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Counting points for genus 2 hyperelliptic curves of two special types over finite fields

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Counting points for genus 2 hyperelliptic curves of two special types over finite fields

Abstract

Counting points for genus 2 hyperelliptic curves of two special types over finite fields

참고문헌 (15)

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  2. I. Blake, "Elliptic curves in cryptography, London Math. Soc. Lecture Note Series", pp.265~ (1999)
  3. N. Elkies, "Elliptic and modular curves over finite fields and related computational is-sues", Computational perspectives on number theory, AMS, 1998, pp.7, 21~76
  4. P. Gaudry, "Counting points on hyperelliptic curves over finite fields, ANTS-IV", LNCS, 1838, pp.297~312 (2000), Springer-Verlag
  5. P. Gaudry, "A low-memory parallel version of Matsuo, Chao and Tsujii's algorithm", Proceedings of Algorithm Number Theory Sympositum-ANTS VI, 3076, pp.208~222 (2004), Springer-Verlag
  6. M. D. Huang, "Counting points on curves over finite fields", J. Symb. Comp, 25(1), pp.1~21 (1998)
  7. K. S. Kedlaya, "Counting points on hyperelliptic curves using Monsky-Washnitzer co-homology", J. Ramanujan Math. Soc, 16, pp.323~338 (2001)
  8. R. Lercier, "Algorithmique des courbes elliptiques dans les corps finis", Thse, Ecole polytechnique, ~ (1997)
  9. Yu. I. Manin, "The Hasse-Witt matrix of an algebraic curve", AMS Trans. Ser, 2(45), pp.245~264 (1965)
  10. R. H. Hudson, "Binomial Coecients and Jacobi Sums", Trans. Amer. Math. Soc., 281, pp.431~505 (1984)
  11. D. Mumford, "Tata Lectures on Theta II", Progress in Mathematics, 43 (1984)
  12. J. Pila, "Frobenius maps of abelian varieties and finding roots of unity in finite fields", Math. Comp, 55(192), pp.745~763 (1990)
  13. T. Satoh, "The canonical lift of an ordinary elliptic curve over a finite field and its point counting", J. Ramanujan Math. Soc, 15, pp.247~270 (2000)
  14. R. Schoof, "Elliptic curves over finite fields and the computation of square roots mod p", Math. Comp, 44, pp.483~494 (1985)
  15. H. Yui., "On the jacobian varieties of hyperelliptic curves over fields of characteristic p≥ 2", J. Algebra, 52, pp.378~410 (1987)

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