F（2v＋ 1） q Based on the pseudo-symplectic space over q of characteristics 2, combining the definition of low density parity check （LDPC） codes with the knowledge of graph theory, two kinds of LDPC codes with larger girth are constructed. By the knowledge of bipartite graph and the girth properties of LDPC codes, both the girth of the code C（m1 ,2v ＋ 1 ,q） and the code C（m2 ,2v ＋ 1 ,q） are computed are 8. The girth is larger, the performance of LDPC codes is better. Finally, according to the properties of the check matrix and the linear relation between the column vectors of the check matrix, both the minimum distances of the two codes are obtained are 2q ＋ 2.
In a common authentication code with arbitration, the dishonest arbiter may make a threat to the security of authentication system. In this paper, an authentication code with double arbiters over symplectic geometry is constructed, and the relevant parameters and the probabilities of successful attacks are calculated. The model not only prevents deception from the opponent and members of the system, but also effectively limits the attacks of single arbiter. Moreover, the collusion attacks from arbiters and participators are difficult to succeed.
To achieve secure communication in wireless sensor networks （WSNs）, where sensor nodes with limited computation capability are randomly scattered over a hostile territory, various key pre-distribution schemes （KPSs） have been proposed. In this paper, a new KPS is proposed based on symplectic geometry over finite fields. A fixed dimensional subspace in a symplectic space represents a node, all 1-dimensional subspaces represent keys and every pair of nodes has shared keys. But this naive mapping does not guarantee a good network resiliency. Therefore, it is proposed an enhanced KPS where two nodes have to compute a pairwise key, only if they share at least q common keys. This approach enhances the resilience against nodes capture attacks. Compared with the existence of solution, the results show that new approach enhances the network scalability considerably, and achieves good connectivity and good overall performance.
