We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes which take advantage of the user's ability to precompute. We also provide bounds for our techniques. We show that precomputation allows for a reduction in the order of the time complexity for the cases where the number of colluding servers is a fixed percentage of the number of servers. Moreover, with precomputation, any percentage (less than 100%) of collusions can be tolerated, compared to the previous upper bound of 50% when no precomputation is used.