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