有限域GF（2m）上基于基转换的正规基快速求逆方案

An Effective Inversion Method for Normal Basis in GF（2m） Using Basis Conversion

有限域GF(2m)在椭圆曲线密码体制中有着非常重要的应用,密码体制的整体效率大部分取决于GF(2m)上的运算效率。该文给出了有限域GF(2m)上使用正规基表示时的一种快速求逆方案,该方案基于基转换技术,更改运算元素的表示基,采用多项式基的AI求逆算法进行运算。实验表明,此方案比普通的正规基求逆算法更加快速。

GF（2m） plays an important role in elliptic curve cryptosystems.The efficiency of the cryptosystems mostly depends on the operation speed in GF（2m）.This paper presents an efficient inversion technique in normal basis.This technique uses basis conversion to change the representation basis of the elements,and than uses the AI algorithm in polynomial basis to calculate the inversion.The test shows that the technique is faster than ordinary inversion approach in normal basis.