﻿ GF(2<sup>m</sup>)上椭圆曲线标量乘快速算法研究

# GF(2m)上椭圆曲线标量乘快速算法研究Research on Fast Algorithms for Scalar Multiplication of Elliptic Curve over GF(2m)

Abstract:
Elliptic curve cryptography finds numerous applications because of its excellent and unique properties. This paper focused on the scalar multiplication of Elliptic curve. We proposed the recursion formula to compute over based on the idea of trading inversions for multiplications, which reduced the inversion to only once. At the same time, this paper also gave an ac- celerated algorithm for computing , which saved two inversions compared to computing it directly. The result suggests that the proposed algorithms are more efficient than the normal al- gorithms when the ratios are more than 7.4 and 5.9 respectively.

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