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To achieve secure communication between sensor nodes in wireless sensor networks (WSNs), it is important to be able to establish efficient key predistribution mechanisms. Here, a matrix-based key predistribution scheme for WSN is presented, as shown in the following process. First, LU matrix-based method is employed to decompose the polynomial pool, which substitutes for the key pool to establish the shared keys. Second, the shared key is computed by the shared polynomial. Third, we can always compute the common polynomial with mutual authentication. The analysis indicates that the proposed scheme allows 100% connectivity regardless of the number of keys. To evaluate the efficiency of the network-wide memory overhead, each row or column of L and U matrices is divided into two parts: nonzero-element part and zero-element part. The results demonstrate that this method provides references for increasing the efficiency of LU matrix-based algorithms. By introducing polynomial-based key predistribtion, the resilience against node capture has been greatly enhanced as well.