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分析了素数域GF(Fp)(p>3)上形如y2=x3+ax+b安全椭圆曲线的构造方法.依据椭圆曲线阶与迹的关系,提出一种快速构造安全椭圆曲线的新方法.首先选择判别式Δ≠0的椭圆曲线和具有大素因子的阶,然后由素数p与迹的关系找出基点,最后由基点计算出点群.方法类似于复乘(CM)方法,但又不计算类不变量,而是通过查表的方式直接找出基点.数字例子验证了方法的正确性和有效性.与已有研究结果相比,方法具有明显的优势.
The construction method of a secure elliptic curve such as y2 = x3 + ax + b on the GF (Fp) (p> 3) prime prime field is analyzed.A new method to construct a safe elliptic curve is proposed based on the relationship between the elliptic curve and the trace First select the elliptic curve with discriminant Δ ≠ 0 and the order with large prime factor, and then find the base point by the relationship between prime number p and track, and finally calculate the point group from the base point. The method is similar to the complex multiplication (CM) method, but But does not calculate the class invariants, but directly find out the base point through the way of look-up table.The numerical example verifies the correctness and validity of the method.Compared with the existing research results, the method has obvious advantages.