Montgomery形式椭圆曲线的生成研究

Researches on generation of Montgomery form elliptic curve

文章详细分析了O-K-S算法[1],并给出改进算法。改进的算法有效地生成了广义Mersenne素数域上可抵抗时间分析攻击且阶恰好只能被4整除的Montgomery形式椭圆曲线,并且运用了早期终止策略和伪随机选取方法,在一定程度上提高了此类曲线的生成效率。

This paper analyzes the O-K-S algorithm in detail and gives an improved algorithm. The improved algorithm generate a Montgomery-form elliptic curve, whose cofactor is exactly 4 and which can prevent the timing-attack over a Mersenne prime finite field. Furthermore, the early-abort strategy and pseudo-random method are used to effectively improve the generation speed of these elliptic curves.