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Paper: Computing Supersingular Isogenies on Kummer Surfaces

Authors:
Craig Costello
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DOI: 10.1007/978-3-030-03332-3_16
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Presentation: Slides
Conference: ASIACRYPT 2018
Abstract: We apply Scholten’s construction to give explicit isogenies between the Weil restriction of supersingular Montgomery curves with full rational 2-torsion over $$\mathbb {F}_{p^2}$$ and corresponding abelian surfaces over $$\mathbb {F}_{p}$$. Subsequently, we show that isogeny-based public key cryptography can exploit the fast Kummer surface arithmetic that arises from the theory of theta functions. In particular, we show that chains of 2-isogenies between elliptic curves can instead be computed as chains of Richelot (2, 2)-isogenies between Kummer surfaces. This gives rise to new possibilities for efficient supersingular isogeny-based cryptography.
BibTeX
@inproceedings{asiacrypt-2018-29197,
  title={Computing Supersingular Isogenies on Kummer Surfaces},
  booktitle={Advances in Cryptology – ASIACRYPT 2018},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={11274},
  pages={428-456},
  doi={10.1007/978-3-030-03332-3_16},
  author={Craig Costello},
  year=2018
}