Welcome to the resource topic for 2024/459
Title:
Isogeny problems with level structure
Authors: Luca De Feo, Tako Boris Fouotsa, Lorenz Panny
Abstract: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 restriction of the isogeny to a full N-torsion subgroup and no ‘‘torsion information’’ at all lies a spectrum of interesting intermediate problems, raising the question of how easy or hard each of them is. Here we explore modular isogeny problems where the torsion information is masked by the action of a group of 2\times 2 matrices. We give reductions between these problems, classify them by their difficulty, and link them to security assumptions found in the literature.
ePrint: https://eprint.iacr.org/2024/459
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .