Efficient Subquadratic Space Complexity Binary Polynomial Multipliers Based on Block Recombination

Some applications like cryptography involve a large number of multiplications of binary polynomial. In this paper, we consider two-, three-, and four-way methods for parallel implementation of binary polynomial multiplication. We propose optimized three- and four-way split formulas which reduce the space and time complexity of the best known methods. Moreover, we present a block recombination method which provides some further reduction in the space complexity of the considered two-, three-, and four-way split multipliers.