There have been a number of results dealing with Hamiltonian properties in powers of graphs. In this paper we show that the square and the total graph of a K,,,-free graph are vertex pancyclic. We then discuss some of the relationships between connectivity and Hamiltonian properties in K,.3-free graphs.
In this paper, we present two new centralized group key management protocols based on the Chinese Remainder Theorem (CRT). By shifting more computing load onto the key server we optimize the number of re-key broadcast messages, user-side key computation, and number of key storages. The first protocol is the base Chinese Remaindering Group Key (CRGK) protocol, which with a group of n users requires the key server to do O(n) XORs, additions, multiplications, and Extended Euclidean Algorithm computations and broadcast 1 re-key message; each individual user is required to do only 1 modulo arithmetic and 1 XOR operation for each group key update. The second protocol is the Fast Chinese Remaindering Group Key (FCRGK) protocol, which only requires the key server to do O(n) XORs, additions, and multiplications most of the times with no change to the number of re-key messages and user computation per group key update. For both protocols each user only needs to store 2 keys all the time. One special attraction for our FCRGK protocol is that it allows most of the re-keying computation to be done preemptively, which means when a user-join or user-leave event happens the response time for the key server to send out the new group key can be very short.
Without physical boundaries, a wireless network faces many more security threats than a wired network does. Therefore, in the IEEE 802.16 standard a security sublayer is specified in the MAC layer to address the privacy issues across the fixed Broadband Wireless Access (BWA). Several articles have been published to address the flaws in IEEE 802.16 security after the IEEE standard 802.16-2001 was released. However, the IEEE standard 802.16-2004 revision does not settle all the discovered problems and additional flaws remain. This paper gives an overview of the IEEE 802.16 standard, focusing on the MAC layer and especially the security sublayer. We analyze the security flaws in the standard as well as in related works, and illustrate possible attacks to the authentication and key management protocols. Possible solutions are also proposed to prevent these attacks. Finally, we propose a security handover protocol that should be supported in the future 802.16e for mobility.
In this article w e show that the standard results concerning longest paths and cycles in graphs can be improved for K,,,-free graphs. We obtain as a consequence of these results conditions for the existence of a hamiltonian path and cycle in K,,,-free graphs.There have been a great many results in recent years dealing with graphs that do not contain a copy of K l , , as an induced subgraph. It appears that this class of graphs is better behaved, in many respects, than graphs in general. It has been shown that for such graphs G, (i) If G is connected of even order then G has a I-factor Throughout this paper 6 will denote the minimal degree of a vertex in the graph. Other terminology not defined in this paper will agree with that in Behzad and Chartrand [2].For graphs that are not necessarily hamiltonian there are several results dealing wth longest paths and cycles. Dirac has shown [3] that if G is a connected graph then G has a path of length 26 or a hamiltonian path. Dirac also proved that if G is a 2-connected graph, then G has a cycle of length at least 26 or a hamiltonian cycle. The examples showing that Dirac's results are sharp are not K,,,-free, and if we add K,,3-free to the hypothesis, we obtain slightly larger lower bounds on the longest paths and cycles in graphs. To prove this, we first need a couple of lemmas about maximal cycles and paths in K,,,-free graphs. The proofs of the these lemmas are straightforward and hence are not included.
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