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

Andrea Basso; Luciano Maino

Paper 2024/624

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

Andrea Basso

, University of Bristol, IBM Research - Zurich

Luciano Maino

, University of Bristol

Abstract

We introduce a new PKE protocol, POKÉ, 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 POKÉ that shows encryption and decryption taking about a hundred milliseconds at security level I: POKÉ is thus the most efficient encryption protocol from isogenies, and it outperforms existing protocols by more than an order of magnitude.

Note: The original POKE paper included multiple constructions, some of which were insecure. This paper is a rework of the original submission that focuses only on the PKE protocol.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published by the IACR in EUROCRYPT 2025
Keywords: Isogenies Public-Key Encryption HD isogenies
Contact author(s): andrea basso @ ibm com
luciano maino @ bristol ac uk
History: 2025-02-24: last of 2 revisions; 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 and Luciano Maino},
      title = {{POKÉ}: A Compact and Efficient {PKE} from Higher-dimensional Isogenies},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/624},
      year = {2024},
      url = {https://eprint.iacr.org/2024/624}
}