IKBFU's Vestnik

2010 Issue №10

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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.