基于改进KOA方法的模2域多项式乘法器的实现

Implementation of an Ecc Polynomial-Basis Multiplier Based on the Improved KOA Method

有限域上的多项式乘法器是实现ECC底层运算的关键模块。本文基于Karatsuba-Offman提出的分治思想来简化两个多精度操作数的模乘。通过反复调用一个乘法器进行模乘并将结果逐次累加,减少了单精度操作数乘法的次数,从而降低了运算的复杂度。实验结果显示,这种方法在增加一定路径延时的代价下获得更小的芯片面积和功耗。设计原型改进后适用于无线局域网等要求低功耗、小面积的安全设备中。

The Polynomial-Basis Multiplier in the finite field is the key module to realizing ECC basic operations.The KOA method based on the recursive divide-and-conquer approach is presented in this paper.So multiplying two multi-precision operands becomes less complex by reducing the number of single-precision multiplications,which must be performed by replacing a multiplication with several additions.The experimental results show that the iterative application of Karatsuba＇s method for polynomial multiplications can reduce the chip area and energy needed to run elliptic curve cryptography.As a tradeoff,the execution time is a little more but can be accepted.The prototype suits portable applications such as mobile devices.