摘要： 圆锥曲线密码算法是一种新型的公钥密码算法，其参数选择会直接影响密码算法的安全性。该文分析了由于圆锥曲线的参数选择不当造成圆锥曲线密码算法安全性降低的原因，并给出了有限域Fp及环Zn上产生安全圆锥曲线的方法。扩展了张明志提出的圆锥曲线群的定义，从而构造了适用于特征为2的有限域上圆锥曲线的方程。

关键词: 圆锥曲线, 有限域, 环, 特征

Abstract: Conic curve cryptosystem is a new public-key cryptosystem, the parameters selection of conic curve could affect the security of conic curve cryptosystem. The reason that security deterioration in the case of unsuitable parameters are selected over conic curve is analyzed, and the algorithm of generating a secure conic curve equation based on finite field Fp or ring Zn is given. It expands the definition of conic curve group which is proposed by Zhang Mingzhi, and the new equation could be applied on the finite field whose characteristic is 2.

Key words: conic curve, finite field, ring, characteristic

中图分类号: 

• TP309.7