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Secure message transmission schemes in interconnection networks can be achieved by constructing multiple vertex-disjoint paths or independent spanning trees. The extended network of crossed cube (ECC for short) has the advantages such as easy to be deployed and low ratio between number of vertices and diameter. In this paper, we have studied a secure message transmission scheme in ECC by constructing n independent spanning trees in n S and proposed a constructive algorithm with the time complexity ) (N O , where N is the number of n S . Furthermore, the maximum length of the vertex-disjoint paths between any two vertices is shown to be n 2 +3. In addition, simulation of vertex-disjoint paths based on JUNG has also been discussed. Introduction Multiple vertex-disjoint paths between arbitrary two vertices in interconnection networks can be used to transmit different parts of a message. Every part of the message can use its own encryption methods in its corresponding path with safety. Such vertex-disjoint paths can be constructed based on the multiple independent spanning trees (ISTs) [1, 2]. Towards the conjecture that for any n -connected graph ) 1 (  n G , there are n ISTs rooted at an arbitrary vertex on G [1, 2], it was only solved for 4  n [1, 2, 3, 4], but remains open for 5  n . Thus, the results on special graphs are still the focus of researchers and many results have been obtained, such as hypercubes [5, 6], crossed cubes [7], even networks [8], odd networks [9], folded hyper-stars [10], multidimensional torus networks [11], recursive circulant graphs [12], Gaussian networks [13], 2-chordal rings [14], and so on. In comparison with the hypercube, the crossed cube has good properties such as lower vertex degree and diameter, higher connectivity, symmetry, and etc [15, 16]. But in the real world, it is difficult to build interconnection networks based on crossed cubes, because according to the structure of crossed cubes, a computer is needed to connect many neighbor computers. However, to install two Ethernet cards in a computer is feasible and as a consequence the extended crossed cube ECC is proposed [17], which is easy to be deployed and has low ratio between number of vertices and diameter. In this paper, we study a secure message transmission scheme in the ECC by 757 Advances in Computer Science Research (ACRS), volume 54 International Conference on Computer Networks and Communication Technology (CNCT2016)

A Secure Message Transmission Scheme in an Extended Network of Crossed Cubes