Paper 2022/904

Patient Zero and Patient Six: Zero-Value and Correlation Attacks on CSIDH and SIKE

Fabio Campos, RheinMain University of Applied Sciences Wiesbaden, Radboud University Nijmegen
Michael Meyer, University of Regensburg
Krijn Reijnders, Radboud University Nijmegen
Marc Stöttinger, RheinMain University of Applied Sciences Wiesbaden
Abstract

Recent works have started side-channel analysis on SIKE and show the vulnerability of isogeny-based systems to zero-value attacks. In this work, we expand on such attacks by analyzing the behavior of the zero curve $E_0$ and six curve $E_6$ in CSIDH and SIKE. We demonstrate an attack on static-key CSIDH and SIKE implementations that recovers bits of the secret key by observing via zero-value-based resp. exploiting correlation-collision-based side-channel analysis whether secret isogeny walks pass over the zero or six curve. We apply this attack to fully recover secret keys of SIKE and two state-of-the-art CSIDH-based implementations: CTIDH and SQALE. We show the feasibility of exploiting side-channel information for the proposed attacks based on simulations with various realistic noise levels. Additionally, we discuss countermeasures to prevent zero-value and correlation-collision attacks against CSIDH and SIKE in our attacker model.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint.
Keywords
post-quantum cryptographyisogeny-based cryptography CSIDH SIKE side-channel analysis zero-value attacks
Contact author(s)
campos @ sopmac de
michael @ random-oracles org
krijn @ cs ru nl
marc stoettinger @ hs-rm de
History
2022-07-12: approved
2022-07-12: received
See all versions
Short URL
https://ia.cr/2022/904
License
No rights reserved
CC0

BibTeX

@misc{cryptoeprint:2022/904,
      author = {Fabio Campos and Michael Meyer and Krijn Reijnders and Marc Stöttinger},
      title = {Patient Zero and Patient Six: Zero-Value and Correlation Attacks on CSIDH and SIKE},
      howpublished = {Cryptology ePrint Archive, Paper 2022/904},
      year = {2022},
      note = {\url{https://eprint.iacr.org/2022/904}},
      url = {https://eprint.iacr.org/2022/904}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.