Paper 2023/1229
Two Remarks on Torsion-Point Attacks in Isogeny-Based Cryptography
, Florida Atlantic UniversityAbstract
We fix an omission in [Petit17] on torsion point attacks of isogeny-based cryptosystems akin to SIDH, also reprised in [dQuehen-etal21]. In these works, their authors represent certain integers using a norm equation to derive a secret isogeny. However, this derivation uses as a crucial ingredient ([Petit17] Section 4.3), which we show to be incorrect. We then state sufficient conditions allowing to prove a modified version this lemma. A further idea of parametrizing solutions of the norm equation will show that these conditions can be fulfilled under the same heuristics of these previous works. Our contribution is a theoretical one. It doesn't invalidate the attack, which works as well in practice, but gives a correct mathematical justification for it. We also simplify the argument of Theorem 3 in [dQuehen-etal21] to show that the requirement that $m$ be small is unnecessary.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- Post-quantum cryptographyelliptic curve cryptographyisogenies
- Contact author(s)
- sicaf @ fau edu
- History
- 2023-08-15: approved
- 2023-08-13: received
- See all versions
- Short URL
- https://ia.cr/2023/1229
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/1229,
author = {Francesco Sica},
title = {Two Remarks on Torsion-Point Attacks in Isogeny-Based Cryptography},
howpublished = {Cryptology ePrint Archive, Paper 2023/1229},
year = {2023},
note = {\url{https://eprint.iacr.org/2023/1229}},
url = {https://eprint.iacr.org/2023/1229}
}
