一种改进的椭圆曲线标量乘的快速算法

Fast Algorithm of Scalar Multiplication on Emptic Curve Cryptosystem

椭圆曲线密码体制(ElliPtic Curve Cryptosystem,简称ECC)是最有效的公钥密码体制之一,密钥更短、安全性更强。点乘和标量乘是椭圆曲线密码体制中的核心运算,是最耗时的运算。宽度w的非相邻型(w-NAF)算法通常被用来加速椭圆曲线上的标量乘,通过对这种算法的改进和优化,提高算法的效率,并结合分段并行理论提出了一种双标量乘法算法。对新算法进行了分析和测试,其效率在普通算法的基础上有明显提高,具有实用性。

Elliptic Curve Cryptosystem（ECC） is one of the most effective public-key cryptosystems, shorter key, higher security. Point multiplication and scalar multiplication of points are key operations in el- liptic curve cryptograph. They are the the costliest computations. Width- w non-adjacent-form（ ω- NAF） algorithm is usually used to speed up the operation of the point multiplication on elliptic curves cryptograph. Some improvements are done to make it more effective in this paper. Furthermore, a new algorithm of double scalar multiplication is put forward combined with the subsection and parallel method. This paper gives a detailed analysis and precise measure of the new algorithm. The improved algorithm is much more efficient than before, thus making it a functional algorithm of excellent value.