Paper 2024/624
POKE: A Framework for Efficient PKEs, Split KEMs, and OPRFs from Higher-dimensional Isogenies
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.
Metadata
- Available format(s)
- Category
- Cryptographic protocols
- Publication info
- Preprint.
- Keywords
- IsogeniesPKEsplit KEMOPRF
- Contact author(s)
- andrea basso @ bristol ac uk
- History
- 2024-04-26: approved
- 2024-04-22: received
- See all versions
- Short URL
- https://ia.cr/2024/624
- License
-
CC BY-NC-SA
BibTeX
@misc{cryptoeprint:2024/624, 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{https://eprint.iacr.org/2024/624}}, url = {https://eprint.iacr.org/2024/624} }