40 citations · 51 across the 7 of their papers we have counts for
7 papers
Computing endomorphism rings of supersingular elliptic curves and connections to pathfinding in isogeny graphs
Kirsten Eisentraeger, Sean Hallgren, Chris Leonardi +2
Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of th…
As Easy as : Hilbert's Tenth Problem for Subrings of the Rationals and Number Fields
Kirsten Eisentraeger, Russell Miller, Jennifer Park +1
Hilbert's Tenth Problem over the field of rational numbers is one of the biggest open problems in the area of undecidability in number theory. In this paper we construc…
Undecidability in function fields of positive characteristic
Kirsten Eisentraeger, Alexandra Shlapentokh
We prove that the first-order theory of any function field K of characteristic p>2 is undecidable in the language of rings without parameters. When K is a function field in one var…
Descent on Elliptic Curves and Hilbert's Tenth Problem
Graham Everest, Kirsten Eisentraeger
Descent via an isogeny on an elliptic curve is used to construct two subrings of the field of rational numbers, which are complementary in a strong sense, and for which Hilbert's T…
A CRT algorithm for constructing genus 2 curves over finite fields
Kirsten Eisentraeger, Kristin Lauter
We present a new method for constructing genus 2 curves over a finite field with a given number of points on its Jacobian. This method has important applications in cryptography, w…
Integrality at a prime for global fields and the perfect closure of global fields of characteristic p>2
Kirsten Eisentraeger
Let k be a global field and \pp any nonarchimedean prime of k. We give a new and uniform proof of the well known fact that the set of all elements of k which are integral at \pp is…