POKE: A Compact and Efficient PKE from Higher-dimensional Isogenies

We introduce a new PKE protocol, POKE, based on isogenies of unknown degree. The protocol relies on two new techniques: the first constructs an SIDH square while also working with higher-dimensional representations, whereas the second allows us to obtain a shared secret even when all curves in the commutative diagram are known. The resulting protocol is compact and extremely efficient. We provide a proof-of-concept implementation in SageMath of POKE that shows encryption and decryption taking less than a hundred milliseconds: POKE is thus the most efficient encryption protocol from isogenies, and it outperforms existing protocols by more than an order of magnitude.