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 formulas, along with more efficient forms for translated isogenies, which require only 2 S + 2 m 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 3 M + 6 S + 2 m 0 per bit, compared to 5 M + 4 S + 1 m 0 for the standard Montgomery ladder.
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