TL;DR
This paper thoroughly analyzes supersingular isogeny graphs, exploring their structure, properties, and implications for cryptography, including graph distances, involutions, and experimental diameter data, advancing understanding of their complexity and security.
Contribution
It provides new insights into the structure and properties of supersingular isogeny graphs, including analysis of subgraphs, involutions, and experimental diameter measurements, with implications for cryptographic security.
Findings
Distances of connected components in the spine graph analyzed
Heuristics on shortest paths preserved by Frobenius involution
Experimental diameters of supersingular isogeny graphs compared with LPS and Ramanujan graphs
Abstract
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 Lauter for the construction of cryptographic hash functions [CGL06]. These are large expander graphs, and the hard problem is to find an efficient algorithm for routing, or path-finding, between two vertices of the graph. We consider four aspects of supersingular isogeny graphs, study each thoroughly and, where appropriate, discuss how they relate to one another. First, we consider two related graphs that help us understand the structure: the `spine' , which is the subgraph of given by the -invariants in , and the graph , in which both curves and isogenies must be defined over . We show how to…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
