Abstract: The efficiency and the security of scalar multiplication are the bottleneck problems of elliptic curve cryptosystem.Aimed at the scalar multiplication implementation in ECC，this paper researches on a scalar multiplication algorithm against the SPA and the DPA attacks，and proposes a new improved algorithm.Random variable is first introduced，scalar is encoded.It adopts a bottom layer fast algorithm and the sliding window algorithm，which takes improvements in efficiency and security.When sliding window length is 4，scalar quantity binary long for 160，192 and 224 bits，the improved efficiency of the algorithm are 26.9%，21.5% and 27.2%.

Key words: Elliptic Curve Cryptosystem（ECC）, side channel attacks, simple power analysis, differential power analysis, scalar multiplication, sliding window algorithm

摘要： 标量乘法的效率和安全性是椭圆曲线密码体制的瓶颈问题，针对椭圆曲线上标量乘法的实现方法，对普通抗SPA和DPA攻击的标量乘算法进行了研究，并提出一种改进算法。改进算法引入随机变量，将标量进行编码，采用点的底层域快速算法和滑动窗口算法，达到兼顾效率和安全性的目标。当滑动窗口长度为4，标量的二进制位长分别为160、192和224 bit时，改进算法效率分别提高了26.9%，21.5%和27.2%。

关键词: 椭圆曲线密码系统, 侧信道攻击, 简单能量分析, 差分能量分析, 标量乘法, 滑动窗口算法