The Nash’s Balance in the Theory of Games for A Secure Model Mechanism in Routing Protocol of Manet

The present work is dedicated to study attacks and countermeasure in MANET. After a short introduction to what the Mobile Ad hoc Networks (MANETs) are and network security we present a survey of various attacks in MANETs pertaining to fail routing protocols. We present the different tools used by these attacks and the mechanisms used by the secured routing protocols to counter them. We also study a mechanism of security, named the reputation, proposed for the MANETs and the protocol which implements it. We also propose a secure mechanism which is based on the reputation. Our work ends with a proposal analytical model to the modules of our mechanism and the equilibrium states of our model.


INTRODUCTION
Today ad hoc networks (MANET) are a more and more adopted technology.This is mainly due to the continuing development of networks, the growing need for mobility, miniaturization of networking devices, universal access to information and its sharing.In order to transmit messages between two given nodes in networks in general, we have to determine the best route to take by using routers.In MANETs the other intermediate network nodes will be used as gateways or relays.As these nodes can be mobile, and as the network topology varies, the problem of routing, which is about finding an optimal multihop route, is the most difficult challenge to overcome in MANETs.
Indeed, this routing is a problem of optimization under such constraints like topology changes, volatility of links, limited storage and processing capacity, low bandwidth, low power level in batteries, etc.These binding characteristics make MANETs very vulnerable to attacks comparing to wired networks or infrastructure-based wireless networks.
In mobile ad-hoc networks, nodes act as both routers and terminals.For the lack of routing infrastructure, they have to cooperate to communicate.Cooperation at the network layer takes place at the level of routing, i.e. finding a path for a packet, and forwarding, i.e. relaying packets for other nodes.Misbehavior means aberration from regular routing and forwarding behavior resulting in detrimental effects on the network performance.Misbehavior arises for several reasons.When a node is faulty its erratic behavior can deviate from the protocol and thus produce non intentional misbehavior.Intentional misbehavior aims at providing an advantage for the misbehaved node.An example for an advantage gained by misbehavior is power saved when a selfish node does not forward packets for other nodes.An advantage for a malicious node arises when misbehavior enables it to mount an attack.
Electronic copy available at: https://ssrn.com/abstract=3426974 In spite of the evolution ad hoc mobile networks during the last decade it still problems related security which remain unsolved.The document is structured: we presented in the first some of the attacks and the countermeasures met in the .MANET, in the second we have analyzed the cooperative mechanism and their vulnerabilities and the end we have described our proposal mechanism and we analyzed our mathematical model to deduce the balance states.

BACKGROUND
An attack is an action which aims at compromising the security of the network.They are many and varied in these MANET: BlackHole attack: consists in dropping some routing messages that node receives [1,2,3,4,5].It was declined in several particularity alternatives, having different objectives, among which we can quote:  Routing loop, which makes it possible for a node to create loops in the network;  Grayhole, which lets pass only the packages of routing and diverts the data;  Blackmail, which makes it possible for a node attacker to isolate another node.
Selfish attack: consists in not collaborating for the good performance of the network.We can identify two types of nodes which do not wish to take part in the network.Defective nodes i.e. do not work perfectly.Those which are malevolent, it is those which intentionally, try to tackle the system: attack on the integrity of the data, the availability of the services, the authenticity of the entities (denial-of-service, interception of messages, usurpation of identity, etc).Selfish nodes are entities economically rational whose objective is to maximize their benefit [9,10].
Overflow routing tables: consists of malicious nodes to cause the overflow routing tables of nodes being used as relay [4,20,28].
Sleep deprivation: consists to make a node to remain in a state of activity and to make him consume all its energy [04], 11,13].
Although some solutions were proposed none of them can't satisfy all the constraints on the ad hoc networks.Among the mechanisms to fend off these attacks, we can cite:

Cooperative mechanism
The basic mechanisms of security prove to be effectively ensured the traditional security functionalities which are the confidentiality, the integrity and above all the authentication.They thus ensure to prevent many attacks which disrupt the process of routing.On the other hand, they do not prove to be adapted to resolve the problem of the selfish nodes.Indeed, the cryptographic mechanisms, so effective they are don't ensure a node takes part in the process of routing by relaying all the packets.However, in the context of the ad hoc networks, it's a primordial functionality as far as this type of network is based on the cooperation between the nodes.That's why some protocols aim at more specifically for the incitement to cooperate.Among these solutions, we set those which are based on a reputation nodes elaborated in the course of time according to the observations [1].Among the protocols which are based on the reputation we can cite CORE which will be the subject of our contribution article.

The CORE mechanism
The mechanism of CORE [1,9] is used to impose the cooperation of the nodes.In CORE each entity of the network encourages the collaboration of other entities by using metric cooperation called reputation.This reputation is based on the analysis of the behavior (Watchdog) associated each node.A Boolean vector represents a good (with one 1) or a bad (with one 0) behavior.A punishment mechanism is adopted as solution to prevent a selfish behavior for gradually refusing the communication services to the entities which have bad behavior.This punishment is applied if the metric of reputation (Pathrater) reached a threshold and in this case we declare that the selfish nodes constitute a denial of service and they will be put in the blacklist.Thus the legitimate nodes (which cooperate) reach to save energy.

Vulnerabities of CORE
CORE suffers unfortunately from important defects.First, it doesn't really resolve the problem of selfish [1].Immediately, all the selfish nodes see their packets rejected systematically and in this, the protocol is effective.But on the other hand, a quantity of data remains lost, reducing significantly the efficiency of the network.The protocol is based on assumptions (secure routing, single and nonusurpable addresses) which still remain to make a reality.It's a common disadvantage to all the reputation protocols.Indeed, this one is based on the information observed for the nodes and consequently requires an authentication mechanism in order to affect the marks to the legitimate which could store nonexistent links thus causing the Overflow attack [1].In addition, it's difficult to avoid the problem of fictitious denunciation (Blackmail) [1] in which a malicious node generates false messages to put up the legitimate nodes on the blacklist.The mechanism of the reputation is potentially vulnerable face up to the cooperative nodes (BlackHole Cooperative) [1] which agree between them to assign good marks and to allocate in the other hand, bad marks the legitimate nodes.Moreover, in that case the nodes couldn't make the distinction between the useful and the useless messages, and will be obliged to forward all the messages which come through them for having their good reputation.This could generate a waste of energy (sleep deprivation) [11] and moreover the constant monitoring nodes would engender a network overload causing a reduction in the bandwidth.In our algorithm we try to fend off the four vulnerabilities cited for endowing CORE with a mechanism called DRI table [22,23].

Operation of DRI Table
The DRI or the data table of routing information which is used to identify nodes of cooperative black hole, it consists in adding two additional bits of information.These bits have as values 0 for "FALSE" and 1 for " TRUE " for intermediate nodes answering the RREQ of node source.Each node updates an additional table of information of data routing (DRI) [22,23].The following figure represents the structure of the table.In the DRI table, the first bit named "From" represents the information on the packet of the node data routing (the node from which the packets comes) while the second bit "Through" represents the information on the packet by the node of data routing (the node through which its forwards the packets).
Electronic copy available at: https://ssrn.com/abstract=3426974 For example the entry "1,0" for node A means that the node B forwards the packets data coming from A but it doesn't forward any packet of data through A. The entry "1,1" for the node C means that the node B forwards the packets data coming from C and the packets of data through C.This example is represented in table 1.If the source node used IN before the new route discovery for routing the data, then IN is a reliable node and the source node begins to forward data towards IN.This obliges the attacking nodes to cooperate and to relay messages until the destination to appear in the DRI of its neighbor.This solution can be also adapted to counter the attacks like Overflow, Blackmail and also Selfish.

A PROPOSAL SOLUTION AGAINST THE COOPERATIVE BLACKHOLE, BLACKMAIL, OVERFLOW AND SELFISH ATTACKS: X CORE
The Reputation and Punishment concepts, or Payment, can encourage the nodes to fully play their role not to lose their good behavior but these solutions cannot counter some attacks in MANETs as the above attacks.

Description of XCORE
Define In the existing CORE, we include DRI table and we estimate the table if we receive a routing packet.To making this estimation, we calculate the times that the node has forwarded the packets coming from another node and the times that the node has forwarded the packets through another node.
If the Rate_Send_Reception rate of the DRI is equal to [0, 0] we declare that this link is fictitious (it's an Overflow attack).Else when a node sends a routing message, we estimate this message.If it's a route error, we will check its validity by looking at the DRI.If Rate_Send_Reception is [0, 0] then we confirm that it's a defective node else we consider that it's an invalid message (if it is a Blackmail attack) and in this case we continue to estimate the reputation.If the reputation is < 0 we consider that it's a denied of service node (a Selfish node) else we declare that it's a cooperating node.

End
Electronic copy available at: https://ssrn.com/abstract=3426974 For lack of simulators and models which take into account the protocol CORE and also the complexity of protocol CORE the majority of the authors use other means like the MATLAB software to make their CORE simulations [09].

Modelling of XCORE mechanism with the theorical games
To model our proposition we use the prisoner's dilemma (PD) of the game theory [24,25,26].In this traditional model of the PD, two players take with a decision to cooperate (C) or defect (D).If the players cooperate they receive a benefit (G).If the two players decide to defect they receive a punishment (P).In the case or only one player cooperates and the other defect, the benefit will be M for the defected player and N for the cooperated player.
The PD is a member of the class named plays with two players, whose sum of the benefits is not null.The dilemma is dictated to the following expressions: M > G > P > N, G > (M+ N) / 2. The matrix representation is illustrated in the table: In this section we propose a modelling of some of these attacks like sleep Deprivation and Selfish for using mathematical tools named the game theory which is an analysis's tool of human behaviours.It took an increasing development since the joint publication of Von Neumann and Morgenstern "The Theory of Games and Economic Behavior" in 1944 [24,25,26,27,28].
In [9] the author models the cooperation of the nodes.It is based on the game theory to evaluate the reputation i.e. the behavior of the nodes when they receive messages and transmit them.In the sleep deprivation and Selfish attacks, some nodes receive the messages and decide to process them or not; more they can receive a great quantity of messages coming from an attacking node, thus causing energy consumption.So, we can adapt this approach to model our above mentioned attacks because in this approach the author treats the behavior of the malicious nodes and in the case of our attacks we have to treat the behavior of the malicious nodes.
In the case of our modelling of the attacks sleep deprivation and Selfish, we consider nodes which integrate the network and will decide to communicate.If each of the nodes sends a message and the other decides to process it, each of them consumes energy.On the other hand if the message is not processed (non-cooperation), the sent node loses its energy while the other node saves its energy.This strategic situation can be described in a more formal way.Electronic copy available at: https://ssrn.com/abstract=3426974 In a general way, if we noted by σ the benefit when we execute the function  for a reiterated game k times for some time t;


If this instant t=1, we apply the cooperation i.e.Consume (sent and processed), the benefit is and so on and so forth.
The general formula to calculate the benefit is given by: is the benefit got in time t by the node ni on the node nj for executing the function f ) (k  is a function which depends on time recording the values of σk σk represents the benefit obtained with the kth iteration when we execute the action ) (k  .
For example, if node A sends and B doesn't process, A consumes -2 Joules and B saves 2 Joules and vice versa.If node A sends and B processes, each of them consumes -2 Joules.If the nodes do not send nor process, they will save 2 Joules.The following Table gives us an example of energy consumption for the nodes which are communicated.
For the modelling of DRI module, always we consider the example of nodes A and B. That is two nodes A and B, each one has two possible strategies (forward or never forward).We have the following table which represents the matrix of DRI.
Electronic copy available at: https://ssrn.com/abstract=3426974For example, if the nodes A and B forward the packets of the one through the other, each one benefits an entry equal to 1 for its DRI table, if node A forwards the packets through B and B has never forwarded through A, A benefits an entry equal to 1, B benefits 0 and vice versa.If the nodes have never forwarded the packets of the one of the other, they perceive an entry equal to 0. The game theory makes it possible to predict the game balances more particularly the Nash's balance i.e. the states in which no player or node doesn't wish to modify his behavior taking into account the behavior of the other.

THE BALANCES IN THE THEORY OF GAME
The analysis's game makes it possible to predict the balance which will emerge if the players are rational.By balance, we understand a state or a situation in which no player doesn't wish to modify his behavior taking into account the behavior of the other players.In a more precise way, a balance is a combination of strategies such none player hasn't incitement to change its strategy taking in consideration of the strategies of the other players.Once the balance is reached in a game (any the manner of which it was obtained), it's no reason to leave it there.In order to be able to use the concept of the game balance in our analysis, we must be more precise this concept significance.
We know that a balance consists of strategy combination choices (a strategy choice by player) and we know that once the stopped choices, no modification will intervene i.e. no player or groups players haven't an incentive to modify his actions if it supposes that its rivals will not modify either theirs.
The games which we study here correspond to situations in which each player only stops his strategy choices without consulting the other players.Such games are called selfish games because they don't offer the possibility of a formal or flexible cooperation, i.e. a coordination of the various players' strategies.Thus, when we want to determine the selfish game balances, we will not consider the incentives of the player groups to modify their behaviors jointly being given the behavior of the remaining players; we will consider only the incentives of the players taken individually [25, 26. 29] Electronic copy available at: https://ssrn.com/abstract=3426974  .For each simulation if we suppose that the population is  , the following expression is valid: The evaluation of the score obtained by each player who adopts a strategy determined with iteration n is: In total, the profit allotted to each strategy is:   NB: So for all i and j, ui= uj, one deals with a situation of full cooperation.If n= 2, and ui+ uj= 0, one deals with a full conflict situation.In other words a game which has two players is with worthless sum if ui(s) + uj(s) = 0 whatever the profile of strategies s ∈ S. In this case, the profits of a player are equal to the losses of the other, so that one can say that the players are opponents with the usual direction.The following table illustrated a situation of balance.The full cooperation allows the nodes to gain trust in order to build a stable and reliable network, and also an available bandwidth, because the traffic due to the number of the route discovery messages decreases.
Electronic copy available at: https://ssrn.com/abstract=3426974 The pure conflict causes not only a dysfunction of the network because no node participates in the route discovery, but also attacks Selfish and BlackHole.
If the nodes opt for different strategies i.e. (0,1) or (1,0), the nodes are neither in pure cooperation nor in pure conflict situation, so the reputation must be calculated in time to be able to consider the nodes as selfish or not.

RESULTS AND DISCUSSIONS
Cooperation is intended as the willingness of a node to perform networking functions for the benefit of others nodes.However, cooperation has a non-negligible energetic cost that can lead to a selfish behavior, especially in battery powered environment such as mobile ad hoc networks.Thus to support the cooperation of the nodes, our model suggests to use the DRI table to detect the declaration of fictitious nodes (Overflow attack) just as the sending of false messages which announce a malicious node whereas last is legitimate causing an attack blackmail like illustrating in the tables below.
The nodes can be satisfied with these contained informations in these tables to see whether the node is legitimate or not, which makes it possible to encourage the cooperation (against the selfish) and also to be able to save energy in the event of presence of the virtual nodes (against the sleep deprivation ).
We presented the equilibrium in the theory of games and our model came to equilibrium situation named the Nash's balance.In the future we propose to implement all the modules of our mechanism in order to make real test because in this work we presented only theorical test.

CONCLUSIONS
In our work we have presented the specificities of the MANET as well as the problems of the security routing protocols in these types of network.We presented some attacks met in MANETs, their functioning mode thus the mechanisms used and the protocols which implement them to counter these attacks.
We analyzed the functioning mode of CORE and brought out some of its vulnerabilities, and then we proposed a new algorithm, named XCORE, which improves the basic CORE.This algorithm ensures to resist the attacks BlackHole cooperative, Blackmail, Overflow, and Selfish.We modelled the modules of XCORE by using the theory game to see the impact of selfish and the energy consumption.
We presented the equilibrium in the theory of games and our model came to equilibrium situation named the Nash's balance.In the future we propose to implement the XCORE and ours models in order to make evaluations of performance with CORE.

Figure 1 .
Figure 1.The structure of the DRI table

Figure 2
Figure 2 illustrates the operation of XCORE proposed.

Figure 2 . 3 . 2 .
Figure 2. Functioning of XCORE si in i S and any player i.If we suppose that the population taking part in the reiterated game DP uses, with an identical distribution on the players, the strategies K and L. The nth iteration, sees each represented by a distribution of population: Wn players the strategy L. The profit of the players who use the strategy K when they oppose to the strategy L is represented by

Table 1 .
Example of DRI table utilisationTo discover a route towards the destination node the source node (SN) broadcasts a RREQ message.The intermediate node (IN) which produces a RREP must provide the hop of the next node (NHN) and its DRI entry.According to the RREP message from the intermediate node, the source node will control its own DRI table to see if the intermediate nodes will a trustworthy node.

Table 2 .
The matrix form of PD That is two nodes A and B, each one has two possible strategies (to consume or save) which can be materialized by a function noted ρ .With each combination of choice is associated a benefit noted σ for node A and the node B. The table gives us examples of benefit in energy.On line we have the choices of node A and in column those of the node B. In each box of table, the first benefit of energy is that of node A and the second benefit is that of the node B.

Table 3 .
The energy consumption of PD

Table 4 .
An example of the PD energy consumption

Table 5 .
The matrix of DRI

Table 6 .
An example of the matrix DRI

Table 7 .
An example of the Nash' balance DRI