> Most PAKE systems nowadays use Diffie-Hellman assumptions, which can be broken by a quantum computer. There are some ideas on how to transition their underlyi

> Most PAKE systems nowadays use Diffie-Hellman assumptions, which can be broken by a quantum computer. There are some ideas on how to transition their underlying algorithms to the post-quantum world; but these seem to be so inefficient as to render their deployment infeasible. Isogeny based PAKEs exist! (e.g. https://eprint.iacr.org/2018/886 https://eprint.iacr.org/2018/886) Their weakness is not infeasible performance, but rather the lack of a totally satisfactory security proof based on previous assumptions.