Jacques M Bahi
email: jacques.bahi@femto-st.fr

Jean-François Couchot
email: jean-francois.couchot@femto-st.fr

Nicolas Friot
email: nicolas.friot@femto-st.fr

Christophe Guyeux
email: christophe.guyeux@femto-st.fr

Application of Steganography for Anonymity through the Internet

Keywords: Privacy, Internet, Steganography, Security, Chaotic iterations

In this paper, a novel steganographic scheme based on chaotic iterations is proposed. This research work takes place into the information hiding security framework. The applications for anonymity and privacy through the Internet are regarded too. To guarantee such an anonymity, it should be possible to set up a secret communication channel into a web page, being secure. To achieve this goal, we propose an information hiding scheme being stego-secure, which is the highest level of security in a well defined and studied category of attacks called "watermark-only attack". This category of attacks is the best context to study steganographybased anonymity through the Internet. The steganalysis of our steganographic process is also studied in order to show its security in a real test framework.

I. INTRODUCTION

In common opinion or for non specialists, anonymity through the Internet is only desirable for malicious use. A frequent thought is that individuals who search or use anonymity tools have something wrong or shameful to hide. Thus, as privacy and anonymity software as proxy or Tor [START_REF] Www | Tor: Anonymity online -protect your privacy. defend yourself against network surveillance and traffic analysis[END_REF] are only used by terrorists, pedophiles, weapon merchants, and so on, such tools should be forbidden. However, terrorism or pedophilia existed in the absence of the Internet. Furthermore, recent actualities recall to us that, in numerous places around the world, to have an opinion that diverges from the one imposed by political or religious leaders is something considered as negative, suspicious, or illegal. For instance, Saudi blogger Hamza Kashgari jailed, may face execution after tweets about Muhammad. Generally speaking, the so-called Arab Spring, and current fighting and uncertainty in Syria, have taught to us the following facts. First, the Internet is a media of major importance, which is difficult to arrest or to silence, bearing witness to the need for democracy, transparency, and efforts to combat corruption. Second, claiming his/her opinions, making journalism or politics, is dangerous in various states, and can lead to the death penalty (as for numerous Iranian bloggers: Hossein Derakhshan [START_REF] Wikipedia | Hossein derakhshan -wikipedia, the free encyclopedia[END_REF], Vahid Asghari, etc.).

Considering that the freedom of expression is a fundamental right that must be protected, that journalists must be able to inform the community without risking their own lives, and that to be a defender of human rights can be dangerous, various software have emerged these last decades to preserve anonymity or privacy through the Internet. Excepting of the Mix-Network principle [START_REF]Mix network -wikipedia, the free encyclopedia[END_REF], the most famous tool of this kind is probably Tor, the onion router. Tor client software routes Internet traffic through a worldwide volunteer network of servers, in order to conceal a user's location or usage from anyone conducting network surveillance or traffic analysis. Another example of this kind is given by Perseus [START_REF] Esiea | Perseus technology for anonymity through the internet[END_REF], a firefox plugin that protect personal data, without infringing any national crypto regulations, and that preserve the true needs of national security. Perseus replaces cryptography by coding theory techniques, such that only agencies with a strong enough computer power can eavesdrop traffic in an acceptable amount of time. Finally, anonymous proxy servers around the world can help to keep machines behind them anonymous: the destination server (the server that ultimately satisfies the web request) receives requests from the anonymizing proxy server, and thus does not receive information about the end user's address.

These three solutions are not without flaws. For instance, when considering anonymizers, the requests are not anonymous to the anonymizing proxy server, which simply moves the problem on: are these proxy servers worthy of trust? Perseus can be broken with enough computer power. And due to its central position and particular conception, Tor is targeted by numerous attacks and presents various weaknesses (bad apple attack, or the fact that Tor cannot protect against monitoring of traffic at the boundaries of the Tor network).

Considering these flaws, and because having a variety of solutions to provide anonymity is a good rule of thumb, a steganographic approach is often regarded in that context [START_REF] Guyeux | An improved watermarking algorithm for internet applications[END_REF]. Steganography can be applied in several ways to preserve anonymity through the Internet, encompassing the creation of secret channels through background images of websites, into Facebook photo galleries, on audio or video streams, or in non-interpreted characters in HTML source codes. The authors' intention is not to describe precisely these wellknown techniques, but to explain how to evaluate their security. They applied it on a new algorithm of steganography based on chaotic iterations and data embedding in least significant coefficients. This state-of-the-art in information hiding security is organized as follows.

In Section II, some basic reminders concerning both mathematical notions and notations, and the Most and Least Significant Coefficients are given. Our new steganographic process called DI 3 which is suitable to guarantee anonymity of data for privacy on the Internet is presented in Section III. In Section IV, a reminder about information hiding security is realized. The attacks classification in a steganographic framework are given, and the level of security of DI 3 is studied. In the next section the security of our new scheme is evaluated. Then, in Section-VI the steganalysis of the proposed process is realized, and it is compared with other steganographic schemes in the literature. This research work ends by a conclusion section, where our contribution is summarized and intended future researches are presented.

II. BASIC REMINDERS A. Mathematical definitions and notations

Let S n denotes the n th term of a sequence S, and V i the i th component of a vector V . For a, b ∈ N, we use the following notation: a; b = {a, a + 1, a + 2, . . . , b}. Remark 1: On the one hand, "S is injective" reflects the fact that all the n terms of the sequence S are distinct. On the other hand, "S is onto" means that all the values of the set 1; N are reached at least once.

B. The Most and Least Significant Coefficients

We first notice that terms of the original content x that may be replaced by terms issued from the watermark y are less important than other: they could be changed without be perceived as such. More generally, a signification function attaches a weight to each term defining a digital media, depending on its position t.

Definition 4: A signification function is a real sequence (u k ) k∈N .
Example 1: Let us consider a set of grayscale images stored into portable graymap format (P3-PGM): each pixel ranges between 256 gray levels, i.e., is memorized with eight bits. In that context, we consider u k = 8 -(k mod 8) to be the k-th term of a signification function (u k ) k∈N . Intuitively, in each group of eight bits (i.e., for each pixel) the first bit has an importance equal to 8, whereas the last bit has an importance equal to 1. This is compliant with the idea that changing the first bit affects more the image than changing the last one.

Definition 5: Let (u k ) k∈N be a signification function, m and M be two reals s.t. m < M .

• The most significant coefficients (MSCs) of x is the finite vector

u M = k k ∈ N and u k M and k ≤| x | ;
• The least significant coefficients (LSCs) of x is the finite vector

u m = k k ∈ N and u k ≤ m and k ≤| x | ;
• The passive coefficients of x is the finite vector

u p = k k ∈ N and u k ∈]m; M [ and k ≤| x | .
For a given host content x, MSCs are then ranks of x that describe the relevant part of the image, whereas LSCs translate its less significant parts. Using the concept described in this section, it is now possible to expose our new steganographic scheme.

III. THE NEW PROCESS: DI 3

In this section, a new algorithm, which is inspired from the scheme CIS 2 described in [START_REF] Friot | Chaotic iterations for steganography -stego-security and chaos-security[END_REF], is presented. Unlike CIS 2 which require embedding keys with three strategies, only one is required for DI 3 . Thus it is easyer to implement for Internet applications, especially in order to guarantee anonymization. Moreover, because in DI 3 there is no operation to mix the message, this new scheme seems to be faster than CIS 2 , which is a major advantage to have fast response times on the Internet.

Let us firstly introduce the following notations. P ∈ N * is the width, in term of bits, of the message to embed into the cover media. λ ∈ N * is the number of iterations to realize, which is s.t. λ > P. The initial state x 0 ∈ B N is for the N LSCs of a given cover media C supposed to be uniformly distributed. m ∈ B P is the message to hide into x 0 . Finally, S ∈ S P is a strategy such that the finite sequence S k , k ∈ λ -P + 1; λ is injective.

Remark 2: The width P of the message to hide into the of the cover media x 0 has to be far smaller than the number of LSCs.

The proposed information hiding scheme is defined by an iterative process applied on LSCs of the cover media as follow:

Definition 6 (DI 3 Data hiding scheme):

∀(n, i) ∈ N * × 0; N -1 :

x n i = x n-1 i if S n = i m S n if S n = i.
The stego-content is the Boolean vector y = x λ ∈ B N , which will replace the former LSCs (LSCs of the cover media are replaced by the vector y).

Remark 3:

The implementation of this data hiding scheme is exposed in a complementary work [START_REF] Bahi | A robust data hiding process contributing to the development of a semantic web[END_REF].

IV. DATA HIDING SECURITY AND ROBUSTNESS

A. Security and robustness

Even if security and robustness are neighboring concepts without clearly established definitions [START_REF] Perez-Freire | Watermarking security: a survey[END_REF], robustness is often considered to be mostly concerned with blind elementary attacks, whereas security is not limited to certain specific attacks. Indeed, security encompasses robustness and intentional attacks [START_REF] Kalker | Considerations on watermarking security[END_REF], [START_REF] Comesaña | Fundamentals of data hiding security and their application to spreadspectrum analysis[END_REF]. The best attempt to give an elegant and concise definition for each of these two terms was proposed in [START_REF] Kalker | Considerations on watermarking security[END_REF]. Following Kalker, we will consider in this research work the two following definitions: Definition 7 (Security [START_REF] Kalker | Considerations on watermarking security[END_REF]): Watermarking security refers to the inability by unauthorized users to have access to the raw watermarking channel [...] to remove, detect and estimate, write or modify the raw watermarking bits. In this article, we will focus more specifically on the security aspects, which have been formalized in the Simmons' prisoner problem.

B. The prisoner problem

In the prisoner problem of Simmons [START_REF] Simmons | The prisoners' problem and the subliminal channel[END_REF], Alice and Bob are in jail, and they want to, possibly, devise an escape plan by exchanging hidden messages in innocent-looking cover contents (Fig. 2). These messages are to be conveyed to one another by a common warden, Eve, who over-drops all contents and can choose to interrupt the communication if they appear to be stego-contents.

C. Classification of Attacks

In the steganography framework, in the Simmons' prisoner problem context, attacks have been classified in [START_REF] Cayre | Kerckhoffs-based embedding security classes for woa data hiding[END_REF] as follows.

Definition 9 (Classes of attacks):

WOA: A Watermark-Only Attack occurs when an attacker has only access to several watermarked contents. KMA: A Known-Message Attack occurs when an attacker has access to several pairs of watermarked contents and corresponding hidden messages. KOA: A Known-Original Attack is when an attacker has access to several pairs of watermarked contents and their corresponding original versions. CMA: A Constant-Message Attack occurs when the attacker observes several watermarked contents and only knows that the unknown hidden message is the same in all contents.

A synthesis of this classification is given in Table I.

In this article, we will focus more specifically on the "Watermark-Only Attack" situation, which is the most relevant category when considering anonymity and privacy protection through the Internet.

D. Reminder about Stego-Security

The stego-security, defined in the Watermark-Only Attack (WOA) framework, is the highest security level that can be defined in this setup [START_REF] Cayre | Kerckhoffs-based embedding security classes for woa data hiding[END_REF].

Definition 10 (Stego-Security): Let K be the set of embedding keys, p(X) the probabilistic model of N 0 initial host contents, and p(Y |K 1 ) the probabilistic model of N 0 watermarked contents. Moreover, each host content has been watermarked with the same secret key K 1 and the same embedding function e. Then e is said stego-secure if:

∀K 1 ∈ K, p(Y |K 1 ) = p(X).
Until now, only three schemes have been proven stegosecure. On the one hand, the authors of [START_REF] Cayre | Kerckhoffs-based embedding security classes for woa data hiding[END_REF] have established that the spread spectrum technique called Natural Watermarking is stego-secure when its distortion parameter η is equal to 1. On the other hand, we have proposed in [START_REF] Guyeux | Chaotic iterations versus spread-spectrum: chaos and stego security[END_REF] and [START_REF] Friot | Chaotic iterations for steganography -stego-security and chaos-security[END_REF] two other data hiding schemes satisfying this security property.

V. SECURITY STUDY

Let us prove that, Proposition 1: DI 3 is stego-secure.

Proof: Let us suppose that x 0 ∼ U B N , m ∼ U B P , and S ∼ U (S P ) in a DI 3 setup, where U(X) describes the uniform distribution on X. We will prove by a mathematical induction that ∀n ∈ N, x n ∼ U B N . The base case is obvious according to the uniform repartition hypothesis.

Let us now suppose that the statement x n ∼ U B N holds for some n ( P (x n = k) = 1 2 N ). For a given k ∈ B N , we denote by ki ∈ B N the vector defined by: ∀i ∈ 0

; N -1 , if k = (k 0 , k 1 , . . . , k i , . . . , k N-2 , k N-1 ), then ki = k 0 , k 1 , . . . , k i , . . . , k N-2 , k N-1
, where x is the negation of the bit x.

Let p be defined by: p = P x n+1 = k . Let E j and E be the events defined by: ∀j ∈ 0

; P -1 , E j = (x n = kj )∧(S n = j)∧(m S n = k j ),E = (x n = k)∧(m S n = x S n ). So, p = P E ∨ N-1 j=0 E j .
On the one hand, ∀j ∈ 0; P -1 , the event E j is a conjunction of the sub-events (S n = j) and other subevents. ∀j ∈ 0; P -1 , all the sub-events (S n = j) are clearly pairwise disjoints, so all the evente E j are pairwise disjoints too.

On the other hand, ∀j ∈ 0; P -1 , the events E j and E are disjoints, because in E j , a conjunction of the sub-event (x n = kj ) with other sub-events appears, whereas in E a conjunction of the sub-event (x n = k) with other sub-events appears, and the two sub-events (x n = kj ) and (x n = k) are clearly disjoints.

As a consequence, using the probability law concerning the reunion of disjoint events we can claim that: p = P (E)+ N j=0 P (E j ). Now we evaluate both P (E) and P (E j ). 1) The case of P (E): As the two events (x n = k) and

(m S n = x S n ) concern two different sequences, they are clearly independent. Then, by using the inductive hypothesis:

P (x n = k) = 1 2 N . So, p(E) = P (x n = k) × P (m S n = x S n ) = 1 2 N × [P (m S n = 0)P (x S n = 0) + P (m S n = 1)P (x S n = 1)] = 1 2 N × [P (m S n = 0)P (x S n = 0) +P (m S n = 1)(1 -P (x S n = 0))] = 1 2 N × 1 2 P (x S n = 0) + 1 2 (1 -P (x S n = 0)) = 1 2 N+1 .
2) Evaluation of P (E j ): As the three events (x n = kj ), (S n = j), and (m n = k j ) deal with three different sequences, they are clearly independent. So

P (E j ) = P (x n = kj ) × P (S n = j) × P (m S n = k j ) = 1 2 N × 1 P × 1 2 = 1 P × 1 2 N+1
, due to the hypothesis of uniform repartition of S and m.

Consequently, p = P (E) +

P j=0 P (E j ) = 1 2 N+1 + P j=0 1 P × 1 2 N+1 = 1 2 N . Finally, P x n+1 = k = 1
2 N , which leads to x n+1 ∼ U B N . This result is true ∀n ∈ N, we thus have proven that the stego-content y is uniformly distributed in the set of possible stego-contents:

y ∼ U B N when x ∼ U B N .
Remark 4 (Distribution of LSCs): We have supposed that x 0 ∼ U B N to prove the stego-security of the data hiding process DI 3 . This hypothesis is the most restrictive one, but it can be obtained at least partially in two possible manners. Either a channel that appears to be random (for instance, when applying a chi squared test) can be found in the media. Or a systematic process can be applied on the images to obtain this uniformity, as follows. Before embedding the hidden message, all the original LSCs must be replaced by randomly generated ones, hoping so that such cover media will be considered to be noisy by any given attacker.

Let us remark that, in the field of data anonymity for privacy on the Internet, we are in the "watermark-only attack" framework. As it has been recalled in Table I, in that framework, the attacker has only access to stegocontents, having so no knowledge of the original media, before introducing the message in the random channel (LSCs). However, this assumption of the existence of a random channel, natural or artificial, into the cover images, is clearly the most disputable one of this research work. The authors' intention is to investigate such hypothesis more largely in future works, by investigation the distribution of several LSCs contained in a large variety of images chosen randomly on the Internet. Among other things, we will check if some well-defined LSCs are naturally uniformly distributed in most cases. To conduct such studies, we intend to use the well-known NIST (National Institute of Standards and Technology of the U.S. Government) tests suite, the DieHARD battery, or the stringent TestU01 [START_REF] Simard | Testu01: A software library in ansi c for empirical testing of random number generators[END_REF]. Depending on the results of this search for randomness in natural images, the need to introduce an artificial random channel could be possibly removed.

Remark 5 (Distribution of the messages m): In order to prove the stego-security of the data hiding process DI 3 , we have supposed that m ∼ U B P . This hypothesis is not really restrictive. Indeed, to encrypt the message before its embedding into the LSCs of cover media if sufficient to achieve this goal. To say it different, in order to be in the conditions of applications of the process DI 3 , the hidden message must be encrypted.

Remark 6 (Distribution of the strategies S): To prove the stego-security of the data hiding process DI 3 , we have finally supposed that S ∼ U (S P ). This hypothesis is not restrictive too, as any cryptographically secure pseudorandom generator (PRNG) satisfies this property. With such PRNGs, it is impossible in polynomial time, to make the distinction between random numbers and numbers provided by these generators. For instance, Blum Blum Shub (BBS) [START_REF] Junod | Cryptographic secure pseudo-random bits generation: The Blum-Blum-Shub generator[END_REF], Blum Goldwasser (BG), or ISAAC, are convenient here.

VI. STEGANALYSIS

The steganographic scheme detailed along these lines has been compared to state of the art steganographic approaches, namely YASS [START_REF] Solanki | Yass: Yet another steganographic scheme that resists blind steganalysis[END_REF], HUGO [START_REF] Pevný | Using high-dimensional image models to perform highly undetectable steganography[END_REF], and nsF5 [START_REF] Fridrich | Statistically undetectable jpeg steganography: dead ends challenges, and opportunities[END_REF].

The steganalysis is based on the BOSS image database [START_REF] Bas | Break our steganographic system -the ins and outs of organizing boss[END_REF] which consists in a set of 10 000 512x512 greyscale images. We randomly selected 50 of them to compute the cover set. Since YASS and nsF5 are dedicated to JPEG support, all these images have been firstly translated into JPEG format thanks to the mogrify command line. To allow the comparison between steganographic schemes, the relative payload is always set with 0.1 bit per pixel. Under that constrain, the embedded message m is a sequence of 26214 randomly generated bits. This step has led to distinguish four sets of stego contents, one for each steganographic approach.

Next we use the steganalysis tool developed by the HugoBreakers team [START_REF] Kodovský | Ensemble classifiers for steganalysis of digital media[END_REF] based on AI classifier and which won the BOSS competition [START_REF] Bas | Break our steganographic system -the ins and outs of organizing boss[END_REF]. Table II summarizes these steganalysis results expressed as the error probabilities of the steganalyser. The errors are the mean of the false alarms and of the missed detections. An error that is closed to 0.5 signifies that deciding whether an image contains a stego content is a random choice for the steganalyser. Conversely, a tiny error denotes that the steganalyser can easily classify stego content and non stego content. The best result is obtained by HUGO, which is closed to the perfect steganographic approach to the considered steganalyser, since the error is about 0.5. However, even if the approach detailed along these lines has not any optimization, these first experiments show promising results. We finally notice that the HugoBreakers's steganalyser should outperform these results on larger image databases, e.g., when applied on the whole BOSS image database.

VII. CONCLUSION AND FUTURE WORK

Steganography is a real alternative to guarantee anonymity through the Internet. Unlike the principle of onion routers or Mix-networks, such a protocol using steganography doesn't require any third party potentially corrupted. Only the two parties who want to anonymously communicate are involved in the protocol. Each one holds a secret key for embedding and extraction of the message in the cover media. So to guaranty the anonymity of the communication, only the stealth and the undetectability of the message is required. It is assured by the security of the steganographic process. For instance, the scheme presented in this article offers a secure solution to achieve this goal, thanks to its stego-security. Even if this new scheme DI 3 does not possess topological properties (unlike the CIS 2 ), its level of security seems to be sufficient for Internet applications. Indeed, we take place into the Watermark Only Attack (WOA) framework, where stegosecurity is the highest level of security. Additionally, this new scheme is faster than CIS 2 . This is a major advantage for an utilization through the Internet, to respect response times of web sites. Moreover, for this first version of the process, the steganalysis results are promising.

In future work, various improvements of this scheme are planed to obtain better scores against steganalysers. For instance, LSCs will be embedded into various frequency domains. The robustness of the proposed scheme will be evaluated too [START_REF] Bahi | Steganography: a class of secure and robust algorithms[END_REF], to determine whether this information hiding algorithm can be relevant in other Internet domains interesting by data hiding techniques, as the semantic web. Finally a cryptographic approach of information hiding security is currently investigated, enlarging the Simmons' prisoner problem [START_REF] Bahi | A complexity approach for steganalysis[END_REF], and we intend to evaluate the proposed scheme in this framework.

Definition 1 :Definition 2 :

 12 Let k ∈ N * . The set of all sequences which elements belong into 1; k , called strategy adapters on 1; k , is denoted by S k . The support of a finite sequence S of n terms is the finite set S (S) = S k , k < n containing all the distinct values of S. Its cardinality is s.t. #S (S) n. Definition 3: A finite sequence S ∈ S N of n terms is injective if n = #S (S). It is onto if N = #S (S). Finally, it is bijective if and only if it is both injective and onto, so n = N = #S (S).

Example 2 :

 2 These two definitions are illustrated on Figure 1, where the significance function (u k ) is defined as in Example 1, m = 5, and M = 6. (a) Original Lena. (b) MSCs of Lena. (c) LSCs of Lena (×17).

Figure 1 .

 1 Figure 1. Most and least significant coefficients of Lena.

Figure 2 .

 2 Figure 2. Simmons' prisoner problem[START_REF] Simmons | The prisoners' problem and the subliminal channel[END_REF]


Jacques M Bahi
email: jacques.bahi@femto-st.fr

Jean-François Couchot
email: jean-francois.couchot@femto-st.fr

Nicolas Friot
email: nicolas.friot@femto-st.fr

Christophe Guyeux
email: christophe.guyeux@femto-st.fr

A Robust Data Hiding Process Contributing to the Development of a Semantic Web

Keywords: Semantic Web, Information Hiding, Steganography, Robustness, Chaotic Iterations

In this paper, a novel steganographic scheme based on chaotic iterations is proposed. This research work takes place into the information hiding framework, and focus more specifically on robust steganography. Steganographic algorithms can participate in the development of a semantic web: medias being on the Internet can be enriched by information related to their contents, authors, etc., leading to better results for the search engines that can deal with such tags. As media can be modified by users for various reasons, it is preferable that these embedding tags can resist to changes resulting from some classical transformations as for example cropping, rotation, image conversion, and so on. This is why a new robust watermarking scheme for semantic search engines is proposed in this document. For the sake of completeness, the robustness of this scheme is finally compared to existing established algorithms.

I. INTRODUCTION

Social search engines are frequently presented as a next generation approach to query the world wide web. In this conception, contents like pictures or movies are tagged with descriptive labels by contributors, and search results are enriched with these descriptions. These collaborative taggings, used for example in Flickr [START_REF]The frick collection[END_REF] and Delicious [START_REF]Delicious social bookmarking[END_REF] websites, can participate to the development of a Semantic Web, in which every Web page contains machine-readable metadata that describe its content. To achieve this goal by embedding such metadata, information hiding technologies can be useful. Indeed, the interest to use such technologies lays on the possibility to realize social search without websites and databases: descriptions are directly embedded into media, whatever their formats.

In the context of this article, the problem consists in embedding tags into internet medias, such that these tags persist even after user transformations. Robustness of the chosen watermarking scheme is thus required in this situation, as descriptions should resist to user modifications like resizing, compression, and format conversion or other classical user transformations in the field. Indeed, quoting Kalker in [START_REF] Kalker | Considerations on watermarking security[END_REF], "Robust watermarking is a mechanism to create a communication channel that is multiplexed into original content [...] It is required that, firstly, the perceptual degradation of the marked content [...] is minimal and, secondly, that the capacity of the watermark channel degrades as a smooth function of the degradation of the marked content". The development of social web search engines can thus be strengthened by the design of robust information hiding schemes. Having this goal in mind, we explain in this article how to set up a secret communication channel using a new robust steganographic process called DI 3 . This new scheme has been theoretically presented in [START_REF] Bahi | Application of steganography for anonymity through the internet[END_REF] with an evaluation of its security. So, the main objective of this work is to focus on robustness aspects presenting firstly other known schemes in the literature, and presenting secondly this new scheme and and evaluate its robustness. This article is thus a first work on the subject, and the comparison with other schemes concerning the robustness will be realized in future work.

The remainder of this document is organized as follows. In Section II, some basic reminders concerning the notion of Most and Least Significant Coefficients are given. In Section III, some well-known steganographic schemes are recalled, namely the YASS [START_REF] Solanki | Yass: Yet another steganographic scheme that resists blind steganalysis[END_REF], nsF5 [START_REF] Fridrich | Statistically undetectable jpeg steganography: dead ends challenges, and opportunities[END_REF], MMx [START_REF] Kim | Modified matrix encoding technique for minimal distortion steganography[END_REF], and HUGO [START_REF] Pevný | Using highdimensional image models to perform highly undetectable steganography[END_REF] algorithms. In the next section the implementation of the steganographic process DI 3 is detailed, and its robustness study is exposed in Section V. This research work ends by a conclusion section, where our contribution is summarized and intended future researches are presented.

II. MOST AND LEAST SIGNIFICANT COEFFICIENTS

We first notice that terms of the original content x that may be replaced by terms issued from the watermark y are less important than others: they could be changed without be perceived as such. More generally, a signification function attaches a weight to each term defining a digital media, depending on its position t.

Definition 1: A signification function is a real sequence (u k ) k∈N .
Example 1: Let us consider a set of grayscale images stored into portable graymap format (P3-PGM): each pixel ranges between 256 gray levels, i.e., is memorized with eight bits. In that context, we consider u k = 8 -(k mod 8) to be the k-th term of a signification function (u k ) k∈N . Intuitively, in each group of eight bits (i.e., for each pixel) the first bit has an importance equal to 8, whereas the last bit has an importance equal to 1. This is compliant with the idea that changing the first bit affects more the image than changing the last one.

Definition 2: Let (u k ) k∈N be a signification function, m and M be two reals s.t. m < M .

• The most significant coefficients (MSCs) of x is the finite vector

u M = k k ∈ N and u k M and k ≤| x | ;
• The least significant coefficients (LSCs) of x is the finite vector

u m = k k ∈ N and u k ≤ m and k ≤| x | ;
• The passive coefficients of x is the finite vector

u p = k k ∈ N and u k ∈]m; M [ and k ≤| x | .
For a given host content x, MSCs are then ranks of x that describe the relevant part of the image, whereas LSCs translate its less significant parts.

Remark 1: When MSCs and LSCs represent a sequence of bits, they are also called Most Significant Bits (MSBs) and Least Significant Bits (LSBs). In the rest of this article, the two notations will be used depending on the context. One should find more details in [START_REF] Fridrich | Steganography in Digital Media: Principles, Algorithms, and Applications[END_REF].

A. YASS

YASS (Yet Another Steganographic Scheme) [START_REF] Solanki | Yass: Yet another steganographic scheme that resists blind steganalysis[END_REF] is a steganographic approach dedicated to JPEG cover. The main idea of this algorithm is to hide data into 8×8 randomly chosen inside B × B blocks (where B is greater than 8) instead of choosing standard 8×8 grids used by JPEG compression. The self-calibration process commonly embedded into blind steganalysis schemes is then confused by the approach. In the paper [START_REF] Sarkar | Further study on yass: Steganography based on randomized embedding to resist blind steganalysis[END_REF], further variants of YASS have been proposed simultaneously to enlarge the embedding rate and to improve the randomization step of block selecting. More precisely let be given a message m to hide, a size B, B ≥ 8, of blocks. The YASS algorithm follows.

B. nsF5

The nsF5 algorithm [START_REF] Fridrich | Statistically undetectable jpeg steganography: dead ends challenges, and opportunities[END_REF] extends the F5 algorithm [START_REF] Westfeld | F5-a steganographic algorithm[END_REF]. Let us first have a closer look on this latter.

First of all, as far as we know, F5 is the first steganographic approach that solves the problem of remaining unchanged a part (often the end) of the file. To achieve this, a subset of all the LSB is computed thanks to a pseudo random number generator seeded with a user defined key. Next, this subset is split into blocks of x bits. The algorithm takes benefit of binary matrix embedding to increase it efficiency. Let us explain this embedding on a small illustrative example where a part m of the message has to be embedded into this x LSB of pixels which are respectively a 3 bits column vector and a 7 bits column vector. Let then H be the binary Hamming matrix

H =   0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1  
The objective is to modify x to get y s.t. m = Hy. In this algebra, the sum and the product respectively correspond to the exclusive or and to the and Boolean operators. If Hx is already equal to m, nothing has to be changed and x can be sent. Otherwise we consider the difference δ = d(m, Hx) which is expressed as a vector :

δ =   δ 1 δ 2 δ 3   where δ i is 0 if m i = Hx i and 1 otherwise.
Let us thus consider the jth column of H which is equal to δ. We denote by x j the vector we obtain by switching the jth component of x, that is, x j = (x 1 , . . . , x j , . . . , x n ). It is not hard to see that if y is x j , then m = Hy. It is then possible to embed 3 bits in only 7 LSB of pixels by modifying on average 1 -2 3 changes. More generally, the F5 embedding efficiency should theoretically be p 1-2 p . However, the event when the coefficient resulting from this LSB switch becomes zero (usually referred to as shrinkage) may occur. In that case, the recipient cannot determine whether the coefficient was -1, +1 and has changed to 0 due to the algorithm or was initially 0. The F5 scheme solves this problem first by defining a LSB with the following (not even) function:

LSB(x) = 1 -x mod 2 if x < 0 x mod 2 otherwise. .
Next, if the coefficient has to be changed to 0, the same bit message is re-embedded in the next group of x coefficient LSB.

The scheme nsF5 focuses on steps of Hamming coding and ad'hoc shrinkage removing. It replaces them with a wet paper code approach that is based on a random binary matrix. More precisely, let D be a random binary matrix of size x × n without replicate nor null columns: consider for instance a subset of {1, 2 x } of cardinality n and write them as binary numbers. The subset is generated thanks to a PRNG seeded with a shared key. In this block of size x, one choose to embed only k elements of the message m. By abuse, the restriction of the message is again called m. It thus remains x -k (wet) indexes/places where the information shouldn't be stored. Such indexes are generated too with the keyed PRNG. Let v be defined by the following equation:

Dv = δ(m, Dx). (1)
This equation may be solved by Gaussian reduction or other more efficient algorithms. If there is a solution, one have the list of indexes to modify into the cover. The nsF5 scheme implements such a optimized algorithm that is to say the LT codes.

C. MMx

Basically, the MMx algorithm [START_REF] Kim | Modified matrix encoding technique for minimal distortion steganography[END_REF] embeds message in a selected set of LSB cover coefficients using Hamming codes as the F5 scheme. However, instead of reducing as many as possible the number of modified elements, this scheme aims at reducing the embedding impact. To achieve this it allows to modify more than one element if this leads to decrease distortion.

Let us start again with an example with a [START_REF] Fridrich | Steganography in Digital Media: Principles, Algorithms, and Applications[END_REF][START_REF] Bahi | Reliable parallel programming model for distributed computing environments[END_REF] Hamming codes, i.e, let us embed 3 bits into 7 DCT coefficients, D 1 , . . . , D 7 . Without details, let ρ 1 , . . . , ρ 7 be the embedding impact whilst modifying coefficients D 1 , . . . , D 7 (see [START_REF] Kim | Modified matrix encoding technique for minimal distortion steganography[END_REF] for a formal definition of ρ). Modifying element at index j leads to a distortion equal to ρ j . However, instead of switching the value at index j, one should consider to find all other columns of H, j 1 , j 2 for instances, s.t. the sum of them is equal to the jth column and to compare ρ j with ρ j1 + ρ j2 . If one of these sums is less than ρ j , the sender has to change these coefficients instead of the j one. The number of searched indexes (2 for the previous example) gives the name of the algorithm. For instance in MM3, one check whether the message can be embedded by modifying 3 pixel or less each time.

D. HUGO

The HUGO [START_REF] Pevný | Using highdimensional image models to perform highly undetectable steganography[END_REF] steganographic scheme is mainly designed to minimize distortion caused by embedding. To achieve this, it is firstly based on an image model given as SPAM [START_REF] Pevný | Steganalysis by subtractive pixel adjacency matrix[END_REF] features and next integrates image correction to reduce much more distortion. What follows discuss on these two steps.

The former first computes the SPAM features. Such calculi synthesize the probabilities that the difference between consecutive horizontal (resp. vertical, diagonal) pixels belongs in a set of pixel values which are closed to the current pixel value and whose radius is a parameter of the approach. Thus a fisher linear discriminant method defines the radius and chooses between directions (horizontal, vertical. . . ) of analyzed pixels that gives the best separator for detecting embedding changes. With such instantiated coefficients, HUGO can synthesize the embedding cost as a function D(X, Y ) that evaluates distortions between X and Y . Then HUGO computes the matrices of ρ i,j = max(D(X, X (i,j)+ ) i,j , D(X, X (i,j)-) i,j ) such that X (i,j)+ (resp. X (i,j)-) is the cover image X where the the (i, j)th pixel has been increased (resp. has been decreased) of 1.

The order of modifying pixel is critical: HUGO surprisingly modifies pixels in decreasing order of ρ i,j . Starting with Y = X, it increases or decreases its (i, j)th pixel to get the minimal value of D(Y, Y (i,j)+ ) i,j and D(Y, Y (i,j)-) i,j . The matrix Y is thus updated at each round.

IV. THE NEW STEGANOGRAPHIC PROCESS DI 3

A. Implementation

In this section, a new algorithm which is inspired from the schemes CIW 1 and CIS 2 respectively described in [START_REF] Friot | Chaotic iterations for steganography -stego-security and chaos-security[END_REF] and [START_REF] Guyeux | Chaotic iterations versus spread-spectrum: chaos and stego security[END_REF] is presented. Compare to the first one, it is a steganographic scheme, not just a watermarking technique. Unlike CIS 2 which require embedding keys with three strategies, only one is required for DI 3 . So compare to CIS 2 which is also a steganographic process, it is easier to implement for Internet applications especially in order to contribute to a semantic web. Moreover, since DI 3 is a particular instance of CIS 2 , it is clearly faster than this one because in DI 3 there is no operation to mix the message on the contrary on the initial scheme. The fast execution of such an algorithm is critical for internet applications.

In the following algorithms, the following notations are used:

Notation 1: S denotes the embedding and extraction strategy, H the host content or the stego-content depending of the context. LSC denotes the old or new LSCs of the host or stego-content H depending of the context too. N denotes the number of LSCs, λ the number of iterations to realize, M the secret message, and P the width of the message (number of bits).

Our new scheme theoretically presented in [START_REF] Bahi | Application of steganography for anonymity through the internet[END_REF] is here described by three main algorithms:

1) The first one, detailed in Algorithm 1 allows to generate the embedding strategy of the system which is a part of the embedding key in addition with the choice of the LSCs and the number of iterations to realize.

2) The second one, detailed in Algorithm 2 allows to embed the message into the LSCs of the cover media using the strategy. The strategy has been generated by the first algorithm and the same number of iterations is used.

3) The last one, detailed in Algorithm 3 allows to extract the secret message from the LSCs of the media (the stego-content) using the strategy wich is a part of the extraction key in addition with the width of the message. In adjunction of these three functions, two other complementary functions have to be used:

1) The first one, detailed in Algorithm 4, allow to extract MSCs, LSCs, and passive coefficients from the host content. Its implementation is based on the concept of signification function described in Definition 2.

2) The last one, detailed in Algorithm 5, allow to rebuild the new host content (the stego-content) from the corresponding MSCs, LSCs, and passive coefficients. Its implementation is also based on the concept of signification function described in Definition 2. This function realize the invert operation of the previous one.

Remark 2:

The two previous algorithms have to be implemented by the user depending on each application context should be adjusted accordingly: either in spatial description, in frequency description, or in other description. They correspond to the theoretical concept described in Definition 2.

Their implementation depends on the application context. Example 3: For example the algorithm 4 in spatial domain can correspond to the extraction of the 3 last bits of each pixel as LSCs, the 3 first bits as MSCs, and the 2 center bits as passive coefficients.

Algorithm 1: strategy(N, P, λ)

/ * S is a sequence of integers into 0, P -1 , such that (S n0 , . . . , S n0+P -1 ) is injective on 0, P -1 . * / Result: S: The strategy, integer sequence (S 0 , S 1 , . . .). begin n 0 ←-L -P + 1; if P > N OR n 0 < 0 then return ERROR S ←-Array of width λ, all values initialized to 0; cpt ←-0; while cpt < n 0 do S cpt ←-Random integer in 0, P -1 .; cpt ←-cpt + 1; A ←-We generate an arrangement of 0, P -1 ; Result: The message to extract from LSC. begin RS ←-The strategy S written in reverse order.; M ←-Array of width P , all values initialized to 0;

for k ∈ 0, P -1 do S n0+k ←-A k ; return S end
for k ∈ 0, λ do i ←-RS k ; M i ←-LSC i ; return M end

B. Discussion

We first notice that our DI 3 scheme embeds the message in LSB as all the other approaches. Furthermore, among all Result: H: The new rebuilt host content. begin / * Implemented by the user. * / return (M SC, P C, LSC) end the LSB, the choice of those which are modified according to the message is based on a secured PRNG whereas F5, and thus nsF5 only require a PRNG. Finally in this scheme, we have postponed the optimization of considering again a subset of them according to the distortion their modification may induce. According to us, further theoretical study are necessary to take this feature into consideration. In future work, it is planed to compare the robustness and efficiency of all the schemes in the context of semantic web. To initiate this study in this first article, the robustness of DI 3 is detailled in the next section.

V. ROBUSTNESS STUDY

This section evaluates the robustness of our approach [START_REF] Bahi | Steganography: a class of secure and robust algorithms[END_REF]. Each experiment is build on a set of 50 images which are randomly selected among database taken from the BOSS contest [START_REF] Bas | Break our steganographic system -the ins and outs of organizing boss[END_REF]. Each cover is a 512 × 512 greyscale digital image. The relative payload is always set with 0.1 bit per pixel. Under that constrain, the embedded message m is a sequence of 26214 randomly generated bits.

Following the same model of robustness studies in previous similar work in the field of information hiding, we choose some classical attacks like cropping, compression, and rotation studied in this research work. Other attacks and geometric transformations will be explore in a complementary study. Testing the robustness of the approach is achieved by successively applying on stego content images attacks. Differences between the message that is extracted from the attacked image and the original one are computed and expressed as percentage.

To deal with cropping attack, different percentage of cropping (from 1% to 81%) are applied on the stego content image. Fig. 2 (c) presents effects of such an attack. We address robustness against JPEG an JPEG 2000 compression. Results are respectively presented in Fig. 2 (a) and in Fig. 2 (b).

Attacked based on geometric transformations are addressed through rotation attacks: two opposite rotations of angle θ are successively applied around the center of the image. In these geometric transformations, angles range from 2 to 20 degrees. Results effects of such an attack are also presented in Fig. 2 (d).

From all these experiments, one firstly can conclude that the steganographic scheme does not present obvious drawback and resists to all the attacks: all the percentage differences are so far less than 50%.

The comparison with robustness of other steganographic schemes exposed in the work will be realize in a complementary study, and the best utilization of each one in several context will be discuss.

VI. CONCLUSION AND FUTURE WORK

In this research work, a new information hiding algorithm has been introduced to contribute to the semantic web. We have focused our work on the robustness aspect. The security has been studied in an other work [START_REF] Bahi | Application of steganography for anonymity through the internet[END_REF]. Even if this new scheme DI 3 does not possess topological properties (unlike the CIS 2 [START_REF] Friot | Chaotic iterations for steganography -stego-security and chaos-security[END_REF]), its level of security seems to be sufficient for Internet applications. Particularly in the framework of the semantic web it is required to have robust steganographic processes. The security aspects is less important in this context. Indeed, it is important that the enrichment information persist after an attack. Especially for JPEG 2000 attacks, which are the two major attacks used in an internet framework. Additionally, this new scheme is faster than CIS 2 . This is a major advantage for an utilization through the Internet, to respect response times of web sites.

In a future work we intend to prove rigorously that DI 3 is not topologically secure. The tests of robustness will be realized on a larger set of images of different types and sizes, using resources of the Mésocentre de calcul de Franche-Comté [START_REF] Comté | Le mésocentre de calcul de franche-comté, an high-performance computing (hpc) center[END_REF] (an High-Performance Computing (HPC) center) and using Jace environment [START_REF] Bahi | Reliable parallel programming model for distributed computing environments[END_REF], to take benefits of parallelism. So, the robustness and efficiency of our scheme DI 3 will be compared to other schemes in order to show the best utilization in several contexts. Other kinds of attacks will be explored to evaluate more completely the robustness of the proposed scheme. For instance, robustness of the DI 3 against Gaussian blur, rotation, contrast, and zeroing attacks will be regarded, and compared with a larger set of existing steganographic schemes as those described in this article. Unfortunately these academic algorithms are mainly designed to show their ability in embedding. Decoding aspect is rarely treated, and rarely implemented at all. Finally, a first web search engine compatible with the proposed robust watermarking scheme will be written, and automatic tagging of materials found on the Internet will be realized, to show the effectiveness of the approach.

Example 2 :

 2 These two definitions are illustrated on Figure 1, where the significance function (u k ) is defined as in Example 1, m = 5, and M = 6.

Figure 1 .

 1 Figure 1. Most and least significant coefficients of Lena

1 )

 1 Computation of m , which is the Repeat-Accumulate error correction code of m. 2) In each big block of size B × B of cover, successively do: a) Random selection of an 8 × 8 block b using w.r.t. a secret key. b) Two-dimensional DCT transformation of b and normalisation of coefficient w.r.t a predefined quantization table. Matrix is further referred to as b . c) A fragment of m is embedded into some LSB of b . Let b be the resulting matrix. d) The matrix b is decompressed back to the spatial domain leading to a new B × B block.

Algorithm 2 :

 2 embed(LSC, M, S, λ) Result: New LSCs with embedded message. begin N ←-Number of LSCs in LSC; P ←-Width of the message M ; for k ∈ 0, λ do i ←-S k ; LSC i ←-M i ; return LSC end Algorithm 3: extract(LSC, S, λ, P )

Algorithm 4 :

 4 signif icationF unction(H) Data: H: The original host content. Result: M SC: MSCs of the host content H. Result: P C: Passive coefficients of the host content H. Result: LSC: LSCs of the host content H. begin / * Implemented by the user. * / return (M SC, P C, LSC) end Algorithm 5: buildF unction(M SC, P C, LSC) )

Figure 2 .

 2 Figure 2. Robustness of DI 3 scheme facing several attacks (50 images from the BOSS repository)