Computing 2-isogenies between Kummer lines

IACR Cryptol. ePrint Arch. Pub Date : 2024-04-09 DOI:10.62056/abvua69p1

Damien Robert, Nicolas Sarkis

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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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计算库默线之间的 2-isogenies

我们使用 Theta 群来研究库默尔线间的 2 -同源关系，尤其侧重于蒙哥马利模型。这使我们能够恢复已知公式，以及更有效的翻译同源形式，只需 2 S + 2 m 0 即可进行评估。我们利用这些翻译同源建立了一个混合梯子，用于具有有理 2 -扭转的蒙哥马利曲线上的标量乘法，每比特的成本为 3 M + 6 S + 2 m 0，而标准蒙哥马利梯子的成本为 5 M + 4 S + 1 m 0。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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