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Title:
Computing 2-isogenies between Kummer lines
Authors: Damien Robert, Nicolas Sarkis
Abstract:We use theta groups to study 2-isogenies between Kummer lines, with a particular focus on the Montgomery model. This allows us to recover known formula, along with more efficient forms for translated isogenies, which require only 2S+2m_0 for evaluation. We leverage these translated isogenies to build a hybrid ladder for scalar multiplication on Montgomery curves with rational 2-torsion which cost 3M+6S+2m_0 by bits, compared to 5M+4S+1m_0 for the standard Montgomery ladder.
ePrint: https://eprint.iacr.org/2024/037
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