2 This research work takes place in the field of information hiding, considerably developed
3 these last two decades. The proposed method for
4 steganography considers digital images as covers.
5 It belongs to the well-known large category
6 of spatial least significant bits (LSBs) replacement schemes.
7 Let us recall that, in this LSBR category, a subset of all the LSBs of the cover image is modified
8 with a secret bit stream depending on: a secret key, the cover, and the message to embed.
9 In this well studied steganographic approach,
10 pixels with even values (resp. odd values) 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 known steganalysis methods~\cite{DBLP:journals/tsp/DumitrescuWW03,DBLP:conf/mmsec/FridrichGD01,Dumitrescu:2005:LSB:1073170.1073176}.
16 Let us recall too that this drawback
17 can be corrected considering the LSB matching (LSBM) subcategory, in which
18 the $+1$ or $-1$ is randomly added to the cover pixel LSB value
19 only if this one does not correspond to the secret bit.
21 Since it is possible to make that probabilities of increasing or decreasing the pixel value, for instance by considering well encrypted hidden messages, usual statistical approaches
22 cannot be applied here to discover stego-contents in LSBM.
23 The most accurate detectors for this matching are universal steganalysers such as~\cite{LHS08,DBLP:conf/ih/2005,FK12},
24 which classify images according to extracted features from neighboring elements of residual noise.
27 Finally, LSB matching revisited (LSBMR) has been recently introduced in~\cite{Mielikainen06}.
28 It works as follows: for a given pair of pixels, the LSB
29 of the first pixel carries a first bit of the secret message, while the parity relationship
30 (odd/even combination) of the two pixel values carries
31 a second bit of the message.
32 By doing so, the modification
33 rate of pixels can decrease from 0.5 to 0.375 bits/pixel
34 (bpp) in the case of a maximum embedding rate, meaning fewer
35 changes in the cover image at the same payload compared to both
36 LSBR and LSBM. It is also shown in~\cite{Mielikainen06} that such a new
37 scheme can avoid the LSB replacement style asymmetry, and
38 thus it should make the detection slightly more difficult than in the
39 LSBM approach. % based on our experiments
45 Instead of (efficiently) modifying LSBs, there is also a need to select pixels whose value
46 modification minimizes a distortion function.
47 This distortion may be computed thanks to feature vectors that are embedded for instance in steganalysers
49 Highly Undetectable steGO (HUGO) method~\cite{DBLP:conf/ih/PevnyFB10} is one of the most efficient instance of such a scheme.
50 It takes into account so-called SPAM features
51 %(whose size is larger than $10^7$)
52 to avoid overfitting a particular
53 steganalyser. Thus a distortion measure for each pixel is individually determined as the sum of the differences between
54 the features of the SPAM computed from the cover and from the stego images.
55 Thanks to this features set, HUGO allows to embed $7\times$ longer messages with the same level of
56 indetectability than LSB matching.
57 However, this improvement is time consuming, mainly due to the distortion function
61 There remains a large place between random selection of LSB and feature based modification of pixel values.
62 We argue that modifying edge pixels is an acceptable compromise.
63 Edges form the outline of an object: they are the boundaries between overlapping objects or between an object
64 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
65 attempting to be undetectable. Indeed,
66 in a cover image, edges already break the continuity of pixels' intensity map and thus already present large variations with their neighboring
67 pixels. In other words, minor changes in regular areas are more dramatic than larger modifications in edge ones.
68 Our first proposal is thus to embed message bits into edge shapes while preserving other smooth regions.
70 Edge based steganographic schemes have already been studied, the most interesting
71 approaches being detailed in~\cite{Luo:2010:EAI:1824719.1824720} and \cite{DBLP:journals/eswa/ChenCL10}.
72 In the former, the authors show how to select sharper edge regions with respect
73 to a given embedding rate: the larger the number of bits to be embedded, the coarser
75 Then the data hiding algorithm is achieved by applying LSBMR on pixels of these regions.
76 The authors show that their proposed method is more efficient than all the LSB, LSBM, and LSBMR approaches
77 thanks to extensive experiments.
78 However, it has been shown that the distinguishing error with LSB embedding is lower than
79 the one with some binary embedding~\cite{DBLP:journals/tifs/FillerJF11}.
80 We thus propose to take benefit of these optimized embedding, provided they are not too time consuming.
81 In the latter, an hybrid edge detector is presented followed by an ad hoc
83 The Edge detection is computed by combining fuzzy logic~\cite{Tyan1993}
84 and Canny~\cite{Canny:1986:CAE:11274.11275} approaches. The goal of this combination
85 is to enlarge the set of modified bits to increase the payload of the data hiding scheme.
88 One can notice that all the previously referenced
89 schemes~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10}
90 produce stego contents
91 by only considering the payload, not the type of image signal: the higher the payload is,
92 the better the approach is said to be.
93 Contrarily, we argue that some images should not be taken as a cover because of the nature of their signal.
94 Consider for instance a uniformly black image: a very tiny modification of its pixels can be easily detectable.
95 The approach we propose is thus to provide a self adaptive algorithm with a high payload, which depends on the
98 Additionally, in the steganographic context, the data hiding procedure is often required
99 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.
100 Finally, even if the steganalysis discipline
101 has done great leaps forward these last years, it is currently impossible to prove rigorously
102 that a given hidden message cannot be recovered by an attacker.
103 This is why we add to our scheme a reasonable
104 message encryption stage, to be certain that,
105 even in the worst case scenario, the attacker
106 will not be able to obtain the message content.
107 Doing so makes our steganographic protocol, to a certain extend, an asymmetric one.
109 To sum up, in this research work, well studied and experimented
110 techniques of signal processing (adaptive edges detection),
111 coding theory (syndrome-treillis codes), and cryptography
112 (Blum-Goldwasser encryption protocol) are combined
113 to compute an efficient steganographic
114 scheme, whose principal characteristic is to take into
115 consideration the cover image and to be compatible with small computation resources.
117 The remainder of this document is organized as follows.
118 Section~\ref{sec:ourapproach} presents the details of the proposed steganographic scheme.
119 Section~\ref{sec:experiments} shows experiments on image quality, steganalytic evaluation, complexity of our approach,
120 and compares it to the state of the art steganographic schemes.
121 Finally, concluding notes and future work are given in Section~\ref{sec:concl}.
