Definition 1.2 (Distinguishing number of a graph). Let Γ = (V,E) be a graph and let f : V → [r] be a coloring of the set of vertices by r colors. The map f need not be surjective, in fact when r > |V | it cannot be surjective. We say that f is r-distinguishing if the only automorphism of Γ that fixes the coloring f is the trivial automorphism. The distinguishing number of Γ is denoted by D(Γ) a...

In a recent issue of this journal, Matos et al. proposed a new index for discriminating between iron deficiency anemia (IDA) and the thalassemia trait.1 We read their paper with great interest, since we have performed similar research in this field.2 Recently we completed a study in which we compared 25 discriminant formulas incorporating only basic red blood cell (RBC) parameters using a large...

We revisit the different approaches used in the literature to estimate the data complexity of distinguishing attacks on stream ciphers and analyze their inter-relationships. In the process, we formally argue which approach is applicable (or not applicable) in what scenario. To our knowledge, this is the first kind of such an exposition. We also perform a rigorous statistical analysis of the mes...

A coloring of the vertices of a graph G is said to be distinguishing provided that no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, denoted D(G), is the minimum number of colors in a distinguishing coloring of G. The distinguishing number, first introduced by Albertson and Collins in 1996, has been widely studied and a number of interesting res...

The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d colors that is not preserved by any nontrivial automorphism. The restriction to proper labelings leads to the definition of the distinguishing chromatic number χD(G) of G. Extending these concepts to infinite graphs we prove that D(Qא0) = 2 and χD(Qא0) = 3, where Qא0 denotes the hypercube of cou...

A uniform random intersection graph G(n,m, k) is a random graph constructed as follows. Label each of n nodes by a randomly chosen set of k distinct colours taken from some finite set of possible colours of size m. Nodes are joined by an edge if and only if some colour appears in both their labels. These graphs arise in the study of the security of wireless sensor networks, in particular when m...

Recently, Al-Riyami and Paterson [1] proposed four authenticated tripartite key agreement protocols which make use of Weil pairing. In this paper, we show that the protocols are insecure against the man-in-the middle attack, key compromise impersonation attack and several known-key attacks.

Our contributions are applying distinguishing attack on Linearly Filtered NLFSR as a primitive or associated with filter generators. We extend the attack on linear combinations of Linearly Filtered NLFSRs as well. Generally, these structures can be examined by the proposed techniques and the criteria will be achieved to design secure primitive. The attacks allow attacker to mount linear attack ...

An additive and multiplicative privacy homomorphism is an encryption function mapping addition and multiplication of cleartext data into two operations on encrypted data. One such privacy homomorphism is introduced which has the novel property of seeming secure against a known-cleartext attack. An application to multilevel statistical computation is presented, namely classiied retrieval of exac...