[Resource Topic] 2023/376: Efficient computation of $(3^n,3^n)$-isogenies

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Efficient computation of (3^n,3^n)-isogenies

Authors: Thomas Decru, Sabrina Kunzweiler


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.

ePrint: https://eprint.iacr.org/2023/376

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