ChenCL10}.
75 In the former, the authors present the Edge Adaptive
76 Image Steganography based on LSB matching revisited further denoted as
77 EAISLSBMR. This approach selects sharper edge
79 to a given embedding rate: the larger the number of bits to be embedded is, the coarser
81 Then the data hiding algorithm is achieved by applying LSBMR on some of the pixels of these regions.
82 The authors show that their proposed method is more efficient than all the LSB, LSBM, and LSBMR approaches
83 thanks to extensive experiments.
84 However, it has been shown that the distinguishing error with LSB embedding is lower than
85 the one with some binary embedding~\cite{DBLP:journals/tifs/FillerJF11}.
86 We thus propose to take advantage of these optimized embeddings, provided they are not too time consuming.
87 In the latter, an hybrid edge detector is presented followed by an ad hoc
89 The Edge detection is computed by combining fuzzy logic~\cite{Tyan1993}
90 and Canny~\cite{Canny:1986:CAE:11274.11275} approaches.
91 The goal of this combination
92 is to enlarge the set of modified bits to increase the payload of the data hiding scheme.
95 One can notice that all the previously referenced
96 schemes~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10}
97 produce stego contents
98 by only considering the payload, not the type of image signal: the higher the payload is,
99 the better the approach is said to be.
100 Contrarily, we argue that some images should not be taken as a cover because of the nature of their signals.
101 Consider for instance a uniformly black image: a very tiny modification of its pixels can be easily detectable.
102 The approach we propose is thus to provide a self adaptive algorithm with a high payload, which depends on the cover signal.
103 % Message extraction is achieved by computing the same
104 % edge detection pixels set for the cover and the stego image.
105 % The edge detection algorithm is thus not applied on all the bits of the image,
106 % but to exclude the LSBs which are modified.
108 Finally, even if the steganalysis discipline
109 has known great innovations these last years, it is currently impossible to prove rigorously
110 that a given hidden message cannot be recovered by an attacker.
111 This is why we add to our scheme a reasonable
112 message encryption stage, to be certain that,
113 even in the worst case scenario, the attacker
114 will not be able to obtain the original message content.
115 Doing so makes our steganographic protocol, to a certain extend, an asymmetric one.
117 To sum up, in this research work, well-studied and experimented
118 techniques of signal processing (adaptive edges detection),
119 coding theory (syndrome-trellis codes), and cryptography
120 (Blum-Goldwasser encryption protocol) are combined
121 to compute an efficient steganographic
122 scheme, whose principal characteristic is to take into
123 consideration the cover image and to be compatible with small computation resources.
125 The remainder of this document is organized as follows.
126 Section~\ref{sec:ourapproach} presents the details of the proposed steganographic scheme and applies it on a running example. Among its technical description,
127 its adaptive aspect is emphasized.
128 Section~\ref{sub:complexity} presents the overall complexity of our approach
129 and compares it to the HUGO's one.
130 Section~\ref{sec:experiments} shows experiments on image quality, steganalysis evaluation, and compares them to the state of the art steganographic schemes.
131 Finally, concluding notes and future work are given in Section~\ref{sec:concl}.
