Paper 2026/2429 Original: eprint.iacr.org/2026/2429 ↗
Rapid mixing in superspecial isogeny graphs
Abstract
We prove expansion properties of superspecial isogeny graphs in dimension $g \geq 2$, including arbitrary level structure. In particular, we provide explicit bounds for the spectral gap, and a fine characterization of obstructions created by level structures (disconnectedness and periodicity). Without the level structure (the only case which was previously studied), our bounds dramatically improve the state of the art. These isogenies in dimension greater than one have become increasingly important in isogeny-based cryptography, and previous works have already conjectured consequences of their expansion properties. We present several applications of our result: we transform conjectural predecessors into rigorous algorithms, and we give the first algorithm for computing endomorphism rings of superspecial principally polarized abelian varieties in arbitrary dimension, with complexity $\tilde O(p^{g-1})$.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2026-10-09: last updated
- 2026-10-09: published
- Short URL
- https://ia.cr/2026/2429
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/2429,
author = {Maria Corte-Real Santos and Harun Kır and Olivier Taïbi and Benjamin Wesolowski},
title = {Rapid mixing in superspecial isogeny graphs},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2429},
year = {2026},
url = {https://eprint.iacr.org/2026/2429}
}