4 citations · 16 across the 7 of their papers we have counts for
8 papers
Generating sets for maximal orders in rational quaternion algebras
Kirsten Eisenträger, Eyal Z. Goren, Annamaria Iezzi +6
Given a maximal order in a rational definite quaternion algebra, and a prime coprime to the discriminant of , this paper considers subsets of $\…
Connecting Kani's Lemma and path-finding in the Bruhat-Tits tree to compute supersingular endomorphism rings
Kirsten Eisentraeger, Gabrielle Scullard
We give a deterministic polynomial time algorithm to compute the endomorphism ring of a supersingular elliptic curve in characteristic p, provided that we are given two noncommutin…
A topological approach to undefinability in algebraic extensions of
Kirsten Eisentraeger, Russell Miller, Caleb Springer +1
For any subset , consider the set of subfields which contain a co-infinite subset that is universal…
Cycles in the supersingular -isogeny graph and corresponding endomorphisms
Efrat Bank, Catalina Camacho-Navarro, Kirsten Eisentraeger +2
We study the problem of generating the endomorphism ring of a supersingular elliptic curve by two cycles in -isogeny graphs. We prove a necessary and sufficient condition for…
Constructing Picard curves with complex multiplication using the Chinese Remainder Theorem
Sonny Arora, Kirsten Eisentraeger
We give a new algorithm for constructing Picard curves over a finite field with a given endomorphism ring. This has important applications in cryptography since curves of genus 3 a…
Hilbert's Tenth Problem over Function Fields of Positive Characteristic Not Containing the Algebraic Closure of a Finite Field
Kirsten Eisentraeger, Alexandra Shlapentokh
We prove that the existential theory of any function field of characteristic is undecidable in the language of rings provided that the constant field does not contain th…
Hilbert's Tenth Problem and Mazur's Conjectures in Complementary Subrings of Number Fields
Kirsten Eisentraeger, Graham Everest, Alexandra Shlapentokh
We show that Hilbert's Tenth Problem is undecidable for complementary subrings of number fields and that the p-adic and archimedean ring versions of Mazur's conjectures do not hold…
Pairings on hyperelliptic curves
Jennifer Balakrishnan, Juliana Belding, Sarah Chisholm +3
We assemble and reorganize the recent work in the area of hyperelliptic pairings: We survey the research on constructing hyperelliptic curves suitable for pairing-based cryptograph…