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Conference Papers Year : 2023

Efficient Computation of $(3^n , 3^n)$-Isogenies

Abstract

The parametrization of $(3, 3)$-isogenies by Bruin, Flynn and Testa requires over 37.500 multiplications if one wants to evaluate a single isogeny in a point. We simplify their formulae and reduce the amount of required multiplications by 94%. Further we deduce explicit formulae for evaluating $(3, 3)$-splitting and gluing maps in the framework of the parametrization by Bröker, Howe, Lauter and Stevenhagen. We provide implementations to compute $(3^n , 3^n)$-isogenies between principally polarized abelian surfaces with a focus on cryptographic application. Our implementation can retrieve Alice's secret isogeny in 11 seconds for the SIKEp751 parameters, which were aimed at NIST level 5 security.
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Dates and versions

hal-04098198 , version 1 (15-05-2023)
hal-04098198 , version 2 (04-10-2023)

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Thomas Decru, Sabrina Kunzweiler. Efficient Computation of $(3^n , 3^n)$-Isogenies. AfricaCrypt 2023, Jul 2023, Sousse, Tunisia. pp.53-78, ⟨10.1007/978-3-031-37679-5_3⟩. ⟨hal-04098198v2⟩
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