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arXiv · 2101.08761

Loops, Multi-Edges and Collisions in Supersingular Isogeny Graphs

Wissam Ghantous
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Abstract

Supersingular isogeny graphs are known to have very few loops and multi-edges. We formalize this idea by studying and finding bounds for the number of loops and multi-edges in such graphs. We also find conditions under which the supersingular isogeny graph $\Lambda_p(\ell)$ is simple. The methods presented in this paper can be used to study many kinds of collisions in supersingular isogeny graphs. As an application, we introduce the notion of bi-route number for two graphs $\Lambda_p(\ell_1),\Lambda_p(\ell_2)$ and compute bounds for it. We also study the number of edges in common between the graphs $\Lambda_p(\ell_1),\Lambda_p(\ell_2)$.

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BibTeXRIS

Wissam Ghantous. 2021-01-21. Loops, Multi-Edges and Collisions in Supersingular Isogeny Graphs. https://arxiv.org/abs/2101.08761

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