We examine the distinguishing number of the Cartesian product of an arbitrary number of complete graphs. We show that for u1 ≤ · · · ≤ ud the distinguishing number of the Cartesian product of complete graphs of these sizes is either du d e or du 1/s d e + 1 where s = Πd−1 i=1 ui. In most cases, which of these values it is can be explicitly determined.

We analyse several well-known key establishment protocols for mobile communications. The protocols are examined with respect to their security and suitability in mobile environments. In a number of cases weaknesses are pointed out, and in many cases reenements are suggested, either to improve the eeciency or to allow simpliied security analysis.

A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest integer k for which G has a distinguishing k-labeling. In this paper, we apply the principle of inclusion-exclusion and develop recursive formulas to count the number of inequivalent distinguishing k-labelings of a gr...

The distinguishing number D(G) of a graph is the least integer d such that there is a d-labeling of the vertices of G that is not preserved by any nontrivial automorphism of G. We show that the distinguishing number of the square and higher powers of a connected graph G 6= K2,K3 with respect to the Cartesian product is 2. This result strengthens results of Albertson [1] on powers of prime graph...

One key feature of named data networks (NDN) is supporting in-network caching to increase the content distribution for today’s Internet needs. However, previously cached contents may be threatened by side-channel timing measurements/attacks. For example, one adversary can identify distinguishing between uncached and from node, namely edge NDN router. The attacks mitigated proposed methods effec...

RC4, designed by Rivest in 1987, is the most widely deployed stream cipher in practical applications. In this paper, two new class of statistical biases inherent in RC4 are depicted and it is shown that the RC4 keystream is distinguishable from random no matter how many initial bytes have been dumped. RC4A, proposed by Paul and Preneel at FSE 2004 to strengthen the security of RC4, is also foun...

We investigate the distinguishing index D′(G) of a graph G as the least number d such that G has an edge-colouring with d colours that is only preserved by the trivial automorphism. This is an analog to the notion of the distinguishing number D(G) of a graph G, which is defined for colourings of vertices. We obtain a general upper bound D′(G) ≤ ∆(G) unless G is a small cycle C3, C4 or C5. We al...

The output of RC4 was analyzed using the ”book stack” test for randomness from [7]. It is experimentally shown that the keystream generated from RC4 can be distinguished from random with about 232 output bits.

The fixing number of a graph G is the smallest cardinality of a set of vertices S such that only the trivial automorphism of G fixes every vertex in S. The fixing set of a group Γ is the set of all fixing numbers of finite graphs with automorphism group Γ. Several authors have studied the distinguishing number of a graph, the smallest number of labels needed to label G so that the automorphism ...

In this paper we discuss our research in applying classification methods for computer network intrusion detection. Using two different algorithms for classification (decision trees and naive Bayes classifier) we build a predictive model capable of distinguishing between “bad” TCP/IP connections, called intrusions or attacks, and “good” normal TCP/IP connections. We investigate the effect of tra...