Paper 2022/880 Original: eprint.iacr.org/2022/880 ↗
Efficient supersingularity testing over $\mathbb{F}_p$ and CSIDH key validation
Abstract
Many public-key cryptographic protocols, notably non-interactive key exchange (NIKE), require incoming public keys to be validated to mitigate some adaptive attacks. In CSIDH, an isogeny-based post-quantum NIKE, a key is deemed legitimate if the given Montgomery coefficient specifies a supersingular elliptic curve over the prime field. In this work, we survey the current supersingularity tests used for CSIDH key validation, and implement and measure two new alternative algorithms. Our implementation shows that we can determine supersingularity substantially faster, and using less memory, than the state-of-the-art.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2022-07-26: last updated
- 2022-07-05: published
- Short URL
- https://ia.cr/2022/880
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2022/880,
author = {Gustavo Banegas and Valerie Gilchrist and Benjamin Smith},
title = {Efficient supersingularity testing over $\mathbb{F}_p$ and CSIDH key validation},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/880},
year = {2022},
url = {https://eprint.iacr.org/2022/880}
}