Paper 2024/624

POKE: A Framework for Efficient PKEs, Split KEMs, and OPRFs from Higher-dimensional Isogenies

Andrea Basso, University of Bristol, IBM Research - Zurich

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.

Available format(s)
Cryptographic protocols
Publication info
IsogeniesPKEsplit KEMOPRF
Contact author(s)
andrea basso @ bristol ac uk
2024-04-26: approved
2024-04-22: received
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Creative Commons Attribution-NonCommercial-ShareAlike


      author = {Andrea Basso},
      title = {{POKE}: A Framework for Efficient {PKEs}, Split {KEMs}, and {OPRFs} from Higher-dimensional Isogenies},
      howpublished = {Cryptology ePrint Archive, Paper 2024/624},
      year = {2024},
      note = {\url{}},
      url = {}
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