  This paper introduces a variant for the symmetric matrix-based key
distribution in sensor network introduced by Du et al. Our slight modification
shows that the usage of specific structures for the public matrix instead of
fully random matrix with elements in $\mathbb{Z}_q$ can reduce the computation
overhead for generating the public key information and the key itself. An
intensive analysis followed by modified scheme demonstrates the value of our
contribution in relation with the current work and show the equivalence of the
security
