Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3
Résumé
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 fastest, which demonstrates yet another potential of using higher dimensional isogeny graphs in cryptography.
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