SEA算法及安全椭圆曲线的有效选取

SEA Algorithm and Efficient Selection of Secure Elliptic Curve

在椭圆曲线密码体制的实现中 ,首先要选取安全的椭圆曲线 ,选取安全椭圆曲线阶的核心步骤是对椭圆曲线阶的计算 ,SEA算法是计算椭圆曲线的有效算法。本文在实现Fp 上SEA算法的前提下 ,就SEA算法中各方法的综合运用提出了一种方案 ,并且对用SEA算法选取安全椭圆曲线速度上的优化作了一些讨论 ,所获得的一些速度指标和国际公开资料上的指标有可比性。

In the implementation of the Elliptic Curve Cryptosystem, we first have to select a secure elliptic curve. The main step of choosing a secure elliptic curve is the computation of the order of a randomly selected elliptic curve. The SEA algorithm is known as an efficient method to count the orders of elliptic curves. During the implementation of SEA algorithm over GF(p),we provide an efficient scheme of the combination of the methods in the SEA algorithm and discuss how to speed up the selection of a secure elliptic curve. Our implementation of the SEA algorithm and selection of the secure elliptic curve over GF(p) are efficient.