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...

Optimistic fair exchange (OFE) is a protocol for solving the problem of exchanging items or services in a fair manner between two parties, a signer and a verifier, with the help of an arbitrator which is called in only when a dispute happens between the two parties. In almost all the previous work on OFE, after obtaining a partial signature from the signer, the verifier can present it to others...

A distinguishing partition for an action of a group Γ on a set X is a partition of X that is preserved by no nontrivial element of Γ. As a special case, a distinguishing partition of a graph is a partition of the vertex set that is preserved by no nontrivial automorphism. Not all graphs admit a distinguishing partition – for example, the complete graph Kn for n ≥ 2 does not admit a distinguishi...

A group of permutations G of a set V is k-distinguishable if there exists a partition of V into k cells such that only the identity permutation in G fixes setwise all of the cells of the partition. The least cardinal number k such that (G,V ) is k-distinguishable is its distinguishing number, D(G,V ). In particular, a graph Γ is k-distinguishable if its automorphism group Aut(Γ) satisfies D(Aut...