### Overview of effective point counting algorithms for Jacobian of hyperelliptic curve over finite field

- Pages
- 108-111

#### Abstract

Various algorithms for finding of the order of Jacobian, their range of use and efficiency are considered.

#### Reference

1. *Colm** **O** **hEigeartaigh**.* A comparison of point counting methods for hyperelliptic curves over prime fields and fields of characteristic 2 // Cryptology ePrint Archive. 2004.

2. *Haneda M., Kawazoe M., Takahashi T.* Suitable curves for genus-4 HCC over prime fields: point counting formulae for hyperelliptic curves of type..... // Ibid.

3. *Furukawa E., Kawazoe M., Takahashi T.* Counting points for hyperelliptic curves of type..... // Ibid. 2002.

4. *Haloui S.* The minimum and maximum number of rational points on jacobian surfaces over finite fields. URL: http://arxiv. org/abs/1002.3683.2010.

5. *Ravnshoj C. R.* Generators of Jacobians of genus two curves // Cryptology ePrint Archive. 2008.

6. *Ravnshoj C. R.* Non-cyclic subgroups of Jacobians of genus two curves // Ibid.

7. *Ravnshoj C. R.* Non-cyclic subgroups of Jacobians of genus two curves with complex multiplication // Ibid.

8. *Dechene I.* Arithmetic of generalized Jacobians // Ibid. 2006.

9. *Dechene I.* On the security of generalized Jacobian cryptosystems // Ibid.

10. *Galbraith S. D., Smith B. A.* Discrete logarithms in generalized Jacobians // Ibid.

11. *Nagao K.* Improvement of theriault algorithm of index calculus for Jacobian of hyperelliptic curves of small genus // Ibid. 2004.