## CryptoDB

### Paper: Computing Supersingular Isogenies on Kummer Surfaces

Authors: Craig Costello DOI: 10.1007/978-3-030-03332-3_16 Search ePrint Search Google Slides ASIACRYPT 2018 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
}