International Association for Cryptologic Research

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A Direct Key Recovery Attack on SIDH

Authors:
Luciano Maino , University of Bristol
Chloe Martindale , University of Bristol
Lorenz Panny , Academia Sinica
Giacomo Pope , NCC Group, University of Bristol
Benjamin Wesolowski , Univ. Bordeaux and ENS de Lyon, CNRS, INRIA
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Presentation: Slides
Conference: EUROCRYPT 2023
Award: Best Paper Honorable Mention
Abstract: We present an attack on SIDH utilising isogenies between polarized products of two supersingular elliptic curves. In the case of arbitrary starting curve, our attack (discovered independently from [8]) has subexponential complexity, thus significantly reducing the security of SIDH and SIKE. When the endomorphism ring of the starting curve is known, our attack (here derived from [8]) has polynomial-time complexity assuming the generalised Riemann hypothesis. Our attack applies to any isogeny-based cryptosystem that publishes the images of points under the secret isogeny, for example S├ęta [13] and B-SIDH [11]. It does not apply to CSIDH [9], CSI-FiSh [3], or SQISign [14].
BibTeX
@inproceedings{eurocrypt-2023-33024,
  title={A Direct Key Recovery Attack on SIDH},
  publisher={Springer-Verlag},
  author={Luciano Maino and Chloe Martindale and Lorenz Panny and Giacomo Pope and Benjamin Wesolowski},
  year=2023
}