How to not break SIDH

Chloe Martindale; Lorenz Panny

Paper 2019/558 Original: eprint.iacr.org/2019/558 ↗

How to not break SIDH

Chloe Martindale

Lorenz Panny

Abstract

We give a number of approaches which, to a newcomer, may seem like natural ways to attack the SIDH/SIKE protocol, and explain why each of these approaches seems to fail, at least with the specific setup and parameters of SIKE. Our aim is to save some time for others who are looking to assess the security of SIDH/SIKE. We include methods that fail to attack the pure isogeny problem, namely: looking at the $\mathbb F_p$-subgraph, lifting to characteristic zero, and using Weil restrictions. We also include methods that fail to make use of the public 2-power and 3-power torsion points, namely: interpolation techniques, any purely group-theoretic approaches, and constructing an endomorphism à la Petit to exploit the auxiliary points, but with balanced parameters.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2019-05-25: last updated; 2019-05-25: published
Short URL: https://ia.cr/2019/558
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2019/558,
      author = {Chloe Martindale and Lorenz Panny},
      title = {How to not break SIDH},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/558},
      year = {2019},
      url = {https://eprint.iacr.org/2019/558}
}