On weak keys of POKE

Tomoki Moriya

Paper 2026/1002

On weak keys of POKE

Tomoki Moriya

, Mitsubishi Electric Corporation

Abstract

POKE is an isogeny-based public-key encryption (PKE) scheme proposed by Basso and Maino. Among existing isogeny-based PKE schemes, POKE is known to achieve relatively high performance. However, the security of POKE relies on certain ad hoc assumptions, and its security analysis may not yet be fully comprehensive. In this work, we investigate the security of POKE. We show that POKE admits weak keys that reduce the complexity of certain attacks. In the POKE-2D setting, these weak keys do not significantly affect the overall security, since the probability that such keys occur is sufficiently small. In contrast, we demonstrate that POKE-4D is threatened by the presence of these weak keys. Finally, we suggest novel parameters for POKE-4D in order to mitigate the aforementioned weak-key attack. The resulting parameter sizes are comparable to those of POKE-2D. Consequently, the principal advantages of POKE-4D in terms of performance - namely, a more compact prime size and a more efficient encryption algorithm - are no longer preserved.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Preprint.
Keywords: Isogeny-based cryptography POKE Cryptanalysis
Contact author(s): Moriya Tomoki @ bp mitsubishielectric co jp
History: 2026-05-21: revised; 2026-05-20: received; See all versions
Short URL: https://ia.cr/2026/1002
License: CC BY

BibTeX

@misc{cryptoeprint:2026/1002,
      author = {Tomoki Moriya},
      title = {On weak keys of {POKE}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1002},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1002}
}