Séta: Supersingular Encryption from Torsion Attacks

We present Séta (To be pronounced [?e:t?] meaning “walk” in Hungarian.), a new family of public-key encryption schemes with post-quantum security based on isogenies supersingular elliptic curves. It is constructed from trapdoor one-way functions, where the inversion algorithm uses Petit’s so called torsion attacks SIDH to compute an isogeny between curves given endomorphism starting curve and images points. prove OW-CPA IND-CCA variant using OAEP transformation. Several variants for key generation are explored together their impact selection parameters, such as base prime scheme. furthermore formalise “uber” assumption framework which aims generalize computational problems encountered including SIDH, CSDIH, OSIDH ours. Finally, we carefully select parameters achieve balance run-times experimental results our implementation.