Secure pairwise communications for a group of N nodes can require a large number of keys, O(N^{2}) in the worst case. This work proposes a two-part algorithm for large-scale symmetric key pre-distribution: a key assignment algorithm deterministically assigning O(\log_{2}N) keys to each node, and a key discovery algorithm requiring O(\log_{q}N) computations and inter-node messages to find the appropriate secure keys for a pair-wise communication. The lower bound of O(\log N) complexity is achieved by novel applications of the Maximum-Distance Separable (MDS) codes. Compare to previous works, our scheme is deterministic, efficient, and has good security properties against collusion. Using \left(n,k\right)_{q} Reed-Solomon codes as the MDS codes, we show by analysis that (1) in all practical cases, the lower bound of c\log_{2}N keys per node can be reached within 2 levels of recursions with a multiplicative constant c less than 8; (2) channel resilience against r-collusion is roughly 1-R^{d_{\min}}, with R=1-\left(1-1/q\right)^{2r} and d_{\min}=n-k+1.