This paper introduces the new trends of algorithms in computing the order aboard at present. And based on the two kinds of algorithms, the paper expatiates their improvement and optimization.

• 介绍了目前国内外对求椭圆曲线阶的计算算法研究的新动态,并在两大类求阶算法的基础上,对它们的改进和优化做了阐述。