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We provide explicit descriptions for radical 2-isogenies in dimensions one, two and three using theta coordinates. These formulas allow us to efficiently navigate in the corresponding isogeny graphs. As an application of this, we implement different versions of the CGL hash function. Notably, the three-dimensional version is the fastest, which demonstrates yet another potential of using higher-dimensional isogeny graphs in cryptography.

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Radical 2-Isogenies and Cryptographic Hash Functions in Dimensions 1, 2 and 3

  • 会议论文

  • 发表日期：

    2025年

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  • Sabrina Kunzweiler,
  • Luciano Maino,
  • Tomoki Moriya,
  • Christophe Petit,
  • Giacomo Pope,
  • Damien Robert,
  • Miha Stopar,
  • Yan Bo Ti

摘要

We provide explicit descriptions for radical 2-isogenies in dimensions one, two and three using theta coordinates. These formulas allow us to efficiently navigate in the corresponding isogeny graphs. As an application of this, we implement different versions of the CGL hash function. Notably, the three-dimensional version is the fastest, which demonstrates yet another potential of using higher-dimensional isogeny graphs in cryptography.