Key pre-distribution in wireless sensor network is aimed at delivering keys to sensor networks at the low expense of computation, communication, and memory while providing a high degree of security expressed by network resiliency to node capture. In this paper, we introduce a computationally efficient construction for the symmetric matrix-based key distribution. Particularly, this work introduces an original modification over the well known DDHV scheme (by Du et al.). Our modification shows that using a specific structures for the public matrix instead of fully random matrix with elements in Zq can reduce the computation overhead for generating the key information and the key itself at the expense of small memory overhead. Our modification guarantees the same level of security for restricted network size. We show an extensive security analysis of the provided scheme in different settings and compare to the relevant works in the literature to demonstrate its merit.