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计算机工程 ›› 2009, Vol. 35 ›› Issue (23): 138-140. doi: 10.3969/j.issn.1000-3428.2009.23.048

• 安全技术 • 上一篇    下一篇

GF(p)上安全椭圆曲线产生算法

侯爱琴1,辛小龙2,杨世勇3   

  1. (1. 西北大学信息科学与技术学院,西安 710069;2. 西北大学数学系,西安 710069; 3. 西安电子科技大学ISN国家重点实验室,西安 710071)
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2009-12-05 发布日期:2009-12-05

Secure Elliptic Curve Generating Algorithm over GF(p)

HOU Ai-qin1, XIN Xiao-long2, YANG Shi-yong3   

  1. (1. School of Information Science & Technology, Xi’an 710069; 2. Department of Mathematics, Northwest University, Xi’an 710069; 3. ISN National Key Lab, Xidian University, Xi’an 710071)
  • Received:1900-01-01 Revised:1900-01-01 Online:2009-12-05 Published:2009-12-05

摘要: 研究素数域GF(p)(p>3)上的椭圆曲线,讨论阶为素数的椭圆曲线的产生算法,在此基础上,分析阶为2个素数之积的椭圆曲线产生问题,并提出一种GF(p)上安全椭圆曲线的产生算法,给出椭圆曲线及其全体有理点的随机产生实例。仿真实验结果表明,该算法是有效可行的。

关键词: 椭圆曲线群, 阶, 基点

Abstract: This paper analyzes the elliptic curves over prime field GF(p), while p is greater than 3. It discusses an algorithm to generate an elliptic curve with a prime order. On basis of this, the problems for generating an elliptic curve with an order which equals to the product of two prime numbers are studied. A secure elliptic curve generating algorithm over GF(p) is proposed. It gives some examples for producing an elliptic curve and all the points on this elliptic curve under these two circumstances. Simulation experimental results show this algorithm is effective and feasible.

Key words: elliptic curve group, order, base point

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