## IACR paper details

Title | Computing Supersingular Isogenies on Kummer Surfaces |
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Booktitle | Advances in Cryptology – ASIACRYPT 2018 |
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Volume | 11274 |
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Pages | 428-456 |
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Year | 2018 |
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URL | Search for the paper |
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DOI | 10.1007/978-3-030-03332-3_16 (link) |
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Author | Craig Costello |
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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. |
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@article{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
}

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