The resistance distance r i j between two vertices v i and v j of a (connected, molecular) graph G is equal to the effective resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any edge is unity. We show how r i j can be computed from the Laplacian matrix L of the graph G: Let L(i) and L(i, j) be obtained from L by deleting its i-th row and column, and by deleting its i-th and j-th rows and columns, respectively. Then r i j = det L(i, j)/ det L(i).
Block cipher is used widely, as byte-orientation differential, cryptanalysis and linear cryptanalysis of block cipher, which is the security fatal blow. The KEELOQ algorithm is a block cipher algorithm designed by South Africa Willem Smit in the 1980s,in this thesis, based on the summary of the previous attack researches and the detailed rationale of KEELOQ algorithm, taking example by 3DES algorithm, the triple KEELOQ algorithm was proposed, and did the improvement on the key management, this further increased the capture and the difficulty of the crack, improved the safety performance, finally, made an experiments on the paper decode to keeloq, the experimental results show that the algorithm is more safe and more reliable.
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