中文摘要：

圆锥曲线密码体制是一种新型的公钥密码体制,得到了广泛关注,在已有研究成果中,圆锥曲线都是定义在大的素域GF（p）上、特征为2的有限域GF（2m）上、或剩余类环Z/nZ上,其中n=pq是两个奇素数的乘积.为实现更高效的圆锥曲线密码体制,本文讨论有限域GF（pm）上的圆锥曲线,并定义了其上的Frobenius映射,基于此设计了新的快速标量乘算法.理论分析和数值结果都表明,在使用同等的预存储空间的前提下,新算法的时间复杂度较传统算法有很大程度的降低.

英文摘要：

Until now, all the previous studies on conic curve cryptography have been based on the prime field GF （ p ）. The field with characteristic 2, and the ring Z/nZ, where n = pq is the product of two primes In this paper, conic curves defined over the extension field GF （pm） are discussed. The Frobenius map of the points on the conic curves over GF （ pm ） is defined. Based on this, a new method of computing scalar multiplication of conic curve over GF （pm） is presented. The theoretical analysis and numerical comparison about the new method and traditional methods are given. The results show that the new method is more efficient than the traditional ones on the same memory spaces for precomputed points.