Calculation of 3-torsion ideal for some class of hyperelliptic curves | Applied Discrete Mathematics. Supplement. 2019. № 12. DOI: 10.17223/2226308X/12/3

Calculation of 3-torsion ideal for some class of hyperelliptic curves

In the paper, we consider hyperelliptic curves of genus two defined by the Dickson polynomials. For such curves, we calculate the 3-torsion ideal, namely we obtain the four generators of this ideal by using the Mumford - Cantor representation for the 3-torsion divisor and by using of в- and ^-functions.

Download file

Counter downloads: 154

Keywords

гиперэллиптическая кривая, многочлен Диксона, идеал I-кручения, дивизор l-кручения, модулярное уравнение, hyperelliptic curve, Dickson polynomial, l-torsion ideal, l-torsion divisor, modular equation

Authors

Name	Organization	E-mail
Malygina E. S.	I. Kant Baltic Federal University	Ekkat@inbox.ru

Всего: 1

References

Cohen H. and Frey G. Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman and Hall/CRC, 2005.

LidlR., Mullen G.L., and Turnwald G. Dickson Polynomials. Chapman and Hall/CRC, 1993.

Novoselov S. A. Counting points on hyperelliptic curves of type y2 = x2g+1 + ax9+1 + bx. arXiv: 1902.05992. 2019.

Malygina E. S. and Novoselov S. A. Division polynomials for hyperelliptic curves defined by Dickson polynomials // Proc. 8th Workshop on Current Trends in Cryptology. Svetlogorsk, Kaliningrad region, June 4-7, 2019. https://ctcrypt.ru/ematerials2019.

Hindry M. and Silverman J. Diophantine Geometry. An Introduction. Graduate Texts in Mathematics. V. 201. Springer Verlag, 2000.

Kampkotter W. Explizite Gleichungen fur Jacobische Varietatenhyperelliptisher Rurven.Ph. D. Thesis, Universitat Gesamthochschule Essen, 1991.