We present SÉTA, a new family of public-key encryption schemes with post-quantum security based on isogenies of supersingular elliptic curves. We first define a family of trapdoor one-way functions for which the computation of the inverse is based on an attack by Petit (ASIACRYPT 2017) on the problem of computing an isogeny between two supersingular elliptic curves, given the images of torsion points by this isogeny. We use this method as a decryption mechanism to build first a OW-CPA scheme, then we make use of generic transformations to obtain IND-CCA security in the quantum random oracle model, both for a PKE scheme and a KEM. Compared to alternative schemes based on SIDH, our protocols have the advantage of relying on arguably harder problems.