Cyril Lamriben

Pierre-Philippe Cortet

Frédéric Moisy

Leo R M Maas

INSTABILITIES AND TRANSITION IN THREE-DIMENSIONAL FLOWS WITH ROTATION EXCITATION OF INERTIAL MODES IN A CLOSED GRID TURBULENCE EXPERIMENT UNDER ROTATION

Translating a grid in a closed volume of fluid is a convenient way to generate an approximately homogeneous and isotropic turbulence when a compact system is needed, e.g. when experiments are performed in a rotating frame [START_REF] Dalziel | Decay of rotating turbulence : some particle tracking experiments[END_REF][START_REF] Morize | Decaying grid-generated turbulence in a rotating tank[END_REF][START_REF] Bewley | Inertial waves in rotating grid turbulence[END_REF][START_REF] Staplehurst | Structure formation in homogeneous freely decaying rotating turbulence[END_REF]. Such flow excited by a grid translation is, in general, composed of a superposition of (i) a reproducible flow (determined through ensemble averaging) and (ii) a non-reproducible turbulent flow. In the presence of background rotation, both of these two flow components may excite inertial waves [START_REF] Cortet | Viscous spreading of an inertial wave beam in a rotating fluid[END_REF], which propagate because of the restoring nature of the Coriolis force. The excited inertial waves are respectively (i) reproducible -and therefore detectable in the ensemble averageand (ii) non-reproducible -detectable in the individual realizations only- [START_REF] Lamriben | Excitation of inertial modes in a closed grid turbulence experiment under rotation[END_REF]. In a closed container, inertial waves may appear in the form of standing inertial modes, which are the eigenmodes of the container geometry [START_REF] Mcewan | Inertial oscillations in a rotating fluid cylinder[END_REF][START_REF] Maas | On the amphidromic structure of inertial waves in a rectangular parallelepiped[END_REF]. Excitation of inertial modes in grid-generated turbulence has been first observed by Dalziel [START_REF] Dalziel | Decay of rotating turbulence : some particle tracking experiments[END_REF] and are also visible in the experiments of Morize and Moisy [START_REF] Morize | Energy decay of rotating turbulence with confinement effects[END_REF] and Moisy et al. [START_REF] Moisy | Decay laws, anisotropy and cyclone-anticyclone asymmetry in decaying rotating turbulence[END_REF]. They have been characterized by Bewley et al. [START_REF] Bewley | Inertial waves in rotating grid turbulence[END_REF], who found good agreement between the measured frequencies and the numerical results of Maas [START_REF] Maas | On the amphidromic structure of inertial waves in a rectangular parallelepiped[END_REF].

We investigate here the structure of these inertial modes and we explore to what extent they may be reduced [START_REF] Lamriben | Excitation of inertial modes in a closed grid turbulence experiment under rotation[END_REF]. A square water tank is mounted on a rotating platform, and velocity fields in a vertical plane are measured using a corotating Particle Image Velocimetry system. Two grid configurations have been used: a "simple" grid, of mesh size 40 mm, and a "modified" grid, on the top of which a set of inner sidewalls is attached. We demonstrate that, in the latter configuration, the amount of energy stored in the inertial modes is drastically reduced compared to the former one. We make use of the standard Reynolds decomposition to separate the reproducible inertial modes from the turbulence, u(x, t) = U(x, t) + u (x, t), where the ensemble average U(x, t) ≡ u(x, t) is computed over 40 independent decay experiments. We compute the kinetic energies associated to each flow component, namely k tot (t) = u 2 (x, t) , k mean (t) = U 2 (x, t) , and k turb (t) = u 2 (x, t) . The time evolution of these 3 energies is shown in Fig. 1(a), for an experiment performed at a rotation rate of Ω = 0.84 rad s -1 . Both the energy of the total and the mean flow show, superimposed to their overall decay, marked oscillations corresponding to the inertial modes. On the other hand, the turbulent energy shows a monotonic decrease.

In the inset of Fig. 1(a), we plot the ratio of the turbulent to the mean energy : we see that turbulence represents only 50 ± 10% of the energy in the flow. This quite low ratio indicates that the energy injected with the simple grid configuration is evenly distributed among the reproducible inertial modes and the "true turbulence". It is therefore questionable to consider this turbulence as freely decaying, because of the possible energy transfer from the inertial modes to the turbulence. The oscillations in Fig. 1(a) have been analysed in details by computing the temporal spectrum of the ensemble-averaged flow U(x, t). The spectrum shows a series of peaks for frequencies σ in the range [0, 2Ω], as expected for inertial modes. By performing a band-pass filtering of U(x, t) at the peak frequencies, it is possible to extract the spatial structure of each inertial mode. The two dominating modes, of vertical wavenumber unity, are shown in Fig. 2, with associated frequencies perfectly matching the numerical predictions of Maas [START_REF] Maas | On the amphidromic structure of inertial waves in a rectangular parallelepiped[END_REF]. In the modified grid configuration, a set of three parallelepipedic PVC tanks, each consisting in 4 vertical sidewalls, without top and bottom walls, is attached on the top of the grid. Since our grid is translated from the bottom to the top, the inner tanks are upstream of the grid, so that the volume of working fluid is the same as in the simple grid configuration. The time evolution of the 3 kinetic energies is shown in Fig. 1(b) for this modified configuration. In comparison with Fig. 1(a), the oscillations due to the inertial modes are strongly reduced, both for the mean and the total kinetic energies. We also see that the turbulent kinetic energy is now significantly larger than the one of the ensemble-averaged flow. This can be better seen in the inset of Fig. 1(b), showing that turbulence contains, after a transient of about one tank rotation, approximately 85 ± 5% of the total kinetic energy, a value much larger than the 50% obtained with the simple grid configuration. This result proves the efficiency of the modified grid to strongly reduce the production of inertial modes, and therefore to generate a turbulence which is presumably closer to the idealized situation of a free decay.

The present results suggest that the standard assumption of statistical homogeneity may not be appropriate to describe decaying rotating turbulence in a closed container, confirming the findings of Ref. [START_REF] Bewley | Inertial waves in rotating grid turbulence[END_REF]. This calls for the development of new theoretical tools to describe the interaction of turbulence with reproducible inertial modes. However, we have also shown that careful changes in the geometry of the grid allow us to strongly reduce the excitation of reproducible inertial modes, and hence to achieve a nearly "pure" rotating turbulence state. This modified configuration therefore suggests that it is indeed possible to investigate the properties of freely decaying homogeneous turbulence in confined geometry.

Figure 1 :

 1 Figure 1: Total (dashed), mean (continuous) and turbulent (dashed-dotted) kinetic energies as a function of the number of tank rotations Ω t/2π from 40 realizations performed at Ω = 0.84 rad s -1 . Left: simple grid. Right: modified grid with inner tanks. Inset: Ratio of turbulent to total kinetic energy as a function of Ω t/2π.

Figure 2 :

 2 Figure 2: Spatial structure of the 2 dominating inertial modes. The ellipses show the velocity orbit, and the arrows illustrate the velocity field at a given arbitrary phase of the oscillation. The color traces the ellipticity -1 < < 1.


Ardavan Mohajer

Anne Tremier

Ph. D Suzelle Barrington
email: suzelle.barrington@mcgill.ca

Cecile Teglia

Marco Carone

Compost mixture influence of interactive physical parameters on microbial kinetics and substrate fractionation

Keywords: composting, microbial kinetics, respirometry, sludge, wood residues

Composting is a feasible biological treatment for the recycling of wastewater sludge as a soil amendment. The process can be optimized by selecting an initial compost recipe with physical properties that enhance microbial activity. The present study measured the microbial O 2 uptake rate (OUR) in 16 sludge and wood residue mixtures to estimate the kinetics parameters of maximum growth rate μ m and rate of organic matter hydrolysis K h , as well as the initial biodegradable organic matter fractions present. The starting mixtures consisted of a wide range of moisture content (MC), waste to bulking agent (BA) ratio (W/BA ratio) and BA particle size, which were placed in a laboratory respirometry apparatus to measure their OUR over 4 weeks. A microbial model based on the activated sludge process was used to calculate the kinetic parameters and was found to adequately reproduced OUR curves over time, except for the lag phase and peak OUR, which was not represented and generally over-estimated, respectively. The maximum growth rate μ m , was found to have a quadratic relationship with MC and a negative association with BA particle size. As a result, increasing MC up to 50 % and using a smaller BA particle size of 8-12 mm was seen to maximize μ m . The rate of hydrolysis K h was found to have a linear association with both MC and BA particle size. The model also estimated the initial readily biodegradable organic matter fraction, MB 0 , and the slower biodegradable matter requiring hydrolysis, MH 0 . The sum of MB 0 and MH 0 was associated with MC, W/BA ratio and the interaction between these two parameters, suggesting that O 2 availability was a key factor in determining the value of these two fractions. The study reinforced the idea that optimization of the physical characteristics of a compost mixture requires a holistic approach.

Introduction

Composting the sludge produced by treatment plants receiving mainly domestic or food processing wastewaters is a sustainable method of recycling carbon with minimum greenhouse gas production [START_REF] Amlinger | Green house gas emissions from composting and mechanical biological treatment[END_REF]. Composting relies mostly on the ability of microorganisms to biodegrade and stabilise the organic waste, to destroy pathogens and produce an esthetically acceptable soil conditioner [START_REF] Insam | Microbiology of the composting process[END_REF][START_REF] Metcalf | Wastewater Engineering: Treatment and Reuse[END_REF]. Increasing urbanization and industrialization in cities resulted in the production of more sludge waste requiring disposal or anaerobic digestion [START_REF] Adhikari | Urban Food Waste Composting[END_REF]. Otherwise, this sludge waste is landfilled where it is mostly transformed into CH 4 because of ambient anaerobic conditions (Rashmussen and Khalil, 1984). At the landfill site, 45 to 58 % of organic waste on a dry mass basis is transformed into CH 4 , which can be captured at a cost to produce energy (Solid Waste Landfill Guidance, 1999).

Composting consists of 3 to 4 weeks of biodegradation in the active phase, followed by several months of maturation in the curing phase [START_REF] Gupta | Stabilization of primary sewage sludge during vermicomposting[END_REF]. As opposed to the curing phase which stabilizes the more resistant compounds [START_REF] Haug | The practical handbook of composting engineering[END_REF], the microbial activity of the active phase can be manipulated and optimized through a better understanding of the interaction between the physical parameters. For the biodegradation and stabilization of compost mixtures, [START_REF] Mohajer | Microbial oxygen uptake in sludge as influenced by compost physical parameters[END_REF] demonstrated the interaction on O 2 uptake rate (OUR) of physical parameters, namely moisture content (MC), bulking agent (BA) particle size distribution and BA to waste (W) ratio.

The interactive effect of physical parameters on compost decomposition as measured by [START_REF] Mohajer | Microbial oxygen uptake in sludge as influenced by compost physical parameters[END_REF] can be further quantified by estimating microbial degradation parameters. Such microbial parameters can be estimated by assuming that the compost mixture OUR is similar to that of wastewater activated sludge systems decomposing BOD.

The traditional approach to respirometric modeling associates changes in microbial O 2 consumption with the growth and decay of the biomass [START_REF] Spanjers | Respirometry in Control of the Activated Sludge Process: Principles[END_REF]. Past literature has presented models estimating the influence on composting of parameters such as temperature [START_REF] Haug | The practical handbook of composting engineering[END_REF][START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF]Richard and Walker, 2006), moisture content (MC) [START_REF] Richard | Moisture relationships in composting processes[END_REF] and aeration rate (Richard et al., 2006;[START_REF] De Guardia | Influence of aeration rate and biodegradability fractionation on composting kinetics[END_REF].

Certain physical parameters, such as MC and BA properties however, have been shown to be particularly important due to their strong interdependent effect on microbial O 2 uptake [START_REF] Diaz | Factors that affect the process[END_REF][START_REF] Mohajer | Microbial oxygen uptake in sludge as influenced by compost physical parameters[END_REF]. [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF] developed a kinetics model describing microbial growth rate and sludge waste biodegradation. Based on the activate sludge model, the Tremier model estimates kinetic parameters through the linear transformation of O 2 consumption rate measured during the decomposition of organic matter by a heterotrophic biomass. The strength of the Tremier model lies in the fact that it considers the organic matter as split into three different fractions, mainly, the readily biodegradable fraction (MB), the biodegradable fraction requiring hydrolysis (MH) and the inert fraction (IM). Only a few composting models have included the hydrolysis process [START_REF] Hamelers | A theoretical model of composting kinetics[END_REF][START_REF] Liwarska-Bizukojc | Kinetics of the aerobic biological degradation of shredded muncipal solid waste in liquid phase[END_REF], even though it was shown to be rate-limiting [START_REF] Veeken | Effect of temperature on hydrolysis rate of selected biowaste components[END_REF][START_REF] Sole-Mauri | An integrated biochemical and physical model for the composting process[END_REF]. Although the Tremier model does not include all components and variables affecting composting, its strength lies in its simplicity and its inclusion of a hydrolysis step.

Accordingly and for compost mixtures, the objective of this study was to estimate the microbial kinetic parameters and organic matter biodegradation dynamics as a function of the interaction between the physical properties of moisture content (MC), bulking agent to waste ratio (BA/W ratio on a dry basis) and BA particle size. Consisting of slaughter house wastewater sludge and wood residues recycled from a composting operation, the experimental compost mixtures offered a wide range of combinations in term of physical properties. For individual compost mixtures, the O 2 uptake rate (OUR) was measured during 24 days using a respirometry apparatus [START_REF] Mohajer | Microbial oxygen uptake in sludge as influenced by compost physical parameters[END_REF]. With the OUR data, the Tremier model was used to estimate the maximum microbial growth rate, μ m and then the organic matter degradation parameters, namely organic matter hydrolysis rate, K h , and the initial fractions of readily degradable organic matter, MB 0, and that requiring hydrolysis, MH 0 .

Material and Methods

Conceptual approach of the model

The model developed by [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF] assumes that the substrate has three phases: a dry solid phase, an aqueous phase and a porous phase. Within this three phase matrix consisting of the BA and sludge mixture, the organic matter is assumed to offer three different initial fractions each with a specific biodegradation rate: the readily biodegradable faction, MB 0 , the fraction requiring hydrolysis, MH 0 , and that which is inert or not degraded,

MI.

The first fraction, MB 0 , is already soluble and is readily used as a source of carbon and energy by microorganisms. As a carbon source and depending on the biomass growth yield Y, part of MB is transformed to give new biomass. The microbial population grows as a function of available MB and its maximum growth rate and death coefficient:

dX/dt = X t × { μ m × MB t /(K b + MB t ) -b } (1)
where X t is the biomass population in mmol O 2 (kg dry matter) -1 ; t is time in h -1 ; μ m is the maximum growth rate of the biomass in h -1 ; MB t is the mass of readily biodegradable organic matter at time t in mmol O 2 (kg dry matter) -1 ; K b is the saturation constant for MB set at 3 mmol O 2 (kg dry matter) -1 ; and b is the death coefficient of the biomass set at 0.05 h -1 [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF].

The energy needed for biomass growth is supplied through the oxidation of a fraction of MB and the dead biomass expressed as (1-Y) MB and (1-f ) X t . Thus, the O 2 uptake rate (OUR) can be expressed as:

R O2 (t) = X t ×{ (1-Y ) / Y × μ m × MB t /(K b + MB t ) + b × (1-f ) } (2)
where R O2 (t) is the O 2 uptake rate (OUR) at time t in mmol O 2 (kg of dry matter -h) -1 ; Y is the yield coefficient of the biomass growth set at 0.68 (dimensionless); f is the fraction of dead biomass contributing to MI, dimensionless, and MI is the fraction of inert organic matter in mmolO 2 (kg of dry matter) -1 .

The second biodegradable fraction labeled MH supplies MB to the microorganisms through enzymatic hydrolysis:

dMH/dt = X t × { -K h × MH t /X t / (MH t /X t + K mh ) } (3)
where MH t is the fraction of solid or soluble organic matter at time t which requires hydrolysis to become readily biodegradable in mmol O 2 (kg of dry matter) -1 ; K h is the rate of hydrolysis for the fraction MH in h -1 and K mh is the hydrolysis saturation constant for the ratio MH t /X t set at 6.5 (dimensionless).

The resulting mass balance for the readily biodegradable MB fraction can thus be expressed as:

dMB/dt = X t ×{ -1/Y × μ m × MB t /(K b + MB t ) + K h × (MH t /X t ) / (MH t /X t + K mh ) } (4)
The hydrolysis reaction is initiated from the very beginning but becomes the rate limiting process after the peak OUR, as microorganisms are left with the remaining complex organic macromolecules requiring hydrolysis and governed by the rate K h . Resistant organic matter, such as cellulose and lignin accumulated from the biodegradation of the two first fractions, are partly transformed into the third inert fraction MI. The degradation of the first two fractions also leads to the accumulation of dead biomass which, through degradation, is partly accumulated as inert matter, MI. The fraction of dead biomass contributing to MI is defined by the coefficient f with a value of 0.2 [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF].

Parameter Estimation

Equations 1 to 4 were used to estimate the kinetic parameters μ m , K h and X 0 , and the organic matter fractions of MB 0 and MH 0 at time zero (Table 1). The dynamic biological model was fitted to the experimental OUR recorded through respirometry. For each trial, the output parameters of the model were calibrated to the experimental OUR using an optimization program designed by [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF] for the SCILAB software (INRIA, France) based on a least squared method. Default values for Y, f, b, K b , K mh were chosen based on published literature corresponding to 0.68 (dimensionless), 0.2 (dimensionless), 0.05 h -1 , 3 mmol O 2 (kg dry matter) -1 and 6.5 (dimensionless), respectively [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF]. The value of the kinetic parameters μ m and K h and for X 0 , MB 0 and MH 0 were optimized through fitting using linearization methods performed on the exponential rise and subsequent fall of the experimental OUR curves obtained from respirometry. The linearization method corresponds to a simplified way of interpreting the respirometry curve and the values were derived from an identification procedure based on structural identifiable procedures [START_REF] Dochain | Structural identifiability of biokinetic models of activated sludge respiration[END_REF][START_REF] Sperandio | Estimation of wastewater biodegradable COD fractions by combining respirometric experiments in various S0/X0 ratios[END_REF].

Substrate Material and chemical characterization

The experimental materials consisted of sewage sludge from the wastewater treatment facility of a slaughter house and as BA, green waste or twigs and branches recycled from a composting process. For consistency, a large sludge sample obtained prior to the trial was split into 10 kg sub samples and stored until use at -20°C. Table 1 characterizes the experimental materials.

The experimental materials were analyzed for dry matter (DM), organic matter (OM), total organic carbon (TOC), chemical O 2 demand (COD) and total Kjeldahl nitrogen (TKN)

prior to the start of the experiment. The DM was measured by drying the wet samples at 80°C to constant weight. A higher temperature was avoided to prevent the combustion of this type of sample during drying. The OM content was measured by burning the dried ground samples at 550°C for 4 h using the standard method NF U 44-160 [START_REF] Afnor | NF U 44-160 -Amendements organiques et supports de culture -Détermination de la matière organique totale -Méthode par calcination[END_REF]. The TOC was measured by oxidizing the dried ground samples to CO 2 and using infrared spectrometry (SKALAR device) to measure CO 2 production according to the standardized method NF-EN-13137 (Afnor, 2001a). The sample COD was determined by the oxidation of 50 mg of dried ground sample using potassium dichromate, according to an adaptation of the standard method described in the norm NF T 90-101 (Afnor, 2001b) for powdered samples. The TKN content was quantified on 50 mg of dried ground sample by mineralization with a strong acid medium (98% sulphuric acid), followed by steam distillation and titrimetric determination, an adaptation of the standard method NF ISO 11261 [START_REF] Afnor | NF ISO 11261 -Qualité du sol -Dosage de l'azote total -Méthode de Kjeldahl Modifiée[END_REF] for powdered samples. [START_REF] Mohajer | Microbial oxygen uptake in sludge as influenced by compost physical parameters[END_REF] describes the respirometric apparatus used in this study to measure OUR resulting from the biodegradation of the waste mixtures (Figure 1). It consisted of six cylindrical 10 L airtight reactors made of stainless-steel and submersed in a water bath controlled at 40 °C, a temperature was found to produce optimal biodegradation conditions [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF]. Inside the reactor, the substrate material was placed on a 3 mm mesh grid located 70 mm above the cell bottom forming a plenum receiving 65 L h -1 of air via a glass diffuser. As past studies have shown that an intermittent air supply can lead to O 2 limitations [START_REF] Paletski | Stability measurement of biosolids compost by aerobic respirometry[END_REF], a continuous air flow was supplied. Homogenous O 2 diffusion for the trials was ensured by re-circulating part of the exhaust air back into the cells.

Respirometric Measurement Method

The entering and exhaust air streams were monitored for O 2 content using a paramagnetic O 2 gas analyser (MAIHAK Technology, Nimburger, Germany).

To solely test the effect of the experimental physical factors on microbial activity, the apparatus controlled other environmental factors. Along with that of the sample, the temperature of the inlet air was preheated at 40 °C using a copper serpentine 10 mm in diameter, 2 mm in thickness and 2 m in length submerged in the water-bath. The temperature of the sample was monitored by means of a Pt100 temperature probe (OMNI Instruments, UK) inserted in the centre of the cell. The inflowing air was saturated with moisture by bubbling through two water-filled glass bottles immersed in the water-bath. Moisture condensing in the exhaust air was collected in beakers above the water-bath to prevent its return into the sample cells. Once the experiment began, the samples were left inside the respirometric cells until their OUR dropped to a low constant value, usually corresponding to four weeks.

Experimental design and statistical analysis

The 16 experimental mixtures were created by combining low, intermediate and high values of the three physical parameters namely MC, W/BA ratio and BA particle size (Table 2), determined using a response surface method experimental design. Water or dried sludge were mixed with the appropriate amount of BA to obtain MCs of 20, 30, 45, 60 and 70 %, although actual experimentally recorded MC varied slightly (Table 2). The waste mixtures were manually mixed with BA to create W/BA ratios at 1/9.2, 1/7.9, 1/6, 1/4.1 and 1/2.1 on a dry basis. Finally, different BA particle sizes of 8 to12 mm, 12 to 20 mm, 20 to 30 mm, 30 to 40 mm and over 40 mm were achieved by sieving through rotary screens. The C:N ratio of all experimental recipes ranged between 10 and 22, which are acceptable for sludge composting (Table 2).

A 3 kg (wet mass) sample of each mixture was placed in individual cells to prevent BA breakage and to minimize mixture compaction. All O 2 uptake rates (OUR) were expressed on the basis of initial mixture dry mass. Six compost recipes were tested at any one time. In total, 16 compost recipes were tested without duplication because of the wide range of incremental levels used in the combinations selected.

Using the observed experimental respirometric data, univariate linear regression was first performed to delineate the marginal relationships of the measured MC, W/BA ratio and the mean BA particle size in each range, with each of μ m , K h , MB 0 and MH 0 . Multivariate linear regression was subsequently performed to decipher the associations between the physical characteristics of each treatment including their interactions, upon each of the kinetic parameters and substrate matter fractions after 28 days of aeration, using the statistical software package Stata® (Statacorp LP, Texas, USA). The regression model was:

E[Y] =β 0 + β 1 χ 1 + β 2 χ 2 + β 3 χ 3 + β 12 χ 1 χ 2 + β 13 χ 1 χ 3 + β 23 χ 2 χ 3 +β 11 χ 1 ² +β 22 χ 2 ² +β 33 χ 3 ² ( 5
)
where Y is the outcome of interest; β 0 is the intercept; β 1 , β 2, β 3 are the linear coefficients; β 12 , β 13 , β 23 are the interaction coefficients; β 11 , β 22, β 33 are the quadratic coefficients; χ 1 is the MC in %; χ 2 is the BA particle size in mm, dimensionless, and; χ 3 is the W/BA ratio.

Analysis of variance (ANOVA) determined the significance of the models using the F-Test, at a confidence level of 90% (p < 0.1). Moreover, the significance of each regression model parameter (variable or interaction) was determined using a Student Test at a confidence level of 75% (p < 0.25). The regression coefficient R² measured the global fit of the regression model with the experimental data and the adjustment of the models was considered acceptable for R² greater than 55 %.

Results

Model validation

Figures 2 and 3 illustrate the OUR over time for experimental mixtures 4 and 9, respectively, obtained through experimental trials and model simulations using Scilab.

Mixtures 4 and 9 offered the largest and smallest variations between the experimental and simulation curve, respectively, obtained after optimization of the cycles to improve the fit of the simulation curve. For all experimental mixtures, the general OUR curve was reproduced, except for the peak which was generally slightly overestimated. Considering that the area under the curve is used to estimate MB 0 , this model overestimation introduces an error of 5 % at the very most. Furthermore, the model accurately reflected the exponential rise in OUR determining mainly the maximum growth rate μ m of the microbial population. The simulations however, lacked the ability to reproduce the brief lag phase observed at the beginning of the trials where microorganisms were acclimating to mixture conditions.

Nonetheless, the relatively short lag phase of less than 12 hours did not interfere with the subsequent exponential rise in OUR, resulting in similar experimental and simulation curves.

After the peak, the model simulation correlated closely with the subsequent and gradual drop in sample OUR. This period is presumed to correspond mainly to the biodegradation of the more complex organic fraction requiring hydrolysis, MH 0 , resulting in a drop in OUR. As less biodegradable matter remains accessible to the microbes, the OUR recesses to lower levels [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF].

Influence of physical parameters on microbial kinetic coefficients

The experimental OUR curves were used to estimate the maximum growth rate and hydrolysis kinetics in each of the 16 experimental recipes (Table 3). The maximum growth rate μ m varied from 0.07 h -1 achieved in mixture 6 (MC of 30 %, W/BA ratio of 1/7.9 and BA particle size of 30-40 mm), to 0.20 h -1 in mixture 3 (MC of 52 %, W/BA ratio of 1/6 and BA particle size of 8-12 mm). The average μ m for all 16 experimental mixtures was 0.106 h -1 .

These values are somewhat lower than that found in other studies, perhaps due to the characteristic of the sludge waste. [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF] found ranges between 0.13 and 0.34 h -1 using sewage sludge and pine bark in a 1:1 wet mass ratio biodegraded under temperatures of 20 to 70 °C. Activated sludge models suggest a typical value of 0.25 h -1 at 20 °C, but they pertain to the raw volatile solids contained in municipal wastewaters. Kaiser (1996) suggested a μ m value of 0.2 h -1 at 40 °C for the biodegradation modelling of vegetable substrates during composting.

Through regression analysis, the maximum growth rate, μ m , was found to be significantly affected by MC, via a quadratic relationship, and BA particle size (p<0.05) (R² = 0.63):

µ m = 0.1126 + 0.0006 × χ 1 -0.0018 × χ 1 ² -0.0018 × χ 2 +0.0001χ 2 ² (6)
for χ 1 = (MC -45), %; χ 2 = (BA particle size -25), mm

The nature of the quadratic association between MC and growth rate was such that increased moisture levels up to 50 % were associated with larger μ m (Figure 4). A reduction in μ m at levels higher than 50 %, however, resulted in MC reducing the free air space and impeding O 2 availability. The negative association between BA particle size and μ m , on the other hand, reflected the ability of the biomass to maximize surface area attachment and waste biodegradation. Found previously to affect microbial OUR [START_REF] Mohajer | Microbial oxygen uptake in sludge as influenced by compost physical parameters[END_REF], W/BA ratio and its interactions with the other physical parameters did not have a significant impact on μ m as a result of the inoculation effect of the sludge and the BA. The sludge/BA mixture probably contained a high initial microbial population that rapidly expanded upon exposure to aeration, reducing the potential impact that an optimal physical matrix could provide on microbial activity.

Averaged for all 16 experimental recipes, the estimated rate of hydrolysis, K h , had a mean value of 0.098 h -1 over a range of 0.081 h -1 in mixture 11 (MC of 52 %, W/BA ratio of 1/6 and BA particle sizes of over 40 mm) to 0.12 h -1 in mixture 8 (MC of 62 %, W/BA ratio of 1/4.1 and BA particle sizes of 12-20 mm). These values were slightly higher than those suggested by [START_REF] Sole-Mauri | An integrated biochemical and physical model for the composting process[END_REF], which ranged from 0.007 to 0.04 h -1 , depending on the substrate, but were less than those reported by [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF] at 0.1 to 0.2 h -1 depending on the temperature. The rate of hydrolysis was found to be significantly associated to MC and BA particle size (p<0.05) but also influenced by the interaction between W/BA ratio and BA particle size (R² = 0.56):

K h = 0.0986 + 0.0005 × χ 1 -0.0008 × χ 2 -0.0101 × χ 2 χ 3 (7)
for χ 1 = (MC -45), %; χ 2 = (BA particle size -25), mm; χ 3 = (W/BA ratio -0.167), dimensionless.

A higher MC and smaller BA particle size value tended to increase K h . Accordingly, the hydrolysis reaction is favoured by an increasing MC and a large specific surface provided by smaller BA particle size (Figure 5). The importance of a small BA particle size is underlined through the interaction with W/BA. Hence, if the quantity of sludge in the mixture is increased, BA particle size has to decrease not to limit the hydrolysis kinetics.

Influence of physical parameters on the biodegradable organic fraction

The model estimated the readily biodegradable organic matter fraction, MB 0 , and the fraction requiring hydrolysis, MH 0 (Table 1), available for microorganisms in the studied experimental conditions. The MB 0 fraction ranged from a low of 475 mmol O 2 (kg dry matter) -1 in mixture 6 with a relatively large BA particle size of 30-40 mm and a low W/BA ratio and MC of 1/7.9 and 30 %, respectively, to a high of 2 085 mmol O 2 (kg dry matter) -1 for mixture 3 with a smaller particle size of 8-12 mm, higher W/BA ratio of 1/6 and an optimal MC of 50 %. A minimum MH 0 fraction of 7 950 mmol O 2 (kg dry matter) -1 was reached for mixture 1 with the lowest W/BA ratio of 1/9.2 and an intermediate value of BA particle size of 20-30mm. The maximum MH 0 concentration of 18 160 mmol O 2 (kg dry matter) -1 was reached with mixture 5 with a large W/BA ratio of 1/6 and a high of MC of 68 %.

The MB 0 fraction was mainly influenced by BA particle size, and the interaction between MC and W/BA ratio (p<0.05). To a less extent, it was also influenced by individual effects of W/BA ratio (p<0.15) and MC (p<0.25) (R² = 0.64):

MB 0 = 1182 + 6.99 × χ 1 -24.20 × χ 2 + 1861 × χ 3 -275.42 × χ 1 χ 3 (8)
for χ 1 = (MC-45), %; χ 2 = (BA particle size -25), mm; χ 3 = (W/BA ratio -0.167), dimensionless.

Predictably, less BA with a smaller particle size increased MB 0 since the BA is less biodegradable than the sludge. Increasing MC probably allows microorganisms to better reach the available MB 0 . MC and W/BA ratio impacted available MB 0 through a negative interactive effect where an increase in either parameter had a decreasing effect. This negative crossed effect of MC and W/BA resulted from physical restrictions on the accessibility of the organic matter and oxygen to the microorganisms. Indeed, with high moisture and a high quantity of sludge versus BA, the porosity of the medium can be limited, consequently affecting the aeration of the microorganisms. On the other hand, with low moisture and a low quantity of sludge versus BA, conditions for microorganisms activity are also limited.

The sum of MB 0 and MH 0 is equivalent to the total amount of organic matter biodegraded over the four weeks of respirometry. The total concentration ranged from a minimum of 8 912 mmol O 2 (kg dry matter) -1 with mixture 1 with mid level values for both MC (42 %) and BA particle size (20-30 mm) and a low W/BA ratio (1/9.2). A maximum value of 19 585 mmol O 2 (kg dry matter) -1 was obtained with mixture 5 with the highest MC (68 %) and mid-level values for both BA particle size (20-30 mm) and W/BA ratio (1/6). The biodegradable organic matter in the 16 mixtures comprised about 35 % of the total organic matter. As written concerning MB 0 , the Tremier model was designed to evaluate the quantity of organic matter which can be oxidized under experimental conditions rather than the total potential biodegradable matter.

The sum of the MB 0 and MH 0 fractions were associated with MC, W/BA ratio and the interaction between MC and W/BA ratio (p<0.05) (R² = 0.59):

(MB 0 + MH 0 )= 15211 + 114 × χ 1 +14208 × χ 3 -1769 × χ 1 χ 3 (9)
for χ 1 =(MC-45), %; χ 3 =(W/BA ratio -0.167), dimensionless.

Increasing MC up to 50 % along with W/BA, increased the sum of MB 0 and MH 0 as a result of a more favourable water content and a higher sludge fraction. The negative interaction between the two parameters, however, altered the individual main effect (Figure 6). Coupled with larger W/BA ratio, MC above 50 % decreased the sum of MB 0 and MH 0 , most likely due to lower O 2 diffusion as a result of less free-air-space. Thus, these results confirm the notion that the impact of MC and W/BA ratio in composting systems are interconnected, where the level of one parameter was important to interpret the impact of the other. For MC and the W/BA ratio exceeding 50 % and 1/4.1, respectively, [START_REF] Mohajer | Microbial oxygen uptake in sludge as influenced by compost physical parameters[END_REF] also found a reduced OUR. The same conditions produced a reduction in the sum of MB 0 and MH 0 also as a result of less O 2 availability.

Conclusion

With compost mixture respirometry data, this study used the microbial Tremier model adapted from the activated sludge process to obtain microbial kinetic parameters describing maximum microbial growth rate μ m , the rate of organic matter hydrolysis K h and the initial fractions of organic matter being readily degradable MB 0 and requiring hydrolysis MH 0 . These parameters were estimated for 16 experimental mixtures of sludge and wood residue offering various physical parameter combinations of moisture content (MC), waste to bulking agent ratio (W/BA ratio) and bulking agent (BA) particle size.

The model accurately simulated the OUR over time except for brief periods corresponding to the initial lag phase and peak. Differences in the estimated μ m and K h were shown to be mostly explained by the initial physical characteristics of the experimental mixtures and their interaction. The MC had a quadratic relationship with μ m and a positive linear association with K h while particle size had a negative linear association with both.

Bulking agent particle size in the range of 8-12 mm and MC up to 50 % yielded the highest μ m and K h . The sum of the readily degradable fraction of organic matter and that requiring hydrolysis, MB 0 and MH 0 , respectively, were impacted in an interactive manner by both MC and W/BA ratio. Since the Tremier model is based on OUR, the physical parameters were found to impact the actual rather than the total potential value of MB 0 and MH 0 as the results based on O 2 availability explain. The study reinforces the fact that the physical characteristics of the initial compost mixture are optimized through a holistic approach. The interactive association between MC and W/BA ratio, in particular, was important in influencing the degree of biodegradable matter.

List of symbols

b is the death coefficient of the microbial mass, h -1 BA is the bulking agent COD is the chemical oxygen demand, mg O 2 (kg of dry organic matter) -1 DM is the dry matter, % f is the fraction of dead biomass contributing to MI, dimensionless K b is the concentration of organic matter required to obtain half of μ m , mmol O 2 (kg dry organic matter) -1 K mb is the hydrolysis saturation constant for the ratio MH t /X t , mmol O 2 (kg dry organic matter) -1 K h is the hydrolysis rate constant for the fraction MH in h -1 MB 0 is the initial mass of readily biodegradable organic matter at time t, mmol O 2 (kg dry matter) -1 MB t is the mass of readily biodegradable organic matter at time t, mmol O 2 (kg dry matter) -1 MI is the fraction of organic matter which is inert in kg (kg of dry matter) -1 . MH 0 is the initial fraction of solid or soluble macromolecules at time t which first requires hydrolysis to be reduced to the easily biodegradable matter, kg (kg of dry matter) -1 MH t is the fraction of solid or soluble macromolecules at time t which first requires hydrolysis to be reduced to the readily biodegradable matter, kg (kg of dry organic matter) -1 OM is the organic matter, % OUR is the oxygen uptake rate, mmol O 2 (kg of dry organic matter -h) -1 R O2 (t) is the O 2 consumption rate at time t, mmol O 2 (kg of dry organic matter -h) -1 t is time, h -1 TC is the total carbon, % TKN is the total Kjeldahl nitrogen, mg N (kg of dry organic matter) -1 W/BA ratio is the waste (agro-food sludge) to bulking agent (wood residues recycled from a composting centre) ratio on a dry mass basis, dimensionless X is the microbial population, mg biomass (kg dry organic matter) -1 X 0 is the initial mass of microbial population at time 0, mg biomass (kg dry organic matter) -1 X t is the mass of microbial population at time t, mg biomass (kg dry organic matter) -1 Y is the coefficient of biomass growth yield, mmol O 2 (mg biomass) -1 β 0 is the regression intercept, dimensionless β 1 , β 2, β 3 are the linear coefficients, dimensionless μ m is the maximum growth rate of the microbial population, h -1 χ 1 is the MC in % χ 2 is the W/BA ratio, dimensionless χ 3 is the BA particle size in mm [START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF]. . Simulated effect of compost mixture moisture content and bulking agent particle size on the hydrolysis constant K h for the organic matter fraction which is not readily degradable, MH 0 . Figure 6. Simulated effect of compost mixture moisture content and waste to bulking agent (W/BA) ratio on the fraction of organic matter which is degraded during composting (MB 0 + MH 0 ).

Figure 1 .

 1 Figure1. Schematic diagram of respirometry apparatus[START_REF] Tremier | A respirometric method for characterizing the organic composition and biodegradation kinetics and the temperature influence on the biodegradation kinetics, for a mixture of sludge and bulking agent to be composted[END_REF].

Figure 2 .

 2 Figure 2. Oxygen uptake rate over time for mixture 4 (moisture content of 49 %; waste to bulking agent ratio of 1/2.8 dry mass; bulking agent particle size of 20-30mm) with the largest variation between experimental and simulation trials.

Figure 3 .

 3 Figure3. Oxygen uptake rate over time for mixture 9 (moisture content of 56 %; waste to bulking agent ratio of 1/4.1 dry mass; bulking agent particle size of 30-40mm) with the smallest variation between experimental and simulation trials.

Figure 4 .

 4 Figure 4. Simulated effect of compost mixture moisture content and bulking agent particle size on the maximum microbial maximum growth, μ m .

Fig. 5

 5 Fig. 5. Simulated effect of compost mixture moisture content and bulking agent particle size on the hydrolysis constant K h for the organic matter fraction which is not readily degradable, MH 0 .

Table 3

 3 Microbial kinetics and substrate biodegradation components. MB 0 : initial fraction of organic matter being readily degradable; MH 0 : initial fraction of organic matter requiring hydrolysis; DM: dry matter.

	Mixture	Maximum	Hydrolysis	MB 0	MH 0	Total MB +
		growth rate, μ m (h -1 )	rate constant, K h (h -1 )	(mmol O 2 / kg DM)	(mmol O 2 / kg DM)	MH 0 (mmol O 2 / kg DM)
	1	0.1994	0.1258	959	7953	8912
	2	0.1051	0.1014	1264	15342
	3	0.2006	0.1172	2085	13169
	4	0.1100	0.0873	1763	16300
	5	0.1119	0.1165	1429	18156
	6	0.0685	0.0849	475	10729
	7	0.0961	0.1088	1687	14381
	8	0.0978	0.1209	850	14179
	9	0.0951	0.0945	928	14710
	10	0.1155	0.0975	1186	16753
	11	0.1053	0.0813	971	12769
	12	0.0845	0.0847	1025	12580
	13	0.0805	0.0851	1068	14007
	14	0.0960	0.0987	1090	16699
	15	0.1159	0.0872	1293	15083
	16	0.0851	0.0774	993	14621
	Note:

Acknowledgment

This project was accomplished through the collaboration between Cemagref (UR GERE) and

McGill University (Department of Bioresource Engineering). This research is part of a larger project, named ESPACE, financed by the French National Research Agency (ANR), currently being carried out in partnership between Cemagref, Suez-Environment and Institut de Mécanique des Fluides de Toulouse (IMFT). The Natural Science and Engineering Research Council of Canada (NSERC) is also acknowledged for its financial contribution.


Keywords: MANET, multicast, securité, vulnérabilité, SMF, attaques, IETF 1 Henceforth, TTL

Analyse de Vulnérabilité du Protocole "Simple Multicast Forwarding (SMF)" pour des Réseaux Ad Hoc Résumé : Afin d'augmenter le nombre de déploiements de réseaux ad hoc dehors des "testbeds" purement expérimentals, des protocoles de routage des réseaux ad hoc doivent être en mesure de préserver l'intégrité du réseau, même lorsqu'ils sont confrontés avec des participants imprudents ou malicieux. Un premier pas vers la protection d'un réseau ad hoc est d'analyser les vulnérabilités du protocole de routage qui gère la connectivité du réseau. En comprenant comment ces protocoles de routage peuvent être exploités par des personnes ayant de mauvaises intentions, des contre-mesures peuvent être dveloppées. Un protocole de routage pour des réseaux ad hoc, développé par l'Internet Engineering Task Force (IETF) comme protocole de routage de multicast pour la diffusion efficace des données, est appelé "Simplified Multicast Forwarding" (SMF). Ce protocole est analysé, et ses vulnérabilités décrites dans ce rapport.

SMF est constitué de deux composantes indépendantes: (i) la détection des paquets dupliqués et (ii) la sélection des relais, dont chacun présente son propre ensemble de vulnérabilités qu'un attaquant peut exploiter pour compromettre l'intégrité du réseau. Ce rapport explore des vulnérabilités dans chacune des deux composantes, afin d'identifier les vecteurs d'attaque, ainsi de permettre de développer des contre-mesures.

Introduction

Network integrity in wired, multi-hop networks is largely preserved by physically controlling access to the communications channel between routers: know thy peers, know which behavior to expect from thy peers, trust thy peers -and be able to disconnect thy peers if they show not worthy of that trust. In a MANET (Mobile Ad hoc NETwork), often operated over wireless interfaces, such is less obvious: physical access to the media between routers is not delimited by a cable, but is available to anyone within transmission range; the network topology is time-varying, either due to router mobility or due to time-varying characteristics of the channel; traffic is often retransmitted over the same wireless interface as the one over which it was received. Consequently, MANET protocols are conceived to manage conditions where less -or no -a-priori structure is present between peers, and are exposed to characteristics not commonly found in classic wired networks.

This exposure also renders MANET protocol more vulnerable to attacks, although two things shall be noted. First, MANET protocols by way of their lack of a-priori infrastructure knowledge and lack of physical access control to the communications channel are simply "exposing" and rendering more easily exploitable vulnerabilities already present in classic networks (e.g., such as injecting rouge traffic in a network). Second, MANET protocols having to manage specific characteristics (e.g., retransmission of traffic on an interface over which it was received), introduces new, specific protocol mechanisms, which may be open to attacks.

Background and History

The "Simple Multicast Forwarding" (SMF) protocol [START_REF] Macker | Simplified Multicast Forwarding[END_REF] is a multicast routing protocol for MANET-wide efficient broadcasting, employing reduced relay sets for decreasing the number of redundant retransmissions of a data packet. Reduced relay sets so used were introduced in and standardized for IP networks by way of the Optimized Link State Routing Protocol (OLSR [START_REF] Clausen | Optimized Link State Routing Protocol (OLSR)[END_REF]) in 2003, where such were used for substantially reducing the protocol overhead incurred by diffusion of routing protocol control traffic (link state advertisements, in [START_REF] Clausen | Optimized Link State Routing Protocol (OLSR)[END_REF] denoted "TC messages"). The reduced relay set mechanism in OLSR is based on Multi-Point Relays (MPRs) [START_REF] Qayyum | Multipoint relaying: An efficient technique for flooding in mobile wireless networks[END_REF]. This concept was retained and used in an extension of OSPF for MANET areas [START_REF] Clausen | OSPF Multipoint Relay (MPR) Extension for Ad Hoc Networks[END_REF]. The reactive MANET routing protocol AODV [START_REF] Perkins | Ad hoc On-Demand Distance Vector (AODV) Routing[END_REF] also uses MANET-wide broadcast of its control traffic (route requests). [START_REF] Clausen | Optimizing Route Length in Reactive Protocols for Ad Hoc Networks[END_REF] showed that using MPRs for flooding such control traffic resulted not just in reduced channel load, but also in shorter unicast paths. Other experimental routing protocols, including [START_REF] Ogier | Topology Dissemination Based on Reverse-Path Forwarding (TBRPF)[END_REF] and [START_REF] Ogier | Mobile Ad Hoc Network (MANET) Extension of OSPF Using Connected Dominating Set (CDS) Flooding[END_REF], have used different relay set selection mechanisms, and the Internet Engineering Task Force (IETF) is standardizing the MANET routing protocol OLSRv2 [START_REF] Clausen | The Optimized Link State Routing Protocol version 2[END_REF], retaining the MPR concept.

The success of such reduced relay sets for protocol control traffic diffusion lead to investigations into using such also for user data traffic, including [START_REF] Jacquet | Diffusion mechanisms for multimedia broadcasting in mobile ad hoc networks[END_REF] and [START_REF] Clausen | Investigating data broadcast performance in mobile ad-hoc networks[END_REF], ultimately leading to the IETF proposing development of SMF [START_REF] Macker | Simplified Multicast Forwarding[END_REF] as an experimental protocol.

SMF Overview

SMF provides basic IP multicast routing for MANETs. It consists of two main components: multicast "Duplicate Packet Detection" (DPD) and "Relay Set Selection" (RSS).

Multicast Duplicate Packet Detection (DPD)

DPD is used as part of the forwarding process to check if an incoming packet has been previously received (and forwarded) -and therefore should be droppedor not. In MANETs, as illustrated in figure 1, duplicate packets are a common fact of life: router n1 is retransmitting a broadcast packet received from router n0 on the same interface as the one over which it was received, so as to ensure receipt also by router n2 -causing router n0 to receive the packet a second time. DPD is achieved by a router maintaining a record of recently processed multicast packets, and comparing received multicast packets herewith. A duplicate packet detected is silently dropped and not inserted into the forwarding path of that router, nor delivered to an application. DPD, as proposed by SMF, supports both IPv4 and IPv6 and for each suggests two duplicate packet detection mechanisms: 1) header content identification-based DPD (I-DPD), using packet headers, in combination with flow state, to estimate temporal uniqueness of a packet, and 2) hash-based DPD (H-DPD), employing hashing of selected header fields and payload for the same effect.

Relay Set Seletion

RSS produces a reduced relay set for use when relaying information across the MANET. SMF supports the use of several relay set algorithms, including E-CDS (Essential Connected Dominating Set), S-MPR (Source-based Multi-Point Relay), or MPR-CDS. Those algorithms are based on localized election, derived from those explored for efficient topology diffusion in MANET routing protocols.

INRIA

Statement of Purpose

While multicast protocols and efficient flooding mechanisms are well studied for performance and convergence properties, little work considers also security issues and implications of the protocols in use -which assume that the routers in the networks can be "trusted" to perform properly. In any deployment scenario, however, this assumption cannot be taken at face value: the "accessibility" of a wireless communications channel may open access to malicious routers attempting to participate in the network -or an otherwise non-malicious router may simply be misconfigured.

If deployments of MANETs are to become common outside experimental settings, protocols operating in such networks must be resilient to such malice or misconfiguration. A first step towards such resilience is to understand the vulnerabilities of a given protocol and identify probable attack vectors hereon.

This memorandum analyses SMF in order to understand its vulnerabilities. Various threats, from accidental misbehavior of routers or from intentionally malicious attackers, are studied, and threat sources, threat actions, threat consequences, etc. are explored. While the study is generally based on SMF, the components of SMF, such as duplicate packet detection and relay set selection, are common in other multicast routing protocols, and may therefore be also more generally applicable.

While the memorandum has the ambition of being thorough, in matters of security it is prudent to be explicit to not claim completeness of an analysis.

Memorandum Outline

The remainder of the memorandum is organized as follows. In section 2, threats to DPD are first discussed. Possible attacks to the Relay Set Selection Vector (RSSV), which is used for identify different types of RSS algorithms, are presented in section 3. The general threats to RSS are presented in section 4. The memorandum is concluded in section 5.

Threats to Duplicate Packet Detection

The DPD mechanism is based on a unique identity check of the incoming packets. A router needs to record a history of processed multicast packets so as to ensure that a given packet is processed and forwarded at most once -which entails that such history must be maintained for at least the maximum network traversal time of a packet. However, neither IPv4 nor IPv6 contains mechanisms for uniquely identifying a given packet. SMF introduces two mechanisms compensating this: I-DPD and H-DPD. This section discusses attacks on each of these, as well as the consequences on protocol operation that such may have.

Identification-based DPD (I-DPD)

For I-DPD, a DPD identifier in the packet header is used for identification of a packet. In case of fragmented packets, and packets using IPsec, the contained fragment and packet sequence numbers can be used. When neither is present, an additional identifier in the packet header is needed. SMF proposes an IPv6 header option to this effect, recognizing that adding such IP packet header information is not supported for IPv4.

The identification of a packet is, then, based on the source IP address and the sequence number (from IPsec, fragment number or header option). In this way, when each intermediate router receives a packet, it can determine if the packet has been received before.

Pre-play Attack

If a malicious router can obtain the (source IP, sequence number) of a packet, it can inject (invalid) packets with exactly the same identification information into the network. As such an invalid packets propagates through the network, if arriving before the valid packet with same identification information, this valid packets will be discarded as a duplicate. If further sequence numbers are predictable, a malicious router can inject invalid packets with valid sequence numbers in advance, ensuring that subsequent valid packets are discarded as duplicates.

Figure 2 illustrates an example of a pre-play attack. Router a is the source and generates a multicast packet with sequence number n. When the malicious router X receives the packet, it injects an invalid packet with the same sequence number n. Routers which receive the invalid packet first will discard subsequent arrivals of the valid packet. The consequence hereof depends on the network topology: as depicted in figure 2, the attack might not affect routers that are farther away from the malicious router than they are from the source router (i.e., routers e and h), as the valid packet might reach those routers first. For routers closer to the attacker than to the source (i.e., router g and f ), the invalid packet will be received first, causing subsequently arriving valid packets to be dropped. For routers with equal distance (router c and d ), it depends on the link status and the transmission of the routers.

When the succession of sequence numbers from a source is predictable, a malicious router can, upon having observed a valid packet being generated by a legitimate router, conduct a pre-play attack by injecting invalid packets with not-yet-used-but-soon-to-be-used sequence numbers. As shown in figure 3, if an incremental algorithm is used for generating sequence numbers, X can thereby prohibit corresponding valid packets from attaining the part of the network reachable from X without passing through a. The following packets from a with seq = n + 1, seq = n + 2, etc, will be regarded as duplicate packets and discarded.

Another possible pre-play attack is based on the Time-to-Live (TTL) or hop limit field 1 . As routers only forward packets with T T L > 1, a malicious router can forward an otherwise valid packet, while drastically reducing the TTL hereof. This will inhibit recipient routers from later forwarding the same multicast packet, even if received with a different TTL -essentially a malicious router thus can instruct its neighbors to block forwarding of valid multicast packets. As the TTL of a packet is intended to be manipulated by intermediaries forwarding it, classic methods such as signatures are typically calculated with setting TTL fields to some pre-determined value (e.g., 0) -such is for example the case for IPsec Authentication Headers' [START_REF] Kent | IP Authentication Header[END_REF] -rendering such an attack more difficult to both detect and counter. If the malicious router has access to a "wormhole" through the network (a directional antenna, a tunnel to a collaborator or a wired connection, allowing it to bridge parts of a network otherwise distant) it can make sure that the packets with such an artificially reduced TTL arrive before their unmodified counterparts. Figure 4 illustrates an example of this attack, with X being the malicious router. On receiving a packet with T T L = 63 and seq = n, X broadcasts the same packet, but with an artificially reduced T T L = 1. For routers near X, such as c, d, and e, if they receive the packet with the artificially reduced TTL before the valid packet arrives, the valid packet will be discarded. If a wormhole between X and a distant router i exists, X can inject the packet with the artificially reduced TTL to i, and to the part of the network reachable through i -which would subsequently discard later arriving valid packets.

Sequence Number Attack

In a pre-play attack, a malicious router makes use of the DPD mechanism to force other routers to discard otherwise valid packets -thus preventing these from reach parts of the network. A malicious router can also seek to disable DPD, by modifying the sequence number in packets that it forwards. Thus, routers will not be able to detect an actual duplicate packet as a duplicaterather, they will treat them as new packets, i.e., process and forward them. The consequence of this attack is an increased channel load, the origin of which appears to be a router other than the malicious router.

In figure 5, when the malicious router X receives the packet (seq = n) from router a, it simply modifies the sequence number to n + i, and sends it back to the network. Router c will not be able to detect the duplicate packet, which should be discarded.

[1] proposes use of IPsec sequence numbers as packet identifiers. If IPsec is used, authentication and integrity of the packets is usually assumed protected. In a MANET environment, the usage of IPsec is still not well defined -problems include key distribution mechanisms, suitable cryptographic algorithms and the use of IPsec for multicast. Furthermore, to the best of the authors knowledge, few deployments of MANETs employ IPsec. Therefore, this memorandum does not consider the usage of the IPsec options as presented in [START_REF] Macker | Simplified Multicast Forwarding[END_REF].

Hash-based DPD (H-DPD)

In H-DPD, a hash of the non-mutable header fields, options fields and data payload is used as identifier of a packet, replacing explicit sequence numbers. Each packet is, thus, uniquely identified by the IP address of the source of the packet, and this hash-value. When a source host generates a packet, or when a gateway ingresses the packet into the MANET, it calculates the hashvalue hereof. In case the source host or gateway identifies that it recently has 6, generated such that calculating the hash also over this HAV will render the resulting value unique. Note that the hash value in SMF is applied only to provide a low probability of collision, and is specifically not used for cryptographic or authentication purposes. Also note that threats, similar to those discussed in section 2.1 continue to apply for when using H-DPD. One advantage of H-DPD over I-DPD may be, however, that as the hash-value is calculated also over the data payload of the packets, predicting subsequent hash-values and conducting a pre-play attack is somewhat harder.

Introducing a header option, however, also introduces a potential vulnerability: the HAV header option is only used when the source or the ingressing router detects that a previously generated packet has an identical hash value as this packet. A malicious router which discovers the existence of a HAV header in a packet can therefore conclude that a hash collision is possible if the HAV header is absent. Thus, it needs to simply remove the HAV header before retransmitting the packet, which may cause the packet to be dropped by recipients. Again, in doing so the malicious router causes the packet to be dropped not by itself, but by other routers in the network.

As shown in figure 7, a is the source router and X is the malicious router. At the source a, it generates a packet p, and stores the corresponding hash h(p) = x in its DPD cache. The following packet p generated, has the same hash as the previous packet, i.e. h(p ) = h(p) = x. The source router a is able to detect the hash collision by comparing it with the records in its DPD cache. Therefore, a adds an HAV header as shown in figure 6, to avoid a possible collision by having a new hash value h(p + HAV ) = x . When the malicious router X receives packet p , it can conclude that a collision might happen by removing the HAV header. On receiving packet p at router b, a record with hash h(p) = x is saved in the DPD cache. The consequence is that packet p cannot be distinguished by router b after the HAV header being removed because it has the same hash h(p ) = x. Similarly, a malicious router can disrupt DPD by adding an HAV header option to a packet. This modified packet cannot produce the same hash value as the original packet, so it cannot be detected as a duplicate packet. This is similar to the attack in I-DPD, where a malicious router can change the sequence number for the same effect.

In figure 8 Another possible attack for a malicious router is to transmit many packets with identical payload and IP header within a short time interval ("beacons"). This has several implications when H-DPD is used: (i) similar to a "jamming" attack, the increased load on the channel may lead to increased number of collisions of data and control traffic packets. (ii) An (adjacent) router receiving INRIA such a beacon has to calculate and add a HAV header option to the packet header. This operation is time-consuming, and the packet has to be stored while the header option is generated. If a large number of beacons is received by a router, memory and CPU resources may thus be exhausted by this "Denial of Service" attack. (iii) When a packet is retransmitted by the adjacent router, an entry is stored in the hash cache for some amount of time. A large number of beacons within a short time may lead to an overflow of that buffer. Depending on what cache management is used, older -possibly "legitimate" -hash entries may be dropped from the cache, leading to an effective deactivation of the hashbased DPD mechanism.

Threat to Relay Set Selection Vector (RSSV)

Reduced Relay Set Selection (RSS) in SMF is achieved by distributed algorithms that dynamically calculate a topological Connected Dominating Set (CDS). Such algorithms are generally based on the presence of a neighbor discovery protocol, such as the "Neighborhood Discovery Protocol" (NHDP) [START_REF] Clausen | Mobile Ad Hoc Network (MANET) Neighborhood Discovery Protocol (NHDP)[END_REF], providing 1-hop and 2-hop neighborhood information. The relay set is then computed by using one from among a set of possible algorithms, such as E-CDS, S-MPR, etc. These algorithms are not interoperable, hence routers in a MANET must communicate to their neighborhood which algorithm(s) they respectively support. To this end, [START_REF] Macker | Simplified Multicast Forwarding[END_REF] defines a "Relay Set Selection Vector" (RSSV), by way of message and address block TLVs [START_REF] Clausen | Generalized Mobile Ad Hoc Network (MANET) Packet/Message Format[END_REF] to be used with the NHDP HELLO message exchange, allowing a router to declare which RSS algorithms it and its immediate neighbors support 2 .

In SMF, two TLV types are defined for RSS algorithms:

• An SMF message TLV type, which is used to identify the existence of an SMF instance operating in conjunction with NHDP.

• An SMF address block TLV type, which is used to share the RSS algorithm configuration information among 2-hop neighbors.

In both TLVs, a value is assigned to represent each RSS algorithm.

RSSV Spoofing

Given the fact that there may be different RSS algorithms operating concurrently in the same network, a router will have to select relay sets according to compatibility of the algorithms operating in its immediate and 2-hop neighborhoods. A potential attack is, therefore, if a router -intentionally or otherwise -share false RSSV information for itself or for its neighbors. For example, in figure 9, router a is about to select its relays. The following RSS algorithms are used in different routers:

• E-CDS: router b, d, e

• S-MPR: router c, f, g

• MPR-CDS: router h All routers, faithfully, declare their RSSV. Based on the messages from routers b, h and c, router a learns what algorithms are supported by both its direct neighbors and its 2-hop neighbors. This allows router a to observe that while router h provides topological coverage to all of the 2-hop routers (d, e, f, g), router h runs an RSS algorithm different from all of d, e, f, g. Therefore, if a selects h as relay, h may not be able to select relays among d, e, f, g and thus packet forwarding beyond d, e, f, g would not happen. Router a also learns that router b runs the same RSS algorithm as the 2-hop neighbors d, e, reachable via b -and that router c runs the same RSS algorithm as the 2-hop neighbors f, g, reachable via c. Router a can therefore select b and c as relays, knowing that both of these will be able to not only provide coverage to all 2-hop neighbors, but also be able to select proper relays among these 2-hop neighbors. A malicious router, spoofing the RSSV of its 2-hop neighbors, is shown in figure 10: X declares itself with RSSV=MPR-CDS in message TLVs, and further declares that d, e, f, g have RSSV=MPR-CDS. Thus, router a will choose X as sole relay: from the information available to a, X provides optimal topological coverage of the 2-hop neighborhood -and by running the same RSS as (declared for) all 2-hop neighbors, should be able to also do proper relay set selection with these. As a consequence, X will "take control" of the multicast traffic in its neighborhood -in this case, be able to prohibit b and c from being selected as relays and, thus, if X isnot actually forwarding traffic or performing RSS, disrupt network connectivity.

Finally, X might simply declare that all other routers have (only) RSSV=CF, classical flooding, thus degrading the network performance to that of a simple flooding domain.

RSSV Indirect Jamming

In a neighbor discovery based mechanism, a malicious router can intentionally and frequently alter the information declared -including the RSSV -so as to cause generation of inordinate amounts of control traffic by legitimate routers. Such indirect jamming is discussed in [START_REF] Herberg | Security Issues in the Optimized Link State Routing Protocol Version 2 (OLSRV2)[END_REF] for neighborhood discovery and link state advertisement, and also applies for the RSSV, which a malicious router may alter and signal frequently, causing its neighborhood to launch (possibly computationally intensive) RSS recalculations and signal selected relay set (causing increased channel occupation) as well as the change of its neighbor's status.

As shown in figure 11, the malicious router X first declares itself as RSSV=E-CDS at t 0 . Router a will signal the change of its neighbor in its HELLO message at t 1 upon receiving the message from X. In a relatively short time, X advertises in a HELLO that RSSV=S-MPR, and a link to another router b at t 1 . When a receives this message at t 2 , it will believe that X has changed its status, then calculate its MPR set and broadcast a new HELLO message. The above action can be repeated to consume the power of a and the bandwidth.

Threats to Relay Set Selection

[1] provides a framework for RSS, without requiring the use of any specific RSS algorithm. This section will, therefore, not explore the vulnerabilities of a specific RSS algorithm, but rather general threats to the framework of SMF relay set selection.

Eavesdropping

Eavesdropping is a common and easy passive attack in a wireless environment. Once a packet is transmitted, any suitable transceiver can potentially obtain a copy, for immediate or later decoding. Neither the source nor intended destination can detect this. As previously indicated, SMF uses a neighborhood discovery protocol for providing each router with 1-hop and 2-hop topological information. A malicious router can eavesdrop on the NHDP message exchange and thus learn this local topology information, as well as some source and destination addresses of data packets transmitted.

Eavesdropping will not have direct threat to the network nor to SMF, but it can provide crucial network information such as identity of communicating routers, link characteristic, router configuration, etc., enabling other attacks.

Message Timing Attack

As NHDP is used to make relay set selection decisions, vulnerabilities of this protocol also affect SMF operation. NHDP control messages define two types of timing information:

• Validity time, the time upon receipt during which the information contained within the message should be considered valid.

• Interval time, the time after which the next control message from the same router should be expected.

For validity time, since information contained in control messages is considered valid only for the duration indicated, an attacker can simply eavesdrop on NHDP messages from its neighbors, then instantly replay a received such message -but modified to have a low validity time, illustrated in figure 12. Router b broadcasts a HELLO message with valiT ime = 6s. Router a receives the messages and marks the link between itself and b is valid for 6 seconds. X eavesdrops on the messages, obtains the identity of router b, then transmits the HELLO message with valiTime=0.1s. Receipt of this message by a causes a to replace previously received link information, and therefore consider the link between itself and b as invalid after very short time (0.1 second). For SMF, this means that b will not be selected as relay by a even it may provide good connectivity to other parts of the network. A similar threat is possible using the interval time, where a malicious router can behave as described above and also indicate a low interval time. The recipient of this message will expect a subsequent control message within this very short time -which will not arrive. As a consequence, the recipient decreases the link quality, or may even discard this link. Further vulnerabilities to the NHDP exist, described in [START_REF] Herberg | Security Issues in the Optimized Link State Routing Protocol Version 2 (OLSRV2)[END_REF].

Multicast Disruption

RSS algorithms are based on a router having topological information describing its 1-hop and 2-hop neighborhood. Thus, a malicious routers can spoof the links to or identities of other routers in the network, and thus disrupt connectivity and prevent multicast traffic from reaching parts of the network. Figure 13 gives an example hereof, by way of link spoofing. The malicious router, X, eavesdrops on NHDP control traffic, and learns of the existence of e and f as 2-hop neighbors by way of b and c, respectively. X itself participates in NHDP, however declares (spoofs) in its control messages that it, too, has links to all neighbors of b and c -i.e.,declares the dotted links in figure 13. When a is to select relays, it will choose X as its relay -X which may, then, simply not re-transmit any multicast traffic received and thereby disconnecting e and f from a.

A similar attack is possible by way of identity spoofing, as indicated in figure 14. The malicious router, X, eavesdrop on NHDP control traffic and learns of the existence of c as a 2-hop neighbor by way of b. X itself then commences participating in NHDP, but presenting itself under the same identity as b -thus a will see c as a direct neighbor and not select b as relay. As a consequence, c is not able to receive multicast traffic, again being disconnected from the network.

Broadcast Storm

In MANETs, a broadcast storm caused by classical flooding is a serious problem because radio signals of two or more adjacent routers transmitting at the same time are likely to overlap. This can result in redundancy, contention and collisions [START_REF] Tseng | The broadcast storm problem in a mobile ad hoc network[END_REF]. Avoiding broadcast storms is one of the reasons why RSS algorithms are used -in SMF as well as in routing protocols such as [START_REF] Clausen | Optimized Link State Routing Protocol (OLSR)[END_REF]. In contrast to the attacks described in section 4.3, a malicious router may attack an SMF network by attempting to degrade RSS so as to produce classic flooding, illustrated in figure 15. Bold lines with arrows present the intended multicast traffic if the RSS algorithm run properly: b, d, f, h are selected as relays by a, and c, e, g, i just receive packets from a without forwarding.

A malicious router X may disrupt this by overhearing NHDP control traffic, thus learning of the 1-hop neighborhood of a. X may, then, generate control messages performing both identity spoofing and link-spoofing, pretending to be one of the 1-hop neighbors of a (e.g., any or all of b, c, d, e, f, g, h, i ) and declare that links to non-existing routers e.g., z, x, y, v, w exist for these, causing a to select more (or all) of its 1-hop neighbors as relays, degrading into classic flooding.

X may overhear control messages from some of the 1-hop neighbors of a and thus learn of their 2-hop neighborhoods -and spoof links that it thus knows are non-existing. Such would be the case for f and g, for example. For b and i, X may not know what their 2-hop neighbors are, however may "make an educated guess" when selecting links to spoof.

While this reduces network performance by disabling RSS and producing classical flooding, the effect of this attack is only local. Except if X has accom- plices throughout the network, b, c, d, e, f, g, h and i likely will be able to select proper relay sets.

Conclusion

This memorandum has analyzed vulnerabilities of the "Simple Multicast Forwarding" (SMF) Protocol for Mobile Ad Hoc Networks. In addition to vulnerabilities inherited from its use of NHDP for acquiring local topology information allowing reduced relay set selection, SMF introduces two Duplicate Packet Detection mechanisms, each introducing additional vulnerabilities: disrupting network connectivity, as well as allowing a malicious router to incite other routers to produce unnecessary packet re-transmissions -thereby consuming precious channel resources. SMF also provides a framework for enabling different relay set selection algorithms, to be used within SMF. As such algorithms may not be interoperable, this framework introduces a signaling mechanism (RSSV) whereby a router shares the algorithms it support itself -as well as the algorithms supported by its neighbors. Intended to allow a router to select its relays such that the RSS algorithms of these are compatible with algorithms of its 2-hop neighbors, the RSSV also allows a malicious router to present conflicting or incorrect information, skewing relay set selection and possibly disrupting network connectivity.

Using NHDP for acquiring local topology, SMF inherits vulnerabilities of NHDP -and additionally also introduces vulnerabilities by way of eavesdropping, message timing attack, link spoofing, node spoofing, etc., allowing a malicious router to provoke connectivity disruption or a broadcast storm by degrading even RSS behavior to classical flooding.

Figure 1 :

 1 Figure 1: The need for duplicate detection: retransmission over the same interface as a packet was received.

Figure 2 :

 2 Figure 2: Pre-play attack: X is a malicious router, which generates invalid packets with valid sequence numbers.

Figure 3 :

 3 Figure 3: Pre-play attack by predicting sequence number. X is a malicious router, which generates invalid packets with predicted sequence number.

Figure 4 :

 4 Figure 4: Pre-play attack based on TTL values. X is the malicious router which forwards the packets with reduced TTL values.

Figure 5 :

 5 Figure 5: Sequence number attack. X is the malicious router and modifies the sequence number to disturb duplicate packet detection

Figure 6 :

 6 Figure 6: The Hash Assist Value header option in H-DPD mode

Figure 7 :

 7 Figure 7: Attack based on the HAV field: The malicious router X produces a hash collision by removing the HAV field.

  , router a forwards the packet p with h(p) = x to router b and x. The malicious router X, instead of forwarding the original packet unmodified to b, adds an HAV header option with hash h(p + HAV ) = x = x. The router b is unable to detect the duplicate packet and processes and forwards it as a new packet.

Figure 8 :

 8 Figure 8: Attack by adding a HAV header option: The malicious router X disables duplicate packet detection by adding a HAV header option.

Figure 9 :

 9 Figure 9: Relay set selection considering RSSV: Router a makes the decision based on the RSSV declared by TLVs.

Figure 10 :

 10 Figure 10: Attack on the RSSV to disrupt the relay set selection: The malicious router X spoofs the RSSV of d, e, f, g.

Figure 11 :

 11 Figure 11: Indirect jamming in RSSV: The malicious router X changes the declaration of its RSSV frequently to make router a generate more control traffic.

INRIA

Figure 12 :

 12 Figure 12: Validity timing attack: The malicious router X spoofs b and declares a short validity time of the link.

Figure 13 :

 13 Figure 13: Multicast disruption by link spoofing: X spoofs the link to e and f.

Figure 14 :

 14 Figure 14: Multicast disruption by node spoofing. X spoofs the identify of router c to wipe c from the multicast domain

Figure 15 :

 15 Figure 15: The broadcast storm attack: The bold line with arrow represents normal multicast traffic, and the dashed line the redundant traffic caused by having all the 1-hop neighbors of a be selected as relays.

1 1 . 3 5 2 8 3 13 4

 1135813 Background and History . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 SMF Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Multicast Duplicate Packet Detection (DPD) . . . . . . . 4 1.2.2 Relay Set Seletion . . . . . . . . . . . . . . . . . . . . . . 4 Statement of Purpose . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Memorandum Outline . . . . . . . . . . . . . . . . . . . . . . . . Threats to Duplicate Packet Detection 5 2.1 Identification-based DPD (I-DPD) . . . . . . . . . . . . . . . . . 5 2.1.1 Pre-play Attack . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Sequence Number Attack . . . . . . . . . . . . . . . . . . 8 2.2 Hash-based DPD (H-DPD) . . . . . . . . . . . . . . . . . . . . . Threat to Relay Set Selection Vector (RSSV) 11 3.1 RSSV Spoofing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 RSSV Indirect Jamming . . . . . . . . . . . . . . . . . . . . . . . Threats to Relay Set Selection 13 4.1 Eavesdropping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Message Timing Attack . . . . . . . . . . . . . . . . . . . . . . . 14 4.3 Multicast Disruption . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.4 Broadcast Storm . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5 Conclusion

RR n°7638

While several RSS are supported in the same network, it is not clearly specified in the current revision of SMF[START_REF] Macker | Simplified Multicast Forwarding[END_REF] whether a router can concurrently support several different RSS at the same time.RR n°7638