A survey of some recent bit-parallel GF(2n) multipliers
A survey of some recent bit-parallel GF(2n) multipliers
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DOI：
10.1016/j.ffa.2014.10.008
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
H. Fan;M. A. Hasan
中科院分区：
文献类型：
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作者：
H. Fan;M. A. Hasan
本文根据 i) 底层算法的二次和次二次算术复杂性，ii) 用于表示域元素的各种基础，以及 iii) 依赖于多项式和矩阵运算的设计方法，调查了有限域 GF (2 n) 的位并行乘法器。回顾了构建空间和时间高效乘法器的技术，并总结了最新二次和次二次乘法器的复杂性。对于二次乘法器，重点放在多项式基及其泛化上。低次 Karatsuba-Toom 公式及其乘法复杂度主要针对次二次乘法器进行考虑。
This paper surveys bit-parallel multipliers for finite field GF (2 n) according to i) quadratic and subquadratic arithmetic complexities of the underlying algorithms, ii) various bases used for representing the field elements, and iii) design approaches that rely on polynomial and matrix operations. Techniques for constructing space-and time-efficient multipliers are reviewed, and complexities of recent quadratic and subquadratic multipliers are summarized. For quadratic multipliers, the emphasis is placed on polynomial bases and their generalization. Low-degree Karatsuba–Toom formulae and their multiplication complexities are considered primarily for the subquadratic multipliers.