1 This research work takes place in the field of information hiding, considerably developed these 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-known
15 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 fixed by considering the LSB matching (LSBM) subcategory, in which
19 a $+1$ or $-1$ is randomly added to the cover pixel's 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 value 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 Additionally to (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
49 are embedded for instance in the steganalysers
51 The Highly Undetectable steGO (HUGO) method~\cite{DBLP:conf/ih/PevnyFB10},
52 WOW~\cite{conf/wifs/HolubF12}, and UNIWARD~\cite{HFD14}
53 are some of the most efficient instances of such a scheme.
55 HUGO takes into account so-called SPAM features.
56 Thus a distortion measure for each
57 pixel is individually determined as the sum of the differences between
58 the features of the SPAM computed from the cover and from the stego images.
59 The features embedded in WOW and UNIWARD are based on Wavelet-based
60 directional filter. Thus, similarly, the distortion function is
61 the sum of the differences between these wavelet coefficients
62 computed from the cover and from the stego images.
63 Due to this distortion measures, HUGO, WOW and UNIWARD allow
64 to embed messages that are $7$ times longer than the former
65 ones with the same level of
66 indetectability as LSB matching.
67 However, this improvement has a larger computation cost, mainly due to
68 the distortion function
72 There remains a large place between random selection of LSB and feature based modification of pixel values.
73 We argue that modifying edge pixels is an acceptable compromise.
74 Edges form the outline of an object: they are the boundaries between overlapping objects or between an object
75 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
76 attempting to be undetectable. Indeed,
77 in a cover image, edges already break the continuity of pixels' intensity map and thus already present large variations with their neighboring
78 pixels. In other words, minor changes in regular areas are more dramatic than larger modifications in edge ones.
79 Our first proposal is thus to embed message bits into edge shapes while preserving other smooth regions.
81 Edge based steganographic schemes have already been studied,
83 approaches being detailed in~\cite{Luo:2010:EAI:1824719.1824720} and
84 in~\cite{DBLP:journals/eswa/ChenCL10}.
85 In the former, the authors present the Edge Adaptive
86 Image Steganography based on LSB matching revisited further denoted as
87 EAISLSBMR. This approach selects sharper edge
89 to a given embedding rate: the larger the number of bits to be embedded is, the coarser
91 Then the data hiding algorithm is achie\-ved by applying LSBMR on some of the pixels of these regions.
92 The authors show that their proposed method is more efficient than all the LSB, LSBM, and LSBMR approaches
93 through extensive experiments.
94 However, it has been shown that the distinguishing error with LSB embedding is lower than
95 the one with some binary embedding~\cite{DBLP:journals/tifs/FillerJF11}.
96 We thus propose to take advantage of this optimized embedding, provided they are not too time consuming.
97 In the latter, an hybrid edge detector is presented followed by an ad hoc
99 The Edge detection is computed by combining fuz\-zy logic~\cite{Tyan1993}
100 and Canny~\cite{Canny:1986:CAE:11274.11275} approaches.
101 The goal of this combination
102 is to enlarge the set of modified bits to increase the payload of the data hiding scheme.
105 One can notice that all the previously referenced
106 sche\-mes~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10}
107 produce stego contents
108 by only considering the payload, not the type of image signal: the higher the payload is,
109 the better the approach is said to be.
110 For instance, studied payloads range from 0.04 to 0.4 modified bits per pixel.
111 Contrarily, we argue that some images should not be taken
112 as a cover because of the nature of their signals.
113 Consider for instance a uniformly black image: a very tiny modification of its
114 pixels can be easily detected.
115 Practically speaking, if Alice would send
116 a hidden message to Bob, she would never consider
117 such kind of image and a high embedding rate.
118 The approach we propose here is thus to provide a small complexity
119 self adaptive algorithm
120 with an acceptable payload, which
121 depends on the cover signal.
122 The payload is further said to
123 be acceptable if it allows to embed a sufficiently
124 long message in the cover signal.
125 Practically speaking, our approach is efficient enough for
126 payloads close to 0.06 bit per pixel which allows to embed
127 messages of length larger than 15,728 bits in an
128 image of size $512\times 512$ pixels.
130 % Message extraction is achieved by computing the same
131 % edge detection pixels set for the cover and the stego image.
132 % The edge detection algorithm is thus not applied on all the bits of the image,
133 % but to exclude the LSBs which are modified.
135 Finally, even if the steganalysis discipline
136 has known great innovations these last years, it is currently impossible to prove rigorously
137 that a given hidden message cannot be recovered by an attacker.
138 This is why we add to our scheme a reasonable
139 message encryption stage, to be certain that,
140 even in the worst case scenario, the attacker
141 will not be able to obtain the original message content.
142 Doing so makes our steganographic protocol, to a certain extend, an asymmetric one.
144 To sum up, well-studied and experimented
145 techniques of signal processing (adaptive edges detection),
146 coding theory (syndrome-trellis codes), and cryptography
147 (Blum-Goldwas\-ser encryption protocol) are combined in this research work.
148 The objective is to compute an efficient steganographic
149 sche\-me, whose principal characteristic is to take into
150 consideration the cover image and to be compatible with small computation resources.
152 The remainder of this document is organized as follows.
153 Section~\ref{sec:ourapproach} presents the details of the proposed steganographic scheme and applies it on a running example. Among its technical description,
154 its adaptive aspect is emphasized.
155 Section~\ref{sub:complexity} presents the overall complexity of our approach
156 and compares it to HUGO, WOW, and UNIWARD.
157 Section~\ref{sec:experiments} shows experiments on image quality, steganalysis evaluation, and compares them to the state of the art steganographic schemes.
158 Finally, concluding notes and future work are given in Section~\ref{sec:concl}.
