Constructions Of The Key Pre-distribution Schemes Based On Geometric Spaces Of Classical Groups

The problem of key pre-distribution is one of the most challenging security problems in wireless sensor networks.Many key pre-distribution schemes based on combinatorial designs have been proposed by scholars in recent years,but few of them are constructed based on symplectic spaces and unitary spaces over finite fields.We construct a partially balanced t-block design from symplectic spaces over finite fields,a w-balanced incomplete block design from the unitary spaces over finite fields and a transversal design from the m dimensional row vector spaces and the finite fields withq~m elements,then three key pre-distribution schemes are presented based on the three combinatorial designs.The deployment area is divided into several cells of the same size,there are two types of sensor nodes in each cell,which are normal nodes and cluster heads.The normal nodes in different cells cannot communicate directly due to different key pools used by them,so cluster heads are needed as intermediate nodes to establish indirect communication.The cluster heads are divided into three types according to different key pools used by them,the same type cluster heads can communicate with each other,but different types cannot.In the first scheme of the thesis,normal nodes adopt the key pre-distribution scheme based on the partially balanced t-block design,cluster heads adopt the complete key sharing mode to assign keys.Compared with some other schemes,when compromise the same number of nodes the resiliency of our scheme is very small,and with the expanding of network size,the connectivity of the nodes in the cell gradually approaches 1.In the second scheme,normal nodes adopt the key pre-distribution scheme based on the transversal design,cluster heads adopt the key pre-distribution scheme based on the transversal design and the w-balanced incomplete block design.Compared with some other schemes,the scheme has better connectivity and resiliency,when the number of compromised cluster heads is within a certain range,the resiliency of cluster heads is almost 0.