New Block Recombination for Subquadratic Space Complexity Polynomial Multiplication Based on Overlap-Free Approach

In this paper, we present new parallel polynomial multiplication formulas which result in subquadratic space complexity. The schemes are based on a recently proposed block recombination of polynomial multiplication formula. The proposed two-way, three-way, and four-way split polynomial multiplication formulas achieve the smallest space complexities. Moreover, by providing area-time tradeoff method, the proposed formulas enable one to choose a parallel formula for polynomial multiplication which is suited for a design environment.