Computing supersingular isogenies on kummer surfaces

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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 Fp2 and corresponding abelian surfaces over Fp. 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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APA

Costello, C. (2018). Computing supersingular isogenies on kummer surfaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11274 LNCS, pp. 428–456). Springer Verlag. https://doi.org/10.1007/978-3-030-03332-3_16

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