From the 1 of 6 linked papers with an AI index.
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The Spine: A Supersingular Highway
Taha Hedayat, Renate Scheidler, Sarah Arpin
The paper analyzes the spine subgraph of the supersingular ℓ‑isogeny graph for ℓ = 2 and primes p ≡ 71, 119 (mod 120), computing distance, eccentricity, and diameter of its compone…
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…
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…
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…
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…