Paper 2024/509

Distribution of cycles in supersingular $\ell$-isogeny graphs

Eli Orvis, University of Colorado Boulder
Abstract

Recent work by Arpin, Chen, Lauter, Scheidler, Stange, and Tran counted the number of cycles of length $r$ in supersingular $\ell$-isogeny graphs. In this paper, we extend this work to count the number of cycles that occur along the spine. We provide formulas for both the number of such cycles, and the average number as $p \to \infty$, with $\ell$ and $r$ fixed. In particular, we show that when $r$ is not a power of $2$, cycles of length $r$ are disproportionately likely to occur along the spine. We provide experimental evidence that this result holds in the case that $r$ is a power of $2$ as well.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. arXiv
DOI
10.48550/arXiv.2403.14831
Keywords
supersingularisogenyelliptic curveorientationcycle
Contact author(s)
eli orvis @ colorado edu
History
2024-04-01: approved
2024-03-31: received
See all versions
Short URL
https://ia.cr/2024/509
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/509,
      author = {Eli Orvis},
      title = {Distribution of cycles in supersingular $\ell$-isogeny graphs},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/509},
      year = {2024},
      doi = {10.48550/arXiv.2403.14831},
      url = {https://eprint.iacr.org/2024/509}
}
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