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2007•Unpublished venueOpen access

Large Cyclic Subgroups of Jacobians of Hyperelliptic Curves.

Christian Robenhagen Ravnshøj

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Abstract

Abstract. In this paper we obtain conditions on the divisors of the group order of the Jacobian of a hyperelliptic genus 2 curve, generated by the complex multiplication method described by Weng (2003) and Gaudry et al (2005). Examples, where these conditions imply that the Jacobian has a large cyclic subgroup, are given. 1.

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Abstract. In this paper we obtain conditions on the divisors of the group order of the Jacobian of a hyperelliptic genus 2 curve, generated by the complex multiplication method described by Weng (2003) and Gaudry et al (2005). Examples, where these conditions imply that the Jacobian has a large cyclic subgroup, are given. 1.

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Abstract. In this paper we obtain conditions on the divisors of the group order of the Jacobian of a hyperelliptic genus 2 curve, generated by the complex multiplication method described by Weng (2003) and Gaudry et al (2005). Examples, where these conditions imply that the Jacobian has a large cyclic subgroup, are given. 1.

Key concepts: Jacobian matrix and determinant, Hyperelliptic curve, Hyperelliptic curve cryptography, Mathematics, Genus, Order (exchange), Multiplication (music), Pure mathematics

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