Paper 2025/189 Original: eprint.iacr.org/2025/189 ↗
Experimentally studying path-finding problem between conjugates in supersingular isogeny graphs: Optimizing primes and powers to speed-up cycle finding
Abstract
We study the problem of finding a path between conjugate supersingular elliptic curves, a sub-routine of cycle finding algorithm in the graph $\chi_l(\overline{\mathbb{F}_p})$ of all supersingular elliptic curves over $\mathbb{F}_{p^2}$, connected by $l$ isogenies for primes $l,p$. We prove that asymptotically the most time-efficient way of overviewing the graph to find conjugate paths is seeing $i(=3)$ steps together, a question posed in Remark 3.5 by Eisentr{\"a}ger \etal~\cite{eisentrager2020}. We see both theoretically and experimentally that selecting $l,i$ optimally speeds up the cycle finding.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2026-01-05: last updated
- 2025-02-09: published
- Short URL
- https://ia.cr/2025/189
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2025/189,
author = {Madhurima Mukhopadhyay},
title = {Experimentally studying path-finding problem between conjugates in supersingular isogeny graphs: Optimizing primes and powers to speed-up cycle finding},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/189},
year = {2025},
url = {https://eprint.iacr.org/2025/189}
}