ISOMORPHISM CLASSES OF ELLIPTIC CURVES OVER FINITE FIELDS WITH CHARACTERISTIC 3

  • Received : 2009.04.14
  • Accepted : 2009.08.14
  • Published : 2009.09.30

Abstract

We count the isomorphism classes of elliptic curves over finite fields $\mathbb{F}_{3^{n}}$ and list a representative of each isomorphism class. Also we give the number of rational points for each supersingular elliptic curve over $\mathbb{F}_{3^{n}}$.

Keywords

Acknowledgement

Supported by : Korea Research Foundation

References

  1. S. L. M. Barreto, H. Y. Kim, B. Lynn and M. Scott, Efficient Algorithms for Pairing-Based Cryptosystems, eprint 2002/008.
  2. D. Boneh, B. Lynn and H. Scham, Short signatures from the Weil pairing, Proc. of Asiacrypt'01, 514-532, 2001.
  3. R. Lidi and H. Niederreiter, Finite fields, Encyclopedia of Math and its application, 20, Addison-Wesley, 1983.
  4. A. Menezes and N. Koblitz, Elliptic curve public key cryptosystems, Kluwer Academic Publishers, 1993.
  5. R. Schoof, Nonsingular plane cubic curves over finite fields, Journal of Combinatorial Theory A, 46 (1987), 183-211. https://doi.org/10.1016/0097-3165(87)90003-3
  6. J. Silverman, The Arithmetic of elliptic curves, Springer-Verlag, New York, 1986.
  7. E. Waterhouse, Abelian varieties over finite fields, Ann. Sci. Ecole Norm. Sup. 2 (1969), 521-560. https://doi.org/10.24033/asens.1183