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.