# Supersingular Isogeny Key Exchange broken?

Found this report detailing a quantum algorithm for computing isogenies between supersingular elliptic curves.

http://cacr.uwaterloo.ca/techreports/2014/cacr2014-24.pdf

with the quote "recommendation to avoid using base curves defined over Fp in De Feo-Jao-Plut type schemes".

Is it correct then that 'Supersingular Isogeny Key Exchange' of De Feo is broken?

If so, as this is a fast moving field, are there any recommendations for alternate post quantum key exchange with reasonably good key size and speed?

Thank you.

Also, the algorithm given in the mentioned paper has a complexity os $$\tilde{O}(p^{\frac{1}{4}})$$. The best known attack (As mentioned by de Feo, Jao and Plut) on the SSIKE is based on the claw finding problem (see below) and has a complexity of $$\theta(p^{\frac{1}{6}})$$.
Certainly not. This attack has been considered in De Feo's paper and their proposed parameters are resistant against this $O(p^\frac{1}{4})$-complexity attack.