We present linear and nonlinear techniques for design exploration of an iterative algorithm. The nonlinear techniques allow control of processor workload and control of communication between processors. The algorithm considered is the Sunar-Koç optimal normal basis type II multiplication algorithm. Six systolic arrays are obtained. General formulas are provided for each design so that the operation of the system can be determined for a given GF(2^m). The proposed architectures have been implemented using 45-nm CMOS technology and compared with published architectures. The results show that the proposed designs have at least 44.4% lower total computation time compared with the designs of all bit serial multipliers, while having slightly larger area delay product (ADP), up to 19.1%, compared with some of the bit serial multipliers and having smaller ADP values compared with most of the digit serial ones. Moreover, they have at least 46% lower power delay product compared with all bit serial and digit serial multipliers.