Magnetic behaviour of the new hydride CePtAlH x

CePtAl absorbs hydrogen up to a concentration of 1.1(1)H mol -1 at room temperature. The formation of this hydride CePtAlH 1.1 that loses hydrogen in air corresponds to a plateau pressure of 0.08-0.1 MPa. Its absorption-desorption is practically reversible which can present a potential interest for applications (but only a few due to the high price of the material) around room temperature and normal pressure. Hydrogenation of CePtAl induces both: (i) a structural transition but the structure of the hydride is unknown at present; (ii) an increase of its ferromagnetic character; the hydride has a Curie temperature T c =11.6(2) K twice greater than that determined for the initial intermetallic (i.e. 5.6(2) K).

Introduction

Recently, we have shown that the hydrogenation of the CeNiAl compound induces both a structural transition from the hexagonal ZrNiAl-type to the hexagonal AlB 2 -type for the hydride CeNiAlH 1.93 and a valence transition for cerium from tetravalent to trivalent state [1]. The hydrogenation of CeNiAl leads to an expansion of its molar volume favouring the occurrence of spin fluctuation behaviour below 7 K for the hydride. Encouraged by this interesting result, we are now studying the hydrogen absorption-desorption properties of the equiatomic CePtAl compound. This ternary aluminide crystallises in the orthorhombic TiNiSi-type structure where Ce-atoms form a network of chains parallel to the a-axis [2]. Neutron powder diffraction experiments performed on CePtAl reveal a complex magnetic phase diagram: three successive transitions are detected respectively at T c =5.9 K, T 2 =4.3 K and T 3 =2.2 K [3]. But this study shows that the magnetism of CePtAl is dominated by a ferromagnetic component 1.35(4) μ B at 1.5 K of the ordered Ce-moment. This original behaviour results from the existence of a large magnetic anisotropy caused by competition between magnetic exchange interactions existing respectively in the Ce-Ce chains and between themselves [4]. Moreover, specific heat measurements suggest that the reduction of the ordered Ce-moment found in CePtAl can be explained by the existence of the Kondo effect [5]. The magnetic and Kondo interactions are governed by the Ce-Ce interatomic distances (d Ce-Ce ); in this view it is interesting to modify these distances for instance by insertion of hydrogen in the lattice.

In this paper, we report on the synthesis of the hydride CePtAlH x and on its characterisation using X-ray powder diffraction and magnetization measurement.

Experimental details

CePtAl sample was prepared by arc-melting stoichiometric amounts of pure elements (3N for Ce, 3N5 for Pt and 5N for Al) under a protective Ar-atmosphere followed by an annealing treatment under vacuum at 1073 K for 1 month. Its characterisation by electron microprobe analysis reveals a perfect chemical homogeneity. Its checking by X-ray powder diffraction (Philips PW 1050 diffractometer, Cu-Kα radiation) confirms that CePtAl crystallises in the orthorhombic TiNiSi-type with unit cell parameters a=0.7208(5) nm, b=0.4481 (5) nm and c=0.7740 (5) nm in agreement with those reported previously [2]. Hydrogen absorption-desorption measurements were performed using the apparatus described previously [6]. CePtAl sample was crushed (grain size ≤100 μm), and then exposed to hydrogen gas. The amount of H-atom absorbed was determined volumetrically by monitoring pressure changes in a calibrated volume. Magnetization measurements were performed using a Superconducting Quantum Interference Device (SQUID) magnetometer in the temperature range 1.8-300 K and applied fields up to 5 T.

Without any thermal activation treatment, CePtAl absorbs hydrogen at room temperature. Its hydrogen absorptiondesorption capacities are strongly dependent to the number of hydriding-dehydriding cycles (Fig. 1): (i) at the initial cycle n=1, CePtAl starts to absorb hydrogen at a pressure of 0.8 MPa; (ii) for the second one, the amount of H-atom absorbed varies almost linearly with the hydrogen pressure; (iii) finally, one can observe that the sample is successfully activated after three hydriding-dehydriding cycles. At 295 K, CePtAl absorbs hydrogen up to a concentration of 1.1(1) H mol -1 under a pressure of 1.1 MPa (Fig. 2). The plateau pressure at this temperature in the range 0.08-0.1 MPa corresponds to the formation of the hydride CePtAlH 1.1(1) that loses hydrogen in air (as reported on Fig. 3). Its absorption-desorption is practically reversible. Pressure-composition-temperature (PCT) curves realized at various temperatures for CePtAl are presented on Fig. 2. For this study, the sample was hydrided-dehydrided three times before the shown experiments were carried out; so these results are expected to represent the thermodynamically stable state. It appears clearly that the increase of temperature induces a significant decrease of the hydrogen content of the CePtAlH x hydride (x≅0.9(1) at 373 K) and increase of the plateau pressure. The rather large plateau slope observed at 373 K can be attributed to sample temperature inhomogeneities. The thermodynamic data calculated according to the Van't Hoff equation are ∆H=-24 kJ mol -1 and ∆S=180 J mol

-1 K -1 .
The X-ray powder pattern of CePtAl, given in Fig. 3, is completely indexed on the basis of the orthorhombic TiNiSitype structure. On the contrary the pattern relative to CePtAlH 1.1 hydride, characterising a well-crystallised material, clearly shows that hydrogenation leads to a structural transition (Fig. 3). This last structure is unknown at present but under study using transmission electron microscopy. After exposure in air for 5 days at room temperature, the hydride CePtAlH 1.1 is partially decomposed; X-ray diffraction analysis reveals the occurrence of a mixture containing CePtAl and CePtAlH 1.1 (Fig. 3). For instance, the diffraction peaks (111) and (103) relative to CePtAl compound are clearly observed after the exposure. This result agrees with the low dissociation pressure ≅0.1 MPa at 295 K (Fig. 2) of this hydride. After desorption (0.05 MPa for 1 h) the X-ray diffraction analysis reveals the occurrence of a single phase which is similar to CePtAl (as expected). Magnetization measurements were performed on the hydride CePtAlH 1.1 powder enclosed in epoxy resin in order to prevent the hydrogen loss. Above 70 K, the reciprocal magnetic susceptibility χ m -1 of this hydride follows a Curie-Weiss law χ m -1 =(T-θ p )/C m having as Curie constant C m =0.65 emu mol -1 and a large and negative paramagnetic Curie temperature θ p =-44 K. The effective magnetic moment μ eff. =(8C m ) 1/2 =2.3 μ B /Ce-atom is smaller than that calculated for free Ce 3+ ion (2.54 μ B ). Similar investigation performed on CePtAl (before any treatment or even after hydrogen desorption) and gives μ eff. =2.51 μ B /Ce-atom and θ p =-37 K. The temperature dependence below 17 K of the magnetization of CePtAl and CePtAlH 1.1 is shown in Fig. 4. The curve obtained for CePtAl is similar to that observed previously by Kitazawa et al. [5]; the curve exhibits a strong increase at T c =5.8(2) K. A similar behaviour is observed at T c =11.6(2) K for CePtAlH 1.1 hydride. In other words, the hydride has a Curie temperature twice greater than that determined for CePtAl. This fact is confirmed by the curves showing at low temperatures, the field dependence of the magnetization (Fig. 5); these are typical for a ferro-or ferrimagnetic material. At 4 K, the remanence is 0.15 μ B mol -1 and the magnetization takes a low value of 0.5 μ B mol -1 in applied field B=3.5 T. This last value is weak compared to that expected g J J=2.14 μ B mol -1 for Ce 3+ ion which suggests that the magnetic ordering of CePtAlH 1.1 is not purely ferromagnetic.

Conclusion

In conclusion, our study shows that CePtAl absorbs and desorbs hydrogen reversibly at 295 K. This presents a potential interest for application around ambient temperature and pressure. The insertion of hydrogen induces both a structural transition and a strong increase of its ferro (ferri)magnetic character.


J F Wu

E Sicard

A Boyer

S Ben Dhia

J C Li

R J Shen

Enhancing accuracy of low-dropout regulator susceptibility extraction with on-chip sensors

Presented is a new test method that consists in monitoring on-chip internal voltages during susceptibility tests of integrated circuits. An on-chip sensor was installed at several internal nodes within lowdropout regulators to measure the distortion of internal signals induced by the coupling of electromagnetic interference. The comparison between external and internal measurement results shows that onchip sensor techniques enhance the extraction of circuit susceptibility levels, especially at high frequencies.

Introduction: Owing to the increasing complexity of electromagnetic environments, concerns about the susceptibility of low-dropout (LDO) regulators are becoming ever more important, especially in critical embedded electronic systems for automotive or aerospace applications [START_REF] Ben Dhia | Electromagnetic compatibility of integrated circuits: techniques for low emission and susceptibility[END_REF], the performances of which are directly linked to power supply voltage integrity. Recently, various papers have described the failure mechanisms of LDO regulators under conducted electromagnetic interference (EMI), linked to operational amplifiers (opamps) [START_REF] Fiori | Linear voltage regulator susceptibility to conducted EMI[END_REF] or bandgap cells [START_REF] Orietti | Reducing the EMI susceptibility of a Kuijk bandgap[END_REF]. In these papers, measurements of susceptibility were performed with external tools, such as oscilloscopes and power meters. This Letter proposes the use of on-chip measurement methods described in [START_REF] Vrignon | On-chip sampling sensors for high frequency signals measurement: evolution and improvements[END_REF], which give more efficient results by avoiding the effects of parasitic capacitors and inductors associated with bonding, package leads, printed circuit boards (PCBs) and measurement probes that filter the actual phenomena. This Letter presents a study of the conducted susceptibility of an integrated LDO regulator module. The comparison between external and internal measurements shows differences that indicate that only on-chip sensors are able to measure the actual susceptibility level.

Description of test chip and DPI measurement setup:

The LDO regulator under test is part of a test chip designed using the Freescale CMOS 90 nm process. Its purpose was to provide a regulated power supply voltage to a small digital core. The most prominent feature of the chip is the presence of on-chip voltage sensors on several internal nodes, working as frequency aliasing sub-samplers [START_REF] Vrignon | On-chip sampling sensors for high frequency signals measurement: evolution and improvements[END_REF]. High-frequency signals can be measured (up to 10 GHz) with relaxed constraints on hardware bandwidth requirements.

Fig. 1 shows the structure of the voltage regulator module and the basic setup for EMI study. The regulator mainly includes a Kuijk bandgap voltage reference with startup circuit [6] and an output feedback amplifier. Harmonic disturbances from 1 to 2000 MHz are coupled to the V IN power line according to the direct power injection (DPI) standard [5]. Two on-chip sensors were used in this module to monitor bandgap and regulator output voltages inside the chip. Each sensor uses a separate power supply and substrate isolation techniques to prevent conducted disturbances from affecting its operation. DC offset is generated by a parasitic rectification effect intrinsic to the circuit under test. The offset can be positive or negative depending on EMI frequency and amplitude. The first type of distortion can be eliminated by filtering, but the second type cannot and degrades the regulation performance of the LDO. A uniform criterion is defined to analyse the susceptibility, which consists in setting a margin of +100 mV on the offset measured on the regulator output. Fig. 2 shows examples of on-chip sensor 2 measurements for two different RFI frequencies (700 MHz and 1 GHz). On-chip sensor measurements and comparison with external methods: The acquisition is based on an on-chip sample-and-hold circuit that directly probes the voltage within integrated circuit (IC) interconnects. An associated post-processing phase reconstructs the timing waveform. The detailed principle of this on-chip sensor is given in [START_REF] Ben Dhia | IC immunity modeling process validation using on-chip measurements[END_REF].

R 1 Q 1 Q 2 R 3 R 2 V- V+ V- V+ RF VIN 3.3V DC startup circuit sensor1 sensor2 V OUT
With the on-chip sensor, we can use the advantage of inner sampling and enhance our measurement of the actual susceptibility level in the chip, as shown in Figs. 3a andb. First, Fig. 3a shows the susceptibility level of the regulator to conducted harmonic disturbance applied on the V IN pin measured according to two methods: the EMI-induced offset is measured on the regulator output either externally (after output buffer and package) with an oscilloscope or internally with the on-chip sensor 2. When failures arise (+100 mV offset), the two types of measurement give different results between 700 MHz and 1 GHz, indicating different susceptibility levels of the regulator. The characterisation of the harmonic distortion of the regulator output is presented in Fig. 3b. The amplitude of regulator output voltage is measured externally and internally when a failure is detected. The two types of measurement give different results above 600 MHz. It can be seen that, above 1.3 GHz, the amplitude of the regulator output measured externally decreases to almost 0 V while the on-chip sensor gives a totally different result. It indicates a voltage fluctuation of several hundred millivolts and thus gives the actual level of harmonic distortion affecting the regulator output. The differences between internal and external measurements of regulator output distortion presented in Figs. 3a andb can be explained by the contribution of bonding, package, PCB and I/O output buffer structures. Above several hundred megahertz, they act as a lowpass filter, which reduces or even eliminates the disturbance. External measurement methods cannot give the actual amount of degradation of output signal and thus an efficient diagnosis of the electromagnetic susceptibility of an integrated regulator. An on-chip sensor constitutes an accurate measurement method of the susceptibility of each internal block of an IC, such as an integrated LDO regulator.

Conclusions: This Letter has highlighted the difference between external and internal measurement and draws attention to accuracy issues of external measurements of an integrated low-dropout regulator. With the same failure criterion, sensor measurements indicate lower EMI amplitude, thus invalidating the LDO regulator within the range 700 -1000 MHz. Moreover, above 1 GHz the on-chip sensor detects a larger harmonic distortion level of the regulator output than external measurement. External measurement methods underestimate the susceptibility level and the disturbance of the regulator. On-chip measurements constitute an efficient technique for addressing susceptibility issues in critical internal blocks within system-on-chip, systemin-package or 3D circuits.

Fig. 1

 1 Fig. 1 Test chip structure and general setup for DPI measurement

Fig. 2

 2 Fig. 2 Internal failure monitored by on-chip sensor at 700 MHz and 1 GHz

Fig. 3

 3 Fig. 3 Comparison between external and on-chip sensor sampling methods a Internal and external voltage fluctuation measured on regulator output pin to obtain +100 mV offset b Fluctuation measured in amplitude of regulator output voltage under same offset criterion

Acknowledgments: The authors acknowledge the full support of the China Scholarship Council and thank C. Lemoine from INSA, University of Toulouse, France, for software support. # The Institution of Engineering and Technology 2012 8 February 2012 doi: 10.1049/el.2012.0407 One or more of the Figures in this Letter are available in colour online. J.F. Wu, J.C. Li and R.J. Shen (School of Electronic Science and Engineering, NUDT, Changsha, Hunan 410073, People's Republic of China) E-mail: wujianfei990243@gmail.com E. Sicard (INSA, University of Toulouse, 135 av. de Rangueil, Toulouse 31077, France) A. Boyer and S. Ben Dhia (LAAS-CNRS, 7 avenue du colonel Roche, Toulouse 31077, France)


Arnaud Réveillère

Jeremy Rohmer

Frédéric Wertz

Semi-analytical model of brine and CO2 leakage through an abandoned plugged well. Applications for determining an Area of Review and CO2 leakage rate

where:

• 𝑃 1 , 𝑃 2 are the pressure for the column entirely filled with brine resp. CO 2

• 𝛼 𝜖 0,1 is a coefficient proportional to the leakage rate 𝑄 𝐿,𝐶𝑂 2 and inversely proportional to the CO 2 uprising speed in the wellbore (assumed to be 0.16 m.s -1 in average). 𝑑 𝐴𝑜𝑅 = 1.1 10 5 1 -1.2 10 -15 ℎ 𝑐 /𝑘 𝑐 𝑑 𝐴𝑜𝑅

>>>

  Semi-analytical model of brine and CO 2 leakage through an abandoned plugged well. Applications for determining an Area of Review and CO 2 leakage rate Arnaud Réveillère, Jérémy Rohmer, Frédéric Wertz / contact: a.reveillere@brgm.fr www.brgm.fr Conclusions > The model describes the leakage of brine through the leak, and of CO 2,g as a first approach. Compared to the state of the art, it adds the possibility of accounting for density change within the leak, due to either the incoming of dense brine or light CO 2 It shares the advantages (immediate computation) and drawbacks (homogeneous layers) of semianalytical models Compared to a static approach, this dynamic model enables less conservative estimation of the "Area of Review", by including effects of cement plugs, of brine density differences and of leakage-induced pressure effects Application (i): Determining an Area of Review > "Area of review "defined as the area where the pressure changes due to the injection can drive the reservoir brine up to a shallower aquifer of interest > Application of the injection scenario to the PICOREF sector in the Paris basin (France). The Oolithe Blanche layer, or "Dogger", is used for CO 2 storage. 135 abandoned wells reach this layer and the overlying Albian aquifer in the sector. Many CO 2 storage projects target deep saline aquifers located in sedimentary basins. In these regions, historical oil & gas operations have often left abandoned wells with sometimes undetermined plugging records > The risk of leakage through abandoned wells should therefore be assessed, notably for preventing two adverse effects: (i) the pollution of overlying fresh water aquifers through the migration of saline brine, and (ii) the emission of large fluxes of CO 2 in the atmosphere. The present model may be used for describing both Position of the model > Existing semi-analytical models can estimate the leakage flow rate of brine, possibly followed by CO 2 , from the storage aquifer to overlying ones (cf. publications by Nordbotten, Celia and co-authors, 2004-2009) > Based on these approaches, this work includes several novelties: -It considers the pressure increase under the leak when the dense saline brine from the storage reservoir progressively fills in the leak and replaces the native fluid of the wellbore, and then its decrease when the lighter CO 2,g breaks through -The leak is composed of an open wellbore and a porous column of varying height & permeability, which may represent various leaks, from an empty wellbore to a flow in a porous media such as the annular cementation. It either reaches the surface or an overlying aquifer Pressure under the leak modeling > First approach based on: 𝑃 𝐿-(𝑡) = 1 -𝛼 𝑃 1 + 𝛼𝑃 2

>>

  Cf. Wertz, F., Audigane, P., Bouc, Same case study as Application (i), except that the leak directly connects the Dogger aquifer to the surface. A weak cement plug (ℎ 𝑐 = 1𝑚; 𝑘 𝑐 = 10 -13 𝑚 2 ) is considered in the leak, which is located 5 km away from the injection point > Visible decrease of the pressure under the column of fluid after its filling with a lighter mixture of brine and CO 2,g > Due to the low CO 2 viscosity, the CO 2 leakage rate largely increases compared to the previous brine leakage rate > During the brine leakage > During the CO 2 leakage > During the brine leakage, a pressure increase under the leak 𝑃 𝐿-(𝑡) is considered due to the density difference between native and reservoir brine salinities. Paris basin case: when the Dogger brine reaches the Albian aquifer, Adapted from Delmas, J., Brosse, E., Houel, P., 2010. Oil & Gas Sci. and Tech. Vol. 65 (2010), No. 3, pp. 405-434 ℎ 𝑐 ℎ 𝑐 𝑘 𝑐 (𝑚 -1 ) > Dense Dogger brine progressively fills the leak up to the surface; the pressure under the leak increases > Visible cusp on the brine leakage rate due to the end of the pressure increase > CO 2,g breakthrough at 34 years > Borehole filling until 2.6 years Static approach (no plug) Q 0 = 1 Mt/y for 50 y.


Tahani Gazdar
email: tahani.gazdar@etd.univ-avignon.fr

Abderrahim Benslimane
email: abderrahim.benslimane@univ-avignon.fr

Abderrezak Rachedi
email: rachedi@univ-mlv.fr

Abdelfettah Belghith
email: abdelfattah.belghith@ensi.rnu.tn

A Trust-based Architecture for Managing Certificates in Vehicular Ad hoc Networks

In this paper, we propose a secure and distributed public key infrastructure for vehicular ad hoc networks VANETs based on an hybrid trust model which is used to determine the trust metric (Tm) of vehicles. The trust model consists on a monitoring system processing on two aspects: the cooperation of vehicles and the legitimacy of the broadcasted data. We propose a fuzzy-based solution in order to decide about the honesty of vehicles. Then, the vehicles which are trusted (Tm = 1) and have at least one trusted neighbor can be candidate to serve as certification authorities CAs in their clusters. In order to increase the stability of our distributed architecture, the candidate CA which has the lowest relative mobility will be elected as certification authority CA. We conducted a set of simulations in which we evaluate the efficiency and the stability of the clustering algorithm as a function of the speed, the average number of vehicles on the platoon and the percentage of confident vehicles.

I. INTRODUCTION

Vehicular networks are characterized by an open architecture that raises tremendous vulnerabilities [START_REF] Papadimitratos | Securing Vehicular Communications -Assumptions, Requirements, and Principles[END_REF] [START_REF] Parno | Challenges in Securing Vehicular Networks, Proceeding of the Workshop on Hot Topics in Networks (HotNets-IV)[END_REF]. Therefore providing information security is a serious challenge in VANETs. In these networks, the significant number of vehicles and the high speed of vehicles bring out important challenges and compel a strong and evolutionary structure for securing communications. Public Key Infrastructure (PKI) is a good promising choice for enabling communications security in vehicular environments. It is based on a trust third parte called certification authority (CA) which is responsible for certifying the public keys of vehicles. However, in MANETs and particularly VANETs, the conception of PKI must take into account the disconnections in the network. Besides, the CA must always be reachable by all vehicles.

In order to circumvent this shortfall, several research works [START_REF] Sivagurunathan | Authentic Vehicular Environment Using a Cluster Based Key Management[END_REF], [START_REF] Raya | Securing Vehicular Communications[END_REF], [START_REF] Blum | The Threat of Intelligent Collisions[END_REF] proposed distributing the responsibility of the CA among a set of nodes in the network. Almost proposals use the mobility as metric to elect the vehicles that will assume the role of CA. Unlike these works we propose in this paper a distributed PKI where the CAs are dynamically elected according to not only their mobility but also their trust level since the CA provides a critical service that needs a high level of trustworthiness. We extend our previous work [START_REF] Gazdar | Secure Clustering Scheme Based Keys Management in VANETs[END_REF] by proposing a new trust model on which is built our architecture of PKI. According to [START_REF] Govindan | Trust Computations and Trust Dynamics in Mobile Adhoc Networks[END_REF] trust management systems target the information itself, they allow the detection of malicious data and dishonest peers. Using our trust model we aim to evaluate the trust level of the vehicles by inspecting the accuracy of the exchanged information. Particularly, we use a fuzzy-based technique in order to filter out fraudulent information and malicious vehicles. The trust metric is updated according to the instantaneous behavior of the vehicles. We consider two aspects of the exhibited behavior: the cooperativeness and the accuracy of the data that the vehicles exchange.

The paper proceeds as follow. In section 2 we discuss the related work. In section 3 we detail our proposal, first we present the trust model, then we describe our distributed PKI. Section 4 depicts the results of simulation. Finally, section 5 concludes the paper.

II. RELATED WORK

In this section, we present some existing works related to the establishment of PKI in VANETs. Additionally, we describe some existing trust models for vehicular networks. [START_REF] Sivagurunathan | Authentic Vehicular Environment Using a Cluster Based Key Management[END_REF] a self organized key management system based on clusters. In their model, the network is divided into a number of clusters based on the mobility. They admit that in a cluster, vehicles have on average the same velocity, a group can be represented by a single vehicle defined as the cluster head. In their self-organized PKI any user can sign another user's public key. The set of signatures forms the network of trust relationships. Raya et al. proposed in [START_REF] Raya | Securing Vehicular Communications[END_REF] a distributed PKI for VANET managed by many CAs, each corresponding to a region. The different CAs have to be cross-certified so that vehicles from different regions can authenticate each others. This requires that each vehicle stores the public keys of all CAs whose certificates are needed to be verified. In [START_REF] Blum | The Threat of Intelligent Collisions[END_REF], authors use a PKI with virtual infrastructure where a set of elected cluster heads are responsible for disseminating messages after digitally signing them. This solution is intended only for the attack called intelligent collisions. However, a PKI in VANETs must cope with different attacks. Unlike existing architectures and due to the important role of CAs, we admit that only trusted vehicles can assume the responsibilities of CA additionally to the relative mobility metric.

A. Public Key Infrastructure in VANETs

Ramaraj et al. proposed in

B. Trust Models in VANETs

In VANETs, there exist three types of trust models: 1)Entity oriented, 2)Data oriented and 3)Hybrid models. The entity oriented models require the evaluation of the legitimacy of entities (nodes). In [START_REF] Tajeddine | A Privacy-Preserving Trust Model for VANETs[END_REF], the authors propose a trust model where the vehicles are organized off-line into groups and each group has a reputation value. The group reputation increases if the average of its members'opinion about the road state is conform to the real road state. The limit of this approach is that the reputation of the group is correlated to the behavior of all group members.

The data oriented models require the evaluation of the legitimacy of the information received in the messages. The authors in [START_REF] Raya | On Data-Centric Trust Establishment in Ephemeral Ad Hoc Networks[END_REF] propose a data-centric trust model. First, each vehicle computes a report about an event by combining static information such as the event type and dynamic information such as the security state of the vehicle. Then all reports about the same event are combined and their validity is inferred by an inference module in order to calculate the posteriori probability of the events. However, since the inference module uses the prior probability, it is not easy to derive it due to the high mobility in vehicular networks.

The hybrid models combine both entity and data oriented approach. In [START_REF] Dotzer | VARS: A vehicle Ad hoc network reputation System[END_REF], the authors proposed a hybrid approach using a piggybacking technique. Once a vehicle receives a message about an event it appends to the message a trustworthiness opinion about the event before retransmitting it. This opinion is computed combining metrics about direct experiences, indirect trust relationship and opinions of other vehicles received in the message. The drawback of this proposal is that the first opinion attached to the message will affect other opinions since its computing is recursive.

III. THE PROPOSED TRUST MODEL

In the proposed architecture, vehicles playing the role of CA are important because they are responsible for certifying vehicles attached to their clusters. To this end, we need trusted parts for issuing certificates.

We propose in this section an hybrid trust model for evaluating the behavior of vehicles and estimating their corresponding trust metric (T m ). The idea consists on the monitoring and the assessment of the behavior of vehicles in two aspects: their cooperativeness in the network and the legitimacy of the information that they broadcast. Each vehicle must monitor all its 1-hop neighbors and calculate their T m .

In the network, the vehicles broadcast messages related to urgent events occurred on the road which are called warning messages. Each time a monitor vehicle receives a warning message, it evaluates the cooperation rate of the source. After, it computes the reputation of the event reported in the received message. Then, using a fuzzy-based approach the monitor filters out malicious vehicles. Finally, according to the outcome of the monitoring process, it updates the T m of the source. The T m (i) is a continuous value in [0,1]. The vehicle is trusted (confident) if its T m reaches 1. In our proposed PKI, only trusted vehicles are allowed to candidate to be CA. Hereafter, we present the different steps followed by a monitor in order to calculate the T m of its neighbors.

A. Gathering information:

Along its trip, each vehicle broadcasts warning messages that report events happened on the road. In all warning messages, an information about the legitimacy of the event is attached to the messages that we call reputation (Rep V (E): the reputation of event E computed in vehicle V). In fact, around event E(x,y,t) occurring in position (x,y) and at time t, we consider a static geographic zone Z where vehicles are able to directly detect the event using their on board sensors. The vehicle source of the message affects the reputation value of event E as follow. If vehicle V is in Z and it detects the event, then Rep V (E) = 1, else if vehicle V is in Z and it does not detect E but it receives a warning message about E. Then, it denies event E then Rep V (E) = 0. Otherwise vehicle V calculates an aggregated reputation as described in the following step.

B. Evaluating information:

If vehicle V is beyond Z or it has not an exact information about the reputation of E, it computes Rep V (E) by aggregating all information about E, which are received from other vehicles in warning messages as follow:

Rep V (E) = i=|S| i=1 Rep i (E) * d i * T m (i) i=|S| i=1 d i * T m (i) (1)
Where S is the set of vehicles from which V receives warning messages about E, T m (i) is the local trust metric of the vehicle i computed by vehicle V, its default value is T m (i) = 0.1 and d i is the distance between vehicle i and event E. We use the distance between the vehicle and the event because the closer the reporter is to the event location the more accurate its information on the event will be.

C. Evaluating vehicle behavior

The behavior is evaluated by the monitor, based on the cooperativeness of the monitored vehicle and the legitimacy of the information that it broadcasts, as follow:

-The cooperativeness: a monitor calculates a forwarding rate called F . It is expressed as the number of messages forwarded by a monitored vehicle divided by the total number of messages transmitted by the monitor vehicle [START_REF] Rachedi | A Secure and Resistant Architecture against Attacks for Mobile Ad Hoc Networks[END_REF]:

F =
the number of f orwarded messages the total number of transmitted messages

(2) -The legitimacy of the information: Monitor V decides the honesty of monitored vehicle i based on Rep i (E). We use the fuzzy set theory [START_REF] Marmol | LFTM, linguistic fuzzy trust mechanism for distributed networks[END_REF] to classify honesty of vehicles. Each vehicle is classified within one of the honesty levels. First, an accordance degree corresponding to each vehicle i in S is calculated by monitor V as follow:

A i = Rep i (E) Rep V (E) (3)
We define 3 honesty levels represented by fuzzy sets as depicted in figure 1. Then A i is projected into one of

F k → [0, 1]
determining which honesty level each vehicle is belonging to. Hence, the probability that vehicle V is in honesty level 3 (not malicious) is computed as follows [START_REF] Marmol | TRIP: a trust and reputation infrastructure-based proposal for vehicular ad hoc networks[END_REF] :

P m = ϕ 3 ϕ 1 + ϕ 2 + ϕ 3 (4)

D. Updating T m (i):

Initially the monitor affects T m (i) = T 0 (0 < T 0 < 1) to monitored vehicle i . Then, according to the outcome of the evaluation of the behavior that monitored vehicle i exhibits, the monitor update T m (i). If P m is less than threshold δ 2 , vehicle i will have T m (i) = 0, and it is declared malicious. Otherwise, if the value of (F * P m ) is greater than threshold δ 1 then T m (i) increases by γ (1 mod γ= 0), otherwise it decreases by γ. If T m (i) = 1, vehicle i is trusted. It is worth mentioning that the values of δ 1 , δ 2 and γ are defined as a function of the level of accuracy that we aim to perform towards the evaluation of T m (i). The detailed algorithm for updating T m is presented in figure 2.

A. Preliminaries

The basic idea of the proposed architecture consists in establishing a dynamic and distributed public key infrastructure where the role of the CA is distributed among a set of vehicles elected according to a clustering process. The elected clusters heads (CHs) will be the CA in their clusters. A CH is elected according to its trust level T m , the number of its trusted neighbors and the average of its mobility relatively to its neighbors.

B. Clustering Algorithm

In our clustering algorithm, only trusted vehicles (T m = 1) can be candidate CA. Each vehicle in the network periodically broadcasts a Hello message. It contains information about its current speed, its current position, and T m of all its neighbors. The Hello messages are broadcasted up to d hops. They are used to build and update the table of neighbors in each vehicle. Particularly, they are used to calculate the average value of T m for each neighbor. Indeed, upon the receipt of Hello messages, a vehicle updates T m (i) of each neighbor i as well as its own T m as follow:

T m (i) = |N | n=1 T n m (i) |N | (5)
Where: N is the set of Hello messages which contain an information about T m (i).

Initially, when a vehicle enters in the network it waits during a period of time timer 1 for a Hello from an already existing CA or an election beacon from a vehicle candidate CA, so that it replies by a Join message in order to request for the membership in that cluster. Otherwise, at the expiration of the waiting time, if the vehicle is trusted and if it has at least one trusted neighbor, it can candidate to serve as CA. Indeed, it broadcasts a message called election beacon containing its unique identity, the number of its trusted neighbors, its average relative mobility. The election beacon is forwarded up to d+1 hops where, d is the maximal size of the clusters dealing with the number of hops between the CH and the farthest vehicle in the same cluster. Upon the receipt of an election beacon a vehicle requests for the membership to the CA originating such election beacon. In case where a vehicle receives more than one election beacon, its sorts the list of candidates CA according to their relative mobility and the number of their trusted neighbors, in this case the membership request is sent to the header of the list. If the CA accepts the request then it replies with an accept message, otherwise it responds with a reject message. During the clustering process a vehicle passes through a set of states before being attached to a cluster:

-INIT NODE: a vehicle just entering the road, -CA CANDIDATE: a vehicle candidate to be a CA, vehicle, it decides the role of that vehicle in its cluster. In fact, we define 3 types of membership in a cluster: -RA: Registration Authority. Each trusted vehicle located at 1-hop from the CA acquires the role of RA. The set of RA vehicles constitutes the vehicular dynamic demilitarized zone VDDZ. The role of the VDDZ is to protect the CA from unkown and malicious vehicles. -GW: GateWay. All vehicles members of at least 2 adjacent clusters acquire the GW state. A GW must have T m in [0.8,1]. -MN: Member Node. They are simple members of the clusters. Further details can be found in our previous work [START_REF] Gazdar | Secure Clustering Scheme Based Keys Management in VANETs[END_REF].

V. PERFORMANCE EVALUATION

In this section we present the results of the simulation. We pointed out the efficiency and the stability of our clustering algorithm.

A. Simulation set up

We conducted a set of preliminary tests using the network simulator OMNET++ [START_REF] Vargas | OMNeT++ Discrete Event Simulation System User Manual[END_REF]. Particularly we used the frame-work inetmanet with the IEEE802.11 MAC layer. We consider a segment of route with a length=10km. The vehicles enter in the network with a rate λ in v/s (vehicles per second). All vehicles have the transmission range equals to 450m. We consider different arrival rate of vehicles as detailed in table II. All clusters have the same maximum size fixed to 300 vehicles. In all simulations, the periodicity of Hello messages is 2s and timer i = 5s, i=1,2,3.

B. Simulation Results

1) The average number of CAs and RAs: We investigate the average number of CAs elected on the platoon and the average number of RA vehicles per cluster. To this end, we plot in figures 4a and 4b the average number of CAs on the road and the average number of RAs per cluster as a function of the average speed and the arrival rate of vehicles for 50% and 100% of trusted vehicles.

At a speed of 10 m/s and λ 4 = 2v/s, we have on average 2000 vehicles and the maximum range of a cluster is 3. Since the maximum size of a cluster is fixed to 300 vehicles, we need a minimum of 7 cluster heads to cover the entire platoon. With the same speed but for λ 3 = 1.5v/s, we have instead 1750 vehicles and therefore 6 clusters are enough to cover the entire platoon. For λ 2 = 1v/s and λ 1 = 0.5v/s, we have respectively 1000 and 500 vehicles and therefore we require exactly the minimum number of clusters which is 4. From 20 m/s to 40 m/s, the total number of vehicles is less than 1200 for all assumed arrival rates and consequently, only the minimum of 4 clusters is needed to cover the entire platoon. For both cases (50% and 100% of confident vehicles), we found the same result. Indeed, for 100% of confident vehicles we have more confident vehicles which provides more RAs per cluster.

Let us investigate now the average number of RAs per cluster. As depicted in figures 5a and 5b, we clearly observe that the average number of RAs per cluster increases with both the percentage of trusted vehicles and the vehicles arrival rate but decreases when the average speed increases with both the percentage of confident vehicles and the vehicles arrival rate. Indeed, a higher percentage of confident vehicles provides more trusted neighbors to any cluster head and consequently more RAs. This is a positive outcome since a high number of RAs makes more secured the CA.

2) Impact of speed and arrival rate on the efficiency: Let us study now the efficiency of the clustering algorithm. The efficiency relies on the percentage of vehicles that acquire a state in a cluster namely CA, RA, MN or GW. We plot in figures 6a and 6b the efficiency as a function of the average speed, the arrival rate of vehicles and two different assumed percentages of confident vehicles. The efficiency stays above 97% for speeds below 20m/s but it lightly decreases for higher speeds. We remark also that it increases as the arrival rate increases. Indeed, for an arrival rate of λ 4 = 2v/s or even λ 3 = 1.5 v/s the efficiency stays around 100%. For smaller arrival rates and high speeds, the efficiency decreases. Still yet, the efficiency is rather resilient to the decrease in the percentage of trusted vehicles.

3) Impact of speed and arrival rate on the stability: We investigate the stability of the clustering. Particularly, we are interested in the average life time of CAs. Indeed, the longer the elected CAs can maintain their status, the stronger is the stability of the different memberships. We plot in figures 7a and 7b the average life time of CAs.

As portrayed in 7b, the life time is about 100%, independently of the speed and the arrival rates of vehicles. This means that any elected CA stays so until it exits from the assumed road segment. Figure 7a shows the same behavior only when the vehicle arrival rate is high (λ 3 and λ 4 ). However for smaller arrival rates, the average life time of CAs decreases a little bit as the average speed increases. This small decrease is mainly due to the small average number of RAs per cluster at these points. However, the life time stays above 98% even for a speed of 40 m/s. On the other hand and more interestingly we notice that the percentage of trusted vehicles has a small impact on the stability of the clustering scheme.

VI. CONCLUSION

In this paper, we proposed a distributed and secure architecture for vehicular ad hoc networks. It is based on an hybrid trust model aiming at evaluating the behavior of vehicles. In our architecture, the responsibilities of CA in the PKI is distributed among a set of vehicles. They are elected according to a clustering algorithm based on two metrics. Only trusted vehicles which have at least one trusted neighbor can candidate to be CA. Besides, in order to enhance the Second, the monitor assesses the legitimacy of information broadcasted by their neighbors. Therefore, according to its trust metric each vehicle acquires a role (i.e :CA, RA, GW or MN) in its cluster. The simulation results out come the efficiency and the stability of the clustering algorithm.

In our future work, we aim to evaluate the performance of our trust model using the simulation.

Fig. 1 .

 1 Fig. 1. Membership functions

Fig. 2 .

 2 Fig. 2. The State-Transition Diagram of the Trust Model

Fig. 3 .

 3 Fig. 3. The state-transition diagram of the clustering algorithm

Fig. 4 .Fig. 5 .

 45 Fig. 4. The average number of vehicles CA on the platoon

Fig. 6 .Fig. 7 .

 67 Fig. 6. The efficiency of the clustering algorithm

The 2nd International Conference on Communications and Information Technology (ICCIT): Communication Networks and Systems, Hammamet 978-1-4673-1950-8/12/$31.00 ©2012 IEEE


Cléo Baras

Franc ¸ois Cayre

2D BAR-CODES FOR AUTHENTICATION: A SECURITY APPROACH

In this paper, we investigate the authentication problem of real-world goods on which 2D bar-codes (2D-BC) were printed and we take the opponent's point of view. The opponent is assumed to have access to N c noisy copies of a genuine 2D-BC (noise being due to printing and scanning processes). A simple estimator of the 2D-BC based on copies averages is proposed, letting the opponent print a fake 2D-BC which aims at being declared as genuine by the system detector. Performance of the estimator in terms of error probability at the detector side is then derived with respect to N c and compared with experimental results on real 2D-BC. It is shown that the opponent can produce a fake that successfully fools the detector with a reasonable number of genuine goods.

INTRODUCTION

When making sure a real-world good (such as medicine, wine, textile, ...) is genuine [START_REF] Bobee | How technology can help to fight counterfeits?[END_REF], 2D bar-codes (2D-BCs) are an alternative to watermarks. 2D-BCs [START_REF] Picard | Digital authentication with copy-detection terns[END_REF] (also called Data Matrix or Data Grid) are black-and-white visible images encoding a good binary identifier using a (secret) cryptographic key in a pseudo-random way and printed on the goods package. Using an automated detection process based on a scan of the 2D-BC, a correlation score is computed and compared to a pre-determined threshold in order to decide whether the good is genuine or fake.

In this context, an opponent (Eve) aims at producing a fake 2D-BCs declared as genuine by the detector, whereas the goal of the product manufacturer (Bob) is to make such a reproduction difficult or impossible for Eve. Bob will therefore use the production process noises all the more severe as the printed 2D-BCs size is small (around 4 millimeters). He might even deliberately add some noise during his 2D-BC printing process to obtain properties similar to Physical Unclonable Functions [START_REF] Pappu | Physical one-way functions[END_REF]. Besides, Eve, unaware of the good binary identifier encoding, has no choice but to try to estimate the original 2D-BC without getting to the good identifier.

In this paper, this problem is tackled with a security approach inspired by works in digital watermarking [START_REF] Cayre | Watermarking security: Theory and practice[END_REF]. We in-This work was supported, in part, by the French ANR Estampille project. d Fig. 1. A 2D-BC with synchronization elements in gray and identification elements over a ∆ = 255 dynamic range. vestigate the worst case attack framework from Bob's point of view, described in section 2: 1) the opponent has access to N c printed (genuine) versions of the same 2D-BC (since he might have bought several genuine goods); 2) he has the same printing device than Bob and arbitrary precision scanning device; and 3) he has no access to the automated detector 1 . A simple estimator of the original 2D-BC is proposed in section 3. In section 4, estimator performance are derived with respect to N c and compared to experimental results, presented in section 5.

PROBLEM STATEMENT

In the sequel, let M L (E) denotes the set of square matrices with size L × L and elements in E.

2D-BC construction

After encoding with a secret key, the good binary identifier b is added to synchronization elements (that won't be taken into account in the sequel) then modulated following an Onand-Off Keying (OOK) modulation with dynamic range ∆ (typically ∆ = 255). These elements are spread over a matrix I o ∈ M L ({0, ∆}) forming the black-and-white 2D-BC with L × L elements equal to 0 or ∆, depicted in figure 1.

The authentication and counterfeiting processes

Figure 2 gives a brief sketch of our setup. In normal mode, the product manufacturer Bob prints 2D-BCs on goods with a small printing area d × d (typically d is around 4 millimeters). Then Alice, authorized to use the automated detector, scans them to check whether they are genuine or not. The n-th print and scan operation will be denoted as the function P n . • noise N a n due (for instance) to ink dispersion in the paper or inhomogeneous lighting conditions during scan acquisition: the acquired 2D-BC elements U n (i, j) are then in the [0, ∆] range (white and black elements going to gray);

• resampling inherent to the print and scan process and taking into account varying speed of the scanning device during acquisition: each elements of U n is spread over a S × S area , so that U n ∈ M M ([0, ∆]) with M = SL. To put it simply (hypothesis 1), U n can be viewed as the encoding of I o using a repetition code with S repetitions, so that: U n (Si + s, Sj + t) ≈ I o (i, j) with 0 ≤ s, t < S. In practice, S is not necessarily an integer.

Eve, as an opponent having an arbitrary precision scanning device, has access to the N 2D-BCs U n printed by Bob, each collected with a noise N e n . She proceeds to the original 2D-BC estimation, denoted as Îo ∈ M L ({0, ∆}), then prints it on fake products. Finally, her fake 2D-BC Îo , when submitted to Alice's detector, will suffer print and scan distortions (with noise N a n ) equivalent to those of I o in the normal mode.

Authentication system performance

Alice's detector will have to decide between the two hypotheses: H f when the content is fake and H g when the content is genuine. End-to-end performance are related to the wellknown false-alarm and false-detection probabilities (resp. p f a and p f d ), relying on a decision threshold τ delimiting the boundary between fake and genuine contents. p f a and p f d depend on various parameters (encoding techniques, identifier encryption parameters...) that Eve might be unaware of. Therefore, Eve must be able to reproduce the whole 2D-BC I o as accurately as possible, without getting to the original good identifier b. As a consequence, performance can be evaluated with the error probability in the decoding of the original 2D-BC I o respectively when Alice scans a genuine 2D-BC emanating from Bob, denoted by p d e|Hg then a fake 2D-BC emanating from Eve, denoted by p d e|H f and related to the performance of Eve's estimator.

EVE'S ESTIMATOR

Principles

The N c 2D-BCs U n collected by Eve are realizations of the same original 2D-BC I o . Eve aims at producing Îo estimating I o as accurately as possible. A simple estimation will take two steps: a soft output estimation În (i, j) of the element value I o (i, j) in each of Eve's N c 2D-BCs using the repetition code; then the combination of these soft values over the N c contents to produce a hard decision on the 2D-BC element value I o (i, j), yielding the fake Îo .

Our estimator relies on the hypothesis (hyp. 2) that no black element of a 2D-BC should spread more than the half of the surrounding elements as illustrated in figure 4. Indeed, if this hypothesis is violated, then even Alice may well not be able to correctly authenticate the 2D-BC.

A sliding window estimator

Soft output estimation

The soft output estimation În (i, j) of the 2D-BC element I o (i, j) (that is spread in U n with size of S × S) works as follows: in relation with the hypothesis of section 3.1, a sliding window of size S/2 circulates across the S × S elements U n (Si + s, Sj + t) (with s and t varying in [0; S -1]). Then, taking the mean value of U n at window position (Si + S/2, Sj + S/2) yields:

În (i, j) = 1 S 2 S-1 s=0 S-1 t=0
U n (Si + s, Sj + t).

(1)

Hard decision

Combining the soft output decisions among the N c 2D-BCs at element position (i, j) is done by computing the average value of the elements În (i, j) over the N c soft output estimations:

W(i, j) = 1 N c Nc n=1 În (i, j). (2)
Eve's final estimated 2D-BC Îo is then obtained with:

Îo (i, j) = ∆ if W(i, j) ≤ ∆/2 0 otherwise . (3)

A THEORETICAL STUDY OF THE COUNTERFEITING SCENARIO

In this section, we aim at deriving the decoding performances for both normal and pirate modes of operation, that is the respective error probabilities p d e|Hg and p d e|H f , related to the print and scan distortions and to the performance of Eve's estimator. For simplicity reasons, we will assume that 0's and ∆'s are equiprobably distributed in I o (hyp. 3).

A naive print and scan model

In view of a theoretical study, the n-th printing and scanning process P n can be modeled for the 2D-BC element (i, j) using:

• a noise N: The print and scan noises in the normal mode with Bob and Alice can be viewed as a single accumulated noise N a n . Statistical properties of N a n are supposed to be independent from both n and the 2D-BC element (i, j) (hyp. 4). Moreover, it can be assumed that Eve has access to the same printing and scanning devices as those used in the normal mode of operation (hyp. 5) ; thus statistical properties of N e are equal to those of N a . Both will be denoted as N and supposed to follow a N (0, σ 2 N ) distribution (hyp. 6);

• a shift parameter α: according to figure 3, the whole process tends to move extremal values 0 and ∆ towards ∆/2, making the channel all the more error-prone as the noise level increases. This degradation will be modeled by a shift of extremal levels with a parameter α (hyp. 7).

Finally, the acquired 2D-BC U n = P n (I o ) is given, for all 0 ≤ s, t < S, by:

U n (Si + s, Sj + t) = I o (i, j) + N(Si + s, Sj + t) + α if I o (i, j) = 0 -α if I o (i, j) = ∆ . ( 4
)

Decoding error probability in the normal mode (H g )

Let the decoder operating on U n = P n (I o ) with I o emanating from Bob. Due to the model symmetries, the decoding error probability is the probability that the decoded Ĩo (i, j) is ∆ whereas the original 2D-BC element is

I o (i, j) = 0, that is p d e|Hg = Pr [I n (i, j) = ∆|I o (i, j) = 0].
Alice's detector is assumed to work the same way than Eve's estimator but using the single content U n (hyp. 8): regarding the 2D-BC element I o (i, j) = 0, the S 2 observations U n (Si + s, Sj + t) are N (α, σ 2 N ) distributed accordto equation (4). Then, the soft estimated value Ĩn (i, j) (computed by Alice's detector with equation ( 1)) follows a N (α, σ 2 N S 2 ) model. Then, the hard decision on Ĩo (i, j) (using N c = 1 in equation ( 3)) yields:

p d e|Hg = Pr Ĩn (i, j) > ∆ 2 |I o (i, j) = 0 = 1 2 erfc ∆ 2 -α √ 2 σ N S
(5) with erfc the complementary error function.

Decoding error probability in the pirate mode (under H f )

Estimator performance

We are now interested in Eve's ability to correctly estimate I o with respect to the number N c of printed and scanned versions U n she collects, that is the error probability of the estimator p e e (N c ), comparing Îo and I o . Under the same hypotheses than previously, p e e (N c ) = Pr Îo (i, j) = ∆|I o (i, j) = 0 . Regarding the 2D-BC element (i, j) when I o (i, j) = 0, the related S observations U n (Si + s, Sj + t) in the n-th collected 2D-BC still follows a N (α, σ 2 N ) distribution ; thus the soft estimated value În (i, j) is still N α,

σ 2 N S 2 distributed.
Now, the averaged value W(i, j) over the N c values În (i, j) follows N α, σ 2 N S 2 Nc , so that the hard decision on Îo yields:

p e e (N c ) = Pr W(i, j) > ∆ 2 |I o (i, j) = 0 = 1 2 erfc   ∆ 2 -α √ 2σ N S √ Nc   (6)

Decoding error probability under H f

Alice is now scanning the Eve's fake content Îo . The observed 2D-BC Ûn = P n ( Îo ) (after print and scan) is subject to the same decoding process as described in section. 4.2. The decoding error probability under H f is then the probability that the decoded value Ĩo (i, j) is ∆ whereas the genuine information in I o (i, j) is 0. Thus:

p d e|H f = Pr Ĩo (i, j) = ∆|I o (i, j) = 0 .
Taking into account 1) the estimated 2D-BC Îo , 2) the estimator errors and 3) the symetrical configurations regarding value 0 and ∆, it comes (omitting the indexes (i, j) to ease the reading):

p d e|H f = Pr Ĩo = ∆| Îo = ∆, I o = 0 Pr Îo = ∆|I o = 0 +Pr Ĩo = ∆| Îo = 0, I o = 0 Pr Îo = ∆|I o = 0 (7)
Pr Ĩo = ∆| Îo = 0, I o = 0 is independent of the genuine 2D-BC and is directly linked to the error probability of the decoder when the submitted content, that is Îo , is corrupted by a single printing and scanning operation ; thus it is equal to p d e|Hg . Moreover, Pr Ĩo = ∆| Îo = 0, I o = 0 = (1-p d e|Hg ). Finally,

p d e|H f = 1 -[1 -p e e (N c )] p d e|Hg + p e e (N c ) 1 -p d e|Hg . (8)
It can be noticed that p d e|H f is entirely given by p e e (N c ) since p d e|Hg = p e e (1).

RESULTS

Results using the proposed theoretical model

Figure 5 depicts Eve's increasing performance in estimating the original 2D-BC when she accumulates several printed and scanned versions of it. Estimator theoretical performances of equation ( 6) are validated through Bit Error Rate (BER) with Monte-Carlo simulations using 2D-BCs containing 10kbits of information. Moreover, the print and scan channel is modeled using fixed parameters (α and σ 2 N ). In figure 6, we plot, as a function of the number of 2D-BCs Eve has used, the probability of error at the decoder side when a fake is submitted to the system (cf. equation 8). Simulated BERs confirm the accuracy of equation 8. It also shows that when the number of collected contents N c increases, p d e|H f tends to p d e|Hg i.e. Alice's decoder performance in normal mode. This means that, the fake and the genuine 2D-BCs can no longer be distinguished at the decoder side, since the messages obtained after decoding have the same number of error.

Results using real 2D-BC

In this section, we use real 2D-BCs, as depicted in figure 3. They contain a realistic amount of information (1kbit) and they were printed and scanned on a HP PhotoSmart C7200.

In figure 7, we accumulate a varying number of scanned 2D-BCs to estimate the original. We are then able to compute the BER to assess the raw estimator performance. Clearly as expected with theoretical results, Eve can refine her estimation as she has access to more and more 2D-BCs. But the slope of the plots have few in common with these of figure 5 since the print and scan channel model is far from reality.

Plugging the data of the figure 7 into equation 8 (which is independent from the channel model), we can plot the overall fake performance Eve can actually achieve (taking into account errors she might make but compensated by Alice's own errors). The results are given figure 8 where we also plot the bound on Alice's detector (that is the normal mode performance). As expected, the error decoding probability with fake 2D-BC tends to the one for genuine 2D-BC when the number of collected 2D-BC used in Eve's estimated 2D-BC increases; but the number of required contents is greater than expected (with theoretical results).

However, it can be noticed that Eve's goal may not be to estimate perfectly the original 2D-BC. Rather, she might be just as satisfied when she knows Alice's detector will make the same amount of errors given an authentic or a fake 2D-BC. For a bad printing quality, Eve will need a much greater amount of 2D-BCs to achieve Alice's detector bound. However, as the printing quality increases, a fake quickly leads to the same amount of errors as an authentic 2D-BC at Alice's detector side.

CONCLUSION

In this paper, we consider a good authentication system using 2D-BCs from the point of view of the opponent. An estimator that he can use to product a fake was proposed and its performance was derived through theoretical results and simulations on real printed and scanned 2D-BCs.

While both the model and the tests conducted on real data agree on the general conclusion that Eve's estimation performance increases when collecting 2D-BCs, the slope of the curves, however, differs greatly. We believe this is due to the fact that our printing and scanning channel model is rather poor. Future works have two directions: first, improving the opponent estimation ability using for instance (possibly geometrical) channel equalization or a 2D extension of the Viterbi decoder by solving the problem of the complexity of the aforementioned decoder and second, elaborating the product manufacturer counterattack, that is adapting an additional noise to his printing process to efficiently disturb the opponent estimation.

Fig. 2 .

 2 Fig. 2. Description of the authentication system.

Fig. 3 .

 3 Fig. 3. Acquisition examples of a 2D-BC, printed with a HP PhotoSmart C7200 and scanned at 1200dpi. From left to right: original 2D-BC, d = 8mm, d = 6mm, d = 4mm.

Fig. 4 .

 4 Fig. 4. Left: original 2D-BC elements, to be printed & scanned. Center: printed & scanned elements, respecting our hypothesis. Right: printed & scanned elements that do not respect our hypothesis.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Error probability of the estimator on the basis of theoretical equation (6) and evaluated with BER through simulations. Parameters: α = 50, σ 2 N = 0, 3, ∆ = 1, S = 4.

Fig. 7 .

 7 Fig. 7. Estimator performance with real 2D-BC through the estimation of p d e|H f for 3 printing dimensions: d ∈ {4, 6, 8} mm. All 2D-BCs contain 1024 bits and were printed and scanned on a HP PhotoSmart C7200 (scan resolution: 1200dpi).

Fig. 8 .

 8 Fig.8. Overall fake generation performance. When increasing N c , Eve can ultimately reach Alice's decoder bound on authentic 2D-BCs (dashed lines): a fake can produce the same amount of errors as an authentic 2D-BC, which is good enough for Eve's goal.

This framework is closely connected to the well-known sensitivity attack in digital watermarking already studied in[START_REF] Comesana | Blind newton sensitivity attack[END_REF]