A variant of the isogeny puzzle that leaked extra hints. In 2022 those hints let researchers break it completely.
The idea: SIDH needed two people's secret walks to fit together, so each published extra clues: where certain points ended up after their walk. In 2022 Castryck and Decru showed that those clues, combined with a 1997 theorem, pin down the secret walk efficiently. The underlying map stayed hard. The clues were the leak.
Why it matters: A lesson: extra assumptions can fail even when the core problem holds.
On the map: ✗ broken 2022 (Castryck-Decru): the extra torsion points leak the secret
SIDH key exchange revealed where certain auxiliary points (torsion points) land under the secret isogeny, because the protocol needed them to work.
In July 2022 Castryck and Decru[1, 2] used exactly that extra information, together with a 1997 theorem of Kani, to recover secret keys in polynomial time. It is a textbook case of an extra assumption failing while the underlying problem (the isogeny path) survived.
If any of these breaks, this breaks too.
If this breaks, these break with it.