Low-complexity systolic multipliers for GF(2 ^m ) are required in several high-performance cryptographic systems. In this paper, we propose a novel design strategy to derive efficient systolic multiplier for GF(2 ^m ) based on Toeplitz Matrix-Vector Product (TMVP) approach. The proposed work is carried out through two coherent interdependent stages. (i) A novel multiplication algorithm based on TMVP method to obtain subquadratic space complexity is proposed first. (ii) The proposed algorithm is then mapped unto to a novel and efficient architecture which is optimized further to derive a low-complexity systolic structure. The complexity analysis and comparison show that the proposed design outperforms the existing work. The proposed design can thus be used in many practical cryptosystems.