Available online at ScienceDirect. Procedia Computer Science 58 (2015 )

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1 Available online at ScienceDirect Procedia Computer Science 58 (2015 ) Second International Symposium on Computer Vision and the Internet (VisionNet 15) Mathematical Analysis of Trust Computing Algorithms Thangakumar Jeyaprakash a, Rajeswari Mukesh b a.b Department of Computer Science and Engineering, Hindustan University No.1, RajivGandhi Salai, Padur, Chennai, Tamilnadu, India Abstract To overcome a frequent occurrence of routing loops due to communication link failure and to provide an ensured packet delivery among the Vehicular Ad-hoc Networks (VANET), an Optimized Node Selection Routing Protocol (ONSRP) of VANET has been implemented using a Trust Computing Algorithm. Basically, the time efficiency indicates how fast the algorithm runs. In this paper, the Trust Computing algorithm has been analyzed mathematically to find the time complexity of the algorithm currently chosen and hence achieved trusted communication and high packet delivery ratio of data transmission among the Vehicular Adhoc Networks. We could confirm that the ONSRP is optimal by comparing it to the Scalable Hybrid Routing (SHR) communication overhead and packet delivery ratio of the network from both analysis and simulation in the presence of link failures. Keywords: Mathematical Analysis; Routing protocol ; trust ; Vehicular Adhoc Networks; 1. Main text Vehicle to Vehicle Communication (V2V) is an active wireless transmission of data between neighbor vehicles that offers services for important safety improvements. The aim for V2V is essentially that each vehicle on the highway will be able to communicate with each other through Dedicated Short Range Communication (DSRC) for exchanging the messages dynamically. This V2V communications will provide active safety measurements that can assist and alert drivers in preventing 76 percent of the crashes on the roadway, thereby reducing fatalities, injuries and major damages that occur each year in the country. This is achieved by an efficient routing protocol without overhead communication which may lead to frequent communication link failure. In this paper, we analyzed the trust computing algorithm mathematically to find the time complexity of the algorithm to achieve a trusted communication and high packet delivery ratio. Martin et al 1 stated a topology-based routing protocol which discovers the position of the destination. Patroklos et al 2 evaluated a secure routing for Adhoc networks. Maxim Raya et al 3 provide a detailed threat analysis such as false information and Denial of Service etc. They also analyzed the robustness and carried out a quantitative assessment. Harsch et al 4 a security mechanism model and evaluated in Car to Car Consortium. Feilong Tang et al 5 proposed a protocol which reduce the number of hops between the source and the destination and increase the life time of networks. Jalali et al 6 proposed a system to identify the source node is selfish or not. The proposed fuzzy reputation system eliminates the selfish node from the network to maximize the performance of the networks. Khaleel et al 7 proposed a system with carry and forward messages for the utility of Road Side Units efficiently to route packets in VANETs. Vinayakra Jani 8 described the comparative analysis of MANET and VANET based on various design factors. Mahmoud Hashem Eiza and Qiang Niused 9 stated the determination of the reliable routes pre-emptively. Mohammad et al 10 proposed a scalable hybrid routing protocol which combines the protocols in such a way that, if the location information is The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of organizing committee of the Second International Symposium on Computer Vision and the Internet (VisionNet 15) doi: /j.procs

2 106 Thangakumar Jeyaprakash and Rajeswari Mukesh / Procedia Computer Science 58 ( 2015 ) degraded, it automatically uses the reactive routing. It starts with location-based routing and route discovery will be initiated, if the location routing is degraded. Albert Wasef et al 11 proposed a Validation Protocol (EMAP) for an efficient revocation checking process. Zhengming Li 12 has proposed a VANET based Ad-dissemination scheme to support secure packet transmission of data. ChiragBhalodia et al 13 stated when route break occurs, at the same time, the intermediate node will send a route error packet to source and source node reestablish an another route. Wafa Ben Jaballah et al 14 describes the attacks to the state-of-the-art IVC-based safety application and lead them to design a fast and secure multihop broadcast algorithm for vehicular communication. Mushtak Y. Gadkari et al 15 made an attempt to identify the different VANET protocols. 2. Proposed Work To avoid communication link failure and routing loops, we implemented an Optimized node selection routing protocol algorithm Vehicular Ad-hoc Networks; each node keeps a Flag Trust value in its routing table based on distance 17, direction and velocity of the nodes to calculate the trust value for transmission of data. 3.1 Distance of Nodes: N4 N1 N2 N5 N3 Fig. 1. Instance formation of VANET. In figure 1, Assume that in this example node N1, N2, N3, N4, N5 are moving in same direction and velocity. Distance (Do) = (Minimum (D1 D2 D3..Dn)) (1) D1 = Distance between the Last node of path 1 routing table and the Destination node, D2 = Distance between the Last node of path 2 routing table and the Destination node, DN = Distance between the Last node of path N routing table and the Destination node. (2) 3.2. Direction of Nodes: In Figure 1, N1 is a source node and N5 is a destination node. To identify the direction of nodes movement, a node calculates the direction of the neighbor node as follows.

3 Thangakumar Jeyaprakash and Rajeswari Mukesh / Procedia Computer Science 58 ( 2015 ) Direction in degrees (Ao) = D (RWP (i, j) & Min (D1 D2 Dn) (i, j)) (3) D1 = Distance between the Last node of path 1 routing table and the Destination node, D2 = Distance between the Last node of path 2 routing table and the Destination node, DN = Distance between the Last node of path N routing table and the Destination node, D = Destination, RWP = Random way points in the network are. i, j = two successive random way points. 3.3 Velocity of nodes: We utilized the velocity of nodes as a performance parameter to develop our Flag Trust model. The velocity of nodes helps to determines the network topology mobility. It also plays a significant role in determining the estimated communication time between vehicles. At Time T1, Velocity (Vo) = V (Dn) V (N1 N2 N3 Nn) (4) Dn = Destination node, N1 = Velocity of Neighbor node 1 of Dn, N2 = Velocity of Neighbour Node 1 of Dn, Nn = Velocity of Neighbour Node 1 of Dn, Vo = Optimized Velocity. 3. Mathematical Analysis of Trust Computing Algorithm Trust Computing Algorithms are remarkably efficient for searching in an array of nodes. It works by comparing nodes for A[0.n-1]. If an optimized node is found to transmit the data packet from the source to the destination, the algorithm stops, otherwise the same operation is repeated to find the Optimized node. Algorithm: Trust Computing & Optimized Node O(n) : Let Do Minimum distance of the node (i,j), Ơ Direction of the node move towards the destination node and Ѵ Velocity of the neighbor node similar to the destination node //Implements the Trust Computing for the Optimised Node O(n) //Input: An Array of nodes [(A[0.n-1]] nearer to the destination //Output: Calculates the trust value to set the flag of the node 0 or 1 to find the Optimized nodes O(n). i 0; j 0; k 0 t_count α; d_threshold β; No of times data forwarded ɠ count 0; trust 0; for i 0 to n-1 && Do β do Do=Minimum_Distance_of_Node (i,j); Swap A[j]=A[i]; return A[j]; for j i+1 to (n-1-i) && Ơ A[n-1] do Ơ = ((Xi,Yi) (A[j], (A[n-1])));

4 108 Thangakumar Jeyaprakash and Rajeswari Mukesh / Procedia Computer Science 58 ( 2015 ) swap A[k]=A[j]; return A[k]; for k i+j+1 to (n-1-i-j) && Ѵ A[n-1] do if V(A[k]) V (A[n-1]) return V(A[k]); swap O(n) = V(A[k]); α(o(n))= count ++; else return -1 if (α(o(n) ɠ )) SET flag (O(n)) = 1 else SET 0; Algorithm: To find the distance (i,j) : //Implements the Minimum_Distance_of _Node(i,j) //Input: An Array of nodes [(A[0.n-1]] nearer to the destination //Output: Calculates the distance value from node 0 n-1 i 0; j 0; vertex 0; distance 0; for i 0 to n 1 do{ for j 1 to n 2 do{ if (j!=i){ set x_pos1 [n(i) set X]; set x_pos2 [n(j) set X]; set y_pos1 [n(i) set Y]; set y_pos2 [n(j) set Y]; vertex = x_pos1*x_pos2 + y_pos1*$y_pos2; distance (i,j) = sqrt(vertex); print dist "Node i to j: ds(i,j) } } } 4.1 Mathematical Analysis of finding the Optimized node Algorithm: Let us denote C(n) 16, as the number of times the basic operation is to be executed to find the formula with the input size of n. The algorithm makes one basic operation with initial conditions with each loops executed which is repeated for the variable i within the bounds between 0 and n-1. Therefore we get the following sum for C(n). C(n) = (5)

5 Thangakumar Jeyaprakash and Rajeswari Mukesh / Procedia Computer Science 58 ( 2015 ) Using standard formulas and some Manipulation, (6) and (7) follows (6) (7) General Plan for analyzing the efficiency of Algorithms 16 : 1. Find and decide the input size parameter 2. Identify the algorithm s basic operation to be executed C(n) 3. Find the properties such as worst case, best case and average case efficiency. 4. Find out the sum of basic operation. 5. Using standard formulae and rules of sum manipulation, find the time complexity of the algorithm and establish its order of growth According to the equation (7), Equation (8) becomes (8) (9) According to the equation (2)

6 110 Thangakumar Jeyaprakash and Rajeswari Mukesh / Procedia Computer Science 58 ( 2015 ) (10) 2 (11) According to Equation (11), let us compare n (n-1)/2 and n 2 2 ½ = +ve Constant 16 (12) Thus, the Trust Computing algorithm has been analyzed mathematically to find the time complexity of the algorithm and finding the optimized node for the transmission of data from the source node to the destination to achieve a trusted communication and high packet delivery ratio. 4. Results & Comparisons More specifically, we can confirm that the ONSRP is optimal 18 by comparing to the Scalable Hybrid Routing (SHR) communication overhead and packet delivery ratio. Fig. 2 & 3, shows the performance of ONSRP and Scalable hybrid routing protocols. The graph shows a raise in the transmission of packets of ONSRP compared to SHR. On the other scenario, for ONSRP, the increasing density is reducing the communication overhead also by avoiding the frequent route discovery process. Fig. 2.Performance - Packet Delivery Ratio

7 Thangakumar Jeyaprakash and Rajeswari Mukesh / Procedia Computer Science 58 ( 2015 ) a. Fig. 3. Performance - Delay Performance Metrics Node Density SHR ONSRP Delay (Sec) PDR Delay(Sec) PDR Delay (Sec) PDR Delay(Sec) PDR Table 1: Performance Measures In Table 1, the performance metrics such as delay and packet delivery ratio for the node density up to 100 of ONSRP and SHR has been compared and the result analysis shows the ONSRP is optimal in the presence of link failures with efficient packet delivery ratio. Conclusions In this paper, we have analyzed mathematically to find the time complexity of the algorithm in finding the optimized node in the vehicular Adhoc networks for the data dissemination from the source node to the destination to achieve a trusted communication and high packet delivery ratio. Hereby, we could confirm the optimality of the ONSRP by comparing to the Scalable Hybrid Routing (SHR) communication overhead and packet delivery ratio of the network from both analysis and simulation in the presence of link failures.

8 112 Thangakumar Jeyaprakash and Rajeswari Mukesh / Procedia Computer Science 58 ( 2015 ) References 1. M Mauve and Jörg Widmer,"A Survey on Position-Based Routing in Mobile Adhoc Networks", IEEE Network, pp 30-40, December P Argyroudis et al, "Secure Routing for Mobile Adhoc Networks", IEEE communication Surveys, Third Quarter, Volume 7, No 3, pp 2-20, M Raya and JeanPierre Hubaux ",The Security of Vehicular Ad Hoc Networks",SASN 05,ACM, November 7, 2005, Alexandria, Virginia, USA. 4. C Harsch et al "Secure Position-Based Routing for VANETs",IEEE Computer Society, pp 26-31, F Tang, Minyi GUO, Minglu LI, Cho-Li WANG and Mianxiong Dong, "Secure Routing for Wireless Mesh Sensor Networks in Pervasive Environments",International Journal Of Intelligent Control And Systems Vol. 12, No. 4, ,December M Jalali et al,"a Fuzzy Reputation System in Vehicular Ad hoc Networks", Procedia Computer Science,5 (2011) K Mershad, Hassan Artail, and Mario Gerla,"We Can Deliver Messages to Far Vehicles", IEEE Transactions On Intelligent Transportation Systems, Vol. 13, No. 3, September P Vinayakray Jani,"Routing Protocols For Mobile And Vehicular Ad Hoc Networks: A Comparative Analysis", ACTA Technica Corviniensis, September M Hashem Eiza and Qiang Ni, "An Evolving Graph-Based Reliable Routing Scheme for VANETs", IEEE Transactions On Vehicular Technology, Vol. 62, No. 4, May M Al-Rabayah and Robert Malaney, Member, IEEE, A New Scalable Hybrid Routing Protocol for VANETs, IEEE Transactions On Vehicular Technology, Vol. 61, No. 6, July A Wasef and Xuemin (Sherman) Shen,"EMAP: Expedite Message Authentication Protocol for Vehicular Ad Hoc Networks", IEEE Transactions On Mobile Computing, Vol. 12, No. 1,,pp 78 90,January Z Li, Congyi Liu, and Chunxiao Chigan,"On Secure VANET-Based AdDissemination With Pragmatic Cost and Effect Control",IEEE Transactions On Intelligent Transportation Systems, Vol. 14, No. 1, March 2013, pp C Bhalodia et al,"modified Route Maintenance in AODV Routing Protocol",International Journal of Advance Engineering and Research Development (IJAERD),Volume 1,Issue 5,May 2014, e-issn: ,pp W Ben Jaballah, Mauro Conti, Mohamed Mosbah, and Claudio E. Palazzi, "Fast and Secure Multihop Broadcast Solutions for Intervehicular Communication",IEEE Transactions On Intelligent Transportation Systems, Vol. 15, No. 1, February M Gadkari et al," VANET: Routing Protocols, Security Issues and Simulation Tools", IOSR Journal of Computer Engineering (IOSRJCE) ISSN: Volume 3, Issue 3 (July-Aug. 2012), PP A Levitin, Introduction to the design and analysis of Algorithms, Villanova University, Pearson, J Thangakumar, Nancy Vinoliya, Appraising Vehicular Adhoc Network Routing Protocols using NS2, International Journal of Information & Computation Technology, pp , J Thangakumar, Rajeswari Mukesh A survey of Mobility Models of Vehicular Adhoc Networks and Simulators, International Journal of Electronics and Information Engineering(IJEIE), Vol.2, No.2, pp , June 2015.