Subquadratic Space-Complexity Digit-Serial Multipliers Over $GF(2^{m})$ Using Generalized $(a,b)$ -Way Karatsuba Algorithm

摘要: Karatsuba algorithm (KA) is popularly used for high-precision multiplication by divide-and-conquer approach. Recently, subquadratic digit-serial multiplier based on $(a,2)$ -way KA decomposition proposed in [1]. In this paper, we extend a to derive generalized $(a,b)$ with $a\neq b$ . We have shown that and mult-way are special cases of the decomposition. Based decomposition, established two types multipliers, namely, KA-based recombined multiplier. From theoretical analysis, as well as, from synthesis results multipliers significantly less delay area-delay product (ADP) compared existing naive multipliers.