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On the isomorphism classes of Legendre elliptic curves over finite fields 被引量：1

On the isomorphism classes of Legendre elliptic curves over finite fields
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摘要 In this paper,the number of isomorphism classes of Legendre elliptic curves over finite field is enumerated. In this paper, the number of isomorphism classes of Legendre elliptic curves over finite field is enumerated.
作者 WU HongFeng FENG RongQuan
机构地区 College of Science LMAM
出处 《Science China Mathematics》 SCIE 2011年第9期1885-1890,共6页 中国科学：数学（英文版）
基金 supported by National Natural Science Foundation of China (Grant No.10990011) the Science Research Startup Foundation of North China University of Technology
关键词 elliptic curve Legendre curve isomorphism classes CRYPTOGRAPHY Legendre 椭圆曲线 同构类数 有限域
分类号 O174 [理学—基础数学] TN918.1 [电子电信—通信与信息系统]
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参考文献10

  • 1Reza Rezaeian Farashahi,Igor E. Shparlinski.On the number of distinct elliptic curves in some families[J] ,2010
  • 2Husemller D.Elliptic Curves. Graduate Texts in Mathematics . 2004
  • 3Silverman JH.The Arithmetic of Elliptic Curves. . 1986
  • 4D.J.Bernstein,P.Birkner,M.Joye,T.Lange,C.Peters."Twisted Edwards curves". AFRICACRYPT2008 . 2008
  • 5D.V. Chudnovsky,G.V. Chudnovsky."Sequences of numbers gen- erated by addition in formal groups and new primality and factorization tests,". Advances in Applied Mechanics . 1986
  • 6Feng Rongquan,Wu Hongfeng.Number of general Jacobi quartic curves over finite fields. http://eprint.iacr.org/2010/020 . 2010
  • 7Schoof R.Nonsigular plane cubic curves over finite fields. Journal of Combinatorial Theory Series A . 1987
  • 8Koblitz N.Elliptic curve cryptosystems. Mathematics of Computation . 1987
  • 9Menezes A.Elliptic curve public key cryptosystems. . 1993
  • 10Auer R,,Top J.Legendre Elliptic Curves over Finite Fields. Journal of Number Theory . 2002

同被引文献14

  • 1Koblitz N. Elliptic curve cryptosystems [J]. Math Comp, 1987, 48(177): 203-209.
  • 2Miller V S. Use of elliptic curves in cryptography [C] //Proceedings of Advances in Cryptology-Crypto 1985 (LNCS 218). Berlin: Springer-Verlag, 1986: 417-426.
  • 3Joye M, Tibouchi M, Vergnaud D. Huff's model for elliptic curves [C]//Algorithmic Number Theory (ANTS-IX) (LNCS 6197). Berlin: Springer-Verlag, 2010: 234-250.
  • 4Huff G B. Diophantine problems in geometry and elliptic temary forms [J]. Duke Math J, 1948, 15: 443-453.
  • 5Menezes A J. Elliptic Curve Public Key Cryptosystems [M]. Dordrecht: Kluwer Academic Publishers, 1993.
  • 6Farashahi R R, Shparlinski I E. On the number of distinct elliptic curves in some families [J]. Designs Codes and Cryptography, 2010, 54(1): 83-99.
  • 7SchoofR. Nonsigular plane cubic curves over finite field [J]. J Combine, Theory Ser A, 1987, 46: 183-211.
  • 8Fung G, Stroher H, Williams H, et al. Torsion groups of elliptic curves with integralj-invariant over pure cubic fields [J]. Journal of Number Theory, 1990, 36(1): 12-45.
  • 9Feng Rongquan, Nie Menglong, Wu Hongfeng. Twisted Jacobi intersection curve [C]// Proceedings of Theory and Applications of Model of Computation-TAMC 2010 (LNCS 6108). Berlin: Springer-Verlag, 2010: 199-210.
  • 10Bemstein D J, Birkner P, Joye M, et al. Twisted Edwards curves [C]//Serge Vaudenay editor, Progress in Cryptology-AFRICACRYPT 2008 (LNCS 5023). Berlin: Springer- Verlag, 2008: 389-405.

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Science China Mathematics
2011年 第9期

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