Geodesic
On the number of points on the curve $y^2 = x^{7} + ax^4 + bx$ over a finite field
Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 2, pp. 62-79

Voir la notice de l'article provenant de la source Math-Net.Ru

We provide explicit formulae for the number of points on a genus $3$ hyperelliptic curve of type $y^2 = x^{7} + a x^{3} + b x$ over a finite field $\mathbb{F}_q$ of characteristic $p > 3$. As an application of these formulae, we prove that point-counting problem on this type of curves has heuristic time complexity of order $O(\log^4{q})$ bit operations. Tab. 2, bibliogr. 27.
Keywords: hyperelliptic curve, point-counting, characteristic polynomial. 
@article{DA_2022_29_2_a3,
     author = {S. A. Novoselov and Yu. F. Boltnev},
     title = {On the number of points on the curve $y^2 = x^{7} + ax^4 + bx$ over a finite field},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {62--79},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2022_29_2_a3/}
}
TY  - JOUR
AU  - S. A. Novoselov
AU  - Yu. F. Boltnev
TI  - On the number of points on the curve $y^2 = x^{7} + ax^4 + bx$ over a finite field
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2022
SP  - 62
EP  - 79
VL  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2022_29_2_a3/
LA  - ru
ID  - DA_2022_29_2_a3
ER  - 
%0 Journal Article
%A S. A. Novoselov
%A Yu. F. Boltnev
%T On the number of points on the curve $y^2 = x^{7} + ax^4 + bx$ over a finite field
%J Diskretnyj analiz i issledovanie operacij
%D 2022
%P 62-79
%V 29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2022_29_2_a3/
%G ru
%F DA_2022_29_2_a3
S. A. Novoselov; Yu. F. Boltnev. On the number of points on the curve $y^2 = x^{7} + ax^4 + bx$ over a finite field. Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 2, pp. 62-79. http://geodesic.mathdoc.fr/item/DA_2022_29_2_a3/