18 citations · 45 across the 14 of their papers we have counts for
15 papers
The Spine: A Supersingular Highway
Taha Hedayat, Renate Scheidler, Sarah Arpin
We consider the structure of the spine of the supersingular -isogeny graph for one of the cases which arXiv:2502.03613 was not able to fully describe, and $p = 71,…
Supersingular elliptic curves and twisting endomorphisms
Sarah Arpin, Josep M. Miret, Jordi Pujolàs +1
We generalize the notion of twisting endomorphisms, first defined by Castryck-Panny-Vercauteran, to the setting of -oriented supersingular elliptic curves. We give an…
Digital signature schemes based on code equivalence and syndrome decoding from restricted errors
Sarah Arpin, Jason T. LeGrow, Hiram H. López +1
Digital signature schemes are an important cryptographic tool to ensure data authenticity and integrity in many applications that must be resilient to attacks, including those faci…
Isogeny graphs of abelian varieties and singular ideals in orders
Sarah Arpin, Stefano Marseglia, Caleb Springer
Famously, Kohel proved that isogeny graphs of ordinary elliptic curves are beautifully structured objects, now called volcanos. We prove graph structural theorems for abelian varie…
The Spine of a Supersingular -Isogeny graph
Taha Hedayat, Sarah Arpin, Renate Scheidler
Supersingular elliptic curve -isogeny graphs over finite fields offer a setting for a number of quantum-resistant cryptographic protocols. The security analysis of these sche…
Cycles and Cuts in Supersingular L-Isogeny Graphs
Sarah Arpin, Ross Bowden, James Clements +3
Supersingular elliptic curve isogeny graphs underlie isogeny-based cryptography. For isogenies of a single prime degree , their structure has been investigated graph-theoreti…
Generalized class group actions on oriented elliptic curves with level structure
Sarah Arpin, Wouter Castryck, Jonathan Komada Eriksen +2
We study a large family of generalized class groups of imaginary quadratic orders and prove that they act freely and (essentially) transitively on the set of primitively -or…
Finding Orientations of Supersingular Elliptic Curves and Quaternion Orders
Sarah Arpin, James Clements, Pierrick Dartois +3
Orientations of supersingular elliptic curves encode the information of an endomorphism of the curve. Computing the full endomorphism ring is a known hard problem, so one might con…
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…
The Scheme of Monogenic Generators I: Representability
Sarah Arpin, Sebastian Bozlee, Leo Herr +1
This is the first in a series of two papers that study monogenicity of number rings from a moduli-theoretic perspective. Given an extension of algebras , when is generated…
On the arithmetic of a family of superelliptic curves
Sarah Arpin, Richard Griffon, Libby Taylor +1
Let be a prime, let and be powers of , and let and be relatively prime integers not divisible by . Let be the superelliptic curve wit…
Adventures in Supersingularland
Sarah Arpin, Catalina Camacho-Navarro, Kristin Lauter +4
In this paper, we study isogeny graphs of supersingular elliptic curves. Supersingular isogeny graphs were introduced as a hard problem into cryptography by Charles, Goren, and Lau…