摘要： 提高椭圆曲线上点加运算的速度在整个基于FPGA 设计的椭圆曲线密码应用系统实现中极为关键。在对已有的几种投影坐标系下的点加运算进行分析比较的基础上，提出了一种适合于FPGA 设计实现的椭圆曲线上的点加运算方案。同时结合椭圆曲线密码系统具体约束给出了整数线性规划算法，并将该算法应用于曲线点加算法的并行优化处理。试验结果表明，优化后的投影坐标下的点加运算较原来的算法在速度上提高了22%。

关键词: 椭圆曲线；点加；密码系统；FPGA 设计

Abstract: The speed of point addition on elliptic curve is critical in elliptic curve application cryptosystem design based on FPGA device. A point addition algorithm suitable for FPGA realization is proposed with comparison and analysis on several different point addition algorithms in different projective coordinates. Integer linear programming algorithm is provided in terms of application restriction of elliptic curve cryptosystem. The is applied to the elliptic curve point addition and parallel-optimization is carried out at the same time. Experiment results show that the parallel-optimized elliptic curve point addition is 22 percent faster than the original algorithm

Key words: Elliptic curve; Point addition; Cryptosystem; FPGA design