Paper 2019/1202
Rational isogenies from irrational endomorphisms
Wouter Castryck, Lorenz Panny, and Frederik Vercauteren
Abstract
In this paper, we introduce a polynomial-time algorithm to compute a connecting $\mathcal{O}$-ideal between two supersingular elliptic curves over $\mathbb{F}_p$ with common $\mathbb{F}_p$-endomorphism ring $\mathcal{O}$, given a description of their full endomorphism rings. This algorithm provides a reduction of the security of the CSIDH cryptosystem to the problem of computing endomorphism rings of supersingular elliptic curves. A similar reduction for SIDH appeared at Asiacrypt 2016, but relies on totally different techniques. Furthermore, we also show that any supersingular elliptic curve constructed using the complex-multiplication method can be located precisely in the supersingular isogeny graph by explicitly deriving a path to a known base curve. This result prohibits the use of such curves as a building block for a hash function into the supersingular isogeny graph.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published by the IACR in EUROCRYPT 2020
- Keywords
- Isogeny-based cryptographyendomorphism ringsCSIDH
- Contact author(s)
-
wouter castryck @ esat kuleuven be
lorenz @ yx7 cc
frederik vercauteren @ esat kuleuven be - History
- 2020-03-09: revised
- 2019-10-15: received
- See all versions
- Short URL
- https://ia.cr/2019/1202
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2019/1202,
author = {Wouter Castryck and Lorenz Panny and Frederik Vercauteren},
title = {Rational isogenies from irrational endomorphisms},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/1202},
year = {2019},
url = {https://eprint.iacr.org/2019/1202}
}
