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关于环Z_n上的椭圆曲线 被引量：1

On elliptic curves over Z_n
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摘要 基于环Zn上椭圆曲线的射影化定义,深入研究了Zn上椭圆曲线点群中点的结构形式,讨论了点的加法的射影化定义和仿射化定义,指出在仿射化定义条件下文献[1]和[3]在定义点的加法时存在的一个认识上的错误,给出了仿射化定义条件下两种定义方法之间的区别与联系,最后针对仿射化定义条件下某些点的加法无意义的情形进行了讨论,并分析了导致这种情形的根本原因。 Based on the projective definition of elliptic curves,the structure of points on the curve is researched deeply in this paper.Projective and affine definitions of the addition operation are discussed and an error in [1] and [3] is pointed out.Furthermore, the relation between two affine definitions of the addition operation is given.In conclusion,the essential reason is analyzed when the addition operation is not defined by discussing these cases.
作者 王念平 金晨辉
机构地区 解放军信息工程大学电子技术学院
出处 《计算机工程与应用》 CSCD 北大核心 2007年第11期78-80,共3页 Computer Engineering and Applications
关键词 Zn上的椭圆曲线 点的加法 仿射 elliptic curves over Zn addition operation affine
分类号 TN918.1 [电子电信—通信与信息系统]
  • 相关文献

参考文献4

  • 1Koyama K,Maurer U,Okamoto T,et al.New public-key scheme based on elliptic curve over the ring Zn[C]//LNCS 576:Advances in Cryptology,Proceedings of Crypto'91.[S.l.]:Springer -Verlag,1991:252-266.
  • 2Meyer B,Müller V.A public key cryptosystem based on elliptic curves over Z/nZ equivalent to factoring[C]//LNCS 1070:Advances in Cryptology,Proceedings of Eurocrypt'96.[S.l.]:Springer-Verlag,1996:49-59.
  • 3朱文余,孙琦.环Z_n上椭圆曲线的密钥交换协议[J].电子学报,2005,33(1):83-87. 被引量：14
  • 4Koblitz N,A course in number theory and cryptography[M].Berlin:Springer-Verlag,1987.

二级参考文献10

  • 1MingHuaQu ScottVanstone.OnID-BasedCryptosystemsoverZn[R]..成都:庆贺柯召院士九十寿辰暨国际数论学术研讨会上的报告[C].,2000.13-26.
  • 2朱文余 孙琦.环Zn上椭圆曲线及数字签名方案.电子与信息学报(原电子科学学刊),2003,25(1):40-40.
  • 3孙琦 张起帆 彭国华.计算群元的整数倍的一种算法及其在公钥密码体制中的应用[A]..密码学进展-ChinaCrypt2002．第七届中国密码学学术会议论文集[C].北京:电子工业出版社,.117-124.
  • 4W Diffie, M E Hellman. New directions in cryptography [J]. IEEE.Transactions on Information Theory, 1976,22(6) :644 - 654.
  • 5E Okamoto. Key Distribution Systems Based on Idenfication Infonmtion[A]. Advances in Cryptology: Proceedings of Crypto'87[C]. C Pomerance, ed., lecture Notes in Computer Science 293,Springer-Verlag, NY. 1988.194- 202.
  • 6H Sakazaki,E Okamoto,M Mambo. ID-Based Key Distribution System over an Elliptic Curve [A]. American Mathematical Society,Contemporary Mathematics 1999 (225) [C]. 1999. 215 - 224 (Fourth International Conference on Finite Fields).
  • 7Ning Hua Qu, Doug Stinson, Scott Vanstone. Cryptanalysis of the Sakazaki-Okamoto Mambo ID-based Key Distribution System over Elliptic Curves (Extended abstract) [R]. www. cacr. math. uwaterloo.ca/techreports/2001/corr 2001-14. ps.
  • 8Alfred J Menezes, lan F Blake, Xu Hong Gao, Ronald C Mullin, Scott A Vanstone, Tomik Yaghoobian. Apphcations of Finite Fields [M].Massachusetts: Kluwer Academic Publishers, 1993.147.
  • 9R schoof. Elliptic curves over finite fields and the computation of square roots mod p[J]. Mathematics of Computation, 1985,44(170):483 -494.
  • 10T Satoh. The canonical lift of an ordinary elliptic curve over a finite field and its point counting[J] .J Ramanujan Math Soc.2000(15) :281-318.

共引文献13

同被引文献11

  • 1朱文余,孙琦.环Z_n上椭圆曲线的密钥交换协议[J].电子学报,2005,33(1):83-87. 被引量：14
  • 2张宁,辛向军,肖国镇.利用环上的椭圆曲线实现基于身份的加密体制[J].西安电子科技大学学报,2007,34(2):290-293. 被引量：2
  • 3Demytko N. A new elliptic curve based on analogue of RSA [A]. Advances in Cryptology-EUROCRYPT' 93, Lecture Notes in Computer Science 765 [C ]. Berlin: Springer, 1994.40 - 49.
  • 4Meyer B, Mller V. A public key cryptosystem based on elliptic curves over equivalent to factoring[ A]. Advances in Cryptolo- gy-EUROCRYPT' 96,Lecture Notes in Computer Science 1070 [ C]. Berlin: S0rinzer, 1996.49 - 59.
  • 5张亚娟,祝跃飞,黄秋生.环上的椭圆曲线签名体制[A].第九届全国青年通信学术会议论文集[c].北京:电子工业出版社,2004.1.989-994.
  • 6Washington L C. EUiptic Curves:Number Theory and Cryptography[ M]. Washington DC, USA: CRC Press,2003.
  • 7Paillier P. Trapdooring discrete logarithms on elliptic curves over tings[A]. Advances in Cryptology-Asiacrypt' 2000, Lec- ture Notes in Computer Science 1976 [C]. Berlin: Springer, 2000. 573 - 584.
  • 8Galbraith Steven D. Elliptic curve paitlier schemes[ J]. Journal of Cryptology, 2002,15 : 129 - 138.
  • 9Menezes A J, Okamoto T, Vanstone S A. Reducing elliptic curve logarithms to logarithms in a finite field[J].IEEF. Transaction on Information Theory, 1993, 39 ( 5 ) : 1639 - 1646.
  • 10Frey G, Rck H G. A remark concerning m-divisibility and the discrete logrithm in the divisor class group of curves [ J ]. Mathematics of Computation, 1994,62(206) :865 - 874.

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计算机工程与应用
2007年 第11期

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