24 citations · 42 across the 9 of their papers we have counts for
11 papers
Determining the primes of bad reduction of CM curves of genus 3
Sorina Ionica, Pinar Kiliçer, Kristin Lauter +3
In this paper we introduce a new problem called the Isogenous Embedding Problem (IEP). The existence of solutions to this problem is related to the primes of bad reduction of CM cu…
Weighted Subspace Designs from -Polymatroids
Eimear Byrne, Michela Ceria, Sorina Ionica +1
The Assmus-Mattson theorem gives a way to identify block designs arising from codes. This result was broadened to matroids and weighted designs. In this work we present a further t…
Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication
Bogdan Dina, Sorina Ionica, Jeroen Sijsling
We analyze complex multiplication for Jacobians of curves of genus 3, as well as the resulting Shimura class groups and their subgroups corresponding to Galois conjugation over the…
Constructions of new matroids and designs over GF(q)
Eimear Byrne, Michela Ceria, Sorina Ionica +2
A perfect matroid design (PMD) is a matroid whose flats of the same rank all have the same size. In this paper we introduce the q-analogue of a PMD and its properties. In order to…
Genus 3 hyperelliptic curves with CM via Shimura Reciprocity
B. Dina, S. Ionica
Up to isomorphism over C, every simple principally polarized abelian variety of dimension 3 is the Jacobian of a smooth projective curve of genus 3. Furthermore, this curve is eith…
Parity (XOR) Reasoning for the Index Calculus Attack
Monika Trimoska, Sorina Ionica, Gilles Dequen
Cryptographic problems can often be reduced to solving Boolean polynomial systems, whose equivalent logical formulas can be treated using SAT solvers. Given the algebraic nature of…
Modular invariants for genus 3 hyperelliptic curves
Sorina Ionica, Pinar Kilicer, Kristin Lauter +4
In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary oc-tics to Siegel modular forms of genus 3. W…
Constructing genus 3 hyperelliptic Jacobians with CM
Jennifer S. Balakrishnan, Sorina Ionica, Kristin Lauter +1
Given a sextic CM field , we give an explicit method for finding all genus 3 hyperelliptic curves defined over whose Jacobians are simple and have complex multiplic…
Isogeny graphs with maximal real multiplication
Sorina Ionica, Emmanuel Thomé
An isogeny graph is a graph whose vertices are principally polarized abelian varieties and whose edges are isogenies between these varieties. In his thesis, Kohel described the str…
Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
Sorina Ionica
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the -Tate pairing in terms of the action of the Frobenius on the -torsion of…
Pairing the Volcano
Sorina Ionica, Antoine Joux
Isogeny volcanoes are graphs whose vertices are elliptic curves and whose edges are -isogenies. Algorithms allowing to travel on these graphs were developed by Kohel in his t…