Art

J-GLOBAL ID：202002254700354523   Reference number：20A0553723

Counting points on hyperelliptic curves of genus 2 with real models

実モデルを用いた種数2の超楕円曲線上の点の計数

Author (1)： Uchida Yukihiro (Department of Mathematical Sciences, Graduate School of Science, Tokyo Metropolitan University)
Material： JSIAM Letters (Web)  (JSIAM Lett (Web))
Volume： 11  Page： 1-4(J-STAGE)  Publication year： 2019 
JST Material Number： U0115A  ISSN： 1883-0617  Document type： Article
Article type： 短報  Country of issue： Japan (JPN)  Language： ENGLISH (EN)

Thesaurus term： *curve ,  computational geometry ,  mathematical model ,  dimensionless number ,  index number ,  *computational complexity ,  computer algorithm ,  *approximation method ,  exponential function ,  function approximation ,  basis function ,  limit
Semi thesaurus term： error bound ,  degree ,  genera ,  elliptic curve ,  *hyperelliptic curve ,  characteristic

Author keywords (3)： point counting ,  hyperelliptic curves ,  real models

JST classification (3)： System and control theory in general  (IA02010H) ,  Graphic and image processing in general  (JE04010I) ,  Theory of computation  (JB02000A)

Reference (17)：

• 1) T. Satoh, The canonical lift of an ordinary elliptic curve over a finite field and its point counting, J. Ramanujan Math. Soc., 15 (2000), 247-270.
• 2) K. S. Kedlaya, Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology, J. Ramanujan Math. Soc., 16 (2001), 323-338.
• 3) R. Schoof, Elliptic curves over finite fields and the computation of square roots mod $p$, Math. Comp., 44 (1985), 483-494.
• 4) J. Pila, Frobenius maps of abelian varieties and finding roots of unity in finite fields, Math. Comp., 55 (1990), 745-763.
• 5) P. Gaudry and R. Harley, Counting points on hyperelliptic curves over finite fields, in: Proc. of ANTS-IV, W. Bosma, LNCS, Vol. 1838, pp. 313-332, Springer-Verlag, Berlin, 2000.

Terms in the title (4)： モデル ,  種数 ,  楕円曲線 ,  計数