Isogeny problems with level structure

ePrint Report: Isogeny problems with level structure

Luca De Feo, Tako Boris Fouotsa, Lorenz Panny

Given two elliptic curves and the degree of an isogeny between them, finding the isogeny is believed to be a difficult problem---upon which rests the security of nearly any isogeny-based scheme. If, however, to the data above we add information about the behavior of the isogeny on a large enough subgroup, the problem can become easy, as recent cryptanalyses on SIDH have shown.
Between the …

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