Efficient Three-Way Split Formulas for Binary Polynomial Multiplication and Toeplitz Matrix Vector Product

Abstract

In this paper, we present a new three-way split formula for binary polynomial multiplication (PM) with five recursive multiplications. The scheme is based on a recently proposed multievaluation and interpolation approach using field extension. The proposed PM formula achieves the smallest space complexity. Moreover, it has about 40% reduced time complexity compared to best known results. In addition, using developed techniques for PM formulas, we propose a three-way split formula for Toeplitz matrix vector product with five recursive products which has a considerably improved complexity compared to previous known one.