3 papers
math.NT2024
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…
math.NT2018
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…
math.NT2018
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…