【摘要】 椭圆曲线密码体制是公钥密码体制研究的热点。计算椭圆曲线上点的数乘是椭圆曲线密码算法的基础。固定窗口算法利用大整数的2进制表示和适量的预计算,减少椭圆曲线上点的加法运算,从而加快椭圆曲线上点的数乘的运算速度。介绍了利用混合坐标思想,减少有限域上求逆运算的次数,对固定窗口算法进行局部优化的方法。最后给出了固定窗口算法的复杂性分析,并讨论了窗口宽度的最佳选取。更多还原

【Abstract】 Elliptic curve cryptosystem is a hot topic in public key cryptosystems. The scalar multiplication in elliptic curves is the basic to elliptic curve cryptosystem. A fixed window algorithm, which uses 2 representation for large integer and acceptable computations, can greatly reduce the number of points addition, so the efficiency of the scalar multiplication in elliptic curves can be improved . Using mixed coordinates method to decrease the number of inversion in finite fields, a partial optimization algorithm can be obtained. The complexity analysis of the fixed window algorithm and the optimal length of window are also discussed.更多还原