18 citations · 45 across the 14 of their papers we have counts for
4 papers · 1 filter
The Scheme of Monogenic Generators II: Local Monogenicity and Twists
Sarah Arpin, Sebastian Bozlee, Leo Herr +1
This is the sequel paper to arXiv:2108.07185, continuing a study of monogenicity of number rings from a moduli-theoretic perspective. By the results of the first paper in this seri…
Orientations and cycles in supersingular isogeny graphs
Sarah Arpin, Mingjie Chen, Kristin E. Lauter +3
The paper concerns several theoretical aspects of oriented supersingular -isogeny volcanoes and their relationship to closed walks in the supersingular -isogeny graph.…
Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs
Sarah Arpin
In this paper, we add the information of level structure to supersingular elliptic curves and study these objects with the motivation of isogeny-based cryptography. Supersingular e…
Orienteering with one endomorphism
Sarah Arpin, Mingjie Chen, Kristin E. Lauter +3
In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? It is…