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OpenSSH 8.9 and later have added support for the 'Streamlined NTRU Prime' key exchange method, a lattice-based algorithm intended to resist quantum attacks. PuTTY now supports it too.
The system is run in parallel with Curve25519, which is the most commonly used conventional key exchange method these days. So it's at least no less secure than what you were probably using already: to replicate the hashing operation that creates the session keys, an attacker would have to figure out the shared secret output from both methods. So even if NTRU were to turn out to have a huge undiscovered flaw that made that easy, the attacker would still need to break Curve25519 as well.
Due to this safety precaution, we decided it was safe to enable this by default and put it high on the KEX preference list. So if you use an up-to-date version of PuTTY with existing configuration, it will probably have already started speaking NTRU to compatible servers, and (assuming all of this performs as intended) your sessions will be safe even against an adversary recording the network traffic now and intending to apply a quantum computer to it once one becomes available.
This method is called 'NTRU Prime / Curve25519 hybrid kex' in
PuTTY's user interface. For those who prefer to think in terms of raw
SSH protocol ids, the id for this combined system is