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Title:
Patient Zero and Patient Six: Zero-Value and Correlation Attacks on CSIDH and SIKE
Authors: Fabio Campos, Michael Meyer, Krijn Reijnders, and Marc Stöttinger
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.
ePrint: https://eprint.iacr.org/2022/904
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