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Title:
POKE: A Framework for Efficient PKEs, Split KEMs, and OPRFs from Higher-dimensional Isogenies
Authors: Andrea Basso
Abstract:We introduce a new framework, POKE, to build cryptographic protocols from irrational isogenies using higher-dimensional representations. The framework enables two parties to manipulate higher-dimensional representations of isogenies to efficiently compute their pushforwards, and ultimately to obtain a shared secret.
We provide three constructions based on POKE: the first is a PKE protocol, which is one of the most compact post-quantum PKEs and possibly the most efficient isogeny-based PKE to date. We then introduce a validation technique to ensure the correctness of uniSIDH public keys: by combining the validation method with a POKE-based construction, we obtain a split KEM, a primitive that generalizes NIKEs and can be used to instantiate a post-quantum version of the Signal’s X3DH protocol. The third construction builds upon the split KEM and its validation method to obtain a round-optimal verifiable OPRF. It is the first such construction that does not require more than \lambda isogeny computations, and it is significantly more compact and more efficient than all other isogeny-based OPRFs.
ePrint: https://eprint.iacr.org/2024/624
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