José Rubio-Hernán
email: jose.rubiohernan@telecom-sudparis.com

Luca De Cicco
email: luca.decicco@poliba.it

Joaquín García-Alfaro
email: joaquin.garciaalfaro@telecom-sudparis.com

Event-Triggered Watermarking Control to handle Cyber-Physical Integrity Attacks

Keywords: Cyber-Physical Security, Critical Infrastructures, Attack detection, Adversary Model, Networked Control System

The use of control-theoretic solutions to detect attacks against cyber-physical systems is a growing area of research. Traditional literature proposes the use of control strategies to retain, f.i., satisfactory close-loop performance, as well as safety properties, when a communication network connects the distributed components of a physical system (e.g., sensors, actuators, and controllers). However, the adaptation of these strategies to handle security incidents, is an ongoing challenge. In this paper, we analyze the use of a watermark-based detector that handles integrity attacks. We show that (1) the detector is able to work properly under the presence of adversaries using non-parametric methods to escape detection; but (2) it fails at detecting adversaries using parametric identification methods to escape detection. We propose a new strategy that complements the watermark-based detector in order to detect both adversaries. We validate the detection efficiency of the new strategy via simulation.

Introduction

As an evolution of traditional industrial control systems [START_REF] Hespanha | A survey of recent results in networked control systems[END_REF], cyber-physical systems [START_REF] Kim | Cyber-physical systems: A perspective at the centennial[END_REF] combine feedback control technologies with novel computing and communication capabilities. The recently coined cyber-physical security term refers to mechanisms that address security issues associated to these environments. The use of inadequate cyber-physical security mechanisms can have an adverse effect in critical infrastructures, either national or private ones [START_REF] Falliere | [END_REF]. These issues place the study of cyber-physical security mechanisms as a hot research topic.

Given the control-theoretic nature of cyber-physical systems, the control community is actively working to adapt traditional control strategies to detect faults and errors, towards detectors of malicious attacks [START_REF] Han | Stochastic eventtriggered sensor schedule for remote state estimation[END_REF][START_REF] Heemels | Periodic event-triggered control for linear systems[END_REF][START_REF] Salt | Sistemas de control basados en red modelado y diseño de estructuras de control[END_REF]. Motivated by the same objectives, we present in this paper a solution that combines two different control strategies to handle integrity attacks against cyber-physical systems.

The contributions of this paper can be summarized as follows. First, we analyze the effectiveness of a challenge-response detector based on control-theoretic watermarks, under the assumption of integrity cyber-physical attacks. We reexamine the security of an existing contribution by Mo et al. in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF], and revisit its security effectiveness under a new adversarial scenario. We show that under the new assumptions, the original contribution presents some weaknesses. We then propose a new detection strategy that combines event-triggered control strategies with the previous watermark-based detector, in order to cover the new adversaries. Finally, we validate our proposed approach via numerical simulations. Our results show the effectiveness of our novel proposal.

The paper is organized as follows. Section 2 provides the necessary background. Section 3 reviews the watermark-based detector scheme by Mo et al. [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF], provides a new adversary model and reexamines the security of the detector under the new adversary model. Section 4 presents the new detection strategy to handle the uncovered limitations, and validates the approach via numerical simulations. Section 5 reviews related work. Section 6 concludes the paper.

Background

Cyber-Physical Attacks

The use of communication networks and IT components in traditional control systems paves the way to new vulnerability issues. Attacks against these setups are named cyber-physical attacks. These attacks target physical processes through the network. In [START_REF] Teixeira | A secure control framework for resource-limited adversaries[END_REF], authors propose a taxonomy of cyber-physical attacks based on the resources of the adversaries. Such resources are mainly measured in terms of adversary knowledge (e.g., a priori knowledge of the adversary about the system and its security measures). For instance, the knowledge of the adversary about the system is the main resource used to build up complex attacks, and to make them undetectable. Based on the degree of the adversary knowledge, the attacks may succeed at violating system properties, e.g., availability and integrity, as well as at obtaining operational information about the system to make the attacks undetectable.

Based on the adversary knowledge, cyber-physical attacks related to integrity can be classified as: (i) the replay attack where the adversary does not need knowledge about the system model [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF]; (ii) injection attack, where the adversary injects false data or deviation of the legitimate data. These attacks are not detected if the data are compatible with the dynamics of the system [START_REF] Teixeira | A secure control framework for resource-limited adversaries[END_REF], i.e., the adversary must to know the physical processes; and, (iii) covert attack, where the adversary knows perfectly the cyber-physical system behaviour. This attack is defined in [START_REF] Smith | Covert misappropriation of networked control systems: Presenting a feedback structure[END_REF] where the authors conclude that it is not possible to be detected.

Let us now present the techniques developed in the literature against these attacks; (a) signal-based detector method [START_REF] Arvani | Detection and protection against intrusions on smart grid systems[END_REF]; (b) statistical detection method [START_REF] Do | A statistical method for detecting cyber/physical attacks on scada systems[END_REF]; (c) stationary watermark-based detector method, adapting failure detector mechanisms [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF]. In the following sections, we re-examine the watermark-based technique, and the control strategies, in order to propose an improved security technique against integrity attacks. The new detection strategy handles cyberphysical adversaries which are not detected with the aforementioned techniques.

Such cyber-physical adversaries use a parametric technique to obtain the knowledge about the system model.

Control Strategies

Control theory is a well-known topic, where the evolution of the technology has been the main motivation to create new control policies to manage these systems, keeping the control features. Among these new technologies, we can mention the networked control systems (NCSs), where the loop between the different components of the system is closed through the network. A wide range of research has been reported in the literature focusing on managing these new technologies in order to preserve the control properties of the systems. They have generated new challenges in control/estimation, signal processing, and communication in order to solve the new performance problems as limited power transmission, bandwidth constrains, packet drop, delay or security. The networked control systems have motivated to consider control/estimation and communication in a unified way [START_REF] Ke-You | Survey of recent progress in networked control systems[END_REF], in order to solve problems as performance or security. Among all control strategies in NCSs, we have focused on the strategies depending on the transmission policy; sampled-data control, or event-triggered control. Into the sampled-data policy, we find mono-frequency sampling, i.e., the same sampling frequency for all the channels, or multi-frequency sampling, i.e., different sampling frequencies depending on the channel (sensor/controller or controller/actuator) [START_REF] Salt | Sistemas de control basados en red modelado y diseño de estructuras de control[END_REF]. Event-triggered control (ETC) has been also studied depending on the policy to send the events, Periodic event-triggered control (PECT) [START_REF] Heemels | Periodic event-triggered control for linear systems[END_REF] or stochastic events-triggered schedule [START_REF] Han | Stochastic eventtriggered sensor schedule for remote state estimation[END_REF]. This topic is inline with our research since the security in NCSs includes the management of the control properties through the network to avoid that an external entity, an adversary, has the capacity to control these properties and harm the system.

Watermark-based Attack Detection

The watermark-based detector is proposed in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF], with the goal of detecting replay attacks against cyber-physical systems. To analyze the watermark-based detector, the authors use an industrial control system modeled mathematically as a discrete linear time-invariant (LTI) system. This mathematical model is used to describe the dynamic behaviour of the system. The system can be represented as follows:

x t+1 = Ax t + Bu t + w t (2.1)

y t = Cx t + v t (2.2)
where x t ∈ R n is the state's vector, u t ∈ R p is the control signal, y t ∈ R m is the system output, and w t ∈ R n and v t are the process noise and the measurement noise respectively. The noises are assumed to be a zero mean Gaussian white noise with covariance Q, i.e. w t ∼ N (0, Q) and R, i.e. v t ∼ N (0, R) respectively. Moreover, A ∈ R n×n , B ∈ R n×p and C ∈ R m×n are respectively the state matrix, the input matrix end the output matrix.

Let us now define the well-known Linear Quadratic Gaussian (LQG) approach used as a control technique in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF]. This technique has two independent components:

1. a Kalman filter producing an optimal state estimation xt of the state x:

xt|t-1 = Ax t-1 + Bu t-1 xt = xt|t-1 + K t (y t -C xt|t-1 ) (2.3)
where K t denotes the Kalman gain, and xt|t-1 is the a priori system state estimation. 2. a Linear Quadratic Regulator (LQR) providing the control law u t .

u t = Lx t (2.4)
where L denotes the feedback gain of a linear-quadratic regulator.

After describing the model of the plant, hereinafter we present the detection scheme proposed in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF] against replay attacks. The idea is to superpose a watermark signal ∆u t ∈ R p to the optimal control law u t . The new control input u t is given by:

u t = u t + ∆u t (2.5)
Note that the watermark signal is independent from the process noise w t and the output noise v t . To detect the adversaries, the watermark-based detector employs a well-known χ 2 detector [START_REF] Brumback | A chi-square test for fault-detection in kalman filters[END_REF]. The alarm signal g t generates by the detector is defined as:

g t = t i=t-w+1 (r i ) T P -1 (r i ) (2.6)
where w is the size of the detection window, P is the co-variance of input signals from the sensors and r t = y t -C xt|t-1 is the residues generated from the estimator at each t-th time step.

To verify if the system is under attack, g t is compared with a threshold γ. If g t is equal or greater than the threshold, g t ≥ γ, the detector generates an alarm.

Watermark-Based Attack Detection against a new Adversary Model

Let us assume the system employs the detector described in Section 2.3, so that the controller superposes its output with an authentication watermark ∆u t . At steady-state, i.e. after the transient has been exhausted, the output of the system can be considered as the sum of its steady-state value and a component that is due to watermark signal that shall be only known by the controller.

Hereinafter we denote the adversary proposed in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF] as a cyber adversary [START_REF] Rubio-Hernán | Revisiting a watermark-based detection scheme to handle cyber-physical attacks[END_REF]. This attacker has the ability to eavesdrop all the messages sent by the sensors y t and to inject messages with a signal y t to conduct malicious actions without any knowledge about the system model. Let us also define a cyberphysical adversary as the attacker who is able to eavesdrop the message with the intention of improving its knowledge about the system behaviour, in order to conduct malicious actions [START_REF] Rubio-Hernán | Revisiting a watermark-based detection scheme to handle cyber-physical attacks[END_REF].

Based on the way to model the system's behaviour, two different cyberphysical adversaries can be defined. Definition 3.1. An attacker that, only uses the previous input and output of the system to obtain a system behaviour is defined as a non-parametric cyberphysical adversary.

Remark 1. This adversary can use a Finite Impulse Response (FIR) identification model [START_REF] Tripathi | Step size optimization of lms algorithm using aunt colony optimization & its comparison with particle swarm optimization algorithm in system identification[END_REF].

Cyber and non-parametric cyber-physical adversaries can be handled using a non-stationary watermark detector scheme [START_REF] Rubio-Hernán | Revisiting a watermark-based detection scheme to handle cyber-physical attacks[END_REF]. However, if the cyber-physical adversary is able to acquire the parameters of the system, a non-stationary watermark detector scheme is not able to detect the attack. Definition 3.2. An attacker able to estimate the parameters of the system using input and output data to mislead the controller detector is defined as a parametric cyber-physical adversary.

The signal injected by the parametric cyber-physical adversary cannot be detected by the χ 2 detector (cf. Equation (2.6)), using a non-stationary watermarkbased scheme.

Remark 2. This adversary can use an ARX (autoregressive with exogenous input) or an ARMAX (autoregressive-moving average with exogenous input) approach in order to estimate the model of the system [START_REF] Natke | System identification: Torsten söderström and petre stoica[END_REF].

We assume that the main constraint of this adversary is the energy spent to eavesdrop and analyze the communication data, i.e., the number of samples eavesdropped to obtain the system model parameters.

Proof. If the system uses a watermark-based detector, the system control inputs are represented by Equation (2.5), and the outputs are represented by:

y t = C(Ax t + B(u t + ∆u t ) + w t ) + v t (3.1)
note that the watermark can be defined as an independent and identically distributed Gaussian distribution or a stationary Gaussian distribution. Using the ARX approach we can define the system defined in Equations (2.1) and (2.2) as follows:

Y (z) = H(z)U (z) + V (z) (3.2)
where U (z) and Y (z) represent the inputs and the outputs of the plant respectively. V(z) represents the external noise which affects the outputs of the plant. And H(z) is another way to describe the model of the system presented in Section 2.3, using frequency domain.

H(z) = Y (z) -V (z) U (z) = N (z) D(z) = n 0 z m + n 1 z m-1 + ... + n m d 0 z n + d 1 z n-1 + ... + d n (3.3)
where N (z) and D(z) are the polynomial functions which build the model of the system. We prove that under the attacker model of Definition 3.2, the adversary is able to know exactly the watermark signal and thus ∆u t = ∆u t .

Proposition 1. A parametric cyber-physical adversary is able to obtain the system model, H(z), and mislead the controller, eavesdropping the control inputs and the measurements of the sensors. The probability to be detected, is equal to the probability to obtain an erroneous model. This probability, is directly proportional to the order of the system, i.e., the order of D(z), and inversely proportional to the window size to eavesdrop the data channel.

Proof. If the adversary knows all the control inputs, and the measurements of the sensors, then the model obtained by the adversary can be defined as;

H at (z) = (Y (z) -V (z))/U (z).
Comparing the adversary model of the system and the real model system, it is straightforward to prove that both system models are equal, H at (z) = H(z). Nevertheless, the adversary has an error that depends on the order selected to create the model and the number of samples eavesdropped to compute the parameters of the model, the window size. Following the Mean Square Error (MSE):

M SE = H(ζ) T (3.4)
where H(ζ)/ T is the error variance, since the system model used in this paper (cf. Section 2.3) contains no bias error [START_REF] Syberg | Complexity issues, validation and input design for control in system identification[END_REF]. This error is directly proportional to system complexity (flexibility), ζ, and inversely proportional to the samples eavesdropped by the adversary. It is worth to note that the complexity is directly proportional to the system order. Indeed, for a system with a small order is easier to obtain a good approximation model by the adversary.

To summarize, these adversaries look at the real system like a black box. They can increase the order (complexity) of their model to improve the possibility to go into the order's range where the real system could be identified. Nevertheless, they need to use a larger window size to minimize the MSE value. For this reason, the computation cost of the attack increases for a high order of the system, since the adversary needs to increase their order model, as well as, the window size in order to minimize the MSE. It is worth mentioning that the number of samples eavesdropped before the attack, as well as the order system of the adversary, are the main parameters to avoid detection.

Numerical Validation

In the previous sections we have seen that the watermark detector proposed in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF] and the improvement proposed in [START_REF] Rubio-Hernán | Revisiting a watermark-based detection scheme to handle cyber-physical attacks[END_REF] are not able to detect parametric cyber-physical adversaries. We have validated both watermark detector against the parametric cyber-physical adversary presented in Definition 3.2. Hereinafter we present only the detection ratio with respect to this adversary using the detector improvement proposed in [START_REF] Rubio-Hernán | Revisiting a watermark-based detection scheme to handle cyber-physical attacks[END_REF] due to space constraint. Nevertheless, we have obtained the same detection ratio using the detector proposed in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF]. This adversary is able to identify the system model parameters from the input and output plant signals. To validate the watermark detector against the parametric cyber-physical adversary, we define three different use cases:

1. First use-case: the adversary knows only a subset of control inputs and measurements of the sensors. This adversary will be detected by the watermarkbased detector proposed in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF].

Proof. Assuming, on the one hand, a system defined as

H(z) = (Y (z)-V (z))/U (z), where U (z) = U 1 (z) + U 2 (z)
; and, on the other hand, an adversary whose model can be defined as H at1 = (Y (z) -V (z))/U 1 (z), since this attacker only knows a subset of inputs U 1 (z) [START_REF] Weerakkody | Detecting integrity attacks on control systems using robust physical watermarking[END_REF]. Then, if all the inputs and outputs are correlated, the adversary will be detected by the system, since:

H at1 = Y (z) -V (z) U 1 (z) = Y (z) -V (z) U (z) = H(z) (3.5)
proves that the model used by the adversary, H at1 , is different to the real system model.

2.

Second use-case: the adversary has access to all the control inputs and measurements of the sensors. In this case, the parametric cyber-physical adversary could be able to obtain the model of the system with great accuracy. To do so, the adversary has to use the order of the unknown system, p, and to use a large window size, T , to eavesdrop the data in order to get the correct system model. Monte Carlo simulations using systems of order ten, against this adversary. The results present the ratio of detection if the adversary uses a window size equal to 200 and different system orders for the model. If the attacker chooses the correct system order for the model, the ratio of detection is around 7%. Nevertheless, if the adversary order varies in the range [START_REF] Heemels | Periodic event-triggered control for linear systems[END_REF][START_REF] Mo | False data injection attacks against state estimation in wireless sensor networks[END_REF], the detection ratio is not higher than 10%. Out of this range, the ratio of detection increases drastically. Figure 3.1(b) shows the ratio of detection for 200 Monte Carlo simulations using systems of order 25, against seven different parametric cyber-physical adversaries.

The assumed window size is settled to T = 300. If an adversary uses a model of the system with the correct order, the ratio of detection is around 8%. The range of orders where the ratio of detection does not increase drastically is [START_REF] Smith | Covert misappropriation of networked control systems: Presenting a feedback structure[END_REF]28]. If an adversary uses an order in this range, the ratio of detection is not higher than 10%. Otherwise, the likelihood to detect the adversary is high.

Figure 3.2 shows the ratio of detection of the same system, against a parametric cyber-physical adversary with different window sizes (125, 150, 200, 250, and 300), and the correct system order. The results confirm that the adversary needs a bigger window size in order to attack a system using a higher order, with a ratio of detection less than 10%. From these results we can conclude that a parametric cyber-physical adversary, who is capable to eavesdrop and analyze a large number of samples from the communication channel, and using an equivalent order system, is capable of evading detection.

3. Third use-case: This is a particular case of the second use-case, where the adversary knows a subset of inputs (control inputs) and outputs (measurements of the sensors). These inputs and outputs are independent of any other inputs and outputs. For this reason, the adversary is able to attack this subset of the system. In this use-case, the adversary has all the knowledge about a subset of the system since it is independent of the other subsets of the same system.

PIETC Watermark-Based Detection Strategy

In the previous section we have seen that the watermark-based schemes are able to handle attacks carried out by adversaries with limited knowledge about the system dynamics, f.i., the ones defined in our work as either cyber adversaries or non-parametric cyber-physical adversaries (cf. Definition 3.1). Nevertheless, it fails at detecting those adversaries with enough knowledge about the system dynamics, defined in our work as parametric cyber-physical adversaries (cf. Definition 3.2). In this section we present a new detector scheme, hereinafter denoted as periodic and intermittent event-triggered control watermark detector (PIETC-WD). This new detector aims at detecting the three adversary models defined in our work.

Our scheme consists of a local controller located in the sensors and a remote controller creating a distributed controller. The cooperation between the local and the remote controller allows us to create an intrusion detection policy to capture integrity attacks. The local controllers manage the dynamics of the plant, and the remote controller manages the system closed-loop in order to ensure the system against integrity attacks. Notice that our new scheme requires an additional controller together with the sensors, that must have enough computation power to process data estimations, e.g., to predict errors between environmental and estimated data. The actuators do not require additional computational power. Nevertheless, during the time between two consecutive events, they must keep the last data received from the remote controller.

To carry out with our scheme it is necessary to define communication policies among the sensors, the actuators and the remote controller. We define two communication policies for ensuring the system: (i) periodic communication policy, which the communication from the sensors to the remote controller is periodical, with a T sc period, and also from the remote controller to the actuators, with a T ca period; and, (ii) intermittent communication policy, which allows for sending data from the sensors to the remote controller if the local controller produces an alarm. Notice that T sc cannot be equal to T ca to avoid that an intermittent communication takes place while the periodic communication is being sent. Definition 4.1. Periodic and intermittent event-triggered control watermark detector (PIETC-WD) is a detector strategy with distributed control tasks. On the one hand, the sensors control the system periodically, using their local controllers and a local watermark-based detector [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF]. On the other hand, the remote controller uses the estimation error received from each sensor to periodically generate the control inputs. The remote controller also controls the closed-loop communication with an intermittent watermark.

We provide more information about the controllers and the communication policies in the following subsections.

Local Controller Design

The local controller is located in the sensors and uses a watermark in order to verify that the dynamics of the system is correct. Each sensor has a local controller with a LQG approach (cf. Section 2.3). We denote the local controller in each sensor by i ∈ {0, 1, ..., N -1}, where N is the number of sensors in the system. This controller adds a watermark to the sensor measurement before sending the residue to the remote controller:

y (i) t = y (i) t + ∆y (i) t (4.1) r (i) t = y (i) t -C i x(i) t|t-1 (4.2)
where y

(i) t
is the sensor measurement, ∆y

(i) t
is the watermark added by the local controllers, and r (i) t is the residue sent to the remote controller to compute the control input u (i) t . Notice that the new sensor measurement y

(i) t is computed after verifying that y (i) t
is the correct sensor measurement.

Remote Controller Design

The remote controller receives periodically the residue of each sensor, r (i) t , and computes these residues using the LQG approach (cf. Section 2.3) to obtain the state estimation:

xt = xt|t-1 + K t (r t ) (4.3)
where r t is a vector generated by all the residues of the sensors. We can define the control inputs vector, u t , as follows:

u t = L(x t|t-1 + K t r t ) = L(x t|t-1 + K t (r * t + ∆y t )) (4.4)
where r * t is the residues' vector before adding the watermark, and ∆y t is the vector generated by all the sensors' watermarks.

The watermark used intermittently by the remote controller is added to the control inputs. The controller adds a watermark with probability β. Denoting λ t = 1 or 0 as indication function whether the watermark is added or not, we assume that λ s are iid. Bernoulli random variables with E[λ t ] = β.

The intermittence of the watermark communication allows us to define the watermark behaviour as a non-stationary distribution. This watermark, ∆u t (cf. Equation (2.5)), permits us to detect if the closed-loop is being manipulated. It is worth noting that ∆u t is a stochastic signal with the same variance as ∆y t .

Periodic Communication Policy

The periodic communication policy is managed by the sensors. The sensors add the watermark in the measurements received by the plant and send the residue r t to the remote controller. The remote controller uses these residues to generate the control inputs sent to the actuators. The actions of these actuators produce change in the state of the plant that are captured by the sensors. If the real state differ from the state estimated by the sensors, then the sensors will switch from periodic communication policy to intermittent communication policy (cf. Section 4.4).

In order to validate the proposal, let us assume that an attack is started at time T 0 and we compute the residue r (i)

t for t ∈ [T 0 , T 0 + T -1]: r (i) t = y (i) t -C i x(i) t|t-T (4.5)
where y

(i) t
is the sensor measurement sent to the controller by the adversary. Moreover, it is easy to show that the following holds:

x(i) t|t-T = x (i) t|t-T + A t-T0 i (x (i) T0|T0-1 -x (i) T0|T0-1 ) + t-T0-1 j=0 (A j (A i + B i L i )K(∆y (i) t-1-j -∆y (i) t-1-j )) (4.6)
where x (i) is the local estimated state for each sensor when the system is under attack and

A i = (A i + B i L i )(I i -K i C i
) is a stable matrix [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF]. Substitution of (4.6) in (4.5) yields:

r (i) t = y (i) t -C x (i) t|t-T First term -CA t-T0 i (x (i) T0|T0-1 -x (i) T0|T0-1 ) Second term -C t-T0-1 j=0 (A j (A + BL)K(∆y (i) t-1-j -∆y (i) t-1-j ))
Third term

Let us consider separately the three terms in the equation written above: the first term follows the same distribution of (y t -C i x(i) t|t-1 ); since A i is asymptotically stable -i.e. all its eigenvalues are inside the open unit disk of the complex plane -the second term converges exponentially to zero. In fact, the entries of A t-T0 i converge exponentially fast to zero. The third term, under attack, is not equal to zero, since ∆y

(i) t = ∆y (i)
t , and the adversary is detected; for a cyber adversary viewpoint, the measurements of the sensors change all the time and replay measurements are not accepted; likewise, a cyber-physical adversary is not able to obtain the system model using the methodology proposed in Section 3. The parametric cyber-physical adversary model, using the ARX approach [START_REF] Natke | System identification: Torsten söderström and petre stoica[END_REF], is computed as follows:

H at2 = f (R(z), Y (z)) -V (z) U (z) (4.7)
where f is a linear function of the residue R(z), and the output Y (z).

Assuming that the real model is H = (Y (z) -V (z))/U (z), we can see that H at2 = H, and the adversary is not able to obtain the model of the system.

Intermittent Communication Policy

The aforementioned periodic communication policy is managed by the sensors. The sensors produce an alarm if g t ≥ γ. When a sensor produces an alarm, this information is sent immediately to the remote controller. The affected sensor sends the real sensor measurement to the remote controller in order to carry out a second verification. An alarm happens if the control input has been manipulated by an external entity, a problem occurs in the system or the remote controller adds the watermark in the control input.

When the remote controller receives a measurement from a sensor, if a watermark ∆u has not been sent, then the remote controller creates an intrusion alarm. Otherwise, if a watermark has been added to the control input, the controller verifies if this alarm is produced by the watermark. If the residue generated between the real measurements of the sensors and the estimation is under the threshold, the remote controller sends the control input generated before adding the watermark. However, if the residue is over the threshold, it means that an external entity is into the closed-loop, and an alarm is activated.

In order to validate our claims, let us assume the following attack in the communication channel between the sensor and the controller after the controller sends a control input with a watermark. It is started at time T 0 and we compute the residues r t for t ∈ [T 0 , T 0 + T -1]:

r t = y t -C xt|t-T (4.8)
Moreover, it is easy to show that the following holds:

xt|t-T = x t|t-T + A t-T0 (x T0|T0-1 -x T0|T0-1 ) + t-T0-1 j=0 (A j B(∆u t-1-j -∆u t-1-j )) (4.9)
Substitution of (4.9) in (4.8) yields:

r t = y t -C x t|t-T First term -CA t-T0 (x T0|T0-1 -x T0|T0-1 ) Second term -C t-T0-1 j=0 (A j B(∆u t-1-j -∆u t-1-j ))
Third term

The first term follows the same distribution of (y t -C xt|t-1 ); the second term converges exponentially to zero. Since the third term is not equal to zero, ∆u t = ∆u t , the adversary is detected; from the cyber adversary viewpoint, the measurements of the sensors change all the time and replay measurements are not accepted; likewise, the cyber-physical adversary is not able to obtain the system model using the methodology proposed in Section 3.

New Parametric Cyber-Physical Adversary

In this section we present a new parametric cyber-physical adversary with the knowledge about the new detector strategy, in order to evaluate the new detection strategy. This attacker has knowledge about the new communication policies and the existence of the local and the remote watermarks. Nevertheless, the new adversary does not know the watermark co-variances, the controller's parameters used to obtain the correct error between data, and neither the moment when the remote controller forces an intermittent communication.

The new adversary could be able to detect the correlation model between the inputs and the outputs of the plant. This adversary can force the sensors' intermittent communication with malfunction control inputs, and mislead the controller with replay error data to obtain the model. Nevertheless, this adversary is not able to know when the communication is periodic or intermittent, since the attacker does not know when the remote control sends the watermark added to the control inputs which generates the intermittent communication. The intermittent communication does not change the communication between the remote controller and the actuators, but produces an intermittent communication between the sensors and the remote controller, necessary to verify the closed-loop.

Briefly, the new adversary is able to attack the integrity of the system. Nevertheless using the PIETC-WD strategy, the adversary is detected by the controllers of the sensors. The remote controller detects the attack when the remote controller verifies the behaviour of the closed-loop. The adversary cannot avoid the alarm in the sensors (local controller). Nevertheless, the attacker can cut off the communication between the sensors and the remote control misleading the remote controller with correct residues (e.g. replay residues). Moreover, in order to avoid the alarm in the remote controller, the adversary can switch between sending the measurements of the sensors or the residues, but the adversary has a great probability to be detected. We validate the PIETC-WD strategy against the new parametric cyber-physical adversary in the next section.

Numerical Validation

This section validates through numerical simulation the PIETC-WD strategy proposed in previous sections. We validate this strategy using a use case of a chemical plant. This plant has multiple sensors with local controllers, actuators and a remote controller, which manage all the measurements of the sensors and actuators. The sensors used in this use case send information about pressure, temperature, and density. This information is produced when there is an alarm, and also periodically to indicate the behaviour of the system to the controller. This plant has to be controlled periodically since, if during ten consecutive periodical samples, the system receives wrong or malicious control inputs able to disrupt the system, a critical state might be reached.

To avoid that an adversary gets the system into a critical state, we use our detector strategy (PIETC-WD), with a policy for the remote controller's watermark defined as follows:

-The controller's watermark uses a policy based on a probability to add the watermark in a specific window of samples. In this use case, the windows of samples is assumed equal to five. For each sequence of five control input samples, the probability to add the watermark at each sample is β = 50%.

The system is able to produce 2 5 = 32 different sequences with the same probability to be generated, θ = 1/2 5 . Nevertheless, if among these five samples, the system does not send any watermark, three more samples are used to add a watermark to the control input until a new control sequence starts. These three samples added to the original control sequence add 2 3 = 8 more sequences where the five first samples have not watermark, and the three last samples have the following probability to add the watermark:

• The probability to add the watermark in the sixth sample is 60%.

• The probability to add the watermark in the seventh sample is 50% if the watermark is added in the sixth sample. Otherwise, if the watermark is not added, the probability is 60%. • The probability to add the watermark in the eighth sample is 50%, if the watermark is added in the sixth or seventh sample. Otherwise, the probability is 60%.

Figure 4.1 shows the results of 200 Monte Carlo simulations using the above use case and controller's watermark policy, against the cyber and the cyberphysical adversary. These results present that the ratio of detection is around 97% against the new parametric cyber-physical adversary and more than 99% against the other cyber and cyber-physical adversaries using the PIETC-WD strategy with a correct policy for the remote controller's watermark.

Related Work

Security of cyber-physical systems (CPS) is drawing a great deal of attention recently [START_REF] Corman | NITRD Cyber-Physical Security Panel. 35th Symposium on Security and Privacy[END_REF]. Solutions focusing on control approaches for the detection of cyberphysical attacks is the research axis more closely related to this paper. This axis is the one that explicitly considers the interconnection between cyber and physical control domains in networked control systems. Recently, the control system community started to study security of cyber-physical systems both under the methodological point of view and from a more technological standpoint by looking at particular problems arising in, e.g., smart grids. Concerning the methodological aspects, several studies have proposed to adapt classical frameworks to handle security issues in networked control systems.

Among cyber-physical attacks handled in the literature, replay attack is the only attack that the adversary is able to carry out without knowledge about system model. To carry out the rest of the attacks, it is necessary some system knowledge. For example, to execute a dynamic false-data injection attack handled by Mo et al. [START_REF] Mo | False data injection attacks against state estimation in wireless sensor networks[END_REF], the adversary has to have a perfect knowledge of the plant's behaviour, or to execute a covert attack, handled by Smith et al. [START_REF] Smith | Covert misappropriation of networked control systems: Presenting a feedback structure[END_REF], is necessary knowledge of the plant's and controller's behaviour. Otherwise, the adversaries defined in this paper are able to obtain the knowledge of the plant's behaviour in order to attack the system. Concerning the detection mechanism, one line of research has considered the adaptation of fault detection systems to detect a class of attacks [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF][START_REF] Pasqualetti | Cyber-physical security via geometric control: Distributed monitoring and malicious attacks[END_REF][START_REF] Teixeira | A secure control framework for resource-limited adversaries[END_REF]. In particular, Mo et al. show in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF] that it is possible to detect replay attacks by properly watermarking control inputs. Teixeira et al. propose in [START_REF] Teixeira | A secure control framework for resource-limited adversaries[END_REF] a mathematical framework to model several attack strategies. An alternative modeling approach is taken by Pasqualetti et al. in [START_REF] Pasqualetti | Cyber-physical security via geometric control: Distributed monitoring and malicious attacks[END_REF], where the authors propose to employ the theory of geometric control to model cyber-physical systems attacks. In this paper we focus on the interconnection between control strategies and a watermark detector to handle the integrity attacks.

Conclusion

In this paper, we have addressed security issues in cyber-physical system. We have focused on designing a robust distributed control strategy (PIETC-WD strategy), in order to detect parametric cyber-physical adversaries. This adversary is able to acquire the knowledge of the system needed to compromise the control inputs and the measurements of the sensors to attack the system.

We have reviewed the watermark-based detector proposed in [START_REF] Mo | Physical authentication of control systems: Designing watermarked control inputs to detect counterfeit sensor outputs[END_REF]. We have shown that the detector fails at properly handling attacks carried out by parametric cyber-physical adversaries. In particular, we have shown that an adversary that learns about the system model is able to model the watermark from the control signal and succeeds at attacking the system without being detected. We have also shown that the watermark-based detector works against parametric cyber-physical adversary who knows only a set of control inputs, [START_REF] Weerakkody | Detecting integrity attacks on control systems using robust physical watermarking[END_REF]. Nevertheless, if the adversary knows all the control inputs and sensor measurements of the system, and uses the correct orders range with a window size sufficiently long, the watermark-based detector fails.

Finally, we have presented and validated our strategy (PIETC-WD). This strategy is capable to detect cyber and cyber-physical adversaries with a great detection ratio, even if the adversary finds the correct model of the system.

Figures 3. 1

 1 Figures 3.1(a) and (b)show the detection ratio of the watermark detector against a parametric cyber-physical adversary. Figure3.1(a) shows the results of 200 Monte Carlo simulations using systems of order ten, against this adversary. The results present the ratio of detection if the adversary uses a window size equal to 200 and different system orders for the model. If the attacker chooses the correct system order for the model, the ratio of detection is around 7%. Nevertheless, if the adversary order varies in the range[START_REF] Heemels | Periodic event-triggered control for linear systems[END_REF][START_REF] Mo | False data injection attacks against state estimation in wireless sensor networks[END_REF], the detection ratio is not higher than 10%. Out of this range, the ratio of detection increases drastically. Figure3.1(b) shows the ratio of detection for 200 Monte Carlo simulations using systems of order 25, against seven different parametric cyber-physical adversaries. The assumed window size is settled to T = 300. If an adversary uses a model of the system with the correct order, the ratio of detection is around 8%. The range of orders where the ratio of detection does not increase drastically is[START_REF] Smith | Covert misappropriation of networked control systems: Presenting a feedback structure[END_REF] 28]. If an adversary uses an order in this range, the ratio of detection is not higher than 10%. Otherwise, the likelihood to detect the adversary is high.

  Figures 3.1(a) and (b)show the detection ratio of the watermark detector against a parametric cyber-physical adversary. Figure3.1(a) shows the results of 200 Monte Carlo simulations using systems of order ten, against this adversary. The results present the ratio of detection if the adversary uses a window size equal to 200 and different system orders for the model. If the attacker chooses the correct system order for the model, the ratio of detection is around 7%. Nevertheless, if the adversary order varies in the range[START_REF] Heemels | Periodic event-triggered control for linear systems[END_REF][START_REF] Mo | False data injection attacks against state estimation in wireless sensor networks[END_REF], the detection ratio is not higher than 10%. Out of this range, the ratio of detection increases drastically. Figure3.1(b) shows the ratio of detection for 200 Monte Carlo simulations using systems of order 25, against seven different parametric cyber-physical adversaries. The assumed window size is settled to T = 300. If an adversary uses a model of the system with the correct order, the ratio of detection is around 8%. The range of orders where the ratio of detection does not increase drastically is[START_REF] Smith | Covert misappropriation of networked control systems: Presenting a feedback structure[END_REF] 28]. If an adversary uses an order in this range, the ratio of detection is not higher than 10%. Otherwise, the likelihood to detect the adversary is high.

Figure 3 .

 3 Figures 3.1(a) and (b)show the detection ratio of the watermark detector against a parametric cyber-physical adversary. Figure3.1(a) shows the results of 200 Monte Carlo simulations using systems of order ten, against this adversary. The results present the ratio of detection if the adversary uses a window size equal to 200 and different system orders for the model. If the attacker chooses the correct system order for the model, the ratio of detection is around 7%. Nevertheless, if the adversary order varies in the range[START_REF] Heemels | Periodic event-triggered control for linear systems[END_REF][START_REF] Mo | False data injection attacks against state estimation in wireless sensor networks[END_REF], the detection ratio is not higher than 10%. Out of this range, the ratio of detection increases drastically. Figure3.1(b) shows the ratio of detection for 200 Monte Carlo simulations using systems of order 25, against seven different parametric cyber-physical adversaries. The assumed window size is settled to T = 300. If an adversary uses a model of the system with the correct order, the ratio of detection is around 8%. The range of orders where the ratio of detection does not increase drastically is[START_REF] Smith | Covert misappropriation of networked control systems: Presenting a feedback structure[END_REF] 28]. If an adversary uses an order in this range, the ratio of detection is not higher than 10%. Otherwise, the likelihood to detect the adversary is high.

Fig. 3 . 1 .Fig. 3 . 2 .

 3132 Fig. 3.1. Detection ratio function with respect to the adversary order. (a) For systems of order 10 against a parametric cyber-physical adversary with a window size equal to 200. And (b) for systems of order 25 against a parametric cyber-physical adversary with a window size equal to 300

Fig. 4 . 1 .

 41 Fig. 4.1. Detection ratio function with respect to the PIETC-WD strategy with a defined controller's watermark policy; (a) against the new parametric cyber-physical adversary; and (b) against cyber or other cyber-physical adversaries

Acknowledgements. The authors acknowledge support from the Cyber CNI Chair of Institut Mines-Télécom. The chair is held by Télécom Bretagne and supported by Airbus Defence and Space, Amossys, EDF, Orange, La Poste, Nokia, Société Générale and the Regional Council of Brittany. It has been acknowledged by the Center of excellence in Cybersecurity.


Gustavo Gonzalez-Granadillo

Ender Alvarez

Alexander Motzek
email: motzek@ifis.uni-luebeck.de

Matteo Merialdo
email: m.merialdo@rheagroup.com

Joaquin Garcia-Alfaro

Hervé Debar

Towards an Automated and Dynamic Risk Management Response System

Keywords: Dynamic Response System, RORI, Operational Impact, Automatic Response, Critical Infrastructures

Achieving a fully automated and dynamic system in critical infrastructure scenarios is an open issue in ongoing research. Generally, decisions in SCADA systems require a manual intervention, that in most of the cases is performed by highly experienced operators. In this paper we propose a framework consisting of a proactive management software that aims at anticipating the occurrence of potential attacks. It conducts an initial evaluation of reported proactive evidences based on a quantitative metric of monetary return on response investment. The framework evaluates and selects mitigation actions from a pool of candidates, by ranking them in terms of financial and operational impacts. The purpose of this process is to select an optimal set of mitigation actions from financial and operational perspectives and propose them to reduce the risk of threats against the monitored system, without sacrificing an organization's missions in favor of security. A real world case study of a SCADA environment shows the applicability of the model, from the analysis of the input data to the selection of the response plan.

Introduction

Critical infrastructures are systems and assets, whether physical or virtual (e.g., a company, an institution, an organization), which if disrupted, damaged, or destroyed, would have a serious impact on the health, safety, security, or economic well-being of citizens or the effective functioning of governments and other infrastructures depending on it [START_REF] Filiol | Critical Infrastructure: Where we stand today?[END_REF]. Critical Infrastructures include sectors that account for substantial portions of national income and employment, such as energy (including nuclear), ICT, finance, healthcare, food, water, transport, safety, government. Most of these sectors use industrial control systems (ICS) in order to provide control of remote equipment [START_REF] Gordon | Protection of Critical Infrastructure and the role of investment policies relating to National Security[END_REF].

Achieving a fully automated system in critical infrastructure scenarios is an ongoing research area. Generally, decisions in SCADA systems require a manual intervention, that in most cases is performed by highly experienced operators. However, it is possible to automate incident handling. For some threats, a system should be able to automatically select mitigation actions that provide the most suitable response possibilities to reduce identified risks below an admissible level while minimizing potential negative side effects of deliberately taken actions.

In this paper, we propose a dynamic risk management response system (DRMRS) that evaluates, ranks and selects optimal mitigation actions based on financial, operational and threat impact assessment functions. The selected actions are transformed into response plans that are automatically enforced by the system's policy enforcement points (PEPs). These latter are defined as security components that work as gateways or front doors to digital resources. PEPs are capable of applying security rules (e.g., permission, prohibition, obligation) over the triplet {subject, action, object}. Examples of PEP are web servers, portals, firewalls, LDAP directories, SOAP engines, and similar resources [START_REF] Ben Mustapha | Policy Enforcement Point Model[END_REF].

The contributions on this article are summarized as follows:

(1) A model that automatically computes the input parameters of the financial impact metric and provides an indication of the feasibility of each evaluated action. (2) A process that dynamically generate and validate response plans. (3) The implementation and validation of the model. [START_REF] Gonzalez-Granadillo | RORI-based countermeasure selection using the OrBAC formalism[END_REF] The deployment of the model over a real scenario to perform automated responses in a critical infrastructure system.

The remainder of the paper is structured as follows: Sec. 2 introduces the return on response investment metric. Sec. 3 describes our proposed dynamic risk management response system. Sec. 4 details the tool implementation and validation. Sec. 5 depicts a case study to automate the response in a critical infrastructure system. Related work are presented in Sec. [START_REF] Sonnenreich | Return On Security Investment (ROSI) A Practical Quantitative Model[END_REF]. Finally, conclusions and perspective for future work are presented in Sec. 7.

Dynamic Return On Response Investment (RORI)

The Return On Response Investment (RORI) is a cost sensitive metric used to assess, rank and select security countermeasures from a pool of candidates. The process undertaken by the DRMRS extends initial work reported in [START_REF] Gonzalez-Granadillo | RORI-based countermeasure selection using the OrBAC formalism[END_REF]. The approach proposes the combination of authorization models and quantitative metrics, for the selection of mitigation actions. The actions, modeled in terms of contextual rules, are prioritized based on a cost-sensitive metric that extends the return on investment (ROI) concept and all its variants [START_REF] Schmidt | Return on Investment (ROI): Meaning and Use, Encyclopedia of Business Terms and Methods[END_REF][START_REF] Sonnenreich | Return On Security Investment (ROSI) A Practical Quantitative Model[END_REF][START_REF] Mizzi | Return on Information Security Investment: the Viability of an Anti-Spam Solution in a Wireless Environment[END_REF]. The goal is finding an appropriate balance between the financial damages associated to a given threat, and the benefits of applying some mitigation actions to handle the threat, with respect to the loss reduction. The RORI metric is calculated for each mitigation action, according to Eq. 1.

RORI

= (ALE • RM ) -ARC ARC + AIV • 100 (1)
In theory, all parameters composing the RORI metric should be given by expert knowledge, historical data, and/or a risk assessment methodology that evaluates all possible system's threats and gives directions about the most suitable mitigation actions to reduce risk levels down to acceptable values. In practice, however, the estimation of such parameters represents a big challenge and a time consuming task to security administrators. Depending upon the type of organizations, the RORI parameters can be more or less complex to estimate. For small and medium size organizations, the quantification of such parameters, is a process that could be performed within hours of discussions with use case providers and simple simulation runs [START_REF] Gonzalez-Granadillo | RORI-based countermeasure selection using the OrBAC formalism[END_REF]. For large and critical organizations, the process can take several weeks (and even months).

Based on the previous shortcomings, a first improvement has been made in the RORI expression to enhance the Risk Mitigation (RM) function. [START_REF] Gonzalez-Granadillo | A Polytope-based Approach to Measure the Impact of Events Against Critical Infrastructures[END_REF] extends the concept of attack surface used in previous versions of the RORI metric. It identifies authorization and contextual dimensions that may directly contribute to the exposition of system vulnerabilities. New properties associated to the vulnerabilities, such as temporal conditions (e.g., granted privileges only during working hours), spatial conditions (e.g., granted privileges when connected within the company premises), and historical conditions (e.g., granted privileges only if previous instances of the same equivalent events were already conducted) can now be included and combined with the RORI cost-sensitive metric.

An adaptation of the selection process, based on financial and operational assessment functions, has been presented in [START_REF] Gonzalez-Granadillo | Selection of Mitigation Actions Based on Financial and Operational Impact Assessments[END_REF], which reports the combination of both assessment approaches, over a representative set of mitigation actions. The combination, based on a multi-dimensional minimization approach, proposes the choice of semi-optimal responses that, on the one hand, bear the highest financial attractiveness on return on investment; and, on the other hand, bear the lowest probability of conflicting with the organization's missions. This is seen as beneficial for its application in scenarios where highly critical missions and resources must be protected, without sacrificing missions in favor of security.

The remaining of this section details the parameters of the RORI metric and describes the process to automatically compute them in a dynamic system.

Description of the Dynamic RORI Model

Annual Loss Expectancy, ALE expresses the amount of money, e.g., e/year, that an organization may lose if a threat is realized on the system. It includes loss of assets, loss of data, loss of reputation, etc. ALE depends directly on the threat and it is independent on the mitigation actions and the policy enforcement points. Annual Infrastructure Value, AIV depends directly on the policy enforcement point, and expresses the monetary value of the infrastructure, e.g., e/year, regardless of the threat and the implemented mitigation actions.

AIV is greater than zero, i.e., AIV > 0, and includes costs of equipment, personal, service, etc.

Annual Response Cost, ARC provides the information about the amount of money (e.g., e) associated to the implementation of a mitigation action against a threat. ARC is always greater than or equal to zero, i.e., ARC ≥ 0, and includes direct costs, such as cost of implementation, cost of maintenance, other direct and indirect cost, such as potential collateral damages. ARC depends on the mitigation action and the policy enforcement point, but it is independent on the threat. Risk Mitigation, RM represents the level of reduction that is obtained after the implementation of a mitigation action. RM takes values between zero and one hundred, i.e., 0 ≤ RM ≤ 100. RM depends on the threat, the mitigation action, and the policy enforcement point.

Each parameter depends on at least one of the following entities: (i) the threat affecting the system, (ii) the type of mitigation action to be implemented, and (iii) the type of policy enforcement point. Table 1 summarizes this information and details the level of complexity on the estimation of each parameter.

Computation of the Dynamic RORI Parameters

In a dynamic environment, nodes can be active or inactive. Each snapshot of the system may provide a list of different nodes involved in the attack scenario. The evaluation process is therefore unique for each system's snapshot, and is discussed in the following definitions.

Definition 1 (ALE Computation). Since the ALE parameter is associated to the threat, its value remains unchanged for each snapshot of the system. ALE is assessed first qualitatively, and then transformed into quantitative values. We follow the approach proposed in [START_REF]A Guide for Government Agencies Calculating Return on Security Investment[END_REF] that defines six qualitative levels of severity, and seven qualitative levels of likelihood with their corresponding quantitative values. ALE is calculated as the product of the severity transformed into probabilistic costs and the likelihood transformed into probabilistic frequency.

Definition 2 (AIV Computation). The AIV is computed as the sum of the Annual Equipment Cost (AEC) of all policy enforcement points that appears in the system's snapshot, as shown in Eq. 2.

AIV = n i=0 AEC i (2)
Each PEP has an associated AEC that is estimated based on historical information and expert knowledge. Contrary to the ALE, the value of the AIV changes at each snapshot of the system. More details on its estimation can be found in [START_REF] Gonzalez-Granadillo | RORI-based countermeasure selection using the OrBAC formalism[END_REF].

Definition 3 (ARC Computation). The ARC is associated to the implementation of a given mitigation action. The value depends directly on the type of mitigation action (e.g., reboot, shutdown, patching), and the PEP responsible of its implementation. More details on its estimation can be found in [START_REF] Gonzalez-Granadillo | RORI-based countermeasure selection using the OrBAC formalism[END_REF].

Definition 4 (RM Computation). The RM of an action is computed as the product of the effectiveness EF and the threat coverage COV , using Eq. 3.

RM = EF • COV (3)
Effectiveness (EF) of a mitigation action represents the level at which a given action reduces the risk and/or consequences of an attack on the system. EF is intrinsic to the mitigation action type regardless of the threat it mitigates. For instance, a reboot action by itself provides a very low mitigation of a given threat, whereas a patching action provides a very high protection against it. Table 2 summarizes default values associated to mitigation action types. Each value has been assigned based on statistical data and expert knowledge. Coverage (COV) of a given mitigation action represents the number of nodes to which a mitigation action is being executed over the total number of vulnerable nodes, i.e.,

COV = Q i • W F i n j=0 QT j • W F j , (4)
where Q i is the number of nodes from a PEP type that are affected by a given mitigation action, W F i is the weighting factor associated to the affected PEP type, QT j is the total number of active node types in the system, and W F j is the weighting factor associated to each node type.

Dynamic Risk Management Response System

The Dynamic Risk Management Response System (DRMRS) handles identified threats, authorized mitigation actions and strategic policies (i.e., default and contextual policy rules, as well as contextual definitions). It extracts concrete entities from reported threats, and infers concrete policy instances to eventually guide the system into new updates and reconfigurations. These are provided as concrete response plans on a long-term proactive perspective. Response plans are validated by human operators, prior final enforcement. The goal of the DRMRS is the automated administration of policy-related activities, including addition of new rules, removal of unnecessary conditions, and activation of strategic responses (i.e., activation of new mitigation and response plans).

The DRMRS is a dynamic process that involves information coming from different sources of an environment, which are notated and defined as follows.

Abstract Security Policies contain the security policies of the target organization. They include details of the threat (e.g., threatID, attack vector, severity, frequency); details of the Policy Enforcement Point (e.g., name, annual equipment value, PEPType, quantity); and details of the mitigation actions (e.g., ID, ARC, coverage, nodeID, restrictions, effectiveness). Proactive Risk Profile includes information about assets, supporting assets, attack scenarios and detrimental events. These latter are defined as the fact of harming the accomplishment of an organization's objective or mission. Network Inventory contains information of all active devices of the emulation environment providing various attributes, e.g., the PEP Type. Mission Dependency Model contains information about business processes and devices, consequences and requirements. It contains information about entry points, critical resources, and their dependencies and impact to the mission of the organization. Network Dependency Model contains information about direct dependencies between individual resources of an organization or mission. The model is used to identify indirect dependencies and cover transitive impacts to the mission of the organization from widespread events. Attack Graph contains information about all possible attack scenarios. The information includes details of the target and source nodes, as well as the attack paths and its associated likelihood. Authorized Mitigation Actions contain a list of mitigation actions that are authorized to be executed as a reaction to a given threat.

Based on these input data, response plans are generated and evaluated as elaborated in the following sections.

Response Plan Generation Process

The process, as depicted in Fig. 1, starts by obtaining information of the threat scenarios coming from the Abstract Security Policies (ASP) and the information of Detrimental Events (DE) coming from the Proactive Risk Profile (PRP). We compare predefined conditions in both input files. We compare, e.g., if the likelihood of the threat scenario is greater than or equal to the likelihood of the detrimental event (Step 1). In such a case, we collect all attack path IDs that will be used in the attack graph parsing process (Step 2a). If the condition is not met, the process generates an empty response plan (Step 2b). Given the most updated information of the network inventory and the attack vector from the ASP, we generate a concrete attack vector (Step 3). A determination is made on whether there is a partial concrete attack vector (i.e., for each path of the attack vector, we search all active nodes from the network inventory). If at least one concrete attack vector is found, the process searches for a match of entry points and business devices from the obtained attack vector and the mission dependency model (Step 4a). Otherwise, an empty response plan is generated (Step 4b).

Following, we search paths matching the attack graph file and the attack vector (Step 5). A determination is made on whether there is a final concrete attack vector (i.e., for each path of the attack vector, there is a node that matches with the attack graph). If at least one matching node is found, the process collects the set of nodes from the attack vector involved in the attack graph (Step 6a), otherwise, an empty response plan is generated (Step 6b).

Given the list of authorized mitigation actions, a determination is made on whether or not there are involved nodes in the process. If it is the case, the process extracts all mitigation actions associated to the PEP type of the nodes obtained from the Attack Graph (Step 7a), otherwise, an empty response plan is generated (Step 7b). The RORI evaluation is performed on the extracted mitigation actions and response plans are generated accordingly (Step 8).

The output of this module is a set of response plans, which are vectors of mitigation actions, representing individual actions to be performed as a response to an adversary or threat opposed to an organization. A response plan contains an ID, mitigation action IDs and types, a policy enforcement point and the RORI index. Response plans are of two types: individual, when only one mitigation action is proposed; and combined, when two or more mitigation actions are proposed to be implemented. In such a case, a new parameter called "probability of conflict" is included in order to manage restrictions among the proposed actions.

Response Selection and Visualization

This module obtains the generated response plans and performs an operational evaluation in order to select the best response plan in financial and operational terms. We consider that response plans, while highly effective, could lead to operational negative side-effects inside the network and therefore onto a mission. Response plans are therefore evaluated based on local impact and assessments of dependencies inside an organization's business. We perform such an operational impact assessment based on a locally validatable probabilistic approach as proposed by Motzek et al. in [START_REF] Motzek | Probabilistic Mission Impact Assessment based on Widespread Local Events[END_REF]. The operational impact assessment is based on a probabilistic graphical model obtained from a mission-and network dependency model through probabilistic inference and is detailedly discussed in [START_REF] Motzek | Probabilistic Mission Impact Assessment based on Widespread Local Events[END_REF] and [START_REF] Gonzalez-Granadillo | Selection of Mitigation Actions Based on Financial and Operational Impact Assessments[END_REF]. As a result, response plans are enriched with operational information that indicates the impact over the organizational mission(s) in three dimensions: a short-term impact (OI 0 ), mid-term (OI 1 ) and long-term impact (OI 2 ). Based on [START_REF] Gonzalez-Granadillo | Selection of Mitigation Actions Based on Financial and Operational Impact Assessments[END_REF], the number of response plans is reduced to a single response plan that is optimal in each dimension: the financial and the operational impact. Their method searches for a semi-optimal response plan with the lowest operational impact assessment and the highest RORI index.

A response plan is said to be semi-optimal since it might not be the best solution neither in financial nor in operational terms, but it proposes a set of mitigation actions that on the one hand, bear the highest financial attractiveness on return on investment, and, on the other hand, bear the lowest probability of conflicting with a company's mission. This is beneficial for applications, where highly critical missions and resources must be protected, without sacrificing missions in favor of security.

The approach searches for a boundary of acceptable elements (acceptable as a compromise). This boundary is a numerical value representing a normalized deviation (ε) of the optimum. For instance, with ε=0.1, we accept 10% deviation of the optimum in each dimension based on the dimensions absolute scale. The acceptance criteria for the financial and operational impact are different. For the financial impact, we keep response plans whose RORI index are greater or equal to 90% of the highest (best) RORI value. For the operational impact, we keep response plans whose OI i are up to 10% of the lowest (best) OI i value. Then, we check if there is a match in all evaluated response plans. If there is a match, we stop the process; otherwise, we increase the ε value until we find a tuple that matches. In particular, we search the ε where we obtain the smallest set of values. Once a semi-optimal response plan is found, the information is sent to the visualization module, which depicts such results to the security operator.

System Testing and Experimentation

Testing and experimentation consists of demonstrating accomplishment of different functional and non-functional requirements defined for the DRMRS. More specifically, we focus on defining a set of tests that are conducted to verify that each requirement is covered by the component implementation. In summary, functional requirements are used to test the syntactical and semantical correct behavior to input data, i.e., correct computation of ALE, ARV, AIV and RM values. All tests have been conducted by manual code inspection, as well as automatically performed tests on artificial data testing syntactical errors, as well as, real data (see Sec. 5) testing correct semantic behavior. In summary all tests were executed without errors or exceptions.

Additionally, several test cases are executed in order to evaluate the computation time in the combined evaluation of mitigation actions. The number of combination for a set of non-restrictive candidates is given by the expression X = (2 N )(N + 1). Since the total number of combinations grows exponentially, we measure the time at which the system is able to perform the evaluation of multiple candidates. An existing non-functional requirement demands the evaluation of multiple response plans in the range of minutes. Results plotted in Fig. 2 show that a combination of 12 restrictive mitigation actions results into 796 combinations that are obtained in less than one second. For 12 non-restrictive mitigation actions, a total of 4 082 combinations exists, which are performed in less than 10 seconds. Given 24 restrictive mitigation actions, 590 464 combinations are evaluated in almost three hours. Therefore, to keep the evaluation process within a reasonable time (less than one minute), the system processes up to 14 non-restrictive mitigation actions (16 369 combinations). Beyond this threshold more than one minute is required, but the approach scales linearly with the number of processed combinations as evident from Fig. 2.

In addition, several integration tests have been performed to verify and validate the appropriate communication of all the components of the DRMRS framework. Such tests rely on the generation of response plans. The communication between the financial and the operational impact assessor modules is an example of integration among the system's components. The set of response plans generated by the financial impact module is sent for evaluation to the operational impact module, making it possible to generate a single response plan that best satisfies the financial and operational impact assessments.

Case Study: Automated Response in a Critical Infrastructure System

We study the infrastructure environment of an Energy Distribution organization.

The environment consists of a distributed network of Remote Terminal Units (RTU) in energy stations of medium voltage (MV) and high voltage (HV), that acquire data from electrical devices (e.g., PLC, sensors, etc), and send them to the Supervisor Terminal Unit (STU) of the headquarters. The system uses Supervisory Control and Data Acquisition (SCADA) protocols.

Threat Scenario

The threat to analyze is a denial of service against a high voltage node of the C&C infrastructure with the objective of taking the C&C offline. More precisely, the threat will cause an out of service condition on Front End Servers (e.g., FE-X1) which breaks communication path from SCADA Servers to RTUs. There exists an attack vector via ICT Network (via VR-08) targeting first the file server (i.e., File-SRV), second, the archive server (i.e., Archive-SRV), and third, the high voltage Front End devices (i.e., FE-X1, FE-X2).This threat has a severity defined as "grave," which corresponds to a single loss expectancy SLE = 10 000 000 e, and a likelihood defined as "medium," equivalent to an annual rate of occurrence ARO = 2. The Annual Loss Expectancy is therefore equivalent to ALE = 20 000 000 e/year.

Input Information

After receiving input information, the system checks for active PEPs in the simulation environment in order to obtain the AIV. For this threat scenario, the current snapshot shows that there are 17 active PEPs with an AIV equivalent to 6 925 555e, as shown in Table 3. Note that AIV corresponds to the value obtained out of the sum of all PEP's cost, i.e., AEC, that are active at the time of the snapshot. The AIV parameter is a variable value that depends on the time of the evaluation and the PEP that are detected by the system. Following, the system compares the likelihood values of detrimental events in the proactive risk profile against the threat scenario threshold values. For this threat scenario, three detrimental events have greater likelihood values than those associated to the threat scenario, the system therefore retrieves a concrete attack vector for Threat AS01HV : 'EntryPoint=VGROUTER; Tar-get1=WEBSCADA; Target2=FTPSRV; BusinessDevice=FEXSCADA' Based on the information from the mission dependency model, we have retrieved the nodes in paths pointing to Business Devices for threat AS01HV . Each node has a unique identifier, a host name that corresponds to an instantiated device, a PEP Type which corresponds to the abstraction class of the PEP, and a Node Type, which indicates whether the node is an entry point, an intermediate node, a target node or a business device. Please note that business devices are the most critical node types from the emulation environment. They are required to accomplish a business process within the organization. Table 4 summarizes this information.

Table 4. Retrieved node information.

Node Identifier

Host Name PEP Type Node Type b992e600-0de2-496c-kkk0-. . . mferp1 FEXSCADA Business Device 718bc323-9d78-4ada-9629-. . . dorete

FTPSRV Target2 e06496d2-6120-4c9d-a310-. . . LANGUARD MGMSRV Intermediate Node 94d37c8d-bc68-47bf-ad60-. . . ARCHIVESRV FTPSRV Target2 19b2bb1e-9f23-4fe8-902e-. . . KALI MGMSRV Intermediate Node e470baab-5d88-4b20-ac28-. . . FTPSRV01 FTPSRV Target2 876hhezq-77tg-4897-665g-. . . xferp2 FEXSCADA Business Device d3480ddc-fe4a-4b94-9dc5-. . . mferp2 FEXSCADA Business Device b54b235d-116a-49b4-9052-. . . xferp1
FEXSCADA Business Device c9fa4086-d979-4794-9b6e-. . . STWEB WEBSCADA Target1 c6dd8687-c791-4f91-bf58-. . . TPT2000-T2 RTUSCADA Intermediate Node As shown in Table 4, the PEP types of nodes involved in paths leading to critical devices are: WEBSCADA, FEXSCADA, MGMSRV, RTUSCADA, and FTPSRV. Note that none of the nodes are defined as entry points, and those associated to the PEP Type MGMSRV do not have pre-defined authorized mitigation actions. In such a case, they are discarded from our analysis.

Dynamic RORI Evaluation

For the RORI evaluation, we obtain the list of authorized mitigation actions associated to threat AS01HV. Table 5 summarizes this information. As shown in Table 5, each PEP type has an associated weighting factor (WF) that indicates the level of priority or criticality inherent to the type of PEP in the execution of a mission. For instance, management servers (e.g., MGM-SRV) are assigned a WF=1, FTP servers (e.g., FTPSRV) are assigned a WF=2, Web servers (e.g., WEBSCADA) are assigned a WF=3, Front End devices (e.g., FEXSCADA) are assigned a WF=4, and Remote Terminal Units (i.e., RTU) are assigned a WF=5. The COV value is computed using Eq. 4.

To each PEP type none, one or more of the following mitigation actions can be applied: (1) Patching, refers to a piece of software designated to update a computer program or its supporting data, to fix or improve it. This includes fixing or removing security vulnerabilities and other bugs and improving the usability or performance. (2) Reboot, refers to the process of restarting a device or a computer program. (3) Shutdown, refers to completely remove any possibility to access a device by powering off a device.

Each type of mitigation action has an associated effectiveness (EF) and cost (ARC). The EF value is assigned automatically using the information from Table 2, whereas the ARC value is assigned by expert knowledge and statistical data. Using Eq. 1, we compute the RORI value for individual and combined mitigation actions in Table 6. Each response considers the ARC and EF to calculate the risk mitigation value (RM), using Eq. 3, and take into account restrictions among the candidates (e.g., shutdown a given device is totally restrictive to all other actions that could be executed to such device). The mitigation action with the highest RORI index M A 10 , which requires to install a patch for the PEP Type "FTPSRV". More specifically, the node "dorete" requires a patching against two vulnerabilities (i.e., CVE-2008-4250, andCVE-2006-3439). Considering the previous information about mitigation actions, a total of 214 combinations have been performed to evaluate the RORI metric. Table 7 presents the top 5 combination results. As shown in Table 7, the highest RORI index corresponds to the combination of mitigation actions M A 2 , M A 3 , M A 4 , M A 6 , M A 9 , and M A 10 which proposes the following six concrete actions: (1) Reboot node STWEB.

Response Plan Generation

For each evaluated mitigation action (including all possible combinations), a response plan has been generated. Each response plan contains the identification of the mitigation action(s), the PEP responsible for its enforcement, and the associated RORI index. The Response Plans contain mitigation actions applied only to the nodes obtained in the Attack Graph parsing (e.g., STWEB, ARCHIVESRV, FTPSRV01, dorete, etc). For the previous scenario, a total of 224 response plan were generated.

Response Plan Selection and Visualization

To select a semi-optimal response plan, all proposed response plans based on RORI values are evaluated based on their short-, mid-, and long-term impacts onto the company from an operational perspective, i.e., operational impacts OI 0 , OI 1 , OI 2 . These values derived as described in [START_REF] Motzek | Probabilistic Mission Impact Assessment based on Widespread Local Events[END_REF], where a mission dependency model was created by business experts to the company, and a network dependency model was automatically learned from network traffic analyzes. Table 8 shows a comparison of a selected subset of all 224 evaluated response plans. The semi-optimal response plan that matches the criteria is RP 46 , with a deviation of =0.2, a RORI index equivalent to 71.34%, and the following operational impacts: OI 0 = 0.2724, OI 1 = 0.2161, and OI 2 = 0.1781. As a result, the selected response plan is displayed in the visualization module, proposing the enforcement of mitigation actions M A 3 , M A 6 , M A 9 , and M A 10 which correspond to the following four concrete actions:

Related Work

Dynamic systems that automatically evaluate and select the actions to mitigate complex attack scenarios is an open research that represents a big challenge to critical infrastructures. Some research works has been conducted in the assessment of security measures. Kotenko et al. [START_REF] Kotenko | A Cyber Attack Modeling and Impact Assessment Framework[END_REF][START_REF] Kotenko | Dynamical Calculation of Security Metrics for Countermeasure Selection in Computer Networks[END_REF], e.g., propose a framework for cyber attack modeling and impact assessment based on attack graph generation, real-time event analysis techniques, prognosis of future malefactor steps, attack impact assessment, and anytime approach for attack graph building and analysis. We differ from these research as we do not propose new algorithms or methods of attack graph construction, instead, we propose a novel framework that processes input data to generate response plans for pre-defined threat scenarios. Agosta et al. [START_REF] Agosta | A Code Morphing Methodology to Automate Power Analysis Countermeasures[END_REF] propose a software countermeasure framework based on the combination of a cryptographic algorithm implementation with a polymorphic engine which dynamically and automatically transforms the binary code to be protected. The approach enables the generation of multiple versions of the code, to prevent an attacker from recognizing the exact point in time where the observed operation is executed and how such operation is performed. We differ from the previous work since it can only be applied to an algorithm or to a subset of vulnerable instructions, ours is a modular framework that is applied in a whole network to automatically analyze the impact of possible attacks and provide an appropriate response based on multiple criteria.

Ossenbuhl et al. [START_REF] Ossenbuhl | Towards Automated Incident Handling: How to Select an Appropriate Response Against a Network-based Attack?[END_REF], introduce a response selection model that allows mitigating network-based attacks based on an intuitive response selection process that evaluates negative and positive impacts associated with each countermeasure. The model overcomes several challenges in automated response selection, however, several other challenges are left uncovered (e.g., scalability and performance issues, i.e., no alert correlation mechanism has been developed to handle large amount of alerts, security issues, i.e., lack of secured communication channel among the system's components, and applicability issues, i.e., lack of applying responses in more advanced attack scenarios).

Conclusions and Future Work

We introduce a Dynamic Risk Management Response System that evaluates, ranks and selects optimal mitigation actions based on financial, operational and threat impact assessments. The system generates response plans containing mitigation actions and corresponding financial and operational evaluations. There are two main improvements of this approach: (i) the dynamic evaluation performed by the system, and (ii) the automation of the response plan generation.

In terms of dynamicity, the system operates on snapshots of a target system with a regular frequency within minutes. At each snapshot, the current condition are assessed. Upon reception of a risk profile, indicating a possible exploitation of a given threat, the system requests input information and performs corresponding analyses. Input data may vary at each snapshot, indicating, e.g., that one or more PEPs are detected on the system, or that one or more mitigation actions are not authorized for the current snapshot. As a result, every time a system snapshot is performed, values of parameters, such as AIV and RM, dynamically change, which in turn changes RORI indexes for the set of evaluated responses.

In terms of automation, the system performs the process in an automatic chain, from the detection of the threat, to the visualization of the selected response plan. The process is automated to assist security administrators in the decision making process. It does not enforce the mitigation action automatically, but provides an assessment of the current system conditions in order to highlight the appropriate response strategies to administrators. For critical infrastructures, selection of mitigation actions generally requires manual intervention by an operator, an approval by supervisors, or more advanced system operator. Future work will concentrate on managing conflicts among restrictive actions. It is possible that the best response plan suggests an enforcement of mutually exclusive mitigation actions. In such a case, the system should assign priorities to each action being able to discard those with low priority rate.

Fig. 1 .

 1 Fig. 1. Workflow for generating potential response plans.

• 10 5 Fig. 2 .

 52 Fig. 2. Computation time (abscissa) to evaluate all combinations of mitigation actions is linear in the number of combinations (ordinate) (double logarithmic plot).

( 2 )

 2 Install patches to the node STWEB against CVE-2008-4250, and CVE-2006-3439. (3) Shutdown the node mferp2. (4) Shutdown the node TPT2000-T2. (5) Reboot nodes ARCHIVESRV and FTPSRV01 (6) Install patches to the node dorete against CVE-2008-4250, and CVE-2006-3439.

( 1 )

 1 Install patches to the node STWEB against CVE-2008-4250, and CVE-2006-3439. (2) Shutdown the node TPT2000-T2. (3) Reboot nodes ARCHIVESRV and FTPSRV01. (4) Install patches to the node dorete against CVE-2008-4250, and CVE-2006-3439.

Table 1 .

 1 Complexity level on the estimation of the RORI parameters

	Parameter Threat	MA Type	PEP Type Complexity
	AIV		Low
	ALE		Low
	ARC		Medium
	RM		High

Table 2 .

 2 Default effectiveness values associated to mitigation action types.

	Mitigation Action Type	Protection	EF
	Reboot	Very Low	1.00 %
	Shutdown	Low	10.00%
	Backup	Medium	50.00%
	Change Configuration	High	80.00%
	Patching	Very High	100.00%
	Install Software/Hardware	Very High	100.00%

Table 3 .

 3 Input Values of the AIV parameter

	PEP	PEP Type	Description	AEC
	PEP16	FWCEDET	Logical Firewall and IPS working in CEDET 105 000
	PEP2	SRVMSCADA Medium Voltage Server	355 000
	PEP1	SRVXSCADA High Voltage Server	355 000
	PEP3	FEXSCADA	High Voltage Front End	1 320 000
	PEP13	FTPSRV	FTP Server	3 000
	PEP11	HMISCADA	Human-Machine Interface	80 000
	PEP15	NTPSRV	NTP Server	2 000
	PEP20	VRTX	Edge Router on Remote Sites	206 796
	PEP14	USERPC	User PC	1 000
	PEP5	GWMSCADA Medium Voltage Gateway	410 532
	PEP6	GWXSCADA High Voltage Gateway	615 800
	PEP17	FWDR	Firewall IPS/DR	105 000
	PEP10	WEBCADA	Web Server	45 000
	PEP18	MGMSRV	Management Server	3 000
	PEP9	RTUSCADA	Remote Terminal Unit	2 621 927
	PEP4	FEMSCADA	Medium Voltage Front End	660 000
	PEP7	VGROUTER	Virtual Router	36 500
		Annual Infrastructure Value (AIV)	6 925 555

Table 5 .

 5 Authorized mitigation action information.

	PEP Type WF Affected Node	Q COV MA Type EF ARC (e)
	WEBSCADA 3	STWEB	1 0.09 Shutdown 0.15	15.00
				Reboot	0.01	15.00
				Patching 1.00	25.00
	FEXSCADA 4	mferp1, mferp2	4 0.50 Shutdown 0.15	200.00
			xfep1, xferp2	Reboot	0.01	200.00
	MGMSRV	1	LANGUARD, KALI 2 0.00 No action 0.00	0.00
	RTUSCADA 5	TP2000-T2	1 0.16 Shutdown 0.15	15.00
				Reboot	0.01	15.00
	FTPSRV	2	ARCHIVESRV,	3 0.19 Shutdown 0.15	15.00
			FTPSRV01,	Reboot	0.01	15.00
			dorete	Patching 1.00	25.00

Table 6 .

 6 RORI evaluation results for individual mitigation actions.

	MA MA Type	PEP Type	RM	Restrictions	RORI
	M A1 Shutdown	WEBSCADA	0.0141	M A2, M A3	4.07
	M A2 Reboot	WEBSCADA	0.0009	M A1	0.26
	M A3 Patching	WEBSCADA	0.0937	M A1	27.09
	M A4 Shutdown	FEXSCADA	0.0750	M A5	21.66
	M A5 Reboot	FEXSCADA	0.0050	M A4	1.44
	M A6 Shutdown	RTUSCADA	0.0234	M A7	6.76
	M A7 Reboot	RTUCADA	0.0016	M A6	0.46
	M A8 Shutdown	FTPSRV	0.0281	M A9, M A10	8.11
	M A9 Reboot	FTPSRV	0.0019	M A8	0.55
	M A10 Patching	FTPSRV	0.1875	M A8	54.15

Table 7 .

 7 RORI evaluation results for combined mitigation actions.

	MA	ARC	RM	RORI
	M A2,3,4,6,9,10	295.0	0.3085	89.07
	M A3,4,6,9,10	280.0	0.308	88.94
	M A2,3,4,6,10	280.0	0.3075	88.80
	M A3,4,6,10	265.0	0.3071	88.67
	M A2,3,4,7,9,10	295.0	0.2975	85.91

Table 8 .

 8 Financial and operational impact comparison.

	MA	RORI	OI0	OI1	OI2
	RP1	4.07	0.1407	0.1407	0.1407
	RP2	0.26	0.137	0.0799	0.0
	RP3	27.09	0.0247	0.0	0.0
	RP4	21.66	0.0989	0.0989	0.0989
	RP5	1.44	0.9995	0.8247	0.0
	RP6	6.76	0.1855	0.1855	0.1855
	RP7	0.46	0.1745	0.1051	0.0
	RP8	8.11	0.0756	0.0756	0.0756
	RP9	0.55	0.0731	0.0478	0.0
	RP10	54.15	0.038	0.0	0.0

Acknowledgements: This work received funding from the Panoptesec project, as part of the 7th Framework Programme (FP7) of the European Commission (GA 610416).