Elliptic curve isogenies are structure-preserving maps between elliptic curves which have been proposed as a foundation of post-quantum cryptosystems.

Elliptic curve isogenies are structure-preserving maps between elliptic curves which have been proposed as a foundation of post-quantum cryptosystems.

An isogeny between two elliptic curves is a non-constant group homomorphism which is given by rational maps. The problem of finding an isogeny between two given curves is conjectured to be hard even for quantum computers, hence computing random isogenies is a suitable primitive for post-quantum cryptography.

Cryptosystems based on (variants of) this hard problem include the Hard Homogeneous Spaces scheme of CouveignesRostovtsev–Stolbunov and Jao–De Feo's Supersingular-Isogeny Diffie-Hellman with its actively secure variant SIKE.