Paper 2025/1295 Original: eprint.iacr.org/2025/1295 ↗
The computational refined Humbert invariant problem is equivalent to the computational isogeny problem
Abstract
In this paper, we discuss refined Humbert invariants, introduced by Kani in 1994. We show that in the contexts of SQISign and CSIDH, under GRH, the computational isogeny problem is polynomially equivalent to the computational refined Humbert invariant problem. This includes an algorithm to compute the basis of a maximal order of a quaternion algebra given its norm form. Finally, we also review what is known in the literature about computing refined Humbert invariants.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2025-07-15: last updated
- 2025-07-15: published
- Short URL
- https://ia.cr/2025/1295
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2025/1295,
author = {Eda Kırımlı and Chloe Martindale},
title = {The computational refined Humbert invariant problem is equivalent to the computational isogeny problem},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/1295},
year = {2025},
url = {https://eprint.iacr.org/2025/1295}
}