9 citations · 20 across the 4 of their papers we have counts for
8 papers
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…
Ramanujan graphs in cryptography
Anamaria Costache, Brooke Feigon, Kristin Lauter +2
In this paper we study the security of a proposal for Post-Quantum Cryptography from both a number theoretic and cryptographic perspective. Charles-Goren-Lauter in 2006 [CGL06] pro…
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
Sean Ballentine, Aurore Guillevic, Elisa Lorenzo García +4
Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations…
Computing L-series of geometrically hyperelliptic curves of genus three
David Harvey, Maike Massierer, Andrew V. Sutherland
Let C/Q be a curve of genus three, given as a double cover of a plane conic. Such a curve is hyperelliptic over the algebraic closure of Q, but may not have a hyperelliptic model o…
An optimal representation for the trace zero subgroup
Elisa Gorla, Maike Massierer
We give an optimal-size representation for the elements of the trace zero subgroup of the Picard group of an elliptic or hyperelliptic curve of any genus, with respect to a field e…
Index Calculus in the Trace Zero Variety
Elisa Gorla, Maike Massierer
We discuss how to apply Gaudry's index calculus algorithm for abelian varieties to solve the discrete logarithm problem in the trace zero variety of an elliptic curve. We treat in…
Point compression for the trace zero subgroup over a small degree extension field
Elisa Gorla, Maike Massierer
Using Semaev's summation polynomials, we derive a new equation for the -rational points of the trace zero variety of an elliptic curve defined over . Us…
Tame Class Field Theory for Global Function Fields
Florian Hess, Maike Massierer
We give a function field specific, algebraic proof of the main results of class field theory for abelian extensions of degree coprime to the characteristic. By adapting some method…