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Experimental Mathematics Volume 21, 2012 - Issue 1
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Original Articles

On Group Structures Realized by Elliptic Curves over a Fixed Finite Field

Reza Rezaeian Farashahi Department of Computing, Macquarie University, Sydney, NSW, 2109, Australia; Isfahan University of Technology, Department of Mathematical Sciences, P.O. Box 85145, Isfahan, Iran
&
Igor E. Shparlinski Department of Computing, Macquarie University, Sydney, NSW, 2109, Australia
Pages 1-10 | Received 14 Mar 2010, Accepted 19 Oct 2010, Published online: 13 Mar 2012

REFERENCES

  • Avanzi , [Avanzi et al. 05] R. , Cohen , H. , Doche , C. , Frey , G. , Lange , T. , Nguyen , K. and Vercauteren , F. 2005 . Handbook of Elliptic and Hyperelliptic Curve Cryptography , CRC Press .
  • Banks , [Banks et al. 12] W. D. , Pappalardi , F. and Shparlinski , I. E. 2012 . “On Group Structures Realized by Elliptic Curves over Arbitrary Finite Fields” . Exp. Math. , 21 : 11 – 25 .
  • Crandall , [Crandall and Pomerance 05] R. and Pomerance , C. 2005 . Prime Numbers: A Computational Perspective , 2nd edition , Springer .
  • Hardy , [Hardy and Wright 79] G. H. and Wright , E. M. 1979 . An Introduction to the Theory of Numbers , Oxford Univ. Press .
  • Heath-Brown , [Heath-Brown 86] D. R. 1986 . “Artin's Conjecture for Primitive Roots” . Quart. J. Math. , 37 : 27 – 38 .
  • Lenstra , [Lenstra 87] H. W. 1987 . “Factoring Integers with Elliptic Curves” . Ann. of Math. , 126 : 649 – 673 .
  • Rück , [Rück 87] H.-G. 1987 . “A Note on Elliptic Curves over Finite Fields” . Math. Comp. , 49 : 301 – 304 .
  • Schoof , [Schoof 87] R. 1987 . “Nonsingular Plane Cubic Curves over Finite Fields” . J. of Combin. Theory , 46 : 183 – 211 .
  • Silverman , [Silverman 95] J. H. 1995 . The Arithmetic of Elliptic Curves , Springer .
  • Tsfasman , [Tsfasman and Vlăduţ 91] M. and Vlăduţ , S. G. 1991 . Algebraic Geometric Codes , Kluwer .
  • Voloch , [Voloch 88] J. F. 1988 . “A Note on Elliptic Curves over Finite Fields” . Bull. Soc. Math. Franc. , 116 : 455 – 458 .
  • Washington , [Washington 08] L. C. 2008 . Elliptic Curves: Number Theory and Cryptography , CRC Press .
  • Waterhouse , [Waterhouse 69] W. C. 1969 . “Abelian Varieties over Finite Fields” . Ann. Sc. Ec. Norm. Sup. (4) , 2 : 521 – 560 .

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