Communication Overhead. In this part, we compare the communication over- head of the proposed scheme with several existing schemes. We assume that the sizes of the elements in G1 and G are 128 bytes and 40 bytes, respectively. In addition, let the output of a hash function and the size of the time stamp are 20 bytes and 4 bytes, respectively. Moreover, we assume that the origin messages are included in the finite field Z∗ and have a size of 20 bytes. whether T ′ − Tvi ≤ ∆t holds. We focus on the analysis of the communication
Communication Overhead. To measure the overhead of the communication, we use the size of the package exchange between the source node and the destination node as the criterion. If the source node needs to transit too large a package, it will consume the frequency bandwidth excessively. Therefore, the efficiency of the bandwidth allocation would not be very high. And the power cost of message exchanges would also reduce the life expectancy of the network. In Du et al.’s scheme, the node only needs to compare the indices of the pre- distributed secrets. With these indices, the node can check whether there is any overlap secret in the other node. If a node is pre-distributed into s secret, the size of these indices is s log2 n and the communication overhead of the Xxx et al. is the same.
Communication Overhead. Since LKE and iLKE are two in-situ key establishment schemes, messages are transmitted for keying information distribution as well as pairwise key establishment. Compared to the existent key predistribution schemes, the additional traffic may appear to be a deathful weakness for the two schemes. However, polynomial shares are only transmitted
Communication Overhead. The communication overhead is measured by the number of the messages. That is to say the overall communication overhead of the scheme is the summation of messages exchanged in cluster and messages exchanged among clusters. In order to compare these protocol conveniently, we assume the size of group is n, and the size of the each cluster is k. In IKA phase, members in cluster perform BD protocol and the message overhead is C1 b =n k [2k+k(k−1)] = n+nk. Among clusters the members perform TGDH protocol. According to Table 2. we know that the message overhead which the leaf nodes need to send is k ∑n/k i=1 hi , where hi is the height of leaf node i. So the message overhead in performing TGDH is t C1 : K ∑ i=1 n/k hi <K ∙ n/k ∙ log n/k = n ∙ log n/k . Therefore, we can compute the overall communication overhead in IKA phase as b t C1=C1 + C1 =n + nk + n · log n/k. In AKA (we only discuss single member joining in for short), a new member join in a certain cluster, all the members in this cluster must choose the random value again, so the overhead of
Communication Overhead. The proposed scheme communication overhead as compared with other existing schemes [8], [12], [23] and the computed values are shown in Tables 3, 4 and 5 and then design graph according to these computed values which are shown in Fig. 5. Communication overhead of our proposed scheme with schemes [8], [12], [23] is represented in Fig. 5 where our scheme shows 84.2% as compared to scheme [8], 85.7% efficiency than scheme [12] and 78.57% than [23]. TABLE III. COMMUNICATION OVERHEAD COMPARISON WITH X. XXXXXXX ET AL. Scheme Communication Overhead Communication Overhead Reduction in Percent X. Xxxxxxx et al. [8] (1024+192)bits % = 84.2 % Proposed (128+16+48) bits TABLE IV. COMMUNICATION OVERHEAD COMPARISON WITH X. XXXXX ET AL. Scheme Communication Overhead Communication Overhead Reduction in Percent X. Xxxxx et al. [12] (1024+320)bits % = 85.7 % Proposed (128+16+48) bits TABLE V. COMMUNICATION OVERHEAD COMPARISON WITH XXX ET AL. Scheme Communication Overhead Communication Overhead Reduction in Percent Xxx et al. [23] 2(160+160+128)bits % = 78.57 % Proposed (128+16+48) bits ( ) Proposed Scheme
Communication Overhead. − − − − − Each party performs 2 passes, except for Un−1 and Un, who perform one pass. The total number of passes is 2n−2. In the first n−1 passes, the communication overhead of the pass from party Ui to Ui+1 includes i elliptic curves and i(2n − 1 − i)/2 corresponding pairs of points. For the next pass from Un to U1, there are n− 1 elliptic curves and n(n− 1)/2 pairs of points. For the last n− 2 passes, the pass from party Ui to Ui+1 includes n 1 i elliptic curves and (n 1 i)(n i)/2 pairs of points. − − Overall, each party sends n 1 elliptic curves and n(n 1)/2 pairs of elliptic curve points. In general, without compression or optimization, it takes two finite field elements to represent the curve and one finite field element plus one bit to represent the point. If p is a k-bit prime, then each party transfers: (n − 1) · 2 · (2k) + (n(n − 1)/2) · (2k + 1) bits. A time-space trade-off is possible: For any collection of points lying on the same curve and having orders which are pairwise relatively prime, we can trans- mit this entire collection by sending only a single point on the curve, using the projection onto the elliptic curve of the standard Chinese Remainder Theorem × isomorphism Z/a Z/b =∼ Z/ab, valid for gcd(a, b) = 1. The trade-off is that per- forming this conversion each way takes time. In our software we do not perform this conversion.
Communication Overhead. As the establishment of direct keys between a pair of nodes does not require handshakes between them, the major com- munication overhead lies with the establishment of indirect keys. Just like most existing security schemes that require handshakes between end nodes to negotiate a shared key, this overhead is inevitable. However, few analytical results about server to facilitate key agreement between any two nodes. − The trusted server can be a potential failure point. Distributed methods are more secure. A simple method is the full pairwise key distribution, in which each pair of nodes in a network of N nodes is preloaded with a distinct symmetric key. Each node, however, must keep N 1 symmetric keys. Another two basic distributed methods are proposed by Xxxx [2] and Xxxxxx et al. [3], which feature the same amount of memory cost as the full pairwise key approach. Those distributed methods lack scalability and thus only suitable in small networks. Probabilistic schemes [4]–[22] can provide a certain level of scalability with the tradeoff that they can not guarantee that every pair of nodes establish a shared key. The memory cost of those schemes increases linearly with respect to the total number of nodes if they need to achieve a certain level of security or communication efficiency [23]. Moreover, those schemes are targeted at the key establishment between neighboring nodes, while our scheme can achieve the end-to- end key agreement. O O √ √ Combinatorial design techniques are proposed in [24], [25]. They can ensure key sharing between any pair of nodes. In their schemes, however, each key is reused by many sensor nodes. This leads to poor resilience to node compromise in that one compromised node can expose keys belongs to other noncompromised nodes. In addition, the memory cost of their schemes is roughly ( N) where N is the total number of nodes, while the memory cost of our scheme can be ( k N ), which is more scalable. PIKE [23] organizes the network into a 2-dimension grid, Then, Shamir’s (s+1,T ) threshold secret sharing scheme [31] can be applied. Specifically, T shares can be calculated as g(1), g(2),... , g(T ) , (33) ≥ where T s + 1. Next, node u transmits the T shares to node v through multiple secure paths by following the method proposed in [30]. Suppose u and v have j mismatches in their IDs, which means there are j disjoint secure paths between them. Then node u may transmit T/j shares along each secure path to node v. Once node v gets s ...
