GF(2^m)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(2^m)

摘要: 椭圆曲线密码自提出以来便因其优良的性质而得到了广泛的应用。本文针对椭圆曲线上关键的标量乘运算，根据将耗时较多的求逆转换为乘法的思想，推导出了 上计算 的递推公式，将求逆次数减少到一次。同时提出了计算 的加速算法，比直接计算节省了2次求逆。分析表明，在逆乘率分别大于7.4和5.9时，改进算法的效率优于逐次计算。

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.