Two Remarks on Torsion-Point Attacks in Isogeny-Based Cryptography

ePrint Report: Two Remarks on Torsion-Point Attacks in Isogeny-Based Cryptography

Francesco Sica

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.


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attacks authors cryptography eprint report equation fix point report secret