Paper 2022/1026 Original: eprint.iacr.org/2022/1026 ↗
An attack on SIDH with arbitrary starting curve
Abstract
We present an attack on SIDH which does not require any endomorphism information on the starting curve. Our attack has subexponential complexity thus significantly reducing the security of SIDH and SIKE; our analysis and preliminary implementation suggests that our algorithm will be feasible for the Microsoft challenge parameters $p = 2^{110}3^{67}-1$ on a regular computer. Our attack applies to any isogeny-based cryptosystem that publishes the images of points under the secret isogeny, for example Seta and B-SIDH. It does not apply to CSIDH, CSI-FiSh, or SQISign.
Metadata
- Available format(s)
PDF- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- History
- 2022-08-25: last updated
- 2022-08-08: published
- Short URL
- https://ia.cr/2022/1026
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2022/1026,
author = {Luciano Maino and Chloe Martindale},
title = {An attack on SIDH with arbitrary starting curve},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1026},
year = {2022},
url = {https://eprint.iacr.org/2022/1026}
}