Victoria Acker
email: victoria.acker@inrae.fr

Jean-Louis Durand

Romain Barillot

Simulation of leaf growth response to elevated atmospheric carbon dioxide concentration ([CO2]) using CN-Wheat, a model of morphogenesis driven by trophic dynamics

Keywords: climate change, morphogenesis, wheat, FSPM, CO2

Simulation of leaf growth response to elevated atmospheric carbon dioxide concentration ([CO2]) using CN-Wheat, a model of morphogenesis driven by trophic dynamics

Introduction

The Earth is facing an increase in the atmospheric carbon dioxide concentration ([CO2]). Elevated [CO2] affects plant growth and development by modifying a range of physiological processes. Stimulation of leaf area development by elevated [CO2] is important in terms of plant productivity because green leaf area determines total biomass and final grain yield. As atmospheric [CO2] is currently a limiting factor for C3 photosynthesis, it has been demonstrated that the primary effect of elevated [CO2] is a stimulation of photosynthesis due to both enrichment of substrate for Rubisco carboxylation and an inhibition of competitive Rubisco oxygenation (Long et al., 2006). High [CO2] also induces stomatal closure leading to a decrease of transpiration per leaf area unit. Elevated [CO2] has also been shown to reduce plant demand for nitrogen (Dong et al., 2022). The resulting interactions between water, photoassimilates and nitrogen are complex, and the underlying mechanisms by which elevated [CO2] affects leaf growth are still not clearly understood. To address remaining knowledge gaps and uncertainties in estimating the effects of elevated [CO2] and climate change on plants, research should expand experiments under a wider range of growing conditions and improve the representation of responses to climate in models. Functional Structural Plant Models (FSPMs), which account for the interactions between biological processes and environmental factors, are among key tools to explore plant responses to climate change and possible adaptation mechanisms. In this work, we evaluated the ability of CN-Wheat (Barillot et al., 2016 andGauthier et al., 2020), a wheat FSPM, to simulate leaf growth response to contrasting CO2 concentrations.

Model description

CN-Wheat represents the plant as a collection of tillers. Tillers are considered as a set of botanical modules representing several mature and growing shoot organs (blades, sheaths, internodes and growth zones), a root compartment and a common pool mimicking the phloem and allowing fluxes of metabolites among organs. Each organ includes structural, mobile (sucrose, nitrates, and amino acids) and storage (fructans, proteins) materials. CN-Wheat accounts for the main biological processes occurring in plants: resource acquisition (N uptake, photosynthesis) and allocation within the plant, morphogenesis (leaf and internode growth) and senescence. Leaf growth is represented as a self-regulated system driven by: i) the local concentrations of carbon (C) and nitrogen (N) in the growth zones which regulate the rate of organ elongation, specific structural mass and width, ii) coordination rules linking the timing of leaf extension between successive phytomers. CN-Wheat allows for a dynamic representation of the 3D geometry of plants, which is used to compute light distribution at organ scale. In this work, CN-Wheat sensitivity to [CO2] was assessed by simulating the growth of wheat plants for ~105 days and exposed to low [CO2] = 200 ppm, medium [CO2] = 360 ppm, and high [CO2] = 800 ppm. Only the morphogenesis of the main stem leaves was considered, the tillering was kept constant between simulations. Except for [CO2], virtual set-up was similar to Gauthier et al. (2020) and come from plants grown in the field in Grignon (France) in 1998 and 1999.

Results and Discussion

Simulation results indicated that [CO2] increased plant photosynthesis by ~40% between [CO2]

= 200 ppm and 800 ppm (data not shown). LAI increased by ~20% between [CO2] = 200 ppm and 800 ppm but was similar between 360 and 800 ppm (Fig. 1a). On the contrary, N content in shoot was lower at high [CO2] until day 55 (Fig. 1b). N concentration increased on this day, due to particular weather conditions. After that date, N concentration started to decrease drastically at [CO2] = 200 ppm, as a result of complex interactions. At the end of the simulation, cumulated blade transpiration was ~40% lower at [CO2] = 800 and 360 than at 200 ppm. Phyllochron was little affected by [CO2] (Fig. 1d), except for the last leaf which appeared later at low [CO2]. There was no difference in leaf length across [CO2] treatments (data not shown), but leaf width increased with CO2. On the last leaf, width was ~30% higher at [CO2] = 800 than at 200 ppm (Fig. 1e). The specific structural leaf weight (Fig. 1f) was also greater at [CO2] = 800 than 200 ppm (~25%). Overall, CO2 effects were greater between 200 and 360 ppm than between 360 and 800 ppm.

Conclusion

CN-Wheat showed interesting properties for exploring leaf growth response to [CO2] for plants grown in optimal water conditions. The further step is the implementation of water dynamics within CN-Wheat to extend the approach in simulating the response of leaf growth to [CO2] x drought interactions.

Figure 1 :

 1 Figure 1: Simulation results of dynamics of LAI (a), N mass of shoot (b), cumulated leaf transpiration (c), phyllochron (d), leaf width (e), and specific structural leaf weight (f) as function of the leaf index, at three different [CO2]: 200 ppm, 360 ppm and 800 ppm.


Thibault Cholez
email: thibault.cholez@loria.fr

Isabelle Chrisment
email: isabelle.chrisment@loria.fr

Olivier Festor
email: olivier.festor@loria.fr

Evaluation of Sybil Attacks Protection Schemes in KAD

Keywords: P2P networks, DHT, Sybil attack, security, defense, KAD

In this paper, we assess the protection mechanisms entered into recent clients to fight against the Sybil attack in KAD, a widely deployed Distributed Hash Table . We study three main mechanisms: a protection against flooding through packet tracking, an IP address limitation and a verification of identities. We evaluate their efficiency by designing and adapting an attack for several KAD clients with different levels of protection. Our results show that the new security rules mitigate the Sybil attacks previously launched. However, we prove that it is still possible to control a small part of the network despite the new inserted defenses with a distributed eclipse attack and limited resources.

Motivation and scope of work

Peer-to-Peer (P2P) networks have proven their ability to host and share a large amount of resources thanks to the collaboration of many individual peers. They are known to have many advantages compared to the client-server scheme: P2P networks scale better; the cost of the infrastructure is distributed and they are fault tolerant. Most currently deployed structured P2P networks are based on Distributed Hash Tables (DHT). Each peer is responsible for a subset of the network. This organization improves the efficiency of P2P networks ensuring routing in O(log n) but can also lead to security issues like the Sybil Attack.

The Sybil Attack, as described by Douceur [START_REF] Douceur | The sybil attack[END_REF], consists in creating a large number of fake peers called the "Sybils" and placing them in a strategic way in the DHT to take control over a part of it. Douceur proved that the Sybil Attack cannot be totally avoided as long as the malicious entity has enough resources to create the Sybils. This problem was not considered when designing most of the major structured P2P networks. In this context, the goal of the defense strategies described in the literature is to limit the Sybil Attack as completely stopping it is impossible. Proposed solutions are based on a strong identification of the peer [START_REF] Dinger | Defending the sybil attack in p2p networks: Taxonomy, challenges, and a proposal for self-registration[END_REF] or on a trusted central authority [START_REF] Castro | Secure routing for structured peer-to-peer overlay networks[END_REF]. In [START_REF] Singh | Defending against eclipse attacks on overlay networks[END_REF], the authors propose to bound the degree of overlay nodes by anonymous auditing to limit localised attacks but they also rely on a central certification to limit the number of Sybils. A strong identification being not adapted to many P2P applications, other strategies are possible to limit the Sybil attack considering that a distributed assignment with free identifiers is possible but, in compensation, must be verified by resource consuming proofs [START_REF] Rowaihy | Limiting sybil attacks in structured p2p networks[END_REF] or an underlying social network [START_REF] Yu | Sybilguard: defending against sybil attacks via social networks[END_REF]. The most successfully completed protection against the Sybil attack [START_REF] Lesueur | A sybil-resistant admission control coupling SybilGuard with distributed certification[END_REF] uses distributed certification coupled with a social network, but no studies consider practical protections set in a real network.

Even if defense against the Sybil attack has been largely investigated, most of the proposed solutions are difficult to set up and are not always well suited for the P2P paradigm. Things are even worse when considering all the constraints of a large public P2P network like KAD without a managed support infrastructure and with the need of backward compatibility. KAD provides a file sharing application based on the academic Kademlia [START_REF] Maymounkov | Kademlia: A peer-to-peer information system based on the xor metric[END_REF] DHT and has been proven vulnerable and totally unprotected against Sybil attacks that can highly affect the network [START_REF] Steiner | Exploiting KAD: possible uses and misuses[END_REF]. In this context, managing and protecting the KAD network seems very challenging.

The latest versions of the major KAD clients have introduced new protection mechanisms to limit the Sybil attack, making the previous experiments concerning the security issues of KAD like [START_REF] Steiner | Exploiting KAD: possible uses and misuses[END_REF] inefficient. These newly implemented protection mechanisms have neither been described nor been evaluated and assessed. The purpose of this study is to evaluate the implemented security mechanisms against real attacks. We will then be able to have an updated view of KAD vulnerabilities: Is the network still vulnerable to the attack proposed in [START_REF] Steiner | Exploiting KAD: possible uses and misuses[END_REF]? Is it now fully protected? Which vulnerabilties have been corrected and which ones keep being a threat? This work is a first and necessary step to design improved defense mechanisms in future works. As far as we know, this paper is also the first attempt to experiment and assess practical protections set by the P2P community to protect a real network.

This document is structured as follows. Section 2 describes the background of KAD, the Sybil attacks performed on it, and the new defense mechanisms. We then present in Section 3 our evaluation of the mechanisms including our methodology, the results obtained by the different versions of KAD clients and the impact of our distributed eclipse attack. Finally, Section 4 concludes the paper with a discussion on the validity of the built-in protections and outlines our future works.

KAD and the Sybil attack

Overview of KAD

KAD is a structured P2P network based on the Kademlia distributed hash table routing protocol [START_REF] Maymounkov | Kademlia: A peer-to-peer information system based on the xor metric[END_REF]. KAD is implemented by the popular eMule file sharing application and its multi-platform version aMule, both are open source. Historically, these clients were mainly designed to join the eDonkey network composed of autonomous distributed servers. However, many major eDonkey servers have been closed by lawsuits so that the eDonkey network is becoming less attractive and users are progressively migrating toward the fully decentralized P2P network, KAD. With an estimated number of concurrent online users around 4 millions, KAD is the widest deployed structured P2P network.

Each node of KAD has a 128bits KADID defining its position in the DHT. Two types of requests are used to discover the network: the Hello REQ is used by a peer to announce itself and the Kademlia REQ is used to discover new peers toward a specific address. The routing is based on the XOR metric: to fill the routing table, each node registers at level i K-contacts (called a K-bucket), each contact being at a distance between 2 128-i and 2 127-i from its KADID regarding the XOR metric. The deeper the contact is in the tree, the closer it is to the node and the better the peer knows this part of the DHT; this provides routing in O(log n). The routing is done in an iterative way with parallel lookups: asking at first the n closest contacts to the target ID found in the routing table for even closer nodes toward the target with Kademlia REQ, waiting for their responses and then reiterating.

As a file sharing application, the purpose of the DHT is to retrieve information like keywords and files. When sharing a new file, the binary and all the keywords are hashed separately with a MD5 function generating KADIDs and then published. The peers in charge of a file or a keyword are those close enough to their hash. This distance is called the tolerance zone and is set to the first common 8bits (most significant bits). The double indexation allows retrieval of a particular file, given a set of keywords. To publish a file, two types of requests are sent:

-KADEMLIA2 PUBLISH KEY REQ requests are sent to the hash of the keyword and associate a keyword with a file -KADEMLIA2 PUBLISH SOURCE REQ requests are sent to the hash of the file and associate a file to a source (a node able to upload the file)

Previous attacks in KAD

Recent investigations showed that KAD can be cheated in several ways using few resources and resulting in important outages. Steiner et al [START_REF] Steiner | Exploiting KAD: possible uses and misuses[END_REF] were the first to successfully launch a real Sybil attack on KAD, resulting in the full control of a part of the network. The attack is divided in two steps. The first step consists in a crawler gathering information about what peer is in a zone of the network and what its routing table is. This is done by issuing route requests (Kademlia REQ) toward some predefined node IDs in order to obtain new contacts close to those IDs. When almost all nodes of the zone are known by the crawler, the second step consists in individually contacting each node of the list to pollute its routing table with Sybils. Previously trivial, injection of Sybils is now protected by several mechanisms studied in the forthcoming sections.

In [START_REF] Chan-Tin | Attacking the kad network[END_REF], the authors describe an attack that allows denial of service on a great part of the network with few resources. This attack does not rely on a classical injection of Sybils but hijacks the references of contacts in the routing table. Malicious nodes are able to overwrite a legitimate routing table entry (KADID/IP address) with their own reference by sending a simple Hello REQ announcing this KADID. This weakness highlights a real lack of identity management in KAD. Thanks to the information acquired by a crawler, this vulnerability allows to partition the network or to do a massive denial of service. A search request starts from bad references and is then kept by them, until it terminates without any real result, or fails because of a timeout. The experiments on PlanetLab show that the attack is effective and does not use much bandwidth with some optimizations. The authors also noticed the improvements of the latest versions of the clients which could mitigate their attack, but they did not evaluate them.

Protections in KAD

The importance of these weaknesses forced the developers to react by setting up new protections in the latest versions of the clients. Even if older clients are still vulnerable, progressive updates should be able to mitigate the attacks and constitute a healthy basis for the network. KAD clients implement different levels of protection regarding their version. For similar versions, eMule and aMule are based on the same code and behave in the same way. No protection: aMule 2.1.3 was chosen as a client without any protection against the Sybil attack. Basically, aMule accepts all incoming messages without any check: requests can be sent as fast as the client can handle them. There is no restriction regarding the KADID or the IP address of the sender. As long as the sender of a request matches a place left in a K-bucket, it can be added. With the KADID of the target and a good knowledge of the routing table mechanisms, it is possible to quickly take control of a legitimate peer.

Packet tracking and flood protection:

The packet tracking function records the history of recently received and sent packets (12 minutes). This history is used for two purposes. The first goal is to be able to detect and drop unsolicited request answers. The second purpose is to set up a protection against flooding.

With the history and time of previously received packets, it is possible to detect if an IP address is a source of flooding. For each type of KAD request, a threshold is defined per peer under which the number of received requests is considered legitimate. If the threshold is not highly exceeded, the packets over the limit are simply dropped. If the rate of received requests is more than five times above the limit, the sender is considered as an attacker and his IP address is banned from the client. Moreover, KAD contacts are only able to update themselves in other's routing tables if they provide the proper private key corresponding to the public key initially presented (supported by 0.49a+ nodes), in order to make it impossible to hijack them. Finally, contacts which fail the challenge are marked unverified and are not used for routing tasks. Theses protections avoid attacks using IPspoofing and contact overwriting. It is a response to the routing attack issues described in [START_REF] Chan-Tin | Attacking the kad network[END_REF] and one of the solutions proposed by the authors.

IP

Evaluation of the protection mechanisms

In this section we evaluate different KAD clients and the mechanisms described above when facing a Sybil attack.

Methodology

As the injection of Sybils is the basis for attacking the network, we measure how permeable the routing table of a single peer is regarding the different levels of protection, and how restricted in their are the Sybils when they pass the protections. To evaluate the behavior of the defense mechanisms, we developed a basic attack software with the initial objective of polluting the routing table of a single peer running an unprotected version of KAD client. We then incrementally added the protection mechanisms by evaluating newer versions of the client and modified our attack accordingly.

For some of our experiments, our Sybil attack does not target the entire network as the one in [START_REF] Steiner | Exploiting KAD: possible uses and misuses[END_REF] but only aims a single client. In fact, the protection mechanisms that we want to study are local to the client and do not require any interaction between peers. In consequence, the results obtained when evaluating a single client are sufficient and can be easily generalized as a good indicator of what the network will be in the future when most of them will be up to date.

Our attack announces Sybils by sending many Hello REQ with forged KA-DIDs. The main difficulty of this attack is to announce the right identity for each Sybils to match the algorithm filling the routing table of the target and as consequence, maximize the pollution. Designing the generation of Sybil identities requires knowledge of the structure and algorithms of KAD routing table.

Looking at the code of KAD, the real structure of its routing table is slightly different from the proper binary tree defined in Kademlia [START_REF] Maymounkov | Kademlia: A peer-to-peer information system based on the xor metric[END_REF]. First of all, all leafs can be split until level 4 without restriction, resulting in 16 K-Buckets covering the entire address space and used to route the farthest destinations. Then, at the level 4, the closest K-buckets with an index below 4 (which means that considering the 4 first bits: KADID XOR ContactID <= 4) can keep splitting until having an index of 8 or 9 by involving further bits as shown in figures 1. The depth of the routing table is not hardly limited but is limited de facto by the size of the network because fewer contacts are possible for deep buckets whose split becomes unlikely.

With this knowledge of the routing table and a targeted KADID, preparing the attack consists in generating a set of proper masks so that: targetID XOR Fig. 1. KAD routing table scheme mask = SybilID. The value of the masks are defined to generate SybilIDs progressively filling all the routing table of the targeted peer from the top to the bottom, by hitting the right K-bucket.

As we inject specifically forged contacts, they can hit deeper K-buckets in the routing table so that the size of the table under attack is higher than the size during a normal run. From the target point of view, the announcement of very close Sybils is considered as if the DHT space was more populated and consequently closer contacts easily findable.

Results

No protection: The first client attacked was aMule 2.1.3. This version is unprotected resulting to the realization of the simplest and most effective Sybil attack possible. Sybils KADIDs are forged as described previously and announced with a rate of 4 per second which is sufficient to populate the K-buckets faster that the normal algorithm without overloading the target client.

Actually, KAD contacts are periodically checked by sending an Hello REQ and waiting for the Hello RES to keep the routing table up to date. But this version also presents a kind of optimization that becomes a major design flaw when considering the Sybil attack. In fact, every Hello RES from an IP address (whatever its KADID is) acknowledges every contact with this IP address. As all Sybils share the same IP address, a single Hello RES aknowledges this IP address and is sufficient to keep hundreds of Sybils alive. Moreover, a peer can announce itself with a Hello RES instead of a Hello REQ, and still be added to the table. Following this discovery, our attack sends Hello RES so that each new Sybil acknowledges and maintains the previous ones in the routing table without any message exchange.

Fig. 3. Filling of the routing table under attack

The first results show that the routing table of the unprotected version is almost fully corrupted under attack (graph 2): at the end of an attack lasting 300s, the routing table of aMule counts 70% of Sybils (689 Sybils for 953 contacts). The major part of the routing table which is not polluted is made up of 200 good contacts saved from the previous execution and pre-loaded to bootstrap. Graph 3 shows at which speed the routing table of aMule is filled regarding if attacked or not. Even if the speed of Hello RES sent by the Sybils was moderate, we can clearly see the Sybil attack as the routing table abnormally grows under the announcements of Sybils. Theses results confirm the need for the following protection mechanisms.

Flooding protection:

The second experiment aims to evaluate the flood protection. So, we launched an attack against the eMule 0.49a client with the IP limitation disabled. To be successful, the attack had to be improved in two ways. First, the packet tracking used to implement the flood protection drops Hello RES without previous Hello REQ so that the weakness described above to maintain Sybils is not possible anymore. Therefore, we modified our attack to keep each Sybil alive by responding to the Hello REQ messages from the victim. The problem is that Hello REQ messages do not include the targeted KADID whereas Hello RES messages need it. A normal peer just has to manage its own KADID so that it clearly knows what to respond to a Hello REQ message. On the contrary, our Sybil attack manages multiple identities and does not know which KADID is addressed by the Hello REQ message. To bypass this limitation and find with which KADID to answer, each Sybil communicates on a different UDP port so that we can retrieve the wanted KADID. With this modified attack, we are able to maintain Sybils alive in the long run. Secondly, we sent Hello REQ messages every 30 seconds to be under the threshold.

Our experiments show that the flooding protection works as expected. The limitation rate before dropping Hello REQ is set to 3 packets per minute and above 15 packets per minute, our IP address is banned. The results are shown in graph 4. We can see that even if the attack is clearly slowed down, taking more than 8 hours to inject the same number of Sybils where previous attack only took few minutes, the routing table is still polluted with more than 60% of Sybils (540/873). The flooding limitation can protect the majority of short connections to the KAD network, but longer connections still suffer from a widely infected routing table. Adding IP limitation: Our previous attacks were performed from a computer using a single IP address. With IP limitation enabled, we effectively measure that only the first Sybil enters the routing table, the other KADIDs presenting the same IP address can not pass. To bypass this limitation, we modified our attack using raw sockets so that each Sybil is announced with its own randomly spoofed IP address. The graph 5 shows that Sybils with spoofed IP addresses totally break this protection. The first time we launched the attack to evaluate the IP limitation, we disabled the flooding protection. When activating both of them in a second time, we noticed that the flooding protection is also completely bypassed by the IP spoofing. In fact, the packet tracking used to detect flooding measures the number of incoming requests from a given IP address. When spoofing IP addresses, each message appears to be from a different source so that the flooding is not detected. Even if IP spoofing can not be used to spy or eclipse content in the network, spoofed IP addresses were used in [START_REF] Chan-Tin | Attacking the kad network[END_REF] with contact overwriting to partition the KAD network. This attack remains possible at this point, but the very last version of the clients implements a protection to mitigate both IP and KADID spoofing.

Adding identity verification: The attack launched to test the identity verification mechanisms is the same as the one described above, using Sybils with Fig. 6. Evolution of the contacts status in a normal run Fig. 7. Evolution of the contacts status under Sybil attack spoofed IP addresses. Part of the behavior of this last mechanism seems strange and disappointing because the Sybils that fail the three-way handshake are still added (at least temporary) to the routing table and marked as "unverified". The rate of unverified contacts is high even without attack during the first 15 minutes of connection (graph 6). Even if unverified contacts are not used for routing tasks, they can take the place of potentially good contacts in a K-bucket, resulting in a reduction of the routing efficiency for the peer. The positive aspects are that all Sybils are marked as unverified (graph 7) and that unverified contacts are dropped faster from the routing table than with the classical 1-hour timeout. Moreover, unverified contacts can not update themselves before being checked, so that Sybils with spoofed IP addresses really are active for only a limited time. As expected, we also experimented that KADID overwriting is from now on impossible without the proper private key and mitigates the attack described in [START_REF] Chan-Tin | Attacking the kad network[END_REF].

The results obtained with the very last version show significant improvements of the Sybil attack defense. As expected, IP address limitation coupled with identity verification avoids the Sybil attack from a single source when it previously would have been able to infect and spy or DoS the whole network.

Distributed eclipse attack

At this point, we have tested the resilience of the routing table to Sybils with the new protection mechanisms. But a massive Sybil attack is not the only and smartest way to damage the network. More localized Sybil attacks are possible and need fewer resources. The eclipse attack is another well-known issue of the KAD network as described in [START_REF] Steiner | Exploiting KAD: possible uses and misuses[END_REF]. It consists in placing few malicious peers very close to the target ID in the DHT and making them known. Prior to the attack, the authors used a "crawler" in a tolerance zone to know many contacts and promote their Sybils. As all requests toward the target will pass through this zone where the peers are polluted, and considering the KAD search algorithm "return the X closest nodes...", the requests will arrive at malicious nodes with a high probability.

More than the massive injection of Sybils, we think that the heart of the eclipse attack is the possibility to freely chose its KADID very close to a target which keeps being possible. As this issue is not yet handled in the last versions of KAD, the eclipse attack remains a threat even if the IP limitation now requires its distribution (involving several public IP addresses). We did a distributed eclipse attack with 24 nodes from PlanetLab and EmanicsLab1 . Our client is based on aMule 2.2.2, compiled to run as a daemon and modified in several points to make the attack. Our client uses a forged KADID to be very close (96 bits) to the hash of a given keyword. For this specific ID, our client spies the incoming requests and eclipses the keyword by answering to Publication requests and denying Search requests. To improve its efficiency, our client announces itself actively by periodically sending Kademlia routing and Hello requests toward predefined KADIDs in order to be known in the network and attract requests, as an alternative to a centralized crawler.

We first launched our attack on the keyword "the", known to be the most indexed keyword in the network. Despite a massive indexation of publish requests by our Sybils (16000 requests per minute), we cannot totally eclipse the keyword. So, we analysed the results obtained by a search request on "the" and we found out that all the answers came from the same IP address managing 256 KADIDs sharing 120bits with the keyword, but not denying any Search request. In other words, "the" was already the target of another classical Sybil attack, always possible as a large part of the network is not yet updated with the new clients. In a second time, we launched our attack on the keyword "document", receiving "only" 115 publish requests per minute but resulting in its total eclipse. Even if the needed bandwidth depends on the size of the attack and the popularity of the targeted ID, it keeps very small (few KB/s by node).

In conclusion, distributed and localized attacks do not require substantial resources and keep being a real threat despite the new mechanisms as long as the KADID can be freely chosen and the malicious nodes placed very close to a given target. Controlling a small botnet, or more generally some IP addresses distributed over multiple subnets, allows a malicious user to control several entries of KAD.

Conclusion

Considering the previous attacks and our evaluation of an old client, KAD was totally unprotected and very easily and badly hurt by a Sybil attack from a single computer. The local solution chosen by the authors of eMule fits the constraints of the network: no infrastructure cost and backward compatibility. The network is progressively being composed of new clients including the protections and becomming more robust. We have shown that the new defensive rules really make the Sybil attack harder to perform and successfuly mitigate the previously experimented attacks at a low cost. Where an attack could have been launched from a single computer few months ago [START_REF] Steiner | Exploiting KAD: possible uses and misuses[END_REF], similar results can only be achieved now with a botnet or a more complex distributed architecture.

Even if these security mechanisms are a step forward, they are not yet sufficient. We have shown that a distributed eclipse attack focused on a particular ID still remains possible with a moderate cost. This result shows that the main weakness of KAD has shifted to the possibility to reference many KADIDs with the same IP address to the left possibility to freely choose its KADID. Moreover, if we consider an attacker with many resources, particularly considering the number of IP addresses, the overall protection can be threatened due to the specific design using local rules. As all protections are local to the client, a same pool of IP addresses can potentially infect all peers. Considering this, an attacker with several hundreds of spaced IP addresses can massively infect the network (for example, if controlling a medium-sized Botnet) and realize large attacks on the network scale. Thus, the IP limitation as currently defined, seems to be a very short-lived protection mechanism when considering IPv6. A single personal broadband connection could be assigned with a /64 or even more, which is sufficient to launch massive Sybil attacks with one different public IPv6 address per Sybil. The rules concerning the IP address limitation will have to be adapted carefully in order not to become inefficient.

However, even if not perfect, the defenses against the Sybil attack studied in this paper are absolutely generic and can be easily applied to every structured P2P network. We think that this kind of "common-sense" protection based on self-management is the minimum that every implementation of a structured P2P network should have, unless being totally unaware of the Sybil attack issues. In our future work, we will design and evaluate new security mechanisms to mitigate the distributed eclipse attack. It is interesting to consider the impact of this attack on the routing table of KAD and on the indexing and search processes. Being given the existing security rules of the indexing scheme, evaluating the remaining weaknesses will lead us to design new constraints improving the local protection.

Fig. 2 .

 2 Fig. 2. Propagation of Sybils in the routing table

Fig. 4 .Fig. 5 .

 45 Fig. 4. Propagation of Sybils in the routing table with flood protection enabled

Table 1

 1 sums up the protections implemented in each of the clients.

	Clients	Flood protection IP limitation IP verification
	eMule 0.48a / aMule 2.1.3	No	No	No
	eMule 0.49a / aMule 2.2.1	Yes	Yes	No
	eMule 0.49b / aMule 2.2.2	Yes	Yes	Yes

Table 1 .

 1 Protection enabled according to the client version

Table 2 .

 2 address limitation: The IP address limitation tries to mitigate the Sybil attack, considering that public IP addresses are more or less restricted per participant. Before adding a new peer in the routing table, its IP address is checked and dropped if it is already used. This verification limits to one the number of KADID per IP address in the routing table. This really helps protecting a client against a Sybil attack which needs a lot of public IP addresses to be significant. The IP address limitation also takes care of IP addresses from the same /24 subnetwork or smaller. In fact, at most ten IP addresses from the same /24 subnetwork can be added to the routing table to prevent a single entity with many resources to be able to launch an attack. These ten peers are also constrained to be in different K-buckets of the routing table, or in other words to have spaced KADIDs. This is done to prevent the entity owning a /24 subnet to launch a localized attack which needs to have Sybils very close to the target ID. This pro-Three-way handshake is achieved differently regarding the client version

	Clients	Sequence	Nb of messages Encryption
	eMule 0.48a	Hello REQ -Hello RES -	4	No
		Hello REQ(challenge) -Hello RES(challenge)
	eMule 0.49a Hello REQ -Hello RES -PING -PONG	4	Yes
	eMule 0.49b Hello REQ -Hello RES -Hello RES ACK	3	Yes

tection does not affect NATed users which can fully participate to the network with the very unlikely constraint that two NATed peers with the same public IP address can not be referenced in the same routing table of another contact.

Identities verification:

The last KAD clients implement even more protections concerning identity management. They aim to limit the identity spoofing (both IP address and KADID) between peers. Before adding a contact, KAD now uses a three-way handshake for new contacts, making sure they do not use a spoofed IP. Older version are verified with a similar check as presented in table 2. Oldest clients are checked with a second Hello REQ -Hello RES exchange including a random KADID as a challenge for the responding peer. Newer clients use an exchange of PING and PONG messages which add cryptographic identification. Finally, the last versions do the three-way handshake in the most effective way with the specially added new message Hello RES ACK.

EmanicsLab is an autonomous testbed network based on PlanetLab architecture and sponsored by the European Network of Excellence EMANICS

Acknowledgment: This paper was partially supported by the French Ministry of Research project, MAPE, under contract ANR-07-TLCOM-24 and by the EC IST-EMANICS Network of Excellence (#26854).


Gilles Burel
email: gilles.burel@univ-brest.fr

André Quinquis
email: andre.quinquis@ensieta.fr

Stéphane Azou
email: stephane.azou@univ-brest.fr

Interception and Furtivity of Digital Transmissions

Keywords: Digital transmissions, Interception, Time-frequency analysis, Furtivity, Chaos, Spectrum surveillance, Spread spectrum, Unscented Kalman filters

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I. Introduction

The proliferation of high performance digital transmission devices has enhanced the role of collecting and securing information in order to provide intelligence on the enemy's intentions and capabilities without revealing one's own intentions. The modern concept is that interception and furtivity of transmissions is an important part of an overall military strategy which concentrates on collecting information through interception of enemy communications while maintaining the capability of discretely operating one's own data transmissions.

However, these considerations are not restricted to the military domain. Indeed, the development of wireless transmissions (e.g. wireless indoor domestic networks or cellular telephones) points out the need of mastering interception techniques (to protect transmissions, or for spectrum surveillance) as well as the need of research on furtive and secure transmissions.

In this paper, we present an overview of some researches about interception and furtivity of transmissions developed in our laboratory.

In Section 2, we show how modern mathematical tools such as time-frequency analysis, can be adapted for the detection and analysis of classical narrow band digital transmissions. Experimental results show that a high attenuation of interferences can be obtained, thus enhancing discrimination capabilities.

However, digital transmissions are not always narrow-band. Indeed, a technique that is often used to hide transmissions in noise is spread spectrum. In Section 3, we show that spread spectrum signals can be detected and demodulated in a non cooperative context, even at a very low signal to noise ratio. Once demodulated, the spread spectrum signal becomes narrow-band, and techniques presented in Section 2 can be used for further analysis.

Introduction

Nowadays digitally modulated signals such as ASK (Amplitude Shift Keying), PSK (Phase Shift Keying) among others are very important for telecommunications systems. Such signals can be found in many civilian as well as military applications such as: interference identification and spectrum management, identification of non-licensed transmitters, electronic warfare, surveillance and threat analysis, control of communication quality, etc.

In COMmunication INTelligence (COMINT) applications, the modulation types are considered as signal signatures. Therefore, the modulation recognition is an essential key to demodulate as well as to decode and understand the transmitted message.

In the last two decades, many researchers have been interested by automatic recognition and identification algorithms for communication signal. In fact, since 1990, many algorithms have been proposed [START_REF] Azzouz | Automatic Modulation Recognition of Communication Signals[END_REF]. The main differences among these algorithms are their sensitivity to Signal to Noise Ratio (SNR), the type of modulation that they can deal with, and the applications where they can be used.

Generally, modulation algorithms consist of various steps depending on the field of interest. First of all, if we are only interested in modulation types, a simple modulation classifier can deal with this case. Once the modulation type has been classified, one may seek other features for signal identification purpose. For example, one can seek for a state number, a symbol duration among others.

To distinguish the different versions of modulation, algorithms often enclose the computation of state number. For instance, many studies aim at distinguishing the different MPSK or the different MFSK versions [START_REF] Polydoros | On the Detection and Classification of Quadrature Digital Modulations in Broad-band Noise[END_REF]. With regard to the symbol duration, we can quote the methods based on the level crossing, the derivation or a wavelet transform, for example. On the other hand, it seems that the carrier frequency is a main feature in many applications.

Most of the Frequency-domain estimation methods are based on the signal spectrum. The performances of such methods depend on the estimation techniques (Welch, …) and the estimation window (such as Hamming, Hanning, …). Indeed, the experimental studies show that this technique is sensitive to noise. To increase the robustness of the approach, new methods based on recent developments are possible.

Time frequency distributions (TFD)

Most TFDs of current interest are members of Cohen's bilinear class which can be generated by Fourier transformation of a weighted version of the ambiguity function (AF) of the signal to be analyzed. That is, if TFR(t,f) is a bilinear TFD of the signal x(t), then with A( ,F) the ambiguity function of the signal:

) 1 ( 2 , , , fdF d Ft f j e F F A f t TFR
If ( ,F)=1 we obtain the classical Wigner-Ville distribution (WVD). Different choices of the kernel function are possible to obtain many TFDs. In recent years, it has become apparent that no single kernel can give adequate performance for a large class of signals; hence, there has been increasing interest in signal-dependent or adaptive TFRs (ATFRs). It was proposed [START_REF] Baraniuk | A signal-dependent time-frequency representation: Optimal kernel design[END_REF] an ATFR based on kernels with Gaussian radial cross sections: The function ( ) controls the spread of the Gaussian at radial angle ; we will call ( ) the spread function. The angle is measured between the radial line through the point ( ,f) and the axis:

f arctan .
A high quality time-frequency representation results when the kernel is well matched to the component of a given signal. The radial Gaussian kernel is adapted to a signal by solving the following optimization problem: By focusing the volume under the optimal kernel, the parameter controls the tradeoff between interference suppression and smearing of the auto-components.

The shape of a radial Gaussian kernel is completely parameterized by the spread function; so, finding the optimal kernel opt for a signal is equivalent to find the optimal function opt ( ) for the signal. The algorithm includes four stages (Fig. 1)

Fig. 1 -Adaptive time-frequency representation algorithm

In the first stage, the AF of the signal is computed. In the second stage the optimization problem is solved for the optimal kernel. Next, we compute the product between AF of the signal x and opt obtained as result of the second stage. Finally, we compute the bidimensional Fast Fourier Transform (FFT2D) in order to obtain the adaptive time-frequency distribution of the signal x.

This distribution has many attractive qualities; the most important (in this context) is the time-frequency interference suppression. So, we may imagine many applications, such as the time-frequency signal analysis or the signal classification using the most adapted kernel function as a discriminative element.

The limitation of this method is that it designs only one kernel for the entire signal. So, for signals with characteristics that change over time, it is necessary to use a procedure that

) 2 ( 2 2 2 * , dt Ft j e t x t x F A ATFR x AF 0 -kernel volume control opt AF x Signal x Computing AF Computing opt 2 0 0 2 , , max rdrd r r A 2 0 2 2 4 1 d Computing AF x ( ,f)* opt ( ,f) Computing FFT2D(AF 0 ) Legend = 1-D data = 2-D data
adapts the kernel each time in order to achieve optimal local performance. Moreover, the choice of the parameter is another problem that appears in practice.

To obtain the optimal local performances, we apply this procedure on short slide window over the signal. That is, we adapt the kernel for all the sequences obtained by windowing. Let us name this new transformation as «Short ATFR». Furthermore, we prefer the use of this transform, because it is well adapted for real-time problem.

Comparative results

In order to compare the presented method with the classical TFRs we consider an FSK signal (Frequency Shift Keying) with eight frequency steps, presented in figure 2. We show also his ideal time-frequency distribution.

In figure 3, we show the results obtained by applying the described time-frequency distributions and we observe the superior performance of the ATFR. The SPWVD (Fig. 3.a) precludes some interference terms, but affects the time-frequency support which is not well conserved. Another problem with this distribution is the choice of the smoothing windows, that is hard in practice. Moreover, between atoms 3 and 4, respectively 5 and 6 strong interference terms appear. The same comment can be formulated when using CWD (Fig.

Fig. 2: FSK signal and its ideal time-frequency representation

Fig. 3 -Comparison of time-frequency distributions. From left to right and top to bottom: (a) Smoothed pseudo Wigner-Ville distribution with g window width 33 and h window width123; (b) Choi Williams distribution with smoothing parameter =3.5; (c) ATFR with =2; (d) Short ATFR of volume =25 and window width 32

The results obtained by the ATFR use denote the quality of this transformation: ATFR precludes almost all interferences and better preserves the time-frequency support (Fig. 3.c). Ideally, a TFR should have the same nonzero support, i.e., duration and bandwidth, as the signal under analysis. These properties state that if a signal starts at time t 1 (and at a frequency f 1 ) and stops at time t 2 (and frequency f 2 ), then an ideal TFR should start and stop at the same time-frequency point. These properties ensure the fidelity of the signal approximation in the time-frequency plane. Furthermore, we can accurately estimate the signal characteristics.

In order to evaluate the support conservation capability of the TFR, a set of quality parameters is introduced : 1) Degree of time support conservation (DTSC): this parameter is defined for a certain timefrequency atom and represents the time support of this atom. We prefer to use the DTSC normalized at the support of entire signal. That is :

T dt TSCn D
where dt is the temporal support and T is the number of samples of the signal. 2) Degree of frequency support conservation (DFSC): this parameter is defined as the frequency support of a time-frequency atom; we prefer to use the DFSC normalized at the sampling frequency (F s ). where E u is the energy of auto-terms and E i the energy of interference terms. In the ideal case, this factor must be .

Table 1 shows the obtained parameters for each transformation, as well as their ideal values. We observe the high performances of the short ATFR, provided by the kernel adaptation over time. In figure 3.d we demonstrate the superiority of Short ATFR facing ATFR (that computes a single kernel for the entire signal).

Table 1 -Time-frequency distribution performances

We observe the superior performances of the ATFR facing classical interference terms suppression methods, but its quality is poorer than the short ATFR; this result illustrates the benefits of the kernel time adaptivity.

Conclusion

The novel approach precludes almost all the interference terms and, simultaneously, better keeps the time and frequency resolution. There are two major drawbacks: first, the choice of the kernel volume parameter is sometimes difficult to do and supposes more knowledge about the signal spreading in time and frequency. On the other hand, the adaptive Gaussian kernel designed in the ambiguity plane works only with signals having multiple components of the same nature.

Furthermore, we can improve the performances of this approach using the locally kernel design. Our future work will be devoted to this, by experimenting the time-frequency distributions using adaptive signal expansion for the linear modulations, and using the warping operators for the non-linear ones.

Introduction

Spread spectrum signals have been used for secure communications for several decades. Nowadays, they are also widely used outside the military domain, especially in Code Division Multiple Access (CDMA) systems [START_REF] Magill | Spread-Spectrum Technology for Commercial Applications[END_REF]. Due to their low probability of interception, these signals increase the difficulty of spectrum surveillance.

Direct-Sequence Spread Spectrum transmitters (DS-SS) use a periodical pseudorandom sequence to modulate the baseband signal before transmission. In the context of spectrum surveillance, the pseudo-random sequence used by the transmitter is unknown (as well as other transmitter parameters such as duration of the sequence, symbol frequency and carrier frequency). Hence, in this context, a DS-SS transmission is very difficult to detect and demodulate, because it is often below the noise level.

The research work developed in our laboratory aims at: 1. detecting the presence of a spread spectrum transmission in a non-cooperative context 2. then, estimating the transmitter parameters (including its spreading sequence).

Once the spreading sequence has been estimated, a classical spread-spectrum receiver can demodulate the signal.

Blind detection of a spread spectrum transmission

In a DS-SS transmission, the symbols a k are multiplied by a pseudo-random sequence which spreads the bandwidth. At the output of the receiver filter, the downconverted signal is:

) ( ) ( ) ( ) ( ) ( t n kT t h a t n t s t y s k k
where s(t) is the spread-spectrum signal (variance 2 s ), n(t) is the noise (variance 2 n ), and h(t) stands for the spreading waveform (more precisely, it is the convolution of the pseudo-random sequence with the transmission filters and the channel).

In a cooperative context, the pseudo-random sequence, as well as the carrier and symbol frequencies, are known by the receiver. The receiver correlates the received signal with the pseudo-random sequence, in order to retrieve the symbols. In a non-cooperative context, these parameters are unknown. Furthermore, classical second order detection methods are useless, because the autocorrelation function of a DS-SS signal is similar to the autocorrelation of a white noise. The method we have developed for blind detection of a DS-SS transmission hidden under the noise level is based on fluctuations of correlation estimators [START_REF] Burel | Detection of Spread Spectrum Transmissions using fluctuations of correlation estimators[END_REF]. The received signal is divided into non-overlapping windows of duration T (the exact value of T does not matter; ideally, the window should contain a few symbols, but the methods works over a large range of values). Within each window, we compute an estimation of the correlation:

dt t y t y T R T m yy ) ( ) ( 1 ) ( ˆ* 0 ) (
where m is the window's index. Using M windows, we can estimate the second order moment of the estimated autocorrelations:

M m m yy R M 1 2 ) ( ) ( 1 ) (
This is a measure of the fluctuations of the autocorrelation estimator.

If no signal is hidden in the noise (i.e. y(t)=n(t) ), we can predict the average value and standard deviation of the fluctuation curve ( ). For simplicity, let us consider the case of a receiver filter with flat frequency response in [-W/2, +W/2] and zero outside. In that case, we can prove [START_REF] Burel | Detection of Spread Spectrum Transmissions using fluctuations of correlation estimators[END_REF] that the theoretical average value and standard deviation of the fluctuations are: . If a signal is hidden in the noise, we can prove that its contribution to the fluctuation curve is negligible, except for values of which are multiples of the symbol period. In this later case, the average value of its contribution is:

4 ) ( s s s T T m
Then the ratio between the mean value of the peaks created by the DS-SS signal (if there is one such signal hidden in the noise), and the standard deviation of the fluctuations due to the noise is: The reader must not be surprised to see a ratio between a mean and a standard deviation: indeed, it is this ratio which is significant to determine if the peaks due to the DS-SS signal may be hidden by the fluctuations due to the noise (see the display below). This equation shows that the performances of our method can always be improved by increasing the number of windows M (at the expense of longer computation time). Figure 4 shows an example of the detector output. The curve represents ( ) (i.e. the fluctuations of the correlation estimator), as a function of (in s). The two horizontal lines show

Fig. 4 -Example of detector output

We can clearly see that peaks are present, and that they go far above the theoretical upper bound. Hence, there is no doubt that a spread spectrum signal is hidden in the noise. Indeed, there was, here, a signal hidden 8dB below the noise level. Furthermore, the distance between the peaks provides an estimation of the symbol period Ts.

Blind estimation of the spreading sequence

Once a spread spectrum transmission is detected, the problem is to estimate the spreading sequence. The method we have developed is based on eigenanalysis techniques. The received signal is divided into temporal windows, the size of which is the symbol period (this period has been estimated from the distance between the peaks on the fluctuations curve). Each window provides a vector which feeds the eigenanalysis module. Let us carefully examine the structure of the signal (Fig. 5). Since the window duration is equal to the symbol period, a window always contains the end of a symbol (for a duration T s -t 0 ), followed by the beginning of the next symbol (for a duration t 0 ), where t 0 is an unknown desynchronization. Hence, the presence of the signal will contribute to align the subspace spanned by the first and second eigenvectors with the subspace spanned by vectors 0 h and 1 h shown on figure 6.

One method [START_REF] Burel | Blind estimation of the pseudo-random sequence of a directsequence spread spectrum signal[END_REF] consists in trying to identify these vectors from the subspace: the sequence can be reconstructed from the two first eigenvectors, and that useful information, such as the desynchronization time, can be extracted from the eigenvalues. Another, slower, but more robust method [START_REF] Bouder | A robust synchronisation procedure for blind estimation of the symbol period and the timing offset in spread spectrum transmissions[END_REF], consists in first performing a blind synchronization (the criteria is maximization of the first eigenvalue), and then estimating the spreading sequence from the first eigenvector. Experimental results show that the method can provide a good estimation, even when the received signal is far below the noise level. Fig. 7 shows the estimated and true sequences. It is clear that the binary sequence can be recovered from the sign of the estimation. Here, the signal was hidden 8dB below the noise.

IV. Furtive transmissions based on chaotic signals

Since the results of Pecora and Caroll [START_REF] Pecora | Synchronization in chaotic systems[END_REF] about the synchronization capabilities of chaotic systems, there has been tremendous interest worldwide in the possibilities of exploiting chaos in communication systems. Due to its random-like behavior and its wideband characteristics, a chaotic dynamical system can be very helpful for discretion purposes. Chaos not only spreads the spectrum of the information signal but also acts as an encryption key. Thus, without knowledge of the type of nonlinearity on which the transmission is based (the chaotic dynamic), it will be extremely difficult for the unauthorized user to access the information. Furthermore, such signals are potentially robust against channel imperfections such as multipath propagation or jamming. As a result of their sensitive dependence on initial conditions, chaotic systems are able to produce large sets of uncorrelated signals. This extreme sensitivity can be demonstrated by giving two very close initial states to a chaotic map ; After a few iterations, the two resulting sequences will look completely decorrelated. This can be observed even for very simple (one-dimensional discrete-time) chaotic dynamical systems. The large signal set generated is an attractive feature in a multiple access transmission context. Another advantage of a chaos-based communication system is a less complicated circuitry in comparison with conventional spread spectrum approaches. Consequently, the weight and volume requirements of the devices are reduced and efficiency is increased. It may be possible to put a complete transmitter or receiver on one small chip.

Currently, most of the previously mentioned advantages are only projected advantages, as noted in [START_REF]Towards a new digital communication technology based on nonlinear dynamics and chaos[END_REF]. Nevertheless, the spectacular success of the recent research on communications with chaos is strong evidence that future nonlinear devices will actually have many of these advantages.

Methods for chaos-based digital communications

Many different chaotic modulations have been proposed since the work of Pecora and Caroll. These techniques may be classified into the following main families : Chaos Shift Keying (CSK), Differential CSK (DCSK), Chaotic Masking, Direct-Sequence/Frequency Hopping Spread Spectrum, Predictive Control and Chaotic Pulse Position Modulation. Some of these methods are overviewed in [START_REF] Hasler | Synchronization of chaotic systems and transmission of information[END_REF] [START_REF] Hasler | Communications using chaos, Int. Conf. On Signals & Electron. Syst[END_REF]. A detailed explanation is available in [START_REF] Serbanescu | Communicatii de Bande Larga folosind Sisteme Dinamice Haotice[END_REF].

In a chaos-based digital communication system, the information to be transmitted is mapped to chaotic waveforms. As in conventional communication schemes, the transmitted symbols are recognized at the receiver using either coherent or noncoherent demodulation techniques. The first solution is based on a chaotic synchronization process, in order to recover the original chaotic signal from the noisy received signal. To do so, a precise knowledge about the transmitter is required, including its chaotic dynamic. Conversely, a noncoherent demodulator relies on statistical properties of the received signal only. Such an approach has the advantage of robustness against channel imperfections (noise, multipath, Doppler) but it is not particularly suited for discretion purposes, as a limited knowledge about the transmitter is sufficient to recover the data symbols.

As demonstrated in [START_REF] Pecora | Synchronization in chaotic systems[END_REF], in the noise-free case, two coupled identical chaotic systems (the master and the slave) are able to synchronize, that is the slave will asymptotically reproduce the driving signal, for arbitrary initial conditions. However, in practice, we have to cope with disturbed channels or parameter mismatch between chaotic oscillators. As a consequence, a perfect synchronization becomes impossible and even a rough approximation of the original signal is not that easy. Moreover, the synchronization is lost and recovered (partially) every time the transmitted symbol is changed.

Usually, a low signal-to-noise ratio is a necessary condition to secure the transmission. For practical applications, the modulation scheme and especially the chaotic synchronization method have to be chosen carefully to avoid severe performance degradations in this context. We believe that chaotic Direct-Sequence Spread Spectrum (DS-SS) [START_REF] Heidari-Bateni | A chaotic direct-sequence spread spectrum system[END_REF] or Chaotic Pulse Position Modulation (CPPM) [START_REF] Sushchik | Chaotic Pulse Position Modulation : A robust method of communicating with chaos[END_REF] are very promising methods to succeed in getting competitive well secured digital communication systems. These two approaches allow multiple users to operate simultaneously in time over the same frequency band by using chaotic codes (Code Division Multiple Access).

Chaotic Direct Sequence Spread Spectrum transmission system

A Chaotic DS-SS (CD3S) transmitter has a structure similar to that encountered in a standard DS-SS transmitter. The only difference is that the pseudo-noise (PN) code is replaced with a chaotic code. Hence, each data symbol is multiplied by a different portion of the spreading code, due to its aperiodicity. A possible structure for a CD3S transmitter is illustrated by figure 8. Here, chaotic markers, whose length is identical to the processing gain (number of chips of the spreading sequence per data symbol), are regularly inserted in order to synchronize the receiver. The wideband chaotic signal is then upsampled and a shaping filter is applied before modulating a sinusoidal carrier.

Fig. 8-Block diagram of a Chaotic DS-SS transmitter

A recent study carried out in our laboratory, about communicating with a CD3S system underwater [START_REF] Azou | A chaotic direct sequence spread-spectrum system for underwater communication[END_REF], have led to encouraging results. Two demodulators currently under investigation are described below.

Master-Slave CD3S demodulator (Fig. 9): Though very basic, this kind of demodulation, initially proposed by Milanovic et al. [START_REF] Milanovic | Combating noise and other channel distortions in chaotic communications[END_REF], performs well if the spreading chaotic map is properly selected (favorable correlation properties). Here, the original spreading code is estimated owing to a master-slave coupling. Then, symbol decision is just given as the sign of the output of a correlator, operating over symbol duration. Figure 11 shows the Bit Error Rate performance of this demodulator on an Additive White Gaussian Noise (AWGN) channel.

Dual Unscented Kalman Filtering (UKF) CD3S demodulator (Fig. 10): This original scheme, detailed in [START_REF] Azou | Design of a chaos-based spread-spectrum communication system using dual Unscented Kalman Filters[END_REF], uses recent results on state space adaptive filtering [START_REF] Julier | A new method for the nonlinear transformation of means and covariances in filters and estimators[END_REF] to achieve the chaotic synchronization. A dual estimation algorithm is implemented to track simultaneously the state of the received chaotic signal and the corresponding dynamic model (the symbol is an unknown parameter of the dynamic model). Symbol decision is made according to the sign of the averaged output of the second filter over symbol duration. Figure 12 illustrates BER performance of this scheme on AWGN channel.

V. Conclusion

In this paper, we have shown that adaptation of modern mathematical tools, such as time-frequency analysis, statistical analysis of fluctuations, unscented Kalman filters, offer promising results, both on the interception and furtivity aspects. While research about these aspects is still mainly confined to the military domain, it is likely to play an increasing role in the civilian domain in a near future, due to the high demand for privacy of communications, as well as to the need of efficient regulation and control.

  3.b).Even if CWD uses a kernel with Gaussian shape (like ATFR), the results are unwell, because this kernel has a fixed position in the ambiguity plane, unadapted to the signal.

3 )

 3 Interferences attenuation factor (IAF): this parameter represents a quality measure of the interference time-frequency suppression, defined by

  no signal is hidden in the noise, the curve ( ) should remain around

  predicted average value of the fluctuation if noise only were present) and

  (tau) moy. theorique (bruit seul) max. theorique (bruit seul)

Fig. 5 - 6 -

 56 Fig. 5 -Structure of the signal Fig. 6 -Generating vectors

Fig. 7 -

 7 Fig. 7 -Estimated spreading waveform (top) and true spreading sequence (bottom)

Fig. 9 -Fig. 10 -Fig. 11 -Fig. 12 -

 9101112 Fig. 9 -Block diagram of the Master-Slave CD3S demodulator


domain: sdv sde

text:
Nathalie Cheviron
email: nathalie.cheviron@versailles.inra.fr

Virginie Grondin

Sylvie Nelieu

Olivier Crouzet

Mickael Hedde

Christian Mougin
email: christian.mougin@versailles.inra.fr

Mickael Hedde

La

Grondin Virginie

Nélieu Sylvie

Mickaël Hedde

Mougin Christian

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