Welcome to the resource topic for 2025/189
Title:
Experimentally studying path-finding problem between conjugates in supersingular isogeny graphs: Optimizing primes and powers to speed-up cycle finding
Authors: Madhurima Mukhopadhyay
Abstract:We study the problem of finding a path between conjugate supersingular elliptic curves over \mathbb{F}_{p^2} for a prime p, which is important for cycle finding in supersingular isogeny graphs. We see that for any given p, there is some l corresponding to p which accelerates the process of conjugate path-finding. Also, time-wise, the most efficient way of overviewing the graph is seeing i(=3) steps at once. We have outlined methods in which the next vertex of any pseudo-random walk should be chosen to reach conjugate vertex faster. We have experimentally investigated the paths between frobenius conjugates for wide ranges of small prime l. We introduce sets to experimentally learn about the structure of the isogeny graphs when short cycles are present.
ePrint: https://eprint.iacr.org/2025/189
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