6 papers
Elliptic curves over Hasse pairs
Eleni Agathocleous, Antoine Joux, Daniele Taufer
We call a pair of distinct prime powers a Hasse pair if . For such pairs, we study the relation between the set…
On homomorphic encryption using abelian groups: Classical security analysis
Eleni Agathocleous, Vishnupriya Anupindi, Annette Bachmayr +3
In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism wi…
Elliptic Curves with positive rank and no integral points
Eleni Agathocleous
We consider all \emph{odd} fundamental discriminants and their mirror discriminants , and we study the family of elliptic curves $E_{D'}: y^{2} = x^{…
On the Selmer group and rank of a family of elliptic curves and curves of genus one violating the Hasse principle
Eleni Agathocleous
We study an infinite family of -invariant zero elliptic curves and their -isogenous curves , where and a…
The 3-part of the Ideal Class Group of a certain family of real cyclotomic fields
Eleni Agathocleous
In this paper we study the structure of the part of the ideal class group of a certain family of real cyclotomic fields with class number exactly and conductor equal to…
On the class numbers of real cyclotomic fields of conductor
Eleni Agathocleous
The class numbers of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows and method…