Paper 2021/919 Original: eprint.iacr.org/2021/919 ↗
The supersingular isogeny path and endomorphism ring problems are equivalent
Abstract
We prove that the path-finding problem in $\ell$-isogeny graphs and the endomorphism ring problem for supersingular elliptic curves are equivalent under reductions of polynomial expected time, assuming the generalised Riemann hypothesis. The presumed hardness of these problems is foundational for isogeny-based cryptography. As an essential tool, we develop a rigorous algorithm for the quaternion analog of the path-finding problem, building upon the heuristic method of Kohel, Lauter, Petit and Tignol. This problem, and its (previously heuristic) resolution, are both a powerful cryptanalytic tool and a building-block for cryptosystems.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2021-09-10: last updated
- 2021-07-09: published
- Short URL
- https://ia.cr/2021/919
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2021/919,
author = {Benjamin Wesolowski},
title = {The supersingular isogeny path and endomorphism ring problems are equivalent},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/919},
year = {2021},
url = {https://eprint.iacr.org/2021/919}
}