1 citations · 3 across the 8 of their papers we have counts for
8 papers
Generators of Jacobians of Genus Two Curves
Christian Robenhagen Ravnshoj
We prove that in most cases relevant to cryptography, the Frobenius endomorphism on the Jacobian of a genus two curve is represented by a diagonal matrix with respect to an appropr…
Non-Cyclic Subgroups of Jacobians of Genus Two Curves
Christian Robenhagen Ravnshoj
Let E be an elliptic curve defined over a finite field. Balasubramanian and Koblitz have proved that if the l-th roots of unity m_l is not contained in the ground field, then a fie…
Non-Cyclic Subgroups of Jacobians of Genus Two Curves with Complex Multiplication
Christian Robenhagen Ravnshoj
Let E be an elliptic curve defined over a finite field. Balasubramanian and Koblitz have proved that if the l-th roots of unity m_l is not contained in the ground field, then a fie…
Pairings on Jacobians of Hyperelliptic Curves
Christian Robenhagen Ravnshoj
Consider the jacobian of a hyperelliptic genus two curve defined over a finite field. Under certain restrictions on the endomorphism ring of the jacobian we give an explicit descri…
p-torsion of Genus Two Curves Over Prime Fields of Characteristic p
Christian Robenhagen Ravnshoj
Consider the Jacobian of a hyperelliptic genus two curve defined over a prime field of characteristic p and with complex multiplication. In this paper we show that the p-Sylow subg…
Embedding Degree of Hyperelliptic Curves with Complex Multiplication
Christian Robenhagen Ravnshoj
Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cy…
Generators of Jacobians of Hyperelliptic Curves
Christian Robenhagen Ravnshoj
This paper provides a probabilistic algorithm to determine generators of the m-torsion subgroup of the Jacobian of a hyperelliptic curve of genus two.
Large Cyclic Subgroups of Jacobians of Hyperelliptic Curves
Christian Robenhagen Ravnshoj
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…